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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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)
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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 Economic
Analysis)
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Survey of Current Business, August 2010
Inflation as measured by the price of
gross domestic purchases*
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 = 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
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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
Real output
q1
q2
Prices
p1
p2
Ratio:
period 2 to
period 2 period 1
1
1
100
1
100
1
1
1
0.010
1.00
0.010
1.00
How would we measure total output and prices?
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The growth picture for index numbers:
the real numbers!
Output (109 2005 $)
Sector
1958
Computers
Non computers
2008
Rate per year Growth Factor
0.00002
157.03200
31.8%
8,049,116.8
2,578
13,155
3.3%
5.1
Source: Bureau of Economics Analysis
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Growth of sector
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 year
Lt = ∑ 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
period 1
Real output
q1
q2
Prices
p1
p2
Nominal output
= ∑piqi
Quantity indexes
Laspeyres (early p)
Paasche (late p)
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Ratio:
period 2 to
period 2 period 1
1
1
100
1
100
1
1
1
0.010
1.00
0.010
1.00
2.0
2.0
1.0
2.000
1.010
101.000
2.000
50.50
1.98
HUGE
difference!
What to do?
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
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) = λ g(qt1) + (1-λ) g(qt2)
The class of 2nd order approximations is called “superlative.”
This is a superlative index called the Törnqvist index.
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period 1
Real output
q1
q2
Prices
p1
p2
Ratio:
period 2 to
period 2 period 1
1
1
100
1
100
1
1
1
0.010
1.00
0.010
1.00
2.0
2.0
1.0
1.00
10.00
10.00
2.000
1.010
101.000
2.000
50.50
1.98
Nominal output
= ∑piqi
Utility = (q1*q2)^.5
Quantity indexes
Laspeyres (early p)
Paasche (late p)
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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)
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period 1
Real output
q1
q2
Prices
p1
p2
Nominal output
= ∑piqi
Utility = (q1*q2)^.5
1
1
Ratio:
period 2 to
period 2 period 1
100
1
100
1
1
1
0.010
1.00
0.010
1.00
2.0
2.0
1.0
1.00
10.00
10.00
Quantity indexes
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Fisher (geo mean of L
and P)
1.421
14.213
10.00
Törnqvist (wt.
average growth rate)
1.000
10.000
10.00
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[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
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