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Public Economics Lectures Part 1: Introduction

Public Economics Lectures Part 1: Introduction 23
Public Economics Lectures Part 1: Introduction Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 1: Introduction 1 / 49What is Public Economics? Public economics focuses on answering two types of questions 1 How do government policies a¤ect the economy? 2 How should policies be designed to maximize welfare? Three motivations for studying these questions: 1 Practical Relevance 2 Academic Interest 3 Methodology Public Economics Lectures () Part 1: Introduction 2 / 49Motivation 1: Practical Relevance Interest in improving economic welfare interest in public economics Almost every economic intervention occurs through government policy (i.e. involves public economics) via two channels: Price intervention: taxes, welfare, social insurance, public goods Regulation: min wages, FDA regulations (25% of products consumed), zoning, labor laws, min education laws, environment Government directly employs one sixth of U.S. workforce Public Economics Lectures () Part 1: Introduction 3 / 49Motivation 1: Practical Relevance Stakes are extremely large because of broad scope of policies Ex. Tax reforms immediately a¤ect millions Contentious debate on the appropriate role of government in society Romney: replacing Medicare with decentralized private insurance will improve health outcomes and reduce costs Obama: Romney’s proposal will worsen health outcomes and raise costs Only one of these views can be correct Injecting science into these debates has great practical value Public Economics Lectures () Part 1: Introduction 4 / 49Motivation 2: Academic Interest Public economics is typically the end point for many other sub…elds Macro, development, labor, and corporate …nance questions often ultimately motivated by a public economics question Ex 1: Macro studies on costs of business cycles and intertemporal models of household behavior Ex 2: Labor studies on employment e¤ects of the minimum wage Natural to combine public …nance with another …eld Understanding public …nance can help ensure that you work on relevant topics Public Economics Lectures () Part 1: Introduction 5 / 49Motivation 3: Methodology Public economics is at the frontier of a methodological transformation in applied microeconomics Data-driven approach to answering important policy questions Combines a broad set of skills: applied theory, applied econometrics, simulation methods Useful skill set for many applied …elds in economics Topics in the course re‡ect a broad set of methodological themes Public Economics Lectures () Part 1: Introduction 6 / 49Theme 1: Connecting Theory to Data Modern public economics tightly integrates theory with empirical evidence to derive quantitative predictions about policy What is the optimal income tax rate? What is the optimal unemployment bene…t level? Traditional approach: theoretical models and numerical simulations Theory often makes weak predictions: optimal tax rate between 0 and 100% Numerical simulations rely on strong assumptions Recent work derives robust formulas that can be implemented using well-identi…ed empirical estimates Public Economics Lectures () Part 1: Introduction 7 / 49Theme 2: Quasi-Experimental Empirical Methods Research in public economics exploits a variety of quasi-experimental research designs to identify parameters of interest Event studies, regression discontinuity, synthetic control Good way to learn practical lessons in applied econometrics What is “identi…cation by functional form”and why is it undesirable? Is the LATE or ATE of greater interest in your problem? When is propensity score reweighting credible? When do weak instrument problems arise and how can they be …xed? Emphasis on non-parametric graphical techniques rather than parametric regression models Public Economics Lectures () Part 1: Introduction 8 / 49Anscombe (1973):Dataset 1 β=0.5 (0.12) 0 5 10 15 20 Years of Schooling Public Economics Lectures () Part 1: Introduction 9 / 49 Earnings (1000) 0 5 10 15Anscombe (1973):Dataset 2 β=0.5 (0.12) 0 5 10 15 20 Years of Schooling Public Economics Lectures () Part 1: Introduction 10 / 49 Earnings (1000) 0 5 10 15Anscombe (1973):Dataset 3 β=0.5 (0.12) 0 5 10 15 20 Years of Schooling Public Economics Lectures () Part 1: Introduction 11 / 49 Earnings (1000) 0 5 10 15Anscombe (1973):Dataset 4 β=0.5 (0.12) 0 5 10 15 20 Years of Schooling Public Economics Lectures () Part 1: Introduction 12 / 49 Earnings (1000) 0 5 10 15Theme 3: “Big Data” Compelling implementation of quasi-experimental methods requires a lot of data Recent availability of very large datasets has transformed research in applied microeconomics Scanner data on consumer purchases Tax and social security records School district databases Public Economics Lectures () Part 1: Introduction 13 / 49Use of Pre­Existing Survey Data in Publications in Leading Journals, 1980­2010 100 80 60 40 20 0 1980 1990 2000 2010 Year AER JPE QJE ECMA Note: “ Pre­existing survey”datasets refer to micro surveys such as the CPS or SIPP and do not include surveys designed by researchers for their study. Sample excludes studies whose primary data source is from developing countries. Public Economics Lectures () Part 1: Introduction 14 / 49 Micro­data Based Articles using Survey Data (%)Use ofAdministrative Data in Publications in Leading Journals, 1980­2010 100 80 60 40 20 0 1980 1990 2000 2010 Year AER JPE QJE ECMA Note: “ Administrative”datasets refer to any dataset that was collected without directly surveying individuals (e.g., scanner data, stock prices, school district records, social security records). Sample excludes studies whose primary data source is from developing countries. Public Economics Lectures () Part 1: Introduction 15 / 49 Micro­data Based Articles using Admin. Data (%)United States Tax Data 7 billion tax records covering full pop. from 1996 to today Includes a rich set of information on individuals Earnings from W-2’s (covers non-…lers) Employer ID College attendance Retirement savings, charitable contributions Housing and mortgage interest Geographical location Birth, death, marriage, children, family structure Analogous corporate databank contains information for 5 million …rms per year, linked to workers Public Economics Lectures () Part 1: Introduction 16 / 49What are the Bene…ts of Administrative Data? 1 Higher quality information: virtually no missing data or attrition Current Population Survey non-response rate now 31% for income 2 Longitudinal tracking over long periods Match rates of 95% over 20+ years in studies of long-term impacts of early childhood education Chetty et al. 2011, Chetty, Friedman, Rocko¤ 2012 Public Economics Lectures () Part 1: Introduction 17 / 49Earnings atAge 28 vs. Teacher Value­Added in Elementary School 21,200 21,000 20,800 1 SD TVA = 182 (73) 20,600 20,400 ­0.2 ­0.1 0 0.1 0.2 Teacher Value­Added Source: Chetty, Friedman, Rockoff 2012 Public Economics Lectures () Part 1: Introduction 18 / 49 Earnings at Ag e 28What are the Bene…ts of Administrative Data? 1 Higher quality information: virtually no missing data or attrition Current Population Survey non-response rate now 31% for income 2 Longitudinal tracking over long periods Match rates of 95% over 20+ years in studies of long-term impacts of early childhood education Chetty et al. 2011, Chetty, Friedman, Rocko¤ 2012 3 Very large sample sizes: 2,000 times the size of the CPS Can develop new research designs Public Economics Lectures () Part 1: Introduction 19 / 49Earned Income Tax Credit Schedule for Single Earners with One Child in 2008 4k This income level maximizes tax refund 3k 2k 1k 0k 0k 5k 10k 15k 20k 25k 30k 35k Family Earnings Public Economics Lectures () Part 1: Introduction 20 / 49 EITC Credit Amount (1000)U.S. Income Distributions for EITC­Eligible Individuals with Children in 2008 5% 4% 3% 2% 1% 0% 0 10K 20K 30K 40K Total Earnings (Real 2010 ) One child Two children Public Economics Lectures () Part 1: Introduction 21 / 49 Percent of Tax FilersFraction of Tax Filers Who Report Income that Maximizes EITC Refund in 1996 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0 –0.7% Source: Chetty, Friedman, Saez 2012 Public Economics Lectures () Part 1: Introduction 22 / 49Fraction of Tax Filers Who Report Income that Maximizes EITC Refund in 1999 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0 –0.7% Source: Chetty, Friedman, Saez 2012 Public Economics Lectures () Part 1: Introduction 23 / 49Fraction of Tax Filers Who Report Income that Maximizes EITC Refund in 2002 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0 –0.7% Source: Chetty, Friedman, Saez 2012 Public Economics Lectures () Part 1: Introduction 24 / 49Fraction of Tax Filers Who Report Income that Maximizes EITC Refund in 2005 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0 –0.7% Source: Chetty, Friedman, Saez 2012 Public Economics Lectures () Part 1: Introduction 25 / 49Fraction of Tax Filers Who Report Income that Maximizes EITC Refund in 2008 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0 –0.7% Source: Chetty, Friedman, Saez 2012 Public Economics Lectures () Part 1: Introduction 26 / 49Theme 4: Behavioral Models Recent work in public economics draws on insights from psychology and economics literature Strong evidence that individuals fail to optimize Raises new policy questions Suggests new policy instruments E.g. information, social incentives Public Economics Lectures () Part 1: Introduction 27 / 49Correlation Between Response to EITC and EITC Filer Density by ZIP Code 3.5% 3.0% 2.5% 2.0% 1.5% 2 R = 0.6 1.0% ­2 0 2 4 6 log (Number of EITC Filers Per Square Mile) Public Economics Lectures () Part 1: Introduction 28 / 49 Fraction Self­Emp Reporting Income that Maxes RefundBackground Facts: Size and Growth of Government Government expenditures = 1/3 GDP in the U.S. Higher than 50% of GDP in some European countries Decentralization is a key feature of U.S. govt One third of spending (10% of GDP) is done at state-local level (e.g. schools) Two thirds (20% of GDP) is federal Public Economics Lectures () Part 1: Introduction 29 / 49Federal Government Revenue and Expenditure 1930­2009 1930 1940 1950 1960 1970 1980 1990 2000 2010 Year Revenue Expenditure Source: Office of Management and Budget, Historical Tables, FY 2011 Public Economics Lectures () Part 1: Introduction 30 / 49 Revenue and spending (% of GDP) 20 0 10 30 40 50Total Government Spending by Country, 1970­2007 Sweden Canada OECD Avg. United States 1970 1975 1980 1985 1990 1995 2000 2005 Year Source: OECD Economic Outlook (2009) Public Economics Lectures () Part 1: Introduction 31 / 49 Percent of GDP 20 30 40 50 60Federal Revenues (% of total revenue) Other Excise Other 4.2% 4.2% 2.7% E Exc xciise se 1 12. 2.6% 6% Inc Income ome IInc ncom ome e 4 44% 4% P Payr ayroll oll 45 45.4% .4% Pay Payrrol olll 15 15..9% 9% 3 37. 7.5% 5% Cor Corp por orat ate e 2 23. 3.2% 2% C Corp orpor orat ate e 1 12. 2.1% 1% 1960 2008 Source: Office of Management and Budget, historical tables, government receipts by source Public Economics Lectures () Part 1: Introduction 32 / 49State/Local Revenues (% of total revenue) Income Tax 5.9% Federal Grants 9.4% IInc ncom ome  e T Tax ax Pr Prop opert ertyy 1 14. 4.3% 3% T Ta ax 1 x 15. 5.7% 7% P Pro ropert pertyy F Fed eder eral al T Tax ax Ot Oth her er Gran Grants ts Sa Salles es  Tax Tax 38 38.2% .2% 17 17.7% .7% 19. 19.1% 1% 17 17.9% .9% S Sal ale es  s Tax Tax Ot Oth her er 28 28.8% .8% 3 33% 3% 1960 2007 Source: U.S. Census Bureau, 2007 Summary of State & Local Government Public Economics Lectures () Part 1: Introduction 33 / 49Federal Spending (% of total spending) Education, welfare, housing 4% Education, welfare, housing 9.7% Other Other 11.2% 11.2% Other 12.4% Social Social Social Security Security Security 13.5% Health Health 19.5% 19.5% 23.1% 23.1% Health, 2.9% Net Interest UI and Net Net 8.3% Disability Interest Interest 8.9% 12.3% 12.3% UI and Disability, 6.3% 1960 2001 Source: Office of Management and Budget, historical tables, government outlays by function Public Economics Lectures () Part 1: Introduction 34 / 49International Tax Revenue by Type of Tax (2001, % of Total) Mexico Norway Norway OECD Av OECD Average erage Payroll Payroll Payroll Payroll Payroll 20.5% 20.5% Consumption Consumption Consumption Consumption 24.3% 26.7% 26.7% 32.6% 32.6% 31.3% 31.3% Wealth, Individual Individual 2.2% Consumption Income Income Individual Individual 73.5% 24.2% 24.2% Corporate Corporate Income Income Wealth, 2.2 Wealth, 2.2% % Income 21.7% Income 21.7% Wealth, 5.5 Wealth, 5.5% % 26% 26% Corporate Inc Corporate Income, 9.3 ome, 9.3% % Source: OECD 2002 Public Economics Lectures () Part 1: Introduction 35 / 49Government Intervention in the Economy Organizing framework: “When is government intervention necessary in a market economy?” Market …rst, govt. second approach Why? Private market outcome is e¢ cient under broad set of conditions (1st Welfare Thm) Course can be split into two parts: 1 How can govt. improve e¢ ciency when private market is ine¢ cient? 2 What can govt. do if private market outcome is undesirable due to redistributional concerns? Public Economics Lectures () Part 1: Introduction 36 / 49E¢ cient Private Market Allocation of Goods Amy’s Consumption Bob’s Consumption Public Economics Lectures () Part 1: Introduction 37 / 49First Role for Government: Improve E¢ ciency Amy’s Consumption Bob’s Consumption Public Economics Lectures () Part 1: Introduction 38 / 49Second Role for Government: Improve Distribution Amy’s Consumption Bob’s Consumption Public Economics Lectures () Part 1: Introduction 39 / 49First Welfare Theorem Private market provides a Pareto e¢ cient outcome under three conditions 1 No externalities 2 Perfect information 3 Perfect competition Theorem tells us when the government should intervene Public Economics Lectures () Part 1: Introduction 40 / 49Failure 1: Externalities Markets may be incomplete due to lack of prices (e.g. pollution) Achieving e¢ cient Coasian solution requires an organization to coordinate individuals –that is, a government This is why govt. funds public goods (highways, education, defense) Questions: What public goods to provide and how to correct externalities? Public Economics Lectures () Part 1: Introduction 41 / 49Failure 2: Asymmetric Information and Incomplete Markets When some agents have more information than others, markets fail Ex. 1: Adverse selection in health insurance Healthy people drop out of private market unraveling Mandated coverage could make everyone better o¤ Ex. 2: capital markets (credit constraints) and subsidies for education Ex. 3: Markets for intergenerational goods Future generations’interests may not be fully re‡ected in market outcomes Public Economics Lectures () Part 1: Introduction 42 / 49Failure 3: Imperfect Competition When markets are not competitive, there is role for govt. regulation Ex: natural monopolies such as electricity and telephones This topic is traditionally left to courses on industrial organization and is not covered in this course But taking the methodological approach of public economics to problems traditionally analyzed in IO is a very promising area Public Economics Lectures () Part 1: Introduction 43 / 49Individual Failures If agents do not optimize, government intervention (e.g. by forcing saving via social security) may be desirable This is an “individual”failure rather than a market failure Conceptual challenge: how to avoid paternalism critique Why does govt. know better what’s desirable for you (e.g. wearing a seatbelt, not smoking, saving more) Di¢ cult but central issues for optimal policy design Public Economics Lectures () Part 1: Introduction 44 / 49Redistributional Concerns Even when the private market outcome is e¢ cient, may not have good distributional properties E¢ cient markets generally seem to deliver very large rewards to small set of people (top incomes) Government can redistribute income through tax and transfer system Public Economics Lectures () Part 1: Introduction 45 / 49Why Limit Government Intervention? One solution to these issues would be for the government to oversee all production and allocation in the economy (socialism). Serious problems with this solution 1 Information: how does government aggregate preferences and technology to choose optimal production and allocation? 2 Government policies distort incentives (behavioral responses in private sector) In practice, there are sharp tradeo¤s between costs and bene…ts of government intervention Public Economics Lectures () Part 1: Introduction 46 / 49Equity-E¢ ciency Tradeo¤ Amy’s Consumption Bob’s Consumption Public Economics Lectures () Part 1: Introduction 47 / 49Three Types of Questions in Public Economics 1 Positive analysis: What are the observed e¤ects of government programs and interventions? 2 Normative analysis: What should the government do if we can choose optimal policy? 3 Public choice/Political economy Develops theories to explain why the government behaves the way it does and identify optimal policy given political economy concerns Criticism of normative analysis: fails to take political constraints into account Public Economics Lectures () Part 1: Introduction 48 / 49Course Outline 1 Tax Incidence and E¢ ciency 2 Optimal Taxation 3 Income Taxation and Labor Supply 4 Corporate Taxation 5 Social Insurance 6 Public Goods and Externalities Public Economics Lectures () Part 1: Introduction 49 / 49Public Economics Lectures Part 2: Incidence of Taxation Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 2: Tax Incidence 1 / 140Outline 1 De…nition and Introduction 2 Partial Equilibrium Incidence 3 Partial Equilibrium Incidence with Salience E¤ects 4 Partial Equilibrium Incidence: Empirical Applications 5 General Equilibrium Incidence 6 Capitalization 7 Mandated Bene…ts Public Economics Lectures () Part 2: Tax Incidence 2 / 140References on Tax Incidence Kotliko¤ and Summers (1987) handbook chapter Atkinson and Stiglitz text chapters 6 and 7 Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 3 / 140De…nition Tax incidence is the study of the e¤ects of tax policies on prices and the distribution of utilities What happens to market prices when a tax is introduced or changed? Increase tax on cigarettes by 1 per pack Introduction of Earned Income Tax Credit (EITC) Food stamps program E¤ect on price distributional e¤ects on smokers, pro…ts of producers, shareholders, farmers, ... Public Economics Lectures () Part 2: Tax Incidence 4 / 140Economic vs. Statutory Incidence Equivalent when prices are constant but not in general Consider the following argument: Government should tax capital income b/c it is concentrated at the high end of the income distribution Neglects general equilibrium price e¤ects Tax might be shifted onto workers If capital taxes less savings and capital ‡ight, then capital stock may decline, driving return to capital up and wages down Some argue that capital taxes are paid by workers and therefore increase income inequality (Hassett and Mathur 2009) Public Economics Lectures () Part 2: Tax Incidence 5 / 140Overview Tax incidence is an example of positive analysis Typically the …rst step in policy evaluation An input into thinking about policies that maximize social welfare Theory is informative about signs and comparative statics but is inconclusive about magnitudes Incidence of cigarette tax: elasticity of demand w.r.t. price is crucial Labor vs. capital taxation: mobility of labor, capital are critical Public Economics Lectures () Part 2: Tax Incidence 6 / 140Overview Ideally, we would characterize the e¤ect of a tax change on utility levels of all agents in the economy Useful simpli…cation in practice: aggregate economic agents into a few groups Incidence analyzed at a number of levels: 1 Producer vs. consumer (tax on cigarettes) 2 Source of income (labor vs. capital) 3 Income level (rich vs. poor) 4 Region or country (local property taxes) 5 Across generations (social security reform) Public Economics Lectures () Part 2: Tax Incidence 7 / 140Partial Equilibrium Incidence: Key Assumptions 1 Two good economy Only one relative price partial and general equilibrium are same Can be viewed as an approx. of incidence in a multi-good model if the market being taxed is “small” there are no close substitutes/complements in the utility fn 2 Tax revenue is not spent on the taxed good Tax revenue is used to buy untaxed good or thrown away 3 Perfect competition among producers Relaxed in some studies of monopolistic or oligopolistic markets Public Economics Lectures () Part 2: Tax Incidence 8 / 140Partial Equilibrium Model: Setup Two goods: x and y Government levies an excise tax on good x Excise or speci…c tax: levied on a quantity (e.g. gallon, pack, ton) Ad-valorem tax: fraction of prices (e.g. sales tax) Let p denote the pretax price of x and q = p+t denote the tax inclusive price of x Good y, the numeraire, is untaxed Public Economics Lectures () Part 2: Tax Incidence 9 / 140Partial Equilibrium Model: Demand Consumer has wealth Z and has utility u(x,y) q ¶logD ¶D Let = = denote the price elasticity of demand D ¶q ¶logq D(q) Elasticity: % change in quantity when price changes by 1% Widely used concept because elasticities are unit free Public Economics Lectures () Part 2: Tax Incidence 10 / 140Partial Equilibrium Model: Supply Price-taking …rms Use c(S) units of the numeraire y to produce S units of x Cost of production is increasing and convex: 0 00 c (S) 0 and c (S) 0 Pro…t at pretax price p and level of supply S is pSc(S) With perfect optimization, the supply function for good x is implicitly 0 de…ned by the marginal condition p = c (S(p)) p ¶S Let = denote the price elasticity of supply S ¶p S(p) Public Economics Lectures () Part 2: Tax Incidence 11 / 140Partial Equilibrium Model: Equilibrium Equilibrium condition Q = S(p)= D(p+t) de…nes an equation p(t) dp Goal: characterize , the e¤ect of a tax increase on price dt First consider some graphical examples to build intuition, then analytically derive formula Public Economics Lectures () Part 2: Tax Incidence 12 / 140Tax Levied on Consumers Price S C 27.0 Consumer A Burden = 4.50 22.5 22.5 Supplier Burden = 3.00 D 19.5 B 15.0 15.0 7.50 D+t D Quantity 1250 1500 Public Economics Lectures () Part 2: Tax Incidence 13 / 140Tax Levied on Producers Price S+t S 7.50 B 30.0 C 27.0 Consumer A Burden = 4.50 22.5 22.5 Supplier Burden = 3.00 D 19.5 D Quantity 1250 1500 Public Economics Lectures () Part 2: Tax Incidence 14 / 140Perfectly Inelastic Demand Price D S+t S 27.0 Consumer burden 22.5 7.50 Quantity 1500 Public Economics Lectures () Part 2: Tax Incidence 15 / 140Perfectly Elastic Demand Price S+t S 7.50 22.5 D Supplier burden 15.0 Quantity 1500 Public Economics Lectures () Part 2: Tax Incidence 16 / 140Formula for Tax Incidence Implicitly di¤erentiate equilibrium condition D(p+t)= S(p) to obtain: dp ¶D 1 = ¶S ¶D dt ¶p ( ) ¶p ¶p dp D ) = dt S D Incidence on consumers: dq dp S = 1+ = dt dt S D Public Economics Lectures () Part 2: Tax Incidence 17 / 140Formula for Tax Incidence P S 1 –excess supply of E created by imposition of tax 1 P 1 /S /D dp = E/Ý ? Þ 2 /p /p 2 –re­equilibriation of market P 2 through producer price cut /D /S /D ö dp/dt = /Ý ? Þ /p /p /p D 1 D 2 Q /D E = dt× /p Public Economics Lectures () Part 2: Tax Incidence 18 / 140Tax Incidence with Salience E¤ects Central assumption of neoclassical model: taxes are equivalent to dx dx prices ( = ) dt dp In practice, are people fully aware of marginal tax rates? Chetty, Looney, and Kroft (2009) test this assumption and generalize theory to allow for salience e¤ects Part 1: Test whether “salience”(visibility of tax-inclusive price) a¤ects behavioral responses to commodity taxation Does e¤ect of a tax on demand depend on whether it is included in posted price? Part 2: Develop formulas for incidence and e¢ ciency costs of taxation that permit salience e¤ects and other optimization errors Public Economics Lectures () Part 2: Tax Incidence 19 / 140Chetty et al.: Empirical Framework Economy with two goods, x and y Prices: Normalize the price of y to 1 and let p denote the (…xed) pretax price of x. Taxes: y untaxed, x subject to an ad valorem sales tax t (not included in posted price) Tax-inclusive price of x is q =(1+t)p Let demand for good x be denoted by x(p,t) Public Economics Lectures () Part 2: Tax Incidence 20 / 140Chetty et al.: Empirical Framework If agents optimize fully, demand should only depend on the total tax-inclusive price: x(p,t) = x((1+t)p,0) Full optimization implies price elasticity equals gross-of-tax elasticity: ¶logx ¶logx  = S x,p x,1+t ¶logp ¶log(1+t) To test this hypothesis, log-linearize demand fn. x(p,t) to obtain estimating equation: logx(p,t)= a+blogp+qblog(1+t) q measures degree to which agents under-react to the tax: ¶logx ¶logx x,1+t q = / = ¶log(1+t) ¶logp x,p Public Economics Lectures () Part 2: Tax Incidence 21 / 140Chetty et al.: Two Empirical Strategies Two strategies to estimate q: 1 Manipulate tax salience: make sales tax as visible as pre-tax price E¤ect of intervention on demand: v = logx((1+t)p,0)logx(p,t) Compare to e¤ect of equivalent price increase to estimate q: v (1q)= log(1+t) x,p 2 Manipulate tax rate: compare and x,p x,1+t q = / x,1+t x,p Public Economics Lectures () Part 2: Tax Incidence 22 / 140Chetty et al.: Strategy 1 Experiment manipulating salience of sales tax implemented at a supermarket that belongs to a major grocery chain 30% of products sold in store are subject to sales tax Posted tax-inclusive prices on shelf for subset of products subject to sales tax (7.375% in this city) Data: Scanner data on price and weekly quantity sold by product Public Economics Lectures () Part 2: Tax Incidence 23 / 140Public Economics Lectures () Part 2: Tax Incidence 24 / 140Documenting Salience Mechanism Concern with posting tax inclusive prices: may have in‡uenced behavior through various channels besides salience Common problem in …eld experiments termed “Hawthorne e¤ects” Di¢ cult to rule out all mechanisms, but helpful to present evidence that mechanism of interest is very powerful Public Economics Lectures () Part 2: Tax Incidence 25 / 140TABLE 1 Evaluation of Tags: Classroom Survey Mean Median SD Original Price Tags: Correct tax­inclusive price w/in 0.25 0.18 0.00 0.39 Experimental Price Tags: Correct tax­inclusive price w/in 0.25 0.75 1.00 0.43 T­test for equality of means: p  0.001 N=49 Students were asked to choose two items from image. Asked to report “Total bill due at the register for these two items.” Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 26 / 140Chetty et al.: Research Design Quasi-experimental di¤erence-in-di¤erences Treatment group: Products: Cosmetics, Deodorants, and Hair Care Accessories Store: One large store in Northern California Time period: 3 weeks (February 22, 2006 –March 15, 2006) Control groups: Products: Other prods. in same aisle (toothpaste, skin care, shave) Stores: Two nearby stores similar in demographic characteristics Time period: Calendar year 2005 and …rst 6 weeks of 2006 Public Economics Lectures () Part 2: Tax Incidence 27 / 140Effect of Posting Tax­Inclusive Prices: Mean Quantity Sold TREATMENT STORE Period Control Categories Treated Categories Difference Baseline 26.48 25.17 ­1.31 (0.22) (0.37) (0.43) Experiment 27.32 23.87 ­3.45 (0.87) (1.02) (0.64) Difference 0.84 ­1.30 DD =­2.14 TS over time (0.75) (0.92) (0.64) Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 28 / 140Effect of Posting Tax­Inclusive Prices: Mean Quantity Sold TREATMENT STORE Period Control Categories Treated Categories Difference Baseline 26.48 25.17 ­1.31 (0.22) (0.37) (0.43) Experiment 27.32 23.87 ­3.45 (0.87) (1.02) (0.64) Difference 0.84 ­1.30 DD =­2.14 TS over time (0.75) (0.92) (0.64) CONTROL STORES CONTROL STORES Period Period Control Categori Control Categories es Treated Catego Treated Categories ries Difference Difference Baseline Baseline 30.57 30.57 27.94 27.94 ­­2.63 2.63 (0.24) (0.24) (0.30) (0.30) (0.32) (0.32) Experiment Experiment 30.76 30.76 28.19 28.19 ­­2.57 2.57 (0.72) (0.72) (1.06) (1.06) (1.09) (1.09) DD DD = 0.06 = 0.06 Difference Difference 0.19 0.19 0.25 0.25 CS CS over time over time (0.64) (0.64) (0.92) (0.92) (0.90) (0.90) Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 29 / 140Effect of Posting Tax­Inclusive Prices: Mean Quantity Sold TREATMENT STORE Period Control Categories Treated Categories Difference Baseline 26.48 25.17 ­1.31 (0.22) (0.37) (0.43) Experiment 27.32 23.87 ­3.45 (0.87) (1.02) (0.64) Difference 0.84 ­1.30 DD =­2.14 TS over time (0.75) (0.92) (0.64) CONTROL STORES CONTROL STORES Period Period Control Categori Control Categories es Treated Catego Treated Categories ries Difference Difference Baseline Baseline 30.57 30.57 27.94 27.94 ­­2.63 2.63 (0.24) (0.24) (0.30) (0.30) (0.32) (0.32) Experiment Experiment 30.76 30.76 28.19 28.19 ­­2.57 2.57 (0.72) (0.72) (1.06) (1.06) (1.09) (1.09) DD DD = 0.06 = 0.06 Difference Difference 0.19 0.19 0.25 0.25 CS CS over time over time (0.64) (0.64) (0.92) (0.92) (0.90) (0.90) DDD Estimate ­2.20 (0.58) Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 30 / 140Statistical Signi…cance and Permutation Tests Standard error computations always require speci…c assumptions about error structure Ex: allow for correlation in purchases across products within a store-week-category cell Standard parametric approach is to cluster standard errors by store-week-category But appropriate level of clustering is often unclear Should we also allow for correlation across stores or categories? Public Economics Lectures () Part 2: Tax Incidence 31 / 140Non-Parametric Permutation Tests Useful technique for inference with correlated errors: permutation (Fisher’s exact) test Pretend intervention occurred in each of the other cells (store, week, category) of the sample and recompute DDD estimate Calculate where actual treatment e¤ect lies in empirical CDF of placebo treatment e¤ects Public Economics Lectures () Part 2: Tax Incidence 32 / 140Public Economics Lectures () Part 2: Tax Incidence 33 / 140Non-Parametric Permutation Tests Key assumption underlying permutation test: treatment is truly random Probability of treatment cannot vary across cells True by construction in experiment But may not hold in settings where policy changes are endogenous Ex: unemployment bene…ts increased during recessionary periods Nevertheless, often a useful benchmark Public Economics Lectures () Part 2: Tax Incidence 34 / 140Chetty et al.: Strategy 2 Compare e¤ects of price changes and tax changes Alcohol subject to two state-level taxes in the U.S.: Excise tax: included in price Sales tax: added at register, not shown in posted price Exploiting state-level changes in these two taxes, estimate q Addresses concern that experiment may have induced a Hawthorne e¤ect Public Economics Lectures () Part 2: Tax Incidence 35 / 140Per Capita Beer Consumption and State Beer Excise Taxes ­.02 ­.015 ­.01 ­.005 0 .005 .01 .015 .02 Change in Log(1+Beer Excise Rate) Source: Chetty, Looney, and Kroft(2009) Public Economics Lectures () Part 2: Tax Incidence 36 / 140 Change in Log Per Capita Beer Consumption ­­.1 .1 ­­..05 05 0 .05 .1Per Capita Beer Consumption and State Sales Taxes ­.02 ­.015 ­.01 ­.005 0 .005 .01 .015 .02 Change in Log(1+Sales Tax Rate) Source: Chetty, Looney, and Kroft(2009) Public Economics Lectures () Part 2: Tax Incidence 37 / 140 Change in Log Per Capita Beer Consumption ­.1 ­.05 0 .05 .1Effect of Excise and Sales Taxes on Beer Consumption Dependent Variable: ΔLog(per capita beer consumption) Bus Cyc, Baseline 3­Year Diffs Food Exempt Alc Regs. (1) (2) (3) (4) ΔLog(1+Excise Tax Rate) ­0.87 ­0.89 ­1.11 ­0.91 (0.17) (0.17) (0.46) (0.22) ΔLog(1+Sales Tax Rate) ­0.20 ­0.02 ­0.00 ­0.14 (0.30) (0.30) (0.32) (0.30) x x x Business Cycle Controls Alcohol Regulation Controls x x x Year Fixed Effects x x x x F­Test for Equality of Coeffs. 0.05 0.01 0.05 0.04 Sample Size 1,607 1,487 1,389 937 Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 38 / 140Tax Incidence with Salience E¤ects Letfx(p,t,Z),y(p,t,Z)g denote empirically observed demands Place no structure on these demand functions except for feasibility: (p+t)x(p,t,Z)+y(p,t,Z)= Z Demand functions taken as empirically estimated objects rather than optimized demand from utility maximization Supply side model same as above Market clearing price p satis…es D(p,t,Z)= S(p) where D(p,t,z)= x(p,t,z) is market demand for x. Public Economics Lectures () Part 2: Tax Incidence 39 / 140Tax Incidence with Salience E¤ects Pre­tax price p S DÝpt = 0Þ S DÝpt Þ S(p) 1 –excess supply of E 1 p 0 created by imposition of tax /S /D dp = E/Ý ? Þ 2 /p /p p 1 2 –re­equilibriation of market /D /S /D S ö dp/dt = /Ý ? Þ through pre­tax price cut S /p /p /t S,D S S E = t /D//t Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 2: Tax Incidence 40 / 140Tax Incidence with Salience E¤ects: Formula Incidence on producers of increasing t is dp ¶D/¶t D = =q dt ¶S/¶p¶D/¶p S D 1 Incidence on producers attenuated by q 2 No tax neutrality: taxes on producers have greater incidence on producers than non-salient taxes levied on consumers Intuition: Producers need to cut pretax price less when consumers are less responsive to tax Public Economics Lectures () Part 2: Tax Incidence 41 / 140Tax Incidence: Empirical Applications 1 Evans, Ringel, and Stech 1999: Cigarette excise taxes 2 Hastings and Washington 2010: Food stamps 3 Rothstein 2010: Earned Income Tax Credit Public Economics Lectures () Part 2: Tax Incidence 42 / 140Evaluating Empirical Studies Consider ideal experimental design …rst Then formulate a feasible design and analyze its ‡aws relative to ideal design Frontier for empirical papers: tradeo¤ between quality of research design and importance/novelty Public Economics Lectures () Part 2: Tax Incidence 43 / 140Developing Empirical Research Designs All of the empirical studies we will consider here start by formulating clear research designs Why develop an explicit design rather than simply use all available variation in tax rates? Consider estimating e¤ect of a treatment (e.g., tax) T on outcome y y = a+bT + i i i Treatment is assigned based on a “selection”model T = a +b X +h i T i T i Treatment may be non-random: cov(X , )6= 0, cov(h , )6= 0 i i i i Public Economics Lectures () Part 2: Tax Incidence 44 / 140Developing Empirical Research Designs Traditional approach to accounting for confounding factors or selection: control for observables X when estimating treatment e¤ect i y = a+bT +gX + i i i i Can be done using OLS regression, matching, propensity-score reweighting, etc. Problem with these approaches: don’t know source of variation in T i Must be some reason that one person got treated and another did not even if they are perfectly matched on observables (e.g., twins) h must be correlated with T to have variation in TjX i i i i But that same unobserved factor could also a¤ect outcome: no way to know if cov(h , )= 0 i i Cannot be sure that estimate of treatment e¤ect b is consistent Public Economics Lectures () Part 2: Tax Incidence 45 / 140Developing Empirical Research Designs A “research design”is a source of variation in h that is credibly i unrelated to i Ex: a reform that a¤ects people above age 65 but not below People at age 64 and 65 likely to have similar outcomes cov(h , )= 0 i i General lesson: “controlling”for confounding factors using regression or reweighting will rarely give you convincing estimates However, reweighting can be a useful technique to obtain better control groups when paired with a quasi-experimental research design More on this below (Dinardo, Fortin, Lemieux 1996) Public Economics Lectures () Part 2: Tax Incidence 46 / 140Evans, Ringel, and Stech (1999) Question: How do cigarette tax increases a¤ect prices? Do they take money from cigarette companies or smokers? Partial equilibrium is a plausible approximation for cigarettes, so use that framework here Public Economics Lectures () Part 2: Tax Incidence 47 / 140Cigarette Taxation: Background Cigarettes taxed at both federal and state levels in U.S. Total revenue of about 35 billion per year, similar to estate taxation Federal tax increased from 0.39 to 1.01 per pack in 2009 Variation among states: from 30 cents per pack in VA to 4.35 in NY in 2012 Controversial commodity due to health and paternalism concerns Public Economics Lectures () Part 2: Tax Incidence 48 / 140Evans, Ringel, and Stech (1999) Since 1975, more than 200 state tax changes natural experiments to investigate tax incidence Exploit these state-level changes in excise tax rates using simple di¤-in-di¤ research designs Idea: Suppose federal govt. implements a tax change. Compare cigarette prices before and after the change D =P P A1 A0 Identi…cation assumption: absent the tax change, there would have been no change in cigarette price Public Economics Lectures () Part 2: Tax Incidence 49 / 140Di¤erence-in-Di¤erence But what if price ‡uctuates because of climatic conditions or trends in demand? First di¤erence (and time series) estimate biased Can relax ID assumption using di¤-in-di¤ DD =P P P P A1 A0 B1 B0 State A: experienced a tax change (treatment) State B: does not experience any tax change (control) Identifying assumption for DD: “parallel trends:”absent the policy change, P P would have been the same for A and B 1 0 Public Economics Lectures () Part 2: Tax Incidence 50 / 140Public Economics Lectures () Part 2: Tax Incidence 51 / 140Parallel Trends Assumption Can use placebo DD to test parallel trends assumption Analogous to permutation test: pretend reform occurred at other points and replicate estimate If DD in other periods is not zero, then DD likely biased t=1 Useful to plot long time series of outcomes for treatment and control Pattern should be parallel lines, with sharp change just after reform Rest of U.S. a good control for MI in example above but not AZ Public Economics Lectures () Part 2: Tax Incidence 52 / 140Triple Di¤erence Some studies use a “triple di¤erence”(DDD) Chetty, Looney, Kroft (2009): experiment using treatment/control products, treatment/control stores DDD = DD DD TS CS DD : di¤erence of treat., cntrl products in treat. store TS DD : di¤erence of treat., cntrl. products in cntrl. store CS DDD is mainly useful as a robustness check: DD 6= 0, unconvincing that DDD removes all bias CS DD = 0, then DD = DDD but DD has smaller s.e. CS Public Economics Lectures () Part 2: Tax Incidence 53 / 140Fixed E¤ects ERS have data for 50 states, 30 years, and many tax changes Want to pool all this data to obtain single incidence estimate Fixed e¤ects generalize DD with S 2 periods and J 2 groups Suppose that group j in year t experiences policy T of intensity T jt Want to identify e¤ect of T on price P. OLS regression: P = a+bT +e jt jt jt With no …xed e¤ects, the estimate of b is biased if treatment T is jt correlated with e jt Ex: states with higher taxes may have more anti-tobacco campaigns Public Economics Lectures () Part 2: Tax Incidence 54 / 140Fixed E¤ects Include time and state dummies to solve this problem: P = a+g +d +bT +e jt j jt jt t Fixed e¤ect regression is equivalent to partial regression ˆ ˆ P = bT +e jt jt jt ˆ b where P = P P P and T is de…ned analogously jt jt j t jt Identi…cation obtained from within-state variation over time Note: common changes that apply to all groups (e.g. fed tax change) captured by time dummy; not a source of variation that identi…es b Public Economics Lectures () Part 2: Tax Incidence 55 / 140Fixed E¤ects vs. Di¤erence-in-Di¤erence Advantage relative to DD: more precise estimates by pooling several changes Disadvantage: …xed e¤ects is a black-box regression, more di¢ cult to check trends non-parametrically as with a single change Combine with graphical, non-parametric evidence around certain policy changes ˆ ˆ Also useful to scatter residuals P vs. T jt jt Same parallel trends identi…cation assumption as DD Potential violation: policy reforms may respond to trends in outcomes Ex: tobacco prices falling state decides to raise tax rate Public Economics Lectures () Part 2: Tax Incidence 56 / 140Evans, Ringel, and Stech (1999) Implement a …xed e¤ects model for prices Regress price on state+year …xed e¤ects, covariates, and tax rate (in cents) Also estimate demand elasticities using …xed e¤ects estimator Regress log quantity consumed on state/year …xed e¤ects, covariates, and real tax rate (in cents) Public Economics Lectures () Part 2: Tax Incidence 57 / 140Public Economics Lectures () Part 2: Tax Incidence 58 / 140Evans, Ringel, and Stech: Incidence Results 100% pass through implies supply elasticity of =¥ at state level S Theory suggests that pass through would be lower at national level Important to understand how the variation you are using determines what parameter you are identifying Public Economics Lectures () Part 2: Tax Incidence 59 / 140Public Economics Lectures () Part 2: Tax Incidence 60 / 140Evans, Ringel, and Stech: Demand Elasticity Demand model estimate implies that: =0.42 D 10% increase in price induces a 4.2% reduction in consumption How to compute price elasticity of demand when using variation arising from tax changes? Tax passed 1-1 onto consumers, so we can substitute DP =DT here ˆ Then compute from b=(DQ/Q)/DT from regression coe¢ cient D of log demand on cigarette tax: P DQ ˆ = = b/P D QDT with P (price) and Q (quantity) are sample means Public Economics Lectures () Part 2: Tax Incidence 61 / 140IV Estimation of Price Elasticities How to estimate price elasticity of demand when tax and prices do not move together 1-1? Instrument for prices using taxes First stage, taking note of F-stat: 0 0 0 P = a +g +d +bT +e jt jt jt t j Second stage: b Q = a+g +d +lP +e jt j jt jt t Reduced form, using T as an instrument for P : jt jt Q = a+g +d +mT +e jt j jt jt t 2SLS regression coe¤. is ratio of redued-form to …rst-stage coe¤.: ˆ ˆ l= mˆ/b 2SLS rescales reduced-form to account for DP/DT6= 1 Public Economics Lectures () Part 2: Tax Incidence 62 / 140Evans, Ringel, and Stech: Long Run Elasticity DD before and after one year captures short term response: e¤ect of current price P on current consumption Q jt jt F.E. also captures short term responses What if full response takes more than one period? Especially important considering nature of cigarette use F.E. estimate biased. One solution: include lags (T ,T ,...). j,t1 j,t2 Are identi…cation assumptions still valid here? Tradeo¤ between LR and validity of identi…cation assumptions Public Economics Lectures () Part 2: Tax Incidence 63 / 140Evans, Ringel, and Stech: Distributional Incidence Use individual data to see who smokes by education group and income level Spending per capita decreases with the income level Tax is regressive on an absolute level (not only that share of taxes relative to income goes down) Conclusion: Taxes levied on cigarette companies lead to poor paying more for same goods, with no impact on companies Public Economics Lectures () Part 2: Tax Incidence 64 / 140Public Economics Lectures () Part 2: Tax Incidence 65 / 140Cigarette Tax Incidence: Other Considerations 1 Lifetime vs. current incidence (Poterba 1989) Finds cigarette, gasoline and alcohol taxation are less regressive (in statutory terms) from a lifetime perspective High corr. between income and cons share in cross-section; weaker corr. with permanent income. 