Intermediate macroeconomics Notes

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Intermediate Macroeconomics Julio Gar n Robert Lester Eric Sims University of Georgia Colby College University of Notre Dame January 22, 2017 This Version: 1.0.1Chapter 1 Macroeconomic Data In this chapter we de ne some basic macroeconomic variables and statistics and go over their construction as well as some of their properties. For those of you who took principles of macroeconomics, this should be a refresher. We start by describing what is perhaps the single most important economic indicator, GDP. 1.1 Calculating GDP Gross domestic product (GDP) is the current dollar value of all nal goods and services that are produced within a country within a given period of time. \Goods" are physical things that we consume (like a shirt) while \services" are intangible things that we consume but which are not necessarily tangible (like education). \Final" means that intermediate goods are excluded from the calculation. For example, rubber is used to produce tires, which are used to produce new cars. We do not count the rubber or the tires in used to construct a new car in GDP, as these are not nal goods people do not use the tires independently of the new car. The value of the tires is subsumed in the value of the newly produced car counting both the value of the tires and the value of the car would \double count" the tires, 1 so we only look at \ nal" goods. \Current" means that the goods are valued at their current period market prices (more on this below in the discussion of the distinction between \real" and \nominal"). GDP is frequently used as a measure of the standard of living in an economy. There are many obvious problems with using GDP as a measure of well-being as de ned, it does not take into account movements in prices versus quantities (see below); the true value to society of some goods or services may di er from their market prices; GDP does not measure non-market activities, like meals cooked at home as opposed to meals served in a restaurant (or things that are illegal); it does not say anything about the distribution of resources among society; etc. Nevertheless, other measures of well-being have issues as well, so we will focus 1 There are many nuances in the NIPA accounts, and this example is no exception. Tired included in the production of a new car are not counted in GDP because these are not nal goods, but replacement tires sold at an auto shop for an already owned car are. More generally, depending on circumstances sometimes a good is an intermediate good and other times it is a nal good. 18on GDP. Let there be n total nal goods and services in the economy for example, cell phones (a good), haircuts (a service), etc. Denote the quantities of each good (indexed by i) produced in year t by y for i= 1; 2;:::;n and prices by p . GDP in year t is the sum of prices times i;t i;t quantities: n GDP =p y +p y +⋅⋅⋅+p y = p y Q t 1;t 1;t 2;t 2;t n;t n;t i;t i;t i=1 As de ned, GDP is a measure of total production in a given period (say a year). It must also be equal to total income in a given period. The intuition for this is that the sale price of a good must be distributed as income to the di erent factors of production that went into producing that good i.e. wages to labor, pro ts to entrepreneurship, interest to capital (capital is some factor of production, or input, that itself has to be produced and is not used up in the production process), etc. For example, suppose that an entrepreneur has a company that uses workers and chain-saws to produce rewood. Suppose that the company produces 1000 logs at 1 per log; pays its workers 10 per hour and the workers work 50 hours; and pays 100 to the bank, from which it got a loan to purchase the chain-saw. Total payments to labor are 500, interest is 100, and the entrepreneur keeps the remaining 400 as pro t. The logs contribute 1000 to GDP, 500 to wages, 100 to interest payments, and 400 to pro ts, with 500 + 100 + 400 = 1,000. The so-called \expenditure" approach to GDP measures GDP as the sum of consumption, C; investment, I; government expenditure, G; and net exports, NX. Net exports is equal to exports, X, minus imports, IM, where exports are de ned as goods and services produced domestically and sold abroad and imports are de ned as goods and services produced abroad and purchased domestically. Formally: GDP =C +I +G +(X −IM ) (1.1) t t t t t t Loosely speaking, there are four broad actors in an aggregate economy: households, rms, government (federal, state, and local), and the rest of the world. We measure aggregate expenditure by adding up the spending on nal goods and services by each of these actors. Things that households purchase food, gas, cars, etc. count as consumption. Firms produce stu . Their expenditures on new capital, which is what is used to produce new goods (e.g. a bulldozer to help build roads), is what we call investment. Government expenditures includes everything the government spends either on buying goods (like courthouses, machine guns, etc.) or on services (including, in particular, the services provided by government employees). The latter half basically counting government payments to workers as expenditure is making use of the fact that income = expenditure from above, as there is no other feasible 19way