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A Comparison of the Real-Time Performance of Business …
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A Comparison of the Real-Time Performance of Business
Cycle Dating Methods
Marcelle Chauvet*
University of California, Riverside
Jeremy Piger
University of Oregon
First Draft: March 14, 2005
This Draft: February 9, 2007
Abstract: We evaluate the ability of formal rules to establish U.S. business cycle turning point
dates in real time. We consider two approaches, a nonparametric algorithm and a parametric
Markov-switching dynamic-factor model. Using a new "real-time" data set of coincident
monthly variables, we find that both approaches would have accurately identified the NBER
business cycle chronology had they been in use over the past 30 years, with the Markov-
switching model most closely matching the NBER dates. Further, both approaches, and
particularly the Markov-switching model, yielded significant improvement over the NBER in the
speed with which business cycle troughs were identified.
Keywords: Turning Point, Markov-Switching, Dynamic-Factor Model, Vintage Data
JEL Classification: C22, E32
*
Chauvet: Department of Economics, Riverside, CA 92524-0247 (marcelle.chauvet@ucr.edu). Piger:
Department of Economics, 1285 University of Oregon, Eugene, OR 97403 (jpiger@uoregon.edu). We
have received helpful comments from two anonymous referees, Jon Faust, Robert Rasche, and seminar
participants at the 2005 Winter Meeting of the Econometric Society. Research assistance by Michelle
Armesto and Garrett Holland was invaluable in the completion of this project. We owe special thanks to
Robert Rasche for his assistance in obtaining the real-time data set. We are also grateful to Don Harding
for sharing his Gauss code. Much of this paper was completed while Piger was a Senior Economist at the
Federal Reserve Bank of St. Louis. The views expressed in this paper should not be interpreted as those of
the Federal Reserve Bank of St. Louis or the Federal Reserve System.
1. Introduction
There is a long tradition in business cycle analysis of separating periods in which there is
broad economic growth, called expansions, from periods of broad economic contraction, called
recessions. Understanding these phases and the transitions between them has been the focus of
much macroeconomic research over the past century. In the United States, the National Bureau
of Economic Research (NBER) establishes a chronology of "turning point" dates at which the
shifts between expansion and recession phases occur. These dates are nearly universally used in
work requiring a definition of U.S. business cycle phases. Since 1978, business cycle dates have
been established in real time by the NBER's Business Cycle Dating Committee, which is
currently composed of seven academic economists.
The NBER's announcements garner considerable publicity. Given this prominence, it is
not surprising that the business cycle dating methodology of the NBER has received some
criticism. For example, because the NBER's decisions represent the consensus of individuals
who likely bring differing techniques to bear on the question of when turning points occur, the
dating methodology is charged as being neither transparent nor reproducible. Also, the NBER
has been hesitant to revise business cycle turning point dates, despite the fact that economic data
are revised substantially. Finally, the NBER business cycle peak and trough dates are often
determined with a substantial lag. For example, the March 1991 and November 2001 business
cycle troughs were not announced by the NBER until nearly two years after the fact.
An alternative to the NBER procedures is to use formal rules to date business cycle
turning points. Such rules immediately address the first two criticisms above. That is, given that
the rules take the form of a formal algorithm or statistical model applied to data, they are both
transparent and reproducible. Also, because the rules can be applied to revised data, they
1
provide a straightforward approach to revision of business cycle dates. In this paper we evaluate
whether or not such rules can also address the third critique. That is, do these rules provide more
timely identification of business cycle dates? Of course, any gain in timeliness must be weighed
against any loss of accuracy in establishing the dates. In order to measure accuracy, we take it as
given that the NBER established the correct turning point dates in real time, thus making the
NBER chronology the standard for accuracy.
Why are we interested in the speed with which business cycle turning points can be
identified? The NBER is likely more concerned with establishing the correct turning point dates
than establishing these dates quickly, which breeds additional caution. This caution comes at a
low cost if the primary objective is to provide a historical record of business cycle phases.
However, as there is substantial evidence that interesting economic dynamics and relationships
vary over business cycle phases, economic agents are likely also interested in real-time
monitoring of whether a new phase shift has occurred. In this paper we provide some formal
evidence regarding the speed with which such real-time monitoring can reveal a new turning
point in economic activity.
