Acquired Skills and Learned Abilities
Wage Dynamics of Blue-collar Workers in Internal Labor Markets*
ISS Discussion Paper Series
F-153
January 2015
Masaki Nakabayashi†
Institute of Social Science
The University of Tokyo

Abstract
Workers’ abilities are hidden information. Thus, when hiring, firms first use education asa proxy for abilities, and then learn about workers’ abilities by tracking products. If thislearning is asymmetric inside and outside major firms’ internal labor markets, the market
expects work experience and schooling to be complements for experience before workers
gain long-term employment, which hides the learning effect. Once workers gain longterm employment, the learning effect becomes evident. Furthermore, the employer learns
more quickly in the early stages of internal career, and this privately learned information
could improve the efficiency of in-house training programs.
Key words: asymmetric employer learning; cross-sectional skill distribution; longitudinal employer learning; internal labor markets.
JEL: J31; L22; M52.
* This research has been funded by a JSPS Grant-in-Aid (22243022).
†

The author is motivated and encouraged by comments from Hideshi Itoh, Michael Waldman, Susumu Cato,
Takashi Shimizu, Daiji Kawaguchi, Yuji Genda, Rosa Ferrer, Fumitoshi Moriya, Hideo Owan, Fumio Ohtake,
Masaru Sasaki, Kengo Yasui, Carol Scotese, Ryuichi Tanaka, Konosuke Odaka, Takashi Kurosaki, Norihito Abe,
Shingo Ishiguro, Chiaki Moriguchi, Naofumi Nakamura, Junichiro Ishida, Kazufumi Yugami, Shinpei Sano,
Keisuke Kawata, Keiko Yoshida, and John M. Abowd. The author also thanks the participants at the Annual
International Industrial Organization Conference 2014, the North American Winter Meeting of the Econometric Society 2014, Royal Economic Society Annual Conference 2013, Society of Labor Economists Meetings
2012, Osaka Workshop on Economics of Institutions and Organizations, Contract Theory Workshop, Kansai
Labor Workshop, Western Economic Association International Conference 2011, Southern Economic Association Meeting 2011, and at seminars held in Hitotsubashi University, Keio University, National Graduate Institutefor Policy Studies, the University of Tokyo, University of California, Irvine, Free University of Berlin, London
School of Economics and Political Science, and University of Tübingen. Corresponding address: Institute ofSocial Science, The University of Tokyo, Hongo 7-3-1, Tokyo 103-0033, Japan. E-mail: mn@iss.u-tokyo.ac.jp

1 Introduction: Warp and weft
Workers’ innate abilities and acquired skills determine their current productivity. Thus, it is efficient to correlate the wage distribution with the cross-sectional distribution of innate abilities
and acquired skills. Abilities also determine the speed and depth of future skill acquisition.
Therefore, when recruiting, employers are interested in workers’ innate abilities as well as
skills they have already acquired. However, workers’ innate abilities are generally private information when they enter the labor market and, hence, employers use a proxy to predict theseabilities. If innate abilities affect skill acquisition at school as well as productivity and skill acquisition in the workplace, educational background can be used as a proxy for abilities. Thus,
employers often use education as a signal of abilities, and not just as certificates of acquired
skills (Spence (1973); Arrow (1973); Riley (1979); Hungerford and Solon (1987); and Jaeger
and Page (1996)). Then, after workers join the labor market, employers gradually learn about
workers’ true on-the-job abilities from their products in the longitudinal dimension (Farberand Gibbons (1996)).
The cross-sectional distribution of acquired skills affects differences in current productivity. At the same time, employers learn about workers’ abilities in the longitudinal dimension.
As a result, the two dimensions can provide a mixed picture in terms of empirical results,
which have focused attention on the interaction term between years of schooling and work
experience. If skill acquisition at both school and the workplace are affected by abilities, theseacquired skills should be complements in the cross-sectional distribution, as assumed by Gibbons and Waldman (2006). Then, the interaction term between schooling and work experiencein a wage regression should have a positive coefficient. This assumption is supported by some
empirical research, such as Rubinstein and Weiss (2006) and Habermalz (2006).
However, Mincer (1974) found that this interaction term has a negative coefficient,1 which
other studies have confirmed. Following the literature on the signaling role of schooling,
Farber and Gibbons (1996) give a clear-cut prediction. Employers first use education as asignal of ability when workers join the market. Then, they learn more about these abilities
based on workers’ experience after joining the labor market. Wages increase as workers’
productivity increases owing to skill acquisition from work experience, but the signaling roleof schooling declines as employers learn about workers’ abilities. Thus, the relative impactof schooling on wage growth declines. This employer learning effect provides a non-positivecoefficient for the interaction term between schooling and work experience in a wage equationin the antilogarithmic term, and a negative coefficient in a wage equation in the logarithmic
term, as in Mincerian equations. Based on US data sets, this prediction is supported by studies
such as Altonji and Pierret (2001), Pinkston (2006), Lange (2007), and Schönberg (2007).
In summary, as we show in section 2, if the cross-sectional complementarity between
schooling and work experience dominates, then the interaction term should have a positivecoefficient. However, if the employers’ longitudinal learning effect dominates, then the coefficient should be negative. This simple point has been overlooked in the existing literature on
this topic. Of course, the reality lies somewhere between these two extremes. In the United
1