to \value" some government activities (like providing defense). This number does not include transfer payments (social security, Medicaid, etc.) and interest payments on debt from the government (which together amount to a lot). The reason transfer payments do not count in government expenditure is that these transfers do not, in and of themselves, constitute expenditure on new goods and services. However, when a retiree takes her Social Security payment and purchases groceries, or when a Medicaid recipient visits a doctor, those expenditures get counted in GDP. Finally, we add in net exports (more on this in a minute). In summary, what this identity says is that the value of everything produced, GDP , must be t equal the sum of the expenditures by the di erent actors in the economy. In other words, the total value of production must equal the total value of expenditure. So we shall use the words production, income, and expenditure somewhat interchangeably. If we want to sum up expenditure to get the total value of production, why do we subtract imports (IM in the notation above)? After all, GDP is a measure of production in a country in a given period of time, while imports measure production from other countries. The reason is because our notion of GDP is the value of goods and services produced within a country; the expenditure categories of consumption, investment, and government spending do not distinguish between goods and services that are produced domestically or abroad. So, for example, suppose you purchase an imported Mercedes for 50,000. This causes C to go up, but should not a ect GDP. Since this was produced somewhere else, IM goes up by exactly 50,000, leaving GDP una ected. Similarly, you could imagine a rm purchasing a Canadian made bulldozer I and IM would both go up in equal amounts, leaving GDP una ected. You could also imagine the government purchasing foreign-produced warplanes which would move G and IM in o setting and equal directions. As for exports, a Boeing plane produced in Seattle but sold to Qatar would not show up in consumption, investment, or government spending, but it will appear in net exports, as it should since it is a component of domestic production. There are a couple of other caveats that one needs to mention, both of which involve how investment is calculated. In addition to business purchases of new capital (again, capital is stu used to produce stu ), investment also includes new residential construction and inventory accumulation. New residential construction is new houses. Even though households are purchasing the houses, we count this as investment. Why? At a fundamental level investment is expenditure on stu that helps you produce output in the future. A house is just like that you purchase a house today (a \stock"), and it provides a \ ow" of bene ts for many years going forward into the future. There are many other goods that have a similar feature we call these \durable" goods things like cars, televisions, appliances, etc. At some level we ought to classify these as investment too, but for the purposes of national income 20accounting, they count as consumption. From an economic perspective they are really more like investment; it is the distinction between \ rm" and \household" that leads us to put new durable goods expenditures into consumption. However, even though residential homes are purchased by households, new home construction is counted as a component of investment. Inventory \investment" is the second slightly odd category. Inventory investment is the accumulation (or dis-accumulation) of unsold, newly produced goods. For example, suppose that a company produced a car in 1999 but did not sell it in that year. It needs to count in 1999 GDP since it was produced in 1999, but cannot count in 1999 consumption because it has not been bought yet. Hence, we count it as investment in 1999, or more speci cally inventory investment. When the car is sold (say in 2000), consumption goes up, but GDP should not go up. Here inventory investment would go down in exactly the same amount of the increase in consumption, leaving GDP una ected. We now turn to looking at the data, over time, of GDP and its expenditure components. Figure 1.1 plots the natural log of GDP across time. These data are quarterly and begin 2 in 1947. The data are also seasonally adjusted unless otherwise noted, we want to look at seasonally adjusted data when making comparisons across time. The reason for this is that there are predictable, seasonal components to expenditure that would make comparisons between quarters dicult (and would introduce some systematic \choppiness" into the plots download the data and see for yourself). For example, there are predictable spikes in consumer spending around the holidays, or increases in residential investment in the warm summer months. When looking at aggregate series it is common to plot series in the natural log. This is nice because, as you can see in Appendix A, it means that we can interpret di erences in the log across time as (approximately) percentage di erences reading o the vertical di erence between two points in time is approximately the percentage di erence of the variable over that period. For example, the natural log of real GDP increases from about 6.0 in 1955 to about 6.5 in 1965; this di erence of 0.5 in the natural logs means that GDP increased by approximately 50 percent over this period. For reasons we will discuss more in detail below, plotting GDP without making a \correction" for in ation makes the series look smoother than the \real" series actually is. To the eye, one observes that GDP appeared to grow at a faster rate in the 1970s than it did later in the 1980s and 1990s. This is at least partially driven by higher in ation in the 1970s (again, more on this below). 