D B S －１８－０３

Minimum Wage Effects Across Heterogeneous Markets

Hiroko Okudaira
Miho Takizawa
Kenta Yamanouchi

November 2018

（Abstract）
Previous studies have reached little consensus on the employment effect of minimum
wage. This paper argues that local labor markets are heterogeneous, in that the impactof minimum wage is concentrated in specific markets. In particular, we estimate theextent of surplus between each plant’s value of marginal product of labor and wage
rate and examine whether the minimum wage impact varies across markets withdifferential surplus. We find that an increase in minimum wage significantly reduced
employment growth only in markets with a relatively small surplus. Markets withhigh surplus experienced no decline in employment growth.

DBS Discussion Paper Series supported by the OMRON Foundation.DBS

Minimum Wage Effects Across Heterogeneous Markets ∗Hiroko Okudaira†

Miho Takizawa‡

Kenta Yamanouchi§

click here for the latest version
November, 2018

Abstract
Previous studies have reached little consensus on the employment effect of minimum wage. This
paper argues that local labor markets are heterogeneous, in that the impact of minimum wage isconcentrated in specific markets. In particular, we estimate the extent of surplus between eachplant’s value of marginal product of labor and wage rate and examine whether the minimum wage
impact varies across markets with differential surplus. We find that an increase in minimum wage
significantly reduced employment growth only in markets with a relatively small surplus. Markets
with high surplus experienced no decline in employment growth.

Keywords: minimum wage; monopsonistic labor market; production function estimation.
JEL Classification:J21; J23: J31.

∗
The analysis using the Manufacturing Census was conducted following an agreement approved by the Japanese
Ministry of Economy, Trade and Industry. The analysis using the Wage Census was conducted following an agreement
approved by the Japanese Ministry of Health, Labour and Welfare. The authors are grateful to Richard Blundell,Mahmoud El-Gamal, Eric French, Daiji Kawaguchi, Toru Kitagawa, Kozo Kiyota, Hyejin Ku, Kotaro Tsuru, Attila
Lindner, Hiroaki Mori, David Neumark, Masao Ohgaki, Fumio Ohtake, Tatsushi Oka, Martin Weidner, Yasutora
Watanabe, and Jeff Wooldridge, as well as seminar participants at EALE, AASLE, the Japanese Economic Association
meeting, and Keio University for their helpful comments. Yuki Umeoka provided excellent research assistance. Okudairaacknowledges research grants from the Japan Society for the Promotion of Science (Grant-in-aid for Scientific Research
15K03434, JSPS Postdoctoral Fellowship for Research Abroad) and Okayama University. Takizawa acknowledges a
research grant from JSPS (Grant-in-aid for Scientific Research 17K03716). The authors acknowledge research grants
from Nomura Foundation and Murata Foundation.
†
Business School, Doshisha University, Imadegawa-dori, Karasuma Higashi-iru, Kamigyo-ku, Kyoto city, Kyoto
602-8580, Japan (hokudair@mai.doshisha.ac.jp).
‡
Department of Economics, Toyo University, 5-28-20, Hakusan, Bunkyo-ku, Tokyo, 112-8606, Japan (takizawa@toyo.jp).
§
Department of Economics, Keio University, 2-15-45, Mita, Minato-ku, Tokyo, 108-8345, Japan (ymdkntr40723331@yahoo.co.jp).

11

Introduction

The extent of market power in the labor market is an important topic in testing the employment
effect of minimum wage. In a simple competitive labor market model, employers have little control
over wages and reduce employment levels immediately when minimum wage rises. On the other
hand, in a monopsonistic labor market model, employers have some power to control wages andworkers are paid less than the value of the marginal product of labor. In the presence of such asurplus, the profit-seeking employers react to an increase in minimum wage differently from thosein a competitive labor market model, sometimes resulting in a rise in employment level ( Card andKrueger, 1994; Manning, 2003). However, despite the divergent consequences that the two models
predict, studies have paid little attention to the detection of the extent of market power in testing
the employment effect of minimum wage. In fact, there was a lack of convincing evidence to support
the existence of monopsony labor market (Kuhn, 2004).
Only recently, a growing number of studies presented the evidences of market power ( Staiger etal., 2010; Falch, 2010; Ransom and Sims, 2010; Dube et al., 2016; Benmelech et al., 2018; Azar etal., 2017, 2018). For instance, Benmelech et al. (2018) constructed the Herfindahl-Hirschman Index(HHI) from the Longitudinal Business Database to measure the labor market concentration, andfound that the employer concentration is negatively associated with local wages. Interestingly, Azaret al. (2018) highlighted large geographical variations in the employer concentration. Analyzing alarge-scale data set from Burning Glass Technologies—which collects job vacancy information fromapproximately 40,000 websites—they found that the less-populated commuting zones as well as thezones in the Great Plains tended to have lower employer concentrations. An important takeaway tothe study of minimum wage is that the local labor markets are heterogeneous, in that employers can
respond to an increase in minimum wage differently across local labor markets.
This paper directly estimates the labor market surplus by examining how far an employer is fromits competitive optimal decisions, and tests whether the employment effect of minimum wage differs
across regions depending on the extent of surplus. Specifically, we estimate the surplus or wage
markdown that employers would face in labor markets with any frictions, which is defined as thediscrepancy between the value of the marginal product of labor (VMPL) and the wage rate. The
original idea comes from Petrin and Sivadasan (2013), who examined the correlation between plants
surplus and the reform of firing restrictions in Chile. Taking a very similar approach, Dobbelaere et2al. (2015) and Dobbelaere and Mairesse (2013) proposed a way to test market imperfections bothin the labor and product markets. By applying the approach from the previous studies to Japanesemanufacturing census data from 2001 to 2014, we first estimate the production functions and obtain
estimates for the elasticities of factor inputs to calculate the surplus in the labor market. We thenuse the estimated extent of the surplus to examine whether the employment effect of minimum wage
differs according to the extent of frictions faced by employers in the local labor market. In our main
specification, we follow the framework of Meer and West (2016) and focus on employment growthrather than employment level, to account for the possibility that job destruction occurs gradually
over time.
Our identification of the minimum wage effect relies on a quasi-natural experiment where a series
of Japanese government policies substantially increased regional minimum wages over a decade.
The first event took place in 2007, when the Minimum Wage Act was amended to provide a legal
framework to increase regional minimum wages to or above the amount of welfare benefits defined ineach region. Importantly, those regions exposed to this shock were those in urban areas or with cold
weather, and not necessarily the regions that shared specific economic trends. Moreover, because acentral policy such as this had much more influence on the determination of regional minimum wages
than local authorities used to, it alleviates our concern that preexisting local employment trends may
confound the results. The government’s initiatives on minimum wage have continued in the following
decade due to Prime Minister Abe’s wage-boosting policy, which provides us with an opportunity to
exploit minimum wage variations that are less likely to reflect local economic trends over a relatively
long time period. We test the exogeneity of these events by adopting the suggestion of Meer andWest (2016), and indeed found that preexisting local trends had no predictive power.
Consistent with a standard competitive labor market model, our main analysis revealed thatplants significantly reduced employment growth in response to increases in minimum wage. However,
the estimated negative impact masks the heterogeneity in plants’ behavioral response: an increase inminimum wage affected plants in our sample in noticeably different ways, depending on the surplus
that plants face. We found that in response to an increase in minimum wage, plants that initiallyexperienced a large surplus did not significantly reduce their employment growth. While our main
data does not contain wages and hours of work for individual employees, the prediction from anothersource of administrative wage records confirms that the effects of minimum wage are concentrated3

in plants with a larger proportion of minimum wage workers. Although the lack of individual hourly
wage information prevents us from obtaining precise estimates, the results found in this paper largely
support the view that the local labor markets are heterogeneous and plants respond to the minimum
wage shock, depending on the extent of frictions they face in the labor market.
Our method differs from those employed in the previous literature in an important way. The sizeof the surplus or wage markdown allows us to infer whether a plant behaves as a monopsonist in
the local labor market. Previous studies have mostly identified the market power of monopsonistic
firms by estimating labor supply elasticity in the short run (Staiger et al., 2010; Falch, 2010; Dubeet al., 2018), by estimating the elasticity of the separation rate with respect to wages in the long run(Ransom and Oaxaca, 2010; Ransom and Sims, 2010; Hirsch et al., 2010; Manning, 2003), and more
recently by calculating HHI (Benmelech et al., 2018; Azar et al., 2017, 2018). We depart from theliterature by directly estimating the extent of exploitation or surplus each plant faces. Importantly,
our estimates measure an important aspect of labor market friction. Our estimates for the surplus
are negatively associated with the number of rival plants in the same prefecture and industry.
This paper also contributes to the literature by adding another mechanism through which themixed employment effects of minimum wage may be observed. 1 Previous studies have already analyzed how firms could otherwise respond to the minimum wage shock. Draca et al. (2011) examined
the impact of minimum wage on firm profitability using a plant-level data set from the UK, andfound no statistically significant behavioral response by firms. Instead, firms significantly reduced
their profits to cover the increases in the total wage bill. 2 Horton (2017) ran field experiments in the
online labor market to find that the implementation of a minimum wage reduced the hours worked,
half of which was explained by increases in worker productivity, indicating labor-labor substitution.
Aaronson et al. (2018) employed the contiguous-county comparison approach in Dube et al. (2010)
to analyze the restaurant industry in the US and found evidence consistent with the model where an
increased minimum wage induces the exit of labor-intensive restaurants and entry of capital-intensive
1
Influential case studies by Card and Krueger (1994, 2000) in New Jersey and Pennsylvania found no disemployment
effects, while Neumark and Wascher (1992) found significantly negative employment effects of an increase in minimum
wage among teenagers in the state-level data set. Dube et al. (2010) constructed a data set containing all contiguousborder-county pairs in the US to generalize a case study by Card and Krueger (1994) and showed that an increase inminimum wage has a significantly positive earnings effect but no significant employment effect. Neumark et al. (2014)
criticized Dube et al. (2010)’s approach by showing that they failed to include sufficient identification variations andtest the need to control for local trends. Allegretto et al. (2018) argued against Neumark et al. (2014) by adopting a
synthetic control approach.
2
In a similar strand of literature, Bell and Machin (2015) found that an unexpected announcement to raise theminimum wage in the UK significantly reduced the stock market values of firms hiring low-wage workers.