2 Behavioral models (Gruber and Koszegi 2004) If agents have self control problems, incidence conc. on poor is bene…cial to the extent that they smoke less 3 Intensive vs. extensive margin: Adda and Cornaglia (2006) Use data on cotinine (biomarker) levels in lungs to measure inhalation Higher taxes lead to fewer cigarettes smoked but no e¤ect on cotinine in lungs, implying longer inhalation of each cigarette Public Economics Lectures () Part 2: Tax Incidence 66 / 140Hastings and Washington 2010 Question: How does food stamps subsidy a¤ect grocery store pricing? Food stamps typically arrive at the same time for a large group of people, e.g. …rst of the month Use this variation to study: 1 Whether demand changes at beginning of month (violating PIH) 2 How much of the food stamp bene…t is taken by …rms by increased prices rather than consumers (intended recipients) Public Economics Lectures () Part 2: Tax Incidence 67 / 140Hastings and Washington: Data Scanner data from several grocery stores in Nevada Data from stores in high-poverty areas (15% food stamp recipients) and in low-poverty areas (3%) Club card data on whether each individual used food stamps Data from other states where food stamps are staggered across month used as a control Research design: use variation across stores, individuals, and time of month to measure pricing responses Public Economics Lectures () Part 2: Tax Incidence 68 / 140Public Economics Lectures () Part 2: Tax Incidence 69 / 140Public Economics Lectures () Part 2: Tax Incidence 70 / 140Public Economics Lectures () Part 2: Tax Incidence 71 / 140Hastings and Washington: Results Demand increases by 30% in 1st week, prices by about 3% Very compelling because of multiple dimensions of tests: cross-individual, cross-store, cross-category, and cross-state Interesting theoretical implication: subsidies in markets where low-income recipients are pooled with others have better distributional e¤ects May favor food stamps as a way to transfer money to low incomes relative to a subsidy such as the EITC Public Economics Lectures () Part 2: Tax Incidence 72 / 140Rothstein 2010 How does EITC a¤ect wages? EITC payments subsidize work and transfer money to low income working individuals (50 bil/year) This subsidy could be taken by employers by shifting wage Ex: inelastic demand for low-skilled labor and elastic supply wage rate adjusts 1-1 with EITC Policy question: are we actually transferring money to low incomes through this program or are we just helping business owners? Public Economics Lectures () Part 2: Tax Incidence 73 / 140Rothstein: Model Rothstein considers a model of the labor market with three types of agents 1 Employers 2 EITC-eligible workers 3 EITC-ineligible workers Extends standard partial eq incidence model to allow for di¤erentiated labor supply and di¤erent tax rates across demographic groups Heterogeneity both complicates the analysis and permits identi…cation Identi…cation strategy: compare wage changes across groups who were a¤ected di¤erently by expansions of EITC program from 1992-94 Public Economics Lectures () Part 2: Tax Incidence 74 / 140Public Economics Lectures () Part 2: Tax Incidence 75 / 140Public Economics Lectures () Part 2: Tax Incidence 76 / 140Rothstein: Empirical Strategy Two main challenges to identi…cation: 1 EITC 1992-1994 expansion when nation coming out of recession Compare to other workers (EITC ineligible, slightly higher incomes) 2 Violation of common trends assumption: technical change, more demand for low-skilled workers in 1990s. Compare to trends in pre-period (essentially a DDD strategy) Two dependent variables of interest: 1 Prices Measure how wages change for a worker of given skill 2 Quantities Measure how demand and supply for workers of each skill type change because of EITC Basic concept: use two moments –wage and quantity changes to back out slopes of supply and demand curves Public Economics Lectures () Part 2: Tax Incidence 77 / 140Rothstein: Empirical Strategy Ideal test: measure how wage of a given individual changes when EITC is introduced relative to a similar but ineligible individual Problem: data is CPS repeated cross-sections. Cannot track “same individual.” Moreover, wage rigidities may prevent cuts for existing employees. Solution: reweighting procedure to track “same skill”worker over time (DiNardo, Fortin, and Lemieux 1996) Public Economics Lectures () Part 2: Tax Incidence 78 / 140DFL Reweighting Generalizes propensity score reweighting Used to examine changes in distributions semi-parametrically, conditioning on observables Example: suppose wages are a function purely of height When EITC is expanded, average observed height of workers falls because less-skilled (shorter) people enter the labor force We want to identify how wage distribution changes for people of given height Solution: hold “…xed”height semi-parametrically by reweighting the distribution of wages ex-post to match heights ex-ante. Public Economics Lectures () Part 2: Tax Incidence 79 / 140DFL Reweighting Example: 100 short, 100 tall pre-reform and 200 short, 100 tall post-reform Then put 2/3 weight on tall and 1/3 on short when calculating wage distribution after reform Compare reweighted post-reform distribution to pre-reform distribution to assess e¤ect of expansion on wages Key assumption for causal interpretation of changes: selection on observables Here it is height; more generally, experience, age, demographics, etc. Public Economics Lectures () Part 2: Tax Incidence 80 / 140Public Economics Lectures () Part 2: Tax Incidence 81 / 140Public Economics Lectures () Part 2: Tax Incidence 82 / 140Public Economics Lectures () Part 2: Tax Incidence 83 / 140Public Economics Lectures () Part 2: Tax Incidence 84 / 140Rothstein: Results Basic DFL comparisons yield perverse result: groups that bene…ted from EITC and started working more had more wage growth Potential explanation: demand curve shifted di¤erentially –higher demand for low skilled workers in 1990s. To deal with this, repeats same analysis for 1989-1992 (no EITC expansion) and takes di¤erences Changes sign back to expected, but imprecisely estimated Public Economics Lectures () Part 2: Tax Incidence 85 / 140Public Economics Lectures () Part 2: Tax Incidence 86 / 140Rothstein: Results Ultimately uses quantity estimates and incidence formula to back out predicted changes Wage elasticity estimates: 0.7 for labor supply,0.3 for labor demand Implications using formulas from model: EITC-eligible workers gain 0.70 per 1 EITC expansion Employers gain about 0.70 EITC-ineligible low-skilled workers lose about 0.40 On net, achieve only 0.30 of redistribution toward low income individuals for every 1 of EITC Public Economics Lectures () Part 2: Tax Incidence 87 / 140Rothstein: Caveats 1 Identi…cation heavily complicated by recession, trends (SBTC); no clean control group 2 Data limitations: no panel data; problems in measurement –no annual income, cannot measure MTR 3 Short run vs. long run e¤ects; important due to evidence of nominal wage rigidities. 4 Pure extensive-margin analysis. Intensive margin would go the other way b/c EITC is not a marginal subsidy to wage for a very large fraction of the population. Public Economics Lectures () Part 2: Tax Incidence 88 / 140General Equilibrium Analysis Now move beyond two-good partial equilibrium model to analyze impacts on all prices Typical goal: trace out full incidence of taxes back to original owners of factors Partial equilibrium: “producer”vs. consumer General equilibrium: capital owners vs. labor vs. landlords, etc. Public Economics Lectures () Part 2: Tax Incidence 89 / 140General Equilibrium Analysis Two types of GE models: 1 Static: many sectors or many factors of production Workhorse analytical model: Harberger (1962): 2 sector and 2 factors of production Computational General Equilibrium: many sectors, many factors of production model 2 Dynamic Characterize impacts over time or across generations Asset price e¤ects: capitalization Public Economics Lectures () Part 2: Tax Incidence 90 / 140Harberger 1962 Two Sector Model 1 Fixed total supply of labor L and capital K (short-run, closed economy) 2 Constant returns to scale in both production sectors 3 Full employment of L and K 4 Firms are perfectly competitive Implicit assumption: no adjustment costs for capital and labor Public Economics Lectures () Part 2: Tax Incidence 91 / 140Harberger Model: Setup Production in sectors 1 (bikes) and 2 (cars): X = F (K ,L )= L f(k ) 1 1 1 1 1 1 X = F (K ,L )= L f(k ) 2 2 2 2 2 2 with full employment conditions K +K = K and L +L = L 1 2 1 2 Factors w and L fully mobile in eq., returns must be equal: w = p F = p F 1 1L 2 2L r = p F = p F 1 2 1K 2K Demand functions for goods 1 and 2: X = X (p /p ) and X = X (p /p ) 1 1 1 2 2 2 1 2 Note: all consumers identical so redistribution of incomes via tax system does not a¤ect demand via a feedback e¤ect System of ten eq’ns and ten unknowns: K ,L ,p ,X ,w,r i i i i Public Economics Lectures () Part 2: Tax Incidence 92 / 140Harberger Model: E¤ect of Tax Increase Introduce small tax dt on rental of capital in sector 2 (K ) 2 All eqns the same as above except r =(1dt)p F 2 2K Linearize the 10 eq’ns around initial equilibrium to compute the e¤ect of dt on all 10 variables (dw, dr, dL , ...) 1 Labor income = wL with L …xed, rK = capital income with K …xed Therefore change in prices dw/dt and dr/dt describes how tax is shifted from capital to labor Changes in prices dp /dt, dp /dt describe how tax is shifted from 1 2 sector 2 to sector 1 Kotliko¤ and Summers (Section 2.2) state linearized equations as a fn. of substitution elasticities Public Economics Lectures () Part 2: Tax Incidence 93 / 140Harberger Model: Main E¤ects 1. Substitution e¤ects: capital bears incidence Tax on K shifts production in Sector 2 away from K so aggregate 2 demand for K goes down Because total K is …xed, r falls K bears some of the burden Public Economics Lectures () Part 2: Tax Incidence 94 / 140Harberger Model: Main E¤ects 2. Output e¤ects: capital may not bear incidence Tax on K implies that sector 2 output becomes more expensive 2 relative to sector one Therefore demand shifts toward sector 1 Case 1: K /L K /L (1: bikes, 2: cars) 1 1 2 2 Sector 1 is less capital intensive so aggregate demand for K goes down Output e¤ect reinforces subst e¤ect: K bears the burden of the tax Case 2: K /L K /L (1: cars, 2: bikes) 1 1 2 2 Sector 1 is more capital intensive, aggregate demand for K increases Subst. and output e¤ects have opposite signs; labor may bear some or all the tax Public Economics Lectures () Part 2: Tax Incidence 95 / 140Harberger Model: Main E¤ects 3. Substitution + Output = Overshifting e¤ects Case 1: K /L K /L 1 1 2 2 Can get overshifting of tax, dr dt and dw 0 Capital bears more than 100% of the burden if output e¤ect su¢ ciently strong Taxing capital in sector 2 raises prices of cars more demand for bikes, less demand for cars With very elastic demand (two goods are highly substitutable), demand for labor rises sharply and demand for capital falls sharply Capital loses more than direct tax e¤ect and labor suppliers gain Public Economics Lectures () Part 2: Tax Incidence 96 / 140Harberger Model: Main E¤ects 3. Substitution + Output = Overshifting e¤ects Case 2: K /L K /L 1 1 2 2 Possible that capital is made better o¤ by capital tax Labor forced to bear more than 100% of incidence of capital tax in sector 2 Ex. Consider tax on capital in bike sector: demand for bikes falls, demand for cars rises Capital in greater demand than it was before price of labor falls substantially, capital owners actually gain Bottom line: taxed factor may bear less than 0 or more than 100% of tax. Public Economics Lectures () Part 2: Tax Incidence 97 / 140Harberger Two Sector Model Theory not very informative: model mainly used to illustrate negative result that “anything goes” More interest now in developing methods to identify what actually happens Original application by Harberger: sectors = housing and corporations Capital in these sectors taxed di¤erently because of corporate income tax and many tax subsidies to housing Ex: Deductions for mortgage interest about 80 bn total Harberger made assumptions about elasticities and calculated incidence of corporate tax given potential to substitute into housing Public Economics Lectures () Part 2: Tax Incidence 98 / 140Computable General Equilibrium Models Harberger analyzed two sectors; subsequent literature expanded analysis to multiple sectors Analytical methods infeasible in multi-sector models Instead, use numerical simulations to investigate tax incidence e¤ects after specifying full model Pioneered by Shoven and Whalley (1972). See Kotliko¤ and Summers section 2.3 for a review Produced a voluminous body of research in PF, trade, and development economics Public Economics Lectures () Part 2: Tax Incidence 99 / 140CGE Models: General Structure N intermediate production sectors M …nal consumption goods J groups of consumers who consume products and supply labor Each industry has di¤erent substitution elasticities for capital and labor Each consumer group has Cobb-Douglas utility over M consumption goods with di¤erent parameters Specify all these parameters (calibrated to match some elasticities) and then simulate e¤ects of tax changes Public Economics Lectures () Part 2: Tax Incidence 100 / 140Criticism of CGE Models Findings very sensitive to structural assumptions Ex: assumption of perfect competition Key behavioral elasticities and functional form assumptions Modern econometric methods conceptually not suitable for GE problems The whole point is “spillover e¤ects”(contamination) Need a new empirical paradigm to deal with these problems Public Economics Lectures () Part 2: Tax Incidence 101 / 140Open Economy Application Key assumption in Harberger model: both labor and capital perfectly mobile across sectors Now apply framework to analyze capital taxation in open economies, where capital is more likely to be mobile than labor See Kotliko¤ and Summers section 3.1 for a good exposition Public Economics Lectures () Part 2: Tax Incidence 102 / 140Open Economy Application: Framework One good, two-factor, two-sector model Sector 1: small open economy where L is …xed and K mobile 1 1 Sector 2: rest of the world L …xed and K mobile 2 2 Total capital stock K = K +K is …xed 1 2 Public Economics Lectures () Part 2: Tax Incidence 103 / 140Open Economy Application: Framework Small country introduces tax on capital income (K ) 1 After-tax returns must be equal:  r = F =(1t)F 2K 1K Capital ‡ows from 1 to 2 until returns are equalized; if 2 is large  relative to 1, no e¤ect on r Wage rate w = F (K ,L ) dec. when K dec. b/c L is …xed 1 1L 1 1 1 1 Return of capitalists in small country is unchanged; workers in home country bear the burden of the tax Taxing capital is bad for workers Public Economics Lectures () Part 2: Tax Incidence 104 / 140Open Economy Application: Empirics Mobility of K drives the previous result Empirical question: is K actually mobile across countries? Two strategies: 1 Test based on prices and equilibrium relationships Macro-…nance 2 Look at mobility directly Feldstein and Horioka 1980 Public Economics Lectures () Part 2: Tax Incidence 105 / 140Strategy One: Macro-Finance approach Test based on prices and equilibrium relationships Check whether net returns r are equal across countries General …nding - covered interest parity: obligations that are protected against ‡uctuations in in‡ation and exchange rates have the same returns across countries Di¢ culties in generalization: many assets yield di¤erent returns, unexpected in‡ation, changes in currency exchange rates Need models with uncertainty, risk aversion to deal with other assets Di¢ cult to implement this test for risky assets Public Economics Lectures () Part 2: Tax Incidence 106 / 140Feldstein and Horioka 1980 Second strategy: look at capital mobility directly Feldstein and Horioka use data on OECD countries from 1960-74 Closed economy: S = I; open economy: SI = XM Motivates regression: I/GDP = a+bS/GDP+... Find b= 0.89 (0.07) Public Economics Lectures () Part 2: Tax Incidence 107 / 140Feldstein and Horioka 1980 In closed economy, b= 1 But do not know what b should be in an open economy b may be close to 1 in open economy if 1 Policy objectives involving SI (trade de…cit balance) ¯ ¯ 2 Summing over all countries: S = I as imports and exports cancel out 3 Data problem: S constructed from I in some countries Public Economics Lectures () Part 2: Tax Incidence 108 / 140Open Economy Applications: Empirics Large subsequent literature runs similar regressions and …nds mixed results Generally …nds more ‡ow of capital and increasing over time General view: cannot extract money from capital in small open economies Ex. Europe: tax competition has led to lower capital tax rates Could explain why state capital taxes are relatively low in the U.S. Public Economics Lectures () Part 2: Tax Incidence 109 / 140General Equilibrium Incidence in Dynamic Models Static analysis above assumes that all prices and quantities adjust immediately In practice, adjustment of capital stock and reallocation of labor takes time Dynamic CGE models incorporate these e¤ects; even more complex Static model can be viewed as description of steady states During transition path, measured ‡ow prices (r,w) will not correspond to steady state responses How to measure incidence in dynamic models? Public Economics Lectures () Part 2: Tax Incidence 110 / 140Capitalization and the Asset Price Approach Asset prices can be used to infer incidence in dynamic models (Summers 1983) Study e¤ect of tax changes on asset prices Asset prices adjust immediately in e¢ cient markets, incorporating the full present-value of subsequent changes E¢ cient asset markets incorporate all e¤ects on factor costs, output prices, etc. Limitation: can only be used to characterize incidence of policies on capital owners There are no markets for individuals Public Economics Lectures () Part 2: Tax Incidence 111 / 140Simple Model of Capitalization E¤ects Firms pay out pro…ts as dividends Pro…ts determined by revenues net of factor payments: D q X w L t t t jt jt V = = å å 1+r 1+r dV Change in valuation of …rm ( ) re‡ects change in present value of dt pro…ts dV is a su¢ cient statistic that incorporates changes in all prices dt Empirical applications typically use “event study”methodology Examine pattern of asset prices or returns over time, look for break at time of announcement of policy change Problem: clean shocks are rare; big reforms do not happen suddenly and are always expected to some extent Public Economics Lectures () Part 2: Tax Incidence 112 / 140Capitalization: Empirical Applications Classic application: Cutler (1988) on e¤ect of Tax Reform Act of 1986 on corporations Focus on two more recent studies here 1 Friedman 2008 E¤ect of Medicare Part D on drug companies 2 Linden and Rocko¤ 2008 E¤ect of a sex o¤ender moving into neighborhood on home values Public Economics Lectures () Part 2: Tax Incidence 113 / 140Friedman 2008 Medicare part D passed by Congress in 2003; enacted in 2006 Expanded Medicare coverage to include prescription drugs (provided coverage for 10 mil additional people) What is the incidence of Medicare part D? How much of the expenditure is captured by drug companies through higher pro…ts? Basic research design: event study Plot excess (market adjusted) returns for drug companies around FDA approval of drugs Public Economics Lectures () Part 2: Tax Incidence 114 / 140Event Study Designs Event studies are a powerful research design when treatments are staggered in time across individuals Use a group of treated individuals as counterfactuals for each other to account for time series trends Good for identifying sharp, short-run e¤ects but not longer-term impacts Methodology 1 De…ne "event time" as calendar time minus date of treatment for each treated obs. 2 Plot means/medians, etc. of outcome variable by event time Public Economics Lectures () Part 2: Tax Incidence 115 / 140Excess Returns Around Drug Approval Date Public Economics Lectures () Part 2: Tax Incidence 116 / 140Friedman 2008 Test whether excess returns for high Medicare share drugs is higher after Medicare Part D is passed Let MMS denote medicare market share drug class i. Second-stage i estimating equation: Excess = a+bMMS +gPost2003 +lPost2003 MMS i i t t i Public Economics Lectures () Part 2: Tax Incidence 117 / 140Distribution of Excess Returns around Drug Approval: Pre-Reform (1999-2002) Public Economics Lectures () Part 2: Tax Incidence 118 / 140Distribution of Excess Returns around Drug Approval: Post-Reform (2004-2007) Public Economics Lectures () Part 2: Tax Incidence 119 / 140Friedman: Results Concludes that drug companies’pro…ts increased by 250 bn in present value because of Medicare Part D Rough calibration suggests that drug companies capture about 1/3 of total surplus from program Public Economics Lectures () Part 2: Tax Incidence 120 / 140Linden and Rocko¤2008 Another common application is to housing market to assess WTP for amenities Examples: pollution, schools, crime Rocko¤ and Linden (2008) estimate costs of crime using capitalization approach Research design: examine how house prices change when a registered sex o¤ender moves into a neighborhood Data: public records on o¤ender’s addresses and property values in North Carolina Public Economics Lectures () Part 2: Tax Incidence 121 / 140Public Economics Lectures () Part 2: Tax Incidence 122 / 140Public Economics Lectures () Part 2: Tax Incidence 123 / 140Public Economics Lectures () Part 2: Tax Incidence 124 / 140Public Economics Lectures () Part 2: Tax Incidence 125 / 140Linden and Rocko¤: Results Find house prices decline by about 4% (5500) when a sex o¤ender is located within 0.1 mile of the house Implied cost of a sexual o¤ense given probabilities of a crime: 1.2 million This is far above what is used by Dept of Justice How to interpret evidence: true cost of crime or a behavioral e¤ect? Why does price fall only within 0.1 mile radius? Public Economics Lectures () Part 2: Tax Incidence 126 / 140Mandated Bene…ts We have focused until now on incidence of price interventions (taxes, subsidies) Similar incidence/shifting issues arise in analyzing quantity intervention (regulations) Leading case: mandated bene…ts –requirement that employers pay for health care, workers compensation bene…ts, child care, etc. Mandates are attractive to government because they are “o¤ budget”; may re‡ect salience issues Public Economics Lectures () Part 2: Tax Incidence 127 / 140Mandated Bene…ts Tempting to view mandates as additional taxes on …rms and apply same analysis as above But mandated bene…ts have di¤erent e¤ects on equilibrium wages and employment di¤erently than a tax (Summers 1989) Key di¤erence: mandates are a bene…t for the worker, so e¤ect on market equilibrium depends on bene…ts workers get from the program Unlike a tax, may have no distortionary e¤ect on employment and only an incidence e¤ect (lower wages) Public Economics Lectures () Part 2: Tax Incidence 128 / 140Mandated Bene…ts: Simple Model Labor demand (D) and labor supply (S) are functions of the wage, w Initial equilibrium: D(w )= S(w ) 0 0 Now, govt mandates employers provide a bene…t with cost t Workers value the bene…t at at dollars Typically 0 a 1 but a 1 possible with market failures Labor cost is now w +t, e¤ective wage w +at New equilibrium: D(w +t)= S(w +at) Public Economics Lectures () Part 2: Tax Incidence 129 / 140Mandated Benefit Wage S Rate A w 1 D 1 L 1 Labor Supply Public Economics Lectures () Part 2: Tax Incidence 130 / 140Mandated Benefit Wage S Rate A w 1 B 1 D D 2 1 L 1 Labor Supply Public Economics Lectures () Part 2: Tax Incidence 131 / 140Mandated Benefit Wage S Rate α A w 1 B C w 2 1 D D 2 1 L 1 Labor Supply Public Economics Lectures () Part 2: Tax Incidence 132 / 140Mandated Bene…ts: Incidence Formula Analysis for a small t: linear expansion around initial equilibrium 0 0 (dw/dt+1)D =(dw/dt+a)S 0 0 0 0 dw/dt =(D aS )/(S D ) h S =1+(1a) h h S D where 0 h = wD /D 0 D 0 h = wS /S 0 S If a= 1, dw/dt =1 and no e¤ect on employment More generally: 0 a 1 equivalent to a tax 1a with usual incidence and e¢ ciency e¤ects Public Economics Lectures () Part 2: Tax Incidence 133 / 140Mandated Bene…ts: Empirical Applications Focus here on Acemoglu and Angrist (2001) study of Americans with Disabilities Act Other applications 1 Gruber and Krueger (1991) on workers compensation mandates 2 Gruber (1994) on mandated maternity bene…ts 3 Kolstad and Kowalski (2012) on health insurance mandates Public Economics Lectures () Part 2: Tax Incidence 134 / 140Acemoglu and Angrist (2001) Look at e¤ect of ADA regulations on wages and employment of the disabled The 1993 Americans with Disabilities Act requires employers to: Make accommodations for disabled employees Pay same wages to disabled employees as to non-disabled workers Cost to accommodate disabled workers: 1000 per person on average Theory is ambiguous on net employment e¤ect because of wage discrimination clause Public Economics Lectures () Part 2: Tax Incidence 135 / 140Mandated Benefit with Minimum Wage Wage S Rate A w 1 B minimum wage w 2 D D 2 1 L 1 Labor Supply Public Economics Lectures () Part 2: Tax Incidence 136 / 140Acemoglu and Angrist 2001 Acemoglu and Angrist estimate the impact of act using data from the Current Population Survey Examine employment and wages of disabled workers before and after the ADA went into e¤ect Public Economics Lectures () Part 2: Tax Incidence 137 / 140Public Economics Lectures () Part 2: Tax Incidence 138 / 140Public Economics Lectures () Part 2: Tax Incidence 139 / 140Acemoglu and Angrist: Results Employment of disabled workers fell after the reform: About a 1.5-2 week drop in employment for males, roughly a 5-10% decline in employment Wages did not change Results consistent w/ labor demand elasticity of about -1 or -2 Firms with fewer than 25 workers exempt from ADA regulations; no employment reduction for disabled at these …rms ADA intended to help those with disabilities but appears to have hurt many of them because of wage discrimination clause Underscores importance of considering incidence e¤ects before implementing policies Public Economics Lectures () Part 2: Tax Incidence 140 / 140Public Economics Lectures Part 3: E¢ ciency Cost of Taxation Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 3: E¢ ciency 1 / 106Outline 1 Marshallian surplus 2 Path dependence problem and income e¤ects 3 De…nitions of EV, CV, and excess burden with income e¤ects 4 Harberger Approximation 5 Exact Consumer Surplus (Hausman 1981) 6 Empirical Applications 7 Welfare Analysis in Behavioral Models Public Economics Lectures () Part 3: E¢ ciency 2 / 106De…nition Incidence: e¤ect of policies on distribution of economic pie E¢ ciency or deadweight cost: e¤ect of policies on size of the pie Focus in e¢ ciency analysis is on quantities, not prices Public Economics Lectures () Part 3: E¢ ciency 3 / 106References Auerbach (1985) handbook chapter Chetty, Looney, Kroft (AER 2009) Chetty (Annual Review 2009) Mas-Colell, Whinston, Green Chapter 3 for background on price theory concepts Public Economics Lectures () Part 3: E¢ ciency 4 / 106E¢ ciency Cost: Introduction Government raises taxes for one of two reasons: 1 To raise revenue to …nance public goods 2 To redistribute income But to generate 1 of revenue, welfare of those taxed falls by more than 1 because the tax distorts behavior How to implement policies that minimize these e¢ ciency costs? Start with positive analysis of how to measure e¢ ciency cost of a given tax system Public Economics Lectures () Part 3: E¢ ciency 5 / 106Marshallian Surplus: Assumptions Simplest analysis of e¢ ciency costs: Marshallian surplus Two assumptions: 1 Quasilinear utility: no income e¤ects, money metric 2 Competitive production Public Economics Lectures () Part 3: E¢ ciency 6 / 106Partial Equilibrium Model: Setup Two goods: x and y Consumer has wealth Z, utility u(x)+y, and solves maxu(x)+y s.t. (p+t)x(p+t,Z)+y(p+t,Z)= Z x,y Firms use c(S) units of the numeraire y to produce S units of x Marginal cost of production is increasing and convex: 0 00 c (S) 0 and c (S) 0 Firm’s pro…t at pretax price p and level of supply S is pSc(S) Public Economics Lectures () Part 3: E¢ ciency 7 / 106Model: Equilibrium With perfect optimization, supply fn for x is implicitly de…ned by the marginal condition 0 p = c (S(p)) 0 S Let h = p denote the price elasticity of supply S S Let Q denote equilibrium quantity sold of good x Q satis…es: Q(t)= D(p+t)= S(p) Consider e¤ect of introducing a small tax dt 0 on Q and surplus Public Economics Lectures () Part 3: E¢ ciency 8 / 106Excess Burden of Taxation Price S A 30.0 D 1500 Quantity Public Economics Lectures () Part 3: E¢ ciency 9 / 106Excess Burden of Taxation Price S+t S B Excess Burden 36.0 A 30.0 C t D 1350 1500 Quantity Public Economics Lectures () Part 3: E¢ ciency 10 / 106E¢ ciency Cost: Qualitative Properties 1 Excess burden increases with square of tax rate 2 Excess burden increases with elasticities Public Economics Lectures () Part 3: E¢ ciency 11 / 106EB Increases with Square of Tax Rate P S P 1 A D Q Q 1 Public Economics Lectures () Part 3: E¢ ciency 12 / 106EB Increases withSquare of Tax Rate S+t P 1 S B P 2 P 1 A C t 1 D Q Q Q 2 1 Public Economics Lectures () Part 3: E¢ ciency 13 / 106EB Increases withSquare of Tax Rate S+t +t S+t P 1 2 1 S E P 3 B P 2 Change in EB P 1 A t 2 C D D Q Q Q Q 3 2 1 Public Economics Lectures () Part 3: E¢ ciency 14 / 106Comparative Statics (a) Inelastic Demand (b) Elastic Demand P P S+t S+t S S B P 2 B P 2 P P A 1 1 A C D C t t D Q Q Q Q Q Q 2 1 2 1 Public Economics Lectures () Part 3: E¢ ciency 15 / 106Tax Policy Implications With many goods, the most e¢ cient way to raise tax revenue is: 1 Tax inelastic goods more (e.g. medical drugs, food) 2 Spread taxes across all goods to keep tax rates relatively low on all goods (broad tax base) These are two countervailing forces; balancing them requires quantitative measurement of excess burden Public Economics Lectures () Part 3: E¢ ciency 16 / 106Measuring Excess Burden: Marshallian Surplus How to measure excess burden? Three empirically implementable methods: 1 In terms of supply and demand elasticities 2 In terms of total change in equilibrium quantity caused by tax 3 In terms of change in government revenue Public Economics Lectures () Part 3: E¢ ciency 17 / 106Method 1: Supply and Demand Elasticities 1 EB = dQdt 2 h 1 0 0 2 D EB = S (p)dpdt =(1/2)(pS /S)(S/p) dt 2 h h S D 1 h h dt 2 S D EB = pQ( ) 2h h p S D h D Note: second line uses incidence formula dp =( )dt h h S D Tax revenue R = Qdt Useful expression is deadweight burden per dollar of tax revenue: EB 1 h h dt S D = R 2h h p S D Public Economics Lectures () Part 3: E¢ ciency 18 / 106Method 2: Distortions in Equilibrium Quantity p dQ 0 De…ne h = Q dt Q h : e¤ect of a 1% increase in price via a tax change on equilibrium Q quantity, taking into account the endogenous price change This is the coe¢ cient b in a reduced-form regression: t logQ = a+b + p 0 Identify b using exogenous variation in t. Then: dQ EB = (1/2) dtdt dt dQ p Q = (1/2) ( )( )dtdt dt Q p dt 2 = (1/2)h pQ( ) Q p Public Economics Lectures () Part 3: E¢ ciency 19 / 106Marginal Excess Burden of Tax Increase Excess burden of a tax t is dQ 2 EB(t)=(1/2) t dt Consider EB from raising tax by Dt given pre-existing tax t: dQ 2 2 EB(Dt) = (1/2) (t+Dt) t dt dQ 2 = (1/2) 2tDt+(Dt) dt dQ dQ 2 = t Dt(1/2) (Dt) dt dt 2 First term is …rst-order in Dt; second term is second-order ((Dt) ) This is why taxing markets with pre-existing taxes generates larger marginal EB EB ofDt = 1% is 10 times larger if t = 10% than if t = 0. Public Economics Lectures () Part 3: E¢ ciency 20 / 106First vs. Second-Order Approximations Computing marginal excess burden by di¤erentiating formula for excess burden gives: dEB dQ Dt =t Dt dt dt First derivative of EB(t) only includes …rst-order term in Taylor expansion: 2 dEB 1d EB 2 EB(t+Dt)= EB(t)+ Dt+ (Dt) 2 dt 2 dt First-order approximation is accurate when t large relative toDt Ex: t = 20%,Dt = 5% implies …rst term accounts for 90% of EB But introduction of new tax (t = 0) generates EB only through second-order term Public Economics Lectures () Part 3: E¢ ciency 21 / 106Method 3: Leakage in government revenue To …rst order, marginal excess burden of raising t is: ¶EB dQ =t ¶t dt Observe that tax revenue R(t)= Qt ¶R Mechanical revenue gain: j = Q Q ¶t ¶R dQ Actual revenue gain: = Q+t ¶t dt MEB is the di¤erence between mechanical and actual revenue gain: ¶R dR dQ dQ ¶EB j = QQ+t =t = Q ¶t dt dt dt ¶t Public Economics Lectures () Part 3: E¢ ciency 22 / 106First vs. Second-Order Approximations Why does leakage in govt. revenue only capture …rst-order term? Govt revenue loss: rectangle in Harberger trapezoid, proportional to Dt Consumer and producer surplus loss: triangles in trapezoid 2 (proportional toDt ) Method 3 is accurate for measuring marginal excess burden given pre-existing taxes but not introduction of new taxes Public Economics Lectures () Part 3: E¢ ciency 23 / 106Excess Burden of a Tax Increase: Harberger Trapezoid S+τ+Δτ S+τ P Lost cons. S nd surplus (2 order) E B Lost govt. revenue st (1 order) τ A Δτ C D Lost producer nd surplus (2 order) D Q Q Q 2 1 Public Economics Lectures () Part 3: E¢ ciency 24 / 106General Model with Income E¤ects Drop quasilinearity assumption and consider an individual with utility u(c ,..,c )= u(c) 1 N Individual’s problem: maxu(c) s.t. qc Z c where q = p+t denotes vector of tax-inclusive prices and Z is wealth Labor can be viewed as commodity with price w and consumed in negative quantity Public Economics Lectures () Part 3: E¢ ciency 25 / 106Demand Functions and Indirect Utility Let l denote multiplier on budget constraint First order condition in c : i u = lq c i i These conditions implicitly de…ne: c (q,Z): the Marshallian (“uncompensated”) demand function i v(q,Z): the indirect utility function Public Economics Lectures () Part 3: E¢ ciency 26 / 106Measuring Deadweight Loss with Income E¤ects Question: how much utility is lost because of tax beyond revenue transferred to government? Marshallian surplus does not answer this question with income e¤ects Problem: not derived from utility function or a welfare measure Creates various problems such as “path dependence”with taxes on multiple goods 0 1 0 1 DCS(t t˜)+DCS(t˜ t )6=DCS(t t ) Need units to measure “utility loss” Introduce expenditure function to translate the utility loss into dollars (money metric) Public Economics Lectures () Part 3: E¢ ciency 27 / 106Expenditure Function Fix utility at U and prices at q Find bundle that minimizes cost to reach U for q: e(q,U)= minqc s.t. u(c) U c Let m denote multiplier on utility constraint First order conditions given by: q = mu i c i These generate Hicksian (or compensated) demand fns: c = h (q,u) i i De…ne individual’s loss from tax increase as 1 0 e(q ,u)e(q ,u) Single-valued function coherent measure of welfare cost, no path dependence Public Economics Lectures () Part 3: E¢ ciency 28 / 106Compensating and Equivalent Variation But where should u be measured? 0 1 Consider a price change from q to q 0 Utility at initial price q : 0 0 u = v(q ,Z) 1 Utility at new price q : 1 1 u = v(q ,Z) Two concepts: compensating (CV) and equivalent variation (EV) use 0 1 u and u as reference utility levels Public Economics Lectures () Part 3: E¢ ciency 29 / 106Compensating Variation 0 Measures utility at initial price level (u ) Amount agent must be compensated in order to be indi¤erent about tax increase 1 0 0 0 1 0 CV = e(q ,u )e(q ,u )= e(q ,u )Z How much compensation is needed to reach original utility level at new prices? CV is amount of ex-post cost that must be covered by government to yield same ex-ante utility: 0 0 1 0 e(q ,u )= e(q ,u )CV Public Economics Lectures () Part 3: E¢ ciency 30 / 106Equivalent Variation Measures utility at new price level Lump sum amount agent willing to pay to avoid tax (at pre-tax prices) 1 1 0 1 0 1 EV = e(q ,u )e(q ,u )= Ze(q ,u ) EV is amount extra that can be taken from agent to leave him with same ex-post utility: 0 1 1 1 e(q ,u )+EV = e(q ,u ) Public Economics Lectures () Part 3: E¢ ciency 31 / 106E¢ ciency Cost with Income E¤ects Goal: derive empirically implementable formula analogous to Marshallian EB formula in general model with income e¤ects Literature typically assumes either 1 Fixed producer prices and income e¤ects 2 Endogenous producer prices and quasilinear utility With both endogenous prices and income e¤ects, e¢ ciency cost depends on how pro…ts are returned to consumers Formulas are very messy and fragile (Auerbach 1985, Section 3.2) Public Economics Lectures () Part 3: E¢ ciency 32 / 106E¢ ciency Cost Formulas with Income E¤ects Derive empirically implementable formulas using Hicksian demand (EV and CV) Assume p is …xed ‡at supply, constant returns to scale The envelope thm implies that e (q,u)= h , and so: q i i Z 1 q 1 0 e(q ,u)e(q ,u)= h(q,u)dq 0 q If only one price is changing, this is the area under the Hicksian demand curve for that good Note that optimization implies that h(q,v(q,Z))= c(q,Z) Public Economics Lectures () Part 3: E¢ ciency 33 / 106Compensating vs. Equivalent Variation h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 p 0 D x(p ,Z) x(p ,Z) x 1 0 Public Economics Lectures () Part 3: E¢ ciency 34 / 106Compensating vs. Equivalent Variation h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 EV p 0 D x(p ,Z) x(p ,Z) x 1 0 Public Economics Lectures () Part 3: E¢ ciency 35 / 106Compensating vs. Equivalent Variation h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 CV p 0 D x(p ,Z) x(p ,Z) x 1 0 Public Economics Lectures () Part 3: E¢ ciency 36 / 106Marshallian Surplus h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 Marshallian Surplus p 0 D x(p ,Z) x(p ,Z) x 1 0 Public Economics Lectures () Part 3: E¢ ciency 37 / 106EV, CV, and Marshallian Surplus With one price change: EV Marshallian Surplus CV But this is not true in general with multiple price changes because Marshallian Surplus is ill-de…ned Public Economics Lectures () Part 3: E¢ ciency 38 / 106Excess Burden Deadweight burden: change in consumer surplus less tax paid What is lost in excess of taxes paid? Two measures, corresponding to EV and CV: 1 1 0 1 1 EB(u ) = EV(q q )h(q ,u ) Mohring 1971 0 1 0 1 0 EB(u ) = CV(q q )h(q ,u ) Diamond and McFadden 1974 Public Economics Lectures () Part 3: E¢ ciency 39 / 106h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 EB EB EV CV p 0 D x(p ,Z) x (p ,V(p ,Z)) x 1 C 1 0 Public Economics Lectures () Part 3: E¢ ciency 40 / 106h(V(p ,Z)) h(V(p ,Z)) 1 0 p p 1 Marshallian p 0 D x(p ,Z) x (p ,V(p ,Z)) x 1 C 1 0 Public Economics Lectures () Part 3: E¢ ciency 41 / 106Excess Burden In general, CV and EV measures of EB will di¤er Marshallian measure overstates excess burden because it includes income e¤ects Income e¤ects are not a distortion in transactions Buying less of a good due to having less income is not an e¢ ciency loss; no surplus foregone b/c of transactions that do not occur CV = EV = Marshallian DWL only with quasilinear utility (Chipman and Moore 1980) Public Economics Lectures () Part 3: E¢ ciency 42 / 106Implementable Excess Burden Formula Consider increase in tax t on good 1 to t+Dt No other taxes in the system Recall the expression for EB: EB(t)=e(p+t,U)e(p,U)th (p+t,U) 1 Second-order Taylor expansion: MEB = EB(t+Dt)EB(t) 2 dEB 1 d EB 2 ' Dt+ (Dt) 2 dt 2 dt Public Economics Lectures () Part 3: E¢ ciency 43 / 106Harberger Trapezoid Formula dEB dh 1 = h (p+t,U)t h (p+t,U) 1 1 dt dt dh 1 = t dt 2 2 d EB dh d h 1 1 = t 2 2 dt dt dt 2 d h 1 Standard practice in literature: assume = 0 (linear Hicksian); not 2 dt necessarily well justi…ed b/c it does not vanish as Dt 0 dh 1dh 1 1 2 ) MEB =tDt (Dt) dt 2 dt Formula equals area of “Harberger trapezoid”using Hicksian demands Public Economics Lectures () Part 3: E¢ ciency 44 / 106Harberger Formula Without pre-existing tax, obtain “standard”Harberger formula: 1dh 1 2 EB = (Dt) 2 dt General lesson: use compensated (substitution) elasticities to compute EB, not uncompensated elasticities To implement empirically, estimate Marshallian price elasticity and income elasticity. Then apply Slutsky eqn: ¶h ¶c ¶c i i i = + c j ¶q ¶q ¶Z j j z z z Income E¤ect Hicksian Slope Marshallian Slope Public Economics Lectures () Part 3: E¢ ciency 45 / 106Excess Burden with Taxes on Multiple Goods Previous formulas apply to case with tax on one good With multiple goods and …xed prices, excess burden of introducing a tax t k 1 dh dh k i 2 EB = t t t å i k k 2 dt dt k i6=k k Second-order e¤ect in own market, …rst-order e¤ect from other markets with pre-existing taxes Complementarity between goods important for excess burden calculations Ex: with an income tax, minimize total DWL tax by taxing goods complementary to leisure (Corlett and Hague 1953) Public Economics Lectures () Part 3: E¢ ciency 46 / 106Goulder and Williams 2003 Show that ignoring cross e¤ects by using one-good formula can be very misleading Di¤erentiate multiple-good Harberger formula w.r.t. t : k dEB dh dh k i =t å t k i dt dt dt k k i6=k k If t is small (e.g. gas tax), what matters is purely distortion in other k markets, e.g. labor supply As t 0, error in single-market formula approaches ¥ k Public Economics Lectures () Part 3: E¢ ciency 47 / 106Goulder and Williams 2003 Basic formula hard to implement because it requires estimates of all cross-price elasticities Goulder and Williams make formula empirically implementable by making 3 assumptions: 1 No income e¤ects 2 Ignore interactions with commodities other than labor (other taxes are small) 3 Assume good is of “average”substitutability with labor: cross partial ¶l equals mean cross-partial across consumption goods ¶t k Public Economics Lectures () Part 3: E¢ ciency 48 / 106Goulder and Williams Formula Obtain following formula for marginal excess burden of raising tax on good k: dEB t Q t L k k L = h h s k k L dt p p k k k t , p , and Q are the tax, price, and quantity consumed of good k k k k h and h are own-price elasticity of good k and labor k L P Q k K s = is budget share of good k k wl(1t ) L Only need estimates of own-price elasticities to implement this formula Why? Consumption tax and labor income tax have equivalent e¤ects Price increase in all consumption goods has the same e¤ect on labor supply as an increase in tax on labor: (1+t) p c = wl å k k k Public Economics Lectures () Part 3: E¢ ciency 49 / 106Goulder and Williams Formula: Intuition Why do we only need to estimate h ? L Step 1: consumption tax and labor income tax have equivalent e¤ects Price increase in all consumption goods has the same e¤ect on labor supply as an increase in tax on labor: (1+t) p c = wl å k k k Public Economics Lectures () Part 3: E¢ ciency 50 / 106Goulder and Williams Formula: Intuition Step 2: Rank goods according to complementarity with labor (i.e. dl cross-partial ) dt k dl Find good at the mean level of dt k A tax increase on this good has same e¤ect as an increase in sales tax t on all consumption goods scaled down by s k Therefore cross-elasticity of l w.r.t. t is equivalent to h s k k L Labor supply elasticity h su¢ cient to calculate cross-elasticity for L good that has “average”level of substitutability Public Economics Lectures () Part 3: E¢ ciency 51 / 106Goulder and Williams Results Calibrate formula using existing elasticity estimates Result: DWL of taxing goods such as gasoline is underestimated by a factor of 10 in practice because of income tax Caveat: is their approach and conclusion valid if there are salience e¤ects? Public Economics Lectures () Part 3: E¢ ciency 52 / 106Hausman 1981: Exact Consumer Surplus Harberger formulas: empirically implementable but approximate Alternative approach: structural estimation of demand model Start by estimating Marshallian demand functions: c(q,Z)= g+aq+dZ Then integrate to recover underlying indirect utility function v(q,Z) Invert to obtain expenditure function e(q,u) and compute “exact”EB Parametric approach: Hausman (AER 1981); non-parametric approach: Hausman and Newey (ECMA 1995) Public Economics Lectures () Part 3: E¢ ciency 53 / 106Harberger vs. Hausman Approach Underscores broader di¤erence between structural and quasi-experimental methodologies Modern literature focuses on deriving “su¢ cient statistic”formulas that can be implemented using quasi-experimental techniques Now develop general distinction between structural and su¢ cient statistic approaches to welfare analysis in a simple model of taxation No income e¤ects (quasilinear utility) Constant returns to production (…xed producer prices) But permit multiple goods (GE) Public Economics Lectures () Part 3: E¢ ciency 54 / 106Su¢ cient Statistics vs Structural Methods N goods: x =(x ,...,x ); prices (p ,...p ); wealth Z 1 N 1 N Normalize p = 1 (x is numeraire) N N Government levies a tax t on good 1 Individual takes t as given and solves N maxu(x ,...,x )+x s.t. (p +t)x + p x = Z 1 N1 N 1 1 i i å i=2 To measure EB of tax, de…ne social welfare as sum of individual’s utility and tax revenue: N1 W(t)=fmaxu(x ,...,x )+Z(p +t)x p xg+tx 1 N1 1 1 i i 1 å x i=2 dW Goal: measure = loss in social surplus caused by tax change dt Public Economics Lectures () Part 3: E¢ ciency 55 / 106Primitives Sufficient Stats. Welfare Change ω 1 ω 2 . K ÝtÞ dW 1 ÝtÞ . dt K ÝtÞ 2 . ω Ν ω=preferences, β = f(ω,t) dW/dt used for constraints y = β X + β X + ε policy analysis 1 1 2 2 ω not uniquely β identified using identified program evaluation Source: Chetty (2009) Public Economics Lectures () Part 3: E¢ ciency 56 / 106Su¢ cient Statistics vs Structural Methods Structural method: estimate N good demand system, recover u Ex: use Stone-Geary or AIDS to recover preference parameters; then calculate “exact consumer surplus”as in Hausman (1981) Alternative: Harberger’s deadweight loss triangle formula Private sector choices made to maximize term in red (private surplus) N1 W(t)=fmaxu(x ,...,x )+Z(p +t)x p xg+tx 1 N1 1 1 å i i 1 x i=2 Envelope conditions for (x ,...,x ) allow us to ignore behavioral 1 N dx i responses ( ) in term in