1 Now Playing: The Biggest Hit in Economics: The Gross Domestic Product

2 Starring Irving Fisher (Yale)

3 Starring Simon Kuznets (Harvard)

4 Starring Steve Landefeld (U.S. Bureau of Economic Analysis)

What do these have in common? Real GDP Consumer price index Unemployment rate Exchange rate of the dollar Inflation rate Real exchange rate 5

Answer…. They are all “indexes” that require some economic theory to construct. Indeed, for most of human history (99.9%), we did not know how to construct them. Understanding the construction of price and output indexes is our main analytical task today. But first, some recent macro data…. 6

7 BEA, Survey of Current Business, August 2013

8 Personal savings rate [Savings/disposable personal income]

9 An important inflation measure (corrected) Fed target

Overview of national accounts “While the GDP and the rest of the national income accounts may seem to be arcane concepts, they are truly among the great inventions of the twentieth century. Like a satellite that can view the weather across an entire continent, so the GDP can provide an overall picture of the state of the economy.” A leading economics textbook. 10

11 Major concepts in national economic accounts 1.GDP measures final output of goods and services. 2.Two ways of measuring GDP lead to identical results: Expenditure = income 3.Savings = investment is an accounting identity. We will also see that it is an equilibrium condition. Note the advanced version of this includes government and foreign sector. 4.GDP v. GNP: differs by ownership of factors 5.Constant v. current prices: correct for changing prices 6.Value added: Total sales less purchases of intermediate goods - Note that income-side GDP adds up value addeds 7.Net exports = exports – imports 8.Net v. gross investment: Net investment = gross investment minus deprecation

12 Now to our puzzler! GDP?

13 How to measure output growth? Now take the following numerical example. Suppose good 1 is computers and good 2 is shoes. How would we measure total output and prices?

The growth picture for index numbers: the real numbers! 14 Source: Bureau of Economics Analysis

15 Some answers We want to construct a measure of real output, Q = f(q 1,…, q n ;p 1,…, p n ) How do we aggregate the q i to get total real, GDP(Q)? – Old fashioned fixed weights: Calculate output using the prices of a given year, and then add up different sectors. – New fangled chain weights: Use new “superlative” techniques

16 Old fashioned price and output indexes L aspeyres (1871): weights with prices of base year L t = ∑ w i,base year (Δq/q) i,t Paasche (1874): use current (latest) prices as weights Π t = ∑ w i,t (Δq/q) i,t

17 Start with Laspeyres and Paasche HUGE difference! What to do?

18 Solution Brilliant idea: Ask how utility of output differs across different bundles. How to implement: Let U(q 1, q 2 ) be the utility function. Assume have {q t } = {q t 1, q t 2 }. Then growth is: g({q t }/{q t-1 }) = U(q t )/U(q t-1 ). For example, assume “Cobb-Douglas” utility function, Q = U = (q 1 ) λ (q 2 ) 1- λ Also, define the (logarithmic) growth rate of x t as g(x t ) = ln(x t /x t-1 ). Then Q t / Q t-1 =[(q t 1 ) λ (q t 2 ) 1- λ ]/[(q t-1 1 ) λ (q t-1 2 ) 1- λ ] g(Q t ) = ln(Q t /Q t-1 ) = λ ln(q t 1/ q t-1 1 ) + (1-λ) ln(q t 2/ q t-1 2 ) g(Q t ) = λ g( q t 1 ) + (1-λ) g( q t 2 ) The class of 2 nd order approximations is called “superlative.” This is a superlative index called the Törnqvist index. 18

19 What do we find? 1. L > Util > P [that is, Laspeyres overstates growth and Paasche understates relative to true.

20 Currently used “superlative” indexes Fisher* Ideal (1922): geometric mean of L and P: F t = (L t × Π t ) ½ Törnqvist (1936): average geometric growth rate: (ΔQ/Q) t = ∑ s i,T (Δq/q) i,t, where s i,T =average nominal share of industry in 2 periods (*Irving Fisher (YC 1888), America’s greatest macroeconomist)

21 Now we construct new indexes as above: Fisher and Törnqvist Superlatives (here Fisher and Törnqvist) are exactly correct. Usually very close to true.

22 Current approaches Most national accounts used Laspeyres until recently –Why Laspeyres? Primarily because the data requirements are less stringent. CPI uses Laspeyres index (sub-par approach!). US moved to Fisher for national accounts in 1995 BLS has constructed “chained CPI” using Törnqvist since 2002 China still uses Laspeyres in its GDP. –Who knows whether Chinese data are accurate?

23 Who cares about GDP and CPI measurement? Some examples where makes a big difference Social security for grandma Taxes for you Target for monetary policy (2 percent per year inflation goal) Estimated rate of productivity growth for budget –and, therefore, Congress’s spending inclinations