2.1 The first wave of COVID-19

During and after the first wave of COVID-19 in Japan, which started in March 2020 and ended in June 2020 (S1 Fig), Japan suffered from economic and social difficulties despite its relative success in mitigating COVID-19 infection spread. Unlike many Western countries where COVID-19 lockdowns were legally enforced, in Japan, social distancing interventions including Japan’s first “COVID-19 state of emergency” (hereafter the first state of emergency) were based on non-compulsory requests made by the central and local governments. However, several mobility indices show that mobility significantly decreased during the period of the first state of emergency (see, for example, S2 Fig). Subsequent reduction in social and economic activities under the first wave had considerable impact on employment.

At the same time, the period from the outset of the COVID-19 crisis in February 2020 to the end of the first wave of COVID-19 in June 2020 was an important stage in Japan’s COVID-19 policy formation during which basic epidemiological, social and fiscal schemes against COVID-19 were constructed (S1 Fig). The first COVID-19 state of emergency was declared on 7th April in seven prefectures, including the Tokyo and Osaka metropolitan areas. On April 16, the State of Emergency Declaration was extended to cover the entire country. Then, as the infection level steadily dropped, the government gradually lifted the state of emergency in multiple phases starting in the middle of May.

During this period, the first and second supplementary budgets as emergent COVID-19 fiscal measures passed on 30th April and 12th June respectively. The total amount of these two supplementary budgets was 57,602 billion JPY (around 520 billion USD given that 1 USD = 110 JPY) and around 10.7% of GDP in 2020 [38]. The largest component of the first supplementary budget was a lump-sum transfer program consisting of a one-time transfer of 100,000 JPY (around 910 USD) to all individuals living in Japan. There were also several other transfer programs that were intended to support firms and their employees under the COVID-19 crisis, but financial supports for people who lost their jobs or incomes due to COVID-19 during this period were mostly realized by the existing three tiers of safety net programs that we explain in the next subsection. See Ando et al. [38] for more detailed background information and the contents of Japan’s fiscal responses against the first wave of COVID-19 and the subsequent first COVID-19 state of emergency.

2.2 Outcomes of interest

Our outcomes of interest are the suicide rate by gender and the utilization of the three tiers of safety net programs before and after the first wave of COVID-19 in Japan. They consist of the monthly panel data of 47 prefectures from January 2018 to September 2020 (33 months)—47 prefectures, such as Tokyo, Kyoto, and Hokkaido, are second-tier local governments while the third-tier local governments consist of 1,718 municipalities. The full sample size is 1,551, although some safety-net outcome variables lack data in some months. We use the administrative aggregated statistics provided by the central government for all of the outcome variables. See also S1 Table for further details about the three tiers of safety net programs such as eligibility, amount per recipient, and duration.

2.3 Treatment variables

For a treatment variable, we use a continuous variable that reflects a sudden and plausibly exogenous regional variation in the COVID-19-induced employment shock. We adopt the unemployment rate as a baseline employment indicator because it is most commonly used in the literature. We also use a supplementary employment indicator based on the statistics of registered full-time-job seekers for a robustness check.

2.4 Summary statistics

Table 1 shows the summary statistics of our dataset. Because the employment-shock variable defined in Eq (1) and covariates are time-invariant and cross-sectional variables, we have 47 observations. The outcome variables such as suicide rates, unemployment benefit recipients, and public assistance recipients include 33-months of data (from January 2018 to September 2020) while the variables of the second-tier safety net programs such as Emergency Small Amount Funds, General Support Funds, and Housing Security Benefit are more restricted due to data limitations.

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Table 1. Summary statistics.

https://doi.org/10.1371/journal.pone.0264829.t001

For Emergency Small Amount Funds and General Support Funds, we use the monthly data between January 2019 and September 2020, but due to limited data availability we do not have the data for February and March 2020; statistics for these two months were missing from the original data provided by the government. In addition, the monthly-level data aggregation from April to July 2020 is slightly irregular, although it should not cause serious estimation bias. More concretely, the number of loan decisions between April and September 2020 in the statistics provided by the central government is aggregated as follows: April data is based on the numbers from 25th March to 2nd May, May data is from 3rd May to 30th May, June data is from 31st May to 27th June, July data is from 28th June to 1st August, August data is from 2nd August to 29th August, and September data is from 30th August to 3rd October. For Housing Security Benefit, we can use only January, February, and March 2019 in the pre-COVID-19 period because of the limited data availability.

