Identifying Business Cycle Turning Points in Real Time

Abstract

this paper are as follows: First, because the NBER's decisions represent the consensus of individuals who bring differing techniques to bear on the question of when turning points occur, the dating methodology is neither transparent nor reproducible. Second, the NBER business cycle peaks and troughs are often determined well after the fact. This practice appears to be largely the result of the NBER's desire to avoid calling false turning points. Of course, the NBER is not the only source of information regarding business cycle turning points. Economists and statisticians have developed many statistical methods that automate the dating of business cycle peaks and troughs (see Boldin, 1994, for a summary). One such technique is the Markovswitching model. This model, popularized by Hamilton (1989) in the economics profession, is capable of statistically identifying shifts in the For an interesting history of the NBER's role in defining and dating the business cycle, see Moore and Zarnowitz (1986)

Full text

Page 1

Identifying Business Cycle Turning Points in
Real Time
Marcelle Chauvet and Jeremy M. Piger
A
broad economic growth, and periods of recession,
in which there is broad economic contraction.
Understanding these phases, collectively called the
business cycle, has been the focus of much macro-
economic research over the past century. In the
United States, the National Bureau of Economic
Research (NBER), a private, nonprofit research
organization, serves a very useful role in cataloging
stylized facts about business cycles and providing
a historical accounting of the dates at which regime
shifts occur. This task began soon after the found-
ing of the NBER in 1920 and has continued to the
present day.1Since 1980, the specific task of dating
“turning points” in U.S. business cycles, or those
dates at which the economy switches from the
expansion regime to the contraction regime and
vice versa, has fallen to the NBER’s Business Cycle
Dating Committee.2
The NBER dates a turning point in the business
cycle when the committee reaches a consensus that
a turning point has occurred. Although each com-
mittee member likely brings different techniques
to bear on this question, the decision is framed by
the working definition of a business cycle provided
by Arthur Burns and Wesley Mitchell (1946, p. 3):
MARCH/APRIL 2003 47
common feature of industrialized economies
is that economic activity moves between
periods of expansion, in which there is
Business cycles are a type of fluctuation
found in the aggregate economic activity of
nations that organize their work mainly in
business enterprises: a cycle consists of
expansions occurring at about the same
time in many economic activities, followed
by similarly general recessions, contractions
and revivals which merge into the expansion
phase of the next cycle.
A fundamental element of this definition is the
idea that business cycles can be divided into distinct
phases, with the phase shifts characterized by
changes in the dynamics of the economy. In particu-
lar, expansion phases are periods when economic
activity tends to trend up, whereas recession phases
are periods when economic activity tends to trend
down. In practice, to date the transition from an
expansion phase to a recession phase, or a business
cycle peak, the NBER looks for clustering in the
shifts of a broad range of series from a regime of
upward trend to a regime of downward trend. The
converse exercise is performed to date the shift back
to an expansion phase, or a business cycle trough.
The NBER’s announcements garner considerable
publicity. Given this prominence, it is not surprising
that the business cycle dating methodology of the
NBER has come under some criticism. Two criti-
cisms that are of primary interest in this paper are
as follows: First, because the NBER’s decisions repre-
sent the consensus of individuals who bring differing
techniques to bear on the question of when turning
points occur, the dating methodology is neither
transparent nor reproducible. Second, the NBER
business cycle peaks and troughs are often deter-
mined well after the fact. This practice appears to
be largely the result of the NBER’s desire to avoid
calling false turning points.
Of course, the NBER is not the only source of
information regarding business cycle turning points.
Economists and statisticians have developed many
statistical methods that automate the dating of
business cycle peaks and troughs (see Boldin, 1994,
for a summary). One such technique is the Markov-
switching model. This model, popularized by
Hamilton (1989) in the economics profession, is
capable of statistically identifying shifts in the
1
For an interesting history of the NBER’s role in defining and dating
the business cycle, see Moore and Zarnowitz (1986).
2
There are currently six members of the committee: Robert Hall of
Stanford University, Martin Feldstein of Harvard University, Jeffrey
Frankel of the University of California at Berkeley, Robert Gordon of
Northwestern University, N. Gregory Mankiw of Harvard University,
and Victor Zarnowitz of Columbia University.
Marcelle Chauvet is an associate professor at the University of
California, Riverside, and an associate policy advisor at the Federal
Reserve Bank of Atlanta. Jeremy M. Piger is an economist at the
Federal Reserve Bank of St. Louis. The authors thank James Bullard,
Michael Dueker, James Hamilton, James Morley, and Michael Owyang
for helpful comments. Mrinalini Lhila and John Zhu provided research
assistance.
©2003, The Federal Reserve Bank of St. Louis.

