1 Economics 122a Fall 2010 Agenda for this week: 1. The classical macro model (Chap 3) 2. How economists measure output/income (Chap 2)

Some announcements Final exam is being debated in the Registrar’s Office. Mistake somewhere. Course is limited to those on course list on web page. Sections will begin next week Wednesday 4:50-4:50 and 5:00-5:50 Thursday 4:50-4:50 and 5:00-5:50 Thursday 7:00-7:50 and 8:00-8:50 (TENTATIVE) 2

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

4 Starring Irving Fisher (Yale)

5 Starring Simon Kuznets (Harvard)

6 Starring Steve Landefeld (Bureau of Economic Analysis)

7 Survey of Current Business, August 2010

Inflation as measured by the price of gross domestic purchases* 8 Note: This is a new concept, not in the textbooks. It reflects the prices of domestic purchases rather than domestic product.

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10 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: Production = 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

11 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! 12 Source: Bureau of Economics Analysis

13 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

14 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

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

16 Solution Brilliant idea: Ask how utility of output differs across different bundles. 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.

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

18 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)

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

Calculation of output for our example Fisher: Growth = (L x P)^.5 = (1.98 x 50.50)^.5 = 10.0 Tornqvist: = exp[ ln(100/1)*0.5+ln(1/1)*0.5 ] = exp[ *0.5+0*0.5 ] = exp[ ] = 10.0 For this, remember that the logarithmic growth of X from 1 to 2 is g = ln(X2/X1). So the index of output is exp(g). 20

21 Current approaches Most national accounts used Laspeyres until recently –Why Laspeyres? Primarily because the data requirements are less stringent. CPI uses Laspeyres index. 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???

22 Who cares about GDP and CPI measurement? Some examples where makes a big difference Social security for grandma Taxes for you Estimated rate of productivity growth for budget –and, therefore, Congress’s spending inclinations Comparisons of military “power” –Overestimates of Soviet GDP in 1980s led Reagan administration to large increase in military budget –People are now worrying about Chinese power because it is now “number 2” Projections of emissions in global warming models