2 You can download the data for yourselves from the Bureau of Economic Analysis. 21Figure 1.1: Logarithm of Nominal GDP 10 9 8 7 6 5 5055606570758085909500051015 Figure 1.2 plots the components of GDP, expressed as shares of total GDP. We see that consumption expenditures account for somewhere between 60-70 percent of total GDP, making consumption by far the biggest component of aggregate spending. This series has trended up a little bit over time; this upward trend is largely mirrored by a downward trend in net exports. At the beginning of the post-war sample we exported more than we imported, so that net exports were positive (but nevertheless still a small fraction of overall GDP). As we've moved forward into the future net exports have trended down, so that we now import more than we export. Investment is about 15 percent of total GDP. Even though this is a small component, visually you can see that it appears quite volatile relative to the other components. This is an important point to which we shall return later. Finally, government spending has been fairly stable at around 20 percent of total GDP. The large increase very early in the sample has to do with the Korean War and the start of the Cold War. 22Figure 1.2: GDP Components as a Share of Total GDP Consumption/GDP Investment/GDP .70 .22 .68 .20 .66 .18 .64 .16 .62 .14 .60 .58 .12 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 Government/GDP Net Exports/GDP .26 .06 .24 .04 .22 .02 .20 .00 .18 -.02 .16 -.04 .14 -.06 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 1.2 Real versus Nominal Measured GDP could change either because prices or quantities change. Because we are interested in the behavior of quantities (which is ultimately what matters for well-being), we would like a measure of production (equivalent to income and expenditure) that removes the in uence of price changes over time. This is what we call real GDP. Subject to the caveat of GDP calculation below, in principle real prices are denominated in units of goods, whereas nominal prices are denominated in units of money. Money is anything which serves as a unit of account. As we'll see later in the book, money solves a bartering problem and hence makes exchange much more ecient. To make things clear, let's take a very simple example. Suppose you only have one good, call ity. People trade this good using money, call it M. We are going to set money to be the numeraire: it serves as the \unit of account," i.e. the units by which value is measured. Let p be the price of goods relative to money p tells you how many units of M you need to buy one unit of y. So, if p= 1:50, it says that it takes 1:50 units of money (say dollars) to buy a good. Suppose an economy produces 10 units of y, e.g. y = 10, and the price of goods in terms of money is p = 1:50. This means that nominal output is 15 units of money (e.g. 1:50× 10, or p⋅y). It is nominal because it is denominated in units of M it says how many units ofM the quantity ofy is worth. The real value is of course justy that is the quantity 23of goods, denominated in units of goods. To get the real from the nominal we just divide by the price level: Nominal Real= Price py = p =y: Ultimately, we are concerned with real variables, not nominal variables. What we get utility from is how many apples we eat, not whether we denominate one apple as one dollar, 100 uruguayan pesos, or 1.5 euros. Going from nominal to real becomes a little more dicult when we go to a multi-good world. You can immediately see why if there are multiple goods, and real variables are denominated in units of goods, which good should we use as the numeraire? Suppose you have two goods, y and y . Suppose that the price measured in units of money of the rst 1 2 good is p and the price of good 2 is p . The nominal quantity of goods is: 1 2 Nominal=p y +p y : 1 1 2 2 Now, the real relative price between y and y is just the ratio of nominal prices, p p . 1 2 1 2 p is \dollars per unit of good 1" and p is \dollars per unit of good 2", so the ratio of the 1 2 prices is \units of good 2 per units of good 1." Formally: p good 2 1 good 1 = = (1.2) p good 1 2 good 2 In other words, the price ratio tells you how many units of good 2 you can get with one unit of good 1. For example, suppose the price of apples is 5 and the price of oranges is 1. The relative price is 5 you can get ve oranges by giving up one apple. You can, of course, de ne the relative price the other way as 15 you can buy 15 of an apple with one orange. We could de ne real output (or GDP) in one of two ways: in units of good 1 or units of good 2: p 2 Real =y + y (Units are good 1) 1 1 2 p 1 p 1 Real = y +y (Units are good 2): 2 1 2 p 2 As you can imagine, this might become a little unwieldy, particularly if there are many goods. It would be like walking around saying that real GDP is 14 units of Diet Coke, or 