# > Econ 100b Created 4/30/1996 Go to Brad De Long's Home Page Lecture Three

## Index Numbers and the Measurement of Unemployment (Economics 100b; Spring 1996)

Associate Professor of Economics, 601 Evans
University of California
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu

January 24, 1996

Real and Nominal GDP
Fixed-Weight Indices, "Deflators", and Chain Indices
The GDP Deflator and the CPI

The problem set associated with this week's lectures is called Macroeconomic Measurement.

Real and Nominal GDP

We choose a base year for measuring real GDP in order to separate out changes in nominal GDP due to overall inflation and deflation from changes due to increases or decreases in the wealth and productivity of the economy.

A price index with a fixed basket of goods: it is sometimes called a "Laspeyres" index.
A price index dual to a fixed-prices quantities index: it is sometimes called a "Paasche" index.
An index with changing baskets of weights chained together is--no surprise--a "Chain" index.

I don't want you to worry about the names "Paasche" and "Laspeyres". I want you to, instead, worry about the problems of making index numbers.

Four key lessons:

• A fixed-weight index takes no account of people's ability to substitute to achieve the same utility when commodities become more expensive...
• A deflator-like index does not take account of the utility lost as changing prices push you away from your original basket of consumption choices.
• For years closer to the present than the base year, real GDP tends to overstate rates of economic growth.
• For years further in the past than the base year, real GDP tends to understate rates of economic growth.

Fixed-Weight Indices, "Deflators", and Chain Indices

Let's begin with a basic problem: we want to create a single index--a single number--that will capture, as best we can, the growing overall amount of production and wealth in the economy.

• Nominal GDP--multiplying every final good (excluding intermediate goods) in the economy by its price, or adding up all the nominal incomespaid to workers and to owners of factors of production, or calculating total expenditure on consumption, investment, government purchases of goods and sercies, and net exports--will not do as an index: it mixes together shifts due to changes in the real wealth and income of society and shifts do to the upward or downward drift of the average dollar prices at which goods are sold.

So what we are looking for is an index of real GDP. To see how you might go about building such an index, let's lump all commodities--all goods and services--into two categories, "computers" and "stuff". You can see the major lessons and problems if we just consider trying to add up two kinds of goods. And the major lessons and problems generalize in a straightforward manner to the real world, in which there are thousands of different commodities.

• In 1941, the U.S. economy produced some 970 billion units of "stuff"--and each unit of "stuff" sold, on average, for \$0.13?. In 1941, the U.S. economy also produced 0 computers--and we do not know how much they would have cost--perhaps infinity, since we did not know how to produce them.
• In 1987, the U.S. economy produced some 4210 billion units of "stuff"--and each unit of "stuff" sold, on average, for \$1. In 1987, the U.S. economy also produced some 150 million "standard computers"--and the average "standard computer" sold for \$1,000.
• In 1995, the U.S. economy produced some 4960 billion units of "stuff"--and each unit of "stuff" sold on average for \$1.27. In 1995, the U.S. economy also produced some 490 thousand "standard computers"--and the average "standard computer" sold for \$450.

Digression: What do I mean by a "standard computer"? Compare my U.C. Berkeley 1995 laptop--12 MB of memory, a 50 MHZ 68040 processor, a 320 MB hard disk--with my Harvard 1991 laptop--8 MB of memory, a 33 MHZ 68030 processor, an 80 MB hard disk. My new laptop is clearly more "computer", but how much more? Dividing its price by the overall computer price index suggests that my current laptop has the horsepower of some ten "standard computers"--while my old laptop had the horsepower of four. But there are enormous problems in even measuring the quantity of even finely-divided groups of commodities.

Nominal GDP grew from \$4,360 billion to \$6,916 billion from 1987 to 1995. What share of that is growth in real output?

One experiment: let's take 1987 as the "base year"--value all production in all other years as if we took it forward or backward in time to 1987, and sold it at the prices that prevailed in 1987. We would then find:

1941 real GDP (in 1987 prices): \$970 worth of stuff plus 0 worth of computers = \$970
1987 real GDP (in 1987 prices): \$4210 worth of stuff plus \$150 worth of computers = \$4360
1995 real GDP (in 1987 prices): \$4960 worth of stuff plus \$490 worth of computers = \$5450

Total growth 1941-1987 (in 1987 prices): +349%
Total growth 1987-1995 (in 1987 prices): +25%

A second experiment: let's take 1995 as the "base year":

1941 real GDP (in 1995 prices): \$1286 worth of stuff plus 0 worth of computers = \$1286
1987 real GDP (in 1995 prices): \$5683 worth of stuff plus \$67 worth of computers = \$5751
1995 real GDP (in 1995 prices): \$6696 worth of stuff plus \$220 worth of computers = \$6916

Total growth 1941-1987 (in 1995 prices): +347%
Total growth 1987-1995 (in 1995 prices): +20%

A third experiment: let's take 1941 as the "base year":

1941 real GDP (in 1941 prices): \$126 worth of stuff plus 0 worth of computers = \$126
1987 real GDP (in 1941 prices): xx worth of stuff plus infinity worth of computers = infinity
1995 real GDP (in 1941 prices): xx worth of stuff plus infinity worth of computers = infinity

Total growth 1941-1987 (in 1941 prices): infinite
Total growth 1987-1995 (in 1941 prices): infinite

Clearly we have a big problem if we try to use 1941 prices to measure recent economic growth.

But--even assuming there are no new goods; nothing produced in 1995 that would have cost an infinite amount to make in 1987--we do get different answers depending on whether we use 1987 or 1995 prices to calculate real GDP growth over those eight years.

Which is the right answer?

Well, what question are you asking? They are both right answers to different questions--but neither of those questions is probably the one that you want answered.

• Using 1987 prices produces a larger number for the amount of growth than corresponds to the question you probably want to ask. Every computer purchased in 1995 is, using 1987 prices, valued as if it were worth fully twice as much as it in fact was...
• Using 1995 prices produces a smaller number for the amount of growth than corresponds to the question you probably want answered. Every computer purchased in 1987 is, using 1995 prices, valued as if it were worth much less relative to other goods at the time than it in fact was...
• The Commerce Department is moving to a "chain-weighted" system for measuring real GDP

The GDP Deflator and the CPI

Price indexes. You could construct a fixed (quantity)-weight price index. You could divide nominal GDP by real GDP, and get something called the implicit price deflator.

• At the Treasury Department, the career civil servants charged with tracking the economy did not like the implicit price deflator...
• The consumer price index is a fixed-quantity-weight index; but they revise the weights (looking forward) about once every five years or so...
• Biases in measurement? Yes:
• The CPI overstates rates of price increase by 1/2 to 1.5 percent per year (and the GDP deflator has similar biases). We are getting richer and more productive faster than the official numbers report.
• Additional bias: For years closer to the present than the base year, real GDP tends to overstate rates of economic growth (and the implicit price deflator tends to understate inflation).
• Additional bias: For years further in the past than the base year, real GDP tends to understate rates of economic growth (and the implicit price deflator tends to overstate inflation).

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# Econ 100b

Created 4/30/1996
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