red, yielding dt dW dx dx 1 1 =x +x +t = t 1 1 dt dt dt dx dW 1 is a “su¢ cient statistic”for calculating dt dt Public Economics Lectures () Part 3: E¢ ciency 57 / 106Heterogeneity Bene…t of su¤ stat approach particularly evident with heterogeneity K agents, each with utility u (x ,...,x )+x k N1 N 1 Social welfare function under utilitarian criterion: K k k W(t) = fmax u (x ,...,x )+Z å k 1 N1 x k=1 N1 K k k k (p +t)x p x g+ tx 1 å i å 1 i 1 i=2 k=1 Structural method: estimate demand systems for all agents Su¢ cient statistic formula is unchanged— still need only slope of dx 1 aggregate demand dt K K K k dW d x dx å 1 k k k=1 1 = x + x +t = t å 1 å 1 dt dt dt k=1 k=1 Public Economics Lectures () Part 3: E¢ ciency 58 / 106Discrete Choice Model Harberger su¢ cient statistic also works with discrete choice Agents have value V for good 1; can either buy or not buy k Let F(V) denote distribution of valuations With 2 goods, utility of agent k is V x +Z(p+t)x k 1 1 Social welfare: Z k k W(t) = f maxV x +Z(p +t)x dF(V )g 1 k 1 1 k k V x k 1 Z k + tx dF(V ) k 1 k V This problem is not smooth at individual level, so cannot directly apply envelope thm. as stated Public Economics Lectures () Part 3: E¢ ciency 59 / 106Discrete Choice Model Recast as planner’s problem choosing threshold above which agents are allocated good 1: ( ) Z ¥ W(t) = max _ V (p +t)dF (V )+Z k 1 k _ V V Z ¥ +t _ dF (V ) k V Again obtain Harberger formula as a fn of slope of aggregate demand dx 1 curve : dt R ¥       _ _ _ d dF (V ) dW k V = 1F V + 1F V +t dt dt dW dx 1 ) = t dt dt Public Economics Lectures () Part 3: E¢ ciency 60 / 106Economic Intuition for Robustness of Harberger Result Deadweight loss is fully determined by di¤erence between marginal willingness to pay for good x and its cost (p ) 1 1 Recovering marginal willingness to pay requires an estimate of the slope of the demand curve because it coincides with marginal utility: 0 p = u (x(p)) Slope of demand is therefore su¢ cient to infer e¢ ciency cost of a tax, without identifying rest of the model Public Economics Lectures () Part 3: E¢ ciency 61 / 106E¢ ciency Cost: Applications 1 Income Taxation Feldstein; Chetty; Gorodnichenko et al. 2 Housing Subsidy Poterba 3 Diesel Fuel Taxation Marion and Muehlegger Public Economics Lectures () Part 3: E¢ ciency 62 / 106Feldstein 1995, 1999 Following Harberger, large literature in labor estimated e¤ect of taxes on hours worked to assess e¢ ciency costs of taxation Feldstein observed that labor supply involves multiple dimensions, not just choice of hours: training, e¤ort, occupation Taxes also induce ine¢ cient avoidance/evasion behavior Structural approach: account for each of the potential responses to taxation separately and then aggregate Feldstein’s alternative: elasticity of taxable income with respect to taxes is a su¢ cient statistic for calculating deadweight loss Public Economics Lectures () Part 3: E¢ ciency 63 / 106Feldstein Model: Setup Government levies linear tax t on reported taxable income Agent makes N labor supply choices: l ,...l 1 N Each choice l has disutility y (l ) and wage w i i i i Agents can shelter e of income from taxation by paying cost g(e) Taxable Income (TI) is N TI = w le å i i i=1 Consumption is given by taxed income plus untaxed income: c =(1t)TI +e Public Economics Lectures () Part 3: E¢ ciency 64 / 106Feldstein Taxable Income Formula Agent’s utility is quasi-linear in consumption: N u(c,e,l)= cg(e) y (l ) i å i i=1 Social welfare: N W(t)=f(1t)TI +eg(e) y (l )g+tTI å i i i=1 Di¤erentiating and applying envelope conditions for l i 0 0 ((1t)w = y (l )) and e (g (e)= t) implies i i i dW dTI dTI =TI +TI +t = t dt dt dt Intuition: marginal social cost of reducing earnings through each margin is equated at optimum irrelevant what causes change in TI Public Economics Lectures () Part 3: E¢ ciency 65 / 106Taxable Income Formula Simplicity of identi…cation in Feldstein’s formula has led to a large literature estimating elasticity of taxable income But since primitives are not estimated, assumptions of model used to derive formula are never tested 0 Chetty (2009) questions validity of assumption that g (e)= t Costs of some avoidance/evasion behaviors are transfers to other agents in the economy, not real resource costs Ex: cost of evasion is potential …ne imposed by government Public Economics Lectures () Part 3: E¢ ciency 66 / 106Chetty Transfer Cost Model: Setup Individual chooses e (evasion/shifting) and l (labor supply) to maxu(c,l,e) = cy(l) e,l s.t. c = y +(1t)(wle)+ez(e) Social welfare is now: W(t) = fy +(1t)(wle)+e z(e)y(l)g +z(e)+t(wle) Di¤erence: z(e) now appears twice in SWF, with opposite signs Public Economics Lectures () Part 3: E¢ ciency 67 / 106Excess Burden with Transfer Costs Let LI = wl be the total (pretax) earned income and TI = wle denote taxable income Exploit the envelope condition for term in curly brackets: dW dz de dwle = (wle)+(wle)+ +t dt de dt dt dTI dz de = t + dt de dt dLI de dz de = t t + dt dt de dt First-order condition for individual’s choice of e: dz t = de dW dLI ) = t (1) dt dt Intuition: MPB of raising e by 1 (saving t) equals MPC Public Economics Lectures () Part 3: E¢ ciency 68 / 106Chetty (2009) Formula With both transfer cost z(e) and resource cost g(e) of evasion: dW dLI de 0 = t g (e) dt dt dt dTI dLI = tfm +(1m) g dt dt t = fmTI +(1m)wl g TI LI 1t EB depends on weighted average of taxable income ( ) and total TI earned income elasticities ( ) LI Practical importance: even though reported taxable income is highly sensitive to tax rates for rich, e¢ ciency cost may not be large Most di¢ cult parameter to identify: weight m, which depends on 0 marginal resource cost of sheltering, g (e) Public Economics Lectures () Part 3: E¢ ciency 69 / 106Gorodnichenko, Martinez-Vazquez, and Peter 2009 Estimate and to implement formula that permits transfer costs LI TI Insight: consumption data can be used to infer LI Estimate e¤ect of 2001 ‡at tax reform in Russia on gap between taxable income and consumption, which they interpret as evasion Public Economics Lectures () Part 3: E¢ ciency 70 / 106Public Economics Lectures () Part 3: E¢ ciency 71 / 106Public Economics Lectures () Part 3: E¢ ciency 72 / 106Gorodnichenko et al: Results dTI Taxable income elasticity is large, whereas labor income elasticity dt dLI is not dt Feldstein’s formula overestimates the e¢ ciency costs of taxation 0 relative to more general measure for “plausible”g (e) 0 Question: could g (e) be estimated from consumption data itself? Public Economics Lectures () Part 3: E¢ ciency 73 / 106Poterba 1992 Estimates e¢ ciency cost of subsidy for housing in the U.S. from mortgage interest deduction First need to de…ne “cost”of owning 1 of housing De…nition: “user cost”–measures opportunity cost of living in home Could rent the house to someone else at percentage rate Rent r = Property Value With marginal income tax rate t and nominal interest i, net user cost taking into account mortgage deduction is c = rti Public Economics Lectures () Part 3: E¢ ciency 74 / 106Poterba 1992 Poterba …rst calculates changes in user cost over 1980s Tax reform in 1986 lowered tax rates for high income and raised user cost of housing sharply Prior to 1986: very high tax rates on high incomes (60%) In 1990, only 28% Nearly tripled the cost of housing Public Economics Lectures () Part 3: E¢ ciency 75 / 106Public Economics Lectures () Part 3: E¢ ciency 76 / 106Poterba 1992 Calculates compensated elasticity using estimates in literature and Slutsky eqn. Rosen (1982): =1 H,r Income elasticity: 0.75 Housing share: 0.25 3 1 ) Compensated elasticity: 1+  '0.8 4 4 Intuition for large elasticity: broker calculates “how much house you can a¤ord”if they spend 30% of income Can “a¤ord”more with larger tax subsidy tax is e¤ectively salient Calculates amount of overconsumption of housing and e¢ ciency cost of housing subsidy Public Economics Lectures () Part 3: E¢ ciency 77 / 106Poterba: Results Tax reforms in 1980s reduced DWL from 12K to 2K for each household earning 250K Still have relatively large ine¢ ciency from subsidizing mortgages This is why President Bush’s Tax Panel recommended cap or elimination of subsidy for homeownership But hard to implement politically Public Economics Lectures () Part 3: E¢ ciency 78 / 106Marion and Muehlegger 2008 Study deadweight cost from taxing diesel fuels, focusing on evasion Diesel fuel used for business purposes (e.g. trucking) is taxed, but residential purposes (e.g. heating homes) is not Substantial opportunity to evade tax 1993: government added red dye to residential diesel fuel Easy to monitor cheating by opening gas tank of a truck First document e¤ect of dye reform on evasion Public Economics Lectures () Part 3: E¢ ciency 79 / 106Public Economics Lectures () Part 3: E¢ ciency 80 / 106Marion and Muehlegger: Excess Burden Calculations Use reform to assess deadweight costs of evasion and taxation Harder to evade elasticity of behavior with respect to tax is much lower after reform Estimate price and tax elasticities before and after reform Use cross-state variation in tax rates and price variation from world market Note di¤erent interpretation of di¤erence between price and tax elasticities in this study relative to tax salience papers Public Economics Lectures () Part 3: E¢ ciency 81 / 106Price and Tax Elasticities By Year Public Economics Lectures () Part 3: E¢ ciency 82 / 106Marion and Muehlegger: Results Elasticities imply that 1% increase in tax rate raised revenue by 0.60% before dye reform vs. 0.71% after reform Reform reduced deadweight cost of diesel taxation MDWL= 40 cents per dollar of revenue raised before dye reform MDWL= 30 cents per dollar after reform Lesson: Deadweight cost depends not just on preferences but also on enforcement technology But again need to think carefully about marginal costs of evasion in this context: social or transfer? Public Economics Lectures () Part 3: E¢ ciency 83 / 106Welfare Analysis in Behavioral Models Formulas derived thus far rely critically on full optimization by agents in private sector How to calculate e¢ ciency costs when agents do not optimize perfectly? Relates to broader …eld of behavioral welfare economics Focus on two papers here: 1 Conceptual Issues: Bernheim and Rangel 2009 2 Applied Welfare Analysis: Chetty, Looney, Kroft 2009 Public Economics Lectures () Part 3: E¢ ciency 84 / 106Behavioral Welfare Economics Abstractly, e¤ect of policies on welfare are calculated in two steps 1 E¤ect of policy on behavior 2 E¤ect of change in behavior on utility Challenge: identifying (2) when agents do not optimize perfectly How to measure objective function without tools of revealed preference? Danger of paternalism Public Economics Lectures () Part 3: E¢ ciency 85 / 106Behavioral Welfare Economics: Two Approaches Approach 1: Build a positive model of deviations from rationality Ex: hyperbolic discounting, bounded rationality, reference dependence Then calculate optimal policy within such models Approach 2: Choice-theoretic welfare analysis (Bernheim and Rangel 2009) Do not specify a positive model to rationalize behavior Instead map directly from observed choices to statements about welfare Analogous to “su¢ cient statistic”approach Public Economics Lectures () Part 3: E¢ ciency 86 / 106Behavioral Welfare Economics: Two Approaches Consider three di¤erent medicare plans with di¤erent copays: L,M,H and corresponding variation in premiums We have data from two environments: 1 On red paper, H M L 2 On blue paper, M H L Public Economics Lectures () Part 3: E¢ ciency 87 / 106Behavioral Welfare Economics: Two Approaches Approach 1: build a model of why color a¤ects choice and use it to predict which choice reveals “true”experienced utility Approach 2: Yields bounds on optimal policy L cannot be optimal given available data irrespective of positive model Optimal copay bounded between M and H Key insight: no theory of choice needed to make statements about welfare Do not need to understand why color a¤ects choice Public Economics Lectures () Part 3: E¢ ciency 88 / 106Bernheim and Rangel 2009: Setup Derive bounds on welfare based purely on choice data In standard model, agents choose from a choice set x2 X Goal of policy is to identify optimal x In behavioral models, agents choose from “generalized choice sets” G =(X,d) d is an “ancillary condition”–something that a¤ects choice behavior but (by assumption) does not a¤ect experienced utility Ex: color of paper, salience, framing, default option Public Economics Lectures () Part 3: E¢ ciency 89 / 106Bernheim and Rangel 2009: Choice Sets Let C(X,d) denote choice made in a given GCS 0 Choice inconsistency if C(X,d)6= C(X,d ) De…ne revealed preference relation P as xPy if x always chosen over y for any d Using P, can identify choice set that maximizes welfare instead of single point With continuous choices, e¤ectively obtain bounds on welfare Public Economics Lectures () Part 3: E¢ ciency 90 / 106Bernheim and Rangel 2009: Compensating Variation 0 Consider a change in choice set from X to X  X Compute CV as amount needed to make agent indi¤erent to restriction of choice set for each d (standard calculation) Lower bound on CV is minimum over all d’s Upper bound on CV is maximum over all d’s Public Economics Lectures () Part 3: E¢ ciency 91 / 106Bernheim and Rangel 2009: Compensating Variation Ex: suppose insurance plans are restricted to drop M option Under red paper condition, CV is 0 –no loss in welfare Under blue paper condition, calculate price cut z on H needed to make agent indi¤erent between M and H. Bounds on CV: (0,z) If L option is dropped, bounds collapse to a singleton: CV = 0. Public Economics Lectures () Part 3: E¢ ciency 92 / 106Bernheim and Rangel 2009: Re…nements Problem: looseness of bounds Bounds tight when ancillary conditions do not lead to vast changes in choices That is, bounds tight when behavioral problems are small In cases where behavioral issues are important, this is not going to be a very informative approach Public Economics Lectures () Part 3: E¢ ciency 93 / 106Bernheim and Rangel 2009: Re…nements Solution: “re…nements”–discard certain d’s as being “contaminated”for welfare analysis E.g. a neuroscience experiment shows that decisions made under red paper condition are more rational Or assume that choice rational when incentives are more salient With fewer d’s, get tighter bounds on welfare and policy Identifying “re…nements”typically requires some insight into positive theory of behavior Public Economics Lectures () Part 3: E¢ ciency 94 / 106Applied Welfare Analysis with Salience E¤ects Chetty, Looney, and Kroft (2009) section 5 Derive partial-equilibrium formulas for incidence and e¢ ciency costs Focus here on e¢ ciency cost analysis Formulas do not rely on a speci…c positive theory, in the spirit of Bernheim and Rangel (2009) Public Economics Lectures () Part 3: E¢ ciency 95 / 106Welfare Analysis with Salience E¤ects: Setup Two goods, x and y; price of y is 1, pretax price of x is p. S Taxes: y untaxed. Unit sales tax on x at rate t , which is not included in the posted price S Tax-inclusive price of x: q = p+t Public Economics Lectures () Part 3: E¢ ciency 96 / 106Welfare Analysis with Salience E¤ects: Setup Representative consumer has wealth Z and utility u(x)+v(y)  S  S Letfx (p,t ,Z),y (p,t ,Z)g denote bundle chosen by a fully-optimizing agent S S Letfx(p,t ,Z),y(p,t ,Z)g denote empirically observed demands Place no structure on these demand functions except for feasibility: S S S (p+t )x(p,t ,Z)+y(p,t ,Z)= Z Public Economics Lectures () Part 3: E¢ ciency 97 / 106Welfare Analysis with Salience E¤ects: Setup Price-taking …rms use y to produce x with cost fn. c Firms optimize perfectly. Supply function S(p) de…ned by: 0 p = c (S(p)) ¶S p Let =  denote the price elasticity of supply S ¶p S(p) Public Economics Lectures () Part 3: E¢ ciency 98 / 106E¢ ciency Cost with Salience E¤ects De…ne excess burden using EV concept Excess burden (EB) of introducing a revenue-generating sales tax t is: S S S EB(t )= Ze(p,0,V(p,t ,Z))R(p,t ,Z) Public Economics Lectures () Part 3: E¢ ciency 99 / 106Preference Recovery Assumptions A1 Taxes a¤ect utility only through the chosen consumption bundle. S Agent’s indirect utility given tax of t is S S S V(p,t ,Z)= u(x(p,t ,Z))+v(y(p,t ,Z)) A2 When tax inclusive prices are fully salient, the agent chooses the same allocation as a fully-optimizing agent:  x(p,0,Z)= x (p,0,Z)= argmaxu(x)+v(Zpx) x A1 speci…es ancillary condition: tax rate and salience does not enter utility directly A2 is a re…nement: behavior when tax is salient reveals true preferences Public Economics Lectures () Part 3: E¢ ciency 100 / 106E¢ ciency Cost with Salience E¤ects Two demand curves: price-demand x(p,0,Z) and tax-demand S x(p ,t ,Z) 0 Two steps in e¢ ciency calculation: 1 Use price-demand x(p,0,Z) to recover utility as in standard model S S 2 Use tax-demand x(p,t ,Z)to calculate V(p,t ,Z) and EB Public Economics Lectures () Part 3: E¢ ciency 101 / 106¶x Excess Burden with No Income E¤ect for Good x ( = 0) ¶Z S p,t C x(p,0) =u'(x) S xÝp ,t Þ 0 G D E S p + t 0 F S /x//t 1 S 2 S EBp? Ýt Þ /x//t S /x//t 2 /x//p S t /x//p A p 0 I B H S /x t S /t x x x x 0 1 1 Source: Chetty, Looney, and Kroft (2009) Public Economics Lectures () Part 3: E¢ ciency 102 / 106E¢ ciency Cost: No Income E¤ects ¶x Without income e¤ects ( = 0), excess burden of introducing a ¶Z S small tax t is S 1 ¶x/¶t S S 2 S EB(t ) ' (t ) ¶x/¶t 2 ¶x/¶p 1 D S 2 S = (qt ) x(p,t ,Z) S 2 p+t Inattention reduces excess burden when dx/dZ = 0. S Intuition: tax t induces behavioral response equivalent to a fully S perceived tax of qt . If q = 0, tax is equivalent to a lump sum tax and EB = 0 because agent continues to choose …rst-best allocation. Public Economics Lectures () Part 3: E¢ ciency 103 / 106E¢ ciency Cost with Income E¤ects Same formula, but all elasticities are now compensated: c S 1 ¶x /¶t S S 2 c S EB(t ) ' (t ) ¶x /¶t c 2 ¶x /¶p c 1 c S 2 S D = (q t ) x(p,t ,Z) S 2 p+t c Compensated price demand: dx /dp = dx/dp+xdx/dZ c S S Compensated tax demand: dx /dt = dx/dt +xdx/dZ Compensated tax demand does not necessarily satisfy Slutsky c S condition dx /dt 0 b/c it is not generated by utility maximization Public Economics Lectures () Part 3: E¢ ciency 104 / 106E¢ ciency Cost with Income E¤ects c S 1 ¶x /¶t S S 2 c S EB(t ) ' (t ) ¶x /¶t c 2 ¶x /¶p c 1 c S 2 S D = (q t ) x(p,t ,Z) S 2 p+t With income e¤ects (dx/dZ 0), making a tax less salient can raise deadweight loss. S Tax can generate EB 0 even if dx/dt = 0 Example: consumption of food and cars; agent who ignores tax on cars underconsumes food and has lower welfare. Intuition: agent does not adjust consumption of x despite change in net-of-tax income, leading to a positive compensated elasticity. Public Economics Lectures () Part 3: E¢ ciency 105 / 106Directions for Further Work on Behavioral Welfare Analysis 1 Normative analysis of tax policy Value of tax simpli…cation Tax smoothing 2 Use similar approach to welfare analysis in other contexts Design consumer protection laws and …nancial regulation in a less paternalistic manner by studying behavior in domains where incentives are clear Public Economics Lectures () Part 3: E¢ ciency 106 / 106Public Economics Lectures Part 4: Optimal Taxation Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 4: Optimal Taxation 1 / 80Outline 1 Commodity Taxation: Ramsey Rule 2 Capital Income Taxation and Retirement Savings 3 Income Taxation: Mirrlees Model 4 Optimal Transfer Programs Public Economics Lectures () Part 4: Optimal Taxation 2 / 80Optimal Commodity Taxation: Introduction Combine lessons on incidence and e¢ ciency costs to analyze optimal design of commodity taxes What is the best way to design taxes given equity and e¢ ciency concerns? Public Economics Lectures () Part 4: Optimal Taxation 3 / 80Overview of Optimal Taxation From an e¢ ciency perspective, would …nance government purely through lump-sum taxation With redistributional concerns, would ideally levy individual-speci…c lump sum taxes Tax higher-ability individuals a larger lump sum Problem: cannot observe individuals’types Therefore must tax economic outcomes such as income or consumption, which leads to distortions Public Economics Lectures () Part 4: Optimal Taxation 4 / 80Ramsey vs. Mirrleesian Approaches Two approaches to optimal taxation 1 Ramsey: restrict attention linear (tx) tax systems 2 Mirrleesian: Non-linear (t(x)) tax systems, with no restrictions on t(x) Ramsey approach: rule out possibility of lump sum taxes by assumption and consider linear taxes Mirrleesian approach: permit lump sum taxes, but model their costs in a model with heterogeneity in agents’skills Public Economics Lectures () Part 4: Optimal Taxation 5 / 80Four Central Results in Optimal Tax Theory 1 Ramsey (1927): inverse elasticity rule 2 Chamley (1985), Judd (1986): no capital taxation in in…nite horizon Ramsey models 3 Diamond and Mirrlees (1971): production e¢ ciency 4 Atkinson and Stiglitz (1976): no consumption taxation with optimal non-linear income taxation Public Economics Lectures () Part 4: Optimal Taxation 6 / 80Ramsey (1927) Tax Problem Government sets taxes on uses of income in order to accomplish two objectives: 1 Raise total revenue of amount E 2 Minimize utility loss for agents in economy Public Economics Lectures () Part 4: Optimal Taxation 7 / 80Ramsey Model: Key Assumptions 1 Lump sum taxation prohibited 2 Cannot tax all commodities (e.g., leisure untaxed) 3 Production prices …xed (and normalized to one): p = 1 i ) q = 1+t i i Public Economics Lectures () Part 4: Optimal Taxation 8 / 80Ramsey Model: Setup One individual (no redistributive concerns) As in e¢ ciency analysis, assume that individual does not internalize e¤ect of t on govt. budget i Captures idea that any one individual accounts for a small frac. of economy Individual maximizes utility u(x ,..,x ,l) 1 N subject to budget constraint q x +..+q x  wl+Z 1 1 N N Z = non wage income, w = wage rate Public Economics Lectures () Part 4: Optimal Taxation 9 / 80Ramsey Model: Consumer Behavior Lagrangian for individual’s maximization problem: L= u(x ,..,x ,l)+a(wl+Z(q x +..+q x )) 1 N 1 1 N N First order condition: u = aq x i i Where a= ¶V/¶Z is marginal value of money for the individual Yields demand functions x (q,Z) and indirect utility function V(q,Z) i where q =(w,q ,..,q ) 1 N Public Economics Lectures () Part 4: Optimal Taxation 10 / 80Ramsey Model: Government’s Problem Government solves either the maximization problem maxV(q,Z) subject to the revenue requirement N tx = t x (q,Z) E i i å i=1 Or, equivalently, minimize excess burden of the tax system minEB(q)= e(q,V(q,Z))e(p,V(q,Z))E subject to the same revenue requirement Public Economics Lectures () Part 4: Optimal Taxation 11 / 80Ramsey Model: Government’s Problem For maximization problem, Lagrangian for government is: L = V(q,Z)+l t x (q,Z)E G i i å i ¶L ¶V G ) = +l x + t ¶x /¶q = 0 i j j i å z ¶q ¶q i i j z z Mechanical Priv. Welfare Behavioral E¤ect Loss to Indiv. Response ¶V Using Roy’s identity ( =ax ): i ¶q i (la)x +l t ¶x /¶q = 0 i j j i å j Note connection to marginal excess burden formula, where l= 1 and a= 1 Public Economics Lectures () Part 4: Optimal Taxation 12 / 80Ramsey Optimal Tax Formula Optimal tax rates satisfy system of N equations and N unknowns: ¶x x j i t = (la) j å ¶q l i j Same formula can be derived using a perturbation argument, which is more intuitive Public Economics Lectures () Part 4: Optimal Taxation 13 / 80Ramsey Formula: Perturbation Argument Suppose government increases t by dt i i E¤ect of tax increase on social welfare is sum of e¤ect on government revenue and private surplus Marginal e¤ect on government revenue: dR = x dt + t dx i i å j j j Marginal e¤ect on private surplus: ¶V dU = dt i ¶q i = ax dt i i Optimum characterized by balancing the two marginal e¤ects: dU+ldR = 0 Public Economics Lectures () Part 4: Optimal Taxation 14 / 80Ramsey Formula: Compensated Elasticity Representation Rewrite in terms of Hicksian elasticities to obtain further intuition using Slutsky equation: ¶x /¶q = ¶h /¶qx ¶x /¶Z j i j i i j Substitution into formula above yields: (la)x +l t ¶h /¶qx ¶x /¶Z = 0 i j j i i j å j 1 ¶h q i ) t = å j x ¶q l i j j ¶ where q = lal ( t x ) å j j j ¶Z Public Economics Lectures () Part 4: Optimal Taxation 15 / 80Ramsey Formula: Compensated Elasticity Representation q is independent of i and measures the value for the government of introducing a 1 lump sum tax q = lal¶( t x )/¶Z j j å j Three e¤ects of introducing a 1 lump sum tax: 1 Direct value for the government of l 2 Loss in welfare for individual of a 3 Behavioral e¤ect loss in tax revenue of ¶( t x )/¶Z å j j j Public Economics Lectures () Part 4: Optimal Taxation 16 / 80Intuition for Ramsey Formula: Index of Discouragement 1 ¶h q i t = j å x ¶q l i j j Suppose revenue requirement E is small so that all taxes are also small Then tax t on good j reduces consumption of good i (holding utility j constant) by approximately ¶h i dh = t i j ¶q j Numerator of LHS: total reduction in consumption of good i Dividing by x yields % reduction in consumption of each good i = i “index of discouragement”of the tax system on good i Ramsey tax formula says that the indexes of discouragements must be equal across goods at the optimum Public Economics Lectures () Part 4: Optimal Taxation 17 / 80Inverse Elasticity Rule Introducing elasticities, we can write Ramsey formula as: N t q j c = å ij 1+t l j j=1 Consider special case where = 0 if i6= j ij Slutsky matrix is diagonal Obtain classic inverse elasticity rule: t q 1 i = 1+t l i ii Public Economics Lectures () Part 4: Optimal Taxation 18 / 80Ramsey Formula: Limitations Ramsey solution: tax inelastic goods to minimize e¢ ciency costs But does not take into account redistributive motives Necessities likely to be less elastic than luxuries Therefore, optimal Ramsey tax system is likely regressive Diamond (1975) extends Ramsey model to take redistributive motives into account Basic intuition: replace multiplier l with average marginal utility for consumers of that good Public Economics Lectures () Part 4: Optimal Taxation 19 / 80Application of Ramsey Approach to Taxation of Savings Standard lifecycle model of consumption max u (c ) s.t. q c  W å t t t t t where q =(1+t )p t t t and t  0 0 Consumption in each period isomorphic to consumption of di¤erent goods  Can apply standard Ramsey formulas to calculate t t Capital income tax is a constant tax q on interest rate: 1 q = t t (1+(1q)r) Public Economics Lectures () Part 4: Optimal Taxation 20 / 80Optimal Capital Income Tax Rate For any q 0, implied tax t approaches¥ as t¥: t q 1+r t t = 1+t =( ) t p 1+(1q)r t ) lim t =¥ t t¥ Ramsey formula implies that optimal t cannot be¥ for any good t Therefore optimal capital income tax rate converges to 0 in long run (Judd 1985, Chamley 1986) Best policy is for govt to tax capital until it accumulates su¢ cient assets to fund public goods and never tax capital again Public Economics Lectures () Part 4: Optimal Taxation 21 / 80Zero Capital Taxation in Ramsey Models Fairly robust result in pure Ramsey framework (Bernheim 2002) But not robust to: Allowing for progressive income taxation (Golosov, Kocherlakota, Tsyvinski 03) Allowing for credit market imperfections (Aiyagari 95, Farhi and Werning 11) Finitely-lived agents with …nite bequest elasts. (Piketty and Saez 12) More general issue: are agents this forward-looking when making savings choices? Return to this in the context of corrective taxes later in the course Public Economics Lectures () Part 4: Optimal Taxation 22 / 80Optimal Income Taxation: Outline 1 Optimal Static Income Taxation: Mirrlees (1971) 2 Empirical Implementation of Mirrlees Model: Saez (2001) 3 Income and Commodity Taxation: Atkinson and Stiglitz (1976) Spring Semester 4 Optimal Transfer Programs: Saez (2002) Public Economics Lectures () Part 4: Optimal Taxation 23 / 80Key Concepts for Taxes/Transfers Let T(z) denote tax liability as a function of earnings z 1 Transfer bene…t with zero earningsT(0) also called demogrant or lumpsum grant 0 0 2 Marginal tax rate T (z): individual keeps 1T (z) for an additional 1 of earnings (relevant for intensive margin labor supply responses) 3 Participation tax rate t =T(z)T(0)/z: individual keeps p fraction 1t of earnings when moving from zero earnings to p earnings z: zT(z)=T(0)+zT(z)T(0)=T(0)+z(1t ) p Relevant for extensive margin labor supply responses   4 Break-even earnings point z : point at which T(z )= 0 Public Economics Lectures () Part 4: Optimal Taxation 24 / 80US Tax/Transfer System, single parent with 2 children, 2009 50,000 50,000 Welfare: 40,000 40,000 TANF+SNAP Tax credits: 30,000 30,000 EITC+CTC Earnings after 20,000 20,000 taxes 45 Degree Line 10,000 10,000 0 0 Gross Earnings (with employer payroll taxes) Source: Saez 2010 AEA Clark Lecture Public Economics Lectures () Part 4: Optimal Taxation 25 / 80 Disposable Earnings 0 5,383 10,765 16,148 21,530 26,913 32,295 37,678 43,060 48,443Optimal Income Tax with No Behavioral Responses Utility u(c) strictly increasing and concave Same for everybody where c is after tax income Income is z and is …xed for each individual, c = zT(z) where T(z) is tax on z Government maximizes Utilitarian objective: Z ¥ u(zT(z))h(z)dz 0 R Subject to budget constraint T(z)h(z)dz E (multiplier l) Public Economics Lectures () Part 4: Optimal Taxation 26 / 80Optimal Income Tax without Behavioral Responses Lagrangian for this problem is: L=u(zT(z))+lT(z)h(z) First order condition: 0 T(z) : 0= ¶L/¶T(z)=u (zT(z))+lh(z) 0 ) u (zT(z))= l ) zT(z)= c constant for all z ) c = z¯E R where z¯ = zh(z)dz average income 100% marginal tax rate; perfect equalization of after-tax income Utilitarianism with diminishing marginal utility leads to egalitarianism Public Economics Lectures () Part 4: Optimal Taxation 27 / 80Mirrlees 1971: Incorporating Behavioral Responses Standard labor supply model: Individual maximizes u(c,l) s.t. c = wlT(wl) where c is consumption, l labor supply, w wage rate, T(.) income tax Individuals di¤er in ability w distributed with density f(w) Govt social welfare maximization: Govt maximizes Z SWF = G(u(c,l))f(w)dw) Z s.t. resource constraint T(wl)f(w)dw E 0 and individual FOC w(1T )u +u = 0 c l where G(.) is increasing and concave Public Economics Lectures () Part 4: Optimal Taxation 28 / 80Social Welfare Function Mirrleesian approach: maximize weighted sum of utilities of ex-post consumption With equal weights G and diminishing marginal utility, we would equate everyone’s income barring information constraints But is this what people really want? Ex: many would argue that it is ok for an entrepreneur to keep the money he earned if he worked hard to get it Is maximizing total ex-post utility the right objective function? Public Economics Lectures () Part 4: Optimal Taxation 29 / 80Social Welfare Function Questions on appropriate social welfare function date to Rawls, Nozick, Sen, and others Notions of “equality of opportunity”and “just deserts”rather than pure consequentalist perspective (Mankiw 2010, Weinzierl 2012) But no widely applied tractable framework besides Mirrleesian approach One recent approach: Saez and Stantcheva’s (2012) “endogenous” welfare weights G(c,T(wl)) Fertile area to make a fundamental contribution Public Economics Lectures () Part 4: Optimal Taxation 30 / 80Mirrlees 1971: Results Optimal income tax trades-o¤ redistribution and e¢ ciency T(.) 0 at bottom (transfer) T(.) 0 further up (tax) full integration of taxes/transfers Mirrlees formulas are a complex fn. of primitives, with only a few general results 0 0 1 0 T (.) 1. T (.) 0 is non-trivial and rules out EITC Seade 1976 0 2 Marginal tax rate T (.) should be zero at the top if skill distribution bounded Sadka-Seade Public Economics Lectures () Part 4: Optimal Taxation 31 / 80Mirrlees: Subsequent Work Mirrlees model had a profound impact on information economics Ex. models with asymmetric information in contract theory But until late 1990s, had little impact on practical tax policy Recently, Mirrlees model connected to empirical literature Diamond (1998), Piketty (1997), and Saez (2001) Su¢ cient statistic formulas in terms of labor supply elasticities instead of primitives Public Economics Lectures () Part 4: Optimal Taxation 32 / 80Optimal Income Taxation: Su¢ cient Statistic Formulas 1 Revenue-maximizing linear tax (La¤er curve) 2 Top income tax rate (Saez 2001) 3 Full income tax schedule (Saez 2001) See also section 4 of Chetty (Ann. Rev. 2009) Public Economics Lectures () Part 4: Optimal Taxation 33 / 80Revenue-Maximizing Tax Rate: La¤er Curve With a constant tax rate t, reported income z depends on 1t (net-of-tax rate) Tax Revenue R(t)= tz(1t) is inverse-U shaped: R(t = 0)= 0 (no taxes) and R(t = 1)= 0 (nobody works)  Tax rate t that maximizes R: 0   0 = R (t )= zt dz/d(1t)  ) t = 1/(1+) MAX where =(1t)/Zdz/d(1t) is the uncompensated taxable income elasticity w.r.t. 1t  Strictly ine¢ cient to have t t Technical note: why write as elasticity of z w.r.t. 1t instead of t? Public Economics Lectures () Part 4: Optimal Taxation 34 / 80Optimal Top Income Tax Rate Now consider constant mtr t above …xed income threshold z¯ Derive optimal t using perturbation argument c u Assume away income e¤ects = = Diamond (1998) shows this is a key theoretical simpli…cation Assume that there are N individuals above z¯ m Denote by z (1t) their average income, which depends on net-of-tax rate 1t Public Economics Lectures () Part 4: Optimal Taxation 35 / 80Public Economics Lectures () Part 4: Optimal Taxation 36 / 80Optimal Top Income Tax Rate Three e¤ects of small dt 0 reform above z¯ Mechanical increase in tax revenue: m dM = Nz z¯dt Behavioral response: m dz m dB = Ntdz =Nt dt d(1t) t m ¯ = N z dt 1t Welfare e¤ect: money-metric utility loss is dM by envelope theorem: If govt. values marginal consumption of rich at g¯2(0,1) dW =g¯dM g¯ depends on curvature of u(c) and SWF Public Economics Lectures () Part 4: Optimal Taxation 37 / 80Optimal Top Income Tax Rate   t m m ¯ dM+dW +dB = Ndt (1g¯)z z¯ z 1t Optimal t such that dM+dW +dB = 0)  t (1g¯)(z /z¯1) m TOP =  1t ¯z /z¯ m TOP  t decreases with g¯ redistributive tastes TOP  ¯ t decreases with e¢ ciency TOP  t increases with z /z¯ thickness of top tail m TOP Note: this is not an explicit formula for top tax rate because z /z¯ is m a fn. of t Public Economics Lectures () Part 4: Optimal Taxation 38 / 80Public Economics Lectures () Part 4: Optimal Taxation 39 / 80Optimal Top Income Tax Rate m In US tax return data, z /z¯ very stable above z¯ = 200K with z m = 2 z¯ m Empirically, thickness parameter z /z¯ unrelated to top tax rate t (Saez 1999) How is this consistent with behavioral responses to taxation m (dz /d(1t) 0)? R Increase in t reduces both zh(z)dz and 1H(z¯) zz¯ R Leaves z = zh(z)dz/(1H(z¯) constant m zz¯ High taxes reduce number of people in tail, but could leave thickness of tail unchanged Public Economics Lectures () Part 4: Optimal Taxation 40 / 80Optimal Top Income Tax Rate Diamond (1998) shows that with Pareto skill distribution, income distribution is Pareto with parameter a invariant to t a 1+a a z m With Pareto distribution (f(z)= ak /z ), = ) a= 2 a1 z¯ 1g¯  ) t = TOP 1g¯ +2¯  Ex: ¯ = 0.5, g¯ = 0.5, a= 2) t = 33% TOP Public Economics Lectures () Part 4: Optimal Taxation 41 / 80Zero Top Rate with Bounded Distribution T S Suppose top earner earns z , and second earner earns z m T S m T Then z = z when z¯ z ) z /z¯ 1 when z¯ z ) t m m dM = Ndtz z¯ 0 dB = Ndt¯ z 1t T Optimal t is zero for z¯ close to z Sadka-Seade zero top rate result T S Result applies literally only to top earner: if z = 2z then m S z /z¯ = 2 when z¯ = z Zero at top no longer considered to be of practical relevance Public Economics Lectures () Part 4: Optimal Taxation 42 / 80Connection to Revenue Maximizing Tax Rate Revenue maximizing top tax rate can be calculated by putting 0 weight on welfare of top incomes m Utilitarian SWF) g¯ = u (z ) 0 when z¯¥ c Rawlsian SWF) g¯ = 0 for any z¯ min(z) If g¯ = 0, we obtain t = t = 1/(1+a¯) TOP MAX ¯ Example: a= 2 and = 0.5) t = 50% La¤er linear rate is a special case where z¯ = 0 m ¯ ) z /z¯ =¥= a/(a1)) a= 1) t = 1/(1+) MAX Public Economics Lectures () Part 4: Optimal Taxation 43 / 80Optimal Non-Linear Income Tax Now consider general problem of setting optimal T(z) Let H(z) = CDF of income population normalized to 1 and h(z) its density endogenous to T(.) Let g(z) = social marginal value of consumption for taxpayers with income z in terms of public funds Let G(z) be the average social marginal value of consumption for R ¥ taxpayers with income above z G(z)= g(s)h(s)ds/(1H(z)) z Public Economics Lectures () Part 4: Optimal Taxation 44 / 80Public Economics Lectures () Part 4: Optimal Taxation 45 / 80General Non-Linear Income Tax 0 Consider small reform: increase T by dt in small band (z,z+dz) Mechanical revenue e¤ect dM = dzdt(1H(z)) Mechanical welfare e¤ect dW =dzdt(1H(z))G(z) Behavioral e¤ect: substitution e¤ect dz inside small band z,z+dz: 0 0 0 dB = h(z)dzT dz = h(z)dzT dt(z)z/(1T ) Optimum dM+dW +dB = 0 Public Economics Lectures () Part 4: Optimal Taxation 46 / 80General Non-Linear Income Tax Optimal tax schedule satis…es:   0 T (z) 1 1H(z) = 1G(z) 0 1T (z) (z) zh(z) 0 0 0 T (z) decreasing in g(z ) for z z redistributive tastes 0 T (z) decreasing in e¢ ciency (z) 0 T (z) decreasing in h(z)/(1H(z)) density Connection to top tax rate: consider z¥ G(z) g¯, (1H(z))/(zh(z)) 1/a 0 ¯) T (z)= (1g¯)/(1g¯ +a¯)= t (z) TOP Public Economics Lectures () Part 4: Optimal Taxation 47 / 80Negative Marginal Tax Rates Never Optimal 0 Suppose T 0 in band z,z+dz 0 Increase T by dt 0 in band z,z+dz dM+dW 0 because G(z) 1 for any z 0 Without income e¤ects, G(0)= 1 Value of lump sum grant to all equals value of public good 0 Concave SWF – G (z) 0 0 dB 0 because T (z) 0 smaller e¢ ciency cost 0 Therefore T (z) 0 cannot be optimal Marginal subsidies also distort local incentives to work Better to redistribute using lump sum grant Public Economics Lectures () Part 4: Optimal Taxation 48 / 80Numerical Simulations of Optimal Tax Schedule Formula above is a condition for optimality but not an explicit formula for optimal tax schedule Distribution of incomes H(z) endogenous to T(.) Therefore need to use structural approach (speci…cation of primitives) to calculate optimal T(.) Saez (2001) speci…es utility function (e.g. constant elasticity): 1 1+ u(c,l) = c(l)  0 ) l =(1T )w Calibrate the exogenous skill distribution F(w) such that actual T(.) yields empirical H(z) Public Economics Lectures () Part 4: Optimal Taxation 49 / 80Public Economics Lectures () Part 4: Optimal Taxation 50 / 80Numerical Simulations Use formula expressed in terms of F(w) to solve for optimal T(z):      Z 0 0 ¥ T (z(w)) 1 1 G (u(s)) = 1+ 1 f(s)ds, 0 1T (z(w)) wf(w) p w R 0 where p = G (u(s))f(s)ds is marginal value of public funds Iterative …xed point method to solve for T(z): 0 0 Start with initial MTR schedule T and compute incomes z (w) using 0 individual FOCs 0 0 Get T (0) using govt budget constraint, compute utilities u (w) R 0 0 Compute p = G (u (s))f(s)ds 0 0 Use formula to calculate T and iterate until convergence (Brewer, 1 Saez, Shephard 2009) Public Economics Lectures () Part 4: Optimal Taxation 51 / 80Public Economics Lectures () Part 4: Optimal Taxation 52 / 80Commodity vs. Income Taxation Atkinson and Stiglitz (1976) analyze optimal combination of income and commodity taxes K consumption goods c =(c ,..,c ) with pre-tax price 1 K p =(p ,..,p ) 1 K h Individual h has utility u(c ,..,c )f (z) 1 K Assumes (1) separability between c and z and (2) homogeneity of consumption sub-utility u Main result: commodity taxation is super‡uous max SWF = max SWF t,T(.) t=0,T(.) Public Economics Lectures () Part 4: Optimal Taxation 53 / 80Atkinson-Stiglitz: Implications for Capital Taxation Two period model: wage rate w in period 1, retired in period 2 Let d= discount rate, y(.) disutility of e¤ort, and utility u(c ) 2 h u (c ,c ,z)= u(c )+ y(z/w) 1 2 1 1+d The budget constraint is c +c /(1+(1q)r) zT(z) 1 2 Capital income tax q is equivalent to tax on c 2  Atkinson-Stiglitz implies that q = 0 in the presence of an optimal income tax Public Economics Lectures () Part 4: Optimal Taxation 54 / 80Atkinson-Stiglitz: Implications for Capital Taxation If low ability people have higher d then capital income tax t 0 is K desirable (Saez 2004) Violates homogeneous utility assumption Savings reveal information about type and relax IC constraint Public Economics Lectures () Part 4: Optimal Taxation 55 / 80Chamley-Judd vs. Atkinson-Stiglitz Chamley-Judd: constrained policy instruments (linear taxes) but dynamic Atkinson-Stiglitz: full set of policy instruments (non linear income tax) but static New dynamic public …nance literature: full set of instruments in dynamic model In dynamic Mirrlees models, optimal capital tax is not zero (Golosov, Kocherlekota, and Tsyvinski 2003) Optimum features a wedge between MRS and MRTS Intuition: payo¤ to distorting savings decisions relaxes IC constraints in optimal income tax problem in next period Does not emerge in Atkinson-Stiglitz because all income is earned in …rst period Public Economics Lectures () Part 4: Optimal Taxation 56 / 80Optimal Transfer Programs Several types of transfer programs are used in practice, each justi…ed by a di¤erent theory and set of assumptions Option 1: Negative Income Tax: TANF (Mirrlees 1971) Bene…ts: no one omitted; low admin costs; no stigma Costs: e¢ ciency loss from less work Option 2: Work-for-welfare: EITC (Saez 2002) Bene…ts: more incentive to work; low admin costs Costs: e¢ ciency loss in phaseout range, no coverage of non-workers Public Economics Lectures () Part 4: Optimal Taxation 57 / 80Optimal Transfer Programs Option 3: Categorical anti-poverty programs: assistance for blind (Akerlof 1978) Bene…ts: tagging relaxes incentive constraint by tying tax rate to immutable qualities Costs: not always feasible and limited coverage Option 4: In-kind transfers: food stamps, public housing (Nichols and Zeckhauser 1982) Bene…ts: E¢ ciency gains from relaxing IC for high-types via ordeals Costs: Paternalism (spend on the right things), ine¢ cient ordeal cost Public Economics Lectures () Part 4: Optimal Taxation 58 / 80Optimal Transfers: Mirrlees Model Mirrlees model predicts that optimal transfer at bottom takes the form of a Negative Income Tax Lump sum grantT(0) for those with no earnings 0 High MTRs T (z) at the bottom to phase-out the lump sum grant quickly NIT optimal because it targets transfers to the most needy Public Economics Lectures () Part 4: Optimal Taxation 59 / 80Optimal Transfers: Participation Responses and EITC Mirrlees result predicated on assumption that all individuals are at an interior optimum in choice of labor supply Rules out extensive-margin responses But empirical literature shows that participation labor supply responses are important, especially for low incomes Diamond (1980), Saez (2002), Laroque (2005) incorporate such extensive labor supply responses into optimal income tax model Generate extensive margin by introducing …xed job packages (cannot smoothly choose earnings) Public Economics Lectures () Part 4: Optimal Taxation 60 / 80Saez 2002: Participation Model Model with discrete earnings outcomes: w = 0 w ... w 0 1 I Tax/transfer T when earning w , c = wT i i i i i Pure participation choice: skill i individual compares c and c when i 0 deciding to work With participation tax rate t , cc = w(1t ) i i 0 i i In aggregate, fraction h of population earns w , with h = 1 å i i i i Participation elasticity is e =(cc )/h¶h /¶(cc ) 0 0 i i i i i Public Economics Lectures () Part 4: Optimal Taxation 61 / 80Saez 2002: Participation Model Social Welfare function is summarized by social marginal welfare weights at each earnings level g i No income e¤ects g h = 1= value of public good å i i i 0 Main result: work subsidies with T (z) 0 (such as EITC) optimal Key requirements in general model with intensive+extensive responses Responses are concentrated primarily along extensive margin Social marginal welfare weight on low skilled workers 1 (not true with Rawlsian SWF) Public Economics Lectures () Part 4: Optimal Taxation 62 / 80Saez 2002: Intuition for EITC Two types: doctors (wage w ) and plumbers (w ) h l Both can choose whether to work, but doctors cannot become plumbers Transfer to 0 income individuals help plumbers but distort doctors’ incentives to work Transfer to those with income of w still help plumbers, but do not l distort doctors’incentives Therefore better to have a larger transfer to w than 0, i.e. have a l subsidy for work = EITC In pure ext margin model, transfer T only distorts behavior of type 1 1 Higher types don’t move down But transfer T distorts behavior of all types on extensive margin 0 Public Economics Lectures () Part 4: Optimal Taxation 63 / 80Saez 2002: Optimal Tax Formula Small tax cut dT 0) dc =dT 0. Three e¤ects: i i i 1 Fiscal E¤ect: loss of tax revenue dM =h dc i i 2 Welfare E¤ect: each worker in job i gains dT so welfare gain i dW = h g dc i i i No …rst order welfare loss for switchers 3 Behavioral E¤ect: dh = e h dc /(c c ) i i i i i 0 Tax loss: dB =(T T )dh =e h dT (T T )/(c c ) i 0 i i i i i 0 i 0 FOC: dM+dB+dW = 0) t TT 1 i i 0 = = (1g ) i 1t cc e i i 0 i g 1) T T 0) work subsidy 1 1 0 Public Economics Lectures () Part 4: Optimal Taxation 64 / 80Public Economics Lectures () Part 4: Optimal Taxation 65 / 80Public Economics Lectures () Part 4: Optimal Taxation 66 / 80Public Economics Lectures () Part 4: Optimal Taxation 67 / 80Public Economics Lectures () Part 4: Optimal Taxation 68 / 80Saez 2002: General Model Model can be extended to allow both intensive and extensive responses Allow higher types to switch to lower jobs General formula for optimal tax is a fn of both intensive and extensive margin elasticity Can be calibrated using empirical estimates of these elasticities Public Economics Lectures () Part 4: Optimal Taxation 69 / 80Public Economics Lectures () Part 4: Optimal Taxation 70 / 80Tagging: Akerlof 1978 We have assumed that T(z) depends only on earnings z In reality, govt can observe many other characteristics X also correlated with ability and set T(z,X) Ex: gender, race, age, disability, family structure, height,... Two major results: 1 If characteristic X is immutable then redistribution across the X groups will be complete until average social marginal welfare weights are equated across X groups 2 If characteristic X can be manipulated but X correlated with ability then taxes will depend on both X and z Public Economics Lectures () Part 4: Optimal Taxation 71 / 80Mankiw and Weinzierl 2009 Tagging with Immutable Characteristics Consider a binary immutable tag: Tall vs. Short 1 inch = 2% higher earnings on average (Postlewaite et al. 2004) T S Average social marginal welfare weights g¯ g¯ because tall earn more Lump sum transfer from Tall to Short is desirable T S Optimal transfer should be up to the point where g¯ = g¯ Calibrations show that average tall person ( 6ft) should pay 4500 more in tax Public Economics Lectures () Part 4: Optimal Taxation 72 / 80Problems with Tagging Height taxes seem implausible, challenging validity of tagging model What is the model missing? 