Estimating the Effects of the Minimum Wage Using the Introduction of Indexation

IZA DP No. 14086 JANUARY 2021 Estimating the Effects of the Minimum Wage Using the Introduction of Indexation* We examine the impacts of the minimum wage on employment using the minimum-wage hike induced by the introduction of indexation of the local minimum wage to the local cost of living. The revision of the Minimum Wage Act in 2007 of Japan essentially required the government to set the minimum wage indexed to the local cost of living, with a fiveyear moratorium period. The government subsequently increased the minimum wage in areas where the cost of living was high relative to the local minimum wage. Allowing for different trends in labor-market outcomes across regions in the pre-treatment period, we find that the minimum-wage hike raised the wages of low-wage workers, but reduced the employment of less-educated young men. A panel analysis based on matched Labor Force Survey data indicates that the minimum-wage hike decreased the job flows of prime-age men and women. JEL Classification: J23, J38, J42, J64, J81


Introduction
Numerous studies have assessed the effects of minimum wage on employment using the regional variation of the minimum wage, as reviewed by Card andKrueger (1995), Neumark andWascher (2008), Meer (2018) and Clemens (2019). Key to the research is how to handle the endogeneity of the local minimum wage, because policymakers set the minimum wage by looking at local labor-market conditions. In the absence of an exogenous source of minimum-wage variation across states, US studies have struggled to control for the regionand time-specific unobserved shocks that could be correlated with minimum wages. One group of researchers controlled for region-and time-specific shocks by using the geographically proximate area as a control group (Dube et al., 2010),while another group of researchers claimed that a traditional region-and time-fixed effects model performs better (Neumark et al., 2015;Meer and West, 2016;Clemens and Wither, 2019). The estimated impact of minimum wage on employment differs substantially depending on how the counterfactual situation is constructed. In contrast with existing studies that attempt to construct counterfactual local labor-market conditions, we exploit the plausibly exogenous minimum-wage hike across regions.
The natural experiment we exploit is the change in the institutional setting of minimumwage determination in Japan. The minimum wage in Japan is statutory, and local minimum wages are set for each of the 47 prefectures. Central and local minimum wage commissions are involved in determining the local minimum wage; in the process, the central minimum wage commission suggests the amount of minimum wage increase for each prefecture. Historically, the commission's suggestions have been linked to the average wage increase of micro-scale establishments based on a survey for this specific purpose. The revision of the Minimum Wage Act in 2007 additionally required the government to set the minimum wage, referring to the amount of welfare benefits that is indexed to the local cost of living. Specifically, the revised Act aimed to close the gap between the amount of welfare benefit and the earnings of full-time minimum wage workers, which are more substantial in urban prefectures and prefectures located in the northern area, where the cost of living is higher. Accordingly, to fill the gap, the minimum wage had been increased more significantly in prefectures where the welfare benefit exceeded the full-time minimum wage earnings in 2006. We leverage this heterogeneous growth of minimum wages across prefectures to estimate the impact of minimum-wage hikes on wages, employment, hours, and one-year transition of employment status. In the estimation, we allow for heterogeneous labor market trends before 2007.
We first confirm that the minimum wage bites the wage distribution based on the Basic Survey of Wage Structure (BSWS), which allows us to precisely calculate the hourly wage based on the wage bill of establishments. We also confirm that the minimum-wage hike increased the fraction of workers whose wage is below 1.05 × the local minimum wage. Only about 3% of workers are minimum-wage workers, and they are concentrated among the less educated, as well as younger and older workers of both sexes. We then analyze the effect of the minimum wage on employment, labor-force participation, and hours worked, using the monthly Labor Force Survey (LFS). Our analysis sample includes people with a high-school education or less to focus on less-skilled workers, but it includes a wide age range (between 19 and 64 years old), dividing workers into three age groups: 19-24, 25-59, and 60-64.
The first stage of the IV estimation shows that the gap between the welfare benefit and minimum-wage earnings in 2006 significantly predicts subsequent minimum wage growth of the region. We find, however, that the gap is associated with the trends of the employment rate before 2007. To address the potential violation of the exclusion restriction, we allow for flexible heterogeneous trends across prefectures before 2007. The second stage of the IV estimation shows that the minimum-wage hike reduces employment among less-educated young men between 19 and 24 years old. On the other hand, we find no precise estimates of the impact of minimum-wage hikes on employment among demographic groups other than less educated young men. We further find no significant impact of minimum-wage hikes on hours worked, conditional on being employed, on any of the demographic groups.
For less-educated young men, the estimated elasticity is -1.2, which is larger than the estimates in the literature. We point to two reasons for this discrepancy. First, the IV estimator estimates the treatment effect of the minimum wage on employment leveraging the increase of the minimum wage due to the introduction of the indexation of the minimum wage; employers can expect a future increase of the minimum wage according to the newly introduced rule and can substitute capital for labor, as found by Brummund and Strain (2020) from the evidence of state minimum-wage indexation. Second and more importantly, we argue that the OLS estimates in the literature suffer from an upward bias due to policy endogeneity, because policy makers are hesitant to increase the minimum wage under adverse labor-market conditions, as suggested by Baskaya and Rubinstein (2012) in the US context. This suggests the importance of seeking the exogeneous source of variation of local minimumwage hikes in a difference-in-difference framework to address the policy endogeneity issue.
We further analyze the effect of the minimum-wage hike on the transition of employment status over a one-year period by constructing short panels. We do this by matching the outgoing rotation groups of adjacent years of the LFS to examine the impact of the minimum wage on the transition of employment status over a one-year period. We find that a minimum-wage hike reduces the transition probability from non-employment to employment among prime-age men, while it increases the probability that employed prime-age women stay employed. Thus, the minimum-wage hike lowers the transition between not being employed and being employed among prime-age men and women. This finding is consistent with theoretical predictions and empirical findings in previous studies indicating that a minimum-wage hike reduces job flow in the labor market (Portugal and Cardoso, 2006;Gittings and Schmutte, 2016;Dube et al., 2016;Brochu and Green, 2019).