S2 Table presents definitions and data sources of all the variables used for analyses. All the data except for the second-tier safety net programs (Emergency Small Amount Funds, General Support Funds, and Housing Security Benefits) are obtained from the websites of the Ministry of Health, Labour, and Welfare (MHLW) and Statistics Bureau of Japan. When it comes to the data of the second-tier safety net programs, we use the datasets that are directly provided by MHLW.

2.5 Descriptive evidence

Before moving on to the econometric analysis, we provide some descriptive evidence that suggests an association between the increase in the unemployment rate and the increases in suicide and safety net use in the midst of the COVID-19 crisis. We firstly provide the nation-level time-series graphs of employment status and outcome variables before and after the onset of the first wave of COVID-19. We then present the scatter plots of suicide rates versus our baseline treatment variable (the COVID-19-induced employment shock measured by the unemployment rate).

Fig 1 describes how the status of employment, suicide, and safety-net provisions in Japan evolved before, during, and after the first wave of COVID-19 in 2020. These nation-level statistics are constructed based on four major employment statistics (labor force participation rate, employment rate, unemployment rate, and jobs-to-applicants ratio) and the outcome variables listed in Section 2.2. See also S2 Table for their definitions and data sources.

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Fig 1. Monthly trends of employment-related variables, suicides and safety-net programs in Japan.

Notes: A vertical line in January 2020 indicates the beginning of the COVID-19 crisis in Japan and a gray area indicates the second quarter of 2020. “Year-on-year” means year-on-year difference. Panels (a) and (b) show different employment-related statistics. Suicides in panels (c) and (d) are counted based on the estimated dates of death. In panel (f), “Emergency Small Amount Funds” and “General Support Funds” are two public temporary loan programs and “Housing Security Benefit” is a temporary housing allowance program. In panel (h), “the elderly” indicates a household with only persons aged 65 or over (and unmarried persons under the age of 18), “single mothers” means households with unmarried women and their children under the age of 18, “the disabled” or “the sick” are households the heads of which are persons with a disability or illness respectively. See Section 2 for more details about these data. Sources: See S2 Table.

https://doi.org/10.1371/journal.pone.0264829.g001

The implications of Fig 1 are summarized as follows. First, panels (a) and (b) show that the employment rate and labor force participation rate have sharply dropped since April 2020, while the unemployment rate and the jobs-to-applicants ratio—the ratio of job offers to job applicants, which is one of the most used monthly administrative employment indicators in Japan—gradually deteriorated.

Second, panels (c) and (d) suggest that suicide rates have been increasing since July 2020. It is of course not clear from these graphs to what degree the COVID-19 crisis has led to the increase in suicides, but some specialists and reports in the mass media have asserted that the sharp deterioration in employment in the first few months of the COVID-19 crisis may have resulted in the slightly lagged increase in suicides [41, 42]. In S3 Table, we also present the numbers of suicides in 2019 and 2020 by sex, age and occupation. These data show that the increase in suicides from 2019 and 2020 stands out in both employed and non-employed women within all age cohorts and young employed men aged 20–29.

Third, panels (e) and (f) show that the utilization of the first and second-tier safety net programs also increased during and after the second quarter of 2020 or the period of the first wave of COVID-19. Outcome values for all the second-tier programs are not zero in the pre-COVID-19 period but discontinuously smaller than those in the COVID-19 period. Note also that the central government has relaxed eligibility requirements for these second-tier programs due to COVID-19 since March 2020.