1 Horizontal Equity concerns impose constraints on feasible policies: Two people earning same amount but of di¤erent height should be treated the same way 2 Height does not cause high earnings In practice, tags used only when causally related to ability to earn disability status or welfare family structure, kids, medical expenses Lesson: Mirrlees analysis T(z) may be most sensible even in an environment with immutable tags Public Economics Lectures () Part 4: Optimal Taxation 73 / 80Nichols and Zeckhauser 1982: In-Kind Redistribution In …rst-best full information model, no reason for in-kind transfers In-kind transfer is tradeable at market price in-kind equivalent to cash In-kind transfer non-tradeable in-kind inferior to cash Nichols and Zeckhauser: potential rationale for in-kind transfers emerges in Mirrlees-type model with informational constraints With heterogeneity in preferences, may be able to relax IC constraints using in-kind transfers Public Economics Lectures () Part 4: Optimal Taxation 74 / 80Nichols and Zeckhauser: Simple Illustration Consider a soup kitchen as an in-kind transfer policy Let S = soup and W = wait in minutes Two agents: poor (P) and rich (R) Utility functions are increasing in S and decreasing in W: U = 2S.5W p U = S1W r R has higher disutility from waiting and lower utility from soup Social welfare SWF = U +U p r Public Economics Lectures () Part 4: Optimal Taxation 75 / 80Soup Kitchen without Wait: Cash Transfer With a total of 100 in soup to give away and no wait times, the soup will be split between the two agents Both get some utility from soup, so both will claim it Assume that they split it equally, resulting in U = 100 p U = 50 r SWF = 150 Equivalent to a cash-transfer program that pays each agent 50 Public Economics Lectures () Part 4: Optimal Taxation 76 / 80Soup Kitchen with Wait Times: In-Kind Transfer Now suppose we impose wait time of 51 minutes R leaves - not worth it to him for 50 in food - gets U = 0 p P gets utility of 20025.5= 174.5 Social welfare with in-kind transfer (wait time) greater than cash transfer (no wait time) Targeting gains outweighing e¢ ciency losses from ordeal Scope for such targeting depends upon degree of heterogeneity in preferences Public Economics Lectures () Part 4: Optimal Taxation 77 / 80Income Taxation as Insurance (Varian 1980) Important assumption in Mirrlees model: no ex-post uncertainty Once skill type is revealed, agent controls income perfectly In practice, there is considerable ex-post uncertainty in incomes (e.g. unemployment shocks) In this case, a progressive tax system could provide insurance Do not want 100% insurance for moral hazard reasons But some insurance desirable if individuals are risk averse Public Economics Lectures () Part 4: Optimal Taxation 78 / 80Varian: Taxation as Insurance Income z = e+e where e is e¤ort and e is a random noise Government observes only z and sets a tax schedule based on z Individual utility U = Eu(zT(z))e  Chooses e = e to maximize this utility E¤ort e low if tax schedule very redistributive Government chooses T(.) to maximize indirect utility: trade-o¤ insurance vs incentives Optimal tax system depends on parameters similar to those in Mirrlees model Public Economics Lectures () Part 4: Optimal Taxation 79 / 80Varian Model: Private Insurance Varian model has received less attention than Mirrlees model One reason: government is not better than private market in providing such insurance In adverse selection (e.g. Mirrlees) models, only government can improve redistributive outcomes once skills are revealed to agents Agents cannot write contracts behind veil of ignorance In pure moral hazard model with ex-post information revelation, private markets should in principle reach optimum themselves In practice, …rms o¤er wage contracts that provide some insurance against bad luck Ex: tenure system in universities, severance payments Public Economics Lectures () Part 4: Optimal Taxation 80 / 80Public Economics Lectures Part 5: Income Taxation and Labor Supply Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 1 / 220Outline 1 Labor Supply Elasticity Estimation: Overview 2 Non-linear budget set methods 3 Summary of elasticity estimates in static models 4 Intertemporal Labor Supply Models 5 Elasticity of Taxable Income 6 Micro vs Macro Elasticities 7 Implications for Preference Parameters Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 2 / 220References Surveys in labor economics: Pencavel (1986) Handbook of Labor Economics vol 1 Heckman and Killingsworth (1986) Handbook of Labor Econ vol 1 Blundell and MaCurdy (1999) Handbook of Labor Economics vol 3 Surveys in public economics: Hausman (1985) Handbook of Public Economics vol 1 Mo¢ tt (2003) Handbook of Public Economics vol 4 Saez, Slemrod, and Giertz (JEL 2011) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 3 / 220Theoretical Issues in Estimation Labor supply elasticity is a parameter of fundamental importance for income tax policy ¶logl c Optimal tax rate depends inversely on = , the ¶logw U=U compensated wage elasticity of labor supply First discuss econometric issues that arise in estimating these (and other) elasticities Use a simple labor supply model to organize the empirical issues Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 4 / 220Baseline Labor-Leisure Choice Model: Key Assumptions 1 One period 2 Intensive-margin, one dimensional choice 3 No frictions or adjustment costs 4 Linear tax system Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 5 / 220Static Model: Setup Let c denote consumption and l hours worked Normalize price of c to one 1+1/ l Agent has utility u(c,l)= ca 1+1/ Agent earns wage w per hour worked and has y in non-labor income With tax rate t on labor income, individual solves maxu(c,l) s.t. c =(1t)wl+y Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 6 / 220Labor Supply Behavior First order condition 1/ (1t)w = al Yields labor supply function logl = a+log(1t)w Here y does not matter because u is quasilinear Log-linearization of …rst order condition for general utility u(c,l) would yield a labor supply fn of the form: logl = a+log(1t)why c Can recover from and h using Slutsky equation Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 7 / 220Problems with OLS Estimation of Labor Supply Equation 1 Econometric issues Unobserved heterogeneity tax instruments Measurement error in wages and division bias tax instruments Selection into labor force panel data 2 Extensive vs. intensive margin responses participation models 3 Non-hours responses taxable income 4 Progressive taxes non-linear budget set methods 5 Frictions macro comparisons, bounds Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 8 / 220Econometric Problem 1: Unobserved Heterogeneity Early studies estimated elasticity using cross-sectional variation in wage rates Problem: unobserved heterogeneity Those with high wages also have a high propensity to work Cross-sectional correlation between w and h likely to yield an upward biased estimate of Solution: use taxes as instruments for (1t)w Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 9 / 220Econometric Problem 2: Measurement Error/Division Bias Wage w is typically not observed; backed out from dividing earnings by reported hours When hours are measured with noise, this can lead to “division bias”  Let l denote true hours, l observed hours e Compute w = where e is earnings l  ) logl = logl +m   ) logw = logelogl = logelogl m= logw m Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 10 / 220Measurement Error and Division Bias Mis-measurement of hours causes a spurious link between hours and wages Estimate a regression of the following form: logl = b +b logw +u 1 2 Then   cov(logl,logw) cov(logl +m,logw m) b Eb = = 2 var(logw) var(logw)+var(m) b Problem:Eb 6= because orthogonality restriction for OLS violated 2 Ex. workers with high mis-reported hours also have low imputed wages, biasing elasticity estimate downward Solution: tax instruments again Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 11 / 220Econometric Problem 3: Selection into Labor Force Consider model with …xed costs of working, where some individuals choose not to work Wages are unobserved for non-labor force participants Thus, OLS regression on workers only includes observations with l 0 i This can bias OLS estimates: low wage earners must have very high unobserved propensity to work to …nd it worthwhile In cross-sections, requires a parametric selection correction (e.g. Heckman 1979) Non-parametric approach: use panel data to estimate within-person intensive-margin changes Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 12 / 220Extensive vs. Intensive Margin Related issue: want to characterize e¤ect of taxes on labor force participation decision With …xed costs of work, individuals may jump from non-participation to part time or full time work (non-convex budget set) Can be handled using a discrete choice model: P = f(a+log(1t)hy) where P2f0,1g is an indicator for whether the individual works Function f typically speci…ed as probit or linear prob model Note: here it is critical to have tax variation; regression cannot be run with wage variation Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 13 / 220Non-Hours Responses Traditional literature focused purely on hours of work and labor force participation Problem: income taxes distort many margins beyond hours of work More important responses may be on those margins Hours very hard to measure (most ppl report 40 hours per week) Two solutions in modern literature: Focus on taxable income (wl) as a broader measure of labor supply (Feldstein 1995) Focus on subgroups of workers for whom hours are better measured, e.g. taxi drivers Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 14 / 220Progressive Taxes and Labor Supply OLS regression speci…cation is derived from model with a single linear tax rate In practice, income tax systems are non-linear Consider e¤ect of US income tax code on budget sets Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 15 / 220Source: Congressional Budget O¢ ce 2005 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 16 / 220Example 1: Progressive Income Tax Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 17 / 220Example 2: EITC Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 18 / 220Example 3: Social Security Payroll Tax Cap Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 19 / 220Example 4: Negative Income Tax Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 20 / 220Progressive Taxes and Labor Supply Non-linear budget set creates two problems: 1 Model mis-speci…cation: OLS regression no longer recovers structural elasticity parameter of interest Two reasons: (1) underestimate response because people pile up at kink and (2) mis-estimate income e¤ects 2 Econometric bias: t depends on income w l and hence on l i i i i Tastes for work are positively correlated with t downward bias in i OLS regression of hours worked on net-of-tax rates Solution to problem 2: only use reform-based variation in tax rates But problem 1 requires fundamentally di¤erent estimation method Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 21 / 220Optimization Frictions Standard methods assume that agents can costlessly adjust hours of work In practice, most hours changes occur with job switches (Altonji and Paxson 1992) And many individuals may be inattentive to change in tax rates Implies that long-run impacts of policies may not be identi…ed from short run variation Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 22 / 220Optimization Frictions and Identi…cation Chetty (2012) formalizes how frictions a¤ect identi…cation of elasticities Agents can choose any x that generates a utility loss less than t exogenous threshold d:   U(x )U(x ) dpx i i i A given price p produces a choice set X(p,d) instead of a single  point x (p) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 23 / 220Construction of Choice Set 151 151 150 150 D Np x Ýp Þ t t 149 149 148 148 147 147 146 146 145 145 144 144 143 143 142 142 141 141 XÝp ,NÞ t 140 140 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 20 22 22 Demand (x) t Source: Chetty 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 24 / 220 Utility u(x ) tIdentification with Optimization Frictions 3.0 ε = 1 2.8 2.6 2.4 2.2 2.0 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 25 / 220 log demand (log x) tIdentification with Optimization Frictions 3.0 ε = 1 2.8 2.6 2.4 2.2 2.0 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 26 / 220 log demand (log x) tIdentification with Optimization Frictions 3.0 ε = 1 2.8 2.6 2.4 2.2 2.0 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 27 / 220 log demand (log x) tIdentification with Optimization Frictions 3.0 ε = 1 2.8 2.6 2.4 2.2 2.0 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 28 / 220 log demand (log x) tOptimization Frictions and Identi…cation Identi…cation problem: Multiple observed elasticitiesb can be generated by a model with a given structural elasticity when d 0 Conversely, multiple structural elasticities consistent with observedb Note that this is not a …nite-sample problem; does not disappear as sample size approaches¥ One focus of current research: how to deal with such frictions and recover ? Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 29 / 220Estimating Elasticities Using Variation in Tax Rates Now discuss literature estimating intensive-margin elasticities using variation in tax rates for identi…cation Begin by analyzing how to estimate elasticities with progressive taxes in models without frictions First discuss traditional NLBS estimation using maximum likelihood methods Then discuss recent literature on bunching estimators Then discuss most recent work on frictions and bunching estimators Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 30 / 220Non-Linear Budget Set Methods Traditional approach to estimating elasticities with non-linear budget sets pioneered by Hausman (1981) Assume an uncompensated labor supply equation: l = a+bw (1t )+gy +u i i i i i 2 Error term u is normally distributed with variance s i Observed variables: w , t , y , and l i i i i Technique: (1) construct likelihood function given observed labor supply choices on NLBS, (2) …nd parameters (a,b,g) that maximize likelihood Important insight: need to use “virtual incomes”in lieu of actual unearned income with NLBS Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 31 / 220Non-Linear Budget Set Estimation: Virtual Incomes w 3 y 3 w 2 y 2 w 1 y 1 ­L L l L 2 1 Source: Hausman 1985 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 32 / 220NLBS Likelihood Function Consider a two-bracket tax system Individual can locate on …rst bracket, on second bracket, or at the kink l K Likelihood = probability that we see individual i at labor supply l i given a parameter vector Decompose likelihood into three components Component 1: individual i on …rst bracket: 0 l l i K 1 1 l = a+bw (1t )+gy +u i i i 1 1 Error u = l(a+bw (1t )+gy ). Likelihood: i i i 1 1 L = f((l(a+bw (1t )+gy )/s) i i i Component 2: individual i on second bracket: l l . Likelihood: K i 2 2 L = f((l(a+bw (1t )+gy )/s) i i i Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 33 / 220Likelihood Function: Located at the Kink Now consider individual i located at the kink point 1 1 If tax rate is t and virtual income y individual wants to work l l K 2 2 If tax is t and virtual income y individual wants to work l l K These inequalities imply: 1 1 2 2 a+bw (1t )+gy +u l a+bw (1t )+gy +u i i K i i 1 1 2 2 l (a+bw (1t )+gy ) u l (a+bw (1t )+gy ) K i i K i Contribution to likelihood is probability that error lies in this range: 2 2 L = F(l (a+bw (1t )+gy ))/s i K i 1 1 F(l (a+bw (1t )+gy ))/s K i Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 34 / 220Maximum Likelihood Estimation Log likelihood function is `= logL å i i Final step is solving max`(a,b,g,s) In practice, likelihood function much more complicated because of more kinks, non-convexities, and covariates But basic technique remains the same Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 35 / 220Hausman (1981) Application Hausman applies method to 1975 PSID cross-section Finds signi…cant compensated elasticities and large income e¤ects Elasticities larger for women than for men Shortcomings of this implementation 1 Sensitivity to functional form choices 2 No tax reforms, so does not solve fundamental econometric problem that tastes for work may be correlated with w Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 36 / 220NLBS and Bunching at Kinks Subsequent studies obtain di¤erent estimates (MaCurdy, Green, and Paarsh 1990, Blomquist 1995) Several studies …nd negative compensated wage elasticity estimates Debate: impose requirement that compensated elasticity is positive or conclude that data rejects model? Fundamental source of problem: labor supply model predicts that individuals should bunch at the kink points of the tax schedule But we observe very little bunching at kinks, so model is rejected by the data Interest in NLBS models diminished despite their conceptual advantages over OLS methods Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 37 / 220Saez 2010: Bunching at Kinks Saez observes that only non-parametric source of identi…cation for elasticity in a cross-section is amount of bunching at kinks Intuition: discontinuous reduction in wage rate at kink yields source of non-parametric identi…cation All other cross-sectional tax variation is contaminated by smooth heterogeneity in tastes Derives an estimator for the compensated taxable income elasticity using amount of bunching at kinks  dz/z excess mass at kink c = = dt/(1t) % change in NTR Currently a popular approach (esp. when adapted to account for frictions) because it yields highly credible estimates Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 38 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 39 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 40 / 220Saez 2010: Bunching at Kinks Saez implements this method using individual tax return micro data (IRS public use …les) from 1960 to 2004 Advantage of dataset over PSID: very little measurement error Finds sharp bunching around …rst kink point of the EITC for self-employed Later shown to be largely due to reporting e¤ects However, no bunching observed at any kink for wage earners Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 41 / 220Earnings Density and the EITC: Wage Earners vs. Self-Employed Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 42 / 220Earnings Density and the EITC: Wage Earners vs. Self-Employed Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 43 / 220Friedberg 2000: Social Security Earnings Test Uses CPS data on labor supply of retirees receiving Social Security bene…ts Studies bunching based on responses to Social Security earnings test Earnings test: phaseout of SS bene…ts above an exempt amount Phaseout rate varies by age group - 50%, 33%, 0 (lower for older workers) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 44 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 45 / 220Friedberg: Estimates Estimates elasticities using Hausman method, …nds relatively large compensated and uncompensated elasticities Haider and Loughran (2008) replicate these results in admin. data over mroe years Find that degree of bunching and implied elasticities are 3 times larger in data with less msmt error Ironically, lost social security bene…ts are considered delayed retirement with an actuarial adjustment of future bene…ts So the one kink where we do …nd real bunching is actually not real Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 46 / 220Why not more bunching at kinks? 1 Small structural elasticity 2 Noise in income generation process Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 47 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 48 / 220Why not more bunching at kinks? 1 Small structural elasticity 2 Noise in income generation process 3 Price misperceptions and salience e¤ects Liebman and Zeckhauser (2009): “Schmeduling” Ito (2012): empirical evidence that average price matters more than marginal price Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 49 / 220Ito (2012) Ito (2012) presents evidence that individuals pay more attention to average prices than marginal prices Paper can be interpreted as estimating price-perception function pe(p+t) Studies electricity consumption in Orange County, CA with two sources of price variation Kinks in rate structure generate variation in marginal price Spatial discontinuity coupled with sharp price increase in 2000 by one utility changes average price Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 50 / 220Consumption Density and Price Schedule in 2007: Bunching Around Kink Points Source: Ito 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 51 / 220A Spatial Discontinuity in Electric Utility Service Areas in Orange County, California Source: Ito 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 52 / 220Changes in Consumption from July 1999 to July 2000, by Distance from the Utility Border Source: Ito 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 53 / 220Changes in Consumption from August 1999 to August 2000, by Distance from the Utility Border Source: Ito 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 54 / 220Why not more bunching at kinks? 1 Small structural elasticity 2 Noise in income generation process 3 Price misperceptions and salience e¤ects 4 Optimization frictions and rigidities in job o¤ers Chetty, Friedman, Olsen, Pistaferri (2011) Chetty, Friedman, Saez (2012) Kleven and Waseem (2012) Gelber, Jones, and Sacks (2012) Bastani and Selin (2012) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 55 / 220Chetty, Friedman, Olsen, Pistaferri: Model Firms post jobs with di¤erent hours o¤ers Workers draw from this distribution and must pay search cost to reoptimize Firm cater to aggregate worker preferences: posted distribution …ts aggregate tastes Therefore not all workers locate at optimal hours Bunching at kink and observed responses to tax reforms attenuated Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 56 / 220Chetty et al. 2011: Testable Predictions Model generates two key predictions: 1 Size Larger tax changes generate larger observed elasticities Large tax changes are more likely to induce workers to search for a di¤erent job 2 Scope Tax changes that apply to a larger group of workers generate larger observed elasticities Firms tailor jobs to preferences of common workers Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 57 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 58 / 220220000 240000 260000 280000 300000 320000 pig NTR (sum) cnt Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 59 / 220 NTR .34 .36 .38 .4 .42 .44 5000 10000 15000 20000 25000 30000 (sum) cntIncome Distribution for Wage Earners Around Top Tax Cutoff ­40 ­30 ­20 ­10 0 10 20 30 40 50 ­50 Taxable Income Relative to Top Bracket Cutoff (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 60 / 220 Frequency 20000 40000 60000 80000 100000Income Distribution for Wage Earners Around Top Tax Cutoff Excess mass=BÝAbÞ ­40 ­30 ­20 ­10 0 10 20 30 40 50 ­50 Taxable Income Relative to Top Bracket Cutoff (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 61 / 220 Frequency 20000 40000 60000 80000 100000Income Distribution for Wage Earners Around Top Tax Cutoff Excess mass (b) = 0.81 Standard error = 0.05 ­40 ­30 ­20 ­10 0 10 20 30 40 50 ­50 Taxable Income Relative to Top Bracket Cutoff (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 62 / 220 Frequency 20000 40000 60000 80000 100000Married Women vs. Single Men Married Women vs. Single Men Married Women Married Women Excess mass ( Excess mass (bb))= = 1.79 1.79 Standard error = Standard error = 0.10  0.10 Single Men Single Men Excess mass ( Excess mass (bb) = 0 ) = 0.25 .25 Standard error = Standard error = 0.04  0.04 ­­50 50 ­­40 40 ­­30 30 ­­20 20 0 0 10 10 20 20 30 30 40 40 50 50 ­­10 10 Taxable Income Relative to Top Bracket Cut Taxable Income Relative to Top Bracket Cutoff (1000s DKr) off (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 63 / 220 Frequenc Frequency (mar y (married  ried women) women) 0 0 10000 10000 20000 20000 30000 30000 10000 10000 20000 20000 30000 30000 Frequenc Frequency (sin y (single men) gle men)Teachers  Teachers vs. Mili vs. Military tary Teachers Teachers Excess mass ( Excess mass (bb))= = 3.54 3.54 Standard error = Standard error = 0.25  0.25 Military Military Excess mass ( Excess mass (bb) = ) = ­­0.12 0.12 Standard error = Standard error = 0.21  0.21 ­­50 50 ­­40 40 ­­30 30 ­­20 20 ­­10 10 0 0 10 10 20 20 30 30 40 40 50 50 Taxable Income Relative to Top Bracket Cut Taxable Income Relative to Top Bracket Cutoff (1000s DKr) off (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 64 / 220 Frequency (teachers) Frequency (teachers) 0 0 2000 2000 4000 4000 6000 6000 8000 8000 0 0 1000 1000 2000 2000 3000 3000 4000 4000 Frequenc Frequency (mil y (military) itary)Taxable Income Distributions i Taxable Income Distributions in 1994 n 1994 Married Women Married Women Excess Mass Excess Mass (b) = (b) = 1.03 1.03 Standard error = Standard error = 0.14  0.14 All Wage Earners All Wage Earners Excess Mass ( Excess Mass (b) b) = 0.61 = 0.61 Standard error = Standard error = 0.08  0.08 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 65 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 4000 4000 6000 6000 8000 8000 10000 10000 12000 12000 14000 14000 0 0 1000 1000 2000 2000 3000 3000 Frequenc Frequency (mar y (married  ried women) women)1995 1995 b = b = 1.25 1.25 s.e s.e. = 0.16 . = 0.16 b b = 0.41 = 0.41 s.e s.e. = 0.08 . = 0.08 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 66 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 4000 4000 8000 8000 12000 12000 0 0 1000 1000 2000 2000 3000 3000 Frequenc Frequency (mar y (married  ried women) women)1996 1996 b = b = 1.55 1.55 s.e s.e. = 0.17 . = 0.17 b b = 0.66 = 0.66 s.e s.e. = 0.09 . = 0.09 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 67 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 4000 4000 8000 8000 12000 12000 0 0 1000 1000 2000 2000 3000 3000 Frequenc Frequency (mar y (married  ried women) women)1997 1997 b = b = 1.26 1.26 s.e s.e. = 0.19 . = 0.19 b b = 0.58 = 0.58 s.e s.e. = 0.01 . = 0.01 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 68 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 5000 5000 10000 10000 15000 15000 0 0 1000 1000 2000 2000 3000 3000 Frequenc Frequency (mar y (married  ried women) women)1998 1998 b = b = 1.71 1.71 s.e s.e. = 0.18 . = 0.18 b b = 0.78 = 0.78 s.e s.e. = 0.09 . = 0.09 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 69 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 4000 4000 12000 12000 8000 8000 0 0 1000 1000 2000 2000 3000 3000 Frequenc Frequency (mar y (married  ried women) women)1999 1999 b = b = 1.49 1.49 s.e s.e. = 0.16 . = 0.16 b b = 0.62 = 0.62 s.e s.e. = 0.08 . = 0.08 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 70 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 4000 4000 8000 8000 12000 12000 0 0 1000 1000 2000 2000 3000 3000 4000 4000 Frequenc Frequency (mar y (married  ried women) women)2000 2000 b = b = 1.50 1.50 s.e s.e. = 0.21 . = 0.21 b b = 0.72 = 0.72 s.e s.e. = 0.09 . = 0.09 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 71 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 6000 6000 10000 10000 14000 14000 0 0 1000 1000 2000 2000 3000 3000 4000 4000 Frequenc Frequency (mar y (married  ried women) women)2001 2001 b = b = 1.44 1.44 s.e s.e. = 0.20 . = 0.20 b b = 0.55 = 0.55 s.e s.e. = 0.10 . = 0.10 210 210 220 220 230 230 240 240 250 250 260 260 270 270 280 280 290 290 300 300 Taxable I Taxable Income  ncome (1000s DK (1000s DKR) R) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 72 / 220 Frequenc Frequency (all  y (all wage earn wage earners) ers) 6000 6000 10000 10000 14000 14000 1000 1000 2000 2000 3000 3000 4000 4000 Frequenc Frequency (mar y (married  ried women) women)Married Women: Taxable I Married Women: Taxable Income Distribution  ncome Distribution at at Midd Middle Ta le Tax Cutoff x Cutoff Excess mass ( Excess mass (bb) = 0 ) = 0.06 .06 Standard error Standard error = = 0.03 0.03 Predicted excess mass = 0.35 Predicted excess mass = 0.35 Standard error = Standard error = 0.02  0.02 ­­50 50 ­­40 40 ­­30 30 ­­20 20 ­­10 10 0 0 10 10 20 20 30 30 40 40 50 50 Taxable Income Rel Taxable Income Relative to Middle Bracket Cutoff ative to Middle Bracket Cutoff Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 73 / 220 Frequenc Frequencyy 10000 10000 20000 20000 30000 30000 40000 40000Observed Elasticity vs. Size of Tax Change All Wage Earners 0.01 0.005 0 ­0.005 0 5% 10% 15% 20% 25% 30% Log Change in Net­of­Tax Rate Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 74 / 220 Observed ElasticitiesAll Teach All Teachers ers ­­50 50 ­­40 40 ­­30 30 ­­20 20 ­­10 10 0 0 10 10 20 20 30 30 40 40 50 50 Wage Earnings Relative Wage Earnings Relative to Statutory Kink (1000s DKR)  to Statutory Kink (1000s DKR) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 75 / 220 Frequenc Frequencyy 0 0 500 500 1000 1000 1500 1500Wage Earnings Distribution: Teachers with Deductions  DKr 20,000 This group This group This group starts paying starts paying starts paying top tax here top tax here top tax here ­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50 Wage Earnings Relative to Statutory Kink (1000s DKR) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 76 / 220 Frequency 0 2000 4000 6000 8000 10000(a) Electricians, 2000 Electricians (3114), 2000 (b) Salesmen, 1996 ­­100 100 ­­50 50 0 0 50 50 100 100 ­­100 100 ­­50 50 0 0 50 50 100 100 Wage E Warning age Es Relativ arnings Relativ e to Top Bracket e to Top Bracket  Cutoff (10  Cutof 00s DKr f ) Wage E Warning age Es Relativ arnings Relativ e to Top Bracket e to Top Bracket  Cutoff (10  Cutof 00s DKr f ) (c) Nurses and Midwifes, 2001 (d) Tellers and Clerks, 1998 ­­100 100 ­­50 50 0 0 50 50 100 100 ­100 ­50 0 50 100 Wage E Warning age Es Relativ arnings Relativ e to Top Bracket e to Top Bracket  Cutoff (10  Cutof 00s DKr f ) Wage Earnings Relative to Top Bracket Cutoff (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 77 / 220 Frequ Frequency ency Frequ Frequency ency 0 0 50 50 100 100 150 150 0 0 20 20 40 40 60 60 80 80 Frequency Frequ Frequency ency 0 0 100 100 200 200 300 300 0 100 200 300 400Modes of Occupation­Level Wage Earnings Distributions ­100 ­50 0 50 100 Modes of Wage Earnings Distributions Relative to Top Bracket Cutoff (1000s DKr) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 78 / 220 Frequency 0 10 20 30Chetty et al. 2011: Lessons Frictions and coordinated …rm responses play a crucial role behavioral responses to taxation NLBS models may …t data better if these factors are incorporated Standard methods of estimating elasticities that ignore these factors likely to underestimate elasticities Limitation: does not yield an estimate of structural elasticity or actual impact of tax system on earnings distribn. Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 79 / 220Chetty, Friedman, Saez (2012) Identi…es impacts of EITC on earnings distribution given existence of frictions Use areas with no knowledge about the EITC schedule as a counterfactual for earnings distribution in absence of EITC Results suggest that earlier Danish study may have signi…cantly understated impact of tax system on earnings distribution Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 80 / 220Income Distribution For Single Wage Earners with One Child Is the EITC having an effect on this 4k 3.5 distribution? 3 3k 2.5 2 2k 1.5 1 1k .5 0 0k 0 5K 10K 25K 20K 25K 30K 35K W­2 Wage Earnings Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 81 / 220 Percent of Wage­Earners EITC Amount ()Empirical Analysis: Two Parts First, develop a proxy for local knowledge about EITC schedule based on income manipulation by self-employed individuals Self-employment income is self-reported easy to manipulate Audit data reveal very high misreporting rates of SE income Second, compare W-2 wage earnings distributions across areas to uncover impacts of EITC of “real”earnings behavior Wage earnings are directly reported to IRS by employers virtually no scope for misreporting Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 82 / 220Outline of Empirical Analysis Step 1: Document variation across neighborhoods in sharp bunching among self-employed Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 83 / 220Earnings Distribution in Texas 5% 4% 3% 2% 1% 0% ­10K 0 10K 20K st Income Relative to 1 Kink Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 84 / 220 Percent of FilersEarnings Distribution in Kansas 5% 4% 3% 2% 1% 0% ­10K 0 10K 20K st Income Relative to 1 Kink Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 85 / 220 Percent of FilersFraction of Tax Filers Who Report SE Income that Maximizes EITCRefund in 2008 4.1 –42.7% 2.8 –4.1% 2.1 –2.8% 1.8 –2.1% 1.5 –1.8% 1.2 –1.5% 1.1 –1.2% 0.9 –1.1% 0.7 –0.9% 0–0.7% Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 86 / 220Outline of Empirical Analysis Step 1: Document variation across neighborhoods in sharp bunching among self-employed Step 2: Establish that variation in sharp bunching across neighborhoods is driven by di¤erences in knowledge about EITC schedule Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 87 / 220Movers: Neighborhood Changes Consider individuals who move across neighborhoods to isolate causal impacts of neighborhoods on elasticities 54 million observations in panel data on cross-zip movers Analyze how changes in neighborhood sharp bunching a¤ect movers’ behavior Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 88 / 220Event Study of Sharp Bunching Around Moves 5% Effect of Moving to th 10 Decile = 1.93 (0.13) 4% Effect of Moving to st 1 Decile = ­0.41 (0.11) 3% 2% 1% 0% ­4 ­2 0 2 4 Event Year Movers to Lowest Movers to Middle Movers to Highest Bunching Decile Bunching Decile Bunching Decile Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 89 / 220 Sharp Bunching for MoversLearning and Memory Knowledge model predicts asymmetric impact of moving: Moving to a higher-bunching neighborhood should raise EITC refund Moving to a lower-bunching should not a¤ect EITC refund Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 90 / 220Change in EITC Refunds vs. Change in Sharp Bunching for Movers 120 100 = 59.7 β (5.7) 80 60 β= 6.0 (6.2) p­value for diff. in slopes: p  0.0001 40 ­1% ­0.5% 0% 0.5% 1% Change in ZIP­3 Sharp Bunching Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 91 / 220 Change in EITC Refund ()Agglomeration: Sharp Bunching vs. EITC Filer Density by ZIP Code 3.5% 3.0% 2.5% 2.0% 1.5% 2 R = 0.6 1.0% ­2 0 2 4 6 log (Number of EITC Filers Per Square Mile) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 92 / 220 Sharp BunchingOutline of Empirical Analysis Step 1: Document variation across neighborhoods in sharp bunching among self-employed Step 2: Establish that variation in sharp bunching across neighborhoods is driven by di¤erences in knowledge about EITC schedule Step 3: Compare wage earnings distributions across low- and high-knowledge neighborhoods to uncover impacts of EITC on earnings Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 93 / 220Income Distribution For Single Wage Earners with One Child Is the EITC having an effect on this 3.5 4k distribution? 3 3k 2.5 2 2k 1.5 1 1k .5 0 0k 0 5K 10K 25K 20K 25K 30K 35K W­2 Wage Earnings Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 94 / 220 Percent of Wage­Earners EITC Amount ()Income Distribution For Single Wage Earners with One Child High vs. Low Bunching Areas 3.5 4k 3 3k 2.5 2 2k 1.5 1 1k .5 0 0k 0 5K 10K 25K 20K 25K 30K 35K W­2 Wage Earnings Lowest Bunching Decile Highest Bunching Decile Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 95 / 220 Percent of Wage­Earners EITC Amount ()Outline of Empirical Analysis Step 1: Document variation across neighborhoods in sharp bunching among self-employed Step 2: Establish that variation in sharp bunching across neighborhoods is driven by di¤erences in knowledge about EITC schedule Step 3: Compare wage earnings distributions across low- and high-knowledge neighborhoods to uncover impacts of EITC on earnings Step 4: Compare impacts of changes in EITC subsidies on earnings across low vs. high knowledge nbhds. to account for omitted variables Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 96 / 220Child Birth Research Design Individuals without children are essentially ineligible for the EITC Birth of a child therefore generates sharp variation in marginal incentives Birth a¤ects labor supply directly, but cross-neighborhood comparisons provide good counterfactuals Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 97 / 220Earnings Distribution in the Year Before First Child Birth for Wage Earners 6% 4% 2% 0% 10K 20K 30K 40K 0 Wage Earnings Lowest Sharp Middle Sharp Highest Sharp Bunching Decile Bunching Decile Bunching Decile Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 98 / 220 Percent of IndividualsEarnings Distribution in the Year of First Child Birth for WageEarners 6% 4% 2% 0% 10K 20K 30K 40K 0 Wage Earnings Lowest Sharp Middle Sharp Highest Sharp Bunching Decile Bunching Decile Bunching Decile Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 99 / 220 Percent of IndividualsSimulated EITC Credit Amount for Wage Earners Around First ChildBirth 1900 1850 ß= 85.4 (7.2) 1800 1750 ­4 ­2 0 2 4 Age of Child Lowest Sharp Middle Sharp Highest Sharp Bunching Decile Bunching Decile Bunching Decile Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 100 / 220 Simulated One­Child EITC Amount ()Changes in Simulated EITC around Births for Wage Earners 200 β= 26.5 100 (1.97) 0 ­100 0% 2% 4% 6% 8% ZIP­3 Self­Employed Sharp Bunching 0 to 1 Child Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 101 / 220 Change in Simulated One­Child EITC Refund ()Changes in Simulated EITC around Births for Wage Earners 200 β= 26.5 100 (1.97) 0 β= ­0.13 (1.08) ­100 0% 2% 4% 6% 8% ZIP­3 Self­Employed Sharp Bunching 0 to 1 Child 2 to 3 Children Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 102 / 220 Change in Simulated One­Child EITC Refund ()Composition of Wage Earnings Responses Where is the increase in EITC refunds coming from? By studying distributional shifts, we estimate that: 73% comes from increase in earnings in phase-in region 27% from reduction in earnings in phase-out region Use neighborhoods with no self-emp. sharp bunching as counterfactual to characterize causal impacts of EITC on earnings distribution Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 103 / 220Impact of EITC on Income Distribution Percent of EITC­Eligible Households Below Threshold 50% of 100% of 150% of 200% of Poverty Line Poverty Line Poverty Line Poverty Line No EITC 13.7% 31.9% 54.3% 77.3% Counterfactual EITC, No Behavioral 9.4% 22.0% 42.1% 71.1% Response EITC, with Avg. Behavioral 8.2% 21.0% 42.0% 71.3% Response EITC with Top Decile Behavioral 6.2% 19.6% 42.0% 71.7% Response Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 104 / 220Elasticity Estimates Based on Change in EITC Refunds Around Birth of First Child Mean Phase­in Phase­out Extensive Elasticity Elasticity Elasticity Elasticity A. Wage Earnings Elasticity in U.S. 2000­2005 0.10 0.14 0.06 0.10 (0.008) (0.011) (0.006) (0.009) Elasticity in top decile ZIP­3's 0.46 0.58 0.30 0.59 (0.017) (0.021) (0.021) (0.033) B. Total Earnings Elasticity in U.S. 2000­2005 0.22 0.34 0.08 0.18 (0.013) (0.020) (0.004) (0.012) Elasticity in top decile ZIP­3's 0.95 1.32 0.34 1.05 (0.026) (0.036) (0.012) (0.039) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 105 / 220Traditional Labor Supply Elasticity Estimates Return to simple model with linear tax Large literature in labor economics estimates e¤ects of taxes and wages on hours worked and participation Now discuss some estimates from this older literature Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 106 / 220Negative Income Tax Best way to resolve identi…cation problems: exogenously increase the marginal tax rate NIT experiment conducted in 1960s/70s in Denver, Seattle, and other cities First major social experiment in U.S. Provided lump-sum welfare grants G combined with a steep phaseout rate t (50%-70%) Analysis by Rees (1974), Ashenfelter and Plant (1990), and others Several groups, with randomization within each; approx. N = 75 households in each group Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 107 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 108 / 220NIT Experiments: Ashenfelter and Plant 1990 Present non-parametric evidence of labor supply e¤ects Compare implied bene…t payments to treated vs control households Di¤erence in bene…t payments aggregates hours and participation responses This is the relevant parameter for expenditure calculations and potentially for welfare analysis (revenue method of calculating DWL) But does not decompose estimates into income and substitution e¤ects Hard to identify the elasticities relevant to predict labor supply e¤ects of other programs Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 109 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 110 / 220NIT Experiments: Findings Signi…cant labor supply response but small overall Implied earnings elasticity for males around 0.1 Implied earnings elasticity for women around 0.5 Response of women is concentrated along the extensive margin Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 111 / 220Problems with Experimental Design Estimates from NIT not considered very credible today for two reasons: 1 Self reported earnings Treatments had …nancial incentives to under-report earnings. Reported earnings not well correlated with actual payments Lesson: need to match with administrative records 2 Selective attrition After initial year, data was collected based on voluntary income reports by families to qualify for the grant Those in less generous groups/far above breakeven point had much less incentive to report Consequently attrition rates were much higher in these groups No longer a random sample of treatment + controls Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 112 / 220Tax Reform Variation Modern studies use tax changes as natural experiments Representative example: Eissa (1995) Uses the Tax Reform Act of 1986 to identify the e¤ect of MTRs on labor force participation and hours of married women TRA 1986 cut top income MTR from 50% to 28% from 1986 to 1988 But did not signi…cantly change tax rates for the middle class Substantially increased incentives to work of wives of high income husbands relative wives of middle income husbands DD strategy: compare women in top 1% households (treatment) with women in 90th percentile and 75th percentile (controls) Data: CPS, 1983-85 and 1989-91 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 113 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 114 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 115 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 116 / 220Eissa 1995: Results Participation elasticity around 0.4 but large standard errors Hours elasticity of 0.6 Total elasticity (unconditional hours) is 0.4+0.6= 1 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 117 / 220Eissa 1995: Caveats Does the common trends assumption hold? Potential story biasing the result: Trend toward “power couples”and thus DD might not be due to taxes In the 1980s, professionals had non-working spouses In the 1990s, professionals married to professionals While for middle class, always married to working middle class wives Problem: starting from very di¤erent levels for T and C groups Liebman and Saez (2006) show that Eissa’s results are not robust using admin data (SSA matched to SIPP) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 118 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 119 / 220Bianchi, Gudmundsson, and Zoega 2001 Use 1987 “no tax year”in Iceland as a natural experiment In 1987-88, Iceland switched to a withholding-based tax system Workers paid taxes on 1986 income in 1987; paid taxes on 1988 income in 1988; 1987 earnings never taxed Data: individual tax returns matched with data on weeks worked from insurance database Random sample of 9,274 individuals who …led income tax-returns in 1986-88 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 120 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 121 / 220Bianchi, Gudmundsson, and Zoega 2001 Large, salient change: Dlog(1MTR) 49%, much bigger than most studies Note that elasticities reported in paper are w.r.t. average tax rates: (L L )/L å 87 A A = L,T/E T /E å 86 86 (E E )/E å 87 A A = E,T/E T /E å 86 86 Estimates imply earnings elasticity w.r.t. marginal tax rate of roughly 0.37 (Chetty 2012) Is this a Frisch or Hicksian elasticity? Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 122 / 220Responses to Low-Income Transfer Programs Particular interest in treatment of low incomes in a progressive tax system: are they responsive to incentives? Recent literature has focused on welfare reform in mid-1990’s Reform modi…ed AFDC cash welfare program to provide more incentives to work by 1 Requiring recipients to go to job training 2 Limiting the duration for which families able to receive welfare 3 Reducing phase out to 66 cents of bene…ts per 1 earnings instead of 100% cli¤ Variation across states because Fed govt. gave block grants with guidelines EITC also expanded during this period: general shift from welfare to “workfare” Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 123 / 220Monthly Welfare Case Loads: 1963-2000 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 124 / 220Welfare Reform: Two Empirical Questions 1 Incentives: did welfare reform actually increase labor supply Test whether EITC expansions and changes in welfare policies a¤ect labor supply 2 Bene…ts: did removing many people from transfer system reduce their welfare? How did consumption change? Focus on single mothers, who were most impacted by reform Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 125 / 220Meyer and Rosenbaum 2001 Study the …rst question: impact of welfare reforms and EITC on labor supply Document dramatic (6 pp, 10%) increase in LFP for single women with children around EITC expansion No change for women without children Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 126 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 127 / 220Employment Rates for Single Women with and without Children 1984 1986 1988 1990 1992 1994 1996 Year Children No Children Source: Meyer and Rosenbaum 2001 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 128 / 220 Employment Rate .7 .8 .9 1Meyer and Rosenbaum 2001 Problem: EITC expansion took place at same time as welfare reform Try to disentangle e¤ects of welfare waivers, changes in AFDC and state taxes, etc. using state-level variation Fit a regression model with following policy variables at state level (interacted with of kids, etc.): EITC AFDC bene…ts Medicaid Waivers Training Child Care Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 129 / 220Meyer and Rosenbaum 2001 From 1984-1996, the extra increase in single mom’s relative to single women without kids is explained by: 1 EITC expansion (60%) 2 Welfare max bene…t reduction (AFDC and food stamps) (25%) 3 Medicaid if work (-10%) (insigni…cant and wrong sign) 4 Welfare waivers (time limits) 15% 5 Child care and training: 15% Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 130 / 220Meyer and Sullivan 2004 Examine the consumption patterns of single mothers and their families from 1984–2000 using CEX data Question: did single mothers’consumption fall because they lost welfare bene…ts and were forced to work? Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 131 / 220Total Consumption: Single Mothers 1984-2000 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 132 / 220Relative Consumption: single women with/without children Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 133 / 220Meyer and Sullivan: Results Material conditions of single mothers did not decline in recent years, either in absolute terms or relative to single childless women or married mothers In most cases, evidence suggests that the material conditions of single mothers have improved slightly Question: is this because economy was booming in 1990s? Is workfare approach more problematic in current economy? Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 134 / 220Changing Elasticities: Blau and Kahn 2007 Identify elasticities from 1980-2000 using “grouping instrument” 1 De…ne cells (year/age/gender/education) and compute mean wages 2 Instrument for actual wage with mean wage Identify purely from group-level variation, which is less contaminated by individual endogenous choice Result: total hours elasticity (including int + ext margin) shrank from 0.4 in 1980 to 0.2 today Interpretation: elasticities shrink as women become more attached to the labor force Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 135 / 220Summary of Static Labor Supply Literature 1 Small elasticities for prime-age males Probably institutional restrictions, need for one income, etc. prevent a short-run response 2 Larger responses for workers who are less attached to labor force Married women, low incomes, retirees 3 Responses driven by extensive margin in short-run Ext margin (participation) elasticity around 0.2 Int margin (hours) elasticity close 0 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 136 / 220Intertemporal Models and the MaCurdy Critique What parameter do reduced-form regressions of labor supply on wages or taxes identify? MaCurdy critique: reduced-form studies did not identify any parameter of interest in a dynamic model Instead, estimate a mix of income e¤ects, intertemporal substitution e¤ects, and compensated wage elasticities MaCurdy (1981) develops a tractable method (two stage budgeting) to identify preference parameters in a life-cycle model of labor supply See Chetty (2006) for a simple exposition of two-stage budgeting Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 137 / 220Life Cycle Model of Labor Supply With time-separable utility, agents maximize T t U = b u(c ,l ) å t t t=0 First order conditions t t l : b u +lw /(1+r) = 0 t l t t t t c : b u +l/(1+r) = 0 t c t Combining yields:u (l )= w u l t t c Intratemporal f.o.c. same as in static model Intertemporal f.o.c.: u /u = b(1+r) c c t t+1 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 138 / 220Dynamic Life Cycle Model: Policy Rules l= u is the marginal utility of initial consumption c 0 The two …rst order conditions imply that t l = l(w ,l/(b(1+r)) ) t t t c = c(w ,l/(b(1+r)) ) t t Current labor and consumption choice depends on current w t All other wage rates and initial wealth enter only through the budget constraint multiplier l (MaCurdy 1981) Easy to see for separable utility: u(c,l) = u(c)v(l) 0 t ) v (l ) = lw /b(1+r) t t 01 t ) l = v (lw /b(1+r) ) t t Su¢ ciency of l greatly simpli…es solution to ITLS model Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 139 / 220Dynamic Life Cycle Model: Frisch Elasticity Frisch intertemporal labor supply elasticity de…ned as: w ¶l t d=( ) j l l ¶w t t Experiment: change wage rate in one period only, holding all other wages, and consumption pro…le constant Can show that d 0: work more today to take advantage of temporarily higher wage In separable case: 01 t l = v (lw /b(1+r) ) t t ¶l l ) j = 0 l t 00 ¶w b(1+r) v (l ) t t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 140 / 220Dynamic Life Cycle Model: Three Types of Wage Changes 1 Evolutionary wage change: movements along pro…le 2 Parametric change: temporary tax cut 3 Pro…le shift: changing the wage rate in all periods Equivalent to a permanent parametric change Implicitly the elasticity that static studies estimate with unanticipated tax changes Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 141 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 142 / 220Frisch vs. Compensated vs. Uncompensated Elasticities Frisch elasticity  Compensated static elasticity Compensated static elasticity  Uncompensated static elasticity Compensated static elasticity: changing wages in all periods but keeping utility constant Uncompensated static elasticity: changing wages in each period with no compensation First inequality is due to inter-temporal substitution: When wage increases only in 1 period, substitute labor from other periods toward this period When it increases in all periods, do not have this motive Second inequality is due to income e¤ects (as in static model) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 143 / 220Frisch vs. Compensated vs. Uncompensated Elasticities Frisch elasticity  Compensated static elasticity Compensated static elasticity  Uncompensated static elasticity Without income e¤ects, all three elasticities are equal Otherwise inequalities are strict Di¤erence in elasticities related to anticipated vs. unanticipated changes Frisch elasticity is of central interest for calibration of macro business cycle models Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 144 / 220Frisch Elasticities Implied by Hicksian Elasticity of 0.33  dwl A i,t i,t F 2 = +r( )  dY wl i,t i,t Income Effect: ­dwl/dY 0.00 0.11 0.22 0.33 0.44 0.55 0.66 0.35 0.00 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.50 0.20 0.33 0.34 0.35 0.36 0.38 0.41 0.44 0.55 0.40 0.33 0.34 0.36 0.39 0.43 0.49 0.55 0.60 EIS 0.60 0.33 0.34 0.37 0.42 0.48 0.56 0.66 0.65 (ρ) 0.80 0.33 0.35 0.38 0.44 0.53 0.64 0.77 0.70 1.00 0.33 0.35 0.39 0.47 0.58 0.71 0.88 0.75 1.20 0.33 0.35 0.41 0.50 0.63 0.79 0.99 0.79 1.40 0.33 0.35 0.42 0.53 0.67 0.87 1.10 0.84 Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 145 / 220Structural Estimates: MaCurdy 1983 and Pencavel 2002 MaCurdy (1983) Structural estimate using panel data for men and within-person wage variation Find both Frisch and compensated wage elasticity of around 0.15 But wage variation is not exogenous Pencavel (2002) Instruments with trade balance interacted with schooling and age Frisch elasticity: 0.2 Uncompensated wage elasticity: 0-0.2 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 146 / 220Card (1991) Critique of ITLS models Critiques value of ITLS model Fails to explain most variation in hours over lifecycle Sheds little light on pro…le-shift elasticities that we care about Di¢ cult to identify key parameters Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 147 / 220Blundell, Duncan, and Meghir 1998 Use quasi-experimental variation coupled with ITLS model to identify Frisch elasticity Group individuals by birth cohort (decade) interacted with education (e.g. high school or more) Tax reforms in the UK in 1980s a¤ected groups very di¤erently Key innovation over pure reduced-form studies: use consumption data as a control for permanent income Yields a structurally interpretable (l constant) elasticity estimate Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 148 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 149 / 220Blundell, Duncan, and Meghir: Results Compensated wage elasticities: 0.15-0.3, depending on number of kids Virtually no income e¤ects Identi…cation assumption is common trends across cohort/ed groups Reforms in 80s went in opposite directions at di¤erent times Secular trends cannot explain everything Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 150 / 220Manoli and Weber 2011 Use variation in retirement bene…ts as a function of job tenure in Austria to estimate intertemp subst. elasticity Administrative panel for full population of Austria, 1980-2005 Question: how much do people delay retirement in order to get higher (anticipated) bene…ts? Rough estimate of intertemp subst. elasticity on extensive margin of 0.2 at annual level Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 151 / 220Lump­Sum Severance Payments at Retirement 0 0 5 5 10 10 15 15 20 20 25 25 30 30 Years of Tenure  Years of Tenure at Retirement at Retirement Source: Manoli and Weber 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 152 / 220 Fraction of Last  Fraction of Last Year's Salary Year's Salary 0 0 .333 .333 .5 .5 .75 .75 1 1Distribution of Tenure at Retirement Quarterly Frequency 10 15 20 25 Years of Tenure at Retirement Source:Manoliand Weber 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 153 / 220 Number of Individuals 0 2000 4000 6000Taxable Income Elasticities Modern public …nance literature focuses on taxable income elasticities instead of hours/participation elasticities Two main reasons 1 Convenient su¢ cient statistic for all distortions created by income tax system (Feldstein 1999) 2 Data availability: taxable income is precisely measured in tax return data Good overview of this literature: Saez et al. 2010 (JEL) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 154 / 220US Income Taxation: Trends The biggest changes in MTRs are at the top 1 Kennedy tax cuts: 91% to 70% in ’63-65 2 Reagan I, ERTA 81: 70% to 50% in ’81-82 3 Reagan II, TRA 86: 50% to 28% in ’86-88 4 Bush I tax increase: 28% to 31% in ’91 5 Clinton tax increase: 31% to 39.6% in ’93 6 Bush Tax cuts: 39.6% to 35% in ’01-03 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 155 / 220Feldstein 1995 Feldstein (1995) estimates the e¤ect of TRA86 on taxable income for top earners Constructs three income groups based on income in 1985 Looks at how incomes and MTR evolve from 1985 to 1988 for individuals in each group using panel Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 156 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 157 / 220Feldstein: Results Feldstein obtains very high elasticities (above 1) for top earners Implication: we were on the wrong side of the La¤er curve for the rich Cutting tax rates would raise revenue Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 158 / 220Feldstein: Econometric Criticisms DD can give very biased results when elasticity di¤er by groups Suppose that the middle class has a zero elasticity so that M Dlog(z )= 0 Suppose high income individuals have an elasticity of e so that H H Dlog(z )= eDlog(1t ) Suppose tax change for high is twice as large: M H Dlog(1t )= 10% andDlog(1t )= 20% e20%0 Estimated elasticity eˆ = = 2e 20%10% Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 159 / 220Feldstein: Econometric Criticisms Sample size: results driven by very few observations (Slemrod 1996) Auten-Carroll (1999) replicate results on larger Treasury dataset Find a smaller elasticity: 0.65 Di¤erent trends across income groups (Goolsbee 1998) Triple di¤erence that nets out di¤erential prior trends yields elasticity 0.4 for top earners Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 160 / 220Slemrod: Shifting vs. “Real”Responses Slemrod (1996) studies “anatomy”of the behavioral response underlying change in taxable income Shows that large part of increase is driven by shift between C corp income to S corp income Looks like a supply side story but government is actually losing revenue at the corporate tax level Shifting across tax bases not taken into account in Feldstein e¢ ciency cost calculations Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 161 / 22018% Wages S­Corp. Partner. Sole P. Dividends Interest Other 16% 14% 12% 10% 8% 6% 4% 2% 0% FIGURE 7 The Top 1% Income Share and Composition, 1960­2000 Source: Saez 2004 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 162 / 220 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000Goolsbee: Intertemporal Shifting Goolsbee (2000) hypothesizes that top earners’ability to retime income drives much of observed responses Analogous to identi…cation of Frisch elasticity instead of compensated elasticitiy Regression speci…cation: TLI = a+b log(1tax )+b log(1tax ) t t+1 1 2 Long run e¤ect is b +b 1 2 Uses ExecuComp data to study e¤ects of the 1993 Clinton tax increase on executive pay Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 163 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 164 / 220Goolsbee 2000 Most a¤ected groups (income250K) had a surge in income in 1992 (when reform was announced) relative to 1991 followed by a sharp drop in 1993 Simple DD estimate would …nd a large e¤ect here, but it would be picking up pure re-timing Concludes that long run e¤ect is 20x smaller than substitution e¤ect E¤ects driven almost entirely by retiming exercise of options Long run elasticity0.4 and likely close to 0 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 165 / 220Gruber and Saez 2002 First study to examine taxable income responses for general population, not just top earners Use data from 1979-1991 on all tax changes available rather than a single reform Simulated instruments methodology Step 1: Simulate tax rates based on period t income and characteristics P MTR = f (y ,X ) t+3 t t t+3 MTR = f (y ,X ) t+3 t+3 t+3 t+3 Step 2 …rst stage: Regress log(1MTR )log(1MTR ) on t+3 t P log(1MTR )log(1MTR ) t t+3 Step 3 second stage: Regress DlogTI on predicted value from …rst stage Isolates changes in laws (f ) as the only source of variation in tax rates t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 166 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 167 / 220Gruber and Saez: Results Find an elasticity of roughly 0.1-0.4 with splines But this is very fragile (Giertz 2008) Sensitive to exclusion of low incomes (min income threshold) Sensitive to controls for mean reversion Subsequent studies …nd smaller elasticities using data from other countries Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 168 / 220Evidence from Danish Tax Reforms Observed Earnings Responses to Small Tax Reforms ­4 ­2 0 2 4 6 % Residual Change in Net­of­Tax Wage Rate Δlog(1­t) Source: Chetty et al. 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 169 / 220 % Residual Change in Wage Earnings ­1.5 ­1 ­0.5 0 0.5 1Imbens et al. 2001: Income E¤ects Estimate income e¤ects using lottery winnings Survey responses matched with administrative data on earnings from Social Security Administration Divide sample into three subgroups: 1 Losers N = 259: “season ticket holders”who won 100-5K 2 Winners N = 237: anyone who won prizes of 22K to 9.7 mil 3 Big Winners N = 43: winners of prizes2 mil total (100K/yr) Estimate marginal propensity to earn out of unearned income of dwl/dy =0.1 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 170 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 171 / 220Taxable Income Literature: Summary Large responses for the rich, mostly intertemporal substitution and shifting Responses among lower incomes small in short run Pattern con…rmed in many settings (e.g. Kopczuk 2009 - Polish ‡at tax reform) But many methdological problems remain to be resolved Econometric issues: mean reversion, appropriate counterfactuals Which elasticity is being identi…ed? Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 172 / 220Macro Evidence Macroeconomists estimate/calibrate elasticities by examining long-term trends/cross-country comparisons Identi…cation more tenuous but estimates perhaps more relevant to long-run policy questions of interest Use aggregate hours data and aggregate measures of taxes (average tax rates) But highly in‡uential in calibration of macroeconomic models Macro models require high elasticities to …t both business cycle and cross-country data Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 173 / 220Prescott 2004 Uses data on hours worked by country in 1970 and 1995 for 7 OECD countries Technique to identify elasticity: calibration Rough logic: posit a utility function u(c,l;) Hicksian elasticity of = 0.8 best matches cross-country evidence Note that this is analogous to a regression without controls for other variables abstracting from GE e¤ects Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 174 / 220Aggregate Hours vs. Net­of­Tax Rates Across Countries (Prescott Data) 7.4 ε =0.7 Prescott Japan 1970­74 Japan 1993­96 US.1970­74 UK 1993­96 7.2 Germany.1970­74 France 1970­74 UK 1970­74 Canada 1993­96 US 1993­96 Canada 1970­74 7 Germany 1993­96 Italy 1970­74 France 1993­96 6.8 Italy 1993­96 ­1 ­.8 ­.6 ­.4 ­.2 Log (1­Tax Rate) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 175 / 220 Log Hours Worked Per AdultBusiness Cycle Fluctuations in Employment Rates in the U.S. .03 .02 .01 0 ­.01 ­.02 ­.03 1950 1960 1970 1980 1990 2000 2010 Year Employment Employment ­ Men (25­54) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 176 / 220 Log Deviation of Employment from HP Filtered TrendReconciling Micro and Macro Estimates Recent interest in reconciling micro and macro elasticity estimates Three potential explanations 1 Statistical Bias: regulations, culture di¤ers in countries with higher tax rates Alesina, Glaeser, Sacerdote 2005 2 Extensive vs. Intensive margin: “Indivisible Labor”Rogerson 1988; Rogerson and Wallenius 2008 L = Nh dlogL dlogN dlogh dlogh = + d(1t) d(1t) d(1t) d(1t) 3 Optimization frictions: short run vs. long run Chetty 2012 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 177 / 220Optimization Frictions Chetty (2012) asks two questions 1 Can frictions quantitatively explain micro-macro puzzle and other puzzles in labor supply literature? 2 Given frictions, what can we say about the “structural”elasticity? Structural elasticity controls long run responses (e.g. Europe vs US) To illustrate potential importance of frictions, …rst calculate utility loss from ignoring tax changes under neoclassical model with = 0.5 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 178 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 179 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 180 / 220Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 181 / 220Setup Consider a static demand model; results hold in dynamic model N individuals with quasilinear utility over two goods: 11/ x u (x,y)= y +a i i 11/ Agent i’s optimal demand for good x: a i  x (p) = ( ) i p  ) logx (p) = alogp+v i i where v = a a denotes i’s deviation from mean demand i i Under orthogonality conditionEvjp = 0, i   Elogx Elogx 1 0 = logp logp 1 0 Observed response to price increase (p to p ) identi…es . 0 1 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 182 / 220Optimization Frictions: Examples Agent pays adjustment cost k to change consumption i Demand set optimally at initial price p 0 Let x(p) denote observed demand at price p De…ne observed elasticity estimated from price increase as Elogx Elogx 1 0 b = logp logp 1 0 Observed elasticity confounds structural elasticity with adjustment cost distribution: b= P(Du k ) i i Behavioral example: price misperception pe(p) Elogpe(p )Elogpe(p ) 1 0 b= logp logp 1 0 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 183 / 220Optimization Frictions Restrict size of frictions by requiring that utility loss is less than exogenous threshold d:   U(x )U(x ) dpx i i i This restriction generates a class of models around nominal model Includes adjustment cost models, inattention, etc. A d class of models maps price to a choice set X(p,d) instead of a  single point x (p) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 184 / 220Construction of Choice Set 151 151 150 150 D Np x Ýp Þ t t 149 149 148 148 147 147 146 146 145 145 144 144 143 143 142 142 141 141 XÝp ,NÞ t 140 140 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 20 22 22 Demand (x) t Source: Chetty 2009 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 185 / 220 Utility u(x ) tIdentification with Optimization Frictions 3.0 ε = 1 2.8 2.6 2.4 2.2 2.0 1.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 186 / 220 log demand (log x) tBounds and Partial Identi…cation ˆ Chetty (2012) derives bounds on given estimates of Approach is closely related to modern econometrics literature on partial identi…cation Also called “set identi…cation”or “moment inequalities”in IO Pioneered by Manski (1993) See Tamer (2010 Annual Review) for a good summary Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 187 / 220Partial Identi…cation Main concept: avoid making strong assumptions about data generating process Instead, derive non-parametric bounds on parameters under worst-case scenarios Classic example: missing data with a binary outcome Traditionally, assume data is missing at random But easy to derive bounds by assuming missing data is all either 0 or 1 Chetty (2012) applies similar logic to handle model uncertainty rather than missing data Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 188 / 220Calculation of Bounds on Structural Elasticity 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 189 / 220 log demand (log x) ta) Upper Bound on Structural Elasticity 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 190 / 220 log demand (log x) tb) Lower Bound on Structural Elasticity 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 log(p ) log(p ) A B Source: Chetty 2009 log price (log p) t Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 191 / 220 log demand (log x) tBounds on Elasticity with Optimization Frictions For small d, the range of structural elasticities consistent with an observed elasticityb in a d class of models is approximately 4d 4d b+ (1r),b+ (1+r) 2 2 (Dlogp) (Dlogp) 1b 2 1/2 where r = (1+ (Dlogp) ) 2d Maps an observed elasticityb, size of price changeDlogp, and degree of optimization frictions d to bounds on . 2 Bounds shrink with (Dlogp) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 192 / 220Extensive Margin Responses Now consider bounds on extensive margin elasticities Assume that x2 0,1 and ‡ow utility is f g u (x,y)= y +b x i i Let F(b ) denote distribution of tastes for x i  Agents optimally buy x if taste b p q = 1F (p) i Let structural extensive elasticity be denoted by   logq (p )logq (p ) A B A B h = logp logp A B b Let q = observed participation rate and h = observed extensive elasticity Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 193 / 220Bounds on Structural Elasticities: δ = 1%, Δ log p = 20% 4.0 Intensive Margin 3.5 Bounds 3.0 2.5 2.0 1.5 Extensive Margin 1.0 Bounds 0.5 0 0 0 0.1 0.1 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.0 0.2 0.2 Observed Elasticit Observed Elasticityy(( ε ε)) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 194 / 220 Elasticity (ε)Extensive vs. Intensive Margin Bounds Bounds on extensive margin elasticities shrink linearly with d rather p than in proportion to d Intuition: agents are not near optima to begin with on extensive margin …rst-order utility losses from failing to reoptimize Marginal agent loses bene…t of price cut if he doesn’t enter market Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 195 / 220Application to Taxation and Labor Supply What can be learned about structural elasticity from existing estimates? Collect estimates from a broad range of studies that estimate intensive margin Hicksian elasticities Calculate bounds on the intensive margin structural elasticity with frictions of d= 1% of net earnings Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 196 / 220Bounds on Intensive­Margin Hicksian Elasticitieswith δ= 1% Frictions å å Study Identification P se(P) Δlog(1­τ) ε ε L U (1) (2) (3) (4) (5) (6) (7) A. Hours Elasticities 1. MaCurdy(1981) Lifecycle wage variation, 1967­1976 0.15 0.15 0.39 0.03 0.80 2. Eissaand Hoynes (1998) U.S. EITC, 1984­1996, Men 0.20 0.07 0.07 0.00 15.29 3. Eissaand Hoynes (1998) U.S. EITC, 1984­1996, Women 0.09 0.07 0.07 0.00 15.07 4. Blundell et al. (1998) U.K. Tax Reforms, 1978­1992 0.14 0.09 0.23 0.01 1.78 5. ZiliakandKniesner(1999) Lifecycle wage, tax variation 1978­1987 0.15 0.07 0.39 0.03 0.80 Mean observed elasticity 0.15 B. Taxable Income Elasticities 6. Bianchi et al. (2001) Iceland 1987 Zero Tax Year 0.37 0.05 0.49 0.15 0.92 7. Gruber and Saez(2002) U.S. Tax Reforms 1979­1991 0.14 0.14 0.14 0.00 4.42 8. Saez(2004) U.S. Tax Reforms 1960­2000 0.09 0.04 0.15 0.00 3.51 9. Jacob and Ludwig (2008) Chicago Housing Voucher Lottery 0.12 0.03 0.36 0.02 0.84 10. Gelber(2010) Sweden, 1991 Tax Reform, Women 0.49 0.02 0.71 0.28 0.86 11. Gelber(2010) Sweden, 1991 Tax Reform, Men 0.25 0.02 0.71 0.12 0.54 12. Saez (2010) U.S., 1st EITC Kink, 1995­2004 0.00 0.02 0.34 0.00 0.70 13. Chetty et al. (2011a) Denmark, Top Kinks, 1994­2001 0.02 0.00 0.30 0.00 0.93 14. Chetty et al. (2011a) Denmark, Middle Kinks, 1994­2001 0.00 0.00 0.11 0.00 6.62 15. Chetty et al. (2011a) Denmark Tax Reforms, 1994­2001 0.00 0.00 0.09 0.00 9.88 Mean observed elasticity 0.15 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 197 / 220Bounds on Intensive­Margin Hicksian Elasticitieswith δ= 1% Frictions å å Study Identification P se(P) Δlog(1­τ) ε ε L U (1) (2) (3) (4) (5) (6) (7) C. Top Income Elasticities 16. Feldstein (1995) U.S. Tax Reform Act of 1986 1.04 0.26 0.37 2.89 17. Auten and Carroll (1999) U.S. Tax Reform Act of 1986 0.57 0.12 0.37 0.21 1.53 18. Goolsbee(1999) U.S. Tax Reform Act of 1986 1.00 0.15 0.37 0.47 2.14 19. Saez (2004) U.S. Tax Reforms 1960­2000 0.50 0.18 0.30 0.14 1.77 20. Kopczuk (2010) Poland, 2002 Tax Reform 1.07 0.22 0.30 0.44 2.58 Mean observed elasticity 0.84 D. Macro/Cross­Sectional 21. Prescott (2004) Cross­country Tax Variation, 1970­96 0.46 0.09 0.42 0.18 1.20 22. Davis and Henrekson (2005)Cross­country Tax Variation, 1995 0.20 0.08 0.58 0.07 0.57 23. Blau and Kahn (2007) U.S. wage variation, 1980­2000 0.31 0.004 1.00 0.19 0.51 Mean observed elasticity 0.32 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 198 / 220Bounds on Intensive­Margin Hicksian Elasticitieswith δ=1% 3 2.5 2 MaCurdy (1981) 1.5 1 0.5 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage Change in Net of Tax Rate Δlog (1 –τ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 199 / 220 ElasticityBounds on Intensive­Margin Hicksian Elasticitieswith δ=1% 3 Feldstein (1995) No disjoint sets: δ= 1% reconciles all estimates 2.5 Goolsbee TRA86 2 Saez (2004) MaCurdy (1981) 1.5 Prescott (2004) 1 Gelber (2010) Davis and Henrekson Blau and Kahn (2005) (2007) 0.5 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage Change in Net of Tax Rate Δlog (1 –τ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 200 / 220 ElasticityBounds on Intensive­Margin Hicksian Elasticitieswith δ=1% 3 Feldstein (1995) Unified Bounds Using All Studies: (0.47, 0.51) 2.5 Goolsbee TRA86 2 Saez (2004) MaCurdy (1981) 1.5 Prescott (2004) 1 Gelber (2010) Davis and Henrekson Blau and Kahn (2005) (2007) 0.5 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage Change in Net of Tax Rate Δlog (1 –τ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 201 / 220 ElasticityBounds on Intensive­Margin Hicksian Elasticities with δ=1% 3 Feldstein (1995) Unified bounds excluding macro+top income: (0.28, 0.54) 2.5 Goolsbee TRA86 2 Saez (2004) MaCurdy (1981) 1.5 Prescott (2004) 1 Gelber (2010) Davis and Henrekson Blau and Kahn (2005) (2007) 0.5 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage Change in Net of Tax Rate Δlog (1 –τ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 202 / 220 ElasticityUnified Bounds on Intensive Margin Elasticity vs. Degree of Frictions 1.2 1 .8 .6 .4 ε =0.33 δ-min .2 δ = 0.5% min 0 1% 2% 3% 4% 5% Optimization Frictions as a Fraction of Net Earnings (δ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 203 / 220 Elasticity (ε)Bounds on Extensive­Margin HicksianElasticitieswith δ=1% Frictions 0.5 Meyer and Rosenbaum (2004) Blau and Kahn (2007) 0.4 Blundell et al. (2011) 0.3 Prescott (2004) Graversen (1998) Jacob and Ludwig (2008) 0.2 EissaandHoynes(2004) Nickell (2003) Davis and Henrekson (2005) 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 Percentage Change in Net of Average Tax Wage Δlog (1 –τ) Source: Chetty 2011 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 204 / 220 Extensive Margin ElasticityMicro vs. Macro Labor Supply Elasticities Chetty, Guren, Manoli, and Weber (2012): can frictions explain gap between micro and macro elasticities? Collect estimates of intensive and extensive margin elasticities adjusted for frictions and evaluate macro predictions Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 205 / 220Aggregate Hours vs. Net­of­Tax Rates Across Countries (Prescott Data) 7.4 ε =0.7 Prescott Japan 1970­74 ε =0.58 micro Japan 1993­96 US.1970­74 UK 1993­96 7.2 Germany.1970­74 France 1970­74 UK 1970­74 Canada 1993­96 US 1993­96 Canada 1970­74 7 Germany 1993­96 Italy 1970­74 France 1993­96 6.8 Italy 1993­96 ­1 ­.8 ­.6 ­.4 ­.2 Log (1­Tax Rate) Prescott (2004) Prediction Based on Micro Elasticity Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 206 / 220 Log Hours Worked Per AdultTable 2: Micro vs. Macro Labor Supply Elasticities Extensive Intensive Aggregate Margin Margin Hours micro 0.25 0.33 0.58 Steady State (Hicksian) macro 0.17 0.33 0.50 micro Intertemporal Substitution (Frisch) macro à Indivisible labor + frictions reconcile micro and macro steady­state elasticities Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 207 / 220Business Cycle Fluctuations in Employment Rates in the U.S. .03 .02 .01 0 ­.01 ­.02 ­.03 1950 1960 1970 1980 1990 2000 2010 Year Employment Real Wages × Micro Extensive Frisch Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 208 / 220 Log Deviation of Employment from HP Filtered TrendTable 2: Micro vs. Macro Labor Supply Elasticities Extensive Intensive Aggregate Margin Margin Hours micro 0.25 0.33 0.58 Steady State (Hicksian) macro 0.17 0.33 0.50 micro 0.32 0.54 0.86 Intertemporal Substitution (Frisch) macro 2.77 0.54 3.31 à Even with indivisible labor, Frisch elasticity of aggregate hours 1 is inconsistent with micro evidence à Challenge: matching employment flucs. with extensive Frisch of 0.3 � Search/labor wedge models provide one solution Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 209 / 220Labor Supply Elasticities: Implications for Preferences Labor supply elasticities central for tax policy because they determine e¢ ciency costs But optimal income tax policy also depends on bene…ts of redistribution (curvature of utility fn.) u(c)y(l) u cc Curvature of u(c): g= c determines how much more low u c income individuals value 1 relative to higher income individuals Risk aversion parameter g also central for social insurance literature and macro models Evidence on labor supply elasticities also contains information about g (King, Plosser, Rebelo 1988; Basu and Kimball 2002; Chetty 2006) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 210 / 220Chetty 2006 Suppose marginal utility of consumption declines quickly, i.e. g large Then as wages rise, individuals should quickly become sated with goods Therefore, they should opt to consume much more leisure when wages rise But this would imply 0 l,w Ex: if marginal utility of consumption drops to zero, agent reduces labor supply 1-1 as wage rises But we know that increases in wages do not cause sharp reductions in labor supply ( 0.1) l,w Places an upper bound on size of g Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 211 / 220Formula for Risk Aversion Let y = unearned inc, w = wage, l = labor supply and u(c,l) = utility At an interior optimum, l must satisfy wu (y +wl,l)=u (y +wl,l) c l Work until point where marginal utility of an additional dollar is o¤set by marginal disutility of work required to earn that dollar Comparative statics of this condition implies (if u = 0): cl wl l,y g=(1+ ) c y l ,w Risk aversion directly related to ratio of income e¤ect to substitution e¤ect Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 212 / 220Labor Supply and Risk Aversion: Intuition Assume y = 0. At initial wage w , agent works l hours 0 0 Consider e¤ect of increasing w by 1% to w 1 Shifts wu curve up by 1% (substitution e¤ect) c ¶logu c Shifts wu curve down by = g% because g is elasticity of MU c ¶logw w.r.t. c (income e¤ect) Therefore, g 1() 0 l,w If u 6= 0, thenu curve shifts when w changes cl l But the shift isu relatively small, so change in l can still be used l to get a bound on g Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 213 / 220u ,u c l Case A: γ  1 ­u(w l,l) l 0 ­u range with l w u (w l,l) w u (w l,l) 0 c 0 1 c 1 complementarity w u (w l,l) 1 c 1 Case B: γ  1 l l l l B 0 A Source: Chetty 2006 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 214 / 220Labor Supply Elasticities and Implied Coefficients of Relative Risk Aversion γ γ Income Compensated Δ Study Sample Identification Elasticity Wage Elasticity Additive c/c=0.15 (1) (2) (3) (4) (5) (6) (7) A. Hours MaCurdy (1981) Married Men Panel ­0.020 0.130 0.46 0.60 Blundell and MaCurdy(1999) Men Various ­0.120 0.567 0.63 0.82 MaCurdy, Green, Paarsch(1990) Married Men Cross Section ­0.010 0.035 1.47 1.81 Eissa and Hoynes (1998) Married Men, Inc  30K EITC Expansions ­0.030 0.192 0.88 1.08 Married Women, Inc  30K EITC Expansions ­0.040 0.088 0.64 1.34 Friedberg (2000) Older Men (63­71) Soc. Sec. Earnings Test ­0.297 0.545 0.93 1.46 Blundell, Duncan, Meghir (1998) Women, UK Tax Reforms ­0.185 0.301 0.93 1.66 Average 0.69 0.94 B. Participation Eissa and Hoynes (1998) Married Men, Inc  30K EITC Expansions ­0.008 0.033 0.44 0.48 Married Women, Inc  30K EITC Expansions ­0.038 0.288 0.15 0.30 Average 0.29 0.39 C. Earned Income Imbens, Rubin, Sacerdote(2001) Lottery Players in MA Lottery Winnings ­0.110 Feldstein (1995) Married, Inc  30K TRA 1986 1.040 0.32 0.41 Auten and Carroll (1997) Single and Married, Inc15K TRA 1986 0.660 0.50 0.65 Average 0.41 0.53 D. Macroeconomic/Trend Evidence Blau and Kahn (2005) Women Cohort Trends ­0.278 0.646 0.60 1.29 Davis and Henrekson (2004) Europe/US aggregate stats Cross­Section of countries ­0.251 0.432 1.74 2.25 Prescott (2004) Europe/US aggregate stats Cross­Country time series ­0.222 0.375 1.78 2.30 Average 1.37 1.95 Overall Average 0.71 0.97 Source: Chetty 2006 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 215 / 220Chetty 2006: Results Labor supply evidence justi…es use of u(c)= logc l,y wl Formula g=(1+ ) useful in tax, insurance, and other y c l ,w applications Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 216 / 220Income Distribution We have covered evidence on two of the three elements critical for optimal income taxation 1 Labor supply elasticities 2 Measurement of preferences/social welfare weights 3 Measurement of income distribution Third piece can be well measured using tax data, even for high incomes (Piketty and Saez 2004) Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 217 / 220Saez 2004: Long-Run Evidence Compares top 1% relative to the bottom 99% Bottom 99% real income increases up to early 1970s and stagnates since then Top 1% increases slowly up to the early 1980s and then increases dramatically up to year 2000. Corresponds to the decrease in MTRs Pattern exempli…es general theme of this literature: large responses for top earners, no response for rest of the population Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 218 / 220Bottom 99% Tax Units 40,000 40% 35,000 35% 30% 30,000 25,000 25% 20,000 20% 15,000 15% 10,000 10% Marginal T Marginal T Marginal Tax ax ax Rate  Rate  Rate Av Av Average Inc erage Inc erage Income ome ome 5% 5% 5% 5% 5,000 0% 0 Source: Saez 2004 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 219 / 220 Marginal Tax Rate 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000Top 1% Tax Units 800,000 80% 700,000 70% 600,000 60% 500,000 50% 40% 400,000 30% 300,000 20% 200,000 Marginal T Marginal T Marginal Tax ax ax Rate  Rate  Rate Av Av Average Inc erage Inc erage Income ome ome 10% 100,000 5% 5% 5% 0% 0 Source: Saez 2004 Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 220 / 220 Marginal Tax Rate 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000Public Economics Lectures Part 6: Social Insurance Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 6: Social Insurance 1 / 178Outline 1 Motivations for Social Insurance 2 Unemployment Insurance 3 Workers’Compensation 4 Disability Insurance 5 Health Insurance Public Economics Lectures () Part 6: Social Insurance 2 / 178De…nition of Social Insurance Transfers based on events such as unemployment, disability, or age Contrasts with welfare: means-tested transfers SI is the biggest and most rapidly growing part of government expenditure today Public Economics Lectures () Part 6: Social Insurance 3 / 178Growth of Social Insurance in the U.S. Social Security Income Health 3.6% Security 0.4% 5% Health 9.4% National Defense Social 20.7% Security Other 20.7% 21.6% National Defense Income 69.4% Other Security 34.8% 14.5% 1953 2008 Source: Office of Management and Budget, historical tables, government outlays by function Public Economics Lectures () Part 6: Social Insurance 4 / 178Social Insurance Spending, 1996 % of Central % of Total Government Government % of GDP Expenditures Expenditures Sweden 32.47% 86.60% 49.58% Germany 28.05% 82.91% 49.44% Mexico 1.36% 8.82% 6.39% Columbia 6.61% 43.33% N/A United Kingdom 17.53% 43.13% 33.77% United States 12.22% 59.76% 30.02% Japan 2.50% 19.44% 16% Czech Republic 11.89% 38.90% 25.75% Source: Krueger and Meyer 2002 Public Economics Lectures () Part 6: Social Insurance 5 / 178Unemployment Benefit Systems in Developed Countries 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (months) Belgium Belgium Hungary Hungary Spain Spain Sweden Sweden USA USA Source: OECD Benefits and Wages 2002 Public Economics Lectures () Part 6: Social Insurance 6 / 178 Net replacement rate (%) 0 20 40 60 80 100 120Main Questions in Social Insurance 1 Why have social (as opposed to private, or any) insurance? 2 What type of SI system maximizes social welfare? Tradeo¤ between two forces: Bene…ts –reducing risk (‡uctuations in consumption) Distortion –changes in incentives for workers and …rms – ine¢ cient behavior and DWL Generate new distortions as you …x the problem you set out to solve – second-best solution Identify optimal policy by combining theoretical models of social insurance with empirical evidence on program e¤ects Public Economics Lectures () Part 6: Social Insurance 7 / 178References 1 Institutional details: see handout posted on course website 2 Expected utility theory: See MWG or other graduate texts 3 Survival analysis: Kiefer (1988 JEL) 4 Surveys: Krueger and Meyer (2002) Handbook chapter 5 Chetty and Finkelstein (2012) Handbook chapter Public Economics Lectures () Part 6: Social Insurance 8 / 178Why have social insurance? Motivation for insurance: reduction in risk for risk-averse individuals Unemp Ins: risk of involuntary unemployment Workers’comp and DI: risk of injuries/disabilities Social Security annuity: risk of living too long But why is government intervention needed to provide this insurance? Possible sources of market failure here: 1 Informational problems (adverse selection) 2 Individual optimization failures (myopia/improper planning) 3 Macroeconomic shocks Public Economics Lectures () Part 6: Social Insurance 9 / 178Adverse Selection as a Motivation for SI Key paper: Rothschild and Stiglitz (1976); see MWG Ch. 13 for a good review More recent “su¢ cient statistic”version that can be connected to data: Einav, Finkelstein, and Cullen (QJE 2010) Consider an environment with asymmetric information, e.g. individuals know risk of losing job but insurer does not Main result: can lead to market failure where no equilibrium supports provision of insurance Government intervention through mandated insurance can increase welfare Public Economics Lectures () Part 6: Social Insurance 10 / 178Rothschild-Stiglitz model Economy with two types, low-risk (L) and high-risk (H) A fraction f of the individuals are high-risk Type L has a chance p of becoming unemployed in a given year L Type H has a chance p p of becoming unemployed. H L In good state (state 1), income is E for both types; in bad state, 1 income is E E . 