We compare two popular business cycle dating methods, both of which are multivariate
in that they use information from many time series to establish business cycle dates. The first is
a nonparametric algorithm, developed and discussed in Harding and Pagan (2002) and denoted
MHP, for multivariate Harding-Pagan, hereafter. The MHP algorithm proceeds by first
identifying turning points as local minima and maxima in the level of individual time series.
Next, economy-wide turning points are established by finding dates that minimize a measure of
the average distance between that date and the turning points in individual series.
2
The second approach is a parametric dynamic factor time-series model that captures
expansion and recession phases as unobserved regime shifts in the mean of the common factor.
The unobserved state variable controlling the regime shifts is modeled as following a Markov
process as in Hamilton (1989). This Markov-switching dynamic factor model (DFMS), as
developed in Chauvet (1998), produces a probability that the economy is in an expansion or
recession at any point in time. These probabilities can then be used to establish turning point
dates using a rule for converting probabilities into a zero / one variable defining which regime
the economy is in at any particular time.
We apply these two approaches to a new "real-time" data set of the four coincident
economic variables highlighted by the NBER in establishing turning point dates: 1) non-farm
payroll employment, 2) industrial production, 3) real manufacturing and trade sales, and 4) real
personal income excluding transfer payments. In particular, the dating methods are applied as if
an analyst had been using them to search for new turning points each month beginning in
November 1976, where the data used is the vintage that would have been available in that month.
This real time dataset was collected for this paper and has not yet been applied in any other
analysis.
The results of this exercise suggest that both approaches are capable of identifying
turning points in real time with reasonable accuracy. That is, the first time these methods declare
a turning point, the chosen date is usually close to that established by the NBER. The most
accurate performance is given by the DFMS model, which provides turning point dates in real
time that are usually within one month, and never more than two months, from the corresponding
NBER date. Both methods achieve this performance with no instances of "false positives", or
turning point dates that were established in real time, but did not correspond to a NBER turning
3
point date. Further, both approaches improve significantly over the NBER in the speed at which
business cycle troughs are identified. In particular, the DFMS model would have identified the
four business cycle troughs in the sample an average of 249 days, or roughly 8 months, ahead of
the NBER announcement, while the MHP algorithm would have led by an average of 166 days,
or about 5.5 months. However, neither approach provides a corresponding improvement in the
speed with which business cycle peaks are identified. Overall, these results suggest that formal
dating rules are a potentially useful tool to be used for real-time monitoring of business cycle
phase shifts.
Our paper makes several contributions to an existing literature on this topic.
Layton (1996) evaluates the performance of Markov-switching models of the U.S. coincident
index for establishing business cycle turning points. Layton uses a "pseudo" real-time analysis
in which fully revised data are used in recursive estimations to evaluate the real-time
performance of the business cycle dating algorithm. The new real-time data set we use here
provides a more realistic assessment of how the dating rules would have performed, as it does
not assume knowledge of data revisions that were not available at the time the rule would have
been used. Chauvet and Piger (2003) use real-time data to evaluate the business cycle dating
performance of univariate Markov-switching models of employment and real GDP, while
Chauvet and Hamilton (2004) do a similar exercise for multivariate Markov switching models.
These papers consider only Markov-switching models, whereas here we compare Markov-
switching models to nonparametric algorithms, which have a long history in dating business
cycles. Harding and Pagan (2003) also provide some comparison of univariate versions of the
dating rules considered here. However, this comparison does not consider multivariate methods
or the real time performance of the methods.
4
In the next section we discuss the two approaches used to establish business cycle turning
points in more detail. Section 3 describes the real-time data set. Section 4 discusses the real-
time performance of the models for dating turning points in the business cycle. Section 5
concludes.
2. Description of the Business Cycle Dating Methods
The NBER dates a turning point in the business cycle when a consensus of the Business
Cycle Dating Committee that a turning point has occurred is reached. Although each Committee
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,
pg. 3):
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.