4

restaurants. Harasztosi and Lindner (2017) exploited a sharp minimum wage hike in Hungary to report that firms did not reduce their profits but increased product prices and substituted labor withcapital in response to the hike. Interestingly, they also found a heterogeneity in firms’ responses that
reductions in the level of employment are limited to firms in tradable sectors, where it is more difficult
to raise product prices. Despite the numerous debates over the ambiguous evidence, there is little
investigation on the potentially heterogeneous effect of minimum wage across local markets. This
paper directly estimates the surplus that employers face in local labor markets and finds that theemployment effect of minimum wage differs depending on the extent of frictions faced by employers
in local labor markets. Thus, aggregating the employment effects across local labor markets can bemisleading to the extent that each employer’s market power differs across markets.
The remainder of the paper is organized as follows. Section 2 introduces the theoretical frameworkused to measure the extent of labor market surplus and summarizes the institutional background.
Section 3 describes the data and identification strategies. Section 4 presents the results along withsome robustness tests. Section 5 concludes.

2

Background

2.1

Measuring Surplus across Labor Markets

Although numerous studies have implied that the employment effects of minimum wage depend on
a firm’s ability to pass costs through to product prices (Harasztosi and Lindner, 2017), job-to-job
turnover rates (Giuliano, 2013; Dube et al., 2016), and the degree of labor market monopsony (Cardand Krueger, 1994), the majority of previous studies have treated labor markets as uniform withineach nation. This paper measures the labor market competitiveness or frictions and examines whether
this presumption is plausible.
To measure frictions in labor markets, we employ an approach proposed in previous studies ( Petrin
and Sivadasan, 2013; Dobbelaere and Mairesse, 2013; Dobbelaere et al., 2015; Lu et al., 2017), whichcalculates market competitiveness from production function estimates. The idea is to estimate howeach plant deviates from its cost minimization behavior. In particular, A plant i at time period t has
the following cost function:

5

T C (Kit , Lit , Mit ) = CK (Kit ) + PM Mit + W (Lit ) Lit ,(1)

where Kit , Lit , and Mit denote capital, labor, and intermediate input, respectively. We assume
perfect competition for intermediate input, and so the price of intermediate input, PM , is constantwithin markets. For the labor markets, we assume the employer has monopsony power and faces anupward-sloping labor supply curve. The wage rate, W (Lit ), is therefore an increasing function of
employment (inverse labor supply curve). CK (Kit ) is the capital cost and the functional form is not
imposed.
The plants choose the amounts of intermediate input and labor to minimize their production
ˉ The first-order condition forcost given a certain amount of production, Qit (Kit , Lit , Mit ) = Q.
intermediate input is derived as follows:
PM = λit

∂Qit
,
∂Mit

(2)

where λit is the Lagrange multiplier and indicates marginal cost. Transforming the above condition,∂Qit /Qit, is derived as
output elasticity with respect to the intermediate input, εMit ≡ ∂M
it /MitεMit =PM Mit.
λit Qit(3)

We define markup as the ratio of the output price, Pit , to marginal cost. Using the above
calculation, the markup can be expressed as the ratio of the output elasticity to the cost share ofMit:intermediate input, αMit ≡ PPMit Q
it

μit ≡

Pit
εMit
=
.
λit
αMit

(4)

The condition of cost minimization for labor input is similarly derived as follows:

Wit



1
1+ L
εit



= λit

∂Qit
,
∂Lit

(5)

∂Lit /Lit
where εLit ≡ ∂Wit /Wit is the wage elasticity of the labor supply. To follow Lu et al. (2017), we measure6the labor market competitiveness, or surplus, by ηit ≡Wit∂Q
λi t ∂L itit

εL= εL it+1 . Under a perfectly competitiveitmarket, ηit = 1. In this case, the wage rate is equalized to the marginal cost of labor. Under amonopsonistic market, on the other hand, the surplus term is strictly less than one ( ηit < 1) andplants can lower the wage rate by reducing labor demand. Using the expression in equation (3), thesurplus is written as follows:ηit =αLit εMit,
αMit εLit(6)∂Qit /Qit
it Litwhere αLit ≡ W
Pit Qit is the cost share of labor input and εLit ≡ ∂Lit /Lit is the output elasticity oflabor input. We use ηit to measure the competitiveness of the local labor market that each plant
faces. The calculation of ηit is straightforward, since we can directly calculate cost shares from ourdata and estimate output elasticities from production function estimations.

2.2

Minimum Wage in Japan

Japanese minimum wage is determined mainly at the regional level. Japan consists of 47 prefectures,
each of which sets its own regional minimum wage and considers a revision annually. It has a wide
and almost complete coverage of workers, with only a limited number of exceptions. 3 In addition
to the regional minimum wage, local labor bureaus also allow a small increment in some industries,
although the number of workers covered by these industry minimums is usually small. We focus on
the variations in regional minimum wages to identify the heterogeneous responses to the minimum
wage increases.
Key to the analyses carried out in this paper is the fact that regional minimum wages have beenraised substantially after 2007. One main reason for this rapid increase is an institutional change inwage policy. It was argued in the early 2000s that welfare recipients in some regions receive higher
benefits than workers who earn minimum wage, leading to an amendment to the Minimum Wage Act
in 2007. The new Minimum Wage Act stipulates that regional minimum wages are to be consistent
with the amount of welfare benefits (Art. 9, Part 3), and legally validates a further increase inminimum wage in regions with relatively high initial benefits. The Japanese government also took
the initiative to continuously raise the minimum wage due to their increasing interest in boosting
3

Exceptions are granted for those workers with physical or mental disabilities and those on probation or basic
training, where permitted by the local labor bureau.

7

wage standards.4
The continuous increases in minimum wage has substantially raised the proportion of workers
affected by it. Figure 1 graphs the overall trend of regional minimum wages in the past decades.
The blue line is the Kaitz index, which represents changes in the average regional minimum wage
against the average market wage. The red line is the proportion of minimum wage workers for aplant with the median proportion of such workers in each year, such proportion being defined as the
proportion of workers whose hourly wage is less than 120% of the regional minimum wage, which was
to be revised in the following months. The data comes from administrative wage records: the Basic
Survey on Wage Structure (BSWS). The two graphs suggest that regional minimum wages have risen
continuously, while a median plant would have faced a spike in the proportion of minimum wage
workers after the amendment to the Minimum Wage Act in 2007. The proportion has risen sharply
from almost zero before 2007 to more than 6% in 2015; thus, an increasing number of plants havebeen exposed to the minimum wage shock in the last several years.
The sharp and continuous increases in minimum wage have raised the proportion of those whowork at minimum wage disproportionately in specific groups of workers and plants. Appendix Figures
1 and 2 graph the proportions of minimum wage workers within certain groups, using data from the
BSWS. minimum wage worker is defined here as a worker whose hourly wage rate is no more than theminimum wage rate that will be effective in the following autumn. To summarize the main points, theproportion of those who work for minimum wage has increased, especially among (1) female workers,(2) young and old workers (age < 20 or age > 60), and (3) workers in medium- or small-sized plants.
The most pronounced change can be found in teenage workers: nearly 20% of them were working
for minimum wage in 2015, which is four times the number in 2005. The proportion also more thandoubled among small-sized plants. 5
The series of policies after 2007 has two important features to our identification strategy. First,
those regions that were exposed to the 2007 amendment shock are unlikely to share specific local
economic trends. The 2007 amendment required regions with initially high welfare benefits to increase
their regional minimum wage to or above the level of their regional benefits. Appendix Figure 3
presents the proportion of minimum wage workers by the extent of exposure to the amendment
shock, where exposed prefectures are defined as those prefectures that initially had benefit levels
4

Examples include annual requests made by Prime Minister Abe to the Council on Fiscal and Economic Policy.
This is in sharp contrast with the modest increases observed among small-sized employers between 1982 and 2002
in an administrative household survey (Kawaguchi and Mori, 2009).
58

lower than minimum wage earnings and that therefore have been exposed to a relatively intense
increase in minimum wage after the 2007 revision of the Minimum Wage Act. Importantly, these
exposed regions are located in both urban (e.g., Tokyo and Osaka) and rural areas (e.g., Hokkaido
and Akita). The welfare benefits were initially high in urban regions because of their relatively highliving costs. Regions with cold weather have also had relatively high benefits because of their highheating costs. Thus, local economic conditions are unlikely to be the primary factor that explains
this differential shock. These variations are part of the identification variation we use to estimate
the impact of minimum wage in this paper.
Second, the central government has taken significant initiative in raising the target amount ofregional minimum wages, attenuating our concern on local economic conditions which can potentiallyconfound with our identification variation. Similar to other countries, local authorities take local
market conditions into account when revising the regional minimum wages by examining local market
statistics.6 However, after the 2007 amendment, the government set a much higher target level ofregional minimum wages before the local authorities made any adjustments, which limits the local
authority’s flexibility to control the absolute level of the minimum wage.
We consider that the 2007 amendment initiated sizable and exogenous increases in those affectedby the minimum wage and exploit this variation to identify the employment effect of the minimum
wage. However, one potential threat to this strategy is the possibility that the changes in minimum
wage still reflects pre-existing local employment trends. Although the 2007 amendment and a subsequent wage-boosting policy had a significant influence on the increases in minimum wage (as seen in
Figure 1), it is still possible for local authorities to make slight adjustments based on their review.
Thus, in order to credibly identify the impact of minimum wage, we need to ensure that the minimum
wage changes after 2007 did not arise from preexisting local employment trends. This paper follows
the estimation framework suggested by Meer and West (2016) to directly test this point. In particular, we examine whether future minimum wages predict current employment changes by focusing
on the post-amendment period during which the national policy was considered to have had a large
and continuous influence in determining the increases in minimum wage.
6
The revision process involves two steps. In the first step, the Central Minimum Wages Council proposes a target
amount to which minimum wages are to be raised, after investigating overall market conditions such as prices andmarket wages. In the second step, the Regional Minimum Wages Council of each prefecture determines how much toraise the minimum wage by taking into account the target amount proposed by the Central Council as well as local
labor market conditions and the standard of living in that region. The revisions take place in October or November
every year.