2 1 Public Economics Lectures () Part 6: Social Insurance 11 / 178Rothschild-Stiglitz: Key Assumptions 1 Static model: individuals arrive in the period either employed or unemployed; no savings/dynamics. 2 No moral hazard: agents choose insurance contract but make no choices after signing a contract. 3 Insurance market is perfectly competitive, so …rms earn zero pro…ts in equilibrium. Public Economics Lectures () Part 6: Social Insurance 12 / 178Rothschild-Stiglitz: Contracts An insurance contract is described by a vector a=(a ,a ) 1 2 Consumption in the two states: (E a ,E +a ) 1 1 2 2 Type i’s expected utility is V (a)=(1p )u(E a )+p u(E +a ) i i 1 1 i 2 2 Any contract that earns non-negative pro…ts is feasible Zero-pro…t condition) …rms price insurance s.t. 1p a = a 2 1 p where p is risk rate of those who purchase contract. Public Economics Lectures () Part 6: Social Insurance 13 / 178Rothschild-Stiglitz: Equilibrium De…nition An equilibrium is de…ned by a set of insurance contracts such that (1) individuals optimize: both types cannot …nd a better contract than the ones they chose (2) …rms optimize: all …rms earn zero pro…ts Two types of equilibrium: 1 Pooling: both types are o¤ered the same contract a. 2 Separating: high-risk types choose a contract a while low-risk types H choose a di¤erent contract a . L Public Economics Lectures () Part 6: Social Insurance 14 / 178Rothschild-Stiglitz: First Best Solution In …rst best, insurer can distinguish types (perfect information) In this case, equilibrium is separating 1p i Plugging in a = a , each type solves 2 1 p i 1p i max(1p )u(wa )+p u(w + a ). i 1 i 1 a 1 p i Solution 1p i 0 0 Set MRS = , i.e. u (c )= u (c ), i.e. full insurance 12 1 2 p i Both types are perfectly insured: earn their expected income (1p )w regardless of the state. i Public Economics Lectures () Part 6: Social Insurance 15 / 178Public Economics Lectures () Part 6: Social Insurance 16 / 178Rothschild-Stiglitz: Second Best Problem Firms cannot distinguish types in practice, because they cannot determine true layo¤ risks, illness history, etc. With contracts above, all the high risk types buy the low risk’s contract and insurer goes out of business Hence optimal contracts di¤er when information is asymmetric Public Economics Lectures () Part 6: Social Insurance 17 / 178Rothschild-Stiglitz: Second Best Solution Result 1: no pooling equilibrium exists If H and L types are pooled in a contract a,low-risk types lose money in expectation. 1p Zero-pro…t condition requires a = a but p p . 2 1 L p Low-risk type gets fewer dollars in state 2 than he should if the insurance were fair for him. Creates an opportunity for a new insurer to enter and “pick o¤”low risk types by o¤ering slightly less insurance at a better price: higher c , lower c 1 2 Only low risk types switch, because they value c more. 1 Public Economics Lectures () Part 6: Social Insurance 18 / 178Public Economics Lectures () Part 6: Social Insurance 19 / 178Rothschild-Stiglitz: Second Best Solution Result 2: in a separating eq, Type H obtains full insurance and Type L is under-insured Intuition: in any sep. eq., both types are getting actuarially fair insurance because of the zero-pro…ts condition For H, no cost to …rm in providing full ins. (worst that can happen is that L will join the pool, raising pro…ts) But for L, full ins. would create an incentive for H to buy this (cheaper) policy, forcing …rm into negative pro…ts Incentive constraints always bind downward –“no distortion at the top”result in standard asymmetric info. models In eq., L gets as much ins as possible without inducing H to deviate and pretend to be low-risk Public Economics Lectures () Part 6: Social Insurance 20 / 178Rothschild-Stiglitz: Gains from Government Mandate There can be gains from government intervention through mandated insurance Consider an example where E = 100,E = 0 1 2 p 1 3 u(c) = c,p = ,p = ,f = 10% L H 4 4 In candidate separating eq., type H gets perfect insurance: r 1 EU = u(100(1p ))= 100 = 5 H H 4 Public Economics Lectures () Part 6: Social Insurance 21 / 178Rothschild-Stiglitz: Second Best Solution Type L gets as much ins. as possible without making H want to deviate at actuarially fair rate for L: s q 1 3 1p L L L 5= 100a + a 1 1 4 4 p L L L Solving gives a = 3.85,a = 11.55 –nowhere near full insurance 1 2 for low risk type. Note that expected utility for low risk type is p p 3 1 EU = 1003.85+ 33.85= 8.2. L 4 4 Public Economics Lectures () Part 6: Social Insurance 22 / 178Rothschild-Stiglitz: Second Best Solution Now suppose govt. comes in and mandates pooled insurance at actuarial rate. Everyone gets an income of 9 3 1 1 7 ( + )100= 100= 70. 104 104 10 H bene…ts from this: now pooling with less risky people p But L bene…ts too Expected utility is 70 8.2 Public Economics Lectures () Part 6: Social Insurance 23 / 178Rothschild-Stiglitz: Second Best Solution Because there are relatively few high risk types, L types bene…t from pooling with them and getting full insurance coverage. Note: pooled contract of 70 could be o¤ered by a private …rm, destroying separating eq. proposed above Hence there is actually no equilibrium in this example Public Economics Lectures () Part 6: Social Insurance 24 / 178Adverse Selection as a Motivation for SI More generally, consider an economy in which people di¤er in their risks of becoming unemployed Adverse selection can destabilize the market: Firm provides UI but lowest-risk (tenured people) drop out) rates have to rise But then even moderate-risk types opt out) rates rise further, more drop out, ... Could cause unraveling to the point where virtually no one is insured by private market UI program that pools everyone can lead to (ex-ante) welfare improvements What tool does the govt. have that private sector does not? Ability to mandate Public Economics Lectures () Part 6: Social Insurance 25 / 178Adverse Selection: Empirical Evidence Empirical evidence shows that adverse selection is a real source of market failures in practice Standard test: “positive correlation”property in equilibrium (Chiappori and Salanie 2000) Are those who buy more insurance more likely to …le claims? Could be driven by both moral hazard + AS but not in certain contexts such as death Example: Finkelstein and Poterba (2004): adverse selection in U.K. annuity market. Annuities = ins. against the risk of living too long. Public Economics Lectures () Part 6: Social Insurance 26 / 178Finkelstein and Poterba 2004 Study two types of annuity markets: compulsory vs. voluntary. Examine two features of annuity contracts degree of backloading (in‡ation indexing and escalation of payments over time) payments to estate in event of death (guarantees and capital protection). Test for positive correlation in two ways 1 In eq., those who purchase backloaded annuities have lower mortality rates 2 In eq., those who purchase annuities with payment to estate have higher mortality rates Both e¤ects should be stronger in voluntary markets Public Economics Lectures () Part 6: Social Insurance 27 / 178Public Economics Lectures () Part 6: Social Insurance 28 / 178Limitations of Positive Correlation Test 1 Does not account for other dimensions of heterogeneity that may confound the correlation Literature on “advantageous selection”(e.g., Finkelstein and McGarry 2006) 2 Correlation does not clearly map into parameters that control welfare costs of selection Einav, Finkelstein, and Cullen (2010) develop “cost curve”tests that map to measures of welfare costs 3 Only applicable in markets that exist, i.e. those that have not totally unravelled Hendren (2012) uses subjective expectations data to bound welfare costs in markets that have unraveled Public Economics Lectures () Part 6: Social Insurance 29 / 178Individual Optimization Failures as a Motivation for SI Given adverse selection, expect individuals to “self-insure”against temp. shocks by building up savings With such bu¤er stocks, still no need for large social safety nets to insure against temporary shocks such as unemployment In practice, individuals appear to be very liquidity constrained when hit by shocks: median job loser has 200 in assets Suggests 1st Welfare thm also does not hold due to individual failures to optimize Individuals may misperceive the probability of a layo¤ Firms may not be able to debias people in equilibrium, leading to role for govt. (Spinnewijn 2009) Public Economics Lectures () Part 6: Social Insurance 30 / 178Aggregate Shocks as a Motivation for SI Private ins. (cross-sectional pooling) relies on idiosyncratic risks so those who are well o¤ can pay those who are poor Government is the only entity able to coordinate risk-sharing across di¤erent groups that are all a¤ected by negative shocks Inter-generational risk sharing required if everyone is poor at the same time Particularly relevant for UI and maybe social security Less so for health-related shocks Public Economics Lectures () Part 6: Social Insurance 31 / 178Optimal Social Insurance Now turn to question of optimal design of SI policies Take as given that market provides no insurance for some reason In the simple Rothschild-Stiglitz model, perfect insurance is optimal But this abstracts from moral hazard Individuals will not work if they have perfect unemp insurance Must take this distortion into account to …nd optimal level of social insurance Public Economics Lectures () Part 6: Social Insurance 32 / 178Unemployment Insurance Potential bene…ts 1 Smoother path of consumption 2 Better job matches Potential distortions 1 Less job search, higher unemployment rate 2 Workers’preferences distorted toward unstable jobs 3 Shirking on the job Public Economics Lectures () Part 6: Social Insurance 33 / 178Optimal UI: Outline 1 Optimal level of UI bene…ts ignoring …rm responses Baily-Chetty model Theory applies to all income security programs discussed later 2 Distortions to …rms’layo¤ decisions due to imperfect exp rating Feldstein model 3 Other issues: Post-unemployment outcomes, general equilibrium e¤ects Public Economics Lectures () Part 6: Social Insurance 34 / 178Replacement Rate Common measure of program’s size is its “replacement rate” net bene…t r = net wage UI reduces agents’e¤ective wage rate from …nding a new job to w(1r) Feldstein (1978): UI makes e¤ective wages very low because of interaction with tax system: (0.5)w 1970: No tax) r = = 72% (1.18.05.07)w Incentives worse for some subgroups: secondary income earner faces MTR of 50%) r = 1.3 Today, federal income taxes paid on UI bene…ts, so rep. rate is 50-60% Public Economics Lectures () Part 6: Social Insurance 35 / 178Unemployment Insurance Benefit Schedule in Michigan, 2009 0 if highest total quarterly earnings  2,871 (220/wk) 0 200 400 600 800 1000 Weekly Wage Earnings in Highest Quarter () Source: Michigan Department of Energy, Labor, and Economic Growth 2009 Public Economics Lectures () Part 6: Social Insurance 36 / 178 Weekly Benefits () 0 100 200 300 362 400Baily-Chetty model Canonical analysis of optimal level of UI bene…ts: Baily (1978) Shows that the optimal bene…t level can be expressed as a fn of a small set of parameters in a static model. Once viewed as being of limited practical relevance because of strong assumptions Chetty (2006) shows formula actually applies with arbitrary choice variables and constraints. Parameters identi…ed by Baily are su¢ cient statistics for welfare analysis) robust yet simple guide for optimal policy. Public Economics Lectures () Part 6: Social Insurance 37 / 178Baily-Chetty model: Assumptions 1 Fixed wages –no GE e¤ects 2 No distortions to …rm behavior (temporary layo¤s); implicitly assume perfect experience rating 3 No externalities such as spillovers to search Public Economics Lectures () Part 6: Social Insurance 38 / 178Baily-Chetty model: Setup Static model with two states: high (employed) and low (unemployed) Let w denote the individual’s income in the high state and w w h l h income in the low state Let A denote wealth, c consumption in the high state, and c h l consumption in the low state Agent is initially unemployed. Controls probability of being in the bad state by exerting search e¤ort e at a cost y(e) Choose units of e so that the probability of being in the high state is given by p(e)= e Public Economics Lectures () Part 6: Social Insurance 39 / 178Baily-Chetty model: Setup UI system that pays constant bene…t b to unemployed agents Bene…ts …nanced by lump sum tax t(b) in the high state Govt’s balanced-budget constraint: et(b)=(1e)b Let u(c) denote utility over consumption (strictly concave) Agent’s expected utility is eu(A+w t(b))+(1e)u(A+w +b)y(e) h l Public Economics Lectures () Part 6: Social Insurance 40 / 178First Best Problem In …rst best, there is no moral hazard problem To solve for FB, suppose government chooses b and e jointly to maximize agent’s welfare: maxe(A+w t)+(1e)u(A+w +b)y(e) h l b,e 1e s.t. t = b e 0 0 Solution to this problem is u (c )= u (c )) full insurance e u Public Economics Lectures () Part 6: Social Insurance 41 / 178Second Best Problem In second best, cannot eliminate moral hazard problem because e¤ort is unobserved by govt. Problem: Agents only consider private marginal costs and bene…ts when choosing e Social marginal product of work is w w h l Private marginal product is w w bt h l Agents therefore search too little from a social perspective, leading to e¢ ciency losses Public Economics Lectures () Part 6: Social Insurance 42 / 178Second Best Problem Agents maximize expected utility, taking b and t(b) as given maxeu(A+w t)+(1e)u(A+w +b)y(e) h l e Let indirect expected utility be denoted by V(b,t) Government’s problem is to maximize agent’s expected utility, taking into account agent’s behavioral responses: maxV(b,t) b,t s.t. e(b)t =(1e(b))b Public Economics Lectures () Part 6: Social Insurance 43 / 178Second Best Problem Problem Optimal Social Insurance maxV(b,t(b)) b s.t. e(b)t(b)= (1e(b))b e(b) = argmaxeu(A+w t)+(1e)u(A+w +b)y(e) h l e Formally equivalent to an optimal Ramsey tax problem with state-contingent taxes Public Economics Lectures () Part 6: Social Insurance 44 / 178Two Approaches to Optimal Social Insurance 1 Structural: specify complete models of economic behavior and estimate the primitives  Identify b as a fn. of discount rates, nature of borrowing constraints, informal ins. arrangements.  2 Su¢ cient Statistic: derive formulas for b as a fn. of reduced-form elasticities Baily-Chetty formula is one example Public Economics Lectures () Part 6: Social Insurance 45 / 178Chetty (2006) Su¢ cient Statistic Formula At an interior optimum, the optimal bene…t rate must satisfy  dV/db(b )= 0 To calculate this derivative, write V(b) as V(b)= maxeu(A+w t(b))+(1e)u(A+w +b)y(e) h l e Since fn has been optimized over e, Envelope Thm. implies: dV(b) dt 0 0 =(1e)u (c ) eu (c ) l h db db ¶e Can ignore terms because of agent optimization ¶b Public Economics Lectures () Part 6: Social Insurance 46 / 178Kaplan 2009 Exploiting f.o.c.’s from agent optimization particularly useful in more complex models Kaplan (2009): unemployed youth move back in with their parents. How does this a¤ect optimal UI? Kaplan takes a structural approach and estimates a dynamic model of the decision to move back home Public Economics Lectures () Part 6: Social Insurance 47 / 178Su¢ cient Statistic Approach to Kaplan 2009 Suppose moving home raises consumption by H and has a cost g(H): V(b) = maxeu(A+w t(b)) h e,H +(1e)u(A+w +b+H)g(H)y(e) l Variable H drops out, as did e, because of agent optimization dV(b) Formula derived for is una¤ected by ability to move home: db dV(b) dt 0 0 =(1e)u (c ) eu (c ) l h db db where c is measured in the data as including home consumption (H) l Public Economics Lectures () Part 6: Social Insurance 48 / 178Chetty (2006) Su¢ cient Statistic Formula The government’s UI budget constraint implies dt 1e b de 1e 1e,b = = (1+ ) 2 db e e db e e dV(b) 1e,b 0 0 =) =(1e)fu (c )(1+ )u (c )g l h db e Setting dV(b)/db = 0 yields the optimality condition 0 0 u (c )u (c ) l h 1e,b = 0 u (c ) e h LHS: bene…t of transferring 1 from high to low state RHS: cost of transferring 1 due to behavioral responses Public Economics Lectures () Part 6: Social Insurance 49 / 178Baily-Chetty Formula 0 0 u (c )u (c ) l h 1e,b = 0 u (c ) e h This equation provides an exact formula for the optimal bene…t rate 0 0 u (c )u (c ) l h Implementation requires identi…cation of 0 u (c ) h 0 0 u (c )u (c ) l h Three ways to identify empirically 0 u (c ) h 1 Baily (1978), Gruber (1997), Chetty (2006): cons-based approach 2 Shimer and Werning (2007): reservation wages 3 Chetty (2008): moral hazard vs liquidity Public Economics Lectures () Part 6: Social Insurance 50 / 178Consumption-Based Formula Write marginal utility gap using a Taylor expansion 0 0 00 u (c )u (c ) u (c )(cc ) l h h l h 00 u (c)c De…ning coe¢ cient of relative risk aversion g= , we can write 0 u (c) 0 0 00 u (c )u (c ) u Dc l h  c (1) h 0 0 u (c ) u c h Dc = g c Gap in marginal utilities is a function of curvature of utility (risk aversion) and consumption drop from high to low states Public Economics Lectures () Part 6: Social Insurance 51 / 178Consumption-Based Formula Theorem  The optimal unemployment bene…t level b satis…es Dc 1e,b  g (b ) c e where Dc c c h l = = consumption drop during unemployment c c h 00 u (c ) h g = c = coe¢ cient of relative risk aversion h 0 u (c ) h dlog1e = = elast. of probability of unemp. w.r.t. bene…ts 1e,b dlogb Public Economics Lectures () Part 6: Social Insurance 52 / 178Consumption-Based Formula Dc 1e,b  g (b ) c e Intuition for formula: LHS is marginal social bene…t of UI, RHS is marginal social cost of UI Extends to model where agent chooses N other behaviors and faces M other constraints, subject to some regularity conditions (Chetty 2006). Envelope conditions used above still hold Empirical work on UI provides estimates of the three key parameters Dc (g, ,). c Public Economics Lectures () Part 6: Social Insurance 53 / 178Empirical Estimates: Duration Elasticity Early literature used cross-sectional variation in replacement rates Problem: comparisons of high and low wage earners confounded by other factors. Modern studies use exogenous variation from policy changes (e.g. Meyer 1990) Public Economics Lectures () Part 6: Social Insurance 54 / 178Weekly Benefit Amount A WBA max After Benefit Increase B WBA max Before Benefit Increase WBA min E E2 E3 1 Previous Earnings Low Earnings Group High Earnings Group Source: Krueger and Meyer 2002 Public Economics Lectures () Part 6: Social Insurance 55 / 178Hazard Models De…ne hazard rate h = number that …nd a job at time t divided by t number unemployed at time t This is an estimate of the probability of …nding a job at time t conditional on being unemployed for at least t weeks Standard speci…cation of hazard model: Cox “proportional hazards” h = a exp(bX) t t Here a is the non-parametric “baseline”hazard rate in each period t t and X is a set of covariates Semi-parametric speci…cation –allow hazards to vary freely across weeks and only identify coe¢ cients o¤ of variation across spells Public Economics Lectures () Part 6: Social Insurance 56 / 178Hazard Models Useful to rewrite expression as: logh = loga +bX t t Key assumption: e¤ect of covariates proportional across all weeks dlogh dlogh t s = b= 8t,s dX dX If a change in a covariate doubles hazard in week 1, it is forced to double hazard in week 2 as well Restrictive but a good starting point; can be relaxed by allowing for time varying covariates X t Public Economics Lectures () Part 6: Social Insurance 57 / 178Meyer 1990 Meyer includes log UI bene…t level as a covariate: logh = loga +b logb+b X t t 1 2 In this speci…cation, dlogh t = b = h ,b t 1 dlogb Note: in exponential survival (constant-hazard) models, = h ,b 1e,b t Meyer estimates =0.9 using administrative data for UI h ,b t claimants Subsequent studies get smaller estimates; consensus: =0.5 h ,b t (Krueger and Meyer 2002) Public Economics Lectures () Part 6: Social Insurance 58 / 178Public Economics Lectures () Part 6: Social Insurance 59 / 178Consumption Smoothing Bene…ts of UI Gruber (1997) takes the Baily formula to the data by estimating consumption smoothing response. Same methodology as Meyer Uses cross-state and time variation and uses drop in food consumption as the LHS variable. Data: PSID food consumption Public Economics Lectures () Part 6: Social Insurance 60 / 178Gruber 1997 Gruber estimates Dc b = b +b 1 2 c w Finds b = 0.24, b =0.28 1 2 Without UI, cons drop would be about 24% Mean drop with current bene…t level (b = 0.5) is about 10% Implies a 10 pp increase in UI replacement rate causes 2.8 pp reduction in cons. drop Suggests that ins. markets are not perfect and UI does play a consumption smoothing role, but estimates are imprecise Key area for future work: admin. consumption data Public Economics Lectures () Part 6: Social Insurance 61 / 178Consumption Smoothing Bene…ts of UI What is substituting for/getting crowded out by UI? Cullen and Gruber (2000) emphasize spousal labor supply Study wives of unemployed husbands Examine wives’labor supply as a fn of level of husbands’UI bene…ts For a 100/wk increase in UI bene…t, wives work 22 hrs less per month In the absence of UI, wives would work 30% more during the spell than they do now Engen and Gruber (1995) document that higher UI bene…ts lower ex-ante savings, another crowdout channel Public Economics Lectures () Part 6: Social Insurance 62 / 178Calibrating the Model Gruber calibrates Baily’s model using his and Meyer’s estimates: Dc 1e,b g  c e  b 1e,b g(b +b ) = 1 2 w e Solving for the optimal replacement rate yields:  b b /e 1 1e,b 1 = ( ) w b g b 2 2 Plugging in = .43 as in Gruber (1997) and e = .95 (5% 1e,b unemployment rate) yields:  b .43/.95 1 (.24) =(  ) w .28 g .28 Public Economics Lectures () Part 6: Social Insurance 63 / 178Calibrating the Model  b Results: varies considerably with g w g 1 2 3 4 5 10  b 0 0.05 0.31 0.45 0.53 0.7 w Gruber: introspection and existing evidence suggests g 2 Implies optimal bene…t level is much lower than observed Public Economics Lectures () Part 6: Social Insurance 64 / 178Measurement of Risk Preferences Parameter that is most poorly identi…ed: g Barseghyan et al. (2012) and Einav et al. (2012) estimate risk preferences across di¤erent domains Do individuals who choose more insurance for health also choose more insurance for long-term disability? Find positive correlation in risk preferences but substantial heterogeneity across domains Suggests that appropriate value of g is highly context-dependent Could be due to behavioral factors and framing but also due to neoclassical factors Public Economics Lectures () Part 6: Social Insurance 65 / 178Chetty and Szeidl (2007): Consumption Commitments Standard expected utility model: one composite consumption good c Composite commodity assumes that people can cut back on all consumption goods at all times freely. E.g. when unemployed, cut consumption of food, housing, cars, furniture, etc. In practice, di¢ cult to adjust many elements of consumption in short run because of …xed adjustment costs Public Economics Lectures () Part 6: Social Insurance 66 / 178Homeowners’Consumption around Unemployment Shocks ­4 ­2 0 2 4 Year relative to unemployment Housing (Home Value) Food Source: Chetty and Szeidl 2007 Public Economics Lectures () Part 6: Social Insurance 67 / 178 Food and Housing Growth Rates ­.075 ­.05 ­.025 0 .025 .05Renters’Consumption around Unemployment Shocks ­4 ­2 0 2 4 Year relative to unemployment Housing (Rent) Food Source: Chetty and Szeidl 2007 Public Economics Lectures () Part 6: Social Insurance 68 / 178 Food and Housing Growth Rates ­.075 ­.05 ­.025 0 .025 .05Commitments and Risk Aversion How do commitments a¤ect risk aversion? Utility over two goods, food and housing: U(f,h)= u(f)+v(h). Adjusting h requires payment of a …xed cost k Agent follows an (S,s) policy Public Economics Lectures () Part 6: Social Insurance 69 / 178Public Economics Lectures () Part 6: Social Insurance 70 / 178Commitments Model: Implications for UI Commitments amplify risk aversion Ex: 50% food, 50% housing Suppose unemployed agent forced to cut expenditure by 10% Then have to cut food cons by 20%, leading to larger welfare loss Model of commitments suggests that g might actually exceed 4 for unemployment shocks g 1 2 3 4 5 10  b 0 0.05 0.31 0.45 0.53 0.7 w Problem: g hard to estimate precisely by context Public Economics Lectures () Part 6: Social Insurance 71 / 178Alternative Formulas for Optimal UI Dc Since g and are hard to identify, recent work has sought c alternative ways of calculating optimal bene…t. Two approaches 1 Moral hazard vs. liquidity (Chetty 2008) 2 Reservation wage response (Shimer Werning 2007) Note that any formula is only one representation of optimal bene…t Public Economics Lectures () Part 6: Social Insurance 72 / 178Chetty 2008: Moral Hazard vs. Liquidity Discrete time dynamic search model Individual lives for T periods Interest rate and discount rate equal to 0 Individual loses job in period t = 0 Let u(c ) denote ‡ow utility over cons. t Dynamic budget constraint: A = A +y c t+1 t t t Asset limit: A  L t Public Economics Lectures () Part 6: Social Insurance 73 / 178Chetty 2008: Baseline Assumptions 1 Assets prior to job loss exogenous 2 No heterogeneity 3 Fixed wages: choose only search intensity, not reservation wage Each of these is relaxed in paper, so model nests search models used in structural literature (e.g. Wolpin 1987) Public Economics Lectures () Part 6: Social Insurance 74 / 178Chetty 2008: Job Search Technology If unemployed in period t, worker …rst chooses search intensity s t Finds a job that begins immediately in period t with probability s t e If job found, consumes c . Jobs are permanent, pay wage w t. t t Public Economics Lectures () Part 6: Social Insurance 75 / 178Chetty 2008: Job Search Technology u If no job found: receives bene…t b , consumes c , enters t+1 t t unemployed Cost of job search: y(s ) t e e e e c c = c = c = = … … tt t+1 t+1 s s tt Period Period tt e e s s c c t+1 t+1 t+1 t+1 1 1­­s s tt u u c c tt 1 1­­s s t+1 t+1 u u c c t+1 t+1 Public Economics Lectures () Part 6: Social Insurance 76 / 178Chetty 2008: Value Functions Value function for agent who …nds a job in period t: V (A )= max u(A A +wt)+V (A ) t t t t+1 t+1 t+1 A L t+1 Value function for agent who does not …nd a job in period t: U (A )= max u(A A +b )+J (A ) t t t t+1 t t+1 t+1 A L t+1 where J (A ) is value of entering next period unemployed. t+1 t+1 Agent chooses s to maximize expected utility t J (A )= maxs V (A )+(1s )U (A )y(s ) t t t t t t t t t s t Public Economics Lectures () Part 6: Social Insurance 77 / 178Chetty 2008: Optimal Search Behavior First order condition for optimal search intensity: 0  y(s )= V (A )U (A ) t t t t t Intuitively, s is chosen to equate the marginal cost of search e¤ort t with the marginal value of search e¤ort. E¤ect of bene…ts on durations: 0 u 00 ¶s /¶b =u (c )/y (s ) t t t t Public Economics Lectures () Part 6: Social Insurance 78 / 178Chetty 2008: Moral Hazard vs. Liquidity Decomposition Bene…t e¤ect can be decomposed into two terms: 0 e 0 u 00 ¶s /¶A = fu (c )u (c )g/y (s ) 0 t t t t t 0 e 00 ¶s /¶w = u (c )/y (s ) 0 t t t t ) ¶s /¶b = ¶s /¶A ¶s /¶w t t t t t t ¶s /¶A is “liquidity e¤ect” t t ¶s /¶w is “moral hazard”or price e¤ect t t Liquidity and total bene…t e¤ects smaller for agents with better consumption smoothing capacity Public Economics Lectures () Part 6: Social Insurance 79 / 178Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 80 / 178Chetty 2008: Formula for Optimal UI 0 e 0 u 00 ¶s /¶A = fu (c )u (c )g/y (s ) 0 t t t t t 0 e 00 ¶s /¶w = u (c )/y (s ) 0 t t t t 0 u 0 e ¶s /¶A LIQ u (c )u (c ) t t t t ) = = e 0 ¶s /¶w MH u (c ) t t t Can show that the Baily formula holds in this model: 0 u 0 e u (c )u (c ) 1e,b t t = e 0 u (c ) e t Combining yields formula that depends solely on duration elasticities:  ¶s /¶A t 1e,b t =   ¶s /¶b ¶s /¶A e t t t t 1e,A 1e,b = A e 1e,b 1e,A b Public Economics Lectures () Part 6: Social Insurance 81 / 178Intuition for Moral Hazard vs. Liquidity Formula Formula is a “revealed preference”approach to valuing insurance Infer value of UI to agent by observing what he would do if money given as a cash-grant without distorted incentives If agent would not use money to extend duration, infer that only takes longer because of price subsidy (moral hazard) But if he uses cash grant to extend duration, indicates that UI facilitates a choice he would make if markets were complete Same strategy can be used in valuing other types of insurance Make inferences from agent’s choices instead of directly computing costs and bene…ts of the policy Key assumption: perfect agent optimization Public Economics Lectures () Part 6: Social Insurance 82 / 178Moral Hazard vs. Liquidity: Evidence Two empirical strategies 1 Divide agents into liquidity constrained and unconstrained groups and estimate e¤ect of bene…ts on durations using changes in UI laws. 2 Look at lump-sum severance payments to estimate liquidity e¤ect. Public Economics Lectures () Part 6: Social Insurance 83 / 178TABLE 1 Summary Statistics by Wealth Quartile for SIPP Sample Net Liquid Wealth Quartile 1 2 3 4 ( ­1,115) (­1,115­128) (128­13,430) (13,430) Median Liq. Wealth 466 0 4,273 53,009 Median Debt 5,659 0 353 835 Median Home Equity 2,510 0 11,584 48,900 Median Annual Wage 17,188 14,374 18,573 23,866 Mean Years of Education 12.21 11.23 12.17 13.12 Mean Age 35.48 35.18 36.64 41.74 Fraction Renters 0.43 0.61 0.35 0.16 Fraction Married 0.64 0.59 0.60 0.63 All monetary variables in real 1990 dollars Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 84 / 178Figure 3a Effect of UI Benefits on Durations: Lowest Quartile of Net Wealth Mean rep. rate = .53 Mean rep. rate = .48 WilcoxonTest for Equality: p = 0.01 0 10 20 30 40 50 Weeks Unemployed Avg. UI benefit below mean Avg. UI benefit above mean Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 85 / 178 Fraction Unemployed .2 .4 .6 .8 1Figure 3b Effect of UI Benefits on Durations: Second Quartile of Net Wealth Mean rep. rate = .53 Mean rep. rate = .48 WilcoxonTest for Equality: p = 0.04 0 10 20 30 40 50 Weeks Unemployed Avg. UI benefit below mean Avg. UI benefit above mean Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 86 / 178 Fraction Unemployed .2 .4 .6 .8 1Figure 3c Effect of UI Benefits on Durations: Third Quartile of Net Wealth Mean rep. rate = .52 Mean rep. rate = .46 WilcoxonTest for Equality: p = 0.69 0 10 20 30 50 40 Weeks Unemployed Avg. UI benefit below mean Avg. UI benefit above mean Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 87 / 178 Fraction Unemployed .2 .4 .6 .8 1Figure 3d Effect of UI Benefits on Durations: Highest Quartile of Net Wealth Mean rep. rate = .52 Mean rep. rate = .43 WilcoxonTest for Equality: p = 0.43 0 10 20 30 40 50 Weeks Unemployed Avg. UI benefit below mean Avg. UI benefit above mean Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 88 / 178 Fraction Unemployed .2 .6 .8 1 .4TABLE 2 Effect of UI Benefits: Cox Hazard Model Estimates (1) (2) (3) (4) (5) Pooled Stratified Stratified with Full Controls Full cntrls No cntrls Avg WBA Max WBA Ind. WBA log UIben ­0.527 (0.267) Q1 x log UIben ­0.721 ­0.978 ­0.727 ­0.642 (0.304) (0.398) (0.302) (0.241) ­0.699 ­0.725 ­0.388 ­0.765 Q2 x log UIben (0.484) (0.420) (0.303) (0.219) Q3 x log UIben ­0.368 ­0.476 ­0.091 ­0.561 (0.309) (0.358) (0.370) (0.156) Q4 x log UIben 0.234 0.103 0.304 0.016 (0.369) (0.470) (0.339) (0.259) Q1=Q4 p­val 0.039 0.013 0.001 0.090 Q1+Q2=Q3+Q4 p­val 0.012 0.008 0.002 0.062 Number of Spells 4529 4337 4054 4054 4054 Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 89 / 178TABLE 3 TABLE 3 Summary Statistic Summary Statistics for s for Mat Mathematica hematica Da Data ta Pooled No Severance Severance (0.83) (0.17) Percent dr Percent dropouts opouts 14% 14% 15% 15% 6% 6% Percent college g Percent college grads rads 17% 17% 13% 13% 34% 34% Percent  Percent married married 58% 58% 56% 56% 68% 68% Mean age Mean age 36.2 36.2 35.2 35.2 40.6 40.6 Median pre Median pre­­unemp unemp annual wage annual wage 20,848 20,848 19,347 19,347 30,693 30,693 Median job tenure  Median job tenure (years) (years) 1.9 1.9 1.5 1.5 4.8 4.8 Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 90 / 178Figure 5 Effect of Severance Pay on Durations 0 5 10 15 20 Weeks Unemployed No Severance Received Severance Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 91 / 178 Fraction Unemployed .5 .6 .7 .8 .9 1Figure 6a Effect of Severance Pay on Durations: Below Median Net Wealth 0 5 10 15 20 Weeks Unemployed No Severance Received Severance Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 92 / 178 Fraction Unemployed .4 .6 .8 1Figure 6b Effect of Severance Pay on Durations: Above Median Net Wealth 0 5 10 15 20 Weeks Unemployed No Severance Received Severance Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 93 / 178 Fraction Unemployed .4 .6 .8 1TABLE 4 Effect of Severance Pay: Cox Hazard Model Estimates Pooled By  Liquid Wealth By Sev. Amt. Severance Pay ­0.233 (0.071) (Netliq  Median) x Sev Pay ­0.457 (0.099) (Netliq  Median) x Sev Pay ­0.088 (0.081) (Tenure  Median) x Sev Pay ­0.143 (0.055) (Tenure  Median) x Sev Pay ­0.340 (0.119) Equality of coeffs p­val 0.01 0.03 N=2428; all specs. include full controls. Source: Chetty 2008 Public Economics Lectures () Part 6: Social Insurance 94 / 178Chetty 2008: Implications for Optimal UI Plug reduced-form estimates of de/dA and de/db into formula to calculate dW/db Welfare gain from raising bene…t level by 10% from current level in U.S. (50% wage replacement) is 5.9 bil = 0.05% of GDP Small but positive In structural models calibrated to match su¢ cient statistics, dW/db falls rapidly with b Small dW/db suggests we are currently near optimal bene…t level Public Economics Lectures () Part 6: Social Insurance 95 / 178Card, Chetty, and Weber 2007 Use discontinuities in Austria’s unemployment bene…t system to estimate liquidity e¤ects Severance payment is made by …rms out of their own funds Formula for sev. pay amount for all non-construction workers: 3 2 0 0 36 60 Job Tenure Public Economics Lectures () Part 6: Social Insurance 96 / 178 Severance Amt. (months of pay)Figure 3 Frequency of Layoffs by Job Tenure 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 97 / 178 Number of Layoffs 0 10000 20000 30000 40000Age by Job Tenure 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 98 / 178 Mean Age 30 31 32 33 34Figure 4 Selection on Observables 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 99 / 178 Mean Predicted Hazard Ratios .8 .85 .9 .95Figure 5a Effect of Severance Pay on NonemploymentDurations 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 100 / 178 Mean Nonemployment Duration (days) 145 150 155 160 165TABLE 3a TABLE 3a Effects of Severance Pay and EB on Durations:  Effects of Severance Pay and EB on Durations: Hazard Model Estim Hazard Model Estimates ates (1) (1) (2) (2) (3) (3) Restricted Restricted Restricted Restricted Full Full Sample Sample Sample Sample Sample Sample Severan Severance p ce pay ay ­­0.122 0.122 ­­0.125 0.125 (0.019) (0.019) (0.017) (0.017) Extended be Extended benefits nefits ­­0.084 0.084 ­­0.093 0.093 (0.018) (0.018) (0.016) (0.016) Sample size Sample size 512,767 512,767 512,767 512,767 650,922 650,922 NOTE­­All specs are Cox hazard models that include cubic polynomials with interactions with sevpayand/or extended benefit dummy. Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 101 / 178Shimer and Werning 2007: Reservation-Wage Model Reservation wage model: probability of …nding job (e) determined by decision to accept or reject a wage o¤er, not search e¤ort Wage o¤ers drawn from distribution w F(x) Agent rejects o¤er if net wage wt is less than outside option b, implying that probability of …nding a job is e = 1F(b+t) Agent’s expected value prior to job search: W(b)=(1F(b+t))Eu(wt)jwt b+F(b+t)u(b) Reservation wage prior to job search satis…es u(w¯ t)= W(b) 0 Public Economics Lectures () Part 6: Social Insurance 102 / 178Shimer and Werning 2007: Reservation-Wage Formula Government’s problem is maxW(b)= maxu(w¯ t)= maxw¯ t 0 0 It follows that dW dw¯ dt 0 = db db db dw¯ 1e 1 0 = (1+  ) 1e,b db e e Public Economics Lectures () Part 6: Social Insurance 103 / 178Shimer and Werning 2007: Reservation-Wage Formula dw¯ 0 Implement formula using estimates of reported by Feldstein and db Poterba (1984) Find gains from raising UI bene…ts 5 times larger than Chetty (2008) But reservation wage elasticity estimates questionable Do greater bene…ts longer durations better outcomes later on? No. Ex: evidence from Austrian discontinuity (Card, Chetty, Weber 2007) Note: all the formulas above take such match quality gains into account via envelope conditions Public Economics Lectures () Part 6: Social Insurance 104 / 178Figure 5a Effect of Severance Pay on NonemploymentDurations 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 105 / 178 Mean Nonemployment Duration (days) 145 150 155 160 165Figure 10a Effect of Severance Pay on Subsequent Wages 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 106 / 178 Wage Growth ­.1 ­.08 ­.06 ­.04 ­.02 0Figure 10b Effect of Severance Pay on Subsequent Job Duration 12 18 24 30 36 42 48 54 60 Previous Job Tenure (Months) Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 107 / 178 Average Monthly Job Ending Hazard in Next Job ­.05 0 .05 .1 .15 .2Figure 9a Effect of Benefit Extension on NonemploymentDurations 12 18 24 30 36 42 48 54 60 Months Employed in Past Five Years Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 108 / 178 Mean Nonemployment Duration (days) 135 140 145 150 155 160 165Effect of Extended Benefits on Subsequent Wages 12 18 24 30 36 42 48 54 60 Months Worked in Past Five Years Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 109 / 178 Wage Growth ­.1 ­.05 0 .05 .1Effect of Extended Benefits on Subsequent Job Duration 12 18 24 30 36 42 48 54 60 Months Worked in Past Five Years Source: Card, Chetty, and Weber 2007 Public Economics Lectures () Part 6: Social Insurance 110 / 178 Average Monthly Job Ending Hazard in Next Job ­.15 ­.1 ­.05 0 .05Spike at Bene…t Exhaustion Most striking evidence for distortionary e¤ects of social insurance: “spike”in hazard rate at bene…t exhaustion Katz and Meyer (1990), Meyer (1990), ... Traditional measure of hazard: exiting UI system Preferred measure based on theory: …nding a job The two could di¤er if workers transit o¤ of UI but are still jobless Ex. may not go to pick up last unemployment check Particularly important in European context, where you can remain registered on UI inde…nitely Public Economics Lectures () Part 6: Social Insurance 111 / 178Time Until Benefits Lapse Empirical Hazard 20 15 10 5 0 Weeks of Eligibility Left Source: Meyer 1990 Public Economics Lectures () Part 6: Social Insurance 112 / 178 Unemployment Exit Hazard 0 .05 .1 .15 .2Job Finding vs. Unemployment Exit Hazards: 20 Week UI 0 10 20 30 40 50 Weeks Elapsed Since Job Loss Job Finding Hazards Unemp Exit Hazards Source: Card, Chetty, Weber 2007b (AER P&P) Public Economics Lectures () Part 6: Social Insurance 113 / 178 Weekly Hazard Rate 0 .05 .1 .15 .2Job Finding vs. Unemployment Exit Hazards: 30 Week UI 0 10 20 30 40 50 Weeks Elapsed Since Job Loss Job Finding Hazards Unemp Exit Hazards Source: Card, Chetty, Weber 2007b (AER P&P) Public Economics Lectures () Part 6: Social Insurance 114 / 178 Weekly Hazard Rate 0 .05 .1 .15 .2Effect of Benefit Expiration on Hazard Rates 0 10 20 30 40 50 Weeks Elapsed Since Job Loss Unemployment Exit Hazards Job Finding Hazards Source: Card, Chetty, Weber 2007b (AER P&P) Public Economics Lectures () Part 6: Social Insurance 115 / 178 Difference in Weekly Hazard UI20­UI30 ­.1 ­.05 0 .05 .1UI and Firm Behavior Preceding discussion assumed perfect experience rating of UI Firms’layo¤ incentives are not distorted But in practice, UI is not perfectly experience rated Feldstein (1976, 1978) shows: Theoretically that imperfect experience rating e¤ect can raise rate of temporary layo¤s Empirically that this e¤ect is large in practice Public Economics Lectures () Part 6: Social Insurance 116 / 178Experience Rating in Washington, 2005 0 2 4 6 8 10 Benefit Ratio (100UI Benefits Paid/Payroll) Washington’ s UI Tax Schedule Perfect Experience Rating Source: Washington State Joint Legislative Task Force on Unemployment Insurance Benefit Equity 2005 Public Economics Lectures () Part 6: Social Insurance 117 / 178 UI Tax Rate (%) 0 2 4 6 8 10UI and Firm Behavior: Feldstein 1976 model Firms o¤er workers stochastic contracts, with wage and probability of temporary layo¤ Two states: high demand and low demand In equilibrium, competitive …rms will o¤er contract that pays worker his marginal product in expectation over two states at cheapest cost to …rm Firm pro…ts by laying o¤ workers with imperfect exp rating Layo¤s generate …rst-order gain in pro…ts at a second-order cost from added risk to worker In an imperfectly experience-rated economy, …rms choose a positive rate of layo¤s in low output state Public Economics Lectures () Part 6: Social Insurance 118 / 178Feldstein 1978: Empirical Results First observation: more than half of …rms are above the max rate or below the min rate No marginal incentive for these …rms to reduce layo¤s. Uses cross-state/time variation in UI bene…ts 10% increase in UI bene…ts causes a 7% increase in temp layo¤ unemployment E¤ect is twice as large for union members as non-union, suggesting worker-…rm coordination. Public Economics Lectures () Part 6: Social Insurance 119 / 178Topel 1983 Feldstein does not directly show that imperfect exp rating is to blame for more temp layo¤s b/c not using variation in experience rating itself Topel (1983) uses state/industry variation in …nancing of UI Variation in tax rate on …rms from min/max thresholds for exp rating Finds that imperfect subsidization accounts for 31% of all temp layo¤ unemployment, a very large e¤ect See Krueger and Meyer (2002) for review of more recent studies, which …nd similar results but smaller magnitudes Public Economics Lectures () Part 6: Social Insurance 120 / 178UI Savings Accounts Alternative to UI transfer-based system (Feldstein and Altman 2007) Instead of paying UI tax to government, pay into a UI savings account. If unemployed, deplete this savings account according to current bene…t schedule If savings exhausted, government pays bene…t as in current system (…nanced using a tax). Idea: people internalize loss of money from staying unemp longer. Reduces distortion from UI while providing bene…ts as in current system. But modelling this formally is di¢ cult: to internalize incentives at retirement, people must be forward looking, but then no need to force them to save. Public Economics Lectures () Part 6: Social Insurance 121 / 178Feldstein and Altman 2007 Address feasibility: How many people hit negative balance on UI account and just go back to old system? Simulate how UI savings accounts would evolve using actual earnings histories from PSID. Calculations imply that only 1/3 of spells will occur with negative balances, so most people still have good incentives while unemployed. Total tax payments are less than half what they are in current system. In their simulation, bene…ts are identical; only question is how costs change. Public Economics Lectures () Part 6: Social Insurance 122 / 178Feldstein and Altman 2007 Calculation of changes in present value of lifetime wealth from switch to UISA by income quintile: Q1 Q2 Q3 Q4 Q5 Present Value Gain: -95 +22 -67 +94 +468 Net PVG is positive Without change in behavior, how is the pie larger? Reason: discounting at 2% but earning 5.5% interest Public Economics Lectures () Part 6: Social Insurance 123 / 178Takeup Mean takeup rate is very low –a major puzzle in this literature (Currie 2004) Why leave money on the table? Andersen and Meyer (1997) show that after-tax UI replacement rate a¤ects level of takeup. So at least some seem to be optimizing at the margin. Takeup low in many govt. programs. (UI, food stamps, EITC, etc.) Possible explanations: myopia, stigma, hassle, lack of info. Public Economics Lectures () Part 6: Social Insurance 124 / 178Black, Smith, Berger, and Noel 2003 Experiment in KY where some UI