Download Economics 154b Spring 2006 National Income

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)
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What do these have in common?
•
•
•
•
•
•
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Real GDP
Consumer price index
Unemployment rate
Exchange rate of the dollar
Inflation rate
Real exchange rate
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
Personal savings rate
[Savings/disposable personal income]
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An important inflation measure (corrected)
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Inflation rate, price of personal consumption
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10
8
6
Fed target
4
2
9
F-12
J-10
D-07
N-05
O-03
S-01
A-99
J-97
J-95
M-93
A-91
M-89
F-87
J-85
D-82
N-80
O-78
S-76
A-74
J-72
J-70
M-68
A-66
M-64
-2
F-62
J-60
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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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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
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
The growth picture for index numbers:
the real numbers!
Sector
Computers
Non computers
Output (billions 2005$)
1960
2012
0.0000337
87.94
3,105.8
15,382.8
Computers
Non computers
Price (2005 = 1)
1960
2012
5,935.7
0.9006
0.1749
1.0560
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 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.
How to implement: 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.
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
•
•
•
•
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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