See Mincer (1974), pp. 92–93.

1

States, the complementarity is observed more strongly in the case of young workers.2 In Germany, the school system is closely linked to the apprentice system and, hence, schooling andwork experience are more complementary than in the United States (Pischke and von Wachter(2008)). Thus, not surprisingly, the employer learning effect is only weakly observed in Germany (Bauer and Haisken-DeNew (2001) and Lluis (2005)). These real-real world situations
have been recognized as mixed, without considering why they occur, though it is essential
in order to understand the diversity of firm organizations in different economies (Waldman(2013)).
Another factor that causes observations to be mixed is that learning by current and potential employers in the market is asymmetric. Current employers learn about their employees’
abilities more quickly than do outside potential employers (Schönberg (2007) and Pinkston(2009)). This implies that longer-term employment makes better employer learning possible(Mansour (2012)).
This asymmetry relates to a reality in the labor market. Employers in an industrial economy are far from uniform. Larger and more productive employers tend to manage longerterm employment and predominantly promote workers from within. Accordingly, they havea longer time to learn about their workers. Such personnel practices are called internal labormarkets. We focus on these internal labor markets, using a newly built long-term panel data setof blue-collar workers in a major manufacturing firm. Here, we examine the warps of learningand the wefts of ability and skill distribution, enabling us to decompose the cross-sectional
skill distribution of workers and the longitudinal learning by employers.
Section 2 presents the underlining theoretical framework and shows how it is transmitted
to empirical contexts. A theoretical key point is that wage determination is distorted particularly for workers upgraded to upper notches of wage ladders. This, in turn, distorts themarket expectation about workers’ skill elements. Section 2 predicts that if employer learning
is asymmetric between current and potential employers, and if skills acquired at workplaces
are sufficiently firm-specific, then, in the mid-career market, employers expect work experience and schooling to be complements for workers who have not been promoted in previous
employment and substitutes for workers who have been promoted. In other words, the market expectation of workers’ skills in the cross-sectional dimension differs before and after
workers are promoted. Therefore, assuming that job seekers in the mid-career recruiting market are dropouts of internal labor markets, our estimation framework separates labor market
experience into before and after gaining long-term employment with a major firm.
Section 3 describes the data set, which needs to be large and to contain detailed intra-firmdata to test our prediction. Thus, we build a new data set from first-hand wage records ofblue-collar workers in a Japanese ironworks. This source of data provides us with two advantages. One is that major Japanese firms upgrade the basic wages for both blue-collar andwhite-collar regular workers every year, depending on observed and predicted performance.
This means that every worker faces a test of fine-tuned promotion every year and the outcome
is recorded. Basic wages do not include bonuses, overtime compensation, or other allowances,which depend on current performance or conditions. This means they do not change during
a fiscal year after being set at the beginning of the year. Therefore, they capture the outcome
2

See Rubinstein and Weiss (2006), pp. 11–16, and Habermalz (2006), p. 130–133.

