OSIPP Discussion Paper: DP-2019-E-007

The Effect of Employer Tenure on Wages in Japan*
May 21, 2019

Ayaka Nakamura†
PhD. Student, Graduate School of Economics, Osaka University
Research Fellow of Japan Society for the Promotion of Science【Keywords】Human capital; Matching;【JEL Classification】J24; J31; R23【Abstract】We estimate the effects of employer tenure on wages based on
the instrumental variable method and by using the Japan Household Panel
Survey (JHPS/KHPS) from 2004 to 2014. We cannot reject the hypothesisthat employer tenure significantly contributes to the wage growth after
correcting for the omitted variable biases due to individuals' unobserved
abilities and unobserved matching qualities, while the ordinary leastsquares estimators imply substantial returns to employer tenure. These
results are robust across subsamples and do not depend on the estimation
method. We conclude that the return to employer tenure may be lessimportant in Japan than has been specified in previous studies.
* We are particularly grateful to Katsuya Takii for his appropriate guidance and valuablecomments. We would also like to thank Fumio Ohtake, Masaru Sasaki and Nobuyoshi Kikuchi for
their useful comments. The data for this analysis, Japan Household Panel Survey (JHPS/KHPS), is
provided by the Keio University Panel Data Research Center.
† Corresponding author: Email: ayaka.nakamura.oc@gmail.com.

The Eﬀect of Employer Tenure on Wages in Japan ∗Ayaka Nakamura †Graduate School of Economics, Osaka University
May, 2019

Abstract
We estimate the eﬀects of employer tenure on wages based on the instrumental
variable method and by using the Japan Household Panel Survey (JHPS/KHPS)
from 2004 to 2014. We cannot reject the hypothesis that employer tenure significantly contributes to the wage growth after correcting for the omitted variable biases
due to individuals’ unobserved abilities and unobserved matching qualities, while
the ordinary least squares estimators imply substantial returns to employer tenure.
These results are robust across subsamples and do not depend on the estimation
method. We conclude that the return to employer tenure may be less important inJapan than has been specified in previous studies.

1

Introduction

It is important to consider and confirm what eﬀect increasing employer tenure would
have on increase in wages for understandng the structure of the labor market and themechanisms of the determinants of the wages. *1 For example, if wages increase withtenure, probably because workers accumulate firm-specific human capital through theirexperience with the employer, they lose that human capital when they switch their employers, and therefore, would expectt their wages to decline. *2 In this case, it is optimal
to remain in a firm. Conversely, if human capital is more general (not employer specific)∗

We are particularly grateful to Katsuya Takii for his appropriate guidance and valuable comments.
We would also like to thank Fumio Ohtake, Masaru Sasaki and Nobuyoshi Kikuchi for their usefulcomments. The data for this analysis, Japan Household Panel Survey (JHPS/KHPS), is provided by
the Keio University Panel Data Research Center.
†Research Fellow of Japan Society for the Promotion of Science, Address: Graduate Schoolof Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan. Email:ayaka.nakamura.oc@gmail.com.
*1
For example, Becker (1962), Mincer (1974), Mortensen (1978), and Hashimoto (1981) have rationalized the upward-sloping wage-tenure profile.
*2
See Addison and Portugal (1989a,b); Altonji and Williams (1998); Carrington (1993); Topel (1990);
Farber (1999), which have examined the cost of displacement using the data of the United States. Abe
et al. (2002) mention about the costs in Japan.

1and productivity depends on the match between the firm and the worker, workers could
improve their productivity and earn higher wages by switching to an employer with ahigher quality match.
Many studies have documented a steep wage profile within Japanese firms. Hashimotoand Raisian (1985) find that wage-tenure profiles are steeper in Japan than in the UnitedStates. Mincer and Higuchi (1988) also reveal that productivity growth resulting fromgreater investment in firm-specific human capital leads to a steeper wage profile, andthus a lower turnover rate, in Japan than in the United States. While some researches
have highlighted that the eﬀect of employer tenure on wages has been weaker than conventionally described, they have still found a positive association between tenure andwages.*3
However, most of these studies cannot succumb to the omitted variable bias if acorrelation between tenure variables and unobservable components exists. For example,
the failure to control for unobserved individual abilities would cause the estimated coefficient of employer tenure to be biased upward. Further, if only those workers who area better match remain with the employer longer, the slope of the wage profile would
be steeper than the true slope. In addition, since workers in firms with higher wages
have less incentive to move to the other firms, such firm, on average, would have longer
employer tenure. Under this condition, since wages aﬀect employer tenure, we cannot
obtain, in general, an unbiased estimator using the OLS. Specifically, there is a concernthat a wage return to tenure based on OLS would likely be overestimated under thiscondition.
This paper aims to correct for omitted variable bias when a regression equation isadditively separable in the observable variables and time-invariant in unobserved components, such as an unobserved matching component or unobserved ability, using recently
accumulated panel data, i.e., the Japan Household Panel Survey (JHPS/KHPS). For thispurpose, we adopt the method introduced by Altonji and Shakotko (1987) and Altonji
and Williams (2005). Hereafter, we refer to the estimation method introduced by Altonji
and Shakotko (1987) and Altonji and Williams (2005) as AS’s instrumental variable (IV)method.
First, we regress wages on individuals’ employer tenure through OLS and AS’s IV
method. AS’s IV method uses deviation from the mean employer tenure as the instrumental variable representing employer tenure for each individual. An IV can beorthogonal to an individual’s time-invariant ability or time-invariant quality of being
matched to an employer by construction. Therefore, insofar as unobserved components
are time-invariant and additively separable in a regression analysis, this IV estimate canprovide a consistent coeﬃcient of employer tenure.
Our results reveal that while wage returns to 2, 5, 10, and 15 years of employer
tenure are 9.4%, 13.3%, 19.3%, and 24.6%, respectively, using the OLS estimator, thecorresponding returns are approximately 3.2%, 4.2%, 5.7%, and 7.2%, respectively, using
AS’s instrumental variable method. Using the As’s IV method, we cannot reject the*3See, for example, Clark and Ogawa (1992); Hashimoto and Raisian (1992); Tsuru et al. (2003);
Ohashi and Nakamura (2004); Yamada and Kawaguchi (2015).

2

hypothesis that an increase in tenure has no eﬀect on wage growth. These results suggestthat employer tenure has little eﬀect on increase in wages after controlling for biases due
to unobserved heterogeneity in the quality of employer matching and individual ability.
There is a significant diﬀerence between the returns to employer tenure by using the
OLS versus AS’s IV methoed, especially for more than 3 years of employer tenure.
The results are surprisingly robust. We also conduct the two-step first-diﬀerence
method (hereafter, 2SFD) as suggested by Topel (1991). He highlight the downward
bias due to the heterogeneity of the match quality included in the AS’s IV estimatorof employer tenure. Topel uses the 2SFD method, taking the first diﬀerence of wages
for workers who remain with the same employer from the previous year. He argues
that the true eﬀect of employer tenure on wages is greater than what is presented by
Altonji and Shakotko (1987). The returns based on the 2SFD estimator also support our
main results, which are based on AS’s IV estimator. It indicates the reduced impact of
employer tenure on wage growth in our sample*4 In sum, the matching theory explains
our results well, indicating that employer tenure is less important than what has beenfound in previous studies.
We follow studies that focus on the relative importance of employer and occupation
using the AS’s IV (e.g., Kambourov and Manovskii, 2009 and Sullivan, 2010),*5 and findthat including occupation tenure in the wage equation does not change the returns to employer tenure in Japan,*6 which contrasts with the results found in the abovementioned
studies.
While this paper attempts to correct for biases included in the series of previous
studies which follow Hashimoto and Raisian (1985), it is not the first study endeavoring
to correct for such biases. Toda (2008) conducts similar research using the same datasetthat we use in this study. Interestingly, he concludes that the human capital theory
explains his results well, whereas the matching theory does not, which contrasts sharply
with our results. Although Toda’s analysis is interesting, his results seem to be influenced
by the short time span in which his data is covered. The longer periods now includedin the data enables us to obtain more robust results. We discuss the diﬀerence between
Toda’s study and ours in detail in Section 5.
The remaining sections of this paper are organized as follows. We briefly review
discussions about returns to employer tenure in Japan in Section 2. In Section 3, we
describe the data and explain how we construct our variables. The earnings function
equation is defined in Section 4, and estimation results are explained in Section 5, where
we examine the importance of employer tenure to wage growth in Japan, compared to*4

In the text, we mainly report the result of the 2SFD estimator based on one of the multiple specifications. Results based on other specifications are reported in Appendix E.
*5They reveal that the correlation between employer tenure and wages is attributable to the experience
gained from an occupation or industry in the United States. Zangelidis (2008) adopts AS’s IV to the
British employment and wage data and find that while occupational experience significantly contributes
to wage growth, industry experience does not.
*6
Some studies also focus on industry-specific human capital (Neal, 1995; Parent, 2000; Weinberg,
2001). Although it is desirable to compare the eﬀect of firm- and industry-specific human capital on
wages using data from Japan, we cannot identify their relative importance because employer and industry
tenure are almost the same for individuals in Japan.

3

previous studies. We also discuss the robustness of the results and conduct the 2SFD
estimation as an alternative method. We conclude with a summary of the findings anda brief discussion in Section 6.