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parameters of a statistical process driving a time
series of interest. These models are quite simple,
making them transparent and reproducible. Also,
Layton (1996) provides some evidence that Markov-
switching models provide timely identification of
business cycle turning points.3
In this paper we take it as given that the NBER
correctly identifies the dates of business cycle turn-
ing points. We then evaluate the real-time perfor-
mance of the Markov-switching model in replicating
the NBER’s business cycle dates. We apply the model
to two datasets, growth in quarterly real gross domes-
tic product (GDP) and growth in monthly economy-
wide employment. We first confirm the result found
elsewhere that the model is able to replicate the
historical NBER business cycle dates fairly closely
when estimated using all available data. Second, we
evaluate the real-time performance of the model at
dating business cycles over the past 40 years; this
is accomplished by estimating the model on recur-
sively increasing samples of data and evaluating
the evidence for a new turning point at the end of
each sample.
This approach builds on the exercise undertaken
in Layton (1996), extending it in two main ways.
First, while Layton used fully revised data in his
recursive estimations, here we use “real-time” data.
That is, for each recursive sample we use only data
that would have been available at the end of the
sample period being considered. This method pro-
vides a more realistic assessment of how the model
would have performed, as it does not assume knowl-
edge of data revisions that were not available at the
time the model would have been used. Second, we
extend Layton’s sample to include the 2001 reces-
sion, in order to investigate the properties of the
model in the most recent business cycle.
The results of this exercise suggest that the
model chooses turning points in real time that are
fairly close to the NBER dates. In addition, we find
evidence that the model would have identified
business cycle turning points faster than the NBER
Business Cycle Dating Committee, with a larger lead
time in the case of troughs. The switching model
achieves this performance with few incidences of
false positives. Overall, these results suggest that the
Markov-switching model is a potentially very useful
tool to use alongside the traditional NBER analysis.
Of course, this line of research is predicated on
the assumption that turning point dates are interest-
ing concepts, and some might question whether
these dates have any worthwhile intrinsic meaning.
We argue that they do. There is much evidence
that the two regimes defined by the NBER turning
point dates are quite different, beyond the distinc-
tion of expansion versus contraction. First, knowl-
edge of which regime the economy is in can improve
forecasts of economic activity (see, for example,
Hamilton, 1989). Second, there is evidence that the
relationship between economic variables changes
over NBER-identified phases. For example, McConnell
(1998) and Gavin and Kliesen (2002) have shown
that the relationship between initial claims for
unemployment insurance and employment growth
is stronger during NBER-dated recessions. Third,
there is growing evidence that fluctuations in output
during NBER recession episodes are purely tempo-
rary, whereas those during NBER expansion episodes
are permanent (see, for example, Beaudry and Koop,
1993, and Kim, Morley, and Piger, 2002). This finding
is suggestive of a “plucking” model for U.S. output,
in which the business cycle is characterized more
by negative deviations from trend output than by
positive deviations.4Such a pattern is not generally
implied by linear macroeconomic models of the
business cycle, suggesting that the NBER dates
define interesting economic episodes from a model-
ing perspective. Finally, the NBER dates, regardless
of whether they have intrinsic meaning, garner
considerable attention from the media and politi-
cians. Thus, if the economics community is going
to produce estimates of turning points, we should
be interested in developing accurate, timely, and
transparent methods for doing so.
In the next section we provide a review of the
Markov-switching model used in this paper. The
third section discusses the full sample and “real-
time” performance of the model for dating turning
points in the business cycle.
THE MARKOV-SWITCHING MODEL OF
BUSINESS CYCLE DYNAMICS
As discussed in the introduction, the NBER defi-
nition of a business cycle places heavy emphasis
on regime shifts in the process driving economic
48
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Chauvet and Piger
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3
The Markov-switching approach to dating business cycle turning
points has recently received media attention: Kevin Hassett advocated
its use on the editorial page of the March 28, 2002, edition of the
Wall Street Journal.
4
The “plucking” terminology was coined by Milton Friedman (1964,
1993).