2

of the employer’s learning in the previous year, providing us with rich information about theannual promotion decisions in their wage records. The second advantage is that we can examine the wage dynamics of blue-collar workers under lighter institutional restrictions. Major
Western firms, either American or European, operate under a collective bargaining frameworkwith trade unions to determine the wages of blue-collar workers. In contrast, in Japan, unions
do not intervene in determining individual wages and, hence, the wages of blue-collar workers
are determined solely by management’s evaluation as those of white-collar workers are.
Section 4 presents our empirical results. Our findings show that schooling and shortterm work experience at younger ages are expected to be complements in the market and thatthe employer learning effect is obscured. However, the employer learning effect is strongly
evident once workers gain long-term employment at the case firm. Furthermore, once a worker
gains employment with the case firm, learning is faster in the earlier internal career stages. The
information learned in these earlier stages is used to screen employees with potential and, thus,
to become trainees of the in-house training program.

2 Theoretical framework
2.1 Skill acquisition and asymmetric employer learning
To describe the skill acquisition process under asymmetric employer learning, our approach isbased on DeVaro and Waldman (2012). The skeleton of their model was provided by Gibbons
and Waldman (1999, 2006). They captured both skill acquisition and symmetric employer
learning within a model, which had been requested by empirical works such as Ariga, Ohkusa
and Brunello (1999). Then DeVaro and Waldman (2012) introduced an asymmetric learning
environment, assuming a competitive labor market. Here, realized performance was only observable by current employers, while potential employers could only observe whether workers
had been promoted, which was the essence of Waldman (1984).
Following the model of DeVaro and Waldman (2012), let φi ∈ (φL , φH ) denote the innate
ability of worker i, i = 1, 2, . . . , n, which is a random draw from a probability density functiong(φ), with g(φ) > 0 for φ ∈ (φL , φH ), and g(φ) = 0 otherwise; let Si denote worker i’s yearsof schooling; and let Mi,t denote worker i’s employment experience until period t. Then,assume that the “on-the-job” skill of worker i, who has Si years of schooling and has Mi yearsof work experience in period t is ηi,t = (φi + bSi )f (Mi,t ) ≡ θi f (Mi,t ), where b > 0, f isincreasing in M, and f (0) > 0. All firms have homogenous production functions and eachfirm consists of job 1 and job 2. The product of worker i assigned to job j in period t is given
by(1)

yi,j,t = (1 + ki,t )(dj + cj ηi,t ) + G(Si ),where 0 < d2 < d1 , 0 < c1 < c2 , G is increasing in S, and ki,t > 0 if worker i was
employed at the same firm in period t − 1. Defining ηi,t = (φi + bSi )f (M), it is assumed that
schooling S and experience M are complements in production. This assumption is justified
if ability positively affects skill acquisition both at school and at the workplace. While Mi,t ,3