Literature
This work contributes to the literature in two ways. First, it identifies the effects of the minimum wage on employment, drawing on a credible, exogenous source of minimum-wage variation. All recent US studies concur on the importance of controlling for region-specific shocks that can be correlated with the minimum wage. They disagree, however, on the proper construction of a counterfactual situation in terms of selecting control areas or modeling underlying region-specific time trends (Dube et al., 2010;Allegretto et al., 2011;Neumark et al., 2015;Meer and West, 2016;Cengiz et al., 2019;Clemens and Wither, 2019). Compared to the situation in the US, where state legislators vote for state minimum-wage hikes, which potentially creates policy endogeneity according to local labor-market conditions, the determination of the Japanese regional minimum wage is arguably more centralized and mechanical. Notably, the introduction of the indexation of the minimum wage to the local cost of living, due to the revision of the Minimum Wage Act in 2007, provides a credible exogenous source of variation of local minimum wages to identify the effect of the minimum wage cleanly. To the best of our knowledge, Baskaya and Rubinstein (2012) is the only recent study that instruments the state minimum wage by the interaction term of the federal minimum wage and states' tendency to let the federal minimum wage bind.
Second, we contribute to the Japanese policy debate. Political liberals traditionally support the minimum-wage hike as a policy tool to alleviate poverty in Japan. The political scene has changed dramatically in recent years; the minimum wage has also gained support from political conservatives as an income policy to boost wages to initiate wage-price dynamics in Japan, where wages have stagnated despite a very tight labor market since the early 2010s. At the Council on Economic and Fiscal Policy on November 24, 2015, Prime Minister Shinzo Abe committed to increasing the minimum wage by 3% annually until the average regional minimum wage reaches 1,000 yen. The International Monetary Fund (IMF) backs this policy stance, 1 and IMF staff economists Aoyagi et al. (2017) reported that minimum-wage hikes have a significant impact on wage increases. Some business owners and economists, however, express concern about job loss among unskilled workers due to minimum-wage hikes.
Numerous studies have examined the impact of minimum wage on employment in Japan. Early studies exploit the cross-sectional variation of the minimum wage to estimate the impact of minimum wage on employment, using cross-sectional data or panel data without prefecture fixed effects (Tachibanaki and Urakawa, 2006;Yugami, 2005;Ariga, 2007). Controlling for prefecture fixed effects is crucial, however, because the level of the minimum wage is systematically correlated with unobserved local labor-market conditions. Several studies have allowed for individual or prefecture fixed effects when estimating the minimumwage impact on employment. Kawaguchi and Mori (2009) (2007) showed that a worker who is prone to be affected by a minimum-wage hike is more likely to lose her job. Overall, minimum-wage studies that control for policy endogeneity and cover the sample period before the 2007 revision of the Minimum Wage Act point to employment loss among less-skilled workers due to minimum-wage hikes.
Only a few studies have exploited minimum-wage hikes after the revision of the Minimum Wage Act in 2007. Higuchi (2013) examined the impact on the employment of non-regular workers based on the Keio Household Panel Survey and concluded that minimum-wage hikes did not affect the employment of non-regular workers. A careful reading of the estimation results, however, reveals that the minimum-wage hikes indeed decreased the employment of non-regular workers, but the impact was not precisely estimated because of the small sample size, around 2,000 observations. Since the number of minimum-wage workers is as limited as 3% of all workers, a large sample is needed. Akesaka et al. (2018) estimated the impact of the recent minimum-wage hike on employment using the Employment Status Survey, which is a large government survey that takes place every five years. They found that a minimum-wage hike reduces the employment of teenage men and reduces the hours worked of all workers.
Our study improves the granularity of that analysis by exploiting the large sample of monthly or annual frequency. Okudaira et al. (2019) reported the impact of minimum-wage hikes after the 2007 revision negatively affected employment, with an estimated elasticity around -0.5 among all workers, relying on the annual Census of Manufacturers. They also examined the heterogeneous impacts depending on the degree of labor-market monopsony. They first identified the degree of monopsony by determining the gap between the observed labor share and the predicted labor share in a perfectly competitive labor market from the estimated production function. Then, they found a more substantial adverse impact in the region where the labor market was estimated to be competitive. In addition, they implemented the instrumental variable estimation by using the gap between the welfare benefit and minimumwage earnings as of 2006 as the instrumental variable. Our study complements their study by covering all industries.
2 Minimum-wage indexation to the local cost of living:

Revision of the Minimum Wage Act in 2007
This section describes the institutional background of minimum-wage setting in Japan for introducing the identification strategy; more details are provided in Appendix A. Regional minimum wages, set for each of the 47 prefectures, were essentially indexed to the local average wage before 2007, because the increase in the local minimum wage was tightly linked to the average annual wage growth of workers in establishments with less than 30 workers, as documented by Tamada (2009). The partial revision of the Minimum Wage Act in 2007, which took effect on July 1, 2008, changed the policy process by adding a new requirement that the monthly earnings of full-time minimum-wage workers should not be lower than public assistance benefits. There was a gap between the monthly earnings of minimum-wage workers and the public assistance benefits in 12 prefectures as of fiscal year 2006. 2 The revised Act aimed to close the gap between the amount of welfare benefits and the earnings of full-time minimum-wage workers, which was more substantial in urban prefectures or prefectures with cold weather in the winter, where the cost of living is higher.
Accordingly, to fill the gap, the minimum wage had been increased more significantly in urban prefectures than in rural prefectures. Between 2007 and 2016, for example, the increase of the minimum wage was 26% in Tokyo and Kanagawa prefectures,urban prefectures,and 12% in Tokushima prefecture, a rural prefecture, as indicated in Figure 1. is not correlated with the minimum-wage growth between 1998 and 2007. The absence of a correlation negates a concern that the correlation between the gap and the subsequent minimum-wage growth is due to the minimum-wage growth's long-term trend.
We attempt to estimate the causal impact of the minimum-wage hike on the change of labor-market outcomes using the gap between the welfare benefit and minimum-wage earnings as of 2006 as the instrumental variable. In this identification strategy, a probable threat to identification is that the initial gap between the minimum wage and welfare benefits is correlated with the underlying trends of labor-market outcomes. To address this concern, 2 A letter submitted to the Minister of Health, Labor and Welfare from the Central Minimum Wage Commission in 2008 reported that the monthly earnings of minimum-wage workers were lower than public assistance benefits in 12 prefectures, including Hokkaido, Aomori, Miyagi, Akita, Saitama, Chiba, Tokyo, Kanagawa, Kyoto, Osaka, Hyogo, and Hiroshima prefectures. The gap amount as of 2006 was 63 yen for Hokkaido, 20 yen for Aomori, 31 yen for Miyagi, 17 yen for Akita, 56 yen for Saitama, 35 yen for Chiba, 100 yen for Tokyo, 108 yen for Kanagawa, 47 yen for Kyoto, 53 yen for Osaka, 36 yen for Hyogo, and 37 yen for Hiroshima.
we estimate the relationship between the gap and the pre-trend of employment; we estimate the following one-year-interval first-difference model: where ∆Emp jt is the annual change in the employment rate in prefecture j in year t, using

Data
This study uses the Labor Force Survey (LFS) to capture labor-market outcomes, including employment status and hours worked. The drawback of the LFS is its lack of accurate measurement of the hourly wage rate. To compensate for this drawback, we also use the Basic Survey on Wage Structure (BSWS). We briefly describe these two data sets below.
Some additional details of these two data sets are presented in Appendix B.
The LFS, the source of the main data set used in this study, is a monthly survey that corresponds to the Current Population Survey in the US. The LFS generates repeated crosssection data, but its rotation sampling structure allows us to construct a short panel data set covering two years. We use the LFS as a source of repeated cross-section data, but we exploit the panel structure for the transition analysis of employment status. We restrict the analysis sample to non-college graduates between the ages of 19 and 64, because, as we will see below, the minimum wage is relevant to non-college-graduate workers. 3 We divide the analysis sample into three age groups: 19-24, 25-59, and 60-64. We pick the ages between 19 and 24 as indicating youth to avoid those who are still in high school, as almost all highschool graduates turn age 19 before graduation. The prime-age people are those between 25 and 59 years old, and the older people are those between 60 and 64 years old. The majority of employers in Japan set the mandatory retirement age at 60, and those workers who experience a mandatory retirement change their employers or transition to a temporary position with the same employer. The analysis sample covers the period between January 2002 and December 2016. A shortfall of the LFS is that it lacks an accurate measurement of the hourly wage rate.
To compensate for the lack of an accurate measurement of hourly wage in the LFS, we use worker-level micro data from the Basic Survey on Wage Structure (BSWS). The BSWS is an annual establishment survey that adopts a two-step random sampling procedure. In the first step, establishments are randomly selected from the population of all establishments that hire 5 or more employees. In the second step, the human resource department of each establishment randomly selects the workers from its payroll records. The BSWS is an ideal data set for analyzing the impact of the minimum wage on wages because of its accurate measurements of individual workers' monthly earnings and monthly hours worked transcribed from payroll records. The BSWS covers both full-and part-time workers, but it does not ask for part-time workers' educational background. Since part-time workers are likely to be low-wage workers and more relevant to minimum wages, we basically do not restrict the analysis sample to less-educated workers. The sampling process of the BSWS uses prefecture × industry × establishment size as the strata. To keep the sampling error within a stratum below a certain level, larger establishments and establishments belonging to a rare industry are oversampled. To reflect the survey's peculiar sampling structure, we use the sampling weight in the regression analysis to recover the population distribution throughout the analysis based on the BSWS. We also use the sampling weight, so that the regression coefficients recover the population average treatment effects (Solon et al., 2015).
Our analysis sample covers the years between 2002 and 2017.