93

Identification Strategy

3.1

Main Data

The main analyses draw on the plant-level administrative data set from the Census of Manufacture,
which is conducted every year by the Japanese Ministry of Economy, Trade and Industry. 7 The
Census of Manufacture covers nearly an entire population of plants in the manufacturing sector
in Japan. It contains detailed information on factor inputs and produced outputs at each plant.
Information on product prices and quantities is also available for some of the plants. We focus
on annual files that cover all plants with 30 or more employees (Kou Hyou).8 Panel A of Table 1
presents summary statistics of this data set. Appendix I provides the details on variable constructions
necessary to estimate production functions. Production functions are estimated with observations
from 2001 to 2014 (see section 3.2). The impacts of minimum wage are estimated with observations
from 2008 to 2014, so as to avoid including endogenous variations of minimum wage prior to the 2007
amendment to the Minimum Wage Act (see section 3.4).

3.2

Estimating the Labor Market Surplus

We measure the labor market surplus using the method explained in section 2.1. To this end, we
first estimate the production function to calculate the output elasticities of intermediate input andlabor. We posit a translog production function defined as follows: 9
ln Qit = βK ln Kit + βL ln Lit + βM ln Mit + βKK (ln Kit )2 + βLL (ln Lit )2 + βM M (ln Mit )2+βKL ln Kit ln Lit + βKM ln Kit ln Mit + βLM ln Lit ln Mit + uit .

(7)

OLS estimates are not consistent because the inputs are positively correlated with unobserved
productivity, E (uit ln Xit ) 6= 0, where Xit ∈ {Kit , Lit , Mit }. We therefore follow the method ofBlundell and Bond (1998, 2000), which proposes using the system GMM to estimate the production
7

The census information is available online in English through the ministrys web page:
http://www.meti.go.jp/english/statistics/tyo/kougyo/index.html
8
The survey also has other types of annual files that contain information on all plants with 29 or fewer employees(Otsu Hyou). Since some of these files lack information on fixed assets, which is necessary to estimate production
functions, we decided not to use these files in this paper.
9
We consider potential substitutions among input factors seriously and do not estimate Cobb-Douglas production
functions here.

10

function.10 . In this method, the unobserved productivity is decomposed into three terms:
uit = δi + ωit + mit ,(8)

where δi denotes average productivity of plant i and is captured by plant fixed effects. ωit denotes
a productivity shock unobserved by the econometrician. The shock is observed by the managers
before determining inputs. This term is therefore the main source of endogeneity. mit denotes ameasurement error or a productivity shock after the amounts of inputs are determined. The average
productivity can be correlated with the levels of inputs but must be independent from the changes
in the inputs, E (δi | Δ ln Xit ) = 0 for t ≥ 2. The measurement error can be correlated with thecontemporaneous levels of inputs, but must be independent from the inputs in the previous periods,
E (mit | ln Xit−s ) = 0 for s ≥ 1.
The dynamic process of the productivity shock is specified asωit = ρωit−1 + ξit ,(9)where ρ is a parameter of the productivity process and ξit is an innovation term. ξit is the deviationfrom the expected productivity shock; it is therefore independent from all of the inputs in the previous
periods, E (ξit | ln Xit−s ) = 0 for s ≥ 1.
Substituting the process into the production function, the following expression is derived asln Qit =XhX+

βX ln Xit − ρβXsj ln Xit−1 + βXX (ln Xit )2 − ρβXX (ln Xit−1 )2

Xh

X,X 0

0

0

βXX 0 ln Xit ln Xit − ρβXX 0 ln Xit−1 ln Xit−1+ρ ln Qit−1 + (1 − ρ) δi + ξit + mit − ρmit−1 .

i

i

(10)

To obtain parameter estimates in this model, we first estimate a vector of parameters γ in thefollowing estimating equation:

10

The translog production function is estimated by the system GMM in Söderbom and Teal (2004) and Lee et al.
(2013).

11

ln Qit =

Xh
X

+

0

0

γX ln Xit + γX ln Xit−1 γXX (ln Xit )2 + γXX (ln Xit−1 )2

Xh

X,X

0

i

i
0
0
0
γXX 0 ln Xit ln Xit + γXX 0 ln Xit−1 ln Xit−1 + γQ ln Qit−1 + di + v it .

(11)

The moment conditions for the first-differenced equations are written as







E 


 





ln Qit−sln Xit−s(ln Xit−s )20ln Xit−s ln Xit−s









 Δv it  = 0, for s ≥ 3.





 

On the other hand, the moment conditions for the levels equations are written as







E 






Δ ln Qit−2
Δ ln Xit−2
Δ (ln Xit−2 )2
0Δ ln Xit−2 ln Xit−2











 (di + v it ) = 0.








Using consistent estimates of the unrestricted parameters and the variance-covariance matrix,0

we impose the restrictions γX = −γX γQ by minimum distance to obtain the restricted parameter
vector.11 The production functions are estimated separately for each industry, on the assumptionthat plants in the same industry face the same technological parameters (β) across regions. Industrylevel estimations allow us to estimate parameters efficiently. We choose industry-level estimation, notindustry-prefecture-level estimation, as it allows us to avoid removing specific industries or prefecturesfrom our sample when their sample size is too small at the industry-prefecture level.
Using estimated parameters, we calculate the output elasticities for each input. In our calculation,
11

We use a Stata command, md ar1, written by Mans Soderbom. See the following website:
http://www.soderbom.net/Resources.htm. Hempell (2005) describes the procedure in detail.

12

we use the median values for the inputs in each industry-prefecture group:ˉ + β̂KL ln L
ˉ + β̂KM ln Mˉε̂K = β̂K + 2β̂KK ln K

(12)

ˉ + β̂KL ln K
ˉ + β̂LM ln Mˉε̂L = β̂L + 2β̂LL ln L

(13)

ˉ + β̂KM ln K
ˉ + β̂LM ln L,ˉε̂M = β̂M + 2β̂M M ln M

(14)ˉ shows the median value for input X. The median values are taken across plant-year
where X
observations from 2001 to 2014; however, as a robustness check, we also use median values from 2000
to 2007 to exclude a potential endogeneity issue between the market scheme and the minimum wage
in a later section. The median values are taken across industry-prefecture groups to account for thefact that plants in different prefectures face different production levels and therefore different output
elasticities.12 The cost shares are also aggregated into industry-prefecture groups by taking medianvalues.13 Finally, the markup and the labor market surplus are measured by taking the ratios ofthese elasticities and cost shares. We drop the observations in the markets where either labor orintermediate elasticity is negative. To deal with extreme values, the observations in markets withthe top 5% of surplus, η, are also dropped.
Although studies have developed various ways to estimate production functions (Olley and Pakes,
1996; Levinsohn and Petrin, 2003; Wooldridge, 2009; De Loecker and Goldberg, 2013; Gandhi et al.,2013; Ackerberg et al., 2015), we adopt the system GMM approach over the other procedures forthe following reasons. First, system GMM allows us to consistently estimate the parameters in
the presence of plant fixed effects, which we consider a realistic specification. We aim to obtainconsistent production function coefficients, rather than productivity estimates in this paper. Second,although we also estimate our production functions with Wooldridge (2009)’s widely adopted methodin our robustness section, it yields negative or large estimates for output elasticities in a non-trivial
proportion of industry-prefecture groups. Due to these implausible values, the number of industryprefecture groups has to be reduced from 1,602 in system GMM to 799 in Wooldridge (2009)’s
method. Although the results of the two methods point to similar implications, we adopt system
12

Another reason is that it allows us to measure regional variations in labor market surpluses, which can arise fromgeographical proximity to rivals.
13
The labor cost share is obtained by dividing the total wage bill by total revenue. The total wage bill includes
salaries, bonuses, and severance payments. The labor cost share thus includes a part of the adjustment cost; however,adjustment costs can arise from expected costs of litigation and other non-pecuniary costs, which can be reflected in
the estimated surplus.

13

GMM as a main framework so as not to disproportionately select specific industry-prefecture groups
into our final minimum wage estimation. 14
Table 2 presents summary statistics from production function estimations with this system GMM
method. The estimates take plausible values. A sum of the three input elasticities ranges aroundunity, suggesting constant returns to scale. Summary statistics for η̂ suggest that most of the industryprefecture groups face some surplus in their local labor market.
Importantly, our estimates of plants’ labor market surplus or wage markdown measure frictionsin the labor market. To intuitively understand this point, Table 3 tabulates the median and average
numbers of rival plants in the same prefecture-industry group by the estimated surplus. Similarly,
Figure 2 draws kernel estimates for distributions of the number of rival plants by η̂. Table 3 andFigure 2 imply that the estimated surplus η̂ tends to correlate positively with the number of rival
plants. In particular, plants with η̂ < 0.4 are likely to have smaller numbers of rivals. Appendix
Tables 1 and 2 provide industry- or region-level summary statistics. Roughly speaking, urban regions
such as Tokyo tend to have higher η̂, while the same proportions are lower in rural regions such as
Hokkaido. This is consistent with a monopsonistic labor market model where employers have control
over wages and enjoy some surplus. Although surplus in the labor market could arise from otherfactors such as the heterogeneous preference of workers and adjustment costs (Petrin and Sivadasan,
2013) and we by no means argue that the number of rival plants have a high predictive power, ourestimates suggest that geographical proximity is one source of friction workers face in local labormarkets.