Si , f (·, ·), G(·), b, dj , cj , and ki,t are public information, yi,j,t is privately observed by thecurrent employer, and φi is privately known to worker i. We do not specify anything about
the possible correlation between φ and S, which allows S to potentially depend on φ and tofunction as a signal of φ. At the end of worker i’s first period, the current employer privately
observes yi,j,t and, thus, learns about θi . Hereafter, we assume that an increase in productivity
owing to a promotion (c2 − c1 ) and/or return on firm-specific skill k is sufficiently large suchthat k > c1 /(c2 − c1 ).
′′′Consider η = (d1 − d2 )/(c2 − c1 ) that solves d1 + c1 η = d2 + c2 η and assume that′(E[φ | S] + bS) f (0) ≡ θE (S)f (0) < η for any S, which implies that any worker is effi′
ciently assigned to job 1 in the first period. Further, assume that (φL + bS) f (1) < η <(φH + bS) f (1), which implies that some workers in their second period are efficiently assigned to job 1, while the others are assigned to job 2.
The structure of the game is as follows. At the beginning of workers’ second period, eachfirm offers each existing worker employed in the previous period a job assignment, or fires theworker. This decision is publicly observed. Then wages are determined before each period by
spot-market contracting. Observing worker i’s job assignment or discharge, employers otherthan the worker’s first-period employer offer a wage, and the worker’s first-period employer
offers a wage weakly greater than the wage offered by others. For simplicity, we assume notransaction costs and a common discount factor.
Further, letting wi,1,t denote the wage paid to worker i assigned to job 1, and wi,2,t denote
the wage paid to job 2, consider an ability level η + (S) in worker i’s second period suchthat yi,1,t − wi,1,t = yi,2,t − wi,2,t if ηi,t = η + (S); that is, profit is indifferent, regardlessof whether worker i is promoted to job 2 in his/her i’s second period. Under this setting,
DeVaro and Waldman (2012) established that there is a perfect Bayesian equilibrium suchthat, in the second period of worker i who was employed by firm A in the first period, if
ηi,t ≥ η + (Si ), then worker i remains at firm A, is assigned to job 2, and is paid wi,2,t (Si , ηi,t ) =d2 + c2 η + (Si ) + G(Si ); however, if ηi,t < η + (Si ), then worker i remains at firm A, is assigned
to job 1, and is paid wi,1,t (Si , ηi,t ) = d1 + c1 (φL + bSi ) f (1) + G(Si ).
On this equilibrium strategy, outside employers offer wages equal to the possible least
on-the-job skill given the publicly available information about job assignments at the current
employer. Then, the current employer counteroffers with a wage only weakly greater thanthat offered by the others. Offering the expected productivity as a wage, given the publicly
available information about the job assignment outcome, which is equal to or greater thanthe lowest possible productivity, cannot be an equilibrium strategy. This is because workers
whose productivity is strictly lower than such an offer would take it, and employers would
predict this adverse selection outcome.
The definition of η + , yi,1,t − wi,1,t = (1 + k) (d1 + c1 η + (Si )) − [d1 + c1 (φL + bSi f (1))] =(1 + k) (d2 + c2 η + (Si )) − (d2 + c2 η + (Si )) = yi,2,t − wi,2,t , is rearranged to(2)

η + (Si ) =k(d1 − d2 ) − c1 (φL f (1) + bSi f (1)).
k(c2 − c1 ) − c1

This is a tradeoff of employer’s benefits between promotion and non-promotion. By curbing
promotion, wage payment is constrained. However, an increase in bSf (1) pushes up the wage
4

by the rate c1 , even for job 1. Thus, an increase in bSf (1) implies a decrease in the promotion
threshold η + .
Then, consider a modified two-period setting. Now, when worker i joins the firm, worker
i + 1 is already there and has not been promoted to job 2. In the second period of worker i,which is the third period for worker i + 1, both workers i and i + 1 are promoted to job 2 if
ηi,t ≥ η + and ηi+1,t ≥ η + , respectively, and retained at job 1 otherwise. Then, we can derive alemma for the market expectation on the cross-sectional skill distribution for i = 1, 2, . . . , n.
Lemma 1. Among the on-the-job skill components, work experience is expected in the market
to be complementary to schooling for workers who have not been promoted, and substitutive
for schooling for workers who have been promoted.
Proof See Appendix I.
Lemma 1 states that, under asymmetric employer learning and a sufficiently high returnon firm-specific skill, work experience and schooling are expected in the market to be complements before workers are promoted, but substitutes once workers have been promoted. This
switch comes from the characteristics of the promotion threshold η + . The production function
equation (1) assumes that schooling and experience are complements. Thus, the promotion
threshold η + decreases in the product of schooling and experience, Sf (M). At the same time,the market can only observe the outcome of the promotion and offers a possible least productivity as a wage. This implies that wages offered for promoted workers increase in η + . It
turns out that schooling and experience are valued as substitutes when determining wages forpromoted workers. Such a distortion does not occur for non-promoted workers.
′
Threshold η is the value under symmetric learning. In other words, the difference D ≡′η + − η captures the distortion due to the asymmetry of information between the current
employer and other employers about workers’ on-the-job skills. Under assumption k >c1 /(c2 − c1 ), D > 0; that is, a less than optimal number of workers are promoted underasymmetric learning.

