JCER Recession Indicator

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Description

Japan Center for Economic ResearchJuly 2017

Estimating the recession probability using the Composite
Index in Japan: A Markov-switching approach
Takashi Miyazaki
Senior Economist, Japan Center for Economic Research
Abstract
This paper aims to estimate a recession probability by applying a methodology based on aMarkov-switching model developed by Chauvet and Hamilton (2005) to the Composite Index(CI) in Japan. We attempt to verify whether a recession probability derived from the leading
index of CI is useful as an early-warning signal of a coming recession.
According to our empirical results, the recession probability derived from the Chauvet andHamilton (2005) methodology, which is based on information up to the next month, signals theearly warning successfully three times out of the past five recessions. It is observed, however,that the recession probability rises in some periods of expansions. This result is interpreted as afalse alarm, if the business cycle date determined by the Economic and Social Research Institute(ESRI) is right.
Given that our motivation in this paper is judging business conditions in real time, werecommend using the Chauvet-Hamilton recession probability as an early warning signal of arecession and using smoothed state probability for identifying a recession period ex-post, basedon the leading index.
The value of recession probability varies depending on the underlying indicator ormethodology employed. Therefore, we need to watch comprehensively and carefully when we
judge the prospects of business conditions. However, detecting a risk of recession early has
important implications including the timing and magnitude of economic policy, especially forpolicy-makers in government and the central bank.
Main results
Table 1 reports on the parameters estimated from Chauvet and Hamilton’s (2005) Markovswitching model using the leading index of Composite Index (CI) released by the Cabinet

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Japan Center for Economic Research
Office as underlying data1. The sample period spans from February 1985 to November 2016. Ina Markov-switching model, it is assumed that there exist states or regimes in an economy and,usually, that interpretation of what each of the regimes represents is left to the researcher. Here,
we assume that there are two regimes where a regime with a relatively high (low) average
growth rate of the leading index is interpreted as an expansion (a recession) period in thebusiness cycle. Applying the Maximum Likelihood Estimation (MLE), estimated average
growth rates in expansion and recession periods are 4.3% and -15.4% (μ1 and μ2), respectively.
Standard deviation of growth rates are assumed to be common in both regimes and are
estimated at about 15% (σ1 and σ2). The probability that expansion continues is 0.98 and thecounterpart for recession is 0.90 (p11 and p22). The average duration of persisting expansion(recession) periods is 42 (10) months (D1 and D2), indicating expansions are likely to appear
approximately 4 times more often than recessions. This result is reflected in the unconditional
probabilities of expansion and recession (π1 and π2).
Table 1. Estimated parameters employing leading index
Value from ESRI
Value from MLE
classification
Average growth rate in expansion period
5.58
4.56
μ1μ2
Average growth rate in recession period-9.50-14.51
Standard deviation of growth rate in expansion period
14.76
σ114.67σ2Standard deviation of growth rate in recession period
17.55
Probability that expansion continues
0.97
0.97
p 11p 22
Probability that recession continues
0.95
0.90
Average duration persisting expansion periods (in months)
38.3
40.0
D1
D2
Average duration persisting recession periods (in months)
18.3
10.1
Unconditional probability of expansion
0.68
0.80
π1π2
Unconditional probability of recession
0.32
0.20
Notes : Value from ESRI classification is based on the sample until June, 2013. MLE signifies Maximum Likelihood
Estimation.
Source : Cabinet Office, Indexes of Business Conditions
ParameterInterpretation

Figure 1 illustrates the behavior of recession probability obtained by applying Chauvet andHamilton’s (2005) methodology into the leading index. Chauvet and Hamilton’s (2005)
recession probability (referred to as CH-type recession probability hereafter) is calculated eachmonth based on the information up to the next month, that is, CH-type recession probability has
a 1-month lag from the latest data available. Following the criterion of Econbrowser, which
supposes that the CH-type recession probability exceeding 67% for two consecutive months is a1

Refer to Econbrowser (http://econbrowser.com/recession-index), Chauvet and Hamilton (2005), andHamilton (2010) for detailed explanation of the methodology employed.
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Japan Center for Economic Research
condition for entering recession, the CH-type recession probability successfully signals an
early-warning alarm preceding recession three times out of the past five recessions. Meanwhile,
there are some phases where the recession probability rises in expansion periods; e.g.,
February–July, 1995, and February–May, 2014. Insofar as we assume that ESRI’s businesscycle dates are right, our recession probability signals a false alarm in these phases. The CHtype recession probability exhibits downward movement from the beginning of 2016 and is
1.5% in September, 2016.
(%)
10090
80
70
60
50
40
30
20
100
90/01