3.3

Identifying Minimum-Wage Plants

The Census of Manufacture provides a broad set of operational information including product prices
at each plant, but unfortunately does not contain information on hours worked or wage rates forindividual workers, which is necessary to measure the extent of minimum wage shock at each plant.
To supplement our analysis, we use another administrative data source to compute the number of
14
Potential biases in production function estimation includes omitted price bias. As is often the case in previous
studies, we deflate the nominal revenues as well as input expenditures by the industry price index. If firms face adownward-sloping demand curve, a negative correlation might arise between firm-level price deviations and input price,
thereby biasing the output elasticity estimates downward. On the other hand, other estimation issues arise if we adjust
the revenues by the output price information. Estimation of a quantity-based production function without any quality
adjustment again leads to downward-biased parameter estimates as the product price reflects the product quality ( De
Loecker and Goldberg, 2013). Although this is a significant issue to be addressed in future research, we consider thisto be beyond the scope of our research, and follow a standard approach to adjust the revenue with industry priceinformation as has been done in previous studies (Petrin and Sivadasan, 2013, for example).

14

minimum wage workers each plant employs, in keeping with the spirit of Draca et al. (2011) andAaronson et al. (2012). In particular, we draw on worker files from the BSWS, which contains
information on individual employees’ hours of work, wages, and benefits, including overtime work
hours and payment at each plant. 15 The BSWS is conducted annually by the Japanese Ministryof Health, Labour and Welfare. 16 This survey contains two types of questionnaire, plant-panel(Jigyosho-hyo), and employee-panel (Kojin-hyo). The survey samples plants with 10 or more regular
employees and plants with five to nine employees in private sectors only. Employees are selectedby a uniform sampling method from the plants that were selected for this survey. 17 We use pooled
cross-sectional data from the BSWS to calculate the proportion of minimum wage workers, the total
wage bill per regular employee, plant size, etc. Observations are limited to those plants/workers inmanufacturing sectors.
To identify the extent of the minimum wage shock to each plant in the Census of Manufacture, wefirst calculate the proportion of minimum wage workers at each plant i at period t from the BSWS.
A worker is defined as a minimum wage worker if his or her hourly wage rate was within 120% of theminimum wage that would be effective in the following October or November. 18 We then estimate
the following simple linear model to identify the characteristics of manufacturing plants that hire
relatively large proportions of minimum wage workers:
Sit = δt + zit β 0 + it(15)

Covariates zit include polynomials of the plant size and annual wage bill per regular employee, andthe ratio of regular workers. We did not include prefecture and industry fixed effects and allowed
individual plant traits to predict the proportion. In so doing, we can avoid the result where thepredicted proportion mostly reflects prefecture or industry variations in minimum wage, leaving
sufficient minimum wage variations even after we limit the sample by the predicted initial proportions
15
Although it is possible to match worker-level information from the Wage Census with the Manufacturing Census
to construct an employer-employee data set, we chose not to do so for the following reasons. First, the Wage Census
oversamples large plants that are less likely to be affected by an increase in minimum wage. Second, the Wage Census
is not a population survey, and matches only 9% of the original sample in the Manufacturing Census ( Kawaguchi etal., 2007).
16
The BSWS information is available in English through the ministry web page (accessed January 19, 2018):
http://www.mhlw.go.jp/english/database/db-slms/dl/slms-04.pdf.
17
In the most recent survey (BSWS2016), 78,095 establishments extracted from the population of 1,429,579 establishments based on prefecture, industry, and size . Responses were received from 57,657 establishments.
18
We chose 120% so as to accommodate the fact that the industry minimum wage could take a value more than 10%
higher than the regional minimum wage.

15

of minimum wage workers. The model is estimated with BSWS observations in manufacturing sectors
from 2008 to 2014. Finally, we compute the predicted proportion of low-wage workers at each plantin the Census of Manufacture, using a common set of covariates zit and the estimated parameters.
Panels B and C of Table 1 present summary statistics for the BSWS and the Census of Manufacturein the corresponding period. A comparison of the two panels suggests that the Census of Manufacture
is comparable to the BSWS in terms of the annual wage bill and ratio of regular workers, although
the BSWS samples slightly larger plants than Census of Manufacture.
Appendix Table 3 provides the estimation results of this model. The estimated models have highexplanatory powers. Adjusted R-squared values range above 0.6. A comparison of columns (1) and(2) suggests that the average annual wage bill per worker and its polynomials alone have sufficiently
high explanatory power. This is consistent with an approach in Draca et al. (2011), where they
defined a treatment status by establishing the average wage to measure the impact of introducing anational minimum wage in the UK. Figure 3 plots fitted values from column (1) of Appendix Table 3
using the BSWS. Predicted proportions of minimum wage workers become increasingly larger when
the annual wage bill per worker at the plant is less than 4 million JPY (≈ 36 thousand USD as ofJanuary 2018). Panel B in Table 1 presents the predicted proportions of minimum wage workers.
The computed proportions take reasonable values (mean = 0.15, p25 = 0.02, p50 = 0.08, p75 =0.23). These values are similar to those observed in the BSWS (mean = 0.17, p25 = 0, p50 = 0.04,
p75 = 0.23; see Panel C in Table 1). In the main analysis with the Census of Manufacture, we use
the computed proportions of minimum wage workers in 2008 to examine whether the impact of theminimum wage is intensified in plants with initially high proportions of minimum wage workers.

3.4

Testing the Impact of Minimum Wage

Similar to some previous studies, we exploit differential increases in the minimum wage across regions
to test its impact; however, studies have raised potential identification issues in using such a differencein-differences (DID) type of regional variation. First, the regional minimum wage could be confoundedby any preexisting trend specific to the local area. Dube et al. (2010) proposes stacking county pairs
across US state borders to control for common local trends among the pairs. A series of arguments
clarified both the importance and difficulty of finding valid counterfactuals to control for the local
preexisting trends (Neumark et al., 2014; Allegretto et al., 2013). Second, despite the first point,

16

including region-specific time trends in a DID framework can be misleading if minimum wage affects
the growth, not the level, of employment (Meer and West, 2016). When the minimum wage isincreased, the adjustment to this new state may take some time and may not be smooth. For
instance, job destruction may occur gradually due to adjustment costs and a slow substitution forother input factors such as capital (Baker et al., 1999). Estimating the employment effect in a levelspecification will then be misleading, because the staggered treatment effect follows a continuous
trend-shaped pattern rather than a discontinuous jump. Controlling for region-specific linear trends
in such a level specification masks the true dynamic treatment effect since it cannot be identified
separately from the local linear trend (Meer and West, 2016).19
One way to avoid such a misspecification is to check whether we ever need to control for regionspecific linear trends in the first place. The local linear trends have been controlled in previous studies
since the preexisting employment trends may predict the current minimum wage Dube et al. (2010).
We follow a suggestion in Meer and West (2016) and estimate the impact of minimum wage on
employment growth and examine whether there are any preexisting local trends that could confoundthe changes in minimum wage. In particular, we estimate the following model of first-differenced
employment levels with leads and lags of log differences in the prefectural minimum wage:Δln(Eit ) =3X

γ s Δln(mwp,t−s ) + δt Ij + fp + Δxpt β + Δνit ,

(16)

s=−2

where ln(Eit ) is a logarithm of employment at plant i at year t. The employment here includes
both regular and non-regular workers. 20 The model controls for industry-specific (j) year effects,
prefecture-level (p) fixed effects, and some time-variant prefecture covariates. Prefecture control
variables (xpt ) include log-population and the proportion of people aged 15–65. If the minimum
wage change does not reflect any preexisting trends, the estimates for the lead terms of Δ ln(mw)should be insignificant and close to zero.
We argue that the above specification is appropriate especially for our case of Japan where we
19

Figures 1 and 3 in Meer and West (2016) provide a graphical representation of this idea by comparing two hypothetical jurisdictions which experienced slowdowns in employment growth due to an increase in the minimum wage at
different points in time. Wolfers (2006) first points out this weakness of analyzing the dynamic impact of policy shockin the level specification, for the case of unilateral divorce laws adoption in the US.
20
We do not divide regular and non-regular employment, because we do not have separate total wage bills for each of
the two groups; we therefore cannot estimate η separately. A main focus of this paper is to examine the labor market
heterogeneity in terms of overall workers.

17

observed exogenous and continuous increases in regional minimum wages after 2007. As discussed
in section 2.1, the regional minimum wage is determined based partially on the local authority’s
examinations of recent market statistics, and could thus reflect preexisting local market conditions.
However, after 2007, minimum wage revisions have largely been based on the amendment to the
Minimum Wage Act and the government’s involvement in boosting the wage floor, rather than on
the examination of the local authorities. Hara (2017) also uses a similar variation in minimum wages
to estimate its impact on worker training in Japan. To test the exogeneity of the post-amendment
variations in minimum wage, we estimate the above model with observations between 2008 to 2014
in the Census of Manufacture, during which the local authorities’ influence is considered to be less. 21
Indeed, our results show no significant estimates for lead terms for Δln(mw), validating our approach.
To reflect the extent that each plant is differently bound by minimum wage, we estimate the above
equation separately for plants with different exposures to the minimum wage shock ( Ŝi,t= 2008 > 0.1,
for instance). Similarly, we also examine the heterogeneity of the plants’ response to the shock acrossdifferent market regimes. In particular, we examine whether an increase in the minimum wage brings
about the same consequences on employment growth as in the competitive labor market, even whenη̂ is low.