6 24cheeseburgers, if Diet Coke or cheeseburgers were used as the numeraire. As such, we have adopted the convention that we use money as the numeraire and report GDP in nominal terms as dollars of output (or euros or lira or whatever). But that raises the issue of how to track changes in GDP across time. In the example above, what if both p and p doubled between two periods, but y and y stayed the same? 1 2 1 2 Then nominal GDP would double as well, but we'd still have the same quantity of stu . Hence, we want a measure of GDP that can account for this, but which is still measured in dollars (as opposed to units of one particular good). What we typically call \real" GDP in the National Income and Products Accounts is what would more accurately be called \constant dollar GDP." Basically, one arbitrarily picks a year as a baseline. Then in subsequent years one multiplies quantities by base year prices. If year t is the base year, then what we call real GDP in year t+s is equal to the sum of quantities of stu produced in year t+s weighted by the prices from year t. This di ers from nominal GDP in that base year prices are used instead of current year prices. LetY denote real GDP in yeart+s,s= 0; 1; 2;::: . Let there t+s be n distinct goods produced. For quantities of goods y , y , ::: , y , we have: 1;t+s 2;t+s n;t+s Y =p y +p y +⋅⋅⋅+p y t 1;t 1;t 2;t 2;t n;t n;t Y =p y +p y +⋅⋅⋅+p y t+1 1;t 1;t+1 2;t 2;t+1 n;t n;t+1 Y =p y +p y +⋅⋅⋅+p y : t+2 1;t 1;t+2 2;t 2;t+2 n;t n;t+2 Or, more generally, using the summation notation covered in Appendix A: n Y = p y for h= 0; 1; 2: t+h Q i;t i;t+h i=1 From this we can implicitly de ne a price index (an implicit price index) as the ratio of nominal to real GDP in a given year: p y +p y +⋅⋅⋅+p y 1;t 1;t 2;t 2;t n;t n;t P = = 1 t p y +p y +⋅⋅⋅+p y 1;t 1;t 2;t 2;t n;t n;t p y +p y +⋅⋅⋅+p y 1;t+1 1;t+1 2;t+1 2;t+1 n;t+1 n;t+1 P = t+1 p y +p y +⋅⋅⋅+p y 1;t 1;t+1 2;t 2;t+1 n;t n;t+1 p y +p y +⋅⋅⋅+p y 1;t+2 1;t+2 2;t+2 2;t+2 n;t+2 n;t+2 P = : t+2 p y +p y +⋅⋅⋅+p y 1;t 1;t+2 2;t 2;t+2 n;t n;t+2 Or, more succinctly, n ∑ p y i;t+h i;t+h i=1 P = for h= 0; 1; 2: t+h n p y ∑ i;t i;t+h i=1 25A couple of things are evident here. First, we have normalized real and nominal GDP to be the same in the base year (which we are taking as year t). This also means that we are normalizing the price level to be one in the base year (what you usually see presented in national accounts is the price level multiplied by 100). Second, there is an identity here that nominal GDP divided by the price level equals real GDP. If prices on average are rising, then nominal GDP will go up faster than real GDP, so that the price level will rise. A problem with this approach is that the choice of the base year is arbitrary. This matters to the extent that the relative prices of goods vary over time. To see why this might be a problem, let us consider a simply example. Suppose that an economy produces two goods: haircuts and computers. In year t, let the price of haircuts be 5 and computers by 500, and there be 100 hair cuts and 10 computers produced. In year t+ 1, suppose the price of haircuts is 10, but the price of computers is now 300. Suppose that there are still 100 haircuts produces but now 20 computers. Nominal GDP in year t is 5,500, and in year t+ 1 it is 7,000. If one uses year t as the base year, then real GDP equals nominal in year t, and real GDP in t+ 1 is 10,500. Using year t as the base year, one would conclude that real GDP grew by about 91 percent from t to t+ 1. What happens if we instead use year t+ 1 as the base year? Then real GDP in year t+ 1 would be 7,000, and in year t real GDP would be 4,000. One would conclude that real GDP grew between t andt+ 1 by 75 percent, which is substantially di erent than the 91 percent one obtains when using t as the base year. To deal with this issue, statisticians have come up with a solution that they call chain- weighting. Essentially they calculate real GDP in any two consecutive years (say, 1989 and 1990) two di erent ways: once using 1989 as the base year, once using 1990 as the base year. Then they calculate the growth rate of real GDP between the two years using both base years and take the geometric average of the two growth rates. Chain-weighting is a technical detail that we need not concern ourselves with much, but it does matter in practice, as relative prices of goods have changed a lot over time. For example, computers are far cheaper in relative terms now than they were 10 or 20 years ago. Throughout the book we will be mainly dealing with models in which there is only one good we'll often refer to it as fruit, but it could be anything. Fruit is a particularly convenient example for reasons which will become evident later in the book. This is obviously an abstraction, but it's a useful one. With just one good, real GDP is just the amount of that good produced. Hence, as a practical matter we won't be returning to these issues of how to measure real GDP in a multi-good world. Figure 1.3 below plots the log of real GDP across time in the left panel. Though considerably less smooth than the plot of log nominal GDP in Figure 1.1, the feature that sticks out most from this gure is the trend growth you can approximate log real GDP 26pretty well across time with a straight line, which, since we are looking at the natural