2

Literature Review

In this section, we briefly explain the debate about the wage profile in Japan. Many
studies have emphasized the importance of the accumulation of firm-specific human capital in Japanese labor market, which is characterized by long-term employment, throughthe training specific to the firm.*7 Hashimoto and Raisian (1985) compare wage profilesof Japan and the United States using the Basic Survey of Wage Structure (1980) andfind that, for male workers, employer tenure is longer, turnover is less frequent, and theearnings-tenure profile is steeper in Japan. They report that five years of employer tenure
is associated with 36.8% of wage growth. Using detailed microdata, Mincer and Higuchi(1988) emphasize that the higher return to employer tenure in Japan is attributable togreater human capital accumulation through on-the-job training.
Later, Clark and Ogawa (1992) extend Hashimoto and Raisian (1985), using the data
for the years 1971, 1976, 1981, and 1986. Although they find that wage profile becomesflatter, and that wage growth from employer tenure declines from 1981 to 1986, employer
tenure still accounts for one-third to one-half of wage growth*8 Hashimoto and Raisian(1992) further extend the analysis by Clark and Ogawa (1992) by adding the data for1985 and 1988. They find that the contribution of employer tenure on wage growth has
recovered in the latter part of the 1980s after declining from the early to mid-1980s,
while wage profile has flattened through the decade.
Yamada and Kawaguchi (2015) believe that a change in the importance of firmspecific human capital due to declining technological progress in the 1990s occur andestimate the returns to employer tenure using the same data as studies listed above
for the period of 1991 to 2008. They report that, for the survey period, five years of
employer tenure is associated with around 3% of wage growth, and the return declines
over time. They find a much smaller return to employer teure than what is reported inprevious studies by, for example, Clark and Ogawa (1992) and Hashimoto and Raisian(1992); their returns are still positive at the 1% significance level.
Although much of the literatures emphasize the importance of the contribution of
firm-specific human capital to wage increases, the importance seems to have declined*7

Hashimoto and Raisian (1985) reveal that workers in Japan have longer employer tenure than thosein the United States. An anecdotal feature of Japanese labor market is lifetime employment, but its
evidence is mixed. Since this practice applies to only 30% of the male labor force, some literatures, inearly as the 1970s, have pointed out that the prevalence of lifetime employment in Japan is exaggerated.
For example, Koike (1977) argues that long-term employment is more prevalent in the United States
than in Japan. Subsequent papers such as Kato (2001) finds little evidence for any decline in the job
retention rates in Japan, whereas Ono (2010) finds that a smaller percentage of workers are employed
under lifetime employment.
*8
They also focus on the heterogeneity of the return across firms of diﬀerent sizes. They find that thecontribution of the employer tenure to the wage growth is the largest in large firms, then in medium-size
firms, and, lastly, in small firms.

4over time. Moreover, these studies have used cross sectional data. Each study has dealt
with the selection problem after understanding the data used, but it is diﬃcult to gage
whether previous studies accurately remove biases due to unobservable components suchas individual fixed eﬀects and the quality of match between employers and workers. The
returns to employer tenure could be even smaller the period between the end of 2000s
and mid-2010s if these biases are removed using panel data.

3

Data

In this section, we explain the data used and how we construct variables for our estimation. The data comes from the Japan Household Panel Survey (JHPS/KHPS) forthe period 2004–14, which is integrated panel data of the Keio Household Panel Survey(KHPS) and the Japan Household Panel Survey (JHPS).
These household panel surveys reflect the composition of Japanes society as a whole,covering a wide range of topics such as employment behavior, poverty dynamics, andtransfer of real property among households. The KHPS is a survey that has been conducted every year since 2004, covering 4,000 households and 7,000 people nationwide.
Approximately 1,400 people were added in 2007 and about 1,000 were added in 2012
to compensate for dropouts from the sample. The JHPS has been conducted annually
since 2009, covering 4,000 households nationwide, focusing on education, health andmedical care in addition to the topics described above. The populations included inthese datasets are men and women aged between 20 and 69 for the KHPS and men andwomen aged 20 old or older in the JHPS. The populations of these samples overlap, butthere is no overlap between respondents in KHPS and JHPS. Every year, each survey isconducted in Januar. When the respondent is married, the spouse responds to the samequestionnaire.
The respondents are selected by a stratified two-stage random sampling method. In
the first stage of the sampling, the entire country is stratified into 24 strata based onregion and city. The number of samples is allocated according to the proportion of theresident basic ledger population in each stratum, then if the number of samples per
survey area is set to roughly 10 (five for KHPS 2007 and KHPS 2012). The number ofsurvey areas in each stratum is decided, and predetermined number of surveyed areas
are randomly selected. The census survey area is used as a sampling unit. In the second
stage, approximately 10 people (five for KHPS 2007 and KHPS 2012) are extracted using
the resident basic ledger of the selected surveyed area as an extracted ledger, based on thedesignated calling number and extraction interval for qualified persons to be surveyed.
The respondent rate is between 82.3% and 94.2% during the survey period.
Following the related research of Altonji and Shakotko (1987) and Kambourov andManovskii (2009), the sample is restricted to employed male heads of household, aged

5

between 20 and 64.*9*10*11 We eliminate observations who, at that time of the interview,
worked for the government or received real hourly wages of less than 250 yen in constant2010 Japanese yen terms. Those who worked fewer than 500 hours or more than 3,120
hours per year,*12 had total earnings of zero in a given year, or reported being selfemployed are also excluded. Since the representativeness of the data is lost by including
responses from spouses, we do not use them for estimation. Earning functions defined in
Section 4 are estimated from the data sample between 2004 and 2014.*13 The estimation
uses 7,648 observations of 2,068 individuals, out of a total of 27,186 observations, 5,112
individual male respondents.*14
Next, we define some variables and explain their constructions. We define occupations and industries using the classifications provided by JHPS/KHPS for 2004–2014.
Appendix A contains the description of occupation and industry codes. We identify employer changes when the respondents report they changed employers, left their employer,or had been on loan*15 within the last year. Transfers*16 are not defined as changing
employers.
Since JHPS/KHPS does not record the length of employer tenure or the total experience each year except in KHPS 2004 and JHPS 2009, we compute the tenure in each year
based on the tenure in 2004 and 2009 using the following procedure.*17*18 (1) Employer*9

In fact, they restricted the data from 18 to 64 years old, the data we use here do not contain samplesof 18 and 19 years old.
*10Here, the head of household refers to the main livelihood maintainer.
*11
Since, in Japan, many firms adopt a system that terminates regular employment when workers turn
60 years old, their wage tend to decline sharply even if they make contract for to be rehired. We also
estimate wage returns to employer tenure for the sample of under 60 year old as a robustness check.
*12
In fact, in the literatures we have followed, the criteria of sample selection do not restrict the upperbound of working hours. However, 3,120 hours of working per year is equivalent to 60 hours of working
per week. The Ministry of Health, Labor and Welfare of Japan has recommended that working hours beless than 60 per week in an eﬀort to eliminate death from overwork (so-called karoshi). Since our variableof wages used for estimation, whose construction is described below in detail, decreases as working hours
increase, we eliminate observations for those who appear to work too much to prevent the hourly wage
from being underestimated. We elimintated 1,630 observations because of this restriction.
*13
The sample used in the estimation contains non-regular worker. Since we believe there is a wage
diﬀerence between regular and non-regular worker, we control this by adding regular worker dummy
variable in the estimation.
*14
We eliminate 10,880 observations because of age limit, 4,122 because they are not household heads,
4,533 because of unemployment, and 1,694 because they work for the government.
*15
Being on loan is defined as moving to the subsidiary or aﬃliate company that belongs to the same
employer.
*16
Transfer is defined as moving to another oﬃce of the same employer.
*17This procedure follows Kambourov and Manovskii (2009). They explain the procedure in more detailin their paper.
*18
A supplemental estimates includes occupation tenure. We construct occupation tenure by a procedure similar to the one used for employer tenure. However, since JHPS/KHPS does not directly ask thelength of occupation tenure, we do not know the occupation tenure when an individual initially enters
the sample. Hence, it is assumed that occupation tenure is the same as his tenure at a particular firm.
This method provides measurement error of occupation, especially for respondents who are relatively
old when entering the sample, and it may estimate return on occupation tenure downward. However,
because there is no alternative, following previous literatures, we decided to apply this method in this6

tenure is set equal to reported tenure the first year an individual enters the sample;(2) employer tenure increases by one year if the individual does not report an employer
switch in that year and works more than 800 hours in the same year; (3) if the individual
works no more than 800 hours during the year, his tenure is not incremented.*19
JHPS/KHPS asks for more details about the working experience of individuals insurveys conducted in 2004 (KHPS) and 2010 (JHPS). The respondents are required to
specify their experiences of schooling, regular employment, non-regular employment, selfemployment, and other employment status from the ages 18 to 70. We regard working
experience to have been increased by a year when the respondent report at least oneof the above employment experiences. We initially identify years of working experience
when an individual enters the survey. The subsequent years of experience are calculated
based on the process described above.
In addition to the employer tenure, which is a continuous variable, we define an “oldjob dummy”, as taking the value of one if the individual is not in his first year withthe current employer and zero otherwise. Following Altonji and Shakotko (1987) andKambourov and Manovskii (2009), we introduce this indicator to capture a discontinuity
in the employer tenure eﬀect after the first year on a new job.
The dependent variable is the logarithm of real hourly wages. The respondents first
select frequency with which their wages are paid as either annually, monthly, daily, or
hourly. Next, respondents specify their wages according to the payment method theychose. For example, a respondent who chooses monthly will specify wages earned permonth. For each respondent, we first obtain annual working hours by multiplying weekly
working hours by 52. Next, we obtain the hourly wage as the sum of annual income
and annual bonus devided by annual working hours.*20 and annual bonus amount by
annual working hours. The nominal hourly wage obtained in this way is converted intoa real hourly wage, using the consumer index price as deflator with 2010 as the baseyear. Table 1 contains the summary statistics of the sample used in the estimation.

4

The Model

In this section, we define an earning function used for estimation and explain the variables
and instrumental variables employed here. First, we define the earning function. To
assess the relationship between wages and employer tenure, we estimate various versions

paper. In the following, estimation, including occupation tenure, will be discussed as an auxiliary result
only.
*19
Total experience is similarly calculated; if the individual works more than 800 hours during thatyear, then experience increases by one, and it is not incremented otherwise.
*20
The annual income is defined as (the wage the worker earns per month)×12 for monthly wage, (thewage the worker earns per day)×(the number of working days per month)×12 for daily wage, and (thewage the worker earns per hour)×(the number of working hours per week)×52 for hourly wage.

