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Number 95-40, November 24, 1995

New Estimates of the Recent Growth
in Potential Output
The level and growth rate of potential output are
important considerations in determining monetary policy. Loosely defined, potential output is
the amount produced when labor and physical
capital are at levels of utilization that create no
pressure on inflation to change-the so-called
"natural" levels of utilization. If an economy
is operating below its potential level, the slack
in resources slows price inflation. Conversely,
inflation is likely to increase if output is above
potential. Of course, over time, actual output
also cannot generally grow faster than potential
output without increases in inflation. In this way,
the growth rate of potential output determines
how fast the economy can expand in a sustainable way, and is thus an important speed limit
for the economy that pol icy shou Id respect.
Estimating the growth rate of potential output
for the entire economy with any degree of certainty
is difficult. This Weekly Letter provides some simple, broad-brush estimates by means of Okun's
Law, which is an often-used empirical regularity
between the growth rates of actual and potential
output and changes in the actual and natural rates
of unemployment. In particular, I consider how
the new "chain-weighted" measure of Gross
Domestic Product (GOP) may change estimates of
the recent trend in potential output. The chainweighted measure of output appears to be consistent with a slower increase in recent potential
output than the traditional fixed-weighted series.
Indeed, I estimate that chain-weighted potential
output has grown at about a 2 percent annual
pace during the first half of this decade-almost
one-half of a percentage point slower than on a
fixed-weighted basis.

Okun's Law
In its most common form, Okun's Law simply
states that, over the business cycle, output and
unemployment tend to move in opposite directions and roughly in proportion to one another;
specifically, the cyclical change in the unemployment rate, that is, its change minus any change
in the natural rate of unemployment, is propor-

tional to the difference between the growth rates
of potential and actual output. (Recent discussions are provided by Braun (1990) and McNees
(1991).) In theory, there is no reason why Okun's
Law should hold. Fluctuations in labor productivity, the average workweek, and labor force
participation could each drive wedges between
the movements in output and unemployment. In
practice, however, the fluctuations in these other
series are well-correlated with movements in the
unemployment rate. For example, the average
workweek tends to fall as unemployment rises
(perhaps because firms try to hoard employees
through downturns by reducing hours worked
instead of firing workers).
The rule of thumb for the factor of proportionality
in Okun's Law is one-half; that is, if output grows
1 percentage poi nt faster than the growth rate of
potential for one year, the unemployment rate
falls by about 0.5 percentage point. The percentage variation in real output is thus twice as
large as the percentage-point fluctuations in the
unemployment rate. This reflects the fact that
fluctuations in productivity, the average workweek, and labor participation tend to damp
movements in unemployment.

Estimates of potential output
With a few assumptions, Okun's Law can be used
to estimate the growth rate of potential output.
First, I will assume that this growth rate is fairly
constant. This is probably nottoo bad of an approximation over short periods of time (Rudebusch
1993); consequently, I will limit my data sample
from 1980 onward.
Second, I will make an assumption about changes
in the natural rate of unemployment. Many have
argued that changes in the composition of the
labor force, especially the effects of the entrance
and aging of the large baby-boom cohort in the
labor market, induced significant changes in
the natural rate. Most notably in the 1980s, the
labor force share of younger workers, who generally have the highest unemployment rates, fell