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activity. In the past 15 years there have been enor-
mous advances in formally modeling regime shifts
in a rigorous statistical framework. In a paper pub-
lished in 1989, James Hamilton developed an
extremely useful tool for statistically modeling
regime shifts in autoregressive time series models.
To understand this model, it is useful to begin with
a simple linear time-series framework for the growth
rate of some measure of economic activity, yt:
( yt–µ)=ρ( yt–1–µ)+εt
εt∼N(0,σ2).
(1)
In this model, the growth rate of economic
activity has a mean denoted by µ. Deviations from
this mean growth rate are created by the stochastic
disturbance, εt. These deviations are serially corre-
lated, modeled as an AR(1) time-series process with
parameter ρ.
Hamilton’s innovation was to allow the param-
eters of the model in (1) to switch between two
regimes, where the switching is governed by a state
variable, St={0,1}. When St=0 the parameters of
the model are different from those when St=1.
Clearly, if Stwere an observed variable, this model
could simply be estimated using dummy variable
methods. However, Hamilton showed that even if
the state is unobserved, the parameters of the model
in each state could be estimated if one is willing to
place restrictions on the probability process govern-
ing St. Hamilton derives an estimation technique
that could be used to estimate the model when the
probability process governing Stis a first-order
Markov chain. This stipulation simply means that
any persistence in the state is completely summa-
rized by the value of the state in the previous period.
Under this assumption, the probability process
driving Stis captured by the following four transition
probabilities:
P(St=1|St–1=1)=p
P(St=0|St–1=1)=1–p
P(St=0|St–1=0)=q
P(St=1|St–1=0)=1–q
(2)
Clearly, conclusions regarding when Stchanges
may depend on which parameters of the model are
allowed to change. For example, the instances when
the data may support regime shifts in the variance
of the disturbance, σ2, may be at different times
from those in the autoregressive parameter, ρ. Thus,
if we are interested in using this model for identify-
ing the NBER’s turning point dates, we should allow
regime switching in those parameters of the model
that seem to change from expansion to recession.
Hamilton showed that allowing the mean growth-
rate parameter, µ, to vary with Stseems to be ade-
quate for this task. In particular, Hamilton specified
the following augmented version of (1):
( yt–µst)=ρ( yt–1–µst–1)+εt
εt∼N(0,σ2)
µst=µ0+µ1St
µ1<0,
(3)
where Stdepends on the transition probabilities in
(2). Here, when Stswitches from 0 to 1, the growth
rate of economic activity switches from µ0to µ0+µ1.
Since µ1<0, the model will estimate these switches
at times when economic activity switches from
high-growth to low-growth states. Hamilton applied
this technique to the growth rate of U.S. gross
national product and found the best fit when µ0>0
and µ0+µ1<0, suggesting the model was capturing
regimes when the economy was expanding versus
regimes when the economy was contracting. The
estimated probability that Stwas equal to 1 con-
ditional on all the data in the sample, denoted
P(St=1|T), corresponded very closely to NBER
recession dates. This finding was particularly strik-
ing in that Hamilton estimated his model with only
one variable describing economic activity.
Since the publication of Hamilton’s paper, a
large number of alternative Markov-switching
models of the business cycle have been studied.
Boldin (1994) fits the Hamilton model to an alter-
native measure of economic activity, namely, the
unemployment rate. Other authors, for example,
Hansen (1992), allow for regime-switching in param-
eters other than the mean growth rate, such as the
residual variance or autoregressive parameters. The
Hamilton model was modified to allow for additional
phases in business cycle dynamics by Sichel (1994),
Kim and Nelson (1999), and Kim, Morley, and Piger
(2002). Finally, building on work by Diebold and
Rudebusch (1996), Chauvet (1998) and Kim and
Yoo (1995) extended the Hamilton model to a multi-
variate framework, estimating a coincident index
of economic activity with a regime-switching mean
growth rate.
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DATING BUSINESS CYCLES WITH THE
SWITCHING MODEL
Model Specification and Estimation
In this paper we work with the model given in
equations (2) and (3), which is applied to two differ-
ent measures of economic activity for which rich
unrevised “real-time” datasets are available. The first
is the growth rate of quarterly real U.S. GDP, yielding
a model very similar to that originally estimated by
Hamilton. The second is a higher-frequency mea-
sure of economic activity, monthly nonfarm payroll
employment.
The model is estimated using Hamilton’s (1989)
nonlinear filter. The algorithm provides the condi-
tional probability of the latent Markov state, which
permits evaluation of the conditional likelihood of
the observable variable. The filter evaluates this
likelihood function, which can be maximized with
respect to the model parameters using a nonlinear
optimization algorithm. The estimation proce-
dure and derivation of the likelihood function are
described in detail in Hamilton (1994). Following
Albert and Chib (1993), we set the autoregressive
coefficient, ρ, equal to 0, a priori. This specification
seems best able to replicate the historical record of
NBER business cycle dates.
Full-Sample Business Cycle Dates
Before analyzing the real-time ability of the
model to date turning points, we are first interested
in their ability to replicate the NBER business cycle
chronology using all available data. Thus, we first
estimate the model using data on (i) growth in real
GDP from the second quarter of 1947 through the
second quarter of 2002 and (ii) data on nonfarm
payroll employment growth from February 1947
through July 2002. The GDP data are from the July 31,
2002, release from the Bureau of Economic Analysis,
and the employment data are from the August 2,
2002, release from the Bureau of Labor Statistics.
As a first step in evaluating the ability of the
model to replicate the NBER turning point dates,
consider Figures 1A and B, which hold the estimated
probability that St=1 conditional on all the data in
the sample, or P(St=1|T), for both applications of
the model. In the graphs, shading indicates NBER-
labeled recessions. The graphs suggest that the
model captures the NBER chronology fairly closely.
During periods that the NBER classifies as expan-
sions, P(St=1|T) is usually close to 0. Near the point
where the NBER recession begins, P(St=1|T) spikes
upward and remains high until around the time
when the NBER dates the end of the recession.
Although visual inspection of the probabilities
suggests comparability, it is difficult to tell how
close the turning points from the Markov-switching
model are to the NBER dates without the tabulation
of specific dates based on the probabilities produced
by the model. To do this, a formal definition is needed
to convert the probabilities produced by the switch-
ing model into turning point dates. One approach,
used by Hamilton (1989) among others, is to classify
a turning point as occurring when P(St=1|T) moves
from below 50 percent to above 50 percent or vice
versa. This approach has an intuitive appeal as it
separates times when an expansion state is more
likely from those when a recession state is more
likely. This rule would be problematic if P(St=1|T)
fluctuated around 50 percent, in which case an
excessive number of business cycle peaks and
troughs would be called. However, since the Markov-
switching model applied to the GDP and employ-
ment series produces probabilities that are generally
close to 0 or 1, we adopt this simple definition.
We augment this definition with one of two rules
specifying how long a phase must persist before a
turning point is identified. For example, suppose
P(St=1|T) moves from below 50 percent to above
50 percent. Should we immediately declare a busi-
ness cycle peak has occurred and the economy has
entered a recession phase? Or should we require
confirmation of the recession phase, by verifying
that P(St+1=1|T), P(St+2=1|T), …P(St+k=1|T) are
all above 50 percent? A smaller value for k increases
the speed at which a turning point might be identi-
fied, but increases the chances of calling a false posi-
tive. Our first rule is defined for maximum speed,
requiring only that a single occurrence of a proba-
bility moving from above (below) 50 percent to below
(above) 50 percent must be observed before a turn-
ing point is determined. Our second rule, consistent
with the NBER tradition of not classifying very short
downturns or expansions as separate regimes,
requires that a recession or expansion last at least 3
months before a new turning point is defined. Note
that for real GDP, which is measured quarterly, this
requirement is met with only a single occurrence
of a probability crossing 50 percent, meaning that
rule 1 is identical to rule 2. For employment data,
which is measured monthly, rule 2 requires three
consecutive probabilities above (below) 50 percent
and will thus differ from rule 1.
Formally, our turning point rules for employ-
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MARCH/APRIL 2003 51
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1.0
0.8
0.6
0.4
0.2
0.0
19501955
1960
1965
1970 1975
1980
1985 1990 1995
2000
A. Full-Sample Estimated P(St = 1) from Markov-Switching Model of Quarterly
Real GDP
NOTE: Data vintage July 31, 2002. Shaded areas denote NBER recession dates.
Figure 1
1.0
0.8
0.6
0.4
0.2
0.0
B. Full-Sample Estimated P(St = 1) from Markov-Switching Model of Monthly
Nonfarm Payroll Employment
NOTE: Data vintage August 2, 2002. Shaded areas denote NBER recession dates.
1950
1960
1970
1980
1990
2000