4

Results

4.1

Test of Preexisting Trends

Table 4 shows the results of our tests of whether there are any preexisting trends in the changes inminimum wage after 2008. Specifically, Table 4 presents the estimation results for equation (16) withvarious combinations of leads and lags for Δln(mwp,t ). These specifications are similar to the first
three columns of Table 4 in Meer and West (2016), although we use plant-level observations froma Japanese manufacturing census, instead of state-level observations from the Business Dynamics
Statistics in the US. The results in Table 4 suggest that the elasticity of employment with respect
to minimum wage is about −0.497. The impact of the first lagged change in minimum wage remains
quite stable across specifications. The elasticity remains around −0.5 across specifications, implyingthat the negative impact found on the first lagged term is not driven by any preexisting employment
21

We limit our observations to those in and after 2008, not 2007, so that we can avoid including information from2006, given that lagged minimum wage has a high explanatory power in our preferred specification, as will be shown
later.

18

trend. In fact, the estimates of lead terms for minimum wage in columns (3) and (4) take insignificant
and small values. Thus, the current employment growth is not statistically associated with the future
growth of minimum wage. The changes in minimum wage are unlikely to reflect preexisting local
trends.
Although regional minimum wages have been raised substantially in the past decades, the resultsin Table 4 blur the plants that are actually exposed to the minimum wage shock. To confirm that
increases in minimum wage are indeed concentrated in plants with a higher proportion of low-wage
workers, we estimate the same models in Table 4, separated by the initial extent of the exposure. In
particular, we divide the sample by the predicted proportions of minimum wage workers as of 2008,
Ŝi,t=2008 , computed from administrative wage records, as was explained in section 3.3.
Table 5 shows the results. Columns (1) and (5) replicate the results from columns (4) and(5) in Table 4. Comparisons across columns confirm that increases in minimum wage indeed havestronger negative impacts on those plants with higher proportions of minimum wage workers. The
employment elasticity is −0.64 in plants with more than 5% of low-wage workers, −0.65 in plants withmore than 10% of low-wage workers, and −1.06 in plants with more than 20% of low-wage workers.
The monotonically increasing pattern is consistent with Figure 3 where the predicted proportions ofminimum wage workers become increasingly higher when plants average annual wage bills are lessthan 4 million JPY. Similar to the findings in Table 4, these results are robust against controls forleads and lags of the minimum wage changes. A comparison between the first and last four columns
indicates that the estimates for elasticity are mostly stable with or without the lead and lag terms
for minimum wage. Although the prediction of proportions of minimum wage workers prevents us
from obtaining precise estimates for the impact of minimum wage, the results in this table suggest
the plausibility of our predicted proportions in reflecting the extent of exposure to the shock. Since
the first lagged term, Δln(mwp,t−1 ), has the largest impact in terms of magnitude, we will focus on
the impact of this term in the remainder of this paper.
The estimated elasticities in Tables 4 and 5 are notably large, compared to those reported inprevious state-level studies in the US. Our results so far suggest that a 10% increase in minimum
wage leads to about a 6% decrease in plant employment if the share of minimum wage workers,
Ŝi,t=2008 , is higher than 10%. Unfortunately, the predicted proportion of minimum wage workers is
not a perfect measurement of the exposed shock. We also condition our estimates on the predicted19

share as of 2008 to allow sufficient within-plant variations in our estimations. Thus, it is possible thatthe plant’s actual proportion of minimum wage worker is much higher than the predicted proportions
indicate. As Figure 1 suggests, an increasing fraction of plants were affected by the minimum wage
after the 2007 amendment. It is also important to note that, since price levels have been relatively
stagnant in Japan, real minimum wage has increased, thereby restricting firms labor-demand decisions
quite severely. Kambayashi et al. (2013) exploited the similar significant bite of minimum wage ina deflationary period to study its impact on the wage inequality. A sharp and rapid increase inminimum wage at face value can have a severe effect in a long and continuous deflationary economy.

4.2

Minimum Wage Effects across Heterogeneous Markets

Production function estimation in section 3.2 revealed that the estimated extent of surplus or wage
markdown, η̂, measures important frictions in the labor market such as the one driven by geographicalproximity with rival plants. This section tests a prediction of a monopsonistic labor market model,
where plants do not reduce their employment level in response to increases in minimum wage.
Panel A of Table 6 estimates the impact of growth in minimum wage on employment growth,
separately by the level of the estimated surplus. The sample is limited to the plants located in themarket for which the surplus is estimated. Recall that η̂ represents the extent of wage markdown.
Plants face no surplus in a competitive labor market, thus, η̂ = 1. Column (1) replicates column (5)in Table 4. We do not add and lead and lagged terms for changes in minimum wage, because wehave obtained quite robust results in controlling for the leads and lags in previous tables, and also
because we prefer to maintain the powers of the test by keeping as many observations as possible
since sample sizes are reduced substantially in some specifications below. 22
The results in this panel are consistent with the presence of surplus. As we limit the sample
to those plants with smaller η̂, the estimates become insignificant and smaller in magnitude, andeven take positive values; increases in minimum wage do not significantly reduce employment growthwhen plants face a large extent of surplus or wage markdowns. This is in contrast to the significant
and negative impact of minimum wage in the baseline case in column (1). As standard competitive
labor market model suggests, plants in a perfectly competitive labor market do not have sufficientwedges before they immediately decrease the employment level in response to an increase in minimum
22

Although not shown in the paper, we also estimated the same sets of specifications with leads and lags of Δ ln(mwp,t ).
None of the lead terms were significant, and we thus did not observe any preexisting employment trend.

20

wage. Importantly, a plant deviates from the competitive model if it has some control over market
wages due to some frictions in the local labor market (Manning, 2003). The initial surplus between
the value of the marginal product of labor and the wage rate imposes less pressure on the plant to
reduce its employment level. A plant can even increase its profit by increasing its employment levelto expand the surplus. This is consistent with our results here since we observe that the magnitudeof the estimate monotonically increases as we restrict our sample to smaller η̂, although they are notstatistically significant.
On the other hand, plants can also deviate from the standard case if they face adjustment costsof labor. In their dynamic model, Bentolia and Bertola (1990) formalized the idea that, even in
a competitive setting, the value of the marginal product of labor deviates from the equilibrium
wage rate when firms face firing or hiring costs. In fact, Petrin and Sivadasan (2013) measures theextent of firing costs for manufacturers in Chile by estimating the wedge between the value of themarginal product of labor and the wage rate from production function estimations. Our estimates
seem consistent with the existence of firing costs: the negative estimates disappear only when η̂ issmaller than 0.4, but not when it is smaller than 1.
However, the results here are likely to reflect market frictions, rather than the adjustment costsof labor, for following reasons. First, when we construct η̂, we use the total wage bill which includes
severance payments. Thus, the surplus measured by η̂ excludes an important part of the adjustment
costs. Second, although the adjustment costs may still arise from expected cost of litigation andother non-pecuniary costs, the regional pattern of η̂ does not match with the potential differences insuch unobserved firing cost at each region. 23 Given that the extent of surplus is negatively associatedwith the number of rival plants in the local labor market (Figure 2 and Table 3), our results suggestthat the heterogeneous estimates have mostly arisen from heterogeneity in labor market frictions.
A key to valid identification in Table 6 is to have sufficient variations in minimum wage changes
by the extent of surplus. If variations in minimum wage are significantly smaller in regions or industries with smaller η̂, the insignificant estimates obtained in Table 6 may reflect small identification
variations, rather than large frictions in the labor market. We consider that this is not the case in
our estimates for the following two reasons. First, despite the fact that the standard error becomes
23

Firing costs can vary across regions in Japan due to differences in local court discretion ( Okudaira, 2018). However,
the observed regional difference in firing costs look different from the estimated surplus by prefecture in Appendix Table
2. In particular, the Osaka District and High Courts are known to have a more stringent interpretation of the firing
regulations than the courts in Tokyo (Okudaira, 2018), a pattern that does not coincide with the regional pattern of η̂
in Appendix Table 2.