Effect on wages
As a preparatory analysis, this section examines how minimum wages affect wages overall, using the BSWS. Figure  In 2017, however, the shares of workers working for the minimum wage increased, and the shape of the wage distribution began to become dented at the minimum-wage level. This result is in contrast with the finding of Kambayashi et al. (2013), who, using data up to 2003, showed that minimum wages acted as a constraint only in rural areas and implied that as a result of the minimum-wage hike since 2007, minimum wages had started to act as a practical constraint in urban areas as well.
As a way to systematically examine the impact of the minimum wage on the lower end of the wage distribution, we first consider if the minimum-wage hike increases the fraction of workers who work near the minimum wage. To do so, we define minimum-wage workers as workers whose hourly wage is below 1.05 × minimum wage. We should note that in the analysis sample covering the years between 2002 and 2017, only 3.7% of workers had earnings in this range of hourly wage. This small fraction suggests that we need to narrowly restrict the analysis sample to those who were likely to have been affected by minimum-wage hikes. Figure 4 shows that the increase of the minimum wage between 2002 and 2017 and the increase in the fraction of workers who earned less than 1.05 × MW in the corresponding period are positively associated.
We next examine the impact of the minimum wage on the wage distribution, using the wage bins defined relative to the minimum wage. The wage bins are: We then define dummy variables for each bin that take 1 if the individual worker's wage falls in the bin. We then estimate the following linear probability model. For example, we estimate the following model for the wage bin (0, M W ): where i is the index for individual, j is prefecture, and t is year. The indicator 1(W ijt < M W jt ) takes 1 if the wage is below MW, and takes 0 otherwise, M W jt is the MW in prefecture j in year t, X ijt is a set of dummy variables defined by age × gender. We estimate the models by weighted least squares using the sampling weight. Standard errors are robust against the within-prefecture error correlation. Table 2 reports the estimation results of the linear probability models, where the dependent variables are the dummy variables that take one if the wage falls within a specific range relative to the minimum wage. Column 1 shows that minimum-wage hikes increase the fraction of non-compliers. On average, 1% of workers work below the minimum wage, and a 10% increase in the minimum wage increases non-compliers by 0.9%. In contrast, Column 2 indicates that a 10% minimum-wage hike increases the fraction of workers whose wage belongs to the range [M W, 1.05M W ) by 1.7 %, whereas about 2% of workers belong to this category. Similarly, Column 3 indicates that minimum-wage hikes increase the fraction of workers whose wage belongs to the range [1.05M W, 1.10M W ), suggesting that minimumwage hikes affect the wage of workers who earn above the minimum wage, which is called the spillover effect or ripple effect. This spillover reaches up to 15% above the minimum wage.
Minimum wages substantially affect the lower end of the wage distribution, but only 3.7% of workers earn below 1.05 × minimum wage. Thus, to assess the impact of minimumwage hikes on employment, we need to focus on very low-skilled workers and identify the characteristics of minimum-wage workers. The caveat is that the BSWS does not record the educational background of part-time workers, who make up about 20% of the analysis sample and are more likely to work as minimum-wage workers; only around 1% of full-time workers are minimum-wage workers, compared to about 10% of part-time workers. With this drawback in mind, Figure 5 plots the fraction of workers that earn below 1.05 × M W by the educational background and age of full-time workers. The fraction of minimum-wage workers is substantially higher among low-educated (high school or less) younger and older workers. Thus, to identify the impact of the minimum wage on employment, we need to focus on low-educated younger and older workers. Indeed, Clemens et al. (2020) demonstrate the need to focus on less-educated workers in minimum wage research in the US context.
To help depict the composition of minimum-wage workers, Appendix Tables C1 and   C2 tabulate the industry and occupation distributions among minimum-wage workers as of 2017. A large fraction of minimum-wage workers worked in the manufacturing sector (23%), wholesale and retail trade (17%), and the hotel and restaurant industry (14%). In terms of occupation, a large fraction of minimum-wage workers worked as sales (35%), service (28%), and manufacturing process (25%) workers.

Econometric model
We have seen that minimum-wage hikes raise the wages of low-wage workers and that lowwage workers are concentrated among less educated and younger and older workers. We now ask whether these wage increases are associated with a decrease in their employment.
Since the number of workers who are affected by minimum-wage hikes is limited, we focus in the same period on the vertical axis. For young males, the increase in the minimum wage is associated with a decrease in employment; the negative association is particularly notable in two large prefectures that experienced a significant increase in the minimum wage, namely Tokyo and Kanagawa. For prime-age and older men, we find a slight negative association.
In contrast, for women, an increase in the minimum wage is positively associated with a change in the employment of those who were young and prime-age. The association of minimum-wage change and employment rate change between 2007 and 2016, however, does not imply that the minimum wage has a causal on employment, because of potential policy endogeneity.
We now lay out the instrumental variable estimation method to attack the policy en-  Table 1.
We set up and estimate the following model by the two-stage least squares:  (2017); thus, the prefecture-specific linear trend is estimated using the pre-treatment period.
Borusyak and Jaravel (2017)  We estimate the model separately by gender and age group (19-24, 25-59, 60-64) to allow for different fixed effects and prefecture-specific time trends, because both the baseline labormarket outcomes and the effect of the minimum wage on outcomes presumably differ across groups. The sample period includes the period when the Act on the Employment of Elderly Persons, which promoted the employment of older people between the ages of 60 and 64, was revised (Kondo and Shigeoka, 2017). The impact of this Act is presumably absorbed by time fixed effects, because it was a national policy without regional variation.

