Recession Indicator―A Technical Note―

公益社団法人 日本経済研究センター

Japan Center for Economic Research
September 8, 2020

About the Revision of Estimation Method†
Senior Economist, Takashi Miyazaki
Background of the revision
Against the background of the spread of the new coronavirus, the leading index of business conditions(hereinafter referred to as the leading CI) published by the Cabinet Office, which is the underlying
data for calculating the recession probability, has fallen significantly from March to April. This
unprecedented rapid deterioration of the leading CI distorted the calculation of this probability, andcould give an erroneous signal to future business conditions. Although this probability has been
calculated and posted as a reference value since April 2020, we have revised the estimation method tomore appropriately indicate the future of the economy, taking into account the latest circumstances.
Changes in the estimation method
The recession probability is calculated using a statistical method called the Markov switching model.1
The changes from the conventional estimation model are as follows.

Change point 1 Changes in probability distribution assumptions
In the conventional model, the recession probability was estimated based on the assumption that therate of change in the leading CI from the previous month follows (standardized) normal distribution.2
Specifically, it is as follows;
𝑦 −𝜇| 𝑆 = 1 ~ 𝑁 0,1
𝜎𝑦 −𝜇| 𝑆 = 2 ~ 𝑁 0,1
𝜎where, 𝑦 represents the rate of change in the leading CI from the previous month, and 𝑆 =𝑗 𝑗 = 1,2

is a state variable which represents expansion period or recession period, 𝑁 0,1represents a standard normal distribution. Then, it is assumed that the mean is different between theexpansion period and the recession period 𝜇 ≠ 𝜇 , and the variance is common to both states=𝜎(See also point of change 2 below).

In this revision, this assumption was revised and the distribution was changed from a normal
distribution to a 𝑡 distribution. The 𝑡 distribution is a fat-tailed distribution which exhibits a large† This work is supported by Shuma Sato (Keio University).
1

For details of the model, please refer to Miyazaki (2016).
Under the normal distribution, the estimation results in a problem that the recession probability rises to near 100% only
after the Lehman shock and during the current Coronavirus crisis, and it remains around 0% in other periods.
2

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skewness or kurtosis, relative to a normal distribution (it tends to take an extreme positive andnegative values), and can flexibly cope with large fluctuations in the leading CI. The degrees offreedom of the 𝑡 distribution was set to 2 based on the fit of the posterior estimation results.
𝑦 −𝜇| 𝑆 =1 ~𝑡 2𝜎
𝑦 −𝜇| 𝑆 =2 ~𝑡 2𝜎
The degrees of freedom of the 𝑡 distribution can be different between the expansion period and therecession period, but there is no significant difference in the estimation results, therefore they are thesame in both states.
Change point 2 Set prior distributions of parameters
In the conventional model, the following five parameters 𝜇 , 𝜇 , 𝜎, 𝑝 , 𝑝were estimated by themaximum likelihood method, where 𝜇 is the average rate of change in the leading CI during theexpansion period, 𝜇 is the average rate of change in the leading CI during the recession period, and𝜎 is the standard deviation of the rate of change in the leading CI (common in the expansion period
and the recession period), 𝑝and 𝑝

are the probabilities of consecutive expansion and recession

periods respectively.
In this revision, we newly take prior distribution into account, that is, Bayesian estimation. The
Bayesian estimation specifies the range of values the parameter can take based on a prior information(assuming prior distributions), multiplies it with the data (likelihood), and updates the information(deriving the posterior distribution). Parameter assumptions in prior distributions3 and the estimatedvalues (parameter values that maximize the probability density of the posterior distribution, i.e.,posterior mode) are summarized in Table 1.
Table 1. Assumption of prior distributions and estimated value (posterior mode)
Prior standard

Estimated value

deviation(Posterior mode)

4.4

2.0

2.74

Normal-9.1

2.0-3.84

𝜎

Inverse gamma

17.7

∞

13.64

𝑝

Beta

0.98

0.02

0.96

𝑝

Beta

0.95

0.02

0.94

Parameter

Prior distribution

Prior mean𝜇Normal𝜇3

Based on the standard assumptions in the existing research, the prior distributions are based on the actual leading CI data ofthe expansion and recession period which were set in the turning point of business cycle defined by the Cabinet Office.
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Recession probability after changing the estimation method
Figure 1 shows the latest estimates as of July 2020, reflecting the above changes4. The recession
probability as of July 2020 is 30.7%. On July 30, the Cabinet Office tentatively designated October
2018 as the "peak" in the expansion phase that began in December 2012. Looking at the estimation
results in Figure 1 for this period, the probability exceeded 67%, which is a benchmark for signaling
entering a recession, for two consecutive months in January 2018, which succeeds in giving a signal of
the recession more half a year earlier than the peak determined by the Cabinet Office.
Most recently, this probability fell below 67% for two consecutive months in March 2020, andhas been on a downward trend since then. According to the ESP forecast survey released by Japan
Center for Economic Research (JCER), the number of economists responding that the "trough" is May
2020 increase. If these views are correct, the behavior of the recession probability suggests that theeconomy has got out of a recession about two months ahead of the real economy.
Figure 1. The latest recession probability estimation (July 2020)
（%）
10090
80
70
60
50
4030
20
10000/01（2015年＝100: CY2015＝100）

02/01

04/01

06/01

08/01

10/01

12/01

14/01

16/01

120
115
110
105
100
95
90
85
80
75
70

20/07
18/01
20/01
（月次: monthly）

景気後退期: Recession period determined by Cabinet Office

景気後退確率: The Recession Indicator

景気後退の目安ライン: 67% line

先行指数（右目盛）: Leading Index (right scale)（資料）内閣府『景気動向指数』を基に日経センター推定。JCER's estimate based on Indexes of Business Conditions.

4In addition to the above change point 1 and 2, various patterns about the distribution the rate of change in the leading CI
from the previous month follows, the degree of freedom of t distribution, parameter assumptions in prior distribution, etc.
Among the various patterns, the most appropriate estimation result was selected by comprehensively considering thelikelihood, the movement of the recession probability, economic advancement, and the latest situation.
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≪Reference≫
Takashi, Miyazaki., 2016, “Estimating a recession probability in Japan using the Composite Index: An
approach employing a Markov-switching model,” JCER Discussion Paper No. 145. (in Japanese).

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