21

larger as we limit the sample from columns (6) to (2), the estimates also get smaller in magnitude
or even positive, suggesting that our insignificant results are not driven merely by small sample size.
Second, despite a relatively small sample size, we do have sufficient actual variations in minimum
wages even for cases with smaller η̂. Figure 4, which shows histograms for the differences in the logarithm of regional minimum wages, confirms this point. Beige bars indicate the distribution when theestimated wage markdown is smaller: η̂ < 0.4. Similarly, red-lined bars indicate the distribution η̂.
While plants with η̂ ≤ 0.4 have slightly larger changes in minimum wage, the two histograms mostly
overlap. At the bottom of each panel in Table 6, we also show the % of minimum wage variation interms of the baseline case in column (1). The % of minimum wage variation is calculated by dividing
the standard deviation in Δln(mwp,t−1 ) in that sample by the same standard deviation in column(1). Although the standard deviation becomes slightly smaller as η̂ decreases, the minimum wage
variations have not been significantly reduced. This tendency is more prominent in specifications
which will be shown below. Thus, the insignificant estimates observed in Table 6 are unlikely to only
be driven by small identification variations. Rather, they suggest the fact that plants with small η̂
did not have to immediately reduce the growth rate of employment due to the surplus they face.
Panel B of Table 6 conducts the same estimations by limiting the observations with at least 10%of minimum wage workers, Ŝi,t=2008 > 0.1. We observe more intensified effects when plants had an
initially larger proportion of minimum wage workers. Again, the negative impact is observed only
when plants have little surplus or larger η̂. Plants facing some frictions in the labor market do notsignificantly reduce their employment growth. Similar to the results in Table 6, the estimates become
substantially smaller in magnitude, suggesting that the insignificant results are not only driven by
the smaller sample size. Although not shown here, similar patterns are observed when we limit
observations with different values of Ŝi,t=2008 . The previous empirical studies have focused on theaggregate employment effect of minimum wage and ignored the potential heterogeneity in local labormarkets faced by plants. The overall impact of the minimum wage often observed in the literaturemasks the heterogeneous response of plants operating in diverse labor markets.
Finally, Panel C of Table 6 conducts a placebo test to examine whether the results in Panels
A and B represent the actual impact of minimum wage. In particular, we limit our observations
to those plants with an initial computed proportion of minimum wage workers less than or equal
to zero: Ŝi,t=2008 ≤ 0. Since these plants did not have minimum wage workers in 2008, they were22much less likely to be exposed to the minimum wage shock after 2007. Indeed, none of our estimates
are significant in Panel C. Importantly, our estimates become smaller in all specifications except incolumn (2). Thus, Panel C reinforces the causal interpretation of the results in Panels A and B thatthe increases in minimum wage slow down the employment growth only in plants facing less surplus.

4.3

Robustness Tests

One important concern on the results in the previous section is the potential endogeneity in labormarket surplus. For instance, if the local labor market becomes competitive and η̂ becomes closer to 1,
the harsh competitive environment may induce firms to invest more in technologies that can substitutelabor inputs away from production, and at the same time improve the efficiency in the production
process in the long run. A reduction in production costs can expand the firm’s production. If this is
the case, it may invite further increases in minimum wage, since economic expansion often accelerates
upward revisions of the minimum wage. Because we construct our labor market parameter, η̂, fromproduction function estimates based on observations in 2001–2014, it is possible that our estimatesusing the level of η̂ in Table 6 disproportionately selects plants in specific prefecture-industry groups.
Furthermore, η̂ also includes the contemporaneous changes in labor input, Lit , since we use industryprefecture-level median values of input factors and cost shares to calculate the output elasticities foreach input (see section 3.2).
In order to address this endogeneity concern, Panels A and B in Table 7 conduct robustness
estimations using the information prior to our main sample period. In particular, panel A constructs
η̂ from the same production function estimates in Table 6 (i.e., system GMM estimations separately
for each industry, 2001–2014), but with median input values and median cost shares from the presample period (2001–2007) only. In Panel B, η̂ is constructed from production function estimatesfrom the pre-sample period only (i.e., system GMM estimations separately for each industry, 2001–
2007), and median input values and median cost shares are taken from observations in pre-sample
period, 2001–2007. Observations in the main minimum wage analyses are limited to those plants
with Ŝi,t=2008 > 0.1.
The results in Panels A and B show that the negative impacts of minimum wage are again
concentrated among those plants with η̂ closer to one. In both panels, the elasticities of employment
with respect to minimum wage take significant and negative values between −0.5 and −0.6 in columns

23

(5) and (6). On the other hand, the estimates for the smaller η̂ are smaller in magnitude and not
significant, except for cases in column (3) where the magnitude of the estimates are slightly larger inboth panels.
It should be noted that a non-trivial proportion of plants are dropped from these specifications dueto the lack of a parameter estimate for η. For instance, in Panel A, we drop plants in those industryprefecture groups where the output elasticities of input factors take unrealistic values such as negative.
In Panel B, those industry-prefecture groups with a relatively fewer plants are dropped from thesample due to the insufficient sample size in production function estimations. Moreover, while theseestimations can mitigate the endogeneity concerns on the surplus, the production function estimations
ignore technological advancements after the Lehman shock since they only use information from prior
to the event. If the market structure has been substantially changed over time, limiting the production
function estimations prior to the 2007 amendment can be misleading. Because of these limitations,
we consider our preferred estimates as those presented in Table 6. However, the estimation results
shown in Panels A and B in Table 7 still point to a similar direction as our previous estimations.
So far, we estimated η̂ using system GMM suggested by Blundell and Bond (2000). As explained
in section 3.2, we adopt system GMM since it provides consistent coefficient estimates in the presenceof plant fixed effects. However, in order to examine the flexibility of our framework over different
estimation procedures, we also estimate production functions by following Wooldridge (2009) to construct η̂. Wooldridge (2009) extends the two-step estimation framework in Levinsohn and Petrin(2003) to a two-equation system which provides more efficient estimators by allowing the error component to be correlated with current labor input but not the labor input at the previous period.
Similar to the previous case, we estimate production functions separately for each industry withobservations between 2001 to 2014. The median values are obtained from observations between 2001
to 2007. Panel C in Table 7 presents the estimation results. Although a pattern in the magnitude ofthe estimate is not as clear as previous cases, we again obtained significant and negative estimates
for a case with little surplus. Unfortunately, in many industry-prefecture groups, this procedure also
provides us with negative output elasticity values and we dropped these industry-prefecture groups
from our sample. Since our final sample size in Table 7 is disproportionately reduced, we consider
that our preferred estimates are those based on system GMM estimations, although the results with
Wooldridge (2009)’s method also point to similar implications.

24

5Conclusion

The overall evaluation of minimum wage depends on the extent to which firms bear its burden.
This paper sheds light on direct aspects of firms internal responses to increases in minimum wage,
so as to examine whether the local labor markets are heterogeneous, and whether the employment
effect of minimum wage differs across markets, depending on employers’ market power or frictions in
the labor market. Specifically, we estimate the surplus between the value of the marginal product oflabor and the wage rate from standard production function estimations. We then tested the minimum
wage impact on employment growth across the extent of surplus that plants enjoy in the local labormarkets.
By applying the estimation framework to a Japanese manufacturing census, we first observedthat plants significantly reduced their employment growth in response to increases in minimum wage.
However, the estimated negative impact masks the heterogeneity in plants’ behavioral response: anincrease in minimum wage affected plants in our sample in rather different ways, depending on thesurplus that plants face. We found that in response to an increase in minimum wage, plants that
initially experienced a large surplus did not significantly reduce their employment growth. Interestingly, albeit insignificant, the estimates become larger and even positive when plants have larger
surplus. While our main data does not contain the wages and hours of work for individual employees,
computation from another source of administrative wage records confirms that the minimum wage
effects are concentrated in plants with larger proportions of minimum wage workers. Although a lackof individual hourly wage information prevents us from obtaining precise estimates, the results foundin this paper largely support the view that the local labor market is diverse and plants respond tothe minimum wage shock depending on the extent of frictions they face in the labor market.

25

.08
.04

.06

.5

.02

.45

0

.4
1990

1995

2000

2005

2010

2015

Kaitz index ( = avg mw/avg wage), left axis
share of mw workers for a median plant, right axis
Source: Basic Surveys on Wage Structures (BSWS)

Figure 1: Kaitz Index and Proportion of Minimum Wage Workers for a Median Plant.
Note: Blue line indicates Kaitz index (left axis). Red line indicates a proportion of minimum wage workers for aplant with median value of the proportion in each year. The data comes from administrative wage records, Basic
Survey on Wage Structures (BSWS).

26

Table 1: Summary Statistics
N

Mean

Std. Dev.

P25

P50

P75

Panel A. Census of Manufactures (2001-14)
lnY
lnL
lnK
lnM
cost share (labor)
cost share (material)

635234635234605489617111630120631158

16.52
4.35
17.11
10.78
.24
.38

1.37
.8
1.78
1.89
.16
.23

15.61
3.74
16.05
9.76
.13
.21

16.35
4.14
17.04
10.8
.2
.38

17.27
4.75
18.12
11.91
.3
.55

Panel B. Census of Manufactures (2008-14)
prefecture share of those aged 15-64log(prefecture population)
computed proportion of MW workers ( Ŝit )annual wage bill per employee (10 4 JP Y )plant size
ratio of regular workers

301372301372301372301372301372301372

.62
14.97
.15
376.84127.56
.34

.02
.79
.18
156.87283.34
.24

.61
14.42
.02
265.58
42
.14

.62
14.86
.08
359.87
63
.27

.64
15.79
.23
464.31
117.5

Panel C. BSWS (2008-14, manufactures)proportion of MW workers (Sit )annual wage bill per employee (10 4 JP Y )plant size
ratio of regular workers

82509
82509
82509
82509

.17
361.18173.69.33.25
151.92495.13.26

0253.6513.13.04
340.9838.25.23447.41
126.48

Table 2: Production Function Estimates

ε̂L
ε̂M
ε̂K
ε̂L + ε̂M + ε̂K
η̂
μ̂

N
1602
1602
1602
1602
1602
1602

Mean
.45
.48
.11
1.03
.67
1.3

Std. Dev.
.23
.14
.13
.25
.35
.52

P25
.26
.4
.06
.87
.43
.97

P50
.4
.48
.12
.96
.6
1.22

P75
.59
.57
.19
1.18
.84
1.54

Note: Translog production functions are estimated separately for each industry group. The estimation procedure follows
System GMM. The estimated production function estimates are then used to calculate the parameters in this table byusing median values for other input variables within each prefecture-industry group (see section 3.2). The data comesfrom Census of Manufactures (METI).

27

Table 3: Number of Rival Plants
ηˆpj

< 0.1

< 0.2

< 0.3

< 0.4

< 0.5

< 0.6

< 0.7

< 0.8

< 0.9

<1

all

median
mean

0
6.8

7
20.6

6
13.9

7
16.8

9
23.5

10
24.14

11
24.3

11
24.4

11
24.1

11
23.9

9
20.9

Note: Figures present median or mean of number of rival plants within the same prefecture-industry group by theextent of wage markdown or surplus or η̂pj . The data comes from Census of Manufactures (METI).