Fundamental to this definition is the idea that business cycles can be divided into distinct
phases. In particular, expansion phases are periods when economic activity tends to trend up
while recession phases are periods when economic activity tends to trend down. In addition, the
definition stresses that these phases are observed in many economic activities, a concept
typically referred to as comovement. In practice, in order to date the shift from an expansion
phase to a recession phase, or a business cycle peak, the NBER looks for clustering in the shifts
5
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. Four monthly series are prominently featured by the NBER in their decisions:
employment, industrial production, real manufacturing and trade sales, and real personal income
excluding transfer payments.
The two business cycle dating methods that we consider in this paper represent attempts
to operationalize the above definition into formal algorithms and statistical models. We turn now
to a more detailed discussion of both methods.
2.1 Harding and Pagan (2002) Algorithm
Based on relatively informal descriptions of NBER procedures laid out in Boehm and
Moore (1984), Harding and Pagan (2002) develop a formal algorithm whereby a common set of
turning points can be extracted from a group of individual time series. The algorithm is
described in detail in Harding and Pagan (2002), and we provide only a brief summary here for a
group of monthly time series. Before using the algorithm, we need to first extract turning point
dates for each of the time series, indexed by i = 1,..., I . Here we employ the commonly used
algorithm of Bry and Boschan (1971) for this purpose, which, roughly speaking, identifies
turning points as local minima and maxima in the path of each time series. To implement the
Bry-Boschan algorithm, we use Gauss code created for Watson (1994). Once the Bry-Boschan
algorithm has been applied to each time series we have a set of I turning point histories, labeled
{P1 , P2 ,..., PI } for peaks and {T1 , T2 ,..., TI } for troughs, where Pi and Ti are vectors of turning
point dates for time series i. The contribution of the Harding and Pagan algorithm is to
consolidate these individual peak and trough dates into a single set of common turning point
6
dates. In order to do this, Harding and Pagan define variables DPit and DTit , which record the
distance in months between month t and the nearest entry in Pi for DPit and Ti for DTit . For
example, if Pi = (20,40,60 ) and t = 45 , then DPit = 5 . For each value of t, we then form DPt
and DTt as the median across the I time series, that is DPt = median( DP1t , DP2t , ..., DPIt ) and
DTt = median( DT1t , DT2t ,..., DTIt ) . Harding and Pagan then define the common peak and
trough dates as local minima in DPt and DTt . Formally, a common peak or trough is defined at
month t if DPt or DTt is a minimum value in a 31 month window centered at time t, that is,
from t -15 to t +15. In practice, these local minimum values may not be unique, and it may be
necessary to break ties. To do so, Harding and Pagan consider higher percentiles than the
median until a unique local minimum is found.
Finally, once the candidate set of common turning points has been obtained, two
censoring procedures are applied. First, for a candidate common peak (trough) to be retained at
time t, the median distance to individual turning point dates, that is the value of DPt ( DTt ), must
not be larger than 15 months. Second turning points are recombined so that they alternate
between peaks and troughs.
2.2 Dynamic Factor Markov-Switching Model
As discussed above, the NBER definition of a business cycle places heavy emphasis on
regime shifts in economic activity. Given this, the Markov-switching model of Hamilton (1989),
which endogenously estimates the timing of regime shifts in the parameters of a time series
model, seems well suited for the task of modeling business cycle phase shifts. In addition, the
NBER definition stresses the importance of comovement among many economic variables. This
7
feature of the business cycle is often captured using the dynamic common factor model of Stock
and Watson (1989, 1991).
Chauvet (1998) combines the dynamic factor and Markov-switching frameworks to
create a statistical model capturing both regime shifts and comovement. Specifically, defining
*
Yit as the log level of the i'th time series, and yit = yit - yi as the demeaned first difference of
Yit , the DFMS model has the form:
y1t 1
*
e1t
* e
y 2t 2 2t
. = . ct + . (1)
. . .
y * I e It
It
That is, the demeaned first difference of each series is made up of a component common to each
series, given by the dynamic factor ct , and a component idiosyncratic to each series, given by
eit . The common component is assumed to follow a stationary autoregressive process:
( L)(ct - S ) = t
t
(2)
where t is a normally distributed random variable with mean zero and variance set equal to
unity for identification purposes, and (L) is a lag polynomial with all roots outside of the unit
circle. The common component is assumed to have a switching mean, given by St = 0 + 1St ,
where S t = {0,1} is a state variable that indexes the regime and 1 < 0 for normalization
8
purposes. The state variable is unobserved, but is assumed to follow a Markov process with
transition probabilities P( S t = 1 | S t -1 = 1) = p and P( S t = 0 | S t -1 = 0) = q . Finally, each
idiosyncratic component is assumed to follow a stationary autoregressive process:
i ( L)eit = it (3)
where i (L) is a lag polynomial with all roots outside the unit circle.