Fourth, panel (g) shows that the year-on-year numbers of recipients and recipient households of the public assistance program, the third-tier and last-resort safety net, are negative both before and after the onset of the COVID-19 crisis, implying that the number of public assistance recipients kept decreasing regardless of the COVID-19 crisis. Panel (h), however, indicates that the counterpart year-on-year number for the household type of “others”, which includes low-income workers and the unemployed, clearly started increasing in April 2020.

In turn, Fig 2 shows the regional variation of the employment shock measured as Eq (1) (panel (a)), namely our treatment variable, and correlations of this employment shock and changes in total, female, and male suicide rates in July 2020 from those in July 2019 (panel (b)-(d)). We use the monthly suicide rates in July because our employment-shock variable is calculated as a shock in the second quarter (i.e., April to June) 2020.

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Fig 2. Changes in the unemployment rate and suicide rates.

Notes: In all four graphs, the X axis is the size of an employment shock defined as in Eq (1). The Y axis in panels (b)-(d) is a change in the suicide rate from July 2019 to July 2020. The size of each circle is based on the population size of each prefecture. The dashed line is the fitted linear regression line based on the Ordinary Least Square (OLS) method. Sources: See S2 Table.

https://doi.org/10.1371/journal.pone.0264829.g002

Panel (a) of Fig 2 shows that the most affected prefectures are Okinawa, Kanagawa, and Osaka and their employment shocks are more than one percentage point. Panel (a) also suggests that these employment shocks are larger in metropolitan areas (Kanagawa, Osaka, Nara, Tokyo, Hyogo, Saitama, Chiba, Kyoto) and prefectures with popular sightseeing spots (Okinawa and Hokkaido). Panels (b)-(d) present some positive correlations between the employment shock and the suicide rates, although suicide rates in the metropolitan areas are not necessarily highest.

3.1 Empirical model

The baseline model specification takes the following event-study specification with time-varying DID coefficients: (2) where Y_it is the outcome variable such as a suicide rate for prefecture i at time t, Empshock_i is a continuous treatment variable of the COVID-19 employment shock defined as in Eq (1), 1[t = τ] is a dummy variable that takes the value of one if t = τ and zero otherwise, π_i and θ_t are prefecture and month fixed effects, respectively, ϕ_i t is an individual (i.e., prefecture) linear trend, and ε_it is an error term.

The coefficients of interest are the time-varying coefficients β_τ, which capture the correlation between EmpShock_i and the outcome trend from January 2020 to time τ. When time τ is before January 2020, β_τ can be interpreted as a placebo estimate that is expected to be around zero if no confounding trends existed before the COVID-19 crisis. When month τ is after January 2020, β_τ captures the association between EmpShock_i and the outcome trend in the COVID-19 period, which is not confounded by pre-existing outcome trends if placebo estimates before January 2020 are around zero. Furthermore, if the assumption of no differential trends among prefectures in the COVID-19 period is plausible, β_τ in the COVID-19 period can be interpreated as a causal effect of EmpShock_i on Y_iτ. We however do not assert such a clear causal interpretation due to possible unobserved confounders in the COVID-19 period.

In the baseline regression analysis we use the weighted least square (WLS) estimation method in which prefecture-level population sizes are used as weights. With this WLS model, the heterogeneous association of the employment shock with an outcome for a larger prefecture is more highly weighted in a DID estimator. In the section of robustness checks, we also use the ordinary least square (OLS) estimation method because it is not clear whether a WLS estimator is more appropriate than an OLS estimator as an estimator of a population average effect when effect heterogeneity exists [43].

In addition, for the outcomes of the second-tier safety net programs (two temporary loan programs and Housing Security Benefit), we do not include an individual linear trend ϕ_i t in Eq (2) because the levels of these outcomes are negligible in the pre-COVID-crisis period compared with the COVID-crisis period (see panel (f) in Fig 1). As robustness checks, we also provide estimation results of all of the other outcomes with an estimation model that does not control for individual linear trends.

