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)
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What do these have in common?
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•
•
•
•
•
•
•
•
…
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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
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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BEA, Survey of Current Business, August 2012
Personal savings rate
[Savings/disposable personal income]
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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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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 = 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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Repeat slide:
Incomes in the National Income Accounts
Table 1.12. National Income by Type of Income
[Billions of dollars]
Bureau of Economic Analysis
Last Revised on: August 29, 2012
1929
National income
Compensation of employees
Proprietors' income
Rental income of persons
Corporate profits after tax
Net interest and misc
Taxes on production and imports
2011
93.9
13,359
51.1
14.1
6.2
9.3
4.6
6.8
8,295
1,157
410
1,448
527
1,098
Source: U.S. Bureau of Economic Analysis (www.bea.gov)
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Share, 2001
62.1%
8.7%
3.1%
10.8%
3.9%
8.2%
Now back to our puzzler!
GDP?
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A puzzler:
What is the growth in overall output (GDP)?
period 1
Real output
q1
q2
Prices
p1
p2
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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
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!
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 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
period 1
Real output
q1
q2
Prices
p1
p2
Nominal output
= ∑piqi
Quantity indexes
Laspeyres (early p)
Paasche (late p)
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1
1
Ratio:
period 2 to
period 2 period 1
100
1
HUGE
100 difference!
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
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
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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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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L > Util > P
Laspeyres
overstates growth
and Paasche
understates relative
to true.
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 (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)
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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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.
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.
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