7

Table 1: Descriptive statistics using JHPS/KHPS, 2004–2014

Mean

SD

Min

Max

Age

45.7276

10.3303

20

64

Educational background
Junior high school
High school
2-year college or vocational
College or more

.0366
.4397
.1117
.4120

.1878
.4964
.3150
.4922

0
0
0
0

1
1
1
1

Married

.8372

.3692

0

1

Union member

.2922

.4548

0

1

Firm size
size < 100
100 ≤ size < 500
size ≥ 500

.3715
.2316
.3970

.4832
.4219
.4893

0
0
0

1
1
1

Regular employee

.8874

.3161

0

1

Log of real hourly wage

7.6036

.5538

6

11

Total experience

25.7539

10.7858

050

Employer tenure

14.5000

11.3053047

Notes: The data come from the JHPS/KHPS for 2004–2014. The sample includes employedmale household heads, aged 20–64. Respondents who are government workers at that time of
the interview, or who receive real hourly wages of less than 250 yen in constant 2010 Japaneseyen, are eliminated. Those who work less than 500 hours or more than 3120 hours per year,
have total earnings of zero in a given year, or report being self-employed are also excluded fromthe sample. Since the representativeness of the data is lost when reponses from spouses areincluded, we do not use them for estimation. 7,648 observations of 2,068 individuals are used
for the estimation.

8

of the following econometric model:*21
ln wijt = β1 Tijt + β2 Wit + β3 OJijt + eijt

(1)

where ln wijt is the log of real hourly wage of individual i working in firm j at period t, Tijt
is employer tenure, and Wit is total labor market experience. OJ is the old job dummy
explained in Section 3. In practice, this equation includes a matrix of characteristics that
contain year dummies and an individual’s observable characteristics such as occupationand industry code. Other dummy variables represent marital status, union membership,
education,*22 size of the firm,*23 and a dummy for regular employees. The education
dummies are a proxy for ability to capture diﬀerences in accumulation of employerspecific human capital among workers who have diﬀerent abilities. If employer-specifichuman capital exists, the coeﬃcients of employer tenure in the wage equation should bedetermined so that the return to employer tenure is positive.
The error term is decomposed as follows.
eijt = µi + λij + εijt

(2)

µi is interpreted as a time-invariant individual-specific component, λij is a time-invariant
employer-match component, and εit is the error term. In addition to the observed variables, such as employer tenure, working experience, and individual characteristics, theseunobserved individual-specific characteristics and matching quality may aﬀect wages aswell. For example, an individual who has higher ability may receive higher wages than
one who has low ability, despite having the same level of overall work experience. Similarly, individuals with the same observable characteristics might receive diﬀerent wages
because some of them are better matched to their employer.
These unobserved factors may cause potentially serious biases because unobserved
match components are likely to correlate with tenure. One would expect that individuals
with a better employer match tend to stay employed to the same employer and receive
higher wages. Also, the correlation between total labor market experience and theemployer-match component is important. We might expect that a worker with more
years of labor market experience would switch employers to obtain a better match (“jobshopping”) than one who has just entered the labor market. Certainly, total experiencecorrelates with the probability of participation in the labor market, and thus, it might
be endogenous as employer tenure. These correlations are likely to cause a bias in an
OLS regression.
To deal with this problem, we employ the instrumental variable method, which is devised by AS and also employed by Kambourov and Manovskii (2009) and Parent (2000),*21
There are studies arguing the existence of industry specific human capital such as Abe (1996). It
is desirable to estimate industry specific human capital at the same time. Our data, however, do notcontain enough variations to endure the estimation since many workers have the same industry tenure
as employer tenure. So, industry tenure is omitted from the estimation.
*22
The dummies of years of education are divided into five: middle school graduates (base), high school
graduates, junior college or vocational school graduates, college degree or higher.
*23
The size of the firm is defined by the number of employees, which is divided into three degrees: lessthan 100 people (base), 100 to 499 people, and 500 people or more.

9

in subsequent studies. As an example, we explain how to construct an instrumental
variable for the employer tenure. Let Tijt denote the employer tenure of individual iwith employer j in period t, and let T ij denote the average tenure of individual i during
the current spell of working in employer j. We construct an instrumental variable forthe employer tenure as follows: Teijt ≡ Tijt − T ij . We instrument the squared and cubed
2 − T 2 . By contruction, this instrumenemployer tenure in a similar way: (Teijt )2 ≡ Tijtij
tal variable is orthogonal to employer-match component.*24 In the same way, we create
an instrumental variable for old job dummy, and total experience with their deviations
from the spell- and individual- specific means, respectively. In the following section, we
present the estimation results of earnings function (1) based on OLS and AS’s IV.

5

The Estimation Results

In this section, we describe the estimation results. First, we explain the main results,
that is, employer tenure brings less wage growth in the Japanese labor market thanprevious literatures have argued when we remove the bias from unobserved individual’sability and match quality between a worker and an employer. Second, we show thatthese main results are robust. We can find the same results in several subsamples basedon various specifications. As a part of robustness check, we employ another estimation
method by Topel (1991). The details of the estimation method are also described in thissection.

5.1

Main Results

In this section, we describe the main estimated results using the econometric model
described in the previous section. Table 2 reports the coeﬃcients of earnings function(1), which is estimated by the OLS and AS’s IV method. This table shows the resultsof the estimation. Table 3 reports the calculated wage returns on employer tenure basedon the coeﬃcients in Table 2. Each number in parentheses, in both tables, represent therobust standard error.
*24

These are systematically valid instrumental variable as long as the match component is timeinvariant. As mentioned by AS, Teim sums to zero over the sample years in which the worker is in
employer j. Let N denote the ultimate employer tenure of an individual with employer j, the covarianceof Teijt and λij isN∑

E[Teijt λij ]=E[Teijt λij ]=t=1

E[(Tijt − T ij )λij ]N∑E[(Tijt − T ij )λij ]

t=1

[

=

E λij

N
∑

]
(Tijt − T ij )t=1=

E[λij · 0].

Thus, Teijt is uncorrelated with employer-match component. Also, this instrumental variable is definitely
correlated with Tijt .

10

Table 2: Earnings function estimates, using the AS’s IV method
OLS

AS’s IV

(1)

(2)

(3)

(4)

Employer tenure.0140∗∗∗(.0020).0134∗∗∗(.0022).0032(.0058).0043(.0062)

Emp.ten.2 × 100-.0132∗∗∗(.0051)-.0125∗∗(.0058)-.0006(.0150)-.0060(.0165)

Old job.0661∗∗(.0283).0733∗∗(.0295).0260(.0460).0265(.0473)

Total experience.0203∗∗∗(.0027).0212∗∗∗(.0028).0398∗∗∗(.0080).0417∗∗∗(.0083)

Experience2-.0004∗∗∗(.0001)-.0004∗∗∗(.0001)-.0007∗∗∗(.0001)-.0008∗∗∗(.0002)

Occupation tenure

No

Yes

No

Yes

Observations

7648

7519

7648

7519

Notes: Robust standard errors are in parentheses.
∗ ∗∗, and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The dependent variable is the log of real hourly wages. Other covariates include
an intercept, year dummies, education dummies, occupation and industry dummies, aunion membership dummy, a marital status dummy, dummies of firm size, and a regular
employee dummy. In addition to those variables, Columns (2) and (4) also include
occupation tenure. Columns (1) and (2) denote the coeﬃcients of earnings function(1) which is estimated by OLS, and columns (3) and (4) denote those computed using
AS’s IV method.

11

Table 3: Estimated returns to employer tenure.
AS’s IV

2SFD

OLS

IV

(1)

(2)

(3)

(4)

(5)

2 years.0935∗∗∗(.0271).0995∗∗∗(.0283).0323(.0430).0348(.0443)-.0130(.0307)

5 years.1327∗∗∗(.0264).1370∗∗∗(.0276).0417(.0434).0463(.0449)-.0323(.0760)10 years.1926∗∗∗(.0268).1945∗∗∗(.0283).0570(.0515).0632(.0537)-.0637(.1503)15 years.2460∗∗∗(.0277).2457∗∗∗(.0296).0720(.0622).0770(.0646)-.0941(.2244)20 years.2927∗∗∗(.0285).2907∗∗∗(.0304).0867(.0731).0879(.0749)-.1235(.3000)25 years.3329∗∗∗(.0289).3295∗∗∗(.0309).1011(.0848).0957(.0858)-.1520(.3786)

Occupation tenure

No

Yes

No

Yes

No

Observations

7519

7519

7519

7519

7824

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
This table reports the calculated wage returns to 2, 5, 10, 15, 20, and 25 yearsof employer tenure based on the coeﬃcients of the corresponding columns of Table
2. Columns (1) and (2) denote the calculated returns estimated using OLS, andcolumns (3) and (4) denote those obtained using AS’s IV method. The corresponding returns based on the 2SFD method are represented in column (5).

12Column (1) of Table 2 shows the coeﬃcients in the earnings fuction (1) estimatedby OLS. The coeﬃcients for all the variables—the employer tenure, old job dummy, andtotal experience—are statistically diﬀerent from zero. The coeﬃcient for employer tenure
and its quadratic term, and for total experience and its quadratic term, suggest thatthe earnings function is concave in employer tenure and total labor market experience,
respectively. The coeﬃcient of the old job dummy variable is approximately 0.07, whichsuggests there is a substantial wage jump between the first and the second year of
employer tenure. The results are quite simlar when occupation tenure is included in theearnings function (1), as shown in column (2) of Table 2.
Columns 1 to 3 of Tables A1 and A2 (in the Appendix) show the results obtainedby adding cubic and quartic terms of employer and occupation tenure, and total experience to the covariates shown in Table 2. Kambourov and Manovskii (2008, 2009) revealthat returns to employer tenure disappear after controlling the occupation tenure in the
United States. Other literatures, such as Shaw (1984, 1987) and Zangelidis (2008), havealso showed that occupation tenure is more important than employer tenure. After obtaining these results, we check to see whether including occupation tenure changes thecoeﬃcients of employer tenure. Our results contrast with those studies, as we found thatneither employer nor occupation tenure have significant eﬀect on wages in Japan. Including the higher-order terms of employer tenure,occupation tenure, and total experience
do not change these results.
Column (3) of Table 2 shows the coeﬃcients in the earnings fuction (1) estimatedusing AS’s IV. Unlike the results obtained using OLS, the coeﬃcients of employer tenure
and its quadratic term and old job dummy are not statistically diﬀerent from zero evenat the 10% level of confidence. Only the coeﬃcients of total labor market experience
are still significantly diﬀerent from zero at the 1% level. As shown in column (4) of
Table 2, the same result is obtained even when occupation tenure is included in theestimation. Columns 4 to 6 of Table A1 and A2 (in the Appendix) show the results
obtained by adding cubic and quartic terms of employer tenure, occupation tenure,and total experience to this estimation. Similar to the previous instance, includingthese higher-order terms of tenure variables do not change the results described above,
consistent with the results of the OLS estimator.
The same can be said from the estimated wage returns based on these coeﬃcients.
The estimated returns to employer tenure based on the coeﬃcients of the column (1) in
Table 2 are 9.4%, 13.3%, 19.3%, and 24.6% for 2, 5, 10, and 15 years, respectively. Allof the returns to employer tenure are significantly positive. In particular, magnitude of
the coeﬃcient of the old job dummy of 0.07 contributes approximately one-third of the
return to 10 years of employer tenure; thus, the old job dummy explains a large part ofthis positive return. This implies that employer tenure after the second year has only amodest eﬀect on wage growth relative to the eﬀect of transitioning from the first to thesecond year of employer tenure. The positive returns to employer tenure based on thecoeﬃcient obtained from OLS are robust even after controlling for occupation tenure.
The corresponding returns using the AS’s instrbbumental variable method are approximately 3.2%, 4.2%, 5.7%, and 7.2%, as showed in column (3) of the same table. It