Chauvet (1998) estimates the DFMS model for U.S. monthly data on non-farm payroll
employment, industrial production, real manufacturing and trade sales, and real personal income
excluding transfer payments. The model produces estimated probabilities of the regime at time t
conditional on the data, denoted P ( St = 1 | T ) , that closely match NBER expansion and
recession episodes. That is, P ( St = 1 | T ) is high during recessions and low during expansions.
In this paper, we use the DFMS model to obtain recessions probabilities in real time.
Also, since we are interested in obtaining specific turning points dates, we will require a rule to
convert the recession probabilities into a zero / one variable that defines whether the economy is
in an expansion or recession regime at time t. Here, we take a conservative, two-step approach,
which we outline for a business cycle peak: In the first step, we require that the probability of
recession move from below to above 80% and remain above 80% for three consecutive months
before a new recession phase is identified. That is, we require that P( S t + k = 1 | T ) 0.8 , for
k = 0 to 2 and P( S t -1 = 1 | T ) < 0.8. In the second step, the first month of this recession phase
is identified as the first month prior to month t for which the probability of recession moves
above 50%. That is, we find the smallest value of q for which P ( S t - q -1 = 1 | T ) < 0.50 and
9
P ( S t - q = 1 | T ) 0.50 . The peak date for this recession phase is then established as the last
month of the previous expansion phase, or month t + q - 1 . An analogous procedure, with the
80% threshold replaced by 20%, is used to establish business cycle troughs.
In order to estimate the parameters of the DFMS model, as well as the recession
probabilities, we use the Bayesian Gibbs Sampling approach described in Kim and
Nelson (1998). The Gibbs Sampler produces a posterior distribution for S t conditional on the
data, T , the mean of which corresponds to the recession probability P( S t = 1 | T ) . These
probabilities are then used to obtain business cycle turning point dates. Priors for the Bayesian
estimation are quite diffuse, and match those used in Kim and Nelson (1998). We set the lag
order of each autoregressive polynomial, (L) and i (L) , equal to two. This choice of lag order
is based on specification tests reported in the studies of Stock and Watson (1991), Chauvet
(1998), and Kim and Nelson (1998), each of which suggests that two lags is sufficient for
dynamic factor models of the four coincident variables we consider here.
3. Real Time Data Set
In this section we describe the real-time data set. We have compiled real-time data on
four coincident variables: 1) nonfarm payroll employment (EMP), 2) industrial production (IP),
3) real manufacturing and trade sales (MTS), and 4) real personal income excluding transfer
payments (PIX). These are the four monthly variables highlighted by the NBER in establishing
turning point dates. We have collected realizations, or vintages, of these time series as they
would have appeared at the end of each month from November 1976 to June 2006. For each
vintage from November 1976 to January 1996, the sample collected begins in January 1959 and
ends with the most recent data available for that vintage. For each vintage from February 1996
10
to June 2006, the sample begins in January 1967. For the series EMP, IP, and PIX, data are
released for month t in month t + 1 . Thus, for these variables the sample ends in month R - 1
for vintage R . For MTS, data are released for month t in month t + 2 . Thus, for this variable
the sample ends in month R - 2 for vintage R . We obtained the EMP and IP data series from
the Federal Reserve Bank of Philadelphia real time data archive described in Croushore and
Stark (2001). Data for PIX and MTS were hand collected as part of a larger real-time data
collection project at the Federal Reserve Bank of St. Louis. This dataset is new and has not yet
been used in any other applications. The appendix provides more detail on the sources used to
collect the PIX and MTS series.