log, means roughly constant trend growth across time. We refer to this straight line as a \trend". This is meant to capture the long term behavior of the series. The average growth rate (log rst di erence) of quarterly nominal GDP from 1947-2016 was 0.016, or 1.6 percent. This translates into an annualized rate (what is most often reported) of about 6 percent (approximately 1:6× 4). The average growth rate of real GDP, in contrast, is signi cantly lower at about 0.008, or 0.8 percent per quarter, translating into about 3.2 percent at an annualized rate. From the identities above, we know that nominal GDP is equal to the price level times real GDP. As the growth rate of a product is approximately equal to the sum of the growth rates, growth in nominal GDP should approximately equal growth in prices (in ation) plus growth in real GDP. Figure 1.3: Real GDP Log real GDP and its trend Detrended real GDP 10.0 .10 .05 9.5 .00 9.0 -.05 8.5 -.10 8.0 Real GDP -.15 Trend 7.5 -.20 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 Figure 1.4 plots the log GDP de ator and in ation (the growth rate or log rst di erence of the GDP de ator) in the right panel. On average in ation has been about 0.008, or 0.8 percent per quarter, which itself translates to about 3 percent per year. Note that 0:008+ 0:008 = 0:016, so the identity appears to work. Put di erently, about half of the growth in nominal GDP is coming from prices, and half is coming from increases in real output. It is worth pointing out that there has been substantial heterogeneity across time in the behavior of in ation in ation was quite high and volatile in the 1970s but has been fairly low and stable since then. 27Figure 1.4: GDP De ator GDP Deflator Inflation - GDP Deflator 120 .04 100 .03 80 .02 60 .01 40 .00 20 0 -.01 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 Turning our focus back to the real GDP graph, note that the blips are very minor in comparison to the trend growth. The right panel plots \detrended" real GDP, which is de ned as actual log real GDP minus its trend. In other words, detrended GDP is what is left over after we subtract the trend from the actual real GDP series. The vertical gray shaded areas are \recessions" as de ned by the National Bureau of Economic Research. There is no formal de nition of a recession, but loosely speaking they de ne a recession as two or more quarters of a sustained slowdown in overall economic activity. For most of the recession periods, in the left plot we can see GDP declining if we look hard enough. But even in the most recent recession (ocial dates 2007Q42009Q2), the decline is fairly small in relation to the impressive trend growth. You can see the \blips" much more clearly in the right plot. During most of the observed recessions, real GDP falls by about 5 percentage points (i.e. 0.05 log points) relative to trend. The most recent recession really stands out in this respect, where we see GDP falling by more than 10 percent relative to trend. A nal thing to mention before moving on is that at least part of the increase in real GDP over time is due to population growth. With more people working, it is natural that we will produce more products and services. The question from a welfare perspective is whether there are more goods and services per person. For this reason, it is also quite common to look at \per capita" measures, which are series divided by the total population. Population growth has been pretty smooth over time. Since the end of WW2 it has averaged about 0.003 per quarter, or 0.3 percent, which translates to about 1.2 percent per year. Because population growth is so smooth, plotting real GDP per capita will produce a similar looking gure to that shown in Figure 1.3, but it won't grow as fast. Across time, the average growth rate of real GDP per capita has been 0.0045, 0.45 percent, or close to 2 percent per year. 28Doing a quick decomposition, we can approximate the growth rate of nominal GDP as the sum of the growth rates of prices, population, and real GDP per capita. This works out to 0:008+ 0:003+ 0:0045 = 0:0155 ≈ 0:016 per quarter, so again the approximation works out well. At an annualized rate, we've had population growth of about 1.2 percent per year, price growth of about 3.2 percent per year, and real GDP per capita growth of about 2 percent per year. Hence, if you look at the amount of stu we produce per person, this has grown by about 2 percent per year since 1947. 1.3 The Consumer Price Index The consumer price index (CPI) is another popular macro variable that gets mentioned a lot in the news. When news commentators talk about \in ation" they are usually referencing the CPI. The CPI is trying to measure the same thing as the GDP de ator (the average level of prices), but does so in a conceptually di erent way. The building block of the CPI is a \consumption basket of goods." The Bureau of Labor Statistics (BLS) studies buying habits and comes up with a \basket" of goods that the average household consumes each month. The basket includes both di erent kinds of goods and di erent quantities. The basket may include 12 gallons of milk, 40 gallons of gasoline, 4 pounds of co ee, etc. Suppose that there are N total goods in the basket, and let x denote the amount of i good i (i = 1;:::;N) that the average household consumes. The total price