2.1. Data
In our empirical analysis, the sample period is from 1 January 2020 to 31 May 2021.
Figure 2 shows some basic statistics of COVID-19 in Japan that can be downloaded from the homepage of Ministry of Health, Labor, and Welfare (
https://www.mhlw.go.jp/stf/covid-19/open-data.html, accessed on 1 June 2021). As we can confirm from these figures, there have been four periods when the infection has spread rapidly. The peak of the first wave came in April 2020. Following the first wave, the peaks of the second, third, and fourth waves are in August 2020, January 2021, and May 2021, respectively.
As we introduced in
Section 1, the main data used in empirical analysis are
, policy indicators, and 3 kinds of index provided by OxCGRT. OxCGRT index is given in
Figure 3. We do not use economic support index in our empirical analysis because economic support generally does not directly control COVID-19 infections. The government provides economic support to the unemployed and companies to combat the recession caused by COVID-19 epidemic. Each specific policy indicator is given in
Figure 4. The gray-shaded area shows the period of emergency state declared by Japanese government.
We use R package EpiEstim to estimate the
from 15 February 2020 to 31 May 2021, which is given in
Figure 5. We can also find obvious 4 peaks of infection spread from
Figure 5. The data of daily infected cases used in the estimation of
is collected from the Johns Hopkins CSEE repository (
https://github.com/CSSEGISandData/COVID-19, accessed on 1 June 2021). When using EpiEstim, we must specify the serial interval (SI) of COVID-19 infection. [
19] fitted the data of 28 infector-infectee pairs on a log-normal distribution of serial interval and obtained the mean and standard deviation of serial interval as 4.7 days (95% confidence interval: 3.7 days, 6.0 days) and 2.9 days (95% confidence interval: 1.9 days, 4.9 days). For other important epidemiological features of COVID-19, ref. [
20] provide the a systematic review of COVID-19 based on current evidence.
Finally, we summarize the descriptive statistics of all data in
Table 2. Augmented Dickey–Fuller (ADF) unit root test shows that all variables used in regression are stationary.
2.2. Regression Analysis
We use a simple log-log specification for time-varying regression.
represents the disturbance term in regression equations.
represents the index series of OxCGRT.
is the time-varying constant and
is the time-varying coefficient.
measures the effect of
on
, which can be explained as 1% change of
can generate
change of
. Generally,
means that the government response can mitigate the spread of epidemic by reducing
. Note that, since the data series of
is high series-correlated, it may be appropriate to include autoregression (AR) or moving average (MA) terms in the regression equation. However, our objective is not to find a time-series model that can fit
well, but to find the statistical significance between
and
. When we treat
and
as fixed coefficients, we can obtain the values of coefficients by running an OLS regression. Results of OLS regression are given in
Table 3. Given the negative value of coefficient on
with 1% statistical significance, although regressions with government response measured by different indices and
have small difference in the size of coefficients, it can be confirmed that the government response does have effect on reducing
, which means that government response does reduce and slow down spread of the COVID-19 epidemic.
These values measure the average effect of government response on fighting the COVID-19 epidemic during the whole sample period. At the same time, given the fact that the COVID-19 epidemic situation in Japan is still not in total control, we also want to know whether the effect of government response changes over time. Flexible Least Squares (FLS) approach proposed by [
21] is a convenient method to do this job. After obtaining the fixed coefficients of Equation (
1) by running the OLS regression, we re-estimate this regression equation in a time-varying context. We can get 3 series of
for which we have 3 kinds of OxCGRT index.
Figure 6 is the plot of time-varying coefficient
estimated from the FLS regression of Equation (
1). When the coefficients are below 0, it means that the government response can effectively reduce
. During whole sample period, at most times, in Japan, the government response has some deterrent effect on the COVID-19 epidemic. However, deterrent changes over time. The gray-shaded area in
Figure 6 indicates the period of emergency state in Japan. The deterrent effect of the 1st emergency state (7 April 2020–25 May 2020) is clearly stronger than the effect of the 2nd emergency state (8 January 2021–21 March 2021).
Table 4 summarizes the average effect of emergency state on COVID-19 epidemic in Japan. The average effect of government response during the period of emergency state is evaluated as the average of regression coefficients during the corresponding period.
From the above analysis, it can be said that the Japanese government’s response on COVID-19 epidemic is basically effective. However, the effect of emergency state, which extends to the third time declaration, is gradually weakening. During the period of emergency state, the government is asking people to refrain from going out or traveling, but it is thought that people have become accustomed to long period of emergency state and have reached the limit of “patience”.
After obtaining
, we use it as a dependent variable in the following regression equation with specific policy indicators.
means the set of policy indicators. For example,
is the time-varying coefficients obtained from the regression of
on government response index, and, if we put all 16 policy indicators that are aggregated in government response index into the
, multicollinearity existing in these policy indicators makes regression unfeasible. To avoid this difficulty, we use stepwise regression proposed by [
22] to choose the best subset of 16 policy indicators. If
is negative and statistically significant, the corresponding policy indicator can be identified as an effective measure to control epidemic.
Table 5,
Table 6 and
Table 7 give the results of variable selection and corresponding regression. A policy indicator that has a statistically significant coefficients with negative sign is identified as effective policy. From these results, we find that, under our identification framework, not all policies may be effective in controlling the COVID-19 epidemic in Japan.
From the regression results in
Table 5, we can find that C1 (school closing), C5 (close public transport), C6 (stay at home requirements), and C7 (restrictions on internal movement) are statistically significant as the effective policies. E1 (income support for households) and E2 (debt/contract relief for households) are also effective. The finding that economic support policies can reduce
is worth noting. During the pandemic, many people lost jobs and had to go outside to find new jobs. Economic support, such as cash payment and debt relief, can reduce the risk of infection by helping households through difficult times. Actually, the Japanese government provided 100,000 yen in cash to all residents in 2020. The validity of this policy can also be confirmed from the above regression results.
H3 (contact tracing) and H8 (protection of elderly people) are identified as effective policies in the stepwise regression of policy indicators in containment and health index. As a specific example of H3, the Japanese government is actively encouraging the public to use the COVID-19 Contact-Confirming Application (
https://www.mhlw.go.jp/stf/seisakunitsuite/bunya/cocoa_00138.html, accessed on 1 June 2021). This application tracks contacts with positive infections and reports those contacts to government agencies. In addition, to protect the elderly people, most elderly and medical facilities have severely restricted visits, given that elderly people infected with COVID-19 are more likely to become severely ill. Containment policies, such as C5 and C6, still show the significant effectiveness in this regression.
From the regression results showed in
Table 7, we can find that containment policies, C5 (close public transport), C6 (stay at home requirements), and C7 (restrictions on internal movement), are still the most effective methods to control the spread of the COVID-19 epidemic. Especially, C5 (close public transport) and C6 (stay at home requirements) are two policies chosen in all 3 regressions of Equation (
2). Note that, actually, in Japan, not all public transportation has been suspended. Public transportation is responding to the COVID-19 epidemic by suspending operations, reducing flights, and advancing the last train time at the request of the government. C6 (stay at home requirements) and C7 (restrictions on internal movement) are old-fashioned methods to control epidemic, but these methods are still the most effective. These methods limit the contact of people to each other and reduce the risk of infection. Note that, although we have differences among different regressions, we can summarize the common conclusion from these results. Containment policies are the most effective methods to control the COVID-19 epidemic.