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ment and GDP growth can be specified using the
following definitions:
Monthly Employment Growth. Definition 1:
A business cycle peak is said to occur in month t+1
if the economy was in an expansion in month t
and
Rule 1: P(St+1=1)≥0.5;
Rule 2: P(St+1=1)≥0.5 and P(St+2=1)≥0.5 and
P(St+3=1)≥0.5.
Definition 2: A business cycle trough is said to
occur in month t if the economy was in a recession
in month t and
Rule 1: P(St+1=1)<0.5;
Rule 2: P(St+1=1)<0.5 and P(St+2=1)<0.5 and
P(St+3=1)<0.5.
GDP Growth. Definition 1: A business cycle peak
is said to occur in quarter t+1 if the economy was
in an expansion in quarter t and P(St+1=1)≥0.5.
Definition 2: A business cycle trough is said to
occur in quarter t if the economy was in a recession
in quarter t and P(St+1=1)<0.5.
Table 1A contains the NBER turning point dates
and the corresponding dates obtained from the
Markov-switching model applied to real GDP growth
based on the above definitions. The agreement
between the two is striking. The Markov-switching
model captures each of the NBER business cycle
peaks and troughs in the sample. The average dis-
crepancy between the 10 NBER business cycle peaks
and the business cycle peaks from the switching
model applied to real GDP growth is approximately
2.4 months, with a maximum discrepancy of 6
months and a standard deviation of 1.8 months.
Business cycle troughs are dated even closer. There
is no discrepancy on average between the nine NBER
business cycle troughs and the business cycle troughs
from the switching model (the two dates are the
same for six of the nine troughs), with a maximum
discrepancy of 6 months and a standard deviation
of around 2.7 months. Generally the model tends
to determine turning points at or before the ones
established by the NBER. The only exception is for
the 1990-91 recession trough, for which the switch-
ing model dates the trough two quarters after the
NBER date.
In addition to capturing each of the NBER busi-
ness cycle dates, the switching model applied to GDP
growth generates no false business cycle dates. That
is, for the whole sample, the probability of recession
only increased (decreased) above (below) 50 percent
near the beginning or end of an actual recession.
Thus, for the model applied to real GDP, an increase
or decrease in the probability of recession above or
below 50 percent sends a very strong signal that a
turning point has actually occurred.
Table 1B shows the NBER turning point dates
and the corresponding dates obtained from the
Markov-switching model applied to monthly employ-
mentgrowth under rule 1 defined above. The agree-
ment between the two sets of dates is very close,
although somewhat less so than that obtained from
GDP. There are two reasons for this. First, we are
using employment at the monthly frequency, which
is a much more noisy series than quarterly GDP.
Second, employment slightly lags the business cycle.
Generally employment falls after a recession begins
and increases after it ends, as employers are reluc-
tant to fire (or hire) until a recession gains intensity
(or there are clear signs of its end). Nevertheless, the
switching model applied to monthly employment
captures each of the NBER business cycle peaks and
troughs in the sample. The average discrepancy
between the NBER peaks and the peaks from the
switching model is approximately 1 month, with a
maximum discrepancy of 9 months and a standard
deviation of 3.6 months. Similarly, the average dis-
crepancy between the NBER trough dates and the
trough dates from the switching model is 1.8 months,
with a maximum discrepancy of 10 months and a
standard deviation of 3.2 months.
The trough dates from the switching model
applied to employment tend to slightly lag the NBER
dates. In particular, all troughs from employment
either lag (five of nine) or coincide (four of nine)
with the NBER’s. The results are mixed for peak
dates: Half of the peak dates from the model either
coincide or lead the NBER peak dates, whereas half
lag the NBER dates.
In addition to the business cycle dates in Table
1B, turning point rule 1 identified three false-positive
business cycle dates, all early in the sample. If the
minimum number of consecutive months that
P(St=1|T) is required to be above (below) 50 percent
before a turning point is identified were increased
to two, only a single false-positive result occurs
(February 1948). Under turning point rule 2 defined
above, in which P(St=1|T) is required to be above
(below) 50 percent for three consecutive months
before a turning point is defined, there are no false-
positive results. This is achieved with no tradeoff in
terms of missed NBER dates; rule 2 still captures
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MARCH/APRIL 2003 53
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Business Cycle Dates—NBER and Markov-Switching Models Estimated Over Full Sample
Peak Trough
Switching
model
Lead/lag
discrepancy
Switching
model
Lead/lag
discrepancy NBERNBER
A. Real GDP
November 1948
July 1953
August 1957
April 1960
December 1969
November 1973
January 1980
July 1981
July 1990
March 2001
1948:Q4
1953:Q3
1957:Q2
1960:Q2
1969:Q3
1973:Q3
1979:Q3
1981:Q2
1990:Q2
2000:Q4
0
0
1Q
0
1Q
1Q
2Q
1Q
1Q
1Q
October 1949
May 1954
April 1958
February 1961
November 1970
March 1975
July 1980
November 1982
March 1991
Not yet announced
1949:Q4
1954:Q2
1958:Q1
1960:Q4
1970:Q4
1975:Q1
1980:Q3
1982:Q4
1991:Q3
2001:Q3
0
0
1Q
1Q
0
0
0
0
–2Q
—
Mean
Median
Standard deviation
0.8Q
1.0Q
0.6Q
0.0Q
0.0Q
0.9Q
B. Nonfarm Payroll Employment
November 1948
July 1953
August 1957
April 1960
December 1969
November 1973
January 1980
July 1981
July 1990
March 2001
October 1948
June 1953
April 1957
May 1960
April 1970
August 1974
April 1980
August 1981
July 1990
February 2001
1M
1M
4M
–1M
–4M
–9M
–3M
–1M
0
1M
October 1949
May 1954
April 1958
February 1961
November 1970
March 1975
July 1980
November 1982
March 1991
Not yet announced
October 1949
August 1954
May 1958
February 1961
November 1970
April 1975
July 1980
December 1982
January 1992
Not yet identified
0
–3M
–1M
0
0
–1M
0
–1M
–10M
—
Mean
Median
Standard deviation
–1.1M
–0.5M
3.6M
–1.8M
–1.0M
3.2M
NOTE: Leads (lags) are represented by + (–) and indicate how many months the switching model anticipates (lags) the NBER dating,
whereas 0 indicates that the two dating systems coincide.
Table 1