4. Performance of the Business Cycle Dating Methods
4.1 Description of Real-Time Simulation Exercise
In order to assess the real time performance of the two business cycle dating methods
described in Section 2, we apply these techniques to the real-time data set described in Section 3.
We assume that an analyst applies the business cycle dating methods on the final day of each
month, which is soon after the release of MTS data for that monthly vintage. Thus, for each
monthly vintage R , we create a monthly data set of EMP, IP, MTS and PIX that would have
been available at the end of month R . The final month of data included in this data set is
determined by the series with the least amount of data available at vintage R . As discussed in
Section 3, this final data point is month R - 2 , which is the last month for which data are
available for MTS. For each vintage R , the MHP algorithm and DFMS model are applied to the
11
data set, and a chronology of turning point dates determined. We will be particularly interested
in evidence of new turning points revealed toward the end of the sample at vintage R .
The choice to restrict the entire data set by the series with the least data available at
vintage R is a conservative assessment of the information available to the analyst. Alternatively,
we could have included the month R - 1 data for EMP, IP and PIX in conjunction with a forecast
for month R - 1 MTS data. While potentially fruitful, we chose not to pursue this approach here
for two reasons. First of all, as will be seen below, the performance of the business cycle dating
methods applied to the restricted data set is already quite good, thus demonstrating the potential
benefits of their use. Second, it is not clear that the additional information for EMP, IP and PIX
would necessarily improve the performance of the dating methods, as revisions from the first to
the second release of these monthly data series, particularly EMP and IP, are often very large.
Finally, it should be noted that there are two elements of this experiment that are not "real
time" in nature. First of all, while the parameters of the DFMS model are re-estimated at each
vintage, the lag orders for the DFMS model specification remain fixed across vintages. The
chosen lag orders were based on specification tests conducted in prior studies, namely Stock and
Watson (1991), Chauvet (1998) and Kim and Nelson (1998). However, because all of these
studies used data not available at the earlier vintages in our data set, for each of these earlier
vintages the chosen lag orders are based on data that would not have been available at that
vintage. Secondly, the rule used to convert recession probabilities obtained from the DFMS
model into turning points dates was selected with knowledge of the estimated recession
probabilities obtained using the full sample of data from the most recent vintage.
12
4.2 Real-Time Performance of the Business Cycle Dating Methods
We now turn to the real-time performance of the business cycle dating methods. Again,
we consider vintages from November 1976 to June 2006. There are, therefore, four NBER
business cycle episodes to identify in real time using these vintages, namely the 1980, 1981-
1982, 1990-1991, and 2001 recessions. We will also be interested in any "false positive" turning
point dates identified by the dating methods.
Tables 1-2 describe the real-time performance of the DFMS model and the MHP
algorithm. The top frame of each table evaluates the performance of the model in capturing
business cycle peaks while the bottom frame evaluates business cycle troughs. The first column
gives the turning point date assigned in real time by the DFMS model or MHP algorithm. In
other words, this column records the date of any new turning points established by the methods.
If this turning point date has a corresponding NBER turning point, the second column gives this
NBER date, while the third column records the discrepancy in months between the NBER date
and the date in column one. The fourth column gives the month in which the date in column one
would have been available. For example, the first entry in column four of Table 1 is July 31,
1980. This is the first date at which the DFMS model, using the data set available, would have
revealed a peak around the January 1980 NBER peak. The fifth column gives the date the
NBER announced the turning point date. The final column gives the amount of time before the
NBER date that the turning point from the dating methods would have been available, which is
the amount of time the date in column 4 anticipates that in column 5.
We begin with Table 1, which shows the results for the DFMS model. The DFMS model
identifies eight turning points in real time, each of which corresponds to a NBER turning point.
Thus, the DFMS model does not generate any false positives. The DFMS model also identifies
13
these eight turning points with a high level of accuracy. In particular, for seven of the eight
turning points, the turning point date identified in real time is within one month of the NBER
date. For the remaining turning point, the peak of the 2001 recession, the date identified by the
model is two months from the NBER date.