2.2 Skill complementarity and learning in panel estimations
Next, let us discuss how Lemma 1 can be placed within empirical contexts. Hereafter, weconsider a setting where t = M for i = 1, 2, . . . , n, and for simplicity, assume that b = 1
and f (M) = M = t. Again, let yi,t denote the output of worker i in period t (t = 1, . . . , T ),and let ηi,t denote the ith worker’s on-the-job skill in period t, which is not observable byemployers. Then, suppose that ηi,t = (φi + Si )t = θi t, where θi = φi + Si denotes theith worker’s ability, which is a time-invariant multiplier of skill acquired at the workplace.
Schooling Si and experience t are observable to employers. However, worker i’s innate ability
φi is not observable, and thus ηi,t is not observable to employers when the worker joins thelabor market, but is later learned by the employers. Further, let xi denote a vector of thetime-invariant characteristics of worker i other than years of schooling, which are observableto employers.

5Following Farber and Gibbons (1996), we assume that the conditional distribution F1 (yi,t |θi , Si , xi ) and the joint distribution F2 (θi , Si , xi ) can be arbitrary and that outputs yi,t are independently drawn from F1 (yi,t | θi , Si , xi ). We assume that all employers know F2 (θi , Si , xi )and F1 (yi,t | θi , Si , xi ) and can observe yi,1, . . . , yi,t for each worker i = 1, . . . , n. Thus, boththe current and potential employers in the market symmetrically learn about the ith employee’s
ability in the market. Furthermore, we assume that owing to competition between employers,
the wage paid to the ith worker in period t is equal to the expected output given all available
information in period t about the ith worker:
wi,t = E yi,t | Si , xi , yi,1 , . . . , yi,t−1 .

(3)We further assume that the conditional expectation E yi,t | Si , xi , yi,1 , . . . , yi,t−1 is a linear
combination of Si , xi , and yi,1 , . . . , yi,t−1.
Then, the linear projection of an n-dimensional vector w whose ith element is wi , denotedby E ∗ (w | ·), yields E ∗ (w | X) = X α̂.3 Normal equations giveα̂ = [X ′ X]−1 X ′ w,
P P
where the hth element of α̂, α̂h , is increasing in Tt=1 ni=1 xh,i wi,t − T nE(xj )E(w) =Cov(xi,h , wi,t ).
Consider an example of panel estimation of worker i’s wage at time t, wi,t ,(4)(5) wi,t = α0 + α1 Si + α2 t + α3 Si t + α4 x4,i + · · · + αj xj,i + · · · + αm xm,i + θiE (Si ) + ǫi,t ,where Si , t, and xi are observable and θiE ≡ E(φi |Si ) + Si . Then, we obtain∆t wi,t = α2 + α3 Si + ∆t θiE (S) + ∆t ǫi,t ≡ α2 + α3 Si + ϕi,t ,(6)where ∆t ǫi,t is independent of other independent variables and is also serially independent.
P
Here, α̂3 in equation (5) is increasing in Cov(Si t, wi,t ) = Tτ=2 Cov(Si τ, ϕi,τ ). In addition, Cov(Si t, wi,t ) contains a two-dimensional effect composed of the cross-sectional effectover workers i = 1, . . . , n and the longitudinal effect over periods t = 1, . . . , T . In the crosssectional dimension, for each τ (τ = 2, . . . , T ), Cov(Sτ, ϕτ ) is increasing in the degree ofcomplementarity between years of schooling (S) and years of work experience (τ ). Thus foreach period t, the covariance between ϕτ and Sτ should be positive in the cross-sectional dimension of workers i = 1, . . . , n if schooling (S) and experience (τ ) are complements for the
productivity difference (∆τ ǫ) among workers i = 1, . . . , n and non-positive otherwise.
In the longitudinal dimension, let us assume that the employers have learned about theemployees’ time-invariant abilities that were hidden when the employees were recruited, given
as φi . This is included in θi , such that ∆τ θiE (S) = ∆τ E(θi | Si , τ − 1) is decreasing in τ andlimτ →∞ ∆τ E(θi | Si , τ − 1) = 0 as θiE approaches a stationary state, which is worker i’s true
ability. Then, for each i, Cov(Si τ, ϕi ) is decreasing in τ and limτ →∞ Cov(Si τ, ϕi ) = 0.
3