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all of the NBER business cycle peaks and troughs
in the sample.
Real-Time Business Cycle Dates
In this section we investigate the real-time per-
formance of the switching model for dating business
cycles. This will involve an out-of-sample evaluation
of the model’s performance. Our out-of-sample
period will be the past 40 years of data, with prior
data used for initial estimation of the model. We
are interested in the following question: Had the
switching model been used to date business cycles
in the past, how would it have performed? We are
particularly interested in the ability of the model to
accurately and quickly identify in real time the six
NBER peaks and five NBER troughs over this period.
We are also interested in the incidence of false busi-
ness cycle dates, that is, business cycle dates identi-
fied by the model that do not correspond to an
NBER-dated peak or trough.
There are two features of such a real-time exer-
cise. First, only data over the sample period that the
business cycle analyst would have had available at
that time should be used. We achieve this first
requirement by using a recursive estimation routine.
This routine works as follows: We begin with data
that extends from the second quarter of 1947 to
the third quarter of 1965 for real GDP and from
February 1947 to October 1964 for employment.
The model is estimated and the probability of a new
turning point at the end of the sample evaluated.
The sample is then extended by one data point, the
model reestimated, and the probability of a turning
point evaluated. This process is repeated until the
final sample is reached, which extends from the
second quarter of 1947 to the second quarter of
2002 for real GDP and from February 1947 to July
2002 for employment.
The second feature of the real-time exercise is
to assume no more knowledge of data revisions
than what would have been known by an econome-
trician estimating the model at the time. Thus, for
each end-of-sample date in the recursive estimation
routine, we use the first available release of these
data. For example, for our first sample for real GDP
data, which extends from the second quarter of
1947 through the third quarter of 1965, we use the
first release of data that included the third quarter
of 1965. For real GDP these data were available by
the beginning of the second month of the fourth
quarter of 1965, which we refer to as the vintage of
this dataset. The monthly employment datasets are
similar, except they are more timely than the GDP
data. In particular, the first release of employment
data for a given month is usually available by the
first week of the subsequent month. We obtained
the real-time datasets for quarterly real GDP and
monthly payroll employment from the Federal
Reserve Bank of Philadelphia.5
In evaluating the evidence for a turning point,
we consider the probability of a recession at the end
of the sample for that particular vintage, that is,
P(ST=1|T), where T denotes the end of the sample
period. This will be referred to as the “real-time
recursive probability” throughout the remainder of
the paper. Such an estimated probability, which is
estimated for time t using time t information, is
often called a “filtered” probability. This is, of course,
less information than econometricians would have
had available to them at the time, as econometricians
would also have had the so-called “smoothed” prob-
abilities for prior dates, that is, P(St=1|T), where
t<T. Thus, while the model might miss a turning
point at time t for the dataset that ends at time t, it
might catch this turning point for the dataset that
ends at T. We do not allow for this possibility in the
following, thus placing the model at a disadvantage
for dating turning points. However, as will be shown,
the model’s performance is still quite good despite
this disadvantage.
Figures 2A and B plot the real-time recursive
probability of a recession at the end of the sample
against the NBER business cycle dates. That is, the
point on the graph for date trepresents the estimated
probability of recession at date t for the recursive
sample that ended on date t. The probabilities are
closely related to the NBER turning points, tending
to increase or decrease substantially only around
NBER peaks and troughs. The real-time recursive
probabilities of recession from the employment
data are noisier than those from GDP growth, which
is not surprising given the higher frequency of the
employment data.
We next move to tabulation of business cycle
dates using turning point rule 1 for converting prob-
abilities into business cycle dates defined in the
section “Full-Sample Business Cycle Dates.” Tables 2A
and B contain the NBER business cycle peak and
trough dates and the corresponding dates identified
in real time by the switching model. The top frame
of each table evaluates the performance of the model
in capturing business cycle peaks. The bottom frame
evaluates business cycle troughs. The first column
54
MARCH/APRIL 2003
5
See Croushore and Stark (2001) for information regarding this dataset.
Chauvet and Piger
R E V I E W