For business cycle peaks, the DFMS model does not show any systematic improvement
over the NBER in the speed at which it identifies turning points. Indeed, the DFMS model
would have identified the four peaks in the sample roughly one month after the NBER
announcement on average, with a maximum lag time of two months. However, the DFMS
model would have identified business cycle troughs much more quickly than the NBER. The
average lead time for the four troughs in the sample is 249 days, or about 8 months, with a
maximum lead time of 449 days for the 1991 business cycle trough. Interestingly, the increase in
speed with which the DFMS algorithm identifies business cycle troughs does not come with a
noticeable loss of accuracy in identifying the NBER date. Indeed, the business cycle trough
dates identified in real time are all within one month of their corresponding NBER date. Given
that the DFMS model treats business cycle peak and trough episodes symmetrically, its improved
timeliness over the NBER for troughs but not peaks is suggestive of an asymmetry in the NBER
approach. One explanation for this is that the NBER may have an asymmetric loss function for
valuing errors made in establishing the dates of business cycle peaks vs. troughs.
The results in Table 1 are derived from a combination of the recession probabilities,
P ( S t = 1 | T ) , with the dating rule used to convert these recession probabilities into recession
dates. For reference, Figures 1 to 4 plot the values of the real-time recession probabilities used
to date each peak and trough in the sample. That is, these figures show a sequence of
14
P ( S t = 1 | T ) that was available at the vintage for which the business cycle peak or trough was
first identified.
Table 2 reports the performance of the MHP algorithm in dating turning points in real
time. Similar to the DFMS model, the MHP algorithm also identifies eight turning points, each
of which corresponds to a NBER turning point date. However, these turning points are identified
less accurately in general than is the case for the DFMS model. In particular, four of the turning
points are at least two months from their corresponding NBER date, with the peaks of the 1980
and 2001 recessions both six months from the NBER date.
Similar to the DFMS model, the MHP algorithm does not show any systematic
improvement over the NBER in the speed with which business cycle peaks are identified, but
does show an improvement in timeliness for business cycle troughs. In particular, the MHP
algorithm identified the four business cycle troughs in the sample an average of 166 days, or
about 5.5 months, ahead of the NBER announcement. While still a substantial increase in
timeliness, it is a smaller improvement than that achieved by the DFMS model.
4.3 Revisions of Business Cycle Dates
The NBER has made revisions to previously established business cycle turning point
dates, most recently in 1975. However, the NBER's business cycle dating committee has not
revised any of the eight turning point dates it has established in real time since its inception in
1978. Does this rigidity suggest that the NBER's business cycle dates are no longer consistent
with the data? Or does it instead suggest that data revealed since the establishment of these
turning point dates have not altered conclusions about their timing? In this section we provide
some evidence on these questions.
15
We can evaluate the importance of data revisions for establishing business cycle turning
point dates by tracking revisions to the dates established in real time using the formal business
cycle dating rules evaluated in this paper. Given the superior performance of the DFMS model
for mimicking the NBER dates established in real time, we focus on this approach. In particular,
we apply the DFMS model to the most recent vintage of data available in our data set, June 2006,
and obtain a chronology of business cycle turning point dates. We then compare the business
cycle turning point dates established in real time by the DFMS model to those established using
the most recent vintage of data. Table 3 contains this comparison.
The results in Table 3 demonstrate that in most cases, data revisions do not appear to be
an important factor for determining the timing of business cycle turning points. In particular, for
seven of the eight turning points in the sample, the date established by the DFMS model using
the final vintage of data available is within one month of that established in real time. Indeed,
for four of the eight turning points there is no revision to the turning point date established in real
time.
The single case where the real-time business cycle date is revised by more than one
month, namely the peak of the 2001 recession, merits further discussion. Note that the peak of
the 2001 recession is established by the DFMS model in real-time to be January of 2001, two
months prior to the March 2001 peak established by the NBER. From Table 1, this peak date
would not have been available from the DFMS model until two months after the official
announcement by the NBER. Thus, the initial date established by the DFMS model is already
based on more information than was available to the NBER. Further, this peak date is moved an
additional two months earlier, to November of 2000, when the DFMS model is applied to the
June 2006 vintage of data. Note that data available in June 2006 is not necessary for the DFMS
16
model to make this revision. In particular, the revision to November of 2000 would have first
been available from the DFMS model by the July 2002 vintage. In sum, data revealed after the
official announcement by the NBER of the March 2001 peak seems to be consistent with this
peak occurring somewhat earlier, and provides one example suggestive that an established
NBER date may be inconsistent with revised data.