claimants were randomly assigned to receive re-employment services E.g., assisted job search, employment counseling, job search workshops, retraining programs Treatment N = 1236 required to receive services in order to get UI bene…ts Control N = 745: exempt from services Public Economics Lectures () Part 6: Social Insurance 125 / 178Public Economics Lectures () Part 6: Social Insurance 126 / 178Public Economics Lectures () Part 6: Social Insurance 127 / 178Public Economics Lectures () Part 6: Social Insurance 128 / 178Black, Smith, Berger, and Noel 2003: Results Treatment group exit UI system earlier, receiving 2.2 fewer weeks of bene…ts on average Most signi…cant increase in exits in wks 2-3, when noti…ed of mandatory services Public Economics Lectures () Part 6: Social Insurance 129 / 178General Equilibrium: Acemoglu and Shimer 1999 UI can be e¢ ciency-enhancing in equilibrium. Standard models focus only on distortionary costs, and assume that total output always lower when UI is provided. But this ignores potentially important GE e¤ect: more risky jobs provided in eq. if workers are insured. Provision of UI raises availability of risky jobs (e.g. tech jobs) and can raise e¢ ciency in equilibrium So if workers are risk averse, tradeo¤ may not be very hard –both raise output and insure them better. Public Economics Lectures () Part 6: Social Insurance 130 / 178Dynamics: Path of UI Bene…ts Classic reference is Shavell and Weiss (1979), who solved for optimal path of bene…ts in a 3 period model. Tradeo¤: upward sloping path more moral hazard but more consumption-smoothing bene…ts. Recent literature that is very active in this area: “new dynamic public …nance”–optimal path of unemployment and disability programs. Hopenhayn and Nicolini (1997) –numerical simulations for case where govt can control consumption Shimer and Werning (2008) –with perfect liquidity and CARA utility, optimal bene…t path is ‡at Public Economics Lectures () Part 6: Social Insurance 131 / 178Optimal Insurance in Behavioral Models We do not have a model consistent with the data that can explain both savings behavior pre-unemployment and search behavior post-unemployment Evidence that unemployment is indeed costly and bene…ts can improve welfare a lot for certain liquidity-constrained groups Simple rational model cannot rationalize level of savings that people have when they get unemployed Interesting direction for future research: optimal SI with behavioral considerations (see e.g., Spinnewijn 2009) Public Economics Lectures () Part 6: Social Insurance 132 / 178Workers Compensation Insurance against injury at work Covers both lost wages and medical bene…ts Rationales for govt. intervention: Market may fail due to adverse selection Workers may be unaware of risks on the job Litigation costs (origin of system in 1920s) Substantial variation in bene…ts across states for di¤erent injuries Public Economics Lectures () Part 6: Social Insurance 133 / 178Maximum Indemnity Benefits in 2003 Type of permanent impairment State Arm Hand Index finger Leg Foot Temporary Injury (10 weeks) California 108,445 64,056 4,440 118,795 49,256 6,020 Hawaii 180,960 141,520 26,800 167,040 118,900 5,800 Illinois 301,323 190,838 40,176 276,213 155,684 10,044 Indiana 86,500 62,500 10,400 74,500 50,500 5,880 Michigan 175,657 140,395 24,814 140,395 105,786 6,530 Missouri 78,908 59,521 15,305 70,405 52,719 6,493 New Jersey 154,440 92,365 8,500 147,420 78,200 6,380 New York 124,800 97,600 18,400 115,200 82,000 4,000 Source: Gruber 2007 Public Economics Lectures () Part 6: Social Insurance 134 / 178Theory of Workers’Compensation Formally very similar to that of unemployment insurance If prob of injury cannot be controlled, model same as Baily-Chetty If prob of injury can be controlled, that distortion must be taken into account in calculation Leisure now includes bene…ts of having more time to heal Similar formal theory, so literature is mostly empirical Public Economics Lectures () Part 6: Social Insurance 135 / 178Outline of Empirical Evidence 1 Monday e¤ects and impact on worker behavior 2 Firm side responses 3 E¤ect on equilibrium wage Public Economics Lectures () Part 6: Social Insurance 136 / 178Public Economics Lectures () Part 6: Social Insurance 137 / 178Day of the Week E¤ect Intertemporal distortions, moral hazard e¤ect of workers’comp. Card & McCall (1994): test if weekend injuries lead to Monday e¤ect. Look at uninsured workers, who should have bigger Monday e¤ect. Find no di¤erence in e¤ect between insured and uninsured. Other explantations: Gaming system for more days o¤. Pure reporting e¤ect if pain does not go away. Suggests that incentives matter a lot. Public Economics Lectures () Part 6: Social Insurance 138 / 178E¤ects of Bene…ts on Injuries Potential incentive e¤ects to look for on worker’s side: Number of claims of injury Duration of injuries Meyer, Viscusi, and Durbin (1995): Implement DD analysis for workers’comp durations Find large e¤ects on duration using reforms in MI and KY Public Economics Lectures () Part 6: Social Insurance 139 / 178Public Economics Lectures () Part 6: Social Insurance 140 / 178Public Economics Lectures () Part 6: Social Insurance 141 / 178Firm Side Responses Purchasing insurance leads to imperfect experience rating and moral hazard Self-insured …rms: stronger incentives to improve safety Also, have incentive to ensure that workers return to work quickly Krueger (1990): compares behavior of self-insured …rms with others Finds self-insured have 10% shorter durations But could be biased by selection Public Economics Lectures () Part 6: Social Insurance 142 / 178E¤ect on Equilibrium Wage Workers’compensation is a mandated bene…t When …rms hire, should adjust wage downwards if workers value bene…t (Summers 1989) Gruber-Krueger (1991) test this using changes in WC laws 85% of WC cost is shifted to workers, no signi…cant employment e¤ect Fishback-Kantor (1995) study initial implementation of program Find 100% shift to workers’wages Both studies suggest that bene…ts valued close to cost Public Economics Lectures () Part 6: Social Insurance 143 / 178Directions for Further Research on WC Decomposition into liquidity vs. moral hazard e¤ects Better evidence on …rm side responses Consumption smoothing bene…ts Public Economics Lectures () Part 6: Social Insurance 144 / 178Disability Insurance See Bound et. al (HLE 1999) for an overview Insures against long-term shocks that a¤ect individuals at home or work Federal program that is part of social security Eligible if unable to “engage in substantial gainful activity”b/c of physical/mental impairment for at least one (expected) year Main focus of literature is sharp rise in the size of the program Public Economics Lectures () Part 6: Social Insurance 145 / 178Source: Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 146 / 178Two Views on the Rise in DI One perspective: moral hazard from a lenient system that leads to ine¢ ciency Another perspective: program is now helping more needy people who have high disutilities of work Empirical work attempts to distentangle these two views Public Economics Lectures () Part 6: Social Insurance 147 / 178Public Economics Lectures () Part 6: Social Insurance 148 / 178Theory of Disability Insurance Key additional element relative to UI models is screening and waiting periods Less relevant for unemployment because it is easy to identify who has a job and who does not Diamond-Sheshinski (1995) build a model that incorporates screening Characterize optimal properties of solution but do not derive an empirically implementable formula for optimal screening rule or bene…t level Public Economics Lectures () Part 6: Social Insurance 149 / 178Diamond and Sheshinski 1995 Individuals have di¤erent disutilities of working y i To max social welfare, not desirable for those with high y to work. i First best: Individual i works i¤ Marginal product y i But govt observes only an imperfect signal of y sets a higher i threshold for disability Result: lower bene…t rate if screening mechanism has higher noise to signal ratio Public Economics Lectures () Part 6: Social Insurance 150 / 178Empirical Evidence: Bound-Parsons Debate Question: Did increase in DI bene…ts cause decline in labor supply? Well-known debate between Bound & Parsons in 1980’s is of methodological interest Parsons (1980) Uses cross-sectional variation in replacement rates Data on men aged 45-59 in 1966-69 NLSY OLS regression: LFP = a+bDIreprate + i i i where DIreprate is calculated using wage in 1966 Finds elasticity of 0.6 Simulations using this elasticity imply that increase in DI can completely explain decline in elderly labor force participation Public Economics Lectures () Part 6: Social Insurance 151 / 178Empirical Evidence: Bound-Parsons Debate Bound highlights key econometric problem in Parson’s speci…cation DIreprate variation correlated with wage Identi…cation assumption: LFP rates equal across wage groups Parson’s solution: “control”for wage rate LFP = a+bDIreprate +f(wage )+ i i i i Does this resolve the problem? Public Economics Lectures () Part 6: Social Insurance 152 / 178Identi…cation by Functional Form LFP = a+bDIreprate +f(wage )+ i i i i This is an example of identi…cation by “functional form” As f is made increasingly ‡exible, standard error on b goes to in…nity Problem is that only source of variation is due to wages To illustrate practice importance, Bound replicates Parson’s regression on sample that never applied to DI and obtains a similar elasticity Motivates literature that focuses on quasi-experiments other sources of non-parametric identi…cation Key idea of non-parametric identi…cation: with su¢ ciently large samples, estimate is identi…ed without parametric assumptions on f Impose functional forms only for computational convenience and precision in …nite samples Public Economics Lectures () Part 6: Social Insurance 153 / 178Empirical Evidence: Bound-Parsons Debate Bound (1990) proposes a technique to bound e¤ect of DI on LFP rate Uses data on LFP of rejected applicants as a counterfactual Idea: if rejected applicants do not work, then surely DI recipients would not have worked Rejected applicants’LFP rate is an upper bound for LFP rate of DI recipients absent DI Illustrate using better data from Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 154 / 178Source: Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 155 / 178Gruber 2000 Exploits di¤erential law change in Quebec and rest of Canada as a natural experiment In 1987, 36% inc. in bene…ts in rest of Canada; in Quebec, no change Estimates e¤ect of law change on labor force participation of men aged 45-59 Uses DD method on NLFP rates of men aged 45-59 Public Economics Lectures () Part 6: Social Insurance 156 / 178Public Economics Lectures () Part 6: Social Insurance 157 / 178Public Economics Lectures () Part 6: Social Insurance 158 / 178Gruber 2000 Implied elasticity of non-employment rate w.r.t. DI bene…t level: 0.25-0.3 Agrees more with Bound than Parsons But estimates are imprecise and only capture short-run e¤ects Public Economics Lectures () Part 6: Social Insurance 159 / 178Maestas, Mullen, Strand 2012 Maestas, Mullen, and Strand (2012) use random variation in examiner assignment to identify e¤ects of DI Disability cases randomly assigned by computer to examiners at state board Substantial discretion generates signi…cant variation across examiners in allowance rates Instrument for receipt of DI w/ examiner’s conditional allowance propensity Another approach: use set of examiner f.e.’s as instruments Use administrative data on DI decisions and earnings from SSA 1 million observations Public Economics Lectures () Part 6: Social Insurance 160 / 178Source: Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 161 / 178Maestas, Mullen, Strand 2012 Estimate causal e¤ects of DI on employment rates using IV regressions First stage: DI = a+f examiner +n i i i i Second stage: y = a+bDI + i i i Note that …rst stage coe¤s. f are average DI allowance rates by i examiner Therefore IV regression is equivalent to examiner-level OLS regression y = a+bDI + e e e Weighting this OLS regression by number of individuals per examiner will yield identical estimate of b Public Economics Lectures () Part 6: Social Insurance 162 / 178Source: Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 163 / 178Maestas, Mullen, Strand 2012 Conclude that DI receipt reduces probability of employment by 28% for marginal applicants Important to recognize that this is a LATE for people who are at the margin of getting DI Severely disabled individuals would be granted DI by all examiners and are not captured in this LATE Hence should be interpreted as an upper bound on ATE Maestas et al. con…rm this by studying heterogeneity in treatment e¤ects by disease severity Public Economics Lectures () Part 6: Social Insurance 164 / 178Source: Mullen, Maestas, Strand (2012) Public Economics Lectures () Part 6: Social Insurance 165 / 178Maestas, Mullen, Strand 2012 Results highlight importance of estimating relevant LATE for policy If policy question is raising DI bene…t, relevant treatment e¤ect is for people on margin w.r.t. bene…t change May not be the same people as those who are on the margin with respect to examiner decision This is the advantage of directly studying the policy of interest Does not require extrapolations from estimated LATE to the policy-relevant su¢ cient statistic Also important to note that paper estimates uncompensated elasticities Critical to distinguish moral hazard vs. liquidity for normative purposes Might still have people with disutility j w working when rejected i i Public Economics Lectures () Part 6: Social Insurance 166 / 178Methodological Note: Weak Instruments Random assignment instrument to judges, classes, etc. now popular in many applications Common problem: weak instruments Arises when each examiner has few cases Not an issue in Maestas et al. but common e.g. in education with 20 kids per class In this case, IV estimate of b will be biased toward OLS Public Economics Lectures () Part 6: Social Insurance 167 / 178Weak Instruments Problem Recall examiner-level OLS regression y = a+bDI + e e e Same observation appears on LHS and RHS of this regression With few individuals, this biases b toward OLS Extreme case: one individual per examiner equivalent to OLS If an examiner gets a draw of particularly sick people, they will both get DI and have low employment rates even if DI has no causal e¤ect Public Economics Lectures () Part 6: Social Insurance 168 / 178Weak Instruments Problem Problem vanishes as number of individuals per examiner grows large Only remaining variation in DI is due to examiner e¤ects e Key question: does number of instruments grow at same rate as sample size? If sample gets bigger by adding more people per examiner, then instruments are asymptotically strong If sample gets bigger by adding more examiners, then instruments and asymptotically weak Public Economics Lectures () Part 6: Social Insurance 169 / 178Weak Instruments: Solutions How to obtain unbiased estimates with weak instruments? Traditional recommendation: LIML Currently preferred alternative: Jackknife IV Leave out own observation for each i when estimating DI in …rst stage e Second stage regression becomes y = a+bDI + i j6=i i Directly …xes own-observation problem and is more robust than LIML (Kolesar et al. 2012, Kolesar 2012) Public Economics Lectures () Part 6: Social Insurance 170 / 178Autor and Duggan 2003 Focus on interaction between DI and UI systems Observe that DI claims rise in recessions, may reduce measured unemployment rate Idea: consider a worker laid o¤ in current recession Given generosity of DI program, instead of claiming UI and searching for a job, he applies for DI One less unemployed person – unemployment rate lower But economic situation is the same: one less person working Test this hypothesis using cross-state variation in employment shocks Public Economics Lectures () Part 6: Social Insurance 171 / 178Autor and Duggan 2003: Bartik Shocks Standard technique to construct state-level employment shocks over a …ve year window: Calculate industry shares in a given state in base year Calculate employment changes over …ve year period by industry using data on national employment (excluding state in question) Project changes in each state’s employment using national changes Ex: if car industry declines over a …ve year period, assign a negative employment shock to Michigan Then correlate state employment shocks with DI applications Public Economics Lectures () Part 6: Social Insurance 172 / 178Public Economics Lectures () Part 6: Social Insurance 173 / 178Employment Shocks and DI Applications: 1979­1984 8 6 MS 4 AR AL GA LA WV 2 KY FL AZ MO MT TN MISC NC OK MA ME PA OH CT IL 0 RI TX NY CA NV VT NJ DE VA MD NM IN IA OR CO MN KS WA NE WI SD ND ­2 NH UT WY HI ID AK ­4 ­6 Coefficient = ­0.094, se = 0.062, t = ­1.51 ­8 ­8 ­6 ­4 ­2 0 2 4 6 8 EChange in Employment/Pop  X Source: Autor and Duggan 2003 Public Economics Lectures () Part 6: Social Insurance 174 / 178 EDI Apps/Pop  XEmployment Shocks and DI Applications: 1984­1989 8 6 MS 4 LA AR KY WV 2 GA MI MT SC OK ME MO AL TX NM FL IN NC TN WA SD RI OH NY 0 KS VA OR PA DE CO IL NV MA CA WY MD AZ IA VT WI HI NE ND MN NJ ID CT NH AK ­2 UT ­4 ­6 Coefficient = ­0.262, se = 0.067, t = ­3.90 ­8 ­8 ­6 ­4 ­2 0 2 4 6 8 EChange in Employment/Pop  X Source: Autor and Duggan 2003 Public Economics Lectures () Part 6: Social Insurance 175 / 178 EDI Apps/Pop  XEmployment Shocks and DI Applications: 1989­1994 8 6 MS WVKY AR 4 AL LA 2 MO SC TN IA NC MA ME NM INGA CO FL TX WA MI MT NV OR OK SD NH AZ 0 DE NY OH WI PA CAIL ID MN UT VT VA RI MD NJ KS WY NE ND ­2 HI CT AK ­4 ­6 Coefficient = ­0.343, se = 0.130, t = ­2.64 ­8 ­8 ­6 ­4 ­2 0 2 4 6 8 EChange in Employment/Pop  X Source: Autor and Duggan 2003 Public Economics Lectures () Part 6: Social Insurance 176 / 178 EDI Apps/Pop  XEmployment Shocks and DI Applications: 1993­1998 8 MS 6 AR WV KY 4 AL SC NC TN ME 2 MO OK DE RI FL GA LA NM KS MT IN NY MI PA MA WY VT 0 CT SDVAAZ NV NE ID OH NH OR IL TX IA WAHI CA NJ MD CO WI AK MN ­2 ND UT ­4 ­6 Coefficient = ­0.849, se = 0.164 t = ­5.18 ­8 ­8 ­6 ­4 ­2 0 2 4 6 8 EChange in Employment/Pop  X Source: Autor and Duggan 2003 Public Economics Lectures () Part 6: Social Insurance 177 / 178 EDI Apps/Pop  XAutor and Duggan 2003 Unemployment would be 0.65% higher if not for post-‘84 trends in DI participation Trace decline in LFP to the rise in DI over the past two decades via: The 1984 inclusion of mental illness in DI eligibility Rising wage inequality (combined with the progressivity of system) Bottom line: DI applications are clearly sensitive to incentives But evidence is insu¢ cient to make welfare statements Essential to decompose bene…t e¤ects into income and price elasticities to make normative judgment Public Economics Lectures () Part 6: Social Insurance 178 / 178Public Economics Lectures Part 7: Public Goods and Externalities Raj Chetty and Gregory A. Bruich Harvard University Fall 2012 Public Economics Lectures () Part 7: Public Goods and Externalities 1 / 111Externalities: Outline 1 De…nition and Basic Model 2 Correcting Externalities 3 Prices vs. Quantities (Weitzman 1974) 4 2nd Best Taxation with Externalities (Sandmo 1975) 5 Empirical Applications Public Economics Lectures () Part 7: Public Goods and Externalities 2 / 111De…nition An externality arises whenever the utility or production possibility of an agent depends directly on the actions of another agent. Important distinction between “pecuniary”vs. “non-pecuniary” externalities Consuming an apple vs. consuming loud music Not a technological distinction; depends on market in place Coasian view: can convert all externalities into pecuniary externalities with appropriate markets, property rights. Only non-pecuniary externalities justify policy intervention Public Economics Lectures () Part 7: Public Goods and Externalities 3 / 111Externalities: Main Questions 1 Theoretical: what is the best way to correct externalities and move closer to the social optimum? 2 Empirical: how to measure the size of externalities? Key di¤erence: cannot use revealed-preference Public Economics Lectures () Part 7: Public Goods and Externalities 4 / 111Model of Externalities Firms produce x cars using c(x) units of the numeraire y Generates x units of pollution: P(x)= x Consumers have wealth Z and quasilinear utility: u(x)+ydP(x) where d = marginal damage (MD) of pollution Social welfare is W = u(x)+Zc(x)dx Let p denote the market price of cars Public Economics Lectures () Part 7: Public Goods and Externalities 5 / 111Model of Externalities: Equilibrium Firms max pro…ts: maxpxc(x) Consumers max utility, taking level of pollution as …xed: maxu(x)+Zpx Demand satis…es 0 D u (x )= p Supply satis…es 0 S c (x )= p PMB equals PMC in equilibrium: 0 D 0 S u (x )= c (x ) But this is not Pareto e¢ cient Public Economics Lectures () Part 7: Public Goods and Externalities 6 / 111Negative Production Externalities: Pollution SMC=PMC+MD Price S=PMC P P M MD D =PMB =SMB 0 Q Q Quantity M Public Economics Lectures () Part 7: Public Goods and Externalities 7 / 111Model of Externalities: Deadweight Loss Perturbation argument: can increase social welfare by reducing production byDx: 0 0 dW = u (x)Dxc (x)DxdDx = dDx 0 ifDx 0 First Welfare Theorem does not hold Analogous result for consumption externalities Public Economics Lectures () Part 7: Public Goods and Externalities 8 / 111Negative Consumption Externalities Price S=PMC=SMC P M MD P D =PMB SMB=PMB­MD 0 Q Quantity Q M Public Economics Lectures () Part 7: Public Goods and Externalities 9 / 111Remedies for Externalities 1 Coasian bargaining solution 2 Pigouvian corrective taxation 3 Regulation 4 Permits (cap-and-trade) Public Economics Lectures () Part 7: Public Goods and Externalities 10 / 111Coasian Solution Externalities emerge because property rights are not well de…ned. Establish property rights to create markets for pollution. Consider example of pollution in a river. If consumer owns river, in competitive equilibrium, …rms pay d for every unit of pollution emitted. 0 Marginal cost of production is now c (x)+d, leading to 1st best. Symmetric solution when …rm owns river. Assignment of property rights a¤ects distribution but not e¢ ciency Public Economics Lectures () Part 7: Public Goods and Externalities 11 / 111Coasian Solution: Limitations 1 Cost of bargaining Ex: air pollution –would require millions of agents to coordinate and bargain To reduce transactions costs, need an association to represent agents This “association”is the government 2 Asymmetric information: competitive equilibrium can break down Often hard to identify precise source of damage E.g. atmospheric pollution very di¤use, marginal damages unclear Public Economics Lectures () Part 7: Public Goods and Externalities 12 / 111Pigouvian Taxation  Impose tax t = MD(Q ) Restores Pareto e¢ ciency and maximizes social welfare Practical limitations: Must know marginal damage function to set t Di¢ cult to measure the marginal damage in practice Public Economics Lectures () Part 7: Public Goods and Externalities 13 / 111PigouvianTax SMC=PMC+MD Price S=PMC+t S=PMC t P P 2 P 1 D =PMB =SMB 0 Q Q Q Quantity 2 1 Public Economics Lectures () Part 7: Public Goods and Externalities 14 / 111Regulation Quantity-based restriction: reduce pollution to …xed level or face legal sanctions Same outcome as Pigouvian taxation: move people to x 2 Disadvantages: no marginal incentives Allocative ine¢ ciency with heterogeneity in costs of pollution reduction Dynamic ine¢ ciency: no incentive to innovate These problems can be solved by cap and trade system Public Economics Lectures () Part 7: Public Goods and Externalities 15 / 111Permits: Cap-and-Trade Cap total amount of pollution and auction permits to …rms Then allow …rms to trade permits to pollute Hybrid of regulation and Coasian solution: create the market In eq., …rms with highest MC of reducing pollution will buy permits; those that can easily reduce pollution will do so If total number of permits is set to achieve the social optimum, both allocative and productive e¢ ciency will be achieved Also have dynamic incentives to innovate because each …rm is bearing a marginal cost of pollution Public Economics Lectures () Part 7: Public Goods and Externalities 16 / 111Weitzman 1974: Prices vs. Quantities Price mechanism (taxes) identical to quantity mechanism (permits) in simple model above. How to choose? Weitzman (1974): with uncertainty re. shape of MB and MC curves, price and quantity no longer equivalent Now the standard method of choosing between regulation and taxes Public Economics Lectures () Part 7: Public Goods and Externalities 17 / 111Weitzman 1974: Prices vs. Quantities Let q denote pollution reduction starting from private market eq., where q = 0. Let B(Q) denote social bene…ts of pollution reduction Let C(Q) denote social costs. In simple model above: 0 MB of pollution reduction is constant, B (Q)= d. 0 0 MC given by loss in surplus from producing one less car: u (x)c (x). More generally, MC should be interpreted as cost of reducing pollution through cheapest method (e.g. cleaner plants) Public Economics Lectures () Part 7: Public Goods and Externalities 18 / 111Market for Pollution Reduction Price PMC =SMC Q Q SMB Q Q Pollution Reduction Public Economics Lectures () Part 7: Public Goods and Externalities 19 / 111Optimal Policy without Uncertainty In eq’m, PMB of pollution reduction is 0) level of pollution reduction is Q = 0. Social optimum: maxB(Q)C(Q) First order condition: 0  0  C (Q )= B (Q ) With no uncertainty, can obtain optimum with either quantity or price policy.  Quantity: require amount Q .  0  Price: set price for pollution reduction of p = C (Q ). Public Economics Lectures () Part 7: Public Goods and Externalities 20 / 111Optimal Policy with Uncertainty Now suppose that there is uncertainty about the marginal costs of reducing pollution. Cost is now C(Q,q) with q unknown. Marginal cost lies between MC and MC , with mean value given LB UB by MC . mean Objective: maximize expected social welfare:   ?   E B(Q )C(Q ,q) E B(Q(p ))C(Q(p ),q) q q 00 00 Optimal choice depends on B (Q)/C (Q) Quantity regulation preferred if MB steep relative to MC Public Economics Lectures () Part 7: Public Goods and Externalities 21 / 111MB steep, Quantity regulation Public Economics Lectures () Part 7: Public Goods and Externalities 22 / 111MB Steep, Price Regulation Public Economics Lectures () Part 7: Public Goods and Externalities 23 / 111Quantity Regulation Price Regulation Public Economics Lectures () Part 7: Public Goods and Externalities 24 / 111Price Band vs. Quantity Band with Steep MB Public Economics Lectures () Part 7: Public Goods and Externalities 25 / 111MB Flat, Quantity MB Flat, Price Regulation regulation Public Economics Lectures () Part 7: Public Goods and Externalities 26 / 111Weitzman: Uncertainty about Bene…ts Now suppose that there is uncertainty about the marginal bene…ts of reducing pollution but that the costs are known Price and quantity policies are again equivalent For a given p, the government knows the Q that will result exactly 0 since p = C (Q) More generally, uncertainty matters only when it is about the cost/bene…t schedule for the agent who chooses level of pollution reduction If consumer chooses level of pollution reduction, then only uncertainty about marginal bene…ts matters Public Economics Lectures () Part 7: Public Goods and Externalities 27 / 111Optimal Second-Best Taxation with Externalities In general, cannot restore 1st best b/c externality is one of many deviations from …rst best. Most important other deviation: govt also uses distortionary taxes to …nance public goods and redistribute income. Sandmo (1975): optimal tax policy with externalities and a revenue requirement. Combination of Ramsey and Pigou problems Public Economics Lectures () Part 7: Public Goods and Externalities 28 / 111Sandmo 1975: Setup Denote by d(x ) the externality cost of consumption of good N N Let w be the wage rate and q = p +t denote post-tax prices. i i i Let Z denote non wage income. Producer prices …xed; all pre tax prices normalized to 1. Individuals have utility functions of the following form: u(x , ..,x ,l)d(x ) 1 N N Utility is maximized subject to: q x + ..+q x  wl+Z 1 1 N N Public Economics Lectures () Part 7: Public Goods and Externalities 29 / 111Sandmo 1975: Setup Individual maximization program L= u(x , ..,x ,l)+l(wl+Z(q x + ..+q x )) 1 1 1 N N N Maximization yields indirect utility v(q). Government maximization program: maxW(q) = v(q)d(q) q s.t. t x  R å i i Analogous to Ramsey tax problem, but here SWF di¤ers from private sector objective Public Economics Lectures () Part 7: Public Goods and Externalities 30 / 111Sandmo 1975 Let q = marginal social welfare gain from 1 of a lump sum tax and l= marginal value of relaxing agent’s budget constraint t = optimal Pigouvian tax rate (when R = 0) ip 0 t = 0 for goods 1 to N1 and t = d (x ) for good N ip ip N t = optimal Ramsey tax rate (when d(x )= 0) ir n Let t denote optimal tax rate in Sandmo model i Public Economics Lectures () Part 7: Public Goods and Externalities 31 / 111Sandmo 1975: Additivity Result Main result: can express optimal tax rate as Ramsey rate plus Pigouvian correction. Consider case where Slutsky matrix is diagonal (zero cross-price elasticities) Then optimal tax on good i, t satis…es i t t i ip c = (q/l)/e ii 1+t i c c qx dx i i ) t = / +t i ip l dp i = t +t ip ir Public Economics Lectures () Part 7: Public Goods and Externalities 32 / 111Sandmo 1975: Additivity Result Useful analytic representation but not an explicit formula for the optimal tax rate Ramsey tax will a¤ect level of cons, which a¤ects optimal Pigouvian tax Conversely, Pigouvian tax will a¤ect optimal Ramsey tax rate Qualitative lesson: no justi…cation to tax goods that are complementary to those that produce negative externalities Just tax fuel, not cars Public Economics Lectures () Part 7: Public Goods and Externalities 33 / 111Double Dividend Debate Claim: gas tax has two “dividends” 1 discourages pollution, raising social welfare 2 allows govt. to reduce other distortionary taxes, improving e¢ ciency True if we are at a corner where revenue req. is below level what is generated by optimal Pigouvian taxes More realistic case: already at a Ramsey-tax interior optimum Public Economics Lectures () Part 7: Public Goods and Externalities 34 / 111Double Dividend Debate Suppose we discover that production of computers generates negative externality. Is there a “double dividend”from taxing computers? No. Already at Ramsey optimum no e¢ ciency gain from raising taxes on PC’s and reducing taxes on other goods Only get single dividend of improving environment Obtain double dividend only if taxes on polluting good were initially too low from a Ramsey perspective. General lesson: separate externality and optimal second-best tax problems. Measure externalities and identify optimal corrective taxes without worrying about other aspects of tax system Public Economics Lectures () Part 7: Public Goods and Externalities 35 / 111Externalities: Empirical Measurement Two approaches Indirect market-based methods Contingent valuation Public Economics Lectures () Part 7: Public Goods and Externalities 36 / 111Edlin and Karaca-Mandic 2006 Accident externalities from driving automobiles. If I drive, I increase probability you will get into an accident externality cost imposed on you How to estimate this externality cost and appropriate Pigouvian tax on driving? Examine relationship between tra¢ c density and per-capita insurance costs and premiums Look at slope to infer size of externality cost Identi…cation assumption: variation in tra¢ c density at state level not correlated with other determinants of premiums (e.g. types of cars, etc.) Public Economics Lectures () Part 7: Public Goods and Externalities 37 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 38 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 39 / 111Edlin and Karaca-Mandic 2006 Tra¢ c density substantially increases marginal insurer costs Insurers set premia to cover average costs in market equilibrium Individual’s marginal cost on other driver’s not internalized Externality is convex Increase in tra¢ c density from average driver has external cost of 2,000 per year in California Comparable …gure in 10 per year in North Dakota Suggests that insurance premiums should be doubled in CA to achieve social optimum Public Economics Lectures () Part 7: Public Goods and Externalities 40 / 111Brookshire et al. 1982 Infer willingness to pay for clean air using e¤ect of pollution on property prices (capitalization) Compare prices of houses in polluted vs non-polluted areas. P = a+Pollution +X b+e i i i i Econometric problems Omitted variables: polluted neighborhoods worse on many dimensions Deeper problem: sorting Recover marginal WTP rather than average WTP People with allergies avoid polluted areas Public Economics Lectures () Part 7: Public Goods and Externalities 41 / 111Chay and Greenstone 2005 Also study home prices but use Clean Air Act as an exogenous change in pollution. Clean Air Act: imposed ceilings on pollution levels by county in mid 1970s. High pollution counties experience sharp reductions in pollution levels relative to low pollution counties Public Economics Lectures () Part 7: Public Goods and Externalities 42 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 43 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 44 / 111Chay and Greenstone 2005 Conclusion: 1% increase in pollution 0.25% decline in house values Clean air act increased house values by 45 bil (5%) in treated counties Conceptual concern with short-run market-based methods: people may not be fully aware of changes in pollution Public Economics Lectures () Part 7: Public Goods and Externalities 45 / 111Glaeser and Luttmer 2003 Without tradeable permits, e¢ ciency costs of regulation can be very high because of allocation distortions Study allocation of apartments under rent control Standard model assumes that with price controls, still have allocative e¢ ciency Those who value the apartments most get them But regulation will generally lead to allocative ine¢ ciency that generates …rst-order welfare losses For small price caps, allocation ine¢ ciency dwarfs undersupply ine¢ ciency Public Economics Lectures () Part 7: Public Goods and Externalities 46 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 47 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 48 / 111Glaeser and Luttmer 2003 Quantify welfare losses from misallocation by comparing consumption patterns in rent-controlled (NYC) and free-market places across demographic groups. Predict apartment size using number in family, income, education, age, etc. using 105 large MSAs Test if actual apartment allocations in NYC match predictions Identifying assumption: preferences stable across MSAs Check: placebo tests using Chicago and Hartford Public Economics Lectures () Part 7: Public Goods and Externalities 49 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 50 / 111Contingent Valuation For some outcomes, it is impossible to have a market value Ex: protecting endangered species Common solution: “contingent valuation”surveys How much would you be willing to pay to avoid extinction of whales? Public Economics Lectures () Part 7: Public Goods and Externalities 51 / 111Diamond and Hausman 1994 Describe problems with contingent valuation using surveys No resource cost to respondents Lack of consistency in responses Framing E¤ects: whales then seals vs. seals then whales WTP to clean one lake = WTP to clean 5 lakes Diamond and Hausman: let experts decide based on a budget voted on by individuals for the environment instead of relying on valuation Public Economics Lectures () Part 7: Public Goods and Externalities 52 / 111Behavioral Economics Applications: Internalities Sin taxes intended to correct “internalities.” Internal costs of smoking cigarettes dwarf the external costs. Suggests that conventional Pigouvian taxation should be small (relative to actual taxes observed on e.g. cigarettes and alcohol). Q: Does addictive nature of cigarettes motivate taxation? A: Highly sensitive to positive model of addiction Challenge: di¢ cult to determine which model is right empirically Public Economics Lectures () Part 7: Public Goods and Externalities 53 / 111Becker and Murphy 1988 Show that addictive goods can be modeled in perfectly rational framework Dynamic model with habit formation Current consumption of the addictive good decreases utility in future periods but increases marginal utility of consumption tomorrow If discount rate high enough, rationally choose to become addicted Implication: no reason for special taxes on these goods; set taxes according to Ramsey rules Public Economics Lectures () Part 7: Public Goods and Externalities 54 / 111Gruber and Koszegi 2004 Hyperbolic discounting preferences for smokers t U = u(c )+b( g u(c )) with b 1. 0 0 t å t1 t U = u(c )+b( g u(c )) 1 1 t å t2 Planner maximizes U with b= 1 (true utility). 0 Individuals overconsume c: fail to take full account of harm to future selves. Taxes reduce demand for each self; can partly correct the internality. Calibration implies corrective tax should be very large. Public Economics Lectures () Part 7: Public Goods and Externalities 55 / 111Bernheim and Rangel 2004 Model of “cue-triggered”addiction. Two selves: Cognitive self with rational preferences Visceral brain triggered by random cues in which addictive good is consumed at any cost. Probability of trigger increases with past consumption levels. Ideal policy: only allow rational consumption, eliminate consumption in hot mode. Corrective taxation may not be desirable: only distorts consumption in rational state, not visceral state. Better solution: regulated dispensation –must place orders one period in advance Public Economics Lectures () Part 7: Public Goods and Externalities 56 / 111O’Donoghue and Rabin 2006 Studies optimal sin taxes in a model with two types of consumers: rational and those who overconsume (e.g., because of self-control problems) Can be thought of as a hybrid of Becker and Gruber-Koszegi models Key result: irrationality among a few consumers leads to substantial role for corrective taxation/subsides. For rational individuals, excess burden due to taxation is second-order (Harberger triangle). For irrational individuals, welfare gains from correction of internality is …rst-order (Harberger trapezoid) Therefore always optimal to have a positive tax; calibrations suggest fairly large corrective taxes Public Economics Lectures () Part 7: Public Goods and Externalities 57 / 111Application: Retirement Savings Many believe that people do not save enough for retirement because of myopia, self-control problems, etc. What are the best corrective policies to increase savings? Price subsidies: 401(k)’s, IRA’s (Du‡o et al. 2006) Nudges: defaults and automatic enrollment in pension plans (Madrian and Shea 2001) Commitment devices (Bernartzi and Thaler 2004; Ashraf, Karlan, and Yin 2006) Information provision and …nancial literacy (Lusardi and Mitchell 2011) Focus on the …rst two here Public Economics Lectures () Part 7: Public Goods and Externalities 58 / 111Du‡o et al. (2006): Price Subsidies Du‡o et al. conduct a randomized experiment providing matches for IRA contributions Subject pool: H&R Block tax …lers Main …nding: provision of a non-zero subsidy signi…cantly increase IRA participation rates Equivalent government Saver’s Credit program has no impact, suggesting that salience matters Public Economics Lectures () Part 7: Public Goods and Externalities 59 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 60 / 111Madrian and Shea (2001): Defaults Madrian and Shea show that defaults have powerful e¤ects on savings behavior even though they do not change budget set Clearly violates neoclassical model Utility consequences of changing retirement savings rate are large Therefore di¢ cult to explain with optimization costs Carroll et al. (2009) propose a model with optimization costs and hyperbolic discounting to explain the pattern Hyperbolic discounters keep postponing plans to set up retirement account because cost of delaying by one period is small Interesting implication: short deadlines may help improve decision making Public Economics Lectures () Part 7: Public Goods and Externalities 61 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 62 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 63 / 111Chetty et al. (2012): Crowdout in Retirement Savings Do defaults increase total savings or just lead to shifting of assets from non-retirement to retirement accounts? Even inattentive individuals still have to satisfy budget constraint by cutting consumption or savings in non-retirement accounts Do price subsidies raise total savings or induce shifting across accounts? Large literature on “crowdout”in retirement savings accounts (Engen, Gale, Scholz 1996; Poterba, Venti, Wise 1996) Data in U.S. on wealth outside retirement accounts very limited Chetty et al. (2012) analyze this question using third-party reported data on all …nancial wealth for population of Denmark Public Economics Lectures () Part 7: Public Goods and Externalities 64 / 111Chetty et al. (2012): Price Subsidies Denmark has two types of pension accounts: capital pensions and annuity pensions Reform in 1999 in Denmark lowered subsidy for saving in capital pensions by 12 cents per DKr Question 1: how did this a¤ect contributions to capital pensions? Question 2: how much money was shifted to annuity pensions and to non-retirement taxable accounts? Public Economics Lectures () Part 7: Public Goods and Externalities 65 / 111Impact of Capital Pension Subsidy Reduction On Capital Pension Contributions Subsidy for Capital Pension Reduced 1995 2000 2005 2010 Year 25­75K Below Top Tax Cutoff 25­75K Above Top Tax Cutoff Public Economics Lectures () Part 7: Public Goods and Externalities 66 / 111 Total Capital Pension Contribution Rate 1.5 2 2.5 3 3.5Impact of 1999 Capital Pension Subsidy Reduction on Distribution of Capital Pension Contributions for Prior Contributors Extensive­margin responders account for 100% of reduction in capital pension ­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100 Percentage Change in Capital Pension Contributions (P –P )/ P t t­1 t­1 1997 to 1998 1998 to 1999 Public Economics Lectures () Part 7: Public Goods and Externalities 67 / 111 Percent of Individuals 0 20 40 60Public Economics Lectures () Part 7: Public Goods and Externalities 68 / 111Difference in Fraction of High Savers Before vs. After Subsidy Change, Pre­Reform (1996­1998) minus Post­Reform (1999­2001) Change in Slope at Cutoff = ­0.8%(0.1%) Crowd­Out of Pension Contribution ΔTaxable Saving /Δ Pension Contrib.: β=­0.99 (0.19) ­75000 ­50000 ­25000 0 25000 50000 75000 Income Relative to Top Tax Cutoff (DKr) Public Economics Lectures () Part 7: Public Goods and Externalities 69 / 111 Change in % with Taxable Savings Above Mean 0 ­2.5 ­2.0 ­1.5 ­1.0 ­0.5Chetty et al. (2012): Automatic Contributions Next, study impacts of automatic contributions Employers make pension contributions on workers behalf automatically Research design: event study when workers switch …rms Retirement savings rate can change sharply when workers switch …rms Do workers o¤set these changes in private savings as neoclassical model predicts? Public Economics Lectures () Part 7: Public Goods and Externalities 70 / 111Event Study around Switches to Firm with 3% Increase in Employer Pension Contrib.: Switchers with Positive Individual Pensions and Savings in Year Prior to Switch Δ Employer Pensions = 5.65 Δ Total Pensions = 4.86 Δ Total Savings = 4.44 ­5 0 5 Year Relative to Firm Switch Employer Pensions Total Pensions Total Savings Public Economics Lectures () Part 7: Public Goods and Externalities 71 / 111 Contribution or Savings Rate (% of income) 2 6 10 14 18Changes in Total Savings Rates vs. Changes in Employer Pension Rates for Firm Switchers, Cond. on Lagged Savings Total Savings Pass­Through Rate: β= 90% (0.9%) ­5 0 5 10 Percent Change in Employer Pension Contributions Public Economics Lectures () Part 7: Public Goods and Externalities 72 / 111 Percent Change in Total Savings Rate ­5 0 5 10Chetty et al. (2012): Active vs. Passive Savers Why do automatic contributions have much larger impacts on total savings than price subsidies? Hypothesis: active vs. passive choice, as in Carrol et al. (2009) Analyze heterogeneity of responses to test key predictions of this model 1 Price subsidies a¤ect active savers 2 Automatic contributions a¤ect passive savers 3 Active savers save more for retirement to begin with Public Economics Lectures () Part 7: Public Goods and Externalities 73 / 111Percent Responding to Capital Pension Subsidy Change in 1999 by Frequency of Active Changes in Other Years 0 20 40 60 80 100 Percentage of Other Years with Change in Individual Pension Contributions Public Economics Lectures () Part 7: Public Goods and Externalities 74 / 111 % with Sharp Response in 1999 0 5 10 15 20 25Pensions Pass­Through of Employer Pension Changes for Firm­Switchers by Frequency of Active Changes in Other Years 0 20 40 60 80 100 Percentage of Other Years with Change in Individual Pension Contributions Public Economics Lectures () Part 7: Public Goods and Externalities 75 / 111 Pass­Through of Emp. Pensions to Total Pensions .88 .9 .92 .94 .96 .98Heterogeneity in Response to Capital Pension Subsidy by Wealth/Income Ratio 0 .5 1 1.5 Wealth/Income Ratio in 1998 Public Economics Lectures () Part 7: Public Goods and Externalities 76 / 111 % with Sharp Response in 1999 10 15 20 25Heterogeneity in Pass­Through of Employer Pensions by Wealth/Income Ratio 0 .5 1 1.5 2 Wealth/Income Ratio in Year Prior to Switch Public Economics Lectures () Part 7: Public Goods and Externalities 77 / 111 Pass­Through of Employer Pensions to Total Savings 40 60 80 100 120Chetty et al. (2012): Correcting “Internalities” Tax subsidies tend to in‡uence the behavior of those who are already saving Need to be an active saver to pay attention and respond to subsidies More general lesson: economic tools (prices) may not be the best way to change the behavior of non-optimizing agents Non-traditional tools such as “nudges”may be more e¤ective Public Economics Lectures () Part 7: Public Goods and Externalities 78 / 111Public Goods: Outline 1 De…nitions and Baseline Model 2 Samuelson Rule 3 Public Goods with Endogenous Private Provision 4 Public Goods with Distortionary Taxation 5 Alternative Instruments Public Economics Lectures () Part 7: Public Goods and Externalities 79 / 111Public vs. Private Goods Private goods bene…t one individual h X  X h å h Public goods bene…t several individuals simultaneously X  X 8h h Ex: can of coke vs. teaching a class Pure: can accommodate any number of users. Impure: subject to congestion radio vs. roads Public Economics Lectures () Part 7: Public Goods and Externalities 80 / 111Private Good Person 1’ s Consumption Person 2’ s Consumption Public Economics Lectures () Part 7: Public Goods and Externalities 81 / 111Public Good Person 1’ s Consumption Person 2’ s Consumption Public Economics Lectures () Part 7: Public Goods and Externalities 82 / 111Public vs. Private Goods Rival vs. non-rival. Pure are non-rival Excludable vs. non-excludable. National Radio: impossible to exclude. Teaching: possible to exclude Most economic analysis focuses on pure public goods Public goods) equilibrium outcome ine¢ cient (large scale production externalities) Public Economics Lectures () Part 7: Public Goods and Externalities 83 / 111Public Goods Model: Setup Economy with H households, indexed by h = 1, ..,H Two goods X and G h X is always private, individual h consumes quantity X h Denote by X = X the total quantity of good X in the economy å h h h Denote by G consumption of good G by h, with G =å G h h h h Utility of h is U = U (X ,G) Public Economics Lectures () Part 7: Public Goods and Externalities 84 / 111Public Goods Model: Setup h Social welfare = weighted sum of utilities, b weight on h h h b  0 and at least one b 0 Production possibility F(X,G)= 0 h Assume that U is increasing in X and G Public Economics Lectures () Part 7: Public Goods and Externalities 85 / 111First Best if G is Private To identify Pareto e¢ cient outcomes, solve: h h h h max b U (X ,G ) å h h h s.t. F( X , G ) 0 l å å h h Lagrangian: h h L= b U lF å First order conditions h h h X : b U = lF X X h h h G : b U = lF G G Public Economics Lectures () Part 7: Public Goods and Externalities 86 / 111First Best if G is Private Taking ratios of FOCs yields h U F G G = h F U X X Set of Pareto e¢ cient allocations is set of allocations that satisfy: h MRS = MRT 8h GX GX Decentralized market equilibrium will implement such an allocation (1st Welfare Thm). Public Economics Lectures () Part 7: Public Goods and Externalities 87 / 111First Best if G is a Pure Public Good To identify Pareto e¢ cient outcomes, now solve: h h h max b U (X ,G) å h h h s.t. F( X , G ) 0 l å å h h FOC’s: h h h X : b U = lF X X h h G : b U = lF G å G h h h h Using b = lF /U from f.o.c. for X we obtain: X X h U F G G = å h U F X h X Public Economics Lectures () Part 7: Public Goods and Externalities 88 / 111Samuelson (1954) Rule Condition for Pareto e¢ ciency: sum of MRS is equal to MRT: h MRS = MRT å GX GX h Intuition: an additional unit of G increases the utility of all households in the public good case With G a private good, an additional unit only increases one individual’s utility Public Economics Lectures () Part 7: Public Goods and Externalities 89 / 111Decentralized Private Provision is Suboptimal Private good X and a pure public good G as above Price of each good is normalized to 1 h Each household starts with an endowment Y of good X. h Individual h contributes G to public good funding. h Consumption of public good is G = G for everyone. å h h h h Consumption of the private good is X = Y G for individual h. Public Economics Lectures () Part 7: Public Goods and Externalities 90 / 111Decentralized Private Provision is Suboptimal Individual h solves h h 1 h H maxU (X ,G + ..