13

0.4
0.3
0.2
0.1

Returns to employer tenure

0.0
0

5

10

15

20

25

Employer tenure
AS's IV OLS

Figure 1: Plot of returns to employer tenure.
can be observed that the wage returns to 10 years of employer tenure based on AS’s IVestimator are around one-third compared to the returns based on the OLS estimator.
In addition to this decrease in the amount of returns, these returns are not statisticallydiﬀerent from zero. This result does not change when we include occupation tenure into
the earnings function (1).
Figure 1 represents the plot of the estimated returns to each year of employer tenure
based on OLS and AS’s IV method. Comparing the returns based on OLS and AS’s IVestimators represented in the columns (1) and (3) of Table 2, respectively, the returns
based on AS’s IV estimators point to significantly diﬀerent amount compared to the returns based on the OLS estimators where the employer tenure is over two years, although
there is almost no significant diﬀerence until the second year of employer tenure. Therefore, we find that the bias from the selection matters not immediately after employment
but rather after some employment period has been accumulated.
The previous literatures, such as Hashimoto and Raisian (1985), Clark and Ogawa(1992), and Hashimoto and Raisian (1992), report almost the same coeﬃcients of employer tenure as the one estimated here based on the OLS estimator. They insist on theimportance of firm-specific human capital based on these coeﬃcients.*25 Our results,*25

Clark and Ogawa (1992) and Hashimoto and Raisian (1992) show that the importance of employer
tenure on the wage growth declines in 1980s, and they report smaller returns to employer tenure than14

contrary to previous studies, suggest that employer tenure has only a modest eﬀect on
wages.
In sum, our main results are that the OLS estimators include a substantial amountof selection bias, and employer tenure may not be as important for wage growth assuggested by previous research when biases from unobserved heterogeneity in ability
and employer matching quality are considered. Further, the magnitude of these biases
become problematic as employer tenure increases.

5.2

Robustness Checks

In this section, we show that the main results described in the previous section arerobust by using two approaches. First, we estimate various specifications using equation(1) applied to various subsamples of the data, confirming that the results are robust,
regardless of the characteristics of the workers. Second, we employ another estimation
method for the earnings function as presented by Topel (1991). Both results suggest that
returns to employer tenure are lower than the findings of previous studies, regardless ofthe estimation methods or the characteristics of the individuals.
5.2.1

Estimation on Various Subsamples

In this section, we divide the sample into various subsamples and employ the same
estimation technique used in the previous section. For example, in many Japanesefirms, regular employees are often reemployed as non-regular employees after they retireat the age of 60. Given this, including workers over the age of 60 could appear as being
inappropriate in the context of assessing human capital accumulation. Alternatively,
firm size might also aﬀect the extent of wage growth, as it is known that wage paid bylarge firms are relatively higher than those paid by small firms (see, e.g., Oi and Idson(1999) and Koike (2005)).
Further, professionals, such as lawyers, doctors, or researchers, would be assumed
to be rewarded by occupation tenure than by employer tenure compared with workers
engaged in other occupations. Since the heterogeneity of tasks across firms would besmall in such professional occupations, the importance of employer tenure might be lower
than for other occupations. We made the same estimation for nonprofessional samples,
to determine whether the result of the entire sample is influenced by individuals in
professional occupations.
Finally, from the viewpoint of human capital accumulation, one could think it appropriate to estimate the earnings function (1) using only the data on regular employees,
so we excluded non-regular employees from the sample.

those in Hashimoto and Raisian (1985). However, they still report substantially larger wage growth thanthat obtained by our estimation.

15

16

.0453
(.0604).0708(.0731).1051(.0866).1480(.1025).1946∗∗∗(.0307).2481∗∗∗(.0318).2995∗∗∗(.0327).3486∗∗∗(.0333)10 years

15 years

20 years

25 years
3036.3761∗∗∗(.0630).3338∗∗∗(.0620).2780∗∗∗(.0601).2087∗∗∗(.0576).1259∗∗(.0561).0697(.0567)

OLS
(3)

3036

.0451
(.1427).0432(.1321).0406(.1192).0374(.1030).0336(.0878).0310(.0843)AS’s IV(4)

Large Firms (≥ 500)

4612

.3166∗∗∗(.0327).2820∗∗∗(.0324).2419∗∗∗(.0317).1963∗∗∗(.0306).1452∗∗∗(.0303).1120∗∗∗(.0312)

OLS
(5)

4612

.1441
(.1355).1128(.1098).0844(.0877).0587(.0684).0359(.0547).0235(.0534)

AS’s IV(6)

Small Firms (< 500)

6489

.3438∗∗∗(.0317).3035∗∗∗(.0313).2536∗∗∗(.0305).1942∗∗∗(.0295).1253∗∗∗(.0291).0794∗∗∗(.0299)

OLS
(7)

6489

.0627
(.1015).0507(.0873).0401(.0737).0306(.0602).0224(.0501).0181(.0495)AS’s IV(8)

Non-Professional

6787.3518∗∗∗(.0362).3068∗∗∗(.0359).2574∗∗∗(.0354).2035∗∗∗(.0347).1452∗∗∗(.0348).1081∗∗∗(.0358)

OLS
(9)

6787

.1132
(.1008).0919(.0876).0727(.0761).0555(.0656).0403(.0587).0322(.0592)

AS’s IV(10)

Regular Employee

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
This table reports the calculated wage returns to 2, 5, 10, 15, 20, and 25 years of employer tenure based on the coeﬃcients of thecorresponding columns of Table 2. Columns (1), (3), (5), (7), and (9) denote the calculated returns estimated using OLS, and columns(2), (4), (6), (8), and (10) denote those obtained using AS’s IV method. We present the returns for calculating which we use the sample
of individuals under 59-year-old in columns (1) and (2), the sample of individuals who belong to firms with more than 500 employees
in columns (3) and (4), the sample of individuals who belong to firms with less than 500 employees in columns (5) and (6), the sample
of individuals excepting workers who respond that s/he works as professional in columns (7) and (8), and the sample of the regular
employees in columns (9) and (10).

6842

.0285
(.0510).1388∗∗∗(.0303)5 years

6842

.0225
(.0505).1043∗∗∗(.0311)

2 years

Observations

AS’s IV
(2)

OLS
(1)

Under 59-year-old

Table 4: Estimated returns to employer tenure, using various subsamples.

Table 4 reports the calculated wage returns on employer tenure based on the estimatesof earnings function (1) in each subsample. The calculations are based on the coeﬃcientsin the corresponding columns of Table A3, shown in Appendix C. Almost all of thecoeﬃcients of earnings function (1) that use the subsamples appear to have tendencies
similar to those in the entire dataset. Regardless of the specification, the calculated
returns to employer tenure become insignificant when AS’s IV method is used, while thecorresponding returns are significantly positive with the usage of OLS..
We also examine how each of the control variables aﬀects the estimation results.
That is, we compare the estimation results by and without adding a control variable tothe earnings function (1). The control variables used for main results are education dummies, firm size dummies, year dummies, marital status dummy, union dummy, regular
employee dummy, and industry and occupation codes. We estimate earnings function(1) by adding these control variables one by one and excluding them from the equation.
None of the variables has a significant eﬀect on the estimation results, and the main
results are supported.
Altonji and Williams (2005) highlight that the method of controlling for time trends
may aﬀect the estimation results. They show that using year dummies instead of detrending wages first by using a time trend index reduces the returns to 10 years of
employer tenure by half in the United States. Here, we use instead year trend for estimating the earnings function (1). The use of alternative time trend, however, does not
aﬀect the estimation results. The wage returns to 10 years of employer tenure is around
20% and 7.5% when we include year variable as trend and use the OLS and AS’s IVestimators, respectively. These returns are almost the same as the returns obtained byincluding year dummies.
So far, we have examined various specifications of the estimation of the earnings
function (1). All of these diﬀerent specification estimations suggest that our main results
are robust, and that the returns to employer tenure become insignificant after controlling
biases from unobserved hets erogeneity.
5.2.2

Alternative Estimation Based on Topel (1991)

In this section, an alternative estimation of the earnings function is implemented based onTopel (1991). He argues that the AS’s IV method would estimate the returns to employer
tenure downward due to a employer-match component, λij . Topel (1991) indicates thatthe employer-match component produces a downward bias in the coeﬃcient of employer
tenure, β1 , and provides the alternative estimation method.*26 Although, following
Altonji and Williams (2005), who compare the sensitivity of both AS’s IV and the 2SFD
estimators, we mainly report the results obtained from AS’s IV estimator in this paper,
it is still nice to examine the robustness of our main results using the 2SFD.
The estimation used by Topel (1991) proceeds in two steps. The first estimates the*26
Although he shows that the diﬀerence between AS’s IV and the 2SFD estimators is due to bias from
employer-match component, λij is −0.0015 (that is, this diﬀerence generates the diﬀerence in returns to
10 years of employer tenure by −0.015), this value explains only less than 1% of the diﬀerence in thecalculated wage returns to 10 years of employer tenure.