The first stage
We first report the estimation results of the first-stage equation, Equation (4). Figure 7 reports the estimated coefficients, γ y , and their 95% confidence intervals. The coefficients

Employment
Next, we report the estimation results of the following reduced-form equation: where Emp   We need an explanation for this large negative impact of minimum wage on employment.
As a baseline, Okudaira et al. (2019) reported an estimated elasticity around -0.5 among all workers based on OLS, using the minimum-wage hikes after the 2007 revision for identification. First, our estimated elasticity based on OLS estimate, -0.98, is larger than the baseline estimate, but the difference is not odd, given that the estimate was obtained for high-school graduates between 19 and 24 years old, a group of low-skilled workers. Second, the larger negative impact of the minimum wage on employment based on the IV estimate than the OLS estimate is consistent with policy endogeneity: When the local economy booms, the government imposes a minimum-wage hike, and thus the OLS estimate is upward biased.
Third, our IV estimator exploits the variation of the minimum wage induced by the introduction of indexation to the local cost of living. Since the government aimed to eliminate the gap between the minimum wage and the local cost of living in the five-year period, employers foresaw the future increase of the minimum wage in 2007. Employers could have adjusted their capital investment with a long-term perspective, and that may well make the estimate larger than the usual estimate. Indeed, Brummund and Strain (2020) report that the disemployment effect of the minimum-wage hike in a state that indexes its minimum wages to inflation is around 3 times larger than the disemployment effect in a state without indexation. They argue that their finding is due to employers' forward-looking capital investment behaviors. Compared with the indexation to the inflation rate, Japan's situation makes the future increase in the minimum wage even more foreseeable, because the government announced its intent to eliminate the gap between the minimum wage and the welfare benefit in 5 years from 2007, and the gap was public information as of 2007.
For prime-age men between 25 and 59 years old, neither the OLS estimate nor the IV estimate is statistically significant. The OLS and IV estimates for those who are ages 60-64 are negative but imprecisely estimated. These results are consistent with the reduced-form estimates reported in Figure 8. We find some suggestive evidence that minimum-wage hikes reduced the employment of older men, but the estimate is not precise enough to conclude anything definitive.
For women, minimum-wage hikes did not affect the employment of any age group in a statistically significant way. The absence of an impact of minimum wage on women's employment rate across all age groups is consistent with the findings from Figure 8. In sum, we cannot conclude anything definitive about the effect of minimum-wage hikes on employment among women.
Overall, we find that the minimum wage reduces employment among less-educated men between 19 and 24 years old. The estimated elasticity based on the IV estimate is -1.2, which is larger than other estimates in the literature. We argue, however, that the upward bias of the OLS estimate due to policy endogeneity and the predictable increase of the minimum wage in our context makes our estimate larger than the previous estimates. We find no precise estimates, however, of the impact of minimum-wage hikes on other demographic groups.

Labor-force participation
We next examine the impact of the minimum wage on labor-force participation. A higher minimum wage could reduce employment, but it could simultaneously encourage labor-force participation (LFP) because of high offered wages under search friction in the labor market.
At the same time, however, a high unemployment rate potentially induced by minimumwage hikes may discourage LFP. Thus, the impact of a minimum-wage hike on LFP cannot be signed a priori. To analyze the impact of the minimum wage on LFP, we estimate the following reduced-form equation: where LF P ijt is the dummy variable indicating LFP, including being unemployed. Other variables are the same as in the employment equation, and the same identification assumption is imposed. Figure 9 shows the estimated θ y in the above equation. We find negative impacts of the initial gap on LFP among younger and older men, though these are imprecisely estimated.
For other demographic groups, we do not find significant impacts. for younger men, the IV estimate for employment is -0.93, but the IV estimate for LFP is -0.56. The smaller negative impact implies that some young men are discouraged from participating in the labor force because of deteriorated job prospects due to the minimumwage hike. While not precisely estimated and only suggestive, the same discussion may apply to older men. As we would expect from the reduced-form estimates, we do not find that the minimum wage has a significant impact on LFP among women.

Hours worked
The analysis heretofore has focused on the effect of the minimum wage on the extensive margin of employment status. The LFS asks for the hours worked in the last week of the previous month for those who were in employment. Using this variable, we estimate the impact of the minimum wage on hours worked, conditional on being employed, to shed light on the intensive margin of the potential adjustment. The estimated model is: where ln(hours) ijt is the natural logarithm of hours worked in the last week of the previous month. Other variables are the same as those in the employment equation, and the same identification assumption is imposed. Figure 10 reports the estimated θ y of the reduced-form model. The estimates show that the initial gap does not systematically affect the weekly hours worked for all demographic groups and that most of the estimated coefficients are statistically insignificant. Table 3 Panel C reports the OLS and IV regression results of the natural logarithm of hours worked based on the same specification as before, using high-school graduate (

Event study method
Recent studies on the minimum wage, such as Meer and West (2016)  attributing an observation to current, past, or future minimum-wage increases is fundamentally difficult. Thus our study does not adopt an event study approach; instead, we address the policy endogeneity issue by estimating the model with an instrumental variable method that exploits the gap between the full-time monthly earnings of minimum wage workers and the amount of public assistance in 2006 as the instrumental variable in this section.