of the basket in any year t is just the sum of the prices in that year times the quantities. Note that the quantities are held xed and hence do not get time subscripts the idea is to have the basket not change over time: Cost =p x +p x +⋅⋅⋅+p x : t 1;t 1 2;t 2 N;t N cpi The CPI in year t, call it P , is the ratio of the cost of the basket in that year relative t to the cost of the basket in some arbitrary base year, b: Cost t cpi P = t Cost b p x +p x +⋅⋅⋅+p x 1;t 1 2;t 2 N;t N = p x +p x +⋅⋅⋅+p x 1;b 1 2;b 2 N;b N N p x ∑ i;t i i=1 = : N p x ∑ i;b i i=1 As in the case of the GDP de ator, the choice of the base year is arbitrary, and the price level will be normalized to 1 in that year (in practice they multiply the number by 100 when 29presenting the number). The key thing here is that the basket both the goods in the basket and the quantities are held xed across time (of course in practice the basket is periodically rede ned). The idea is to see how the total cost of consuming a xed set of goods changes over time. If prices are rising on average, the CPI will be greater than 1 in years after the base year and less than 1 prior to the base year (as with the implicit price de ator it is common to see the CPI multiplied by 100). Figure 1.5 plots the natural log of the CPI across time. It broadly looks similar to the GDP de ator trending up over time, with an acceleration in the trend in the 1970s and something of a attening in the early 1980s. There are some di erences, though. For example, at the end of 2008 in ation as measured by the CPI went quite negative, whereas it only dropped to about zero for the GDP de ator. On average, the CPI gives a higher measure of in ation relative to the de ator and it is more volatile. For the entire sample, the average in ation by the GDP de ator is 0.8 percent per quarter (about 3.2 percent annualized); for the CPI it is 0.9 percent per quarter (about 3.6 percent annualized). The standard deviation (a measure of volatility) of de ator in ation is 0.6 percent, while it is 0.8 percent for the CPI. Figure 1.5: CPI Consumer Price Index Inflation - CPI 250 .020 .015 200 .010 .005 150 .000 100 -.005 -.010 50 -.015 0 -.020 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 The reason for these di erences gets to the basics of how the two indices are constructed and what they are intended to measure. A simple way to remember the main di erence is that the CPI xes base year quantities and uses updated prices, whereas the de ator is based on the construction of constant dollar GDP, which xes base year prices and uses updated quantities. The xing of quantities is one of the principal reasons why the CPI gives a higher measure of in ation. From principles of microeconomics we know that when relative prices change, people will tend to substitute away from relatively more expensive goods and into relatively cheaper goods the so-called substitution e ect. By xing quantities, the CPI 30does not allow for this substitution away from relatively expensive goods. To the extent that relative prices vary across time, the CPI will tend to overstate changes in the price of the basket. It is this substitution bias that accounts for much of the di erence between in ation as measured by the CPI and the de ator. There are other obvious di erences the CPI does not include all goods produced in a country, and the CPI can include goods produced in other countries. Because the de ator is based on what the country actually produces, whereas the CPI is based on what the country consumes (which are di erent constructs due to investment, exports, and imports), it follows that if a country produces much more of a particular product than it consumes, then this product will have a bigger impact on the implicit price de ator than on the CPI. For getting a sense of overall price in ation in US produced goods, the GDP de ator is thus preferred. For getting a sense of nominal changes in the cost of living for the average household, the CPI is a good measure. Chain weighting can also be applied to the CPI. As described above in the context of the GDP de ator, chain-weighting attempts to limit the in uence of the base year. This is an attempt to deal with substitution biases in a sense because relative price changes will result in the basket of goods that the typical household consumes changing. Whether to chain-weight or not, and what kind of price index to use to index government transfer payments like Social Security is a potentially important political issue. If in ation is really 2 percent per year, but the the price index used to update Social Security payments measures in ation (incorrectly) at 3 percent per year, then Social Security payments will grow in real terms by 1 percent. While this may not seem like much in any one year, over time this can make a big di erence for the real burden of Social Security transfers for a government. 