Although not revealed in Table 3, the trough of the 2001 recession is also an interesting
case for investigating the effects of additional and revised data on conclusions about turning
points dates. In particular, from Table 1, the DFMS model would have first established the
trough date of November 2001 by the end of August of 2002. However, for a brief period for
vintages in mid-2003, the recession probabilities from the DFMS model for 2002 and 2003 rose
significantly to levels consistent with a continuation of the 2001 recession. This was the result of
very weak employment data observed in 2002 and 2003, or the so-called "jobless recovery". By
the end of 2003, the recession probabilities would have returned to levels consistent with the
previously established trough date of November 2001. This episode demonstrates that the
caution exercised by the NBER in establishing the trough of the 2001 recession may have been
justified, particularly if their primary objective is to establish turning point dates that are unlikely
to need revision.
4. Conclusions
This paper investigates the ability of formal rules to establish business cycle turning point
dates in real time. Both methods studied, a non-parametric algorithm given in Harding and
Pagan (2002) and the dynamic factor Markov-switching model as in Chauvet (1998), identify the
NBER turning point dates in real time with reasonable accuracy, and with no instances of false
17
positives. Both approaches also provide improvements over the NBER in the timeliness with
which they identify business cycle troughs, but provide no such improvement for business cycle
peaks. Comparing the two methods, the dynamic factor Markov-switching model identifies
NBER turning point dates the most accurately, as well as identifies business cycle troughs with
the largest lead.
18
References
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20
Appendix: Sources of Real-Time Data
Real Personal Income Excluding Transfer Payments
For vintages from November 1976 through March 1990, data for real personal income
excluding transfer payments was collected from Business Conditions Digest. For vintages from
April 1990 through December 1995, data for real personal income excluding transfer payments
was collected from the Survey of Current Business. For vintages from January 1996 through
November 2003, nominal personal income, nominal disposable personal income, and real
disposable personal income were collected from the Federal Reserve Bank of St. Louis ALFRED
database, while data for nominal transfer payments were collected from Economic Indicators,
Business Statistics, the Survey of Current Business, and data archives maintained by the Federal
Reserve Bank of Saint Louis. Data for real personal income excluding transfer payments was
then formed by subtracting nominal transfer payments from nominal personal income, and
dividing by the ratio of nominal to real disposable personal income.
Real Manufacturing and Trade Sales
For vintages from November 1976 through March 1990, data for real manufacturing and
trade sales was collected from Business Conditions Digest, while for vintages from April 1990
through December 1995, real manufacturing and trade sales data was collected from the Survey
of Current Business. For vintages from January 1996 through November 2003, real
manufacturing and trade sales data was collected from Business Cycle Indicators, Business
Statistics, the Survey of Current Business, and data archives maintained by the Federal Reserve
Bank of St. Louis.
21
For a small number of individual vintages, there were gaps in the data available. This
missing data was filled in using the following strategy. Suppose that for the R th vintage, we are
missing data from period t to t + k . Denote this missing data as Yt R , Yt +1 ,..., Yt + k . Suppose that
R R
data is available for Yt -1- h , Yt R - h ,..., Yt + k h , Yt + k +1 , as well as for Yt -1 and Yt + k +1 . Our imputed value
R R- R-h R R
^
for Y jR , denoted Y jR , is then given by:
1
Y R -h r1 (k + 2 )
^R =Y R j
Yj ^ , j = t ,..., t + k ,
j -1
Y R -h r2
j -1
R
Yt + k +1 Y R-h
where r1 = R
, r2 = t + k-+h1 , and the recursion is initialized with Yt -1 = Yt -1 .
R
^R R
Yt -1 Yt -1
In words, this imputation formula fills in the missing data for period j using the actual
growth rate observed in period j from the data recorded at vintage R - h (the first bracketed
term) modified by a amount that does not vary with j (the second bracketed term). This
modification ensures that the difference in total growth observed from period t - 1 to period
t + k + 1 using data from vintages R and R - h is spread evenly over the period t to t + k + 1 .