Impacts on transitions of employment status
Most existing studies on minimum wage have analyzed the effect of minimum-wage hikes on the level of employment, as in this study so far, yet relatively few studies have examined the impact of minimum wage on job turnover. Portugal and Cardoso (2006), arguably the first influential study to examine the impact of minimum-wage hikes on job flow, used Portuguese data and found that higher minimum wages reduce labor-market turnover. Gittings and Schmutte (2016) found a similar pattern using US data. Also using US data, Dube et al.
The dependent variable E ijt is the dummy variable indicating if individual i in prefecture j is employed in year t. The vector X ijt includes the set of age dummy variables, the fraction of each age and sex group in the population, and the unemployment rate of college graduates. We divide the sample by the employment status of the previous year, denoted as E ijt−1 , to allow for the asymmetric effect of the minimum wage on the transitions from non-employment to employment or employment to non-employment. Because this is fundamentally a transition analysis, we did not include the prefecture-specific time-trend term, ξ j · Y ear. Instead, the prefecture fixed effects, θ j , capture the prefecture-level unobserved heterogeneity in the transition. As in the level equation estimation, we are concerned with the endogeneity of M W jt , because the unobserved shock to the labor market absorbed in u ijt may determine the MW. To address this potential endogeneity, we use the interaction terms of the gap between the welfare benefit and minimum-wage earnings in prefecture j in , and year dummy variables as the instrumental variable.
The Panel A of Table 4 tabulates the estimation results for men by employment status in the previous year and age groups. The first three columns report the regression results of current employment status on the effective minimum wage, conditional on being not employed in the previous year. All the estimated coefficients of OLS and IV are negative, suggesting that the higher minimum wage reduces the transition probability from non-employed to employed, but the estimate is not statistically significant for youth. Among prime-age men, a 10% increase of the effective minimum wage reduces the transition probability by about 3.3% according to the IV estimate, whereas the average transition probability is 28%.
The negative impact is not statistically significant for older workers, according to the IV estimate. In contrast, both the OLS and IV estimates reported in columns 4 to 6 in Table   4 show that a higher minimum wage does not affect the probability of staying employed in statistically significant ways among those who were employed in the previous year. Table 4 reports the estimation results of the transition analysis for women.

Panel B of
The IV estimates of Column 1 show that the minimum-wage hike increases the transition probability from non-employment to employment in a statistically significant way among young women. This result contrasts with the results for young men, for whom the minimumwage hike reduces the transition from non-employment to employment. The minimum-wage hike does not affect the transition probability from non-employment to employment among prime-age and older people. In contrast, a minimum-wage hike increases P (E t |E t−1 ) for prime-age women, by 0.08 in a statistically significant way, according to the IV estimate.
A 10% increase in the minimum wage increases the probability of staying employed by 0.8 percentage point relative to its mean 92%. In contrast, an increase of the minimum wage reduces P (E t |E t−1 ) significantly among older women. A 10 percentage-point increase reduces the current employment probability by 1.9 percentage points according to the IV estimate.
Overall, the transition analysis based on short-panel data implies that a minimum-wage hike reduces the transition between non-employment status and employment status among prime-age men and women. Thus, behind the insignificant impact of a minimum-wage hike on the stock of employment among prime age men and women, it reduces the job flow among them.

Conclusion
This paper examined the impact of minimum wages on the labor-market outcomes of various demographic groups, exploiting the heterogeneous increase in regional minimum wages in Japan from 2007 that essentially required minimum-wage commissions to index local minimum wages to the local cost of living.
An analysis of payroll records showed that the minimum wage indeed increased the probability that a worker worked near the minimum wage, suggesting that minimum wages formed the wage floor of low-wage workers in Japan between 2002 and 2017. The estimated impacts of minimum wages on labor-market outcomes were heterogeneous across demographic groups.
The increase of the minimum wage reduced the employment of young, less-educated men (19 -24 years old), with an elasticity around -1.2. In contrast, minimum-wage hikes did not affect the employment of other demographic groups in a statistically significant way. An increase of the minimum wage did not significantly affect the hours worked of any of the demographic groups that we examined.
The estimated elasticity of the minimum wage on employment among less-educated young men, -1.2, is larger than the US estimates for teenagers in the literature, which ranges roughly from 0 to -0.3. This estimate, however, is not far from the estimate, -0.5, using all workers in the manufacturing sector in Japan by Okudaira et al. (2019). Furthermore, even in the US context, Baskaya and Rubinstein (2012) report that the short-run implicit elasticity of teenage employment to the minimum wage ranges between -0.75 and -1.20, using the plausibly exogenous minimum-wage increase for identification. Clemens and Wither (2019) also found the implied elasticity of low-wage workers' employment to the minimum wage to be -1, using the federal minimum-wage hike around 2008 in the middle of the Great Recession.
Both studies suggest that using the minimum-wage hike independent of local labor-market conditions for identification tends to render significant negative estimates. Furthermore, Brummund and Strain (2020)       Note: Based on the Basic Survey of Wage Structure, 2002-2017 waves are all pooled. Minimum-wage workers are defined as the workers whose hourly wage is below 1.05 × MW. The sample is restricted to full-time workers, because educational background is not available for part-time workers.  Regression coefficients and 95% confidence intervals ofδ y of the estimated model: where (W B/M W E) j2006 is the ratio of welfare benefit and minimum-wage earnings in prefecture j in 2006. The model is estimated with the microdata of individuals from the Labor Force Survey. The vector X ijt includes dummy variables for each age, the fraction of each demographic group (men 19-24, 25-59, 60-64 and women 19-24, 25-59, and 60-64) within the population, and the unemployment rate of college graduates of 25-59 years old. When the welfare benefit amount exceeds the minimum-wage earnings, (W B/M W E) j2006 is defined to be 1. The restrictions δ 2002 = δ 2007 = 0 are imposed to identify the prefecture-specific linear time trends ξ j . The 95% confidence intervals are calculated based on the standard errors robust against clustering within prefectures denoted by j. Note: Regression coefficients and 95% confidence intervals ofθ E y of the estimated model: where (W B/M W E) j2006 is the ratio of the welfare benefit and minimum-wage earnings in prefecture j in 2006. The model is estimated with the microdata of individuals from the Labor Force Survey. The vector X ijt includes dummy variables for each age, the fraction of each demographic group (men 19-24, 25-59, 60-64 and women 19-24, 25-59, and 60-64) within the population, and the unemployment rate of college graduates of 25-59 years old. When the welfare benefit amount exceeds the minimum-wage earnings, (W B/M W E) j2006 is defined to be 1. The restrictions θ E 2002 = θ E 2007 = 0 are imposed to identify the prefecturespecific linear time trends λ E j . The 95% confidence intervals are calculated based on the standard errors robust against clustering within prefectures, denoted by j. Note: Regression coefficients and 95% confidence intervals ofθ L y of the estimated model: where (W B/M W E) j2006 is the ratio of the welfare benefit and minimum-wage earnings in prefecture j in 2006. The model is estimated with the microdata of individuals from the Labor Force Survey. The vector X ijt includes dummy variables for each age, the fraction of each demographic group (men 19-24, 25-59, 60-64 and women 19-24, 25-59, and 60-64) within the population, and the unemployment rate of college graduates of 25-59 years old. When the welfare benefit amount exceeds the minimum-wage earnings, (W B/M W E) j2006 is defined to be 1. The restrictions θ L 2002 = θ L 2007 = 0 are imposed to identify the prefecturespecific linear time trends λ L j . The 95% confidence intervals are calculated based on the standard errors robust against clustering within prefectures, denoted by j. Note: Regression coefficients and 95% confidence intervals ofθ H y of the estimated model: where (W B/M W E) j2006 is the ratio of welfare benefit and MW earnings in prefecture j in 2006. The model is estimated with the microdata of individuals from the Labor Force Survey.
The vector X ijt includes dummy variables for each age, the fraction of each demographic group (men 19-24, 25-59, 60-64 and women 19-24, 25-59, and 60-64) within the population, and the unemployment rate of college graduates of 25-59 years old. When the welfare benefit amount exceeds the minimum-wage earnings, (W B/M W E) j2006 is defined to be 1. The restrictions θ H 2002 = θ H 2007 = 0 are imposed to identify the prefecture-specific linear time trends λ H j . The 95% confidence intervals are calculated based on the standard errors robust against clustering within prefectures, denoted by j.