17

combined eﬀect of the linear experience and employer tenure (B = β1 + β2 in equation(1)). The OLS is applied to observations of individuals who does not change theiremployer since the last interview*27 :∆ ln wijt ≡ ln wijt − ln wijt−1 = B + εit − εit−1 .

(3)

Since the original error term in the earnings function is decomposed to eijt = µi +λij +εit ,taking the first diﬀerence of the wage enables us to remove the time-invariant componentsµi and λij from the equation, so only the purely random term remains. Here, current
experience is the sum of the initial experience with an employer, W 0ijt , and employer
tenure, Tijt , that is, Wijt = W 0ijt + Tijt . Then, the original earnings function is writtenasln wijt = B̂Tijt + β2 W 0ijt + νijt .
where B̂ is the OLS estimates from (3) and νijt = Tijt (B − B̂) + εijt . Therefore, thesecond step estimates a coeﬃcient of the linear experience (β2 ) using OLS toln wijt − B̂Tijt = β2 W 0ijt + νijt .

(4)

Finally, the coeﬃcient of the linear employer tenure (β1 ) is obtained as B̂ − β̂2 . We referto this estimator as the two-step first-diﬀerence (2SFD) estimator.
The estimator B̂ is eﬃcient if the diﬀerences between the employer tenure and error
term, εit , are not correlated. We can then obtain an eﬃcient estimator of β2 , and thus
β1 , if the initial experience of the employer, W 0ijt , is correlated neither with µi nor λij .
In practice, the quadratic terms of employer tenure and working experience are also
included in these equations. The coeﬃcients of these terms are estimated in the firststep, and then the predicted values are subtracted from the log of hourly wages in thesecond step. We also include individual characteristics and year dummies, which are
shown in equation (4). We use the same control variables for the estimation using 2SFD
as in the estimation using AS’s IV, namely, education dummies, occupation and industry
dummies, a union membership dummy, a marital status dummy, firm size dummies, anda regular employee dummy.
The results of this estimation are presented in Table 5. The corresponding wage
returns to employer tenure are shown in column (5) of Table 3, which is an estimatebased on the coeﬃcients in column (2) of Table 5. As shown in column (1) of Table 5,
the sum of the coeﬃcients of linear employer tenure and working experience (constantterm in the first step) is significantly negative when we use only the linear term of
the employer tenure and working experience. The estimate of constant term gradually
increases to positive values by adding quadratic, cubic and quartic terms. Corresponding
to this increase, the estimate of the coeﬃcient of linear term of working experience also
increases from negative to positive. The estimates of higher order terms of employer
tenure also vary from negative to positive values. It seems that the 2SFD estimators are
sensitive to the specification of the estimation equation.
*27

Here, we exclude old job dummy, following the specification used by Topel.

18

Table 5: Estimation results, using the method of 2SFD estimation
(1)

(2)

(3)

(4)

-.0245∗∗∗(.0053)-.0098(.0145)-.0023(.0296).0745(.0523).0019(.0260).1900∗∗(.0935)-.0074(.2099)-.0342∗∗(.0165).0566(.0842)First stage
Constant
Emp.ten.2 × 100
Emp.ten.3 × 1000
Emp.ten.4 × 10000-.0119(.0104)

Experience2 × 100-.0293(.0280)Experience3 × 1000-.1873(.1368)-.6877∗(.3899).0228(.0176).1643(.1114)

Experience4 × 10000-.0134(.0109)second stage
Total experience-.0185∗∗∗(.0006)-.0032∗∗∗(.0006).0283∗∗∗(.0012).0943∗∗∗(.0006)

Employer tenure-.0060(.0053)-.0066(.0155)-.0306(.0327)-.0198(.0623)

4818
7827

4815
7824

4815
7824

4815
7824

Observations fromfirst stage
second stage

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The dependent variable is the log of real hourly wages. Other covariates include anintercept, year dummies, education dummies, occupation and industry dummies, a union
membership dummy, a marital status dummy, dummies of firm size, and a regular employee
dummy. The model for estimation is given by the earnings function (1).

19The coeﬃcient of linear employer tenure, β1 , by using the 2SFD is around −0.01,
which is not statistically diﬀerent from zero except when we use only linear term of theemployer tenure and working experience. Negative coeﬃcient of the employer tenure
implies that staying at the same employer for one year longer brings negative wage
return. As a result, the column (5) of Table 3 shows that the calculated return toemployer tenure is also negative throughout all years. Although the negative returns
to employer tenure are a result that neither human capital theory nor matching theory
predicts, this result is consistent with the result from AS’s IV in terms that the returnto employer tenure does not significantly diﬀer from zero.
We oﬀer several caveats regarding the interpretation of the results of the 2SFD
estimator. First, these estimates seem to be sensitive to specifications of the earnings
function. The coeﬃcients and corresponding returns vary greatly depending upon thespecification. For example, the 2SFD estimators are sensitive to how we control for atime trend and which control variables the earnings function includes. Thus, the 2SFD
method has shown to provide an unstable result.*28 We present the other results basedon the 2SFD method in Appendix E.
The 2SFD estimator may also cause another problem. Since unobserved individual
abilities, µi and the employer-match component, λij are included in the error term inthe second step, νijt , both may be correlated with the individual’s initial experience withthe employer, W 0ijt . If so, the 2SFD estimator would produce biased results. This isexactly what Altonji and Williams (2005) point out as a problem of the 2SFD estimator.
After reviewing this criticism from Topel (1991), Altonji and Williams (2005) argue
that the upward bias in the 2SFD estimator of the linear employer tenure coeﬃcient due
to the individual-specific component, µi is more serious than the downward bias of AS’s
IV when using data from of the United States.
They confirm this by replicating Topel’s sample. They use both of the estimation
methods, AS’s IV and the 2SFD, with various specifications to ascertain the impactof each source of bias on the estimation results. Interestingly, the 2SFD estimators intheir estimations are also unstable. They conclude that when the trend in the data isproperly accounted for, Topel’s estimation method suggests that the upward bias due toindividual-specific components is substantial.
However, it is diﬃcult to believe that negative tenure eﬀects contain upward biases. In fact, the 2SFD method could produce a downward bias depending upon thecorrelations between employer tenure, working experience, initial experience with theemployer, the employer-match component, and the individual-specific component. We
discuss the condition under which the 2SFD estimator produces downward a bias whenusing JHPS/KHPS in Appendix D. We find that the coeﬃcient in the regression ofworking experience on employer-match component must be suﬃciently large to produce
a downward bias.
Given the instability of the results and the potential bias in the 2SFD estimator,*28
As we discuss below, Toda (2008) also uses JHPS/KHPS for applying the AS’s IV and the 2SFD
method to Japanese data. He also finds that the results using the 2SFD are unstable depending on how
many higher-order terms of employer tenure and working experience are controlled.

20

AS’s IV estimator appears to be more reliable than the 2SFD estimator. Following theargument put forth by Altonji and Williams (2005), we decide to use the results of the
AS’s IV as our main results. However, note that the results from the 2SFD estimator
are consistent with those from the AS’s IV in that the estimated returns to employer
tenure are not significantly diﬀerent from zero.

5.3

Discussion

Although this study tries to correct for the potential biases of the coeﬃcients of tenurein the earnings equation of previous literatures, it is not the first attempt to correct forsuch biases. Toda (2008) makes a similar attempt. He also uses JHPS/KHPS data toapply AS’s IV and the 2SFD methods to Japan, but his results are not consistent with
our as described above. We discuss the source of the diﬀerences in this section.
Toda (2008) reports that the estimated wage returns on 2, 5, and 10 years of employer
tenure based on AS’s IV are lower than those based on the OLS and that they reverse
after 15 years of employer tenure. Although he does not mention whether the estimatedwage returns are significantly diﬀerent when obtained from AS’s IV method versus OLS,
he interprets his results as suggesting that Japanese workers accumulate firm-specifichuman capital through experience with their employers and concludes that the matchingtheory is not well supported by his results.
His conclusions contrast sharply with ours. Our main results suggest that employer
tenure has little eﬀect on wage growth after taking for unobservable individual ability
and employer-match. We also find that estimated wage returns on employer tenure
derived from AS’s IV are significantly diﬀerent from those computed using OLS whenthe employer tenure is more than three years, which suggests that workers move toemployers with whom they have a better match through job-shopping, as indicated bymatching theory.
The obvious question is what causes this notable diﬀerence between our and Toda’s(2008) results? To answer this question, we replicate Toda’s (2008) estimates. Our
replicated results, using the same data sample and variables that are defined as closely
possible to his definitions, are presented in Appendix F. These results reveal that, we
obtain the same conclusions based on the replicated sample.
Unfortunately, he utilizes only four years of data, which is the only data available atthat time. We assume that this limited dataset makes him unable to provide convincing
evidence to support his conclusions regarding the of Japanese labor market. Note that
Altonji and Shakotko (1987) use 14 years and Altonji and Williams (2005) and Topel(1991) use 16 years of PSID in their studies, respectively. We use the same data covering
11 years.
We believe the data must cover a longer period than what is used in Toda (2008)
for AS’s IV and the 2SFD methods, because these methods rely on variation in average
tenure and in initial experience with the current employer to identify the coeﬃcients of
employer tenure and working experience, respectively. The variations in these variables
are generated from observations of individuals who change to diﬀerent employers. The
fraction of such observations is around 5% in our data. We believe that the length of the21panel data plays an important role in obtaining suﬃcient variation in these estimation
methods, especially in Japan where the probability of a change in employer is lower thanin the United States.
Other diﬀerences in our estimations, such as the way of controlling for trends in theeconomy or definitions of variables, account for less of the diﬀerence between our andToda’s (2008) results. For example, his study does not control for economic trends due toa small number of years contained in his dataset; therefore, his estimation model includes
neither a year trend term nor year dummy terms. We use both ways of controlling for
economic trends in our estimation and find that the method has little eﬀect on thecoeﬃcients of employer tenure when using the AS’s IV method. Associated with this,Toda (2008) uses raw log of hourly wage data as the dependent variable, whereas we
use the real log of wages standardized as of 2010. However, we confirm that the results
for the replicated sample do not change when using the standardized wage approach.
Therefore, we believe the diﬀerence between our and Toda’s (2008) results arises fromusing a longer dataset, which is necessary to obtain more reliable result.

