Let’s go back and ask: “Just what is this ‘Y’?” “Just how do we measure GDP and real GDP?”

Let’s go back and ask:“Just what is this ‘Y’?”“Just how do we measure GDP and real GDP?”

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?

Major concepts in measuring national output: • GDP measures final output of goods and services • Three ways of measuring GDP lead to identical results: - expenditures, production, and income • GDP v. GNP: differs by ownership of factors • Constant v. current prices: correct for changing prices • Value added: Total sales less purchases of intermediate goods - Note that income-side GDP adds up value addeds • Net exports = exports – imports • Net v. gross investment: - Net investment = gross investment minus deprecation

Some answers • We want to construct a measure of real output, Q = f(q1,…, qn ;p1,…, pn) • Fundamental point about measuring real output: • Basically, for components, we first measure nominal output (yi) and then deflate with price index (pi) to get real output (qi): • qi = yi /pi • How do we aggregate the qi to get total real, GDP(Q)? • Old fashioned fixed weights: Then add up the different components of final output to get total output in prices of a given year: • New fangled chain weights: Use new “superlative” techniques

Old fashioned price and output indexes Laspeyres (1871): weights with prices of historical period Lt = ∑ wi,base year (Δq/q)i,t Paasche (1874): use current (latest) prices as weights Πt = ∑ wi,t (Δq/q)i,t

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

How can we possibly resolve the “index number problem”? Brilliant idea: Ask how utility of output differs across different bundles. Let U(q1, q2) be the utility function. Assume have {qt} = {qt1, qt2}. Then growth is: g({qt}/{qt-1}) = U(qt)/U(qt-1). For example, assume “Cobb-Douglas” utility function, Q = U = (q1)λ (q2)1- λ Also, define the (logarithmic) growth rate of xt as g(xt) = ln(xt/xt-1). Then Qt / Qt-1 =[(qt1)λ (qt2)1- λ]/[(qt-11)λ (qt-12)1- λ] g(Qt) = ln(Qt/Qt-1) = λ ln(qt1/qt-11) + (1-λ) ln(qt2/qt-12) g(Qt) = λg(qt1) + (1-λ) g(qt2) The class of 2nd order approximations is called “superlative.” This is a superlative index called the Törnqvist index. 7

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

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

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

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???

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 • projections of emissions in global warming models

Now let’s go back to macroeconomic theory and look at the classical macro model

I. The Basic Classical Model • Aggregate supply: • Endogenous variables: W, P, Y. This defines the AS curve in figure 1. • However, we are one variable short for total equilibrium. • Note on AS: It is vertical because have perfectly flexible wages and prices. AS curve

Aggregate demand The standard way of closing the classical model is through deriving an aggregate demand curve. The simplest approach is to rely upon the quantity theory of prices and money. This holds that money supply is exogenous and money demand is proportional to money output: (3) M = Ms (supply of money exogenous) (4) Md = kPY (demand for money) which gives the AD function: • Y = Ms /kP Note: The quantity theory is not essential here. We need aggregate demand as a function of fiscal, monetary, and other variables. (5) is just a simple and convenient example.

This is the classical AS-AD relationship. Notes: 1. Output is always at potential output. 2. No effect of M (or more generally AD) on output; AD only affects prices (“Money is neutral.”)

Let’s go back and ask: “Just what is this ‘Y’?” “Just how do we measure GDP and real GDP?”