A Minimum-wage determination in Japan and the revision of the Minimum Wage Act in 2007
This section introduces the policy process of how regional minimum wages, set for each of the 47 prefectures, are determined. The Ministry of Health, Labor and Welfare assembles the Central Minimum Wage Council, consisting of the representatives of labor, management, and public welfare, based on the tripartite principle. The Council divides all 47 prefectures into four regional groups, based primarily on regional income level, and provides a recommendation for the amount of the hourly rate of the minimum-wage hike, called a "Criterion (Meyasu)," for each of the four regional groups, based primarily on the average annual wage growth of workers in establishments with less than 30 workers, captured by the Fact-finding Survey on Minimum Wages (Saitei Chingin ni Kansuru Jittai Chosa). The Central Minimum Wage Council generally starts in June and determines the Criterion by the end of July. Upon receiving its Criterion, the Regional Minimum Wage Council, assembled in each of the 47 prefectures based on the tripartite principle, decides the amount of the minimum-wage hike for that prefecture in August, and the new minimum wage comes into effect from October 1. This two-step process using the Criteria has taken place every year since 1978, and local minimum wages have increased every year, with just a few exceptions. The partial revision of the Minimum Wage Act in 2007, which took effect on July 1, 2008, did not principally change the policy process, but the revision added a new requirement that must be considered when determining regional minimum wages. The new requirement is manifested in Article 9, Paragraph 3, which governs regional minimum wages: "When considering [the] living expenses [mentioned in the previous Paragraph of the Act], consistency with policies concerning public assistance benefits shall be considered, so that workers can lead a life with a minimum standard of health and culture" (authors' translation). This provision aims to resolve the so-called reversal phenomenon (gyakuten gensho), which refers to the fact that the total amount of benefits one can receive while being on public assistance has come to exceed the monthly income one can earn when working full-time on minimum wages. The reversal occurred in 12 prefectures as of fiscal year 2006, according to a letter submitted to the Minister of Health, Labor and Welfare from the Central Minimum Wage Commission in 2008. 5 In practice, the aim was to close the gap between the amount of welfare benefits and the earnings of full-time minimum-wage workers in the subsequent two years, and up to five years at maximum in prefectures where significant adverse impacts were expected, by raising minimum wages (Nakakubo, 2009).
Public assistance is a national income transfer program for the poor. Those who pass asset and income tests are eligible to receive the benefit; the tests are intrusive, such that the caseworker investigates all the applicant's assets and the family members' ability to support the welfare applicant. Because of this rigorous approval process, the government estimated that the take-up rate among those eligible is 32.1% as of 2007, based on Comprehensive Survey of Living Conditions. 6 The benefit amount is the difference between the standard 5 The 12 prefectures include Hokkaido, Aomori, Miyagi, Akita, Saitama, Chiba, Tokyo, Kanagawa, Kyoto, Osaka, Hyogo, and Hiroshima. The gap amount as of 2006 was 63 yen for Hokkaido, 20 yen for Aomori, 31 yen for Miyagi, 17 yen for Akita, 56 yen for Saitama, 35 yen for Chiba, 100 yen for Tokyo, 108 yen for Kanagawa, 47 yen for Kyoto, 53 yen for Osaka, 36 yen for Hyogo, and 37 yen for Hiroshima.
6 Estimation of the number of low-income households below the welfare standard amount by the public welfare amount (Seikatsu Hogo Gaku) and total income, including labor earnings and other social security transfers, such as pension benefits. The standard welfare amount depends on the number of family members, the earnings capacity of each member, and the local cost of living. As examples, Ministry of Health, Labor, and Welfare documents that the standard welfare amount for a 68-year-old single-person household is 80,820 yen (about US$800) in metropolitan districts, whereas it is 62,640 yen (about US$620) in rural districts. 7 The difference in welfare benefits largely reflects the difference in housing costs. The regional difference in the standard welfare amount became the source of heterogeneous growth of minimum wages when the revision of the Minimum Wage Act required the indexation of the minimum wage to the standard welfare amount.