One caveat other than the problem of possible confounders, which we will discuss in the next subsection, is that what we examine is the region-level (i.e., prefecture-level) association between the employment shock and the outcomes of interest. In this sense, we do not directly investigate how individual or household-level unemployment is related to individual or household-level suicide and safety net use. Instead, we examine how the prefecture-level employment shock is associated with suicide and safety net use for people and households living in each prefecture. In other words, the parameter β_τ reflects not only direct associations between individual unemployment and individual outcomes, but broader associations between deteriorating prefecture-level employment situations and the well-being and living standard of people and families living in a prefecture.

3.2 Possible confounders

Even if placebo estimates of β_τ before January 2020 in Eq (2) are around zero, it is possible that some regional factors are correlated with both EmpShock_i and Y_it under the COVID-19 crisis, resulting in confounding bias in the estimation of β_τ after January 2020. Such confounding regional factors may exist given the fact that the impact of the COVID-19 crisis has spread through society via various pathways.

In order to mitigate such possible confounding bias, we also estimate the regression model that incorporates pre-determined cross-sectional covariates interacted with monthly dummy variables in the COVID-19 period. These terms capture the COVID-19-induced outcome changes that are better explained by pre-determined factors than by the COVID-19 employment shock. Time-varying covariates, which are more commonly used in the DID literature, cannot be obtained in our analysis with monthly panel data.

For the pre-determined covariates, we use the three variables that reflect the intensity of the COVID-19 crisis and the five variables that represent pre-COVID-19 demographic conditions. The three covariates of the COVID-19 crisis consist of the cumulative COVID-19 infection and death rates at the end of the first wave (i.e., at the end of June 2020 based on S1 Fig) and the monthly average of the Google Mobility index in May 2020, when the first COVID-19 state of emergency was imposed. All of these variables may affect both the employment shock and the outcomes of interest and may cause omitted variables bias. The five demographic variables are the population density measured by inhabitable area, the ratios of employees in the secondary and tertiary (i.e., service) industry, the population size, and the elderly dependency rate (i.e., the ratio between the number of persons aged 65 and over and the number of persons aged between 15 and 64). See Table 1 for the summary statistics of the eight covariates.

Regarding the Google mobility data, it is taken from Google COVID-19 Community Mobility Reports [44]. Google provides prefectural data on people’s visits to six categories of places such as “Grocery and pharmacy”, “Retail and recreation”, “Parks”, “Transit stations”, “Workplace”, and “Residential”. Each indicator shows the percentage change in the number of visitors to (or time spent in) different locations compared to the baseline number computed from January 3rd and February 6th, 2020. Using four of these mobility measures —“Grocery and pharmacy’, “Retail and recreation”, “Transit stations”, and “Workplace” —, we calculated the monthly average values of Google Mobility indicators, following the definition of [45, 46]. See also S2 Fig for nation-level time-series statistics of this mobility index in 2020.

We do not strongly argue that our empirical strategy and the inclusion of the above eight covariates perfectly solve the problem of estimation bias. In this sense, we interpret our estimation results as associations between the COVID-19-induced employment shock and the outcomes of interest, which may reflect causal relations from the former to the latter.

3.3 Suicide prevention by safety net

Another limitation of our research design is that we interpret safety net use as an outcome of financial distress rather than an indicator of financial aid. That is, although it is important to understand how the safety net programs have prevented suicide under the COVID-19 crisis, we do not address this question in this paper. This may be disappointing, but the incidences of suicide and safety net use are expected to be strongly endogenous and we cannot find any proper exogenous variation that can solve this endogeneity problem.

This limitation, however, does not lead to any confounding bias in our estimation of β_τ because the endogenous relationship between outcome variables is not relevant for our empirical strategy. We only need to interpret the association between the COVID-19-induced employment shock and the suicide rate as the one that remained even after the three tiers of safety net programs and other financial benefits contributed to suicide prevention during and after the first wave of COVID-19.

4.1 Suicide rates

Fig 3 shows the estimation results for the suicide rates: the left-hand graphs are estimation results based on Eq (2) using WLS and the right-hand graphs show counterpart results based on a model that additionally controls for the eight covariates. First, placebo estimates in the pre-COVID-19 period are more or less zero, implying that there is no clear statistically significant correlation between the employment shock and all the outcome trends before January 2020. Second, after January 2020, DID estimates for total, female, and male suicide rates are positive from May to July and the lower limits of the 90% confidence intervals are often above or near zero, particularly in July.