Page 9

MARCH/APRIL 2003 55
FEDERAL RESERVE BANK OF ST. LOUIS
Chauvet and Piger
1970 1975
1980
19851990 1995
2000
1.0
0.8
0.6
0.4
0.2
0.0
A. Real-Time Recursively Estimated P(St = 1) from Markov-Switching Model of
Quarterly Real GDP
NOTE: Shaded areas denote NBER recession dates.
Figure 2
1970 1975
1980
198519901995
2000
1.0
0.8
0.6
0.4
0.2
0.0
B. Real-Time Recursively Estimated P(St = 1) from Markov-Switching Model of
Monthly Nonfarm Payroll Employment
NOTE: Shaded areas denote NBER recession dates.

Page 10

gives the first date (labeled “Peak date”) that a turning
point was assigned in real time by the switching
model. The second column gives the date this turn-
ing point would have first been available. For exam-
ple, the first entry in the second column of Table 2A
is February 1970. This is the date at which the busi-
ness cycle peak of the fourth quarter of 1969, listed
in the first column, would have first been identified
using the switching model (as early February is
approximately when the first iteration of GDP data
for the fourth quarter of 1969 would have been
available). The third and fourth columns give the
official NBER business cycle dates and when they
were announced. Note that the NBER Business Cycle
Dating Committee began dating business cycle
peaks and troughs in real time with the 1980 reces-
sion. Thus, the dates of these announcements are
recorded in the table only from this date on. The
fifth column records the discrepancy between the
peak or trough date first assigned by the switching
model and the corresponding date assigned by the
NBER, which is the amount of time the date in col-
umn 1 precedes that in column 3. The final column
shows how far in advance of the NBER date the
switching model date would have been available—
that is, the amount of time the date in column 2
anticipates that in column 4.
Tables 2A and B demonstrate that the switching
56
MARCH/APRIL 2003
Chauvet and Piger
R E V I E W
Recession Dates Obtained in Real Time—NBER and Markov-Switching Model of Real GDP
Estimated Over Recursive Samples
Lead
Peak date
available:
switching model
Peak date
announced:
NBER
announcement
date:
switching model
Peak date:
switching model
Peak date:
NBER
Lead/lag
discrepancy
1969:Q4
1974:Q1
1980:Q2
1981:Q3
1990:Q4
2001:Q3
February 1970
May 1974
August 1980
November 1981
February 1991
November 2001
December 1969
November 1973
January 1980
July 1981
July 1990
March 2001
—
—
0—
—
–2M
2M
2M
0
–1Q
–1Q
0
–1Q
–2Q
June 3, 1980
January 6, 1982
April 25, 1991
November 26, 2001
Mean
Median
Standard deviation
–0.8Q
–1.0Q
0.8Q
0.5M
1.0M
1.9M
Lead
Trough date
available:
switching model
Trough date
announced:
NBER
announcement
date:
switching model
Trough date:
switching model
Trough date:
NBER
Lead/lag
discrepancy
1970:Q4
1975:Q2
1980:Q3
1983:Q1
1992:Q1
2001:Q4
February 1971
August 1975
November 1980
May 1983
May 1992
February 2002
November 1970
March 1975
July 1980
November 1982
March 1991
Not yet
announced
—
—
0—
—
8M
2M
7M
—
–1Q
0
–1Q
–4Q
—
July 8, 1981
July 8, 1983
December 22, 1992
Not yet
announced
Mean
Median
Standard deviation
–1.2Q
–1.0Q
1.6Q
5.7M
7.0M
3.2M
Table 2A