B Data sets
This study uses the Labor Force Survey (LFS) to capture such labor-market outcomes as employment status and hours worked. The drawback of the LFS is the lack of an accurate measurement of the hourly wage rate. To supplement this drawback, we also use the Basic Survey on Wage Structure (BSWS). The LFS is a household survey that randomly selects about 40,000 households by using a geographically stratified sampling structure; we use data from 2002 to 2016 for our analysis, as the sampling structure was substantially revised from 2002. The survey was not conducted in the area severely affected by the natural disaster. This case includes Iwate, Miyagi, and Fukushima prefectures between March and August 2011 and Kumamoto prefecture during May and June 2016. Since the geographic stratum is the region, a collection of prefectures, no survey district may be sampled from a small prefecture. This case includes Wakayama prefecture for July 2009 and June 2014 and Tottori prefecture for July 2015.
The survey has a rotating sample structure; a selected household responds to the first 2 months of the surveys, followed by a 10-month break, and then responds to the last 2 months of the surveys. The surveys of different months can be matched using survey district ID, birth year, birth month, and sex. The fourth-month survey is called the special survey and records educational background, as well as annual income, in addition to the labor-force status recorded in other months. To obtain the educational background of individuals, we used only the households that could be matched to its fourth-month surveys. Given that the fourth month is available, 98% is matched for the third month, 86% is matched for the second month, and 85% is matched for the first month. The labor-force status of each household member selected for the survey is classified as belonging to one of the following nine categories: (1) Mainly working, (2) In school but also working, (3) Homemaker but also working, (4) Working but temporarily out of work, (5) Unemployed, (6) In full-time education, (7) Homemaker, (8) Other (the elderly, etc.), and (9) Unspecified. We define categories 1-3 as working and 4-8 as not working. The analysis sample is restricted mainly assistance section of the social and assistance bureau of the Ministry of Health, Labor and Welfare released on April 9th, 2010. https://www.mhlw.go.jp/stf/houdou/2r98520000005olm-img/2r98520000005oof.pdf (Accessed on November 9, 2020) 7 The document titled Public Assistance System by the Ministry of Health, Labor, and Welfare summarizes the program. https://www.mhlw.go.jp/english/topics/social_welfare/dl/outline_of_the_public_ assistance_system_20101004.pdf (Accessed on November 9, 2020).
to non-college graduates between the ages of 19 and 64, because the minimum wage is relevant to non-college-graduate workers.
A shortfall of the LFS is that it lacks an accurate measurement of the hourly wage rate. The only individual earnings information available in the survey is the range of annual income, which is asked for in the last month of the survey (the second month in the second year). From this annual earnings information and the hours worked in the last week of the previous month, we can construct hourly wage by imposing assumptions. The constructed hourly wage, however, is not precise enough to define those who are treated by the minimumwage hike and those who are not, as was done by Cengiz et al. (2019) and Clemens and Wither (2019). Thus to analyze the impact of the minimum wage on hourly wages, we rely on the BSWS instead. Also, we do not restrict the analysis sample to "low wage" workers in the employment analysis using the LFS, as Cengiz et al. (2019) did using the Current Population Survey in the US.
The BSWS is an ideal data set for analyzing the impact of the minimum wage on wages because of its accurate measurements of individual workers' monthly earnings and monthly hours worked, transcribed from payroll records, and the large sample size, in that it contains around 1.2 million workers annually. This annual survey chooses establishments based on stratified sampling by prefecture, industry, and size of the establishment; it focuses on private establishments with 5-9 employees that belong to firms that hire 9 or fewer employees, and all private and public corporations' establishments with 10 or more employees. According to the Economic Census conducted in 2014, private establishments with 5 or more employees hire 88% of total employees. The survey asks establishments to randomly sample its employees from payroll records and provide information on their employees' scheduled cash earnings and scheduled work hours in June. The survey contains information on about 1.2 million employees at approximately 45,000 establishments each year. Using the information from this survey, we calculate the hourly wage rate for our analysis as [(Scheduled cash earnings -Commuting allowance -Perfect attendance allowance -Family allowance) / Scheduled work hours], following the definition of hourly wage in the Minimum Wage Act. We used 2002-2017 surveys to construct the analysis sample, which includes all individuals between ages 19 and 64. The BSWS is designed to calculate the wages by the cell of prefecture × industry × establishment size with substantial precision. To keep the sampling error below a certain level, larger establishments, which are relatively rare and more heterogeneous in the population, are oversampled. To reflect this peculiar sampling structure of the survey, we use the sampling weight in the regression analysis to recover the population distribution throughout the analysis based on the BSWS. We also use the sampling weight so that the regression coefficients recover the population average treatment effects (Solon et al., 2015).