Note that E ∗ (y | S, x) = E(y | S, x) because E is assumed to be linear.

6

Thus, α̂3 depends on the relative impact of the effect of the complementarity between
schooling and work experience in the cross-sectional dimension and the effect of employer
learning in the longitudinal dimension. Then, α̂3 is increasing in the relative impact of thecomplementarity effect over the employer learning effect and, fixing the complementarity
effect, αˆ3 decreases to 0 as the employer learning effect increases. In addition, suppose thatwages increase with experience t owing to skill acquisition. Then, αˆ3 also depends on therelative impact of Si t on the wage growth compared to other independent variables. Taking
the logarithmic terms, if the complementarity effect dominates the employer learning effect,then α̂3 > 0. However, if the employer learning effect dominates, then αˆ3 ≤ 0.
This reasoning differs from that of Farber and Gibbons (1996) in two regards. First, wedeal directly with the interaction term between schooling and work experience. Farber andGibbons (1996) presented a model highly tailored for the US National Longitudinal Surveyof Youth, which includes Armed Forces Qualification Test (AFQT) scores that are thought
to be correlated with innate abilities of respondents but are unknown to employers of the
respondents. Their estimation strategy is not currently applicable to other countries that do notprovide data equivalent to AFQT scores. Then, a negative coefficient of the interaction term
between schooling and work experience is a convenient indicator of the employer learning
effect. However, Farber and Gibbons (1996) only mention that it does not contradict with
their model, but do not directly inquire how it is related to employer learning. Second, we
explicitly differentiate the cross-sectional effects and longitudinal effects in the interaction
term between schooling and work experience. Farber and Gibbons (1996) emphasized that“[schooling and other observable variables] play a declining role in the market’s inference
process but have a constant estimated effect.”4 Instead, we decompose the coefficient of theinteraction term between schooling and experience into the cross-sectional dimension and thelongitudinal dimension. In the former case, our framework predicts that the estimated effect ofschooling does not change, as in Farber and Gibbons (1996). In the latter case, our framework
predicts that the estimated effect of schooling declines as work experience is acquired. We
infer that this longitudinal effect generates a non-positive coefficient for the interaction term
between schooling and work experience.

2.3 Semi-public estimation framework of employer learning
Next, we consider the internal labor market of the major firm discussed in subsection 2-1:
1) the current employer learns about workers’ abilities better than the other employers; 2)
the other employers can less correctly guess workers’ abilities from publicly available information about job assignments; 3) the return on firm-specific skills is positive, and, therefore
the current employer produces more by hiring current workers in the next period than other
employers do; and 4) the current employer faces a competitive market composed of other
employers.
Then, in the next period, the firm that currently employs a worker offers wages weakly
greater than those offered by other employers, and the current employee does not leave on theequilibrium path. Here, we can assume that the current employer of worker i knows F1 (yi,t |4

Farber and Gibbons (1996), p. 1014.