(CY2010＝100)

93/01

96/01

99/01

02/01

05/01

08/01

11/01

14/01

70
75
80
85
90
95
100
105
110
115
120
17/01
17/03
(Monthly)

Recession
CH-type recession probability
Leading index (right scale, measured inversely)
Note: The CH-type recession probability is up to March 2017. Source: Cabinet office, Indexes of Business Conditons

Figure 1. CH-type recession probability derived from the leading index of CI
Figure 2 displays the behavior of the filtered and smoothed state probabilities derived from theleading index of CI.2 Unlike the CH-type recession probability, the filtered and smoothedprobabilities are revised tracing back to the past whenever new data are released because thesetwo probabilities use the all data available up to the latest value for calculation. Naturally, due tothis property, fluctuations seen in the CH-type recession probability in Figure 1 are smoothed in
the filtered and smoothed probabilities. Although the smoothed probability rather violates ouraim of judging business conditions in real time, it gives the most accurate indicator for recession
ex-post.

2For these two probabilities, Piger (2009) defines the filtered probability as “the probability that theunobserved Markov chain for a Markov-switching model is in a particular regime in period t, conditionalon observing sample information up to period t” and the smoothed probability as “the probability that theunobserved Markov chain for a Markov-switching model is in a particular regime in period t, conditionalon observing all sample information”.
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3Japan Center for Economic Research(%)
10090
80
7060
50
4030
20
100
90/01

93/01

96/01

99/01

02/01

05/01

Recession
Filtered probability
Source: Cabinet office, Indexes of Business Conditions

08/01

11/01

14/01

Smoothed probability

17/01
17/04
(Monthly)

Figure 2. Filtered and smoothed probabilities derived from the leading index of CI
Table 2 compares the leads-lags relationship between the two recession probabilities (i.e., theCH-type recession probability and the smoothed probability) and the recession periods
determined by ESRI. The CH-type recession probability tends to rise prior to entering recession
for about six months to a year. In case of lagging, lags fall within the range of two months. Thesmoothed probability tends to rise prior to entering recession for three months to half a year andlags also fall within the range of 1–2 months. Except for the shortest recession in the postwar
periods, March–November in 2012, we can conclude that our results satisfactorily capture therecent five recessions in advance.
Table 2. Comparison between the recession probabilities and the ESRI’s recession dates
CH-type recession
leads/lags
Smoothed probability
leads/lags
probability exceeds 67%(in months)
exceeds 50%(in months)(2 consecutive months)
(1)
(2)
(3)
(4)
(5)
February, 1991―October, 1993
January, 1990
-13
July, 1990
-7May, 1997―January, 1999
December, 1996
-5June, 1997
+1
November, 2000―January, 2002
January, 2001
+2January, 2001
+2
February, 2008―March, 2009
August, 2007
-6
November, 2007
-3
March, 2012―November, 2012
NoN.A.
NoN.A.
(1) presents the recession periods determined by ESRI. (2) presents the point of time when the CH-type recession probability
exceeds 67% for 2 consecutive months. (3) presents the second column leads/lags the beginning of the first column. (4) presents
the point of time when the smoothed probability exceeds 50%. (5) presents the forth column leads/lags the beginning of the firstcolumn.
Notes : The signs in the third and the fifth column mean that the second or the forth column leads (-) or lags (+) the beginning of
the first column.
Source : Cabinet office, Indexes of Business Conditions
Recession dates determinedby Cabinet officeConcluding remarks
Based on the results presented above, we recommend using the CH-type recession probability
as a signal for warning of the rise of recession risk and using the smoothed probability as amerkmal for identifying the recession period ex-post. The use of the CH-type recession
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4Japan Center for Economic Researchprobability can be justified because we attempt to detect the possibility of a recession in realtime, even if consequently frequency of a false alarm increases. Although we should avoid ahasty judgment on the prospect of business conditions, detecting a recession risk early provides
useful information for policy-makers in the government and central bank.
References(In English)
Chauvet, M. and Hamilton, J. D., 2005. Dating business cycle turning points, NBER Working
Paper No. 11422.
Econbrowser, The Econbrowser Recession Indicator Index, http://econbrowser.com/recessionindex
Hamilton, J. D., 2010a. Calling recessions in real time, NBER Working Paper No. 16162.
Piger, J., 2009. Econometrics: models of regime changes, In Complex Systems in Finance andEconometrics, 190-202. Springer New York.
(In Japanese)
Okimoto, T., 2014. Markov-switching models with applications in macroeconomics andFinance, Journal of the Japan Statistical Society vol. 44(1), 137-157.

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