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Fig 3. DID estimates for suicide rates.

Notes: Each plot indicates a point estimate and a vertical line indicates a 90% confidence interval that is calculated based on a robust standard error clustered at the prefecture level. All the outcomes are measured as the number of suicides per 100,000 people and the treatment variable is the COVID-19-induced employment shock, which is calculated as Eq (1). Estimates are obtained based on Eq (2) with WLS estimation weighted by prefecture population size. Because Eq (2) incorporates individual (i.e. prefecture) linear trends, estimates can be obtained from February 2019. See S4 and S5 Tables for the values of these baseline estimates and standard errors in the COVID-19 period.

https://doi.org/10.1371/journal.pone.0264829.g003

Comparing results in the COVID-19 period between the models without the covariates (right-hand) and with the covariates (left-hand), estimation results are robust in the sense that the positive estimates in July 2020 remain the same. Given that the right-hand results are less biased in the sense that some possible confounding factors are controlled for, in the rest of this paper we discuss the results based on the right-hand graphs. We also interpret that larger confidence intervals in some estimates after controlling for the covariates are partly due to correlations among the treatment variable and the eight covariates: when we regress the treatment variable on the eight covariates using cross-sectional data, the adjusted R squared is 0.352. We nonetheless use all eight covariates because the Variable Inflation Factor (VIF) of the treatment variable is 1.87 and relatively low.

The sizes of the estimates in July 2020 based on the right-hand graphs suggest that the one-percentage-point increase in the COVID-19 employment shock in the second quarter of 2020 is associated with 0.522, 0.518, and 0.521-point increases (or 37.4%, 60.5%, and 26.5% increases from July 2019) in the total, female, and male suicide rates respectively. Note that the rates of increase are calculated as the estimates divided by the total, female, and male suicide rates in July 2019, which are 1.394, 0.856, and 1.963 respectively. In August and September, estimates are around zero, implying that suicides in these months may not directly be related to the second-quarter employment shock in 2020.

Overall, the DID estimates suggest that the COVID-19-induced employment shocks are clearly associated with both female and male suicides. Estimates are more or less robust to the inclusion of the covariates at least in July 2020, just after the second-quarter employment shock. This indicates that confounding bias may not be serious. At the same time, the association between the employment shock and the suicide rate is not clearly observed in August and September 2020 and this finding is also robust to the introduction of the covariates. This implies that the COVID-19 employment shock in the second quarter of 2020 may have a short-run association with suicide in the following month of July 2020, but cannot explain suicide increases in August and September 2020.

The magnitudes of the estimated associations in July 2020 are not small. Simple calculation based on the estimate for total suicides in panel (b) suggests that if a region with a population of 10 million experienced a one-percentage point increase in the unemployment rate caused by the COVID-19 crisis in the second quarter of 2020, which is roughly equivalent to the third-highest employment shock on Osaka (see Fig 2), this could have been associated with an additional 52.2 suicides in July 2020. Another simplified back-of-envelop calculation suggests that if Japan experienced the same one-percentage-point employment shock and there was a homogeneous nationwide association between the employment shock and the estimated 0.522 point increase in suicides, this could have led to an additional 657 suicides when the counterpart monthly suicide number was 1,761 in July 2019. Note that 657 is calculated as 1,258 times 0.522, where 1,258 hundred thousand (i.e. 125.8 million) is Japan’s estimated population in July 2020).

4.2 Safety net use

When it comes to the relation between the COVID-19-induced employment shock and safety net programs, we provide three figures that represent estimation results for the first, second, and third-tier safety net programs respectively.

First, Fig 4 provides estimation results for year-on-year unemployment benefit numbers, the first-tier safety net. As in Fig 3, the left-hand results are based on Eq (2) using WLS and the right-hand results are based on the model that controls for the eight covariates. Note that we also examine the original, not year-on-year, outcome but some differential pre-trends for this outcome are not properly controlled for.

