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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(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

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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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7 BEA, Survey of Current Business, August 2013

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Personal savings rate[Savings/disposable personal income]

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-2

0

2

4

6

8

10

12

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J-60

F-62

M-64

A-66

M-68

J-70

J-72

A-74

S-76

O-78

N-80

D-82

J-85

F-87

M-89

A-91

M-93

J-95

J-97

A-99

S-01

O-03

N-05

D-07

J-10

F-12

Inflation rate, price of personal consumption

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.

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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

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Now to our puzzler!

GDP?

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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. • How would we measure total output and prices?

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

The growth picture for index numbers:the real numbers!

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Source: Bureau of Economics Analysis

Output (billions 2005$)Sector 1960 2012Computers 0.0000337 87.94 Non computers 3,105.8 15,382.8

Price (2005 = 1)1960 2012

Computers 5,935.7 0.9006 Non computers 0.1749 1.0560

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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.

How to implement: 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

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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?

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