6

Conclusion

We estimate the return to employer tenure in Japan using JHPS/KHPS data. The returns to 2, 5, 10 and 15 years of employer tenure are approximately 9.4%, 13.3%, 19.3%,
and 24.6%, respectively, using the ordinary least squares method. The corresponding
returns are approximately 3.2%, 4.2%, 5.7%, and 7.2%, respectively, using AS’s instrumental variable method. The significance of the coeﬃcients obtained using OLS disappears when we use AS’s IV method. Since AS’s IV estimators of employer tenure remove
biass caused from correlations between employer tenure and both employer-match quality and unobserved ability, we can see that selection bias is included in OLS estimators.
We conclude that a substantial part of the eﬀects of employer tenure on wage growth
may come from the fact that individuals with a better employer match and high unobserved abilities remain with an employer for a long time. We conclude that the return toemployer tenure is less important in Japan than what is found in previous studies after
correcting for the biases due to unobserved ability and unobserved matching quality.
This implies that some part of wage returns may come from workers’ job shopping tofind a better employer match. These results are robust across the subsamples and do
not depend on the estimation method.
It is important to note that this study only deals with unobservable abilities anddeviations from matching quality, which are additively separable and time-invariant.
We cannot control for bias from unobserved time-vairant or non-separable components.
Although we present the possibility that the importance of employer tenure on wage
growth is less than what is argued in previous literatures, we cannot conclude that
there is no causal eﬀect of employer tenure on wage growth. Further, we are unable
to claim that workers do not accumulate employer-specific human capital through theirexperience with a specific employer, nor can we state that the theory of delayed payment
contracts does not explain our results. Even if employer-specific human capital exists, if

22the employer pays all cost of training specific to the employer and reaps the rent from
employer-specific human capital, the wage profile may be flat. If we take retirement
allowances into account, our results, which suggest little eﬀect of employer tenure on
wage growth, may be consistent with the theory of delayed payment contracts. At aminimum, our results point out the need to carefully analyze causal eﬀects of employer
tenure in future research.
Another limitation of this study is that we cannot recognize concrete change in thecontent of a job for a given employer. Recent papers divide jobs into certain types oftasks (e.g., cognitive and noncognitive tasks) and focus on the returns to the tasks (see,e.g., Gathmann and Schönberg, 2010; Yamaguchi, 2012; Schulz et al., 2013; Handel etal., 2013, and Kok, 2014).*29 Tsuru et al. (2003) point out compensation structures havebeen shifting from a seniority-based structure to an alternative structure based on theworkers’ skills on the job and on a grade that reflects a worker’s capability. Although
our results are consistent with matching theory, if workers change tasks within thesame employer, the workers may accumulate human capital in terms of tasks and theirwages may increase with respect to their productivity i doing particular tasks. Dividing
jobs into tasks would bring a deeper understanding of the kind of experiences that allow
workers to accumulate human capital. We hope that accumulating more data will enable
us to further conduct this kind of analysis in Japan.

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26

Appendix A

Occupation code

1. Agriculture, forestry, or fishery worker
2. Mine worker
3. Salesperson (retail or wholesale shop manager or worker, outside salesperson, realestate agent, etc.)
4. Service worker (worker, cleaner, etc. at a barber shop, beauty parlor, restaurant,
inn, etc.)
5. Manager (national or local government assembly member; section chief or higher
position at a company, organization or government oﬃce)
6. Clerical worker (general clerk, accountant, operator, sales clerk, etc.)
7. Transportation or communications worker (railway or motor vehicle driver; shipor airplane pilot; conductor; cable or wireless radio operator, etc.)
8. Manufacturing, construction, maintenance or freight worker
9. Information technology engineer (systems engineer, programmer, etc.)
10. Specialized or technical worker *excluding IT engineer (company researcher orengineer; medical practitioner; legal practitioner; teacher; artist; etc.)
11. Public safety employee (SDF, police, fire department, security guard, etc.)
12. Other

Appendix B

Industry code

1. Agriculture
2. Fishery, forestry, marine products
3. Mining
4. Construction
5. Manufacturing (including publishing and printing)
6. Wholesale, retail (including department stores and supermarkets)
7. Restaurants, accommodations
8. Finance, insurance
9. Real estate
10. Transportation
11. Information services and surveys
12. Information and telecommunications other than information services and surveys(telephone and other communications, broadcasting, internet services)2713. Utilities (provision of electricity, gas, water, heat)
14. Medicine, welfare
15. Education, learning support
16. Other services
17. Public service
18. Other

Appendix C

Other Estimation Results

The coeﬃcients that have been obtained from the estimation based on (1) with quadratic,
cubic and quartic terms of tenure and experience variables are presented in Table A1
and A2. The coeﬃcients based on the estimation of the same earning function as above
for various subsamples are showed in Table A3. We can confirm that the coeﬃcients of
employer tenure are qualitatively similar in all of the regressions; we cannot reject the
hypothesis that these coeﬃciesnts are zero. Including the higher-order terms of tenureand experience, and including occupation tenure do not change the results. Furthermore,
the results are the same when we divide into subsamples.

28

Table A1: Earnings function estimates, using the AS’s IV method, occupation
tenure is not included.
OLS

AS’s IV

(1)

(2)

(3)

(4)

(5)

(6)

Employer tenure.0140∗∗∗(.0020).0106∗∗(.0045).0155∗(.0088).0032(.0058).0001(.0095).0054(.0148)

Emp.ten.2 × 100-.0132∗∗∗(.0051).0107(.0269)-.0459(.0864)-.0006(.0150).0244(.0606)-.0433(.1528)-.0004(.0004).0018(.0031)-.0005(.0010).0024(.0057)

Emp.ten.3 × 100
Emp.ten.4 × 1000-.0000(.0000)-.0000(.0000)Old job.0661∗∗(.0283).0799∗∗∗(.0310).0688∗∗(.0348).0260(.0460).0366(.0475).0274(.0510)Total experience.0203∗∗∗(.0027).0058(.0074).0238(.0150).0398∗∗∗(.0080).0113(.0166).0614∗∗(.0289)Experience2-.0004∗∗∗(.0001).0003(.0003)-.0011(.0011)-.0007∗∗∗(.0001).0005(.0007)-.0034(.0021)-.0008∗∗(.0004).0031(.0031)-.0016∗(.0009).0099(.0061)

Exp.3 × 100
Exp.4 × 10000
Observations-.0000∗(.0000)-.0000(.0000)
7648

7648

7648

7648

7648

7648

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The dependent variable is the log of real hourly wages. Other covariates include anintercept, year dummies, education dummies, occupation and industry dummies, a union
membership dummy, a marital status dummy, dummies of firm size, and a regular employee
dummy. Columns (1) to (3) denote the coeﬃcients of earnings function (1) which isestimated by OLS, and columns (4) to (6) denote those computed using AS’s IV method.

29

Table A2: Earnings function estimates, using the AS’s IV method, occupation tenure
is included.
OLS

AS’s IV

(1)

(2)

(3)

(4)

(5)

(6)

Employer tenure.0134∗∗∗(.0022).0084∗(.0050).0087(.0095).0043(.0062).0041(.0103).0019(.0160)

Emp.ten.2 × 100-.0125∗∗(.0058).0218(.0301).0173(.0920)-.0060(.0165).0032(.0646).0514(.1710)-.0006(.0005)-.0000(.0032)-.0003(.0011)-.0028(.0067)

Emp.ten.3 × 100
Emp.ten.4 × 1000-.0000(.0000).0000(.0000)Old job.0733∗∗(.0295).0880∗∗∗(.0325).0807∗∗(.0364).0265(.0473).0285(.0491).0283(.0526)

Occupation tenure.0009(.0017).0040(.0032).0119∗∗(.0052)-.0074(.0045).0014(.0073).0092(.0119)

Occ.ten.2 × 100-.0017(.0050)-.0230(.0198)-.1104∗∗(.0480).0227(.0142)-.0550(.0538)-.1964(.1680).0003(.0003).0031∗∗(.0014).0015(.0010).0081(.0071)

Occ.ten.3 × 100-.0025∗∗(.0011)

Occ.ten.4 × 10000-.0090(.0089)Total experience.0212∗∗∗(.0028).0071(.0079).0306∗(.0169).0417∗∗∗(.0083).0152(.0173).0702∗∗(.0309)Experience2-.0004∗∗∗(.0001).0002(.0003)-.0015(.0012)-.0008∗∗∗(.0002).0004(.0007)-.0039∗(.0022)-.0008∗(.0004).0042(.0034)-.0016(.0010).0113∗(.0064)

Exp.3 × 100
Exp.4 × 10000
Observations-.0000∗∗(.0000)-.0000(.0000)
7519

7519

7519

7519

7519

7519

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The dependent variable is the log of real hourly wages. Other covariates include an intercept,
year dummies, education dummies, occupation and industry dummies, a union membershipdummy, a marital status dummy, dummies of firm size, and a regular employee dummy.
Columns (1) to (3) denote the coeﬃcients of earnings function (1) which is estimated by
OLS, and columns (4) to (6) denote those computed using AS’s IV method.

30

31

-.0013(.0265).0289∗∗(.0116).0159(.0571).0056(.0204).0037(.0076)(6).0013(.0067)(8).0154(.0528).0824∗∗(.0372)-.0089(.0058)(.0022).0130∗∗∗

(9)

.0272
(.0626).0041(.0172).0024(.0067)(10).0166∗∗∗ .0382∗∗∗ .0219∗∗∗ .0380∗∗∗(.0029) (.0089) (.0032) (.0093).0469(.0310)-.0190∗∗∗ .0025(.0054) (.0162)(.0021).0166∗∗∗

(7)

6842

6842

3036

3036

4612

4612

6489

6489

6787

6787

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The dependent variable is the log of real hourly wages. Other covariates include an intercept, year dummies, education dummies,
occupation and industry dummies, a union membership dummy, a marital status dummy, dummies of firm size, and a regular
employee dummy. Columns (1), (3), (5), (7), and (9) denote the coeﬃcients of earnings function (1) which is estimated by OLS,
and columns (2), (4), (6), (8), and (10) denote those computed using AS’s IV method. We present the coeﬃcients for which we
use the sample of individuals under 59-year-old in columns (1) and (2), the sample of individuals who belong to firms with morethan 500 employee in columns (3) and (4), the sample of individuals who belong to firms with les than 500 employee in columns(5) and (6), the sample of individuals excepting workers who repond that s/he works as professional in columns (7) and (8), andthe sample of the regular employees in columns (9) and (10).