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Fig 4. DID estimates for unemployment benefit recipients.

Notes: Each plot indicates a point estimate and a vertical line indicates a 90% confidence interval that is calculated based on a robust standard error clustered at the prefecture level. All the outcomes are measured as the number of recipients per 100,000 people and the treatment variable is the COVID-19-induced employment shock, which is calculated as Eq (1). An outcome variable is year-on-year and calculated as the difference between an outcome value at month t and an outcome value at month t−12. Estimates are obtained based on Eq (2) with WLS estimation weighted by prefecture population size. Because Eq (2) incorporates individual (i.e. prefecture) linear trends, estimates can be obtained from February 2019. See S6 and S7 Tables for the values of these baseline estimates and standard errors in the COVID-19 period.

https://doi.org/10.1371/journal.pone.0264829.g004

To begin with, estimates are slightly increasing but not significantly different from zero in the COVID-19 crisis period if no covariates are introduced in the regression model (left graphs). However, after controlling for the covariates, estimates in the COVID-19 period get larger for all three outcomes, particularly for the outcome of female recipients (right graphs). In July 2020, the one-percentage-point increase in the employment shock is associated with approximately an additional 27.9 total unemployment benefit recipients per 100,000 population (panel (b)).

Second, Fig 5 provides estimates for the second-tier safety net programs: the two temporary loan programs and the Housing Security Benefit. In the COVID-19 period, panels (a) to (d) show that the estimates for the temporary loan programs in the COVID-19 periods are positive and these results are robust to the inclusion of the covariates, while the lower limits of the confidence intervals in panel (b) are below zero in the COVID-19 period. Panel (e) shows a positive association between the employment shock and Housing Security Benefit in the COVID-19 period, but it disappears once the covariates are controlled for in panel (f). At the peak, the one-percentage-point increase in the employment shock is associated with an additional 87.8 accepted applications for General Support Funds in July 2020 (both per 100,000 population, panel (d)).

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Fig 5. DID estimates for second-tier safety net programs.

Notes: Each plot indicates a point estimate and a vertical line indicates a 90% confidence interval that is calculated based on a robust standard error clustered at the prefecture level. All of the outcomes are measured as the number of accepted applications per 100,000 people and the treatment variable is the COVID-19-induced employment shock, which is calculated as Eq (1). Estimates are obtained based on Eq (2) with WLS estimation weighted by prefecture population size. Individual linear trends are not introduced due to discontinuously smaller outcome values in the pre-COVID-19 period. For the outcome of Emergency Small Amount Funds and General Support Funds, data for February and March 2020 is missing. For the outcome of the Housing Security Benefit, the reference year is March 2019 instead of January 2020 due to the lack of data during April 2019 and March 2020. See S8 and S9 Tables for the values of these baseline estimates and standard errors in the COVID-19 period.

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Note that the numbers of accepted applications for these programs are discontinuously smaller in the pre-COVID-19 period, so the pre-COVID-19 estimates and confidence intervals can be obtained but are negligibly smaller than those in the COVID-19 period. This may be one drawback of the examination of pre-trends for these outcomes, but it also means that there are at least no significant differential trends for these outcomes in the pre-COVID-19 period. We also do not incorporate individual linear trends due to this feature. As for the Housing Security Benefit, for which we have very limited prefecture-level monthly data in the pre-COVID-19 period (i.e., only January to March 2019), we at least know that the number of accepted applications discontinuously increased in 2020 at the national level: the average monthly number of accepted applications in fiscal year 2019 (from April 2019 to March 2020) in the whole of Japan was only 331, whereas the corresponding numbers in April, May, and June 2020 were 3,409, 27040, and 34,867 respectively (based on the statistics of MHLM).