1.4 Measuring the Labor Market One of the key economic statistics on which the press is focused is the labor market. This usually takes the form of talking about the unemployment rate, but there are other ways to measure the \strength" or \health" of the aggregate labor market. The unemployment rate is nevertheless a fairly good indicator of the overall strength of the economy it tends to be elevated in \bad" times and low in \good" times. An economy's total labor input is a key determinant of how much GDP it can produce. What is relevant for how much an economy produces is the size of the total labor input. There are two dimensions along which we can measure labor input the extensive margin (bodies) and the intensive margin (amount of time spent working per person). De ne L as the total population, E as the number of people working (note that E ≤L), and h as the average number of hours each working person works (we'll measure the unit of time as an 31hour, but could do this di erently, of course). Total hours worked, N, in an economy are then given by: N =h×E: Total hours worked is the most comprehensive measure of labor input in an economy. Because of di erences and time trends in population, we typically divide this by L to express this as total hours worked per capita (implicitly per unit of time, i.e. a year or a quarter). This measure represents movements in two margins average hours per worker and number of workers per population. Denote hours per capita as n=NL: h×E n= : L As you may have noticed, the most popular metric of the labor market in the press is the unemployment rate. To de ne the unemployment rate we need to introduce some new concepts. De ne the labor force, LF, as everyone who is either (i) working or (ii) actively seeking for work. De ne U as the number of people who are in the second category looking for work but not currently working. Then: LF =E+U: Note thatLF ≤L. We de ne the labor force participation rate,lfp, as the labor force divided by the total working age population: LF lfp= : L De ne the unemployment rate as the ratio of people who are unemployed divided by the labor force: U u= LF U = : U +E Figure 1.6 plot these di erent measures of the labor market: (i) the unemployment rate; E (ii) the employment to population ratio, ; (iii) the natural log of average hours worked per L 3 person; (iv) the labor force participation rate; and (iv) log hours worked per capita, n. To get an idea for how these series vary with output movements, we included NBER \recession 3 Note that there is no natural interpretation of the units of the graphs of average hours per worker and total hours per capita. The underlying series are available in index form (i.e. unitless, normalized to be 100 in some base year) and are then transformed via the natural log. 32dates" as indicated by the shaded gray bars. Figure 1.6: Labor Market Variables Unemployment Rate Employement-Population Ratio 11 66 10 64 9 8 62 7 60 6 5 58 4 56 3 2 54 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 Average Hours Labor Force Participation Rate Hours Per Capita 4.78 68 5.95 4.76 66 5.90 4.74 4.72 64 5.85 4.70 4.68 62 5.80 4.66 4.64 60 5.75 4.62 4.60 58 5.70 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 50 55 60 65 70 75 80 85 90 95 00 05 10 15 A couple of observations are in order. First, hours worked per capita uctuates around a roughly constant mean in other words, there is no obvious trend up or down. This would indicate that individuals are working about as much today as they did fty years ago. But the measure of hours worked per capita masks two trends evident in its components. The labor force participation rate (and the employment-population ratio) have both trended up since 1950. This is largely driven by women entering the labor force. In contrast, average hours per worker has declined over time this means that, conditional on working, most people work a shorter work week now than 50 years ago (the units in the gure are log points of an index, but the average workweek itself has gone from something like 40 hours per week to 36). So the lack of a trend in total hours worked occurs because the extra bodies in the labor force have made up for the fact that those working are working less on average. In terms of movements over the business cycle, these series display some of the properties you might expect. Hours worked per capita tends to decline during a recession. For example, from the end of 2007 (when the most recent recession began) to the end of 2009, hours worked per capita fell by about 10 percent. The unemployment rate tends to increase during recessions in the most recent one, it increased by about 5-6 percentage points, from around 5 percent to a maximum of 10 percent. Average hours worked tends to also decline during recessions, but this movement is small and does not stand out relative to the trend. The 33employment to population ratio falls during recessions, much more markedly than average hours. In the last several recessions, the labor force participation rate tends to fall (which is sometimes called the \discouraged worker" phenomenon, to which we will return below), with this e ect being particularly pronounced (and highly persistent) around the most recent recession. In spite of its popularity, the unemployment rate is a highly imperfect measure of labor input. The unemployment rate can move because (i) the number of unemployed changes or (ii) the number of employed changes, where (i) does not necessarily imply (ii). For example, the number of unemployed could fall if some who were ocially unemployed quit looking for work, and are therefore counted as leaving the labor force, without any change in employment and hours. We typically call such workers \discouraged workers" this outcome is not