Page 11

model calls turning point dates in real time that are
fairly close to the NBER dates. Table 2A shows the
following: For the six NBER peaks in the past 40
years, the switching model applied to real GDP
growth yields business cycle dates in real time that
were exactly equal to the NBER’s in two cases and
one or two quarters away in the other cases. The
average discrepancy for peaks is 2.4 months with a
standard deviation of 2.4 months. For the five NBER
business cycle troughs, the trough dates from the
model applied to real GDP growth coincide with the
NBER dates in two cases and lag one or four quarters
in the other cases. The average discrepancy is 3.6
months with a standard deviation of 4.8 months.
For the model applied to employment, Table 2B
shows that the real-time probabilities of recession
generally lag the NBER turning points, especially in
the case of peak dates. The average discrepancy
between the model and the NBER peak dates is 5.7
months with a standard deviation of 3.3 months.
For trough dates, the average discrepancy is only
1.6 months with a standard deviation of 2.1 months.
Tables 2A and B demonstrate that the model,
when applied to real GDP growth as well as to
employment growth, identifies in real time each of
the NBER business cycle episodes over the past 40
years. However, this performance would be less
impressive if the model also identified numerous
MARCH/APRIL 2003 57
FEDERAL RESERVE BANK OF ST. LOUIS
Chauvet and Piger
Recession Dates Obtained in Real Time—NBER and Markov-Switching Model of Nonfarm
Payroll Employment Estimated Over Recursive Samples
Lead
Peak date
available:
switching model
Peak date
announced:
NBER
announcement
date:
switching model
Peak date:
switching model
Peak date:
NBER
Lead/lag
discrepancy
May 1970
Novemer 1974
April 1980
November 1981
November 1990
September 2001
June 1970
December 1974
May 1980
December 1981
December 1990
October 2001
December 1969
November 1973
January 1980
July 1981
July 1990
March 2001
—
—
–5M
–12M
–3M
–4M
–4M
–6M
—
—
1M
1M
4M
1M
June 3, 1980
January 6, 1982
April 25, 1991
November 26, 2001
Mean
Median
Standard deviation
–5.7M
–4.5M
3.3M
1.8M
1.0M
1.5M
Lead
Trough date
available:
switching model
Trough date
announced:
NBER
announcement
date:
switching model
Trough date:
switching model
Trough date:
NBER
Lead/lag
discrepancy
November 1970
May 1975
July 1980
December 1982
Augugust 1991
July 2002?
December 1970
June 1975
August 1980
January 1983
September 1991
Not yet
identified
November 1970
March 1975
July 1980
November 1982
March 1991
Not yet
announced
—
—
0—
—
11M
6M
15M
—
–2M
0
–1M
–5M
—
July 8, 1981
July 8, 1983
December 22, 1992
Not yet
announced
Mean
Median
Standard deviation
–1.6M
–1.0M
2.1M
10.7M
11.0M
4.5M
Table 2B

Page 12

other “false” business cycle episodes in real time.
Tables 3A and B summarize the incidence of such
false identifications. From Table 3A, over this 40-year
period the dating algorithm applied to real GDP
identified only one false business cycle date, in the
second quarter of 1979. This increase in the proba-
bility of recession signaled an actual slowdown in
the U.S. economy in 1979, associated with the sec-
ond oil shock, and preceded the 1980 recession.
From Table 3B, the model applied to employment
growth identifies two false business cycle dates using
turning point rule 1. The first of these was in June
and July 1971, when the probabilities increased
above 50 percent with no corresponding NBER reces-
sion. The other false turning point for employment
occurs immediately following the 1990-91 recession.
Using turning point rule 1, the switching model ini-
tially dated the trough of this recession as August
1991. However, P(ST=1|T) then increased above
50 percent again from November 1991 to January
1992, thus dating a double-dip recession following
the 1990-91 recession. Using turning point rule 2,
both of these false turning points would have been
ruled out, leaving no false business cycle dates. This
would not have come at the expense of any missed
NBER business cycle episodes, as turning point
rule 2 also captured all 11 NBER turning points.
We now turn to the issue of whether the switch-
ing model applied in real time would have identified
turning points any faster than the NBER Business
Cycle Dating Committee. The sixth column of
Tables 2A and B, generated using rule 1, suggests
that the answer is yes for both peak and trough dates
obtained from the model applied to either real GDP
or employment growth. Business cycle peak dates
were determined an average of 0.5 months and 1.8
months before the NBER announcement, using the
model applied to real GDP growth and employment
growth, respectively. The model improves on the
timeliness of the NBER even more in determining
business cycle trough dates. For the three business
cycle troughs in the past 25 years, the model applied
to GDP would have determined these dates an aver-
age of 5.7 months prior to the NBER, with a maxi-
mum of 8 months for the 1980 trough. When applied
to employment, the model would have determined
trough dates an average of 10.7 months prior to the
NBER announcements. The model provides a longer
lead time when applied to the employment series
partially because the employment series is released
more quickly than the GDP series.
What should one conclude from the above
analysis? We have focused on two evaluation criteria
for the regime-switching model: (i) its ability to
identify business cycle turning points that corre-
spond to NBER business cycle peaks or troughs and
are in fairly close proximity to the NBER dates and
(ii) the speed with which the peaks and troughs are
identified. Whether one prefers the switching model
or to wait for the NBER announcement depends on
the relative weight one attaches to each type of
performance. If the primary interest is to quickly
58
MARCH/APRIL 2003
Chauvet and Piger
R E V I E W
Real-Time Turning Point Signal Error—Markov-Switching Models
A. Real GDP Growth
Turning point evaluation (6 recessions: 6 NBER peaks, 5 troughs)
Correct TP
Missed TP
False TP
11
0
1
B. Employment Growth
Turning point evaluation (6 recessions: 6 NBER peaks, 5 troughs) Rule 1Rule 2
Correct TP
Missed TP
False TP
11 11
0
2
0
0
NOTE: Correct TP refers to prediction of a turning point when an NBER turning point occurs. Missed TP refers to prediction of no
turning point when an NBER turning point occurs. False TP refers to prediction of a turning point when no NBER turning point occurs.
Table 3