dramatically. The general contour of several published estimates (for example, Weiner 1993) suggests that the natural rate fell by about one-half
of a percentage point during the 1980s but has
changed little so far in the 1990s as the demographic composition of the labor force stabilized.
With these assumptions, an estimate of the
growth rate of potential output can be obtained
by comparing the change in the unemployment
rate to the percent change in actual output. Figure 1 demonstrates this exercise. The vertical axis
measures the change in the quarterly average
unemployment rate (excluding the annual 0.05
percentage point decrease in the natural rate during the 1980s), and the horizontal axis measures
the percent change in fixed-weighted real GOP.
(These changes are measured from fourth quarter
to fourth quarter of adjacent years.) The slope of
the solid line gives the factor of proportionality
in Okun's Law. Here that slope is estimated to be
almost exactly one-half, supporting the usual rule
of thumb.
The point at which this line crosses the horizontal axis-that is, where the unemployment
rate does not change-gives an estimate of the
growth rate of potential output. This is because
if the unemployment rate is stable, actual output
must be growing at the same pace as potential
output. At points below (above) the horizontal
axis, unemployment is falling (rising), and the
economy is growing faster (slower) than potential. Over the whole sample from 1980 to 1994,
such an Okun's Law estimate of the growth rate
of potential is 2.4 percent, which is in the usual
range of estimates. In Figure 1, the growth rate
of potential is allowed to take on different values during the period 1980-1989 and during
1990-1994. The solid line is based on the earlier
sample and intersects the horizontal axis at 2.5
percent. The dotted line is based on the later
sample and intersects at 2.3 percent. These numbers are very close; indeed, statistically, there is
a four out of five chance that there has been no
change in the growth rate of fixed-weighted potential output across the two samples. Thus, on a
fixed-weighted basis, potential output appears to
have been growing at a fairly steady pace during
the past 15 years.

Chain-weighted potential output
The estimates of potential output given above
use the traditional fixed-weighted or constantdollar series on real GOP. Ouring 1995, the Bureau of Economic Analysis (BEA) has started to
promote a new chain-weighted measure of real

Figure 1
Okun's Law with Fixed-Weighted GDP
Change in the
unemployment rate





", 88








Fixed-Weighted GOP growth


output. The chain-weighted series provides a
better answer to the question of how to add up
all the diverse goods and services produced in
the economy at each point in time even when the
general level of prices is changing.
The traditional fixed-weighted real GOP series
values each product at its price in 1987-the
base year-rather than at the price actually paid.
This measure of output thus eliminates the increase in the level of nominal spending that
occurs because of general inflation in the price
level. There is, however, a significant shortcoming: a fixed-weighted measure uses the levels of
relative prices in 1987 for valuing various goods
and services in all other years. Thus, if in 1987,
five computers cost as much as one car, the
fixed-weighted GOP series uses this five-to-one
relative price to add up computers and cars in
every year.
To understand the flaw in this procedure, assume
that in 1987, five computers were produced, so
the value of this computer output was equivalent
to the value of one car. Also assume that by 1995
the price of computers fell, so ten computers cost
as much as one car, and the output of computers
rose, so ten computers were being produced. Of
course, in 1995 relative prices, it is still the case
that "one car's worth" of computers is being produced in 1995. However, in the fixed-weighted
measure with a 1987 base year, the ten computers produced in 1995 are worth the same as two
cars. Thus, in some sense, the use of a 1987 base
year overstates the amount of real computer output in 1995. Such a bias in measuring output that

is not produced in the base year is typical of
fixed-weighted measures. The bias is reduced
with the new chain-weighted measures of real
output, which, in essence, use a sequence of
base years, and nearly contemporaneous relative
prices, to value output. (See Motley (1995) for

possibility that the growth rate of potential output
fell at the start of this decade.

Figure 2 examines Okun's Law using the chainweighted measure of real output. The slopes of

Such a drop in the growth rate of potential would
not be too surprising. Growth in the labor force
has slowed significantly so far in the 1990s, as
both working-age population growth decreased
and the labor force participation rate flattened
out. This slowdown could easily have subtracted
a half of a percentage point from the potential

the solid and dotted lines are unchanged at one-

output growth rate. Using the fixed-weighted ag-

half, so the magnitude of the tradeoff in Okun's
Law appears unaffected. Also, over the whole
sample from 1980 to 1994, the estimate of the
growth rate of potential (not shown) is 2.4 percent, as for fixed-weighted GDP. However,
allowing the growth rate of potential to change
between the 1980s and the first four years of the
1990s yields striking results. The solid line for
the earlier sample crosses the horizontal axis at
2.6 percent, while the dotted line for the later
sample crosses at only 2 percent. This represents
a dramatic slowing in the growth rate of potential
output. Statistically, there is only a one in six
chance that there has been no change in the
growth rate of chain-weighted potential output