Third, Fig 6 provides estimation results for year-on-year public assistance benefits: panels (a) and (b) present estimates for the number of recipients and panels (c) and (d) for the number of recipient households. All of the graphs show that estimates in the COVID-19 period are clearly increasing and positive while estimates in the pre-COVID-19 period are around zero. Introduction of the covariates leads to smaller estimates and larger confidence intervals in the COVID-19 period, but baseline findings remain the same—as already discussed, these larger confidence intervals may be explained by correlations among the treatment and the eight covariates. The one-percentage-point increase in the employment shock is associated with approximately an additional 9.7 and 11.6 public assistance recipients per 100,000 population in July and September 2020, respectively (panel (b)). Note that we also examine the original, not year-on-year, outcome but differential pre-trends are not properly eliminated for this outcome, particularly when individual linear trends are not incorporated.

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Fig 6. DID estimates for public assistance.

Notes: Each plot indicates a point estimate and a vertical line indicates a 90% confidence interval that is calculated based on a robust standard error clustered at the prefecture level. All of the outcomes are measured as the number of recipients or recipient households per 100,000 people and the treatment variable is the COVID-19-induced employment shock, which is calculated as Eq (1). An outcome variable is year-on-year and calculated as the difference between an outcome value at month t and an outcome value at month t−12. Estimates are obtained based on Eq (2) with WLS estimation weighted by prefecture population size. Because Eq (2) incorporates individual (i.e. prefecture) linear trends, estimates can be obtained from February 2019. See S10 and S11 Tables for the values of these baseline estimates and standard errors in the COVID-19 period.

https://doi.org/10.1371/journal.pone.0264829.g006

Overall, these estimation results imply that the employment shock under the COVID-19 is positively associated with increases in safety-net utilization in all three tiers of programs in the COVID-19 period. The maximum estimate for each outcome suggests that a higher employment shock is associated with higher utilization. This association is stronger in the case of the two temporary loan programs in the second-tier of the safety net then in the case of the unemployment benefit, which is the first-tier program. Smaller estimates for unemployment-benefit utilization than those for the temporary loan programs may be explained by the fact that the unemployment-benefit coverage rate is low in Japan and that COVID-19-induced employment shocks are more concentrated on contingent workers who are often not eligible for unemployment benefits (Section 2.2).

In addition, even smaller estimates for the third-tier program of public assistance suggests that people facing unemployment and income reduction under the COVID-19 crisis tend to rely on the temporary loan programs rather than public assistance. Given the fact that these temporary loan programs were rarely used in the pre-COVID-19 period, the role of these programs as a safety net in the COVID-19 crisis stands out.

Finally, while the estimates for the temporary loan programs peaked in June or July 2020 (Fig 5), the estimates for public assistance continued to increase through the third quarter of 2020 (Fig 6). This may imply that a certain portion of the unemployed people who used the second-tier safety net programs had to move to public assistance, because the second-tier programs are temporary and their loan and benefit levels are rather limited.

5.1 Weighting and individual trends

Our first robustness check is to present estimation results based on two regression weighting schemes (OLS or WLS) and two model specifications (with or without individual linear trends ϕ_i t in Eq (2)), using the same treatment and outcome variables as in the baseline estimation. The rationales for these robustness checks are as follows. First, as Solon et al. [43] argue, it is not clear a priori whether OLS or WLS regression is more suitable for estimating a population average effect, so we compare OLS and WLS estimates and discuss how they differ and why. Second, while incorporating individual linear trends may be effective for controlling for observed and unobserved differential trends across prefectures, it is useful to examine whether estimation results change if we use a simpler model without individual linear trends.

Estimation results suggest that our primary findings for suicide and all the safety net programs are robust to these different estimation settings except for a few cases. First, S3 Fig shows that estimates for total, female, and male suicide rates in July 2020 are positive and mostly significantly different from zero regardless of estimation settings and the addition of the covariates. Second, S4 Fig illustrates that estimates for unemployment benefit recipients are also increasing during the COVID-19 period although some estimates for male unemployment benefit recipients are not significantly different from zero. Third, in S5 Fig, estimation results for the second-tier programs (i.e., temporary loans and Housing Security Benefits) do not change much under different weighting schemes; as in the baseline analysis we do not incorporate linear individual trends due to discontinuously smaller pre-COVID-crisis outcome values. Fourth, S6 Fig shows, once individual trends are controlled for, both OLS and WLS estimates for public assistance are increasing and positive in the COVID-19 period regardless of the introduction of the covariates, although standard errors are larger if the covariates are incorporated. If individual linear trends are not incorporated, pre-COVID-19 estimates for public assistance outcomes fail to be around zero and positive, implying that DID estimates in the COVID-19 period under this specification have a downward bias.

