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April 5, 1991

Probability of Recession
The current economic downturn is now almost
two quarters old. Even before the contraction
began some commentators were forecasting that
a recession was imminent. These predictions
were typically based on the notion that the longest expansion in the post-war period, which
lasted for seven years, had to run out of steam
at some poi nt.
On a more rigorous level, economists have tried
to predict economic contractions using recession
probability index (RPI) models. Since these models
aim to measure the likelihood of a future recession, they rely on leading economic indicators
as their underlying sources of information.

index, a measure of unfilled orders, the exchange
value of the dollar, a measure of slack work, and
a group of financial variables (interest rates and
spreads between different rates). Each set of
series is weighted to form an index, where the
weights are obtained from state-of-the-art time
series analysis.
The recession index (Chart 1) is calculated by
combining the two indexes. It measures the probability that the economy will be in a recession in
six months.

Chart 1
NBER Recession Index

Probability of
Recession (%)

This Letter presents an overview of two
representative RPI models and examines their
performance, past and present. At the end of
last year, the two models were providing widely
divergent estimates of the probability that the
economy soon would be in a recession. Thus
they did little to mitigate the uncertainty about
the duration and severity of weakness in the



NBER model
The National Bureau of Economic Research
RPI model follows the traditional assumption that
expansions and contractions are part of the same
stable structure, and are responses to random
shocks (policy and others). It is based on two
indexes that were created at the NBER by Stock
and Watson (1989).

The first is the index of coincident economic
indicators (CEI). The CEI is designed to measure
the level of current economic activity and comprises four data series: industrial production, real
personal income less transfer payments, real
manufacturing and trade sales, and employeehours in nonagricultural establishments.
The second is the index of leading economic
indicators, and is designed to predict growth in
the eEl six months hence. This index comprises
seven data series: the new housing authorization








Turning point forecast model
This model is based on different assumptions
from the traditional view, and derives from the
work of Neftci (1982). It assumes that there are
distinct differences in economic patterns between expansions and contractions; therefore,
key variables should behave differently in an
expansion or a contraction. For example, output
tends to inch upward gradually during an expansionary period, whereas it tends to drop very
sharply at the beginning of a contractionary
period. Consequently, forecasting a recession
amounts to predicting a switch in the behavioral
mode of the economy from the expansionary to
the contractionary phase. This prediction is based
on changes in a leading indicator variable.

The turning point index model shown in
Chart 2 was developed by Rudebusch and
Diebold (1989). The monthly index of Leading
Economic Indicators released by the Department
of Commerce (DOC-LEI) is its source of information. For each observation of the DOC-LEI, one
must calculate the probability whether the new
observation represents a shift to a downturn
regime or a continuation of a downturn regime.
The probability is calculated by applying a
Bayesian statistical method.

Chart 2
ThrningPoint Recession Index

Probability of
Recession (%)

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materialize. Thus, over a limited sample period,
simply correlating the probability with the business cycle is not necessarily a good way to judge
the accuracy of the models. For example, a sample period of 10 years would provide over 3,600
observations of daily precipitation, but for the
same period there would likely be only a few
recession episodes. Of course, the larger the
sample, the more appropriate this method of
evaluation becomes.
One criterion that is often used to gauge
reliability is the frequency of false signals.
Leading indicators are notorious for making
this mistake-hence, Nobel laureate economist
Paul Samuelson's famous remark, "The stock
market has predicted nine out of the last five recessions!" A signal is false if the model forecast
of an imminent recession is not followed by an
actual recession within a reasonable period of
time. For example, suppose an assessment criterion interprets the model as signaling a recession
urhr'\t"'It. +hl"1t. 1'"'It.t""h'..."h:l:t" ;r ..... h_un
VVIlt::"1I 1I1'lC; tJlVUOUllllY



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ing this criterion to the post-1968 sample period,
the turning point index records two false signals
(1985 and 1988), whereas the NBER index has


The recession probability indexes provide
advance information about the general condition
of the economy by using various kinds of leading
economic indicators. They do so in a more sophisticated way than do common rule-of-thumb
methods. For example, one rule-of-thumb method
simply looks at the DOC-LEI for three consecutive declines to forecast a future recession. However, RPI models are more systematic because
they account for the magnitude of change as well
as the temporal direction of change in the leading indicators. And in general, RPI models do
substantially outperform rule-of-thumb predictions.
Assessing the accuracy of RPI models is
conceptually difficult, however, since the forecasts are in terms of probabilities, which cannot
be observed. It's essentially the same problem as
assessing the accuracy of predictions about the
probability of rain. If the weatherman says there's
a 70 percent chance of showers today, and instead it just clouds over, the forecast still may
have been accurate. Likewise, though the probability of a recession may be high, it may never