gregate output measure, an apparent increase in
the growth rate of productivity in the 1990s offsets this decline; however, this acceleration in
productivity is just the spurious result of measuring each year's output (particularly computers)
with 1987 relative prices. That is, higher recently
measured productivity growth on a fixedweighted basis did not reflect higher efficiency
gains through increased use of computers, as
some have argued; instead, ironically, it merely
reflected the mismeasurement of computer output. (See Oliner and Wascher (1995).) On a
chain-weighted basis, there is no significant
change in productivity growth in the 1990s, so
the weak labor force growth damps the growth

across the two samples. Thus, there is a definite

of potential.
Glenn Rudebusch
Research Officer

Figure 2
Okun's Law with Chain-Weighted GDP


Change in the

Braun, Steven N. 1990. "Estimation of Current-Quarter
Gross National Product by Pooling Preliminary
Labor-Market Data:' Journal of Business & Economi~ Statistics 8 (July), pp. 293-304.



McNees, Stephen K. 1991. "How Fast Can We Grow?"
New England Economic Review (January/February), pp. 3-14.
Motley, Brian. 1995. "New Measures of Output and
Inflation." FRBSF Weekly Letter 95-24 (July 7).


- -










1990 - 94 .....



Oliner, Stephen D., and William L. Wascher. 1995. "Is
There a Productivity Revolution Under Way in the
United States?" Challenge (Nov.-Dec.) pp. 18-30.

Chain-Weighted GOP growth



Rudebusch, Glenn R. 1993. "The Uncertain Unit Root
in Real GDP:' The American Economic Review 83
(March) pp. 264-272.
Weiner, Stuart E. 1993. "New Estimates of the Natural
Rate of Unemployment." FRB Kansas City Economic Review (Fourth Quarter) pp. 53-70.

Opinions expressed in this newsletter do not necessarily reflect the views of the management of the Federal Reserve Bank of
San Francisco, or of the Board of Governors of the Federal Reserve System. Editorial comments may be addressed to the editor
or to the author. Free copies of Federal Reserve publications can be obtained from the Public Information Department, Federal
Reserve Bank of San Francisco, P.O. Box 7702, San Francisco 94120. Phone (415) 974-2246, Fax (415) 974-3341. Weekly Letter
texts and other FRBSF publications and data are available on FedWest Online, a public bulletin board service reached by setting
your modem to dial (415) 896-0272.

Research Department

Federal Reserve
Bank of
San Francisco
P.O. Box 7702
San Francisco, CA 94120

Pnnted on recycled paper Q
with soybean inks.
\J:I ~

Index to Recent Issues of FRBSF Weekly Letter





Western Banks and Derivatives
Monetary Policy in a Changing Financial Environment
Inflation Goals and Credibility
The Economics of Merging Commercial and Investment Banking
Financial Fragility and the Lender of Last Resort
Understanding Trends in Foreign Exchange Rates
Federal Reserve Policy and the Predictability of Interest Rates
New Measures of Output and Inflation
Rebound in U.s. Banks' Foreign Lending
Is State and Local Competition for Firms Harmful?
Productivity and Labor Costs in Newly Industrializing Countries
Using Consumption to Track Movements in Trend GOP
Output-Inflation Tradeoffs and Central Bank Independence
Inflation-Indexed Bonds
California Dreamin': A Rebound in Net Migration?
Interest Rate Smoothing and Inflation, Then and Now
Russian Banking
Consolidation: California Style
Is Pegging the Exchange Rate a Cure for Inflation? East Asia
Monetary Policy in a Dynamic, Global Environment
The Rhyme and Reason of Bank Mergers


The FRBSF Weekly Letter appears on an abbreviated schedule in june, july, August, and December.