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Number 93-06, February 12, 1993

GDP Fluctuations:
Permanent or Temporary?
Is the sluggish growth in U.s. GOP in recent
years just a temporary cyclical downturn or a
permanent reduction in the growth rate of the
u.s. economy? Up to the late 1970s, the conventional view held that short-run fluctuations in the
economy only reflect temporary cyclical shocks
that leave the long-run trend in output unaffected.
Since the early 1980s, however, an influential
group of researchers has taken the view that shortrun fluctuations also may reflect permanent
changes in output and its trend. These researchers have developed methods for quantifying the
extent to which fluctuations in output may be
attributed to temporary cyclical factors or to
changes in trend:
To shed light on the issues underlying this debate, this Weekly Letter discusses two alternative
approaches to modeling the trend in GOP. The
first assumes that the long-run rate of growth is
constant; the second assumes that the trend
varies randomly in response to shocks to the
economy. The focus here will be on conceptual
and methodological issues rather than on precisely quantifying the relative importance of
long-run and short-run factors in the recent
period of sluggish growth. Such a quantification
was offered in a recent Weekly Letter (93-02).

Constant, or deterministic, trend
If a macroeconomist had been asked at the end
of 1971 whether U.S. output would continue to
fall at around 0.2 percent a year, the average rate
observed over the preceding year, the most likely
answer would have been "no." The macroeconomist probably would have responded that the
contraction the u.s. economy experienced in
1970 was temporary. Output at some point would
be expected to resume growing at a rate close to
4 percent, the average growth rate observed over
the previous decade.
Unable to refrain from giving a lecture, the macroeconomist would have gone on to explain that
the response involves two closely related assumptions about GOP behavior. First, there is a

long-run equilibrium trend in COP associated

with a constant trend rate of growth. The trend
is said to be deterministic, because GOP grows
at the same fixed rate in each period. The deterministic trend is estimated by fitting a straight
line to approximate the long-run tendency of
GOP. The slope of that line provides a measure of
the average rate at which GOP grows over time.
!n the traditional view, the stable GDP trend is
determined by supply factors, such as the capital
stock, the labor force, and technology.
Second, any deviations from the level of COP
determined by the trend are temporary. In particular, past disturbances to GOP do not affect its
current 'Ievel (only the unchanging trend does), or
if they do, their effect dies down to zero as time
passes. In this framework, short-run (cyclical)
fluctuations in GOP reflect shocks to aggregate
demand that temporarily move the economy
away from the long-run trend, and are independent of the supply factors that determine this
This intuitively appealing approach to modeling
GOP behavior underlies the Keynesian textbook
treatment of business cycle fluctuations, as well
as the approach followed by a large number of
empirical macroeconomic models developed
between the 1950s and the 1970s that are still
widely used for forecasting and policy analysis.
The deterministic trend model has a verifiable
implication. If the trend in GOP is indeed unchanging, a forecast of 1989 U.S. GOP made at
the end of 1973 based on data for 1959.Q11973.Q3 (before the first oil price shock) would
be similar to the forecast made at the end of 1985
with data for 1973.Q3-1985.Q4. It is easy to verify that this implication is contradicted by the
data. In 1973, our macroeconomist would have
forecast u.s. GOP for 1989 by assuming an annual growth rate of nearly 4 percent, based oli
the best estimate of the deterministic trend according to data available up to that time. In 1985,
however, because of the much slower rate of
growth experienced between 1975 and 1985, the
estimate of the deterministic trend would have

fallen to just over 2 percent. The greater accuracy
of the 1985 forecast, in comparison to the forecast made in 1973, suggests that there was a
decline in the trend rate of growth in U.s. GOP
during the postwar period.

Chart 1
GDP Trends



Variable, or stochastic, trend
The time-varypmg characteristic of forecasts of
GOp' which is common to many economies, has
prompted a large number of researchers to propose a model where the trend on average grows
by some fixed amount, but is subject to random
shocks in every period that cause growth to
deviate from this average by an unforecastable
amount. A trend that varies in every period in
response to shocks is known as a "stochastic (or
random) trend." In contrast to a model where the
trend in GOP is unchanging, in this framework
all past shocks to GOP affect its current level;
that is, all shocks have some permanent effect
that does not die out over time. For this reason,
some researchers refer to the stochastic trend in
GOP as the permanent component of GOP.









Chart 2
GDP Cycles



There are several ways to model a stochastic
trend. One popular approach, suggested by Beveridge and Nelson (1981), models the trend as the
long-run forecast level of GOp' using all available
information on GOP's behavior up to the present.
This model is intuitive, as the long-run forecast
level of GOP provides information on the longrun tendency in its behavior. Also, under this definition, the trend in GOP changes every period in
response to shocks to the economy.
The deterministic and stochastic trend models of
GOP can convey quite different impressions
of long-run and short-run behavior. Chart 1 compares the log of real GOP in the U.s. to a linear
deterministic trend and to the stochastic trend
based on the Beveridge-Nelson method. Chart 2
illustrates the temporary cycles (the differences
between actual GOP and the estimated trends)
associated with these two trend measures. As can
be seen in Chart 1, the deterministic time trend is
smooth, while the stochastic trend tends to follow
the actual path of GOP quite closely. Conversel,»
Chart 2 shows that the cycle implied by a deterministic time trend is very persistent (movements
away from the trend last a relatively long time),
with large peaks and troughs. The cycle associated with a stochastic trend exhibits much less
persistence, and peaks and troughs are much