Observations.0203∗∗∗(.0034).0887∗∗∗(.0327)-.0109∗(.0065)(.0024).0119∗∗∗(5)-.0003∗∗∗ -.0006∗∗∗ -.0003∗∗∗ -.0008∗∗∗ -.0004∗∗∗ -.0007∗∗∗ -.0003∗∗∗ -.0007∗∗∗ -.0004∗∗∗ -.0007∗∗∗(.0001) (.0002) (.0001)(.0003)(.0001)(.0002)(.0001) (.0002) (.0001) (.0002).0546∗∗∗(.0141)

Total experience .0166∗∗∗ .0322∗∗∗ .0182∗∗∗(.0032) (.0095) (.0046)

Experience2.0292(.0870).0203(.0539).0809∗∗(.0323)

Old job.0296(.0581).0174 -.0270∗∗∗(.0187) (.0089)(.0037).0009(.0105)(4).0206∗∗∗(3)-.0044(.0059)(.0022).0008(.0067).0118∗∗∗

Emp.ten.2 × 100

Employer tenure

(2)

(1)

Under 59-year-old Large Firms (≥ 500) Small Firms (< 500) Non-Professional Regular Employee

Table A3: Earnings function estimates, using various subsamples.

Appendix D

The Biases Included in the 2SFD Estimator

In this section, we examine about the condition that the 2SFD estimators contain an
upward or downward bias.*30 What we do here is to rewrite the bias which is includedin the 2SFD estimator in a form that can be obtained from the data by modifying what
Altonji and Williams (2005) shows. In particular, we rewrite the bias from the correlation
between unobserved ability and initial experience in the current employer included in the
2SFD estimator using the correlation between employer tenure and working experience.
Topel (1991)’s equation (13) shows that the overall bias included in the 2SFD estimator is equals toE(β12SFD ) − β1 = −b1 − γW0 T (b1 + b2 ) − γW0 µ

(A-1)

where
γW0 T ≡

Cov(W0 , T )Var(W0 )(A-2)

γW 0 µ ≡Cov(W0 , µ).
Var(W0 )

(A-3)

and

b1 and b2 are the coeﬃcients of the following auxiliary regression between the unobserved
employer-match and experience and employer tenure:λij = b1 Wit + b2 Tijt + ξijt .

(A-4)

Using additional auxiliary regressions, Altonji and Williams (2005) express (A-1) by parameters that can be calculated from observed data. They specify the following auxiliary
regressions:µi = c1 Wit + c2 Tijt + ωijt ,
(A-5)
and
Tijt = d1 µi + d2 Wit + νijt .

(A-6)

Cov(µij , Wijt ) = 0,

(A-7)

Assuming thatand d1 and d2 satisfy d1 > 0 and d2 > 0, we can show thatc1 = −γW T c2 < 0,
d1 Var(µi )c2 = 2> 0,
d1 Var(µij ) + Var(νijt )
*30

(A-8)

According to Altonji and Williams (2005), the upward bias due to the correlation between tenure
and individual’s time-invariant ability, µ, is more serious than the downward bias due to the correlation
between tenure and employer-matching component, λ in the United States. They report that the diﬀerence between the AS’s IV and the 2SFD estimators due to bias from λ is −0.0015, which leads to thediﬀerence of −0.015 between returns to 10 years of employer tenure.

32)where γW T ≡ d2 = Cov(T,W
Var(W ) , since (A-7) is assumed. The numerator of (A-3) is rewrittenas
Cov(W0 , µ) = Cov(W − T, µ) = − Cov(T, µ) = −d1 Var(µ)(A-9)

The second equation comes from the assumption that Cov(µij , Wijt ) = 0 and the third
equation comes from (A-6). The denominator of (A-3) is rewritten as
Var(W0 ) = Var(W − T ) = Var(W ) − 2 Cov(W, T ) + Var(T ).

(A-10)

Then, (A-3) is rewritten as
d1 Var(µ)
Var(W ) − 2 Cov(W, T ) + Var(T )c2 [d21 Var(µij ) + Var(νijt )]=−Var(W ) − 2 Cov(W, T ) + Var(T )Var(ζ)= −c2
Var(W ) − 2 Cov(W, T ) + Var(T )γW0 µ = −(A-11)

where ζ ≡ T − E(T |W ), which is residual obtained by regressing T on W , and its
variance is equals to d21 Var(µij ) + Var(νijt ) since (A-6) is assumed. Finally, the bias in
the 2SFD estimator is rewritten as:E(β12SFD ) − β2 = − b1 − γW0 T (b1 + b2 )Var(ζ)+ c2.
Var(W ) − 2 Cov(W, T ) + Var(T )(A-12)

From JHPS/KHPS, we obtain γW0 T ≊ −.5, then the second term in this equation is positive as long as b1 + b2 > 0. We also obtain Var(ζ) ≊ 110, Var(W ) ≊120, Var(T ) ≊ 129, and Cov(W, T ) ≊ 46 from the sample, then Var(ζ)/[Var(W ) −2 Cov(W, T ) + Var(T )] ≊ .7. Since c2 is assumed to be positive in (A-8), the third termin this equation is also positive. In addition, b1 is likely to be positive as matching models
and conventional search models show (for example, Burdett, 1978; Jovanovic, 1979), thebias in 2SFD estimator could be negative, provided that −b1 + .5(b1 + b2 ) + .7c2 < 0 ⇔.5(b1 −b2 ) > .7c2 . If the correlation between employer-match component and experience,
b1 , is suﬃciently large, that is, if workers move to better matched employer through theirexperience in Japanese labor market, the 2SFD estimator might include downward bias
in Japan, rather than upward bias that Altonji and Williams (2005) concern about.

Appendix E

Results of the 2SFD with Varioius Specification

We have conduct various specification for estimating the coeﬃcient of employer tenure.
First, we try multiple ways of controlling time trend. The wage equation that have usedby Topel (1991) includes neither time trend nor time dummies since he detrends the33realwage using the wage index from Murphy and Welch (1992) before the first step ofthe estimation. However, Altonji and Williams (2005) argues that the way of controlling
time trend aﬀects the estimated returns to employer tenure.
Then, we follow them and have tried six ways of controlling time trend: (1) Sum ofyear dummies are included in the earnings function (Sum1), (2) Sum of year dummies
are included in the earnings function and year dummies are included in the second step(Sum2), (3) Year dummies are included in the first step (Dum1), (4) Year dummies areincluded in the second step as well as other control variables (Dum2), (5) Year dummies
are included in the first and second step (Dum3), and (6) The first-diﬀerence of the real
wage is detrended by year dummies before the first step (Det).
We try to allow that the first diﬀerence of real wage to depend on the first diﬀerenceof year dummies in the cases Sum1 and Sum2. For this purpose, we define an alternative
earnings function for these cases:
ln wijt = β0 + β1 Tijt + β2 Wijt + βt + eijt

(A-13)

where, like the basic earnings function defined in Section 4, eijt = µi +λij +εijt . Supposethat the coeﬃcient of the initial year of the survey is normalize to be zero (that is,β2004 = 0). Then the first-diﬀerence of this earnings function isln wijt − ln wijt−1 = B + γt + εt − εt−1

(A-14)

where B = β1 + β2 again, and γt = βt − βt−1 . We apply the OLS to equation (A-14)
and obtain B̂, and γ̂t . Thus, the second step equation becomes()∑
ln wijt − B̂Tijt +γ̂τ = β2 W 0ijt + µi + λij + εijt
(A-15)
τ ∈T

where T denotes the set of the year that individual i responds to the survey, and W 0 is
again the initial experience on the employer. We obtain β̂2 by applying the OLS to theequation (A-15), and finally, β̂1 = B̂ − β̂2 is obtained.
For the cases Dum1, Dum2, and Dum3, the earnings equation defined by (1) is used
for estimation. Dum2 is the exactlly the basic estimation that is conducted as the 2SFD
in Section 5.2. Dum1 includes year dummies in the first step and Dum3 includes year
dummies in the first step in addition to year dummies in the second step. The year
dummies in the first and second step play a diﬀerent role. Year dummies in the firststep allow the case when the first diﬀerence of the wage depends on the year-specificshock. On the other hand, year dummies in the second step control the correlation
between time and other control variables. Originally, only time-invariant variables canbe included as the control variable in the 2SFD method, but time-variant variables (e.g.,
occupation and industry an individual engage, firm size, and whether an individual isunion member) should aﬀect the initial wage in the current employer.*31 Those variable
may change over time (even if it is less frequent), and it is valid to include time dummiesin the second step when they are correlated with time.
*31

In fact, Topel (1991) also includes marital dummies and union dummies.

34

Table A4: Estimated returns to employer renure, using 2SFD.
Sum1
(1)

Sum2
(2)

Dum1
(3)

Dum2
(4)

Dum3
(5)

Det
(6)

2 years.0434(.0435).0434(.0434).0435(.0435)-.0130(.0307).0434(.0435)-.0177(.0306)

5 years.1086(.1082).1086(.1082).1088(.1082)-.0323(.0760).1086(.1082)-.0443(.0758)10 years.2171(.2155).2172(.2155).2176(.2155)-.0637(.1503).2172(.2155)-.0889(.1499)15 years.3258(.3229).3259(.3229).3265(.3229)-.0941(.2244).3259(.3229)-.1337(.2239)20 years.4344(.4316).4346(.4316).4353(.4316)-.1235(.3000).4346(.4316)-.1786(.2993)25 years.5431(.5426).5433(.5425).5443(.5425)-.1520(.3786).5433(.5425)-.2238(.3778)Observations

7824

7824

7824

7824

7824

7824

Notes: Robust standard errors are in parentheses.
∗ ∗∗, and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
This table reports the calculated wage returns to 2, 5, 10, 15, 20, and 25 years of
employer tenure using 2SFD. The model for estimation is given by the earnings function
(1).