considered a \good" thing, but it leads to the unemployment rate falling. Another problem is that the unemployment rate does not say anything about intensity of work or part time work. For example, if all of the employed persons in an economy are switched to part time, there would be no change in the unemployment rate, but most people would not view this change as a \good thing" either. In either of these hypothetical scenarios, hours worked per capita is probably a better measure of what is going on in the aggregate labor market. In the case of a worker becoming \discouraged", the unemployment rate dropping would be illusory, whereas hours worked per capita would be unchanged. In the case of a movement from full time to part time, the unemployment rate would not move, but hours per capita would re ect the downward movement in labor input. For these reasons the unemployment rate is a dicult statistic to interpret. As a measure of total labor input, hours per capita is a preferred measure. For these reasons, many economists often focus on hours worked per capita as a measure of the strength of the labor market. For most of the chapters in this book, we are going to abstract from unemployment, instead focusing on how total labor input is determined in equilibrium (without really di erentiating between the intensive and extensive margins). It is not trivial to think about the existence of unemployment in frictionless markets there must be some friction which prevents individuals looking for work from meeting up with rms who are looking for workers. However, later, in Chapter 31 we are going to study a model that can be used to understand why an economy can simultaneously have rms looking for workers and unemployed workers looking for rms. Frictions in this setting can result in these matches from not occurring, resulting in unemployment. Before getting there, we have some journey to go and in the next chapter we de ne what a model is, its importance, and its usefulness. 341.5 Summary Gross Domestic Product (GDP) equals the dollar value of all goods and services produced in an economy over a speci c unit of time. The revenue from production must be distributed to employees, investors, payments to banks, pro ts, or to the government (as taxes). Every dollar a business or person spends on a produced good or service is divided into consumption, investment, government spending. GDP is an identity in that the dollar value of production must equal the dollar value of all expenditure which in turn must equal the dollar value of all income. For this identity to hold, net exports must be added to expenditure. GDP may change over time because prices change or output changes. Changes in output are what we care about for welfare. To address this, real GDP uses constant prices over time to measure changes in output. Changes in prices indexes and de ators are a way to measure in ation and de ation. A problem with commonly uses price indexes like the consumer price index is that they overstate in ation on average. The most comprehensive measure of the labor input is total hours. Total hours can change because the number of workers are changing or because the average hours per worker changes. Other commonly used metrics of the labor market include hours per capita, the unemployment rate, and the labor force participation rate. Key Terms Nominal GDP Real GDP GDP price de ator Numeraire Chain weighting Consumer Price Index Substitution bias Unemployment rate Labor force participation rate 35Questions for Review 1. Explain why the three methods of calculating GDP are always equal to each other. 2. Why are intermediate goods subtracted when calculating GDP under the production method? 3. Why are imports subtracted when calculating GDP under the expenditure method? 4. Discuss the expenditure shares of GDP over time. Which ones have gotten bigger and which ones have gotten smaller? 5. Explain the di erence between real and nominal GDP. 6. Discuss the di erences between the CPI and the GDP de ator. 7. Discuss some problems with using the unemployment rate as a barometer for the health of the labor market. 8. Hours worked per worker has declined over the last 50 years yet hours per capita have remained roughly constant. How is this possible? Exercises 1. An economy produces three goods: houses, guns, and apples. The price of each is 1. For the purposes of this problem, assume that all exchange involving houses involves newly constructed houses. (a) Households buy 10 houses and 90 apples, eating them. The government buys 10 guns. There is no other economic activity. What are the values of the di erent components of GDP (consumption, investment, government spending, exports/imports)? (b) The next year, households buy 10 houses and 90 apples. The government buys 10 guns. Farmers take the seeds from 10 more apples and plant them. Households then sell 10 apples to France for 1 each and buy 10 bananas from Canada for 2 each, eating them too. What are the values of the components of GDP? (c) Return to the economy in part 1a. The government notices that the two richest households consume 40 apples each, while the ten poorest consume one each. It levies a tax of 30 apples on each of the rich households, and gives 6 apples each to the 10 poorest households. All 36

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