Transcript Economics 154b Spring 2006 National Income Accounting and
Now Playing: The Biggest Hit in Economics: The Gross Domestic Product
1 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?
• • • • • • • • • … 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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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*
6 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
National income
1929 2011
93.9
13,359
Share, 2001
Compensation of employees Proprietors' income Rental income of persons Corporate profits after tax Net interest and misc Taxes on production and imports 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)
62.1% 8.7% 3.1% 10.8% 3.9% 8.2%
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Now back to our puzzler!
GDP?
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A puzzler: What is the growth in overall output (GDP)?
Real output q1 q2 Prices p1 p2
period 1 period 2 Ratio: period 2 to period 1
1 1 1 1 100 1 0.010
1.00
100 1 0.010
1.00
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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.
The growth picture for index numbers: the real numbers!
Sector Computers Non computers Output (10 9 2005 $) 1958 2008 Growth of sector Rate per year Growth Factor 0.00002
2,578 157.03200
13,155 31.8% 3.3% 8,049,116.8
5.1
14 Source: Bureau of Economics Analysis
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Some answers
• We want to construct a measure of real output, Q = f(q 1 ,…, q n ;p 1 ,…, p n ) • How do we aggregate the q i 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: L t = ∑ p i,1 q i,2 /∑ p i,1 q i,1 Paasche (1874): weights outputs with fixed prices of a late (or current) year: Π t = ∑ p i,2 q i,2 /∑ p i,2 q i,1
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Start with Laspeyres and Paasche
Real output q1 q2 Prices p1 p2 Nominal output = ∑piqi Quantity indexes
Laspeyres (early p) Paasche (late p) period 1 period 2 Ratio: period 2 to period 1
1 1 100 1 100 1
HUGE difference!
What to do?
1 1 0.010
1.00
0.010
1.00
2.0
2.000
1.010
2.0
101.000
2.000
1.0
50.50
1.98
Solution
Brilliant idea: Ask how utility of output differs across different bundles.
Let U(q 1 , q 2 ) be the utility function. Assume have {q t } = {q t 1 , q t 2 }. Then growth is: g({q t }/{q t-1 }) = U(q t )/U(q t-1 ). For example, assume “Cobb-Douglas” utility function, Q = U = (q 1 ) λ (q 2 ) 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(q t )/U(q t-1 ) = 10.
19 Real output q1 q2 Prices p1 p2 Nominal output = ∑piqi
Utility = (q1*q2)^.5
Quantity indexes Laspeyres (early p) Paasche (late p)
period 1 period 2 Ratio: period 2 to period 1
L > Util > P 1 1 1 1 100 1 0.010
1.00
100 1 0.010
1.00
Laspeyres overstates growth and Paasche understates relative to true.
2.0
1.00
2.0
10.00
1.0
10.00
2.000
1.010
101.000
2.000
50.50
1.98
Solution (cont.)
Continuing with “Cobb-Douglas” utility function, Q = U = (q 1 ) λ (q 2 ) 1- λ Define the (logarithmic) growth rate of x t as g(x t ) = ln(x t /x t-1 ). Then Q t / Q t-1 =[(q t 1 ) λ (q t 2 ) 1- λ ]/[(q t-1 1 ) λ (q t-1 2 ) 1- λ ] g(Q t ) = ln(Q t /Q t-1 ) = λ ln(q t 1/ q t-1 1 ) + (1-λ) ln(q t 2/ q t-1 2 )
g(Q
t ) = λ g( q t 1 ) + (1-λ) g( q t 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 2 nd order approximations called “superlative indexes.”
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Currently used “superlative” indexes
Fisher* Ideal (1922): geometric mean of L and P: F t = (L t × Π t ) ½ Törnqvist (1936): average geometric growth rate: (ΔQ/Q) t = ∑ s i,T (Δq/q) i,t, where s i,T =average nominal share of industry in 2 periods (*Irving Fisher (YC 1888), America’s greatest macroeconomist)
22 Real output q1 q2 Prices p1 p2 Nominal output = ∑piqi
Utility = (q1*q2)^.5
Quantity indexes Fisher (geo mean of L and P) Törnqvist (wt. average growth rate)
period 1 period 2 Ratio: period 2 to period 1
1 1 1 1 2.0
1.00
100 1 0.010
1.00
2.0
10.00
100 1 0.010
1.00
1.0
10.00
1.421
1.000
14.213
10.000
10.00
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.
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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.