>

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)

Brad DeLong
Associate Professor of Economics, 601 Evans
University of California
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net

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:



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.


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.




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.


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.


>

Econ 100b

Created 4/30/1996
Go to
Brad De Long's Home Page


Professor of Economics J. Bradford DeLong, 601 Evans
University of California at Berkeley
Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net/