7θi , Si , xi ) and F2 (θi , Si , xi ) for i = 1, . . . , n and t = 1, . . . , T , and that the firm observes
yi,1 , . . . , yi,t . That is, wage growth depends on the current employer’s learning with arbitrage
with the outside market, where worker i’s ability is signaled by her/his job assignment. The
competitive environment guarantees that wi,t = lE(yi,t | Si , xi , yi,1, . . . , yi,t−1 ), where l ≤1, which captures the efficiency loss due to asymmetric learning in internal labor markets.
While employees’ abilities are learned within the internal labor market, F1 (yi,t | θi , Si , xi )and F2 (θi , Si , xi ) for the current employees, for i = 1, . . . , n, remain only imperfectly known
to outside employers by job assignment. We refer to these properties as semi-public, which
is public in the sense that the current employers face a competitive market and wages are
determined by spot-contracting, but is “semi” in the sense that the wages are affected by theasymmetry of employer learning.
Lemma 1 argues that the mid-career recruiting market expects workers who have notbeen promoted by previous employers to have acquired work experience complementary toschooling. On the equilibrium path, workers do not leave their first-period employers. If
a worker leaves his/her first-period employer, this is when the worker’s belief and his/her
employer’s belief may not be consistent, in which case the worker is not satisfied by the
job assignment outcome. That is, this occurs when a worker believe that he/she should bepromoted, but is not promoted. Thus, workers in the mid-career recruiting market are likely
to be those who have not been promoted. In other words, schooling and work experience
are expected to be complements for workers seeking employment in the mid-career recruiting
market. On the other hand, the market expects workers who have been promoted to haveacquired work experience that is substitutive for schooling. This belief, shared by employers,
turns out to reduce workers’ opportunity cost of time to acquire firm-specific skills, which are
likely to be less complementary to schooling.
To capture this effect of internal labor markets, we separate the ith employee’s experience
into two components, such that t ≡ te and tT = tp + te . Here, tT is total labor market experience, tp is labor market experience prior to joining the case firm, and te denotes tenure after
being employed by this firm. Then, assuming that β = lα, wage equation (4) is reformulated
as(7)

wi,t = β0 + β1 Si + β2 tpi + β3 tei,t + β4 Si tpi + β5 Si tei,t + γ ′ xi + δ ′ xi tei,t + θi + ǫi,t .

Lemma 1 concerns an implication for the cross-sectional distribution. Schooling andwork experience are expected to be complements for non-promoted workers who have left
short-term employment for the mid-career market, which is presumed to be captured by tpi .
Standardizing such that t takes 0 when tei,t = 0, Stpi captures a summary of the employer
learning process until worker i gains long-term employment at tei,t = 0 after he/she entered thelabor market if he/she did not gain long-term employment immediately after graduation andleft former employers. At the same time, for worker i whose tei,t > 0 after gaining long-term
employment, he/she has started to step up promotion ladder in a internal. Then, his/her schooling and work experience are expected to be substitutes as those for already promoted workers,
which is presumed to be captured by Si tei,t . Then, combining Lemma 1 with the characteristicsof the panel estimation discussed above, a prediction about the market’s expectation formedby employer learning, as well as about skill distribution is as follows.
8

Prediction 1. If employer learning is asymmetric between current and potential employers
and the return on firm-specific skill is sufficiently large, then the coefficient of the interaction
term between years of schooling and previous labor market experience before gaining employment with a firm that commits to long-term employment (Stp ) is greater than that of theinteraction term between years of schooling and tenure after gaining employment with the firm
(Ste ); thus, βˆ4 > βˆ5 .

3 Case firm and data
3.1 Case plant
The case plant is one of the oldest modern ironworks in Japan. As a part of a companywide investment plan from the 1950s to the 1960s, the company that operated the ironworks
decided to build a new state-of-the-art plant in a city far from the original plant. The plan was
to decrease the capacity of the original ironworks, and to relocate skilled workers of the caseironworks and other old ironworks to the new plants. The selection for relocation was handledin cooperation with the union, and in principle, anyone willing to move was allowed to be
relocated.

