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Now Playing:The Biggest Hit in Economics:

The Gross Domestic Product

Starring

Irving Fisher (Yale) Simon Kuznets (Harvard) 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• Dow Jones Industrial Average• Real interest rates• Personal savings rate• Inflation rate• Real exchange rate for the Chinese yuan…

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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….

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4 BEA, Survey of Current Business, August 2012

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Personal savings rate[Savings/disposable personal income]

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.

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.

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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:

• Expenditure = 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 addeds

7. Net exports = exports – imports 8. Net v. gross investment:

• Net investment = gross investment minus deprecation

Repeat slide:Incomes in the National Income Accounts

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Share, 2001

National income 93.9 13,359

Compensation of employees 51.1 8,295 62.1%Proprietors' income 14.1 1,157 8.7%Rental income of persons 6.2 410 3.1% Corporate profits after tax 9.3 1,448 10.8%Net interest and misc 4.6 527 3.9%Taxes on production and imports 6.8 1,098 8.2%

2011

Table 1.12. National Income by Type of Income[Billions of dollars]Bureau of Economic AnalysisLast Revised on: August 29, 2012

1929

Source: U.S. Bureau of Economic Analysis (www.bea.gov)

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Now back to our puzzler!

GDP?

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A puzzler: What is the growth in overall output (GDP)?

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

It is time for our first “elevator quiz”Remember the importance of “elevator talks” – 1 minute summary of why you should (a) get a job, (b) be promoted, (c) wow someone, (d) pitch your movie or book, ….

We will have occasional “elevator quizzes” in class.

These are five-minute answers to questions, either forewarned or not.

Not graded unless you are warned in advance (in writing).

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Answer:

Make sure you do real GDP, not nominal GDP (which is constant)Laspeyres and Paasche give very different answers.Fisher and Tornqvist give the “right” answer of 10x.

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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 outputs with fixed prices of a base (first) year:

Lt = ∑ pi,1 qi,2 /∑ pi,1 qi,1

Paasche (1874): weights outputs with fixed prices of a late (or current) year:

Πt = ∑ pi,2 qi,2 /∑ pi,2 qi,1

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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} = {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

As with production functions, the exponent (λ) is the share, here the expenditure share.

If we calculate the ratio of utilities, we find that U(qt)/U(qt-1) = 10.

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L > Util > P

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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Solution (cont.)

Continuing with “Cobb-Douglas” utility function, Q = U = (q1)λ (q2) 1- λ

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)

In English:the growth of output = weighted growth of components, weighted by the expenditure shares.

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

indexes.”

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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

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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 (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???

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Who cares about GDP and CPI measurement?

• Most find that the CPI overstates inflation by up to 1 %-point per year.

Policy applications• Social security for grandma (cost of living escalation)• Taxes for you (indexation of the tax system)• Estimated rate of productivity growth for budget

– and, therefore, Congress’s spending inclinations• Estimates of relative economic standing, military spending,

and the like.