35

Table A5: Estimated returns to employer tenure.

2 years
5 years
10 years
15 years
20 years
25 years
Years of education
Marital status
Union member
Occ/Ind code
Firm size
Regular employee
Observations

Time-invariant(1)

Changing Infrequently
(2)

All
(3)

.0033
(.0307).0085(.0760).0180(.1528).0285(.2245).0399(.3000).0523(.3786)√-.0002(.0307)-.0002(.0758).0005(.1503).0022(.2245).0048(.3001).0084(.3787)√√√-.0130(.0307)-.0323(.0760)-.0637(.1503)-.0941(.2244)-.1235(.3000)-.1520(.3786)
√
√
√
√
√
√

7959

7889

7824

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ Denote statistical significance at the 10%, 5% and 1% level, respectively.
This table rebports the calculated wage returns to 2, 5, 10, 15, 20 and 25 years of employer
tenure using the 2SFD. The model for estimation is given by earning function (1).

Also for the case Det, the earnings equation is given by (1). We first regress thereal log wage to the time dummies before the estimation to detrend the wage, and its
residual is used for the following estimation instead of using the real log wage. It is
the alternative way of detrend used by Altonji and Williams (2005) instead of using thewage index from Murphy and Welch (1992).
Other than the way of controlling time trend is the same as the estimation conductedin Section 5.2. We include quadratic term of employer tenure and working experiencein the equation, and education dummies, occupation and industry dummies, a union
member dummy, a marital status dummy, firm size dummies, and regular employee
dummy are used as control variables here.
The estimated returns to employer tenure in each cases are presented in Table A4.
These returns are substantially diﬀerent depending on the way of controlling time trend
as Altonji and Williams (2005) argue.
36

Second, we change the control variables in the second step of the estimation. Although the key for obtaining consistent estimator using the 2SFD is to drop timeinvariant covariates within an individual as well as individual fixed eﬀect in the firststep, Topel (1991) includes information about marital status, union membership andresidence of respondents as covariates in the second step, which are not ordinarily able
to be dropped in the first step. We examine how choice of control variables aﬀect theestimation results by adding the variables in order. First, we use only time-invariant
variable, years of education. Second, we add variables which change infrequently, marital status and union membership. Finally, we use all variables including occupationand industry dummies, firm size, and regular employee dummy, and this case have been
conducted in Section 5.2. Table A5 shows the estimated return to employer tenure ineach cases described above. Although all estimated returns are not significantly diﬀerent
from zero, their point estimation are diﬀerent: returns by using all variables are negative while those by using only time-invariant vairables are positive. We confirm thatthe 2SFD estimators are sensitive to the choice of control variables, whereas it has little
eﬀect on the AS’s IV estimators.

Appendix F

Replication of Toda’s Results

We have replicated the estimatimation by Toda (2008). He uses JHPS/KHPS for 2004–
2007. In addition to the individuals who respond to the survey, he also uses the information of their spouse. The sample is restricted to male of regular employee aged from 20
to 60. We use the same restriction of the data as him as possible. The earnings functionthat he have used is slightly diﬀerent from us. First, he includes no time trend variable
probably because of the short length of the data he uses. Second, he does not include
old job dummy.
Estimated coeﬃcients and returns which follow the specification of Toda (2008) using
the AS’s IV are presented in Table A6 and Table A7, respectively. Those using the 2SFD
are presented in Table A8 and Table A9, respectively. Although we try to use the same
sample as Toda, the number of observations are diﬀerent: we use 2984 observations for
estimation, whereas Toda uses 4382 observations. However, our replicated results are
qualitatively similar to his. Using the AS’s IV method leads to the higher returns towages than using the OLS. He interprets that human capital theory rather than matchingtheory well explain the results. We obtain almost the same returns to employer tenure
as his when using the 2SFD, except the case when 4th order terms of employer tenure
and working experience are included. Taking this replication and other robustness checkconducted in Section 5, we believe that we have provided more appropriate results as
we have discussed in Section 5.3.

37

38

.0158∗∗∗(.0054)-.1197∗∗∗(.0457).0018∗∗(.0008)-.0174∗∗(.0087)2984(.0098).0280∗∗∗

(5)

2984

-.0001(.0003).0085(.0180)-.1119∗(.0590)(.0266).0623∗∗

(6)

2984

.0018
(.0017)-.0013(.0013).0335(.0263)-.0010(.0036)-.0565(.2093).0537(.0347)(7)

AS’s IV

2984-.0000(.0000).0029(.0146)-.0021(.0043).0516(.0496)-.0000(.0000).0154(.0216)-.4454(.5505).0827(.0509)(8)

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The data come from the JHPS/KHPS for 2004–2007. The sample includes male regular employee, aged 20–60.
The dependent variable is the log of real hourly wages. Other covariates include an intercept, education dummies,
occupation and industry dummies, and dummies of firm size. Columns (1) to (4) denote the coeﬃcients of earnings
function (1) which is estimated by OLS, and columns (5) to (8) denote those computed using AS’s IV method.

2984

2984

Observations

2984

.0000
(.0000)-.0040(.0070)-.0001(.0023).0457(.0312)-.0000∗∗∗(.0000)(.0138)Exp.4 × 10000.0013(.0009)-.0016∗∗∗(.0006)-.0006∗∗∗(.0001)

Experience2

Exp.3 × 100.0601∗∗∗(.0139).0370∗∗∗(.0050)2984-.4682∗∗∗(.1431)(.0076).0607∗∗∗(.0033)(4)(.0009)Total experience

Emp.ten.4 × 1000

Emp.ten.3 × 100

Emp.ten.2 × 100

Employer tenure.0317∗∗∗.0173∗∗∗.0145∗∗∗

(3)

(2)

(1)

OLS

Table A6: Replication of Toda (2008), using AS’s IV method

39.0338∗∗∗(.0063).0819∗∗∗(.0145).1552∗∗∗(.0250).0290∗∗∗(.0017).0724∗∗∗(.0043).1448∗∗∗(.0086)

5 years

10 years

2984.3300∗∗∗(.0359).3014∗∗∗(.0385).2678∗∗∗(.0411).2156∗∗∗(.0394).1308∗∗∗(.0278)(.0134).0588∗∗∗

(3)

2984

.3716∗∗∗(.0391).3238∗∗∗(.0395).3015∗∗∗(.0435).2793∗∗∗(.0475).2051∗∗∗(.0409)(.0225).1039∗∗∗

(4)

2984

.6989∗∗∗(.2456).5591∗∗∗(.1965).4193∗∗∗(.1474).2796∗∗∗(.0982).1398∗∗∗(.0491)(.0196).0559∗∗∗

(5)

2984

.8581∗(.4840).7984∗∗(.4031).6827∗∗(.3200).5111∗∗(.2283).2835∗∗(.1230)(.0515).1201∗∗(6)

2984.8264∗(.4860).7644∗(.3977).6429∗∗(.3133).4699∗∗(.2326).2530∗(.1387)(.0632).1050∗(7)

AS’s IV

2984.8823∗(.4839).7740∗(.3960).6539∗∗(.3129).5152∗∗(.2381).3203∗∗(.1623).1488∗(.0844)(8)

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
This table reports the calculated wage returns to 2, 5, 10, 15, 20, and 25 years of employer tenure basedon the coeﬃcients of the corresponding columns of Table A6. Columns (1) to (4) denote the calculated
returns estimated using OLS, and columns (5) and (8) denote those obtained using AS’s IV method.

2984.3227∗∗∗(.0354).3620∗∗∗(.0215)25 years
2984.2756∗∗∗(.0349).2896∗∗∗(.0172)20 yearsObservations.2197∗∗∗(.0316).2172∗∗∗(.0129)15 years

2 years

(2)

(1)

OLS

Table A7: Estimated returns based on replication of Toda (2008), using the AS’s IV method

Table A8: Replication of Toda (2008), using 2SFD.
(1)

(2)

(3)

(4)

.0319∗∗(.0127).1310∗∗∗(.0359).1639∗∗(.0798).2341(.1437)-.0358(.0734)-.0605(.2519)-.4641(.6003).0047(.0446).1808(.2399)

1st stage
Constant
Emp.ten.2 × 100
Emp.ten.3 × 1000
Emp.ten.4 × 10000-.0227(.0302)-.1768∗∗(.0826)

Experience2 × 100
Experience3 × 1000-.3169(.3851)-.6041(1.1045).0187(.0532).0924(.3351)

Experience4 × 10000-.0066(.0352)

2nd stage
Total Experience.0135∗∗∗(.0286).1013∗∗∗(.0011).1319∗∗∗(.0010).1760∗∗∗(.0010)

Employer Tenure.0184(.0128).0297(.0374).0320(.0774).0580(.1163)

1379
3009

1378
3008

1378
3008

1378
3008

Observations
1st stage
2nd stage

Notes: Robust standard errors are in parentheses.
∗ ∗∗,and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
The data come from the JHPS/KHPS for 2004–2007. The sample includes male regular employee, aged 20–60. The dependent variable is the log of real hourly wages. Other covariates
include education dummies, occupation and industry dummies, and dummies of firm size.

40

Table A9: Estimated returns based on replication of Toda (2008), using 2SFD.
(1)

(2)

(3)

(4)

2 years.0368(.0257).0579(.0748).0617(.1557).0989(.2320)5 years.0920(.0642).1394(.1878).1456(.3947).1954(.5856)

10 years.1839(.1285).2610(.3802).25644(.8133).2745(1.2030)

15 years.2759(.1927).3646(.5813).3600(1.2579).3217(1.1843)

20 years.3679(.2569).4504(.7945).4359(1.7213).3874(2.4805)

Observations

3009

3008

3008

3008

Notes: Robust standard errors are in parentheses.
∗, ∗∗ and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% level, respectively.
This table reports the calculated wage returns to 2, 5, 10, 15, 20, and 25 years of
employer tenure using 2SFD for the replicated sample of Toda (2008).

41