For most outcomes, WLS estimates during the COVID-19 period tend to be higher than the counterpart OLS estimates. We interpret larger WLS estimates as reflecting heterogeneous employment-shock associations with suicide across prefectures: as Fig 2 indicates, prefectures with larger populations may be more clearly associated with the employment shocks and the WLS estimation puts more weights on these prefectures.

5.2 A different reference period

We also provide a different robustness check in which all months before January 2020 are included in the reference period in addition to January 2020 as follows: (3) where the notation of τ ≠ Jan.2020 in Eq (2) is changed to τ > Jan.2020. Because the pre-COVID-19 outcome trends are not correlated with the treatment variable in the baseline estimations based on Eq (2), including all pre-COVID-19 months in the reference period may improve precision by averaging out noise in monthly pre-COVID-19 outcomes without increasing estimation bias.

Supporting information provides the estimation results of this robustness check for the suicide rates (S4 and S5 Tables), unemployment benefit recipients (S6 and S7 Tables), second-tier safety net programs (S8 and S9 Tables), and public assistance (S10 and S11 Tables). In each table, we also provide the baseline estimates in the COVID-19 period that are presented in Figs 3–6 for comparison.

The estimation results of these robustness checks show that we robustly observe similar findings to those in the baseline estimations when we change the reference period from one pre-COVID-19 month to all pre-COVID-19 months. This implies that our results are not driven by specific pre-COVID-19 outcome values in January 2020. In particular, for the second-tier safety net programs, the inclusion of all pre-COVID-19 months in the reference period results in only subtle changes in estimates because their pre-COVID-19 benefit levels are discontinuously smaller than those in the COVID-19 period.

5.3 An alternative treatment

As a final robustness check, we present DID estimation results using an alternative treatment variable of the “full-time” employment shock described in Section 2.3. We provide estimation results based on all four estimation schemes presented in Section 5.1: OLS without linear trends, OLS with linear trends, WLS without linear trends, and WLS with linear trends.

Our estimation results can be summarized as follows. First, contrary to our main findings, estimates for suicide in the COVID-19 period are not significantly different from zero regardless of the addition of the covariates (S7 Fig). Second, estimation results for all three tiers of safety net programs are similar to the baseline results in the sense that estimates are often positive and significantly different from zero in the COVID-19 period (S8–S10 Figs). Significant decreases in estimates for Housing Security Benefit with the introduction of the covariates are also observed in this alternative analysis (S9 Fig). At the same time, estimates for unemployment benefit recipients are smaller when the covariates are incorporated (S8 Fig) and modest differential pre-trends are observed in the results for public assistance outcomes (S10 Fig). These results also suggest that the “full-time” employment shocks have different characteristics than the baseline employment shocks.

No significant association between the “full-time” employment shock and suicide may be explained by the fact that the baseline employment shocks and the “full-time” employment shocks capture partly different COVID-19-induced economic shocks. In fact, S11 Fig shows that the baseline employment shocks (X axis) are largest in prefectures in metropolitan areas or with popular sightseeing spots (e.g. Okinawa, Kanagawa, Osaka, Nara, Hokkaido, Hyogo, Tokyo, Saitama, Chiba, and Kyoto) whereas the alternative “full-time” employment shocks (Y axis) tend to be largest in prefectures with major manufacturing regions (e.g. Gifu, Aichi, Shizuoka, Shiga, Hiroshima, Toyama,and Mie). We speculate that there being no association between the “full-time” employment shocks and suicide is related to the fact that registered full-time-job seekers, who are taken into account in this alternative treatment variable, are more resilient to the risk of suicide. This may also be related to the fact that registered full-time-job seekers are often eligible for unemployment benefits, but further investigation is required.