22
1.0
0.8
0.6
0.4
0.2
0.0
1979:01 1979:07 1980:01 1980:07 1981:01
Figure 1: Real Time Probabilities of Recession Determining the Peak (___) and Trough (---)
of the 1980 Recession, and NBER Recession (Shaded).
1.0
0.8
0.6
0.4
0.2
0.0
1981:01 1982:01 1983:01
Figure 2: Real Time Probabilities of Recession Determining the Peak (___) and Trough (---)
of the 1981-82 Recession, and NBER Recession (Shaded).
23
1.0
0.8
0.6
0.4
0.2
0.0
1990:01 1990:07 1991:01 1991:07
Figure 3: Real Time Probabilities of Recession Determining the Peak (___) and Trough (---)
of the 1990-91 Recession, and NBER Recession (Shaded).
1.0
0.8
0.6
0.4
0.2
0.0
2000:01 2000:07 2001:01 2001:07 2002:01 2002:07
Figure 4: Real Time Probabilities of Recession Determining the Peak (___) and Trough (---)
of the 2001 Recession, and NBER Recession (Shaded).
24
Table 1
Business Cycle Dates Obtained in Real Time NBER and DFMS Model
Peak Date: Peak Date: Lead / Lag Peak Date Available: Peak Date Announced: Days ahead of NBER
DFMS NBER Discrepancy DFMS NBER Announcement
Jan 1980 Jan 1980 0M Jul 31, 1980 Jun 3, 1980 -58
Aug 1981 Jul 1981 -1M Feb 28, 1982 Jan 6, 1982 -53
Jul 1990 Jul 1990 0M Feb 28, 1991 Apr 25, 1991 56
Jan 2001 Mar 2001 2M Jan 31, 2002 Nov 26, 2001 -66
Trough Date: Trough Date: Lead / Lag Trough Date Available: Trough Date Announced: Days ahead of NBER
DFMS NBER Discrepancy DFMS NBER Announcement
Jun 1980 Jul 1980 1M Dec 31, 1980 Jul 8, 1981 189
Oct 1982 Nov 1982 1M May 31, 1983 Jul 8, 1983 38
Mar 1991 Mar 1991 0M Sep 30, 1991 Dec 22, 1992 449
Nov 2001 Nov 2001 0M Aug 31, 2002 July 17, 2003 320
25
Table 2
Business Cycle Dates Obtained in Real Time NBER and MHP Algorithm
Peak Date: Peak Date: Lead / Lag Peak Date Available: Peak Date Announced: Days ahead of NBER
MHP NBER Discrepancy MHP NBER Announcement
Jul 1979 Jan 1980 6M May 31, 1980 Jun 3, 1980 3
May 1981 Jul 1981 2M Feb 28, 1982 Jan 6, 1982 -53
Jul 1990 Jul 1990 0M Mar 31, 1991 Apr 25, 1991 25
Sep 2000 Mar 2001 6M Nov 30, 2001 Nov 26, 2001 -4
Trough Date: Trough Date: Lead / Lag Trough Date Available: Trough Date Announced: Days ahead of NBER
MHP NBER Discrepancy MHP NBER Announcement
Jul 1980 Jul 1980 0 Apr 30, 1981 Jul 8, 1981 69
Oct 1982 Nov 1982 1M Jul 31, 1983 Jul 8, 1983 -23
Jul 1991 Mar 1991 -4M Feb 28, 1992 Dec 22, 1992 298
Oct 2001 Nov 2001 1M Aug 31, 2002 July 17, 2003 320
26
Table 3
Revisions to Business Cycle Dates: DFMS Model
Initial Date: Final Date:
NBER Date
DFMS DFMS
Peaks
Jan 1980 Jan 1980 Jan 1980
Jul 1981 Aug 1981 Jul 1981
Jul 1990 Jul 1990 Aug 1990
Mar 2001 Jan 2001 Nov 2000
Troughs
Jul 1980 Jun 1980 Jun 1980
Nov 1982 Oct 1982 Nov 1982
Mar 1991 Mar 1991 Mar 1991
Nov 2001 Nov 2001 Nov 2001
27