Page 13

determine whether a recession has begun or ended,
the switching model will likely be preferable. If,
instead, the primary interest is to obtain the exact
NBER date of the business cycle peak or trough,
with relatively little weight on the speed with which
this is obtained, the switching model will be of less
interest. We argue that the switching model pre-
sented here provides an improvement in the speed
at which NBER business cycle dates are identified,
with a reasonable tradeoff in the accuracy of the
dates assigned. This performance is impressive given
that the model is based on only a single variable.
The 2001 Recession
The most recent U.S. recession merits further
discussion for at least two reasons. First, data revi-
sions in recent months have caused significant
revisions in the real-time peak date established by
the switching model. Indeed, this revision matches
or exceeds the largest seen in the sample period
considered in Table 2. It is worth exploring further
the reasons for these large revisions. Second, the
trough date for this recession had not yet been
established when this paper was written, providing
us with an out-of-sample experiment of the useful-
ness of the switching model.
In November 2001 the NBER Dating Committee
dated the peak of the previous expansion as March
2001. In contrast, the real-time recursive probability
of a recession, given by P(ST=1|T), first rose above
50 percent in the third quarter of 2001 for the model
applied to real GDP and in September 2001 for the
model applied to employment growth (Tables 2A
and B). A more detailed look at these recession
probabilities is given in the first column of Tables 4A
and B and shows the real-time recursive probability
of a recession at each date over the past several years.
The recent large revisions in GDP and employ-
ment data changed the peak date obtained from the
switching model. The second column of Tables 4A
and B show the smoothed probability of a recession
using the most recent data available, which was the
July 31, 2002, vintage for real GDP and the August
2, 2002, vintage for employment. Using this data,
the switching model dates the recession as begin-
ning much earlier, in the fourth quarter of 2000 for
real GDP growth and in February 2001 for employ-
ment growth. The large revision in the peak date
stems from recent data revisions that indicated sig-
nificantly slower growth than previously recorded
for the first six months of 2001. For example, the
release of real GDP data dated June 27, 2002, from
MARCH/APRIL 2003 59
FEDERAL RESERVE BANK OF ST. LOUIS
Chauvet and Piger
Probabilities of Recession from Markov-
Switching Models
Recursive in
real time (percent)
Full sample
using revised data Period
A. Applied to GDP Growth (percent)
2000
Q1
Q2
Q3
Q4
2001
Q1
Q2
Q3
Q4
2002
Q1
Q2
1.6
1.9
0.5
14.6
7.8
14.2
48.7
67.8
17.4
30.9
60.4
57.3
83.6
86.9
74.2
41.0
12.7
28.4
22.9
28.4
B. Applied to Employment Growth (percent)
2001
Jan 1.1
Feb1.5
Mar6.4
Apr 24.4
May 15.2
Jun22.6
Jul20.3
Aug 27.2
Sep53.4
Oct 94.0
Nov97.6
Dec92.8
2002
Jan88.8
Feb72.2
Mar 63.3
Apr61.9
May 62.8
Jun59.0
Jul 61.2
36.3
50.0
68.2
85.0
89.8
94.2
96.3
97.8
99.1
99.8
99.7
98.8
96.4
94.2
88.0
81.6
73.8
66.4
61.2
Table 4

Page 14

the Bureau of Economic Analysis recorded quarterly
annualized growth of 1.3 and 0.3 percent for the
first and second quarters of 2001, respectively. How-
ever, the data released on July 31, 2002, instead
recorded declines in GDP of 0.6 and 1.6 percent in
these quarters. These data revisions altered the peak
date established by the switching model, pushing it
much earlier—into late 2000 and early 2001.
Again, at the time this paper was written, the
NBER had not yet dated the end of the 2001 reces-
sion. However, the switching model applied to real
GDP growth has already dated the business cycle
trough. The real-time probabilities indicate that the
end of the recession occurred in the fourth quarter
of 2001. This date would have been available with
the initial release of the fourth quarter 2001 GDP
data, in February 2002. Using the revised GDP data
released in late July, the model dates the trough even
earlier, in the third quarter of 2001. Using data up
to the August 2, 2002, vintage, the switching model
applied to employment growth had not yet dated
the end of the recession.
CONCLUSIONS
In this paper we have explored the real-time
performance of a Markov-switching model applied
to real GDP and employment data for replicating
the NBER business cycle chronology over the past
40 years. The model produces business cycle peak
and trough dates that are fairly close to the NBER
dates, using only information that would have been
available at the time the dates were initially estab-
lished. An important feature of the model is that it
generally determines turning-point dates more
quickly than the NBER Business Cycle Dating Com-
mittee. This timing advantage can be large, especially
for business cycle troughs. It accomplishes this
performance with a minimum of “false positive”
business cycle peak or trough dates over the 40-year
period.
Overall, the evidence presented above suggests
that a statistical regime-switching model, such as
the one used in this paper, could be a useful supple-
ment to the NBER Business Cycle Dating Committee
for establishing turning point dates. It appears to
capture the features of the NBER chronology accu-
rately and swiftly; furthermore, the method is trans-
parent and consistent. It would be interesting to
evaluate the real-time performance of multivariate
switching models that incorporate another feature
of NBER recessions, comovement across many
economic variables over the business cycle, to see
whether additional improvements can be made.
We leave this for future research.
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