Another criterion is the frequency of failure to
predict an ensuing recession with some given
lead time (for example, six months). The NBER
index has failed completely to predict the current
recession, whereas the turning point model has
failed twice to signal with any lead time (1974
and 1981). The performance of the latter model
in this regard is most likely related to the fact that
the DOC-LEI is notorious for having widely varying lead times with the business cycle. For the
past 30 years, for example, turning points in the
DOC-LEI have led the contractionary turning
points of the economy by anywhere from 2 to
20 months. Therefore, the turning point index,
which is based on the DOC-LEI, seems to
reflect the same characteristic.

Why did the two models
differ in this downturn?
Recent predictions of the likelihood of a
recession in early 1991 by these models are quite
diverse-14 percent by NBER, and 98 percent
by the turning point model. These models differ
not only in their theoretical underpinnings, but
also in that the NBER model includes a set
of financial variables, while the turning point
model does not. One reason to include financial

variables is that the spread between rates can be
a useful predictor of downturns; for example, the
spread between short-term commercial paper
and T-bills reflects the default risk of the commercial paper, which, in turn, could be sensitive
to an expected recession.
Recent research on the changing role of financial
variables, however, may explain why models that
depend on them for forecasts can miss the mark.
Be"rnanke (1990), among others, found that
various interest rates and the spreads between
them were substantially more useful in explaining and forecasting key macro variables before
1980 than later.
Before 1980, interest rate spreads, in particular,
the spread between short-term commercial paper and T-bills, reflected the stance of monetary
policy, which affects the economy by shifting
credit conditions. The reflection was particularly
clear because banks operated with deposit interest rate ceilings, and because commercial paper
and T-bills were imperfect substitutes as portfolio

the way the contractionary effects of the causal
factors spread across the economy. For example,
some economists point to the deterioration in
consumer confidence in conjunction with the
Middle East situation as a special factor for this
recession. Others cite the diminished credit
availability which started last year for reasons
related to the weakened condition of the financial institutions and stricter regulations.
These differences may explain why the NBER
model, which was designed to conform to the
general average characteristics of past economic
expansions and contractions, failed to detect the
onset of the current economic downturn. More
generally, the divergent performance of the two
models illustrates the pitfalls of stable linkages
among economic indicators that are in fact interrelated in a complicated manner. Movements in
these indicators will depend upon which variables caused the downturn in the first place.
Thus it is unrealistic to expect the indicators
to be correlated consistently with business
cycle developments.

Chan Guk Huh
Monetary tightening tended to raise market rates
above deposit rate ceilings. In order to earn a
better return, depositors, then, would withdraw
their money from banks and invest in marketinstruments. This "disintermediation" created a
"credit crunch" and subsequently an economic
contraction. Typically, depositors wou Id purchase
T-bills, which can be in relatively small denominations, rather than commercial paper, which is
typically in denominations too large for most depositor holders. The inflow of funds to the T-bill
market depressed T-bill yields relative to commercial paper rates in periods when the general
level of rates is higher. Due to the imperfect substitutability between T-bills and commercial
paper, banks would not arbitrage and offset the
widening spread. According to this hypothesis,
it is relatively easy to explain the diminished role
of the spread. Since the early 1980s, the deposit
rates were deregulated and more alternative
financial assets became available, creating
closer substitutability among these assets.
It is likely that the current recession is distinct
from others before in terms of both its causes and


Bernanke, Ben S. 1990. "On the Predictive
Power of Interest Rates and Interest Rate
Spreads." Federal Reserve Bank of Boston
New England Economic Review pp. 51-68.
Diebold, Francis X., and Glenn D. Rudebusch.
1989. "Scoring the Leading Indicators!'
Journal of Business 64, pp. 369-391.
Neftci, Salih N. 1982. "Optimal Prediction of
Cyclical Downturns!' Journal of Economic
Dynamics and Control 4, pp. 225-241.
Stock, James H., and Mark W. Watson. 1989.
"New Indexes of Coincident and Leading
Economic Indicators!' NBER Macroeconomics
Annual pp. 351-394.

Opinions expressed in this newslettei 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 (Judith Goff) 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.

Research Department

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