+G + ..+G ) h h h s.t. X +G = Y . h h Nash equilibrium outcome is U = U X G Samuelson Rule not satis…ed Pareto improvement if each person invested 1/H more dollars in the public good: h h h DW =U (1/H)+U = U (11/H) 0. X G G Market outcome is ine¢ cient: underprovision of G Public Economics Lectures () Part 7: Public Goods and Externalities 91 / 111Optimal Second Best Provision of PG’s Now suppose government provides public good to rectify under-provision in market equilibrium Two complications arise 1 Crowdout of private sector provision Private contributions to charity exceed 250 bn. per year Key model: Bergstrom, Blume, and Varian (1986) 2 Government cannot …nance PGs through lump sum taxation Need to modify Samuelson rule to account for distortionary taxation? Related to Sandmo (1975) analysis of externalities Public Economics Lectures () Part 7: Public Goods and Externalities 92 / 111Bergstrom, Blume, Varian (1986): Setup Individual h solves: h max U (X ,G +Gh) h h h h X ,G s.t. X +G = Y h h h h h FOC is U = U X G Nash equilibrium exists and is unique G s.t. all individuals optimize given others’behavior  Let G denote private equilibrium outcome Public Economics Lectures () Part 7: Public Goods and Externalities 93 / 111Bergstrom-Blume-Varian Model: Crowd-out h Now suppose government introduces lump sum taxes t on each individual h h Revenue used to …nance expenditure on public good T = t å Individual’s optimization problem is now: h maxU(X ,G +G +T) h h h h h h s.t. X +G = Y t Public Economics Lectures () Part 7: Public Goods and Externalities 94 / 111Bergstrom-Blume-Varian Model: Crowd-out Let Z = G +t denote total contribution of individual h. h h h Can rewrite this as: h maxU(X ,Z +Z ) h h h h h s.t. X +Z = Y   This is isomorphic to original problem) Z = G Total public good provision is unchanged Each person simply reduces voluntary provision by t h Public Economics Lectures () Part 7: Public Goods and Externalities 95 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 96 / 111BBV Model: Key Assumptions 1 No corners: assumed the set of contributors are the same in both situations. With corners, transfer neutrality breaks down: tax increase T results in h no private contribution from individuals with G T, but contributions increase on net. h h 2 Ignores direct utility from giving: U(X ,G ,G). Andreoni’s (1990) “warm glow”model. Stigler and Becker (1977) critique: should not simply modify preferences to explain patterns 3 Ignores prestige/signalling motives Glazer and Konrad (1996) Public Economics Lectures () Part 7: Public Goods and Externalities 97 / 111Empirical Evidence on Crowd-Out Two empirical questions motivated by theory 1 How large is the degree of crowd-out in practice? 2 What are the income and price e¤ects on charitable giving? Two strands of empirical literature 1 Field evidence (observational studies) 2 Lab experiments Traditionally, lab experiments have been more in‡uential but recent …eld studies may change this Lab experiments may not capture important motives for giving: warm glow, prestige Public Economics Lectures () Part 7: Public Goods and Externalities 98 / 111Hungerman 2005 Studies crowdout of church-provided welfare (soup kitchens, etc.) by government welfare Uses 1996 Clinton welfare reform act as an instrument for welfare spending One aspect of reform: reduced/eliminated welfare for non-citizens Motivates a di¤-in-di¤ strategy: compare churches in high non-citizen areas with low non-citizen areas before/after 1996 reform Estimates imply that total church expenditures in a state go up by 40 cents when welfare spending is cut by 1 Public Economics Lectures () Part 7: Public Goods and Externalities 99 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 100 / 111Andreoni and Payne (2003, 2008): Fundraising Mechanism Government spending crowds-out private donations through two channels: willingness to donate + fundraising Use tax return data on arts and social service organizations Instrument for government spending using changes in state budget due to federal grants Key …ndings: 1000 increase in government grant leads to 250 reduction in private fundraising 1 more of government grant to a charity leads to 56 cents less private contributions 70 percent (0.40) due to the fundraising channel Suggests that individuals are relatively passive actors Public Economics Lectures () Part 7: Public Goods and Externalities 101 / 111Marwell and Ames 1981 Early lab experiments testing free-rider behavior. Groups of 5 subjects, each given 10 tokens. Can invest tokens in either an individual or group account. Individual: 1 token = 1 for me; Group: 1 token = 50 cents for everyone Nash equilibrium is 100% individual but Pareto e¢ cient outcome is 100% group. Compute fraction invested in group account under various treatments Public Economics Lectures () Part 7: Public Goods and Externalities 102 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 103 / 111Marwell and Ames 1981 Finding: 40 to 60% of tokens were still invested in the public good. Experiment run on various groups of high school and college students. Only one group free-rode a lot: 1st year econ graduate students (20% donation rate). “Economists Free Ride, Does Anyone Else?” Andreoni (1988, 1993) implements experiments with repeated contributions Shows that contributions to public goods fall over time but remain positive Public Economics Lectures () Part 7: Public Goods and Externalities 104 / 111Expanding the Policy Set: Social Prices Traditional public goods and externalities literature focuses on economic incentives Induce public goods provision by changing relative prices of goods Another potential policy tool: manipulation of social prices Exploit concerns for perception by peers to encourage pro-social behavior E.g. have researchers compete on publications and help society in the process Public Economics Lectures () Part 7: Public Goods and Externalities 105 / 111Social Pressure: Existing Evidence Recent examples from psychology and political science Cialdini (2003) on energy conservation: telling people how their energy use compares with averages reduces energy use Gerber et al. (2008): using social pressure to increase voter turnout Public Economics Lectures () Part 7: Public Goods and Externalities 106 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 107 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 108 / 111Social Prices as a Policy Tool: Research in Progress 1 Perez-Truglia and Cruces 2012 Social incentives in campaign contributions and political polarization 2 Chetty, Saez, Sandor 2012 Comparing cash and social incentives to reduce referee times at JPubE 3 Chetty, Mobarak, Singhal Increasing tax revenue in Bangladesh using social incentives Theoretical question: optimal social prices and policy design Public Economics Lectures () Part 7: Public Goods and Externalities 109 / 111Public Economics Lectures () Part 7: Public Goods and Externalities 110 / 111Figure 2b: Turnaround times, DFL reweighted on pre­experiment turnaround 100% 75% 27.3 33.7 44.8 47.8 50% 25% Control = 4 week: p = 0.00 Control = Social: p = 0.01 4 week = Cash: p = 0.00 0% 0 20 40 60 Days since invi Days since invitation tation Control Control Social Social 4 week 4 week Cash Cash Source: Chetty, Saez, Sandor 2010 Public Economics Lectures () Part 7: Public Goods and Externalities 111 / 111 Percentage of Reports Still PendingPublic Economics Lectures Part 5: Corporate Taxation Raj Chetty Harvard University Fall 2013 Public Economics Lectures Corporate Tax 1 / 95Source: Auerbach (2010) Public Economics Lectures Corporate Tax 2 / 95Source: Auerbach (2010) Public Economics Lectures Corporate Tax 3 / 95Corporate Tax Structure in the U.S. Taxes on rms in the U.S. consist of several elements 1 Individual-level taxes on payouts (capital gains, dividends, interest income) 2 Tax on corporate pro ts (earnings minus expenses) at at rate of 34% Expenses include wages+materials, depreciation, and interest payments Acceleration of depreciation used to stimulate investment 3 Firms that are not publicly traded (\S corporations") subject to individual income tax system 4 International tax provisions (transfer pricing, tax havens) Goal: characterize consequences of this tax system and optimal design of corporate taxation Public Economics Lectures Corporate Tax 4 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Public Economics Lectures Corporate Tax 5 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Indiv. vs. Div. tax, Deduction of Accelerated Corp. tax, Corp. profit interest Depreciation Intl. tax tax Policy Instruments Public Economics Lectures Corporate Tax 6 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Indiv. vs. Div. tax, Deduction of Accelerated Corp. tax, Corp. profit interest Depreciation Intl. tax tax Policy Instruments Public Economics Lectures Corporate Tax 7 / 95Neoclassical Model of Firm Behavior Structure analysis using stylized two period model of rm behavior (Chetty and Saez 2010) Results generalize to continuous time model (Auerbach 2001) Firm has cash holdings of X at t = 0 Can raise more funds by issuing equity E , so total cash is: X +E Chooses level of investment, I , with concave payo F (I ) at t = 1 Public Economics Lectures Corporate Tax 8 / 95Neoclassical Model of Firm Behavior Pays out remaining cash as a dividend in period 0 : D = X +EI Rule out share repurchases for now, return to this below Tax  levied on dividend payments in all periods d Tax  on corporate pro ts c Investors can also purchase a govt. bond that pays xed rate r Public Economics Lectures Corporate Tax 9 / 95Neoclassical Model: Manager's Objective Manager maximizes value of the rm: (1 )(1 )f (X +ED) +XD +E d c maxV = (1 )DE + d E;D 1 +r where f (I ) = F (I )I denotes net pro t from investing I 0 No tax benchmark: invest up to point where f (I ) = r To characterize behavior with taxes, divide rms into two types: 0 1. Cash-Rich new view: X s.t. (1 )f (X ) r c 0 2. Cash-Constrained old view: X s.t. (1 )f (X ) r c Public Economics Lectures Corporate Tax 10 / 95Cash-Rich Firms: \New View" Marginal value of issuing equity is negative for cash rich rm (e.g., Microsoft) Even pre-tax return on investment is below interest rate Therefore E = 0 and rm splits cash between D and I according to: 0 (1 )f (XD) = r c 0 Invest to point where after-tax marginal product (1 )f (I ) equals c bond return r Higher corporate tax rate lowers investment Public Economics Lectures Corporate Tax 11 / 95Cash-Rich Firms: \New View" Change in dividend tax rate has no e ect on dividend or investment behavior (Auerbach 1979, Bradford 1981, King 1977)  factors out of V b/c investment nanced from retained earnings d 0 1 of investment + dividend tomorrow yields (1 )(1 )f (I ) c d 1 of dividend yields (1 ) today d Relative price of investment tomorrow vs. today una ected by  d Public Economics Lectures Corporate Tax 12 / 95Cash-Constrained Firms: \Old View" Marginal value of paying dividends is negative for cash-constrained rm (e.g., Twitter) Pre-tax return on investment is above interest rate r Therefore D = 0 and I = X +E . Optimal equity issue E satis es: 0 (1 )(1 )f (X +E ) = r d c 0 Invest to point where marginal net-of-tax return (1 )(1 )f (I ) d c equals interest rate Public Economics Lectures Corporate Tax 13 / 95Cash-Constrained Firms: \Old View" Key result: E , I fall with both  and  d c Dividend tax cuts stimulate equity issues and investment, and dividend payout in period 1 (Poterba and Summers 1985)  does not factor out of value function because marginal investment d is nanced from external capital Public Economics Lectures Corporate Tax 14 / 95Eciency Analysis: Neoclassical Model Denote total dividend payout over 2 years by P = D + (1 )f (I ) +XD=(1 +r) d c Total surplus in the economy is rm value plus tax revenue is W = V + P d d Using envelope theorem (manager optimization), deadweight cost is dW dP  d D =P +P + =  P d d d P d d d d 1 d d D Public Economics Lectures Corporate Tax 15 / 95Eciency Analysis: Neoclassical Model Under old view, 0, so dividend taxes reduce eciency P d New view: Dividend tax has no eciency cost and simply takes money from wealthy shareholders, which may be desirable for redistribution Old view and new view concur that taxes on corporate pro ts are distortionary Sinn (1991): lifecycle view. Old view applies to young rms (entrants) while new view applies to mature rms Distinguishing between competing views important for policy Public Economics Lectures Corporate Tax 16 / 95Empirical Evidence on Dividend Taxation Several studies examine e ects of tax cuts on dividend payouts to test between old view and new view Poterba and Summers (1985) nd a positive link between div payout ratio and (1 ) in U.K. time series d Poterba (2004) reports time series evidence in the U.S. Mixed results from studies of Tax Reform Act of 1986 Public Economics Lectures Corporate Tax 17 / 95Evidence from 2003 Dividend Tax Cut Chetty and Saez (2005) use a quasi-experimental resarch design Study e ect of the 2003 dividend tax cut on initiations of and overall levels of dividend payments 2003 tax cut reduced tax rates on dividend from normal income tax rates to 15% at rate Simple di -in-di design; results directly visible in raw time series Key challenge: dicult to analyze mean e ects due to outliers (typical problem with rms) Public Economics Lectures Corporate Tax 18 / 95Dividend Payments: Aggregate Time Series Regular Dividends Special Dividends 82-1 86-1 90-1 94-1 98-1 02-1 06-1 Quarter Source: Chetty and Saez (2005), using data through 2006Q2. Public Economics Lectures Corporate Tax 19 / 95 Dividends (Real 2004 bil) 0 10 20 30Regular Dividend Initiation Time Series 82-1 84-1 86-1 88-1 90-1 92-1 94-1 96-1 98-1 00-1 02-1 04-1 06-1 Quarter Public Economics Lectures Corporate Tax 20 / 95 Percent of Top 3807 Firms 0 .2 .4 .6 .8 1 1.2Fraction of Dividend Payers 82-1 84-1 86-1 88-1 90-1 92-1 94-1 96-1 98-1 00-1 02-1 04-1 06-1 Quarter Public Economics Lectures Corporate Tax 21 / 95 Percent of Top 3807 Firms 15 20 25 30 35 40 45E ect of Tax Cut on Initiations by Executive Shareholding Public Economics Lectures Corporate Tax 22 / 95E ect of Tax Cut on Initiations by Executive Option Holdings Public Economics Lectures Corporate Tax 23 / 95E ect of Tax Cut on Initiations by Institutional Ownership Public Economics Lectures Corporate Tax 24 / 95Impacts on Investment Yagan (2013) analyzes e ect of dividend tax cut on real outcomes: investment and employee compensation If the dividend tax cut reduces the cost of capital as in the old view, we should expect investment to increase Research design: di -in-di using una ected S corporations as control Public Economics Lectures Corporate Tax 25 / 95U.S. Corporate Investment in National Accounts 1,800 No cut cut from 38.6% to 15% 1,600 1,400 1,200 1,000 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Year Public Economics Lectures Corporate Tax 26 / 95 Billions of real 2010 dollarsYagan (2013) After incorporating, a corporation elects either C or S tax status: Tax rate on Tax rate on annual profits dividends C-corporations 35% Cut in 2003 S-corporations 35% 0% S-corporations: 100 non-institutional shareholders, one stock class Compete in the same narrow industries and at the same scale throughout the United States (common trends) Ex: Home-Depot is a C corp, Menards is an S corp Public Economics Lectures Corporate Tax 27 / 95Payouts to Shareholders 200% 200% .0063 .075 150% 150% .056 .0047 100% 100% .037 .0031 98 99 00 01 02 03 04 05 06 07 08 Year C-corporations (left scale) S-corporations (right scale) Public Economics Lectures Corporate Tax 28 / 95 Payouts per dollar of lagged revenueNet Investment .100 .075 .050 .025 .000 98 99 00 01 02 03 04 05 06 07 08 Year C-corporations S-corporations Public Economics Lectures Corporate Tax 29 / 95 ∆ capital per dollar of lagged capitalEmployee Compensation .18 .17 .16 .15 .14 98 99 00 01 02 03 04 05 06 07 08 Year C-corporations S-corporations Public Economics Lectures Corporate Tax 30 / 95 Compensation per dollar of revenueInvestment Response by Firm Size Decile .5 SD .125 0 -.5 SD -.125 1 2 3 4 5 6 7 8 9 10 Size Decile Public Economics Lectures Corporate Tax 31 / 95 Investment per of lagged capitalCorporate Taxation in an Agency Model Chetty and Saez (2010) develop an agency model of corporate taxation consistent with the ndings in Chetty and Saez (2005) Key idea in corporate nance models of rm behavior: divergence between the interests of the owners and managers of a rm Shareholders: want rm to maximize pro ts But CEO may get utility from running a big company, ying in private jets, or investing in pet projects Public Economics Lectures Corporate Tax 32 / 95Corporate Taxation in an Agency Model To model agency problem, generalize two period model above Firm is nanced from retaining earnings (new view) Now CEO has three options instead of two: 1 Productive investment: I 2 Pet project investment: J 3 Dividends: D = X I J CEO owns a fraction 1 of the shares of the company Public Economics Lectures Corporate Tax 33 / 95Corporate Taxation in an Agency Model Shareholder's payout = rm's pro ts:   (1 )f (I ) +XD c  = (1 ) D + d 1 +r CEO chooses I and J to maximize his personal payo g(J) max  + I;J 1 +r Public Economics Lectures Corporate Tax 34 / 95Corporate Taxation in an Agency Model Optimality conditions in interior: 0 (1 )f (I ) = r c 0 g (J) = (1 )r d Comparative statics: Increase in  raises J, leaves I una ected, and lowers D d Increase in  lowers I leaves J una ected c Public Economics Lectures Corporate Tax 35 / 95Eciency Cost of Dividend Tax in Agency Model Social welfare is g(J) W = + + P d d 1 +r g(J) =f (1 )P + g + (1 )(1 )P + P d d d d d d 1 +r Using envelope theorem for term in curly brackets (objective maximized by private sector), dW dP dP d d = P (1 )P + (1 )(1 ) +P + d d d d d d d d d d d  D =( + (1 )) P P d d 1 D Main result: dividend tax has a rst-order eciency cost Public Economics Lectures Corporate Tax 36 / 95Eciency Cost of Dividend Tax in Agency Model Analogous derivation shows that corporate tax has has standard secord-order deadweight cost dW dP c = c d d c c Dividend tax has higher than DWL from corporate tax Contrary to prediction of both old and new view Public Economics Lectures Corporate Tax 37 / 95Eciency Cost of Dividend Tax in Agency Model Why does a small dividend tax have a rst-order eciency cost in agency model? Intuition: Dividend tax makes Microsoft over-invest relative to Twitter Dividend tax magni es an exisiting ineciency even in new view (retained earnings) case Distorts allocation of investment even if leaving aggregate level of investment (I +J) unchanged Is this true empirically? Public Economics Lectures Corporate Tax 38 / 95Dividends vs. Share Repurchases Preceding models assume that rms can only repay money through dividends But rms can also return money to shareholders by buying back shares Repurchases are taxed at lower capital gains rate rather than dividends Why pay dividends given tax disadvantage? Public Economics Lectures Corporate Tax 39 / 95Explanations for Dividends 1 Agency model (Jensen 1986): rms have free cash ow that they would otherwise waste on perks Dividends are a commitment (why?) and therefore tie rms hands and reduce agency costs 2 Signaling model (Bernheim 1994): taxation of dividends makes them a way to \burn money" Those who have a lower marginal cost of burning money will do more of it in equilibrium The rms with lower marginal costs are the more pro table ones, and so dividends signal pro tability Public Economics Lectures Corporate Tax 40 / 95Bernheim and Wantz (1995) Tax-based test of agency vs. signalling models of dividends Dividend taxes should a ect announcement premium in opposite directions in agency and signalling theory In agency theory, higher taxes mean agents get less per dollar paid out =) lower premium In signalling theory, higher taxes mean higher signalling cost =)higher premium. Use data from 1962-86 and nd that premia are higher in higher tax regimes using time series regressions, supporting signalling model Public Economics Lectures Corporate Tax 41 / 95E ective Tax Rate on Dividends What is the e ective tax rate on dividends with variable tax rates? Dividend tax rates (used to) vary by individuals' tax bracket And non-taxable institutions such as pensions are completely exempt Miller (1977) predicts that non-taxable shareholders hold dividend paying stocks at the time of payment, so e ective tax rate is 0 We know this does not occur: dividend taxes generate revenue Could be because of transaction costs What is the e ective tax rate on dividend payments? Public Economics Lectures Corporate Tax 42 / 95Ex-Dividend Day Premium Elton and Gruber (1970) propose a method to back out implied tax rate based on price change around ex-dividend day Ex-dividend day which is the day when ownership rights to dividend payout are determined Pro t from selling just before the ex-day should equal the pro t from selling on the ex-day to eliminate arbitrage Public Economics Lectures Corporate Tax 43 / 95Ex-Dividend Day Premium With taxes the no-arbitrage condition is: P = P +D(1 ) (1) A B d P is the stock price cum-dividend (just before the ex-dividend day A starts) P is the expected stock price on the ex-day B D is dividend amount per share  is the tax rate on dividend income d Public Economics Lectures Corporate Tax 44 / 95Ex-Dividend Day Premium Rearranging 1, we get: P P A B = 1  d D Left-hand-side of this expression = ex-day premium Right-hand-side = e ective net-of-tax rate on dividends for marginal investor Public Economics Lectures Corporate Tax 45 / 95Chetty, Rosenberg, and Saez (2005) Examine announcement premia and ex-day premia around 2003 tax cut and in the time series since 1962 Do these premia vary as predicted by models of taxation and corporate nance? Public Economics Lectures Corporate Tax 46 / 95Microsoft Dividend Announcement and Ex-Day Price E ects, 2004 Public Economics Lectures Corporate Tax 47 / 95Ex-Dividend Day Premium and Tax Ratio, 1963-2004 Public Economics Lectures Corporate Tax 48 / 95Chetty, Rosenberg, and Saez (2005) Prior empirical results in ex-day and announcement e ect literature are very fragile and based on tenuous parametric assumptions Stock returns are far too volatile to draw reliable conclusions about tax e ects Need to understand determinants of these excess returns before being able to understand tax e ects Public Economics Lectures Corporate Tax 49 / 95Empirical Evidence on Corporate Taxation Next, turn to e ects of changes in corporate tax rates on investment and pro ts Here, all existing models predict that higher corporate taxes should reduce investment What is the magnitude of this e ect? Traditional literature used time series regressions with changes in corporate tax rate Limited quasi-experimental evidence and problems that closely parallel labor supply literature Public Economics Lectures Corporate Tax 50 / 95Corporate Taxable Income Elasticity Devereux, Liu, and Loretz (2013) use corporate tax records in the U.K. to study impacts of taxes on reported pro ts Marginal corporate tax rate jumps from 20% to 32% at 300,000 pounds Study bunching at kink to estimate the elasticity of corporate taxable income with respect to the tax rate (same method as Saez 2010, Chetty et al. 2011) Public Economics Lectures Corporate Tax 51 / 95Bunching at the 300k Tax Kink: 2002-2006 Public Economics Lectures Corporate Tax 52 / 95Cross-Country Comparisons Djankov et al. (2010) conduct a cross-country analysis of the impacts of e ective corporate tax rate Measure corporate tax rate for an identical mid-sized rm using a survey conducted with PriceWaterhouseCoopers OLS regressions of investment and entrepreneurial activity on corporate tax rate Attempt to isolate causal e ect using various controls for observables (e.g., other tax rates, levels of economic development) Implies substantial e ect of taxes on investment: 10 pp increase in corp tax rate leads to 2 pp decrease in I/GDP Public Economics Lectures Corporate Tax 53 / 95E ective Tax Rate and Investment Public Economics Lectures Corporate Tax 54 / 95E ective Tax Rate and Foreign Direct Investment Public Economics Lectures Corporate Tax 55 / 95E ective Tax Rate and Business Density Public Economics Lectures Corporate Tax 56 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Indiv. vs. Div. tax, Deduction of Accelerated Corp. tax, Corp. profit interest Depreciation Intl. tax tax Policy Instruments Public Economics Lectures Corporate Tax 57 / 95Tax Incentives for Investment: Accelerated Depreciation Most common policies to directly change level of investment: changes in depreciation rules and tax credits for investment Frequently used in recessions to attempt to stimulate investment by rms Begin with a simple example to understand why depreciation rules matter Suppose a rm buys a machine for 1000, which wears down by 100 a year Public Economics Lectures Corporate Tax 58 / 95Tax Incentives for Investment: Accelerated Depreciation Consider two tax treatments of the machine 1 Expensing: subtract the full 1000 from pro ts in the year you buy machine 2 Economic depreciation: subtract 100 per year from your pro ts Expensing reduces e ective tax rate for rm given interest rate r 0 Current policy in U.S.: approximate economic depreciation using linear or exponential rules by asset class Public Economics Lectures Corporate Tax 59 / 95Recovery Periods and Depreciations Methods by Type of Capital Public Economics Lectures Corporate Tax 60 / 95 Source: House and Shapiro (2008)E ects of Depreciation Rules on Investment How do depreciation rules a ect rm behavior? Let z = fraction of the machine's cost that can be subtracted as an up-front expense Use two-period model with following simpli cations 1 Investment is nanced purely from retained earnings (new view model) 2 Dividend tax rate  = 0 d 3 All pro ts are returned as dividends in period 2 Let denote pro ts earned in period 0 from previous activity, so that 0 X = (1 ) denotes cash-on-hand c 0 Public Economics Lectures Corporate Tax 61 / 95E ects of Depreciation Rules on Investment Firm's problem (1 )(f (I ) +I ) + (1z)I c c maxV = (1 ) I + zI + c 0 c I 1 +r First order condition for investment: (1 z) c 0 f (I ) = c = r (1 ) c Right hand side is \user cost of capital" (Hall and Jorgenson 1967) User cost c is sucient to determine investment rule No need to separately identify e ect of r,  , z, etc. c Public Economics Lectures Corporate Tax 62 / 95Expensing and the Corporate Cash-Flow Tax No expensing (z = 0): corresponds to baseline case analyzed above Full expensing (z = 1): called \corporate cash- ow tax" and is completely non-distortionary in simple model Investment subsidized at the same rate on the margin as pro ts Firm only taxed on rents earned above \normal" rate of return r Strong push for \fundamental" reform to corporate cash- ow tax (e.g. Auerbach 2010) May generate some distortions with other non-deductible inputs (e.g. entrepreneur's labor), agency problems, and scope for avoidance, but likely to improve eciency Public Economics Lectures Corporate Tax 63 / 95Accelerated Depreciation and Investment Stimulus Even if we don't switch to cash- ow tax, it is clear that increasing z reduces user cost of capital and increases incentive to invest In a dynamic model, particularly strong e ect from temporary accelerated depreciation because of intertemporal substitution e ect How sensitive is investment to accelerated depreciation provisions in practice? Can study this empirically by using enactment of bonus depreciation during recessions Public Economics Lectures Corporate Tax 64 / 95Accelerated Depreciation: Empirical Evidence House and Shapiro (2008) study impacts of accelerated depreciation in 2002 and 2003 tax bills Research design: di -in-di Control group: Assets depreciated over more than 20 years (e.g. buildings) not granted accelerated depreciation Variable intensity of treatment: bigger gains for investments with longer depreciation horizons (below 20 years) Public Economics Lectures Corporate Tax 65 / 95Predicted Impact vs. Tax Depreciation Rate Public Economics Lectures Corporate Tax 66 / 95Public Economics Lectures Corporate Tax 67 / 95Liquidity E ects House and Shapiro estimate an intertemporal substitution elasticity for capital investment w.r.t. user cost above 6 Interpret the responses to tax incentives as price e ects Why? Corporations maximize pro ts (linear utility) in standard model, with no constraints But large literature in past 20 years in corporate nance on \investment cash- ow sensitivity" suggests there are liquidity e ects Public Economics Lectures Corporate Tax 68 / 95Liquidity E ects Ex: Lamont (1997) studies impact of changes in free cash ow in conglomerates Uses shocks to oil prices as an instrument Oil companies signi cantly increase investment in non-oil subsidiaries (relative to others in same industry) when oil prices are high Implies that accelerated depreciation could raise investment partly through an income e ect Open question: how do liquidity constraints interact with impacts of corporate tax policy? Should we give tax breaks to liquidity constrained rms in recessions? Public Economics Lectures Corporate Tax 69 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Indiv. vs. Div. tax, Deduction of Accelerated Corp. tax, Corp. profit interest Depreciation Intl. tax tax Policy Instruments Public Economics Lectures Corporate Tax 70 / 95Financing Investment: Debt vs. Equity Let  denote individual income tax rate on interest income z Debtors who lend z to rm in period 1 get paid z +zi (1 ) in z period 2 Let  denote e ective tax rate on equity payout (combination of e capital gains and dividend) Let  denote corporate pro t tax rate c Public Economics Lectures Corporate Tax 71 / 95Financing Investment: Debt vs. Equity 0 Let marginal return to one more dollar of investment be  = f (I ) Suppose we nance that dollar of investment, paying lenders an interest rate of  Debt is deductible from pro ts, so net return is ((1 ) + )(1 ) =(1 ) c c z z Net return to nancing marginal investment from equity is (1 )(1 ) c e Debt is preferred to equity if (1 ) (1 )(1) z c Public Economics Lectures Corporate Tax 72 / 95Financing Investment: Debt vs. Equity Debt is highly tax-favored in the U.S.:  is close to 40% in U.S. and c highest income tax rate is below that So even without dividend/cap gains taxation, debt is favored So why don't rms use only debt nance? Public Economics Lectures Corporate Tax 73 / 95Neoclassical Explanations E ective tax rate on equity may not be that much higher than debt First, cannot deduct interest payments if they exceed current earnings (but can carry forward) Altshuler and Auerbach (1991) estimate that average value of interest deductibility was 32% in practice Far below statutory corporate rate of 46% Suggests that constraints on deducting interest payments are binding for many rms Marginal value of further debt may not be too high Public Economics Lectures Corporate Tax 74 / 95Neoclassical Explanations E ective tax rate on equity may not be that much higher than debt Second, could have a Miller (1977) equilibrium If some investors face 0 tax rates on equity (e.g. pension funds) then e ective tax rate on equity could be low Clientele e ect: pension funds buy shares before they pay dividends Does not occur fully in practice because we do collect taxes from equity Public Economics Lectures Corporate Tax 75 / 95Corporate Finance Explanations of Debt/Equity Debt and equity are not perfect substitutes in a model with uncertainty and asymmetric information 1 Debt requires xed payments; with uncertain payo s, defaulting on payment leads to potentially large bankruptcy+restructuring costs 2 Limited-liability of debt creates excess risk taking incentives (Myers 1977) for managers (no downside risk), increasing cost of debt nance 3 Debt disciplines managers (Jensen 1986) and so they avoid it so that they are under less pressure With all of these factors, should still see changes in tax rates on interest income and corporate pro ts a ecting debt/equity ratio Public Economics Lectures Corporate Tax 76 / 95E ective Corporate Tax Rate and Debt to Equity Ratio Public Economics Lectures Corporate Tax 77 / 95Empirical Evidence on Taxes and Debt Cross-sectional variation in marginal tax rates created by carry-forward of previous losses Prior losses can be subtracted from current pro ts and used to reduce tax liability Some rms e ectively face 0 marginal corporate tax rate because of this Public Economics Lectures Corporate Tax 78 / 95Empirical Evidence on Taxes and Debt Several studies use cross-sectional and panel variation in  generated c by such variation Regress debt/equity ratio on marginal tax rates (e.g., Auerbach 1985, Graham 1996) General nding: rms who have less incentive to use debt do use less of it Di erence in tax rates explain about 15% of the variance in D/E ratios across rms But aggregate responses to tax reforms such as TRA86 less clear (Gordon and Mackie-Mason 1990) Public Economics Lectures Corporate Tax 79 / 95Empirical Evidence on Taxes and Debt Several important directions for further work 1 Quasi-experimental evidence on how taxes a ect debt/equity ratio 2 Do changes in debt/equity mix generated by taxes ultimately change rms' investment and employment decisions? 3 What is the net impact on social welfare? Should we be subsidizing debt as we do today? Derive and implement optimal policy formulas in modern corporate nance models Public Economics Lectures Corporate Tax 80 / 95Corporate Decisions and Tax Policies Firm’s Decision Organizational Raise Production Payouts Form Capital Report Profits S corp or C corp Debt or Investment Pay Dividends Decisions Where to Locate Equity Pay Interest Indiv. vs. Div. tax, Deduction of Accelerated Corp. tax, Corp. profit interest Depreciation Intl. tax tax Policy Instruments Public Economics Lectures Corporate Tax 81 / 95Choice of Organizational Form Firms can choose to organize themselves as C corps (subject to corporate tax) or S corps (subject to indiv income tax) Tradeo between C and S is quite similar to debt vs equity choice conceptually, and similar puzzles arise Why aren't all rms S corporations? There are legal limits to public visibility and institutional ownership if an S corp. S corporations cannot have more than 100 shareholders, limiting ability to raise equity Public Economics Lectures Corporate Tax 82 / 95Choice of Organizational Form If taxes distort choice of incorporation, could lead to ineciency Ex: under-utilization of external capital for investment There is a correlation between corporate tax rates and fraction of assets in corporate form in time series (Mackie-Mason and Gordon 1997) But again quasi-experimental evidence limited and unclear what the real impacts are Also unclear what optimal tax policy is in modern corporate nance models Should we be giving startups preferential tax treatment? Are S corps. the best way to do this? Public Economics Lectures Corporate Tax 83 / 95International Taxation Another increasingly important dimension of rm organization that may be distorted by tax policy: location U.S. has a worldwide tax system Pay U.S. tax only when you bring money back to the U.S. (e.g., to pay dividends) Repatriations taxed on di erence between tax rate where pro ts are earned and U.S. corporate tax of 35% Ex: if company makes 100 of pro t in Ireland (4% avg corp tax), pay 31 Creates a strong incentive to report pro ts and hold money as retained earnings in foreign \tax havens." Public Economics Lectures Corporate Tax 84 / 95Figure 1. Principal Locations of Non-U.S. Profits of U.S. Multinationals, 2003 (profits as a percentage of the worldwide total) Netherlands Ireland Bermuda United Kingdom Luxembourg Canada Switzerland Germany U.K. Islands Japan 0 2 4 6 8 10 12 14 Percent of total Source: Bureau of Economic Analysis; Operations of U.S. Parent Companies and their Foreign Affiliates, various years. Public Economics Lectures Corporate Tax 85 / 95Transfer Pricing and Pro t Shifting How do rms realize such high pro ts in Bermuda? Set up a subsidiary that provides a service such as accounting in Bermuda Sell this service at a very high cost to the rm's main branch in the U.S., reducing U.S. pro ts Leads to high declared pro ts in Bermuda Government tries to limit this with \transfer pricing" rules Transactions have to be priced at same rate as arms-length transactions on the market But very hard to enforce in practice Public Economics Lectures Corporate Tax 86 / 95Tax Havens and Shifting How much do rms actually shift reported pro ts in response to local tax rates? Hines and Rice (1994) estimate impacts of tax rates on declared pro ts Regress declared pro ts of U.S. multinationals on local tax rates in a sample of tax havens and other countries Identi cation relies on orthogonality of tax rates to other factors (e.g., bureaucracy) Conclusion: a one percentage point higher tax rate reduces reported pro ts by US multinational rms by 3 percent Public Economics Lectures Corporate Tax 87 / 95E ect of Tax Rates on Location of Non nancial Pro ts Public Economics Lectures Corporate Tax 88 / 95Taxes and Repatriation of Pro ts Dharmapala, Foley, and Forbes (2009) study intertemporal subsitution in repatriation of pro ts Homeland Investment Act of 2004: provided a one-time tax holiday for the repatriation of foreign earnings by US multinationals Goal: increase investment and create jobs in the U.S. by bringing money home If US multinationals' domestic activity is nancially constrained, repatriations should increase domestic employment and investment More generally, provides good quasi-experimental evidence on nancial and real impacts of international tax laws Public Economics Lectures Corporate Tax 89 / 95Dharmapala, Foley, and Forbes (2009) Research design: di -in-di with variable intensity of treatment Use variation across tax rates in countries where companies reported pro ts prior to reform Companies with pro ts in countries with low tax rates (tax havens) have a large change in tax incentives from HIA Identi cation assumption: changes in repatriation around 2004 would have been the same across companies with pro ts in di erent counties absent HIA Public Economics Lectures Corporate Tax 90 / 95Total Repatriations by U.S. Multinational Companies Public Economics Lectures Corporate Tax 91 / 95Mean Repatriations for Di erent Types of U.S. Multinationals Public Economics Lectures Corporate Tax 92 / 95The E ects of Repatriations on U.S. Capital Expenditures, U.S. Employment Compensation, and R&D Public Economics Lectures Corporate Tax 93 / 95The E ects of Repatriations on Dividends and Repurchases Public Economics Lectures Corporate Tax 94 / 95Dharmapala, Foley, and Forbes (2009) Conclusion: tax break on repatriations did not directly lead to higher domestic investment or employment by a ected rms Instead, 1 increase in repatriations was associated with an increase of almost 1 in payouts to shareholders But cash returned to shareholders may have been invested in the U.S. economy or consumed What are the implications for optimal taxation? Should we tax foreign source income at all? How to prevent \race to the bottom" in corporate taxation? Public Economics Lectures Corporate Tax 95 / 95
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