0

.01

.02

.03

.04

Distribution of Number of Rival Plants in the Market

0

50
100
number of rival plants within an industry-prefecture cell (2007)
plants with eta < .2
plants with eta < .6
plants with eta < 1

150plants with eta < .4
plants with eta < .8
plants with eta >= 1

Figure 2: Number of Rival Plants within the Same Prefecture-Industry Group by ηˆpj .
Note: The figures show kernel estimates for the number of rival plants in the same prefecture-industry group. The data
comes from Census of Manufactures (METI).

28

Predicted shares of MW workers

0

Fitted values
.5
1

1.5

predictions from BSWS (sample period =2008-14)

0

200

400

600

800

1000

Average annual wage bill per worker (in 10000JPY)
Figure 3: Predicted Proportion of Minimum Wage Workers at Each Plant
Note: The figures show the fitted values from a simple regression model to predict a proportion of minimum wage
workers at each plant. The covariates include; polynomials of plant size and annual wage bill per regular employee,
and ratio of regular workers (column (1) in Appendix Table 1). See section 3.3 for details. The data comes fromadministrative wage records, Basic Survey on Wage Structures (BSWS).

29

Table 4: Test of Pre-existing Local Trends
(1)

(2)

(3)

(4)

-0.538***(0.132)0.107(0.123)0.0400(0.129)-0.125(0.172)-0.499***(0.185)0.0987(0.166)0.0295(0.155)-0.121(0.184)-0.512***(0.186)0.106(0.163)-0.0254(0.201)

0.0481(0.138)-0.119(0.171)-0.497**(0.191)
0.113(0.160)-0.0364(0.200)0.0398(0.131)

281,388281,388

281,014280,112Δln(mwp,t−3 )Δln(mwp,t−2 )Δln(mwp,t−1 )Δln(mwp,t )Δln(mwp,t+1 )Δln(mwp,t+2 )N(5)-0.518***(0.135)281,388

Note: Robust standard errors clustered at the prefecture level in parentheses. *** p <0.01, ** p<0.05, * p<0.1. Eachcolumn controls for industry-specific linear trends and prefecture control variables. Prefecture control variables ( xpt )include log-population and the share of those aged 15-65. The data comes from Census of Manufactures (METI).

30

31

280,1120.0481(0.138)-0.119(0.171)-0.497**(0.191)
0.113(0.160)-0.0364(0.200)0.0398(0.131)
151,091-0.136(0.153)-0.0514(0.184)-0.640**(0.239)0.131(0.200)-0.260(0.253)-0.0304(0.193)(2)
Ŝ > 0.05

110,844-0.293(0.199)0.000622(0.182)-0.646**(0.272)0.0885(0.229)-0.226(0.299)0.0353(0.267)(3)
Ŝ > 0.1

67,403-0.323(0.259)0.136(0.251)-1.057***(0.339)0.226(0.312)-0.277(0.319)-0.208(0.315)(4)
Ŝ > 0.2

281,388-0.518***(0.135)(5)
all

151,830-0.596***(0.178)(6)
Ŝ > 0.05

111,398-0.633***(0.225)(7)
Ŝ > 0.1

67,785-0.891***(0.278)(8)Ŝ > 0.2

of minimum wage workers at the plant in 2008. The data comes from Census of Manufactures (METI).

and prefecture control variables. Prefecture control variables (xpt )include log-population and the share aged 15-65. Ŝ stands for Ŝi,t=2008 > 0.1, or a predicted share

Note: Robust standard errors clustered at the prefecture level in parentheses. *** p <0.01, ** p<0.05, * p<0.1. Each column controls for industry-specific linear trendsN

Δln(mwp,t+2 )Δln(mwp,t+1 )Δln(mwpt )Δln(mwp,t−1 )Δln(mwp,t−2 )Δln(mwp,t−3 )

(1)
all

Table 5: Minimum Wage Effects by Predicted Shares of Minimum Wage Workers

Table 6: Minimum Wage Effects across Heterogeneous Labor Markets
Panel A. all plants
(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1Δln(mwp,t−1 )-0.518***(0.135)0.667(0.723)-0.126(0.409)-0.256**(0.118)-0.372***(0.130)-0.414***(0.127)N% of MW variation

281,388
100 (base)

6,966
87.6

34,491
92.9

120,173
94.0

173,34598.5

199,693
99.0

Panel B. plants with Ŝi,t=2008 > 0.1
(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1Δln(mwp,t−1 )-0.633***(0.225)0.0115(0.937)-0.0823(0.566)-0.497**(0.243)-0.571**(0.231)-0.556**(0.248)N% of MW variation

111,398
100 (base)

5,504
88.7

17,42395.3

44,936
94.4

61,272
98.2

70,272
98.5

Panel C. Plants with Ŝi,t=2008 ≤ 0 (placebo test)

Δln(mwp,t−1 )N% of MW variation

(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1-0.529(0.321)

2.173(2.240)-0.0209(1.046)

0.0576(0.417)-0.0731(0.417)-0.128(0.390)25,526100 (base)

49
147.4

2,662
87.3

12,241
94.8

17,473
98.5

19,89699.0

32

Note: Robust standard errors clustered at the prefecture level in parentheses. *** p <0.01, ** p<0.05, * p<0.1.
Each column controls for industry-specific linear trends and prefecture control variables. Prefecture control variables(xpt )include log-population and the share aged 15-65. The data comes from Census of Manufactures (METI). % of MW
variation is calculated by dividing standard deviation in Δln(mwp,t−1 ) in that sample by the same standard deviationin column (1) or all observations.

33

100
80
Density
40
60
20
0
0

.01

.02

.03

Differences in log(mw)
eta < 0.4

eta > = 0.4

Figure 4: Are There Sufficient Variations within Group?
Note: The histograms represent variations in Δln(mw) by η̂.

34

.04

Table 7: Robustness Against Alternative Parameter Constructions(plants with Ŝi,t=2008 > 0.1).
Panel A. Parameters constructed with median values in pre-sample period (2001-2007)
(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1Δln(mwp,t−1 )-0.657**(0.260)-0.136(0.802)-0.409(0.608)-0.298(0.282)-0.569**(0.232)-0.560**(0.247)N% of MW variation

77,563100 (base)

4,979
87.3

14,24896.5

42,623
95.5

60,61098.5

69,127
100.7

Panel B. Production functions estimated with pre-sample observations only (2001-2007)
(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1Δln(mwp,t−1 )-0.523**(0.250)-0.263(0.498)-0.429(0.387)-0.397(0.319)-0.536*(0.287)-0.608**(0.271)N% of MW variation

93,244100 (base)

15,02896.4

32,41494.0

42,504
95.5

52,47496.0

55,294
96.7

Panel C. Production functions estimated by (Wooldridge, 2009)’s method

Δln(mwp,t−1 )N% of MW variation

(1)
all

(2)
η̂ < 0.2(3)η̂ < 0.4(4)η̂ < 0.6(5)η̂ < 0.8(6)η̂ < 1-0.451*(0.227)1.598(1.393)-1.076(0.720)-0.777(0.653)-0.415(0.449)-0.810**(0.397)60,641100 (base)

2,265
94.0

8,670
95.8

12,293
99.3

20,27792.7

33,922103.3

Note: Robust standard errors clustered at the prefecture level in parentheses. *** p <0.01, ** p<0.05, * p<0.1. In
panel A, η̂ is constructed from the same production function estimates (System GMM, industry-level, 2001-2014) inTable 6, but with median input values & median cost shares from pre-sample period (2001-2007) only. See section 3.2
for the exact procedure to construct the market parameter using these median values. In panel B, η̂ is constructedfrom production function estimates with pre-sample period only (System GMM, industry-level, 2001-2007). Median
input values and median cost shares are taken from those from the pre-sample period, 2001-2007. In panel C, η̂ isconstructed from production function estimates with Wooldridge (2009)’s method (industry-level, 2001-2014). Median
input values and median cost shares are taken from observations from 2001-2007. Each column controls forindustry-specific linear trends and prefecture control variables. Prefecture control variables ( xpt )include
log-population and the share aged 15-65. The data comes from Census of Manufactures (METI). % of MW variation
is calculated by dividing standard deviation in Δln(mwp,t−1 ) in that sample by the same standard deviation incolumn (1) or all observations.

35

0

.05

.1

.15

.2

.25

Male Workers

2005

2010
age < 2040 <= age < 50

2015

20 <= age < 30
50 <= age < 60

30 <= age < 40
60 < age

0

.05

.1

.15

.2

.25

Female Workers

2005

2010
age < 2040 <= age < 50

2015

20 <= age < 30
50 <= age < 60

30 <= age < 40
60 < age

Appendix Figure 1: Shares of MW Workers (waget ≤ mwt+1 ) by Gender and Age Group

Note: Based on authors’ calculation from Basic Survey of Wage Structures (Japanese Ministry of Health, Labour andWelfare).

36

0

.02

.04

.06

.08

by Plant Size (Number of Employees)

2005

2010
size < 30
100 <= size < 10002015
30 <= size < 100
1000 >= size

Appendix Figure 2: Shares of MW Workers (waget ≤ mwt+1 ) by Plant Size

Note: Based on authors’ calculation from Basic Survey of Wage Structures (Japanese Ministry of Health, Labour and

.01

.02

.03

.04

.05

Welfare).

