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

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Economics 122aFall 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 5:00-5:50Thursday 7:00-7:50 and 8:00-8:50 (TENTATIVE)

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Now Playing:

The Biggest Hit in Economics:

The Gross Domestic Product

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Starring

Irving Fisher (Yale)

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Starring

Simon Kuznets (Harvard)

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Starring

Steve Landefeld(Bureau of EconomicAnalysis)

7Survey of Current Business, August 2010

Inflation as measured by the price of gross domestic purchases*

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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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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 = income3. 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 factors5. Constant v. current prices: correct for changing prices6. Value added: Total sales less purchases of intermediate goods

- Note that income-side GDP adds up value addeds7. Net exports = exports – imports 8. Net v. gross investment:

• Net investment = gross investment minus deprecation

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How to measure output growth?

Now take the following numerical example. • Suppose good 1 is computers and good 2 is shoes.

period 1 period 2

Ratio: period 2 to period 1

Real outputq1 1 100 100q2 1 1 1

Pricesp1 1 0.010 0.010p2 1 1.00 1.00

How would we measure total output and prices?

The growth picture for index numbers:the real numbers!

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Output (109 2005 $) Growth of sector

Sector 1958 2008 Rate per year Growth Factor

Computers 0.00002 157.03200 31.8% 8,049,116.8

Non computers 2,578 13,155 3.3% 5.1

Source: Bureau of Economics Analysis

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Some answers

• We want to construct a measure of real output, Q = f(q1,…,

qn ;p1,…, pn)

• How do we aggregate the qi 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

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Old fashioned price and output indexes

Laspeyres (1871): weights with prices of base yearLt = ∑ wi,base year (Δq/q)i,t

Paasche (1874): use current (latest) prices as weights

Πt = ∑ wi,t (Δq/q)i,t

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Start with Laspeyres and Paasche

HUGE difference!

What to do?

period 1 period 2

Ratio: period 2 to period 1

Real outputq1 1 100 100q2 1 1 1

Pricesp1 1 0.010 0.010p2 1 1.00 1.00

Nominal output

= ∑piqi 2.0 2.0 1.0Quantity indexes

Laspeyres (early p) 2.000 101.000 50.50Paasche (late p) 1.010 2.000 1.98

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Solution

Brilliant idea: Ask how utility of output differs across different bundles. Let U(q1, q2) be the utility function. Assume have {qt} = {qt

1, 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 (qt

2) 1- λ]/[(qt-1

1)λ (qt-12)

1- λ]

g(Qt) = ln(Qt/Qt-1) = λ ln(qt1/qt-1

1) + (1-λ) ln(qt2/qt-1

2)

g(Qt) = λ g(qt1) + (1-λ) g(qt

2)

The class of 2nd order approximations is called “superlative.”This is a superlative index called the Törnqvist index.

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What do we find?

1. L > Util > P [that is, Laspeyres overstates growth and Paasche understates relative to true.

period 1 period 2

Ratio: period 2 to period 1

Real outputq1 1 100 100q2 1 1 1

Pricesp1 1 0.010 0.010p2 1 1.00 1.00

Nominal output

= ∑piqi 2.0 2.0 1.0

Utility = (q1*q2)̂ .5 1.00 10.00 10.00

Quantity indexes

Laspeyres (early p) 2.000 101.000 50.50Paasche (late p) 1.010 2.000 1.98

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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)

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Now we construct new indexes as above: Fisher and Törnqvist

Superlatives (here Fisher and Törnqvist) are exactly correct.

Usually very close to true.

period 1 period 2

Ratio: period 2 to period 1

Real outputq1 1 100 100q2 1 1 1

Pricesp1 1 0.010 0.010p2 1 1.00 1.00

Nominal output = ∑piqi 2.0 2.0 1.0

Utility = (q1*q2)̂ .5 1.00 10.00 10.00

Quantity indexes

Fisher (geo mean of L and P) 1.421 14.213 10.00

Törnqvist (wt. average growth rate) 1.000 10.000 10.00

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[4.60517 *0.5+0*0.5 ] = exp[2.302585 ]= 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).

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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???

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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