' .oJ









The smoothness of the deterministic trend, as
well as the high degree of persistence in its associated cycle, reflects the fact that shocks to GOP
do not change the trend in this model. In contrast, shocks to GOP always result in a change in
the stochastic trend in every period. It is worth
reiterating that these differences significantly alter the way we interpret specific business cycle
episodes. For example, as can be seen in Chart 1,
the deterministic trend model suggests that sluggish growth in the early 1990s reflects a purely
temporary (although persistent) cyclical downturn. In contrast, the stochastic trend model
suggests that much of the recently observed sluggishness in U.S. growth is permanent. This last

interpretation would only be revised if the U.S.
experiences several quarters of more rapid
growth that lead to upward revisions in the
estimated stochastic trend.
The key feature of the stochastic trend model that
distinguishes it from the deterministic trend model
is that it may vary in response to shocks in each
period. The extent to which the trend will vary
however, will depend on the particular model of
GOP and of its stochastic trend. For example,
another way of modeling a stochastic trend was
discussed in a recent Weekly Letter (93-02). A
macroeconomic model with two variables is estimated, and some shocks are assumed to have
permanent effects on output (supply shocks),
while other shocks are assumed to have temporary effects (demand shocks). The stochastic
trend in this framework can be thought of as that
component of GOP that is attributable to shocks
with permanent effects. This method of modeling
a stochastic trend has several advantages, as it
uses information from other macroeconomic variables (not just GOp' as in the Beveridge-Nelson
method). Also, the decomposition into trend and
cycle is based on an explicit macroeconomic
model, which facilitates economic interpretation.
This alternative model of the trend also attributes
much of the recent slowdown in GOP to permanent changes in the trend, but its description of
the trend and cycle in GOP differs in a number
of respects from that reported here.

Why do we care?
The ability to distinguish between permanent
and temporary movements in output is important
in deciding whether it is appropriate to use macroeconomic policies that have temporary effects
or to focus on long-run policies that may permanently affect trend behavior. For example, if the
current sluggish pace in economic activity is due
to temporary but highly persistent shocks, a case
may be made in favor of expansionary macroeconomic policies that will bring the level of economic activity back to the long-run trend more
quickly. However, if the sluggishness in output
reflects a permanent decline in the trend rate of
growth of the economy, expansionary macroeconomic policies may not be effective in the long
run, as there is no reason to expect that such policies can raise the trend rate of growth. Instead,
policies to raise productivity or labor skills may
be more appropriate.

Unfortunately, there is no consensus on which of
the two models of the trend is superior. Proponents of the deterministic trend model believe it
is appropriate because the long-run path of GOP
depends on supply factors (such as capital, labor
skills, and natural resources) that change very little in the short run. They argue that any changes
in the trend are infrequent, and can be incorporated by adjusting the deterministic trend model
once the evidence accumulates that such a
change in the trend has occurred. Also, it is not
clear what stochastic trend model, if any, is to be
preferred to the deterministic trend model. As
discussed earlier, there are a number of ways of
modeling a stochastic trend and there is disagreement on how well these various models
reflect the impact on output of permanent
changes in labor productivity or technology.
Proponents of the stochastic trend model believe
that the assumption that the trend is unchanging,
or equivalently, that short-run fluctuations in output have no permanent effects is implausible.
They also point out that the stochastic model is
more general, because it allows researchers to
measure the extent to which short-run fluctuations in output are due to permanent or temporary shocks, rather than rule out permanent
shocks entirely, as in the deterministic trend
model. In particular, the stochastic trend model
may approximate the deterministic trend model, if
the data and the particular specification of the
stochastic trend call for it, to any degree of
As no known statistical method is available to
establish the superiority of either of the two trend
models, disagreement on this question will not
be easily resolved. Further research is needed to
determine which model will ultimately prove
to be more satisfactory.
Ramon Moreno

Beveridge, Stephen, and Charles R. Nelson. 1981
"A New Approach to Decomposition of Economic
Time Series into Permanent and Transitory Components with Particular Attention to Measurement of
the 'Business Cycle!" Journal of Monetary'Economics 7 pp. 151-174.

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.

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Index to Recent Issues of FRBSF Weekly Letter





9/18 92-32
10/9 92-35
10116 92-36
10/23 92-37
10/30 92-38
11/6 92-39
11/13 92-40
11/20 92-41
11/27 92-42
12/4 92-43
12/11 92-44
12/25 92-45
1/22 93-03
1/29 93-04

Are Big U.s. Banks Big Enough?
What's Happening to Southern California?
Money, Credit, and M2
Pegging, Floating, and Price Stability: Lessons from Taiwan
Budget Rules and Monetary Union in Europe
The Slow Recovery
Ejido Reform and the NAFTA
The Dollar: Short-Run Volatility and Long-Run Adjustment
The European Currency Crisis
Southern California Banking Blues
Would a New Monetary Aggregate Improve Policy?
Interest Rate Risk and Bank Capital Standards
NAFTA and U.S. Banking
A Note of Caution on Early Bank Closure
Where's the Recovery?
Diamonds and Water: A Paradox Revisited
Sluggish Money Growth: Japan's Recent Experience
Labor Market Structure and Monetary Policy
An Alternative Strategy for Monetary Policy
The Recession, the Recovery, and the Productivity Slowdown
u.s. Banking Turnaround
Competitive Forces and Profit Persistence in Banking
The Sources of the Growth Slowdown

The FRBSF Weekly Letter appears on an abbreviated schedule in June, July, August, and December.