2005

2010
Exposed prefectures

2015
Other prefectures

Appendix Figure 3: Shares of MW Workers (waget ≤ mwt+1 ) by Extent of Exposed Shock

Note: Based on authors’ calculation from Basic Survey of Wage Structures (Japanese Ministry of Health, Labour andWelfare). Exposed prefectures are defined as those prefectures initially had relatively lower benefit level compared tominimum wage earnings, therefore, were exposed to intense increases in minimum wage after the revision of Minimum
Wage Act, which was approved in 2007. Specifically, exposed prefectures are those prefectures requested by Ministryof Health, Wealth, and Labour to increase minimum wage due to the relatively low benefit level in May 2007:
Hokkaido, Miyagi, Akita, Saitama, Chiba, Tokyo, Kanagawa, Kyoto, Osaka, Hyogo, and Hiroshima.

37

Appendix Table 1: Estimated η by Industry
livestock products
food and fisheriesfine grain millingorganic fertilizers feed
beverage
tobaccotextile goods
sawing lumbering wooden products
furniture equipment
coated paper pulp,paper and paperboard
pre press binging
furs leather and leather products
rubber products
chemical fertilizer
basic inorganic chemical products
basic organic chemical products
organic chemical products
final chemical products
medical and pharmaceutical products
glass and glass products
cement and cement products
ceramics and porcelain
other ceramic and clay products
pi giron crude steel
other iron and steel
refining non-ferrous metal smelting
non-ferrous metal products
metal products for building and construction
other metal products
general industrial machinery
special industrial machinery
other general machinery
equipment for office and service
heavy electrical machinery
electronics-applied equipment,electronic measuring instrument
semiconductor element, integrated circuit device
electronic components
other electrical equipment
motorcarautomotive parts automobile accessories
other transportation equipment
precision machine
plastic products
other manufactured products
Total 0.64

mean
0.35
0.17
1.03
0.36
0.69
0.04
0.64
0.43
0.62
0.77
0.67
0.39
1.34
0.89
0.46
0.01
0.74
0.64
0.69
0.44
1.48
0.86
1.45
0.55
0.59
1.45
1.42
0.97
0.52
0.83
0.58
0.5
0.76
0.26
0.65
1.12
0.94
0.9
1.24
0.44
1.13
0.65
0.44
1.3
0.45

p25
0.3
0.14
0.66
0.21
0.53
0.03
0.57
0.37
0.58
0.66
0.59
0.32
1.22
0.53
0.38
0
0.5
0.56
0.53
0.37
1.46
0.67
1.32
0.31
0.54
1.45
1.4
0.81
0.48
0.75
0.53
0.45
0.7
0.23
0.57
0.75
0.84
0.81
1.24
0.39
0.86
0.6
0.41
1.26
0.58

p50
0.36
0.16
1.05
0.28
0.65
0.03
0.64
0.43
0.62
0.75
0.69
0.37
1.42
0.8
0.42
0
0.67
0.66
0.66
0.4
1.51
0.8
1.56
0.59
0.59
1.45
1.47
0.91
0.5
0.82
0.58
0.5
0.71
0.25
0.61
1.18
0.89
0.88
1.31
0.44
1.06
0.68
0.43
1.3
.76

p75
.4
.19
1.35
.51
.84
.07
.74
.48
.64
.78
.75
.38
1.55
1.16
.52
.02
.9
.7
.71
.47
1.63
.97
1.59
.66
.63
1.45
1.51
1.01
.52
.88
.61
.54
.81
.28
.77
1.36
1.07
.95
1.38
.49
1.4
.69
.46
1.45

Note: This table summarises statistics from plant-level observations. Estimates are obtained from translog production
function estimations. The translog production functions are estimated separately for each industry group. The
estimation procedure follows System GMM. The estimated production function estimates are then used to calculate
ηi by using median values for other input variables within each prefecture-industry group (see section 3.2). The data
comes from Census of Manufactures (METI).

38

Appendix Table 2: Estimated η by Region
Hokkaido
Aomori
Iwate
Miyagi
Akita
Yamagata
Fukushima
Ibaragi
Tochigi
Gunma
Saitama
Chiba
Tokyo
Kanagawa
NiigataToyamaIshikawa
Fukui
Yamanashi
NaganoGifu
Shizuoka
Aichi
Mie
Shiga
Kyoto
Osaka
Hyogo
Nara
Wakayama
Tottori
Shimane
Okayama
Hiroshima
Yamaguchi
Tokushima
KagawaEhime
Kochi
Fukuoka
Saga
Nagasaki
Kumamoto
Ohita
MiyazakiKagoshima
Okinawa
Total

mean
.46
.51
.63
.62
.7
.63
.66
.61
.62
.55
.68
.6
.75
.67
.64
.81
.65
.73
.67
.64
.64
.64
.61
.63
.62
.7
.65
.67
.59
.58
.68
.69
.6
.59
.58
.68
.61
.63
.59
.61
.61
.58
.71
.62
.62
.51
.64
.6367661

p25
.14
.15
.41
.36
.52
.52
.45
.41
.44
.4
.46
.4
.68
.53
.48
.51
.51
.52
.46
.49
.46
.49
.39
.39
.43
.51
.49
.48
.4
.44
.42
.49
.45
.45
.32
.46
.33
.49
.31
.4
.33
.31
.43
.44
.46
.27
.41
.4467094

p50
.48
.38
.54
.52
.6
.57
.56
.47
.51
.49
.59
.51
.79
.6
.63
.61
.67
.74
.66
.6
.54
.5
.52
.54
.5
.67
.6
.56
.49
.54
.61
.71
.56
.55
.61
.59
.54
.62
.52
.61
.49
.63
.51
.59
.54
.51
.52
.5769003

p75
.64
.86
.78
.88
.89
.75
.83
.81
.79
.72
.75
.71
.79
.77
.81
1.07
.75
.74
.83
.77
.67
.78
.65
.75
.83
.82
.7
.77
.71
.68
.78
.78
.66
.65
.71
.89
.76
.74
.67
.69
.69
.76
1.22
.67
.66
.7
.74
.7643339

Note: This table summarises statistics from plant-level observations. Estimates are obtained from translog production
function estimations.The translog production functions are estimated separately for each industry group. The
estimation procedure follows System GMM. The estimated production function estimates are then used to calculate
ηi by using median values for other input variables within each prefecture-industry group (see section 3.2). The data
comes from Census of Manufactures (METI).

39

Appendix Table 3:
Predicting Proportions of minimum wage Workers with Administrative Wage Records(wagebill/worker)(wagebill/worker)2 /103
(wagebill/worker)3 /106
(wagebill/worker)4 /1011
plantsize/103
plantsize2 /106
plantsize3 /1011
plantsize4 /1013
Ratio of regular workers
ConstantN
Adjusted R-squared(1)
proportion(waget < 1.2mwt+1 )(2)
proportion(waget < 1.2mwt+1 )-0.00733***(0.000106)
0.0154***(0.000313)-0.0134***(0.000384)
0.399***(0.0166)-0.0514***(0.00286)
0.0240***(0.00186)-0.330***(0.0350)0.00133***(0.000184)
0.258***(0.00401)
1.201***(0.0132)-0.00887***(0.000111)
0.0181***(0.000349)-0.0154***(0.000445)
0.456***(0.0198)

82,5090.658

82,5090.652

1.557***(0.0122)

Note: Robust standard errors clustered at the prefecture level in parentheses. *** p <0.01, ** p<0.05, * p<0.1. Eachcolumn represents the estimates from a plant-level linear regression to predict a proportion of minimum wage workers
at each plant. wagebill/worker indicates average annual wage bill per worker. plantsize indicates a number of
employees at each plant. The data come from administrative wage records, Basic Survey on Wage Structures(BSWS). See section 3.3 for details.

40Appendix I.
Variable Construction for Production Function Estimation.
1. Gross Output
Gross Output is measured as the sum of shipments, revenues from repairing and fixing services, and revenues
from performing subcontracted work. Gross output is deflated by the output deflator taken from the Japan
Industrial Productivity (JIP) Database 2011 and converted to values in constant prices of 2000.

2. Intermediate Input
Intermediate Input is defined as the sum of raw materials, fuel, electricity and sub-contracting expenses forconsigned production used by the plant. Using the corporate goods price index (CGPI) published by Bank ofJapan, intermediate input is converted to values in constant prices of 2000.

3. Capital Input
Capital Input (Kpt ) is measured as real capital stock, defined as follows:
Kpt = BVpt ∗IN Kjt
,
IBVjt

(17)

where BVpt is the initial net book value of plant p, IN Kjt represents the initial net capital stock of thewhole industry in constant 2000 price, and IBVjt is the initial net book value of the whole industry. That is,
IN KjtIBVjt

stands for the ratio of real value in constant 2000 price to book value of capital stock of the wholeindustry in year t. IN Kjt is calculated as follows. First, as a benchmark, we took the data on the book valueof tangible fixed assets in 1975 from the Financial Statements Statistics of Corporations published by
Ministry of Finance. We then converted the book value of year 1975 into the real value in constant 2000
prices using the investment deflator provided in the JIP 2011. Second, the net capital stock of industry j,
IN Kjt , for succeeding years is calculated using the perpetual inventory method.
IN Kjt = IN Kjt−1 (1 − δjt ) + Ijt ,(18)

Ijt stands for the real investment in industry j and in year t.We used the investment deflator in the JIP
2011. The sectoral depreciation rate (δjt ) used is taken from the JIP 2011.

4. Labor Input
For labor input, we use the total number of workers at each plants.
• Blue collars and white collars, full-time and part-time. We could estimate production functions
separtely for these groups as data is available in limited years. Should we ignore the differential skill
levels across worker group to avoid complexities such as substitution, etc?
• We ignore intensive margin adjustments (labour hour) to accommodate the literature that focuses on
the overall employment effect.

5. Value Added
Value Added is defined as the difference between gross output and intermediate input.

41

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