3.2 Data
This research uses preserved personnel documents for 1,558 blue-collar employees who wererelocated from the ironworks, tracking them from the late 1920s or later, depending on theyear when the employee joined the ironworks, to the 1960s, when they left the ironworks.
Owing to the relocation process where anyone who wanted was allowed to be relocated, apossible sample selection bias can be assumed to be small. However, an attrition bias is inevitable, since the sample includes only employees who worked for the ironworks in the late1960s, at which time the sample period ends. Thus, the sample does not include employees
who left the ironworks before the late 1960s, the time of relocation. It means that the sample
does not include dropouts. Since the firm does not preserve wage records of such dropouts,
we cannot statistically correct the bias. However, this bias is not necessarily serious to our
specific context. Our framework separates previous work experience and tenure at the ironworks, and, for tenure, we only deal with employees who continue to serve on the equilibrium
path. All sample employees are Japanese males. The documents contain all important employee information from the time of recruiting, such as physiological characteristics when
hired, educational background, and basic wage upgrades every year. Recorded wages are basic wages, which were upgraded annually and did not change through the year. Thus, theycaptures the notch at which the employee was placed in a finely designed promotion ladder ineach year. Basic wages do not include bonuses, overtime compensation or other allowances,which depend on current performance or effort. Instead, they capture predictions about theemployee’s ability, which was upgraded every year based on the previous year’s learning by
the employer. Definitions and descriptive statistics of the variables used are in Appendix III.
The total number of observations is 23,120.
9

There are three noteworthy characteristics of the data set. First, different from Western
manufacturing firms, individual wage determination is not affected by negotiations with theunion. In Japanese manufacturing, enterprise unions rather than trade unions are dominant. In
addition, in collective bargaining between management and the enterprise union, they discuss
only the average wage of the firm such that a productivity increase be distributed to the laboras well, but only on average. Unions do not intervene in individual performance evaluations.
Thus, we can extract less noisy information from blue-collar workers’ wages that we could
from white-collar workers’ wages. Second, as a custom of Japanese firms, all regular employees are eligible for a possible upgrade to their basic wages every year. Thus, focusing
on basic wages in the data set means that we can track records of finely tuned promotions.
Third, the data set is not dominated by those who were employed immediately after graduation. The mean of previous labor market experience (years after graduating from school andbefore employment with the firm, tp ≡ PreExperience) did not decrease through the sample
period. Workers had on average three to eight years of previous labor market experience, often
at smaller workplaces, through the sample period.5 During the early twentieth century, whenheavy manufacturing was introduced from the Western world, the typical career pattern formale skilled workers involved gaining experience at several workplaces to acquire relevant
skills and then either gaining employment with a large firm on a long-term basis or starting
one’s own workshop.
Compulsory education was extended from six years to nine years in 1947. Therefore, thedifference in educational background across employees who graduated before 1947 is distributed mainly between those with six years of schooling, who attended mandatory elementary schools, and those with eight years of schooling, who attended an additional two-year highelementary school. Here, high elementary school graduates are the majority. The difference
for graduates after 1947 is distributed mainly between those who spent nine mandatory years
attending a six-year elementary school and a three-year junior high school, and those who
spent twelve years attending an additional three-year high school, with junior high school
graduates as the majority.

3.3 Learning within an internal labor market
The existence of an internal labor market, which “shields” wage determination from the outside market by asymmetric employer learning, is to be empirically established. Persistentcohort effects are thought to be an indicator of the shielding effect of internal labor markets (Baker, Gibbs and Holmstrom (1994)). The market environment would be fully reflected only at entry. Following that, internal wage dynamics would be shielded from themarket if there exists an internal labor market in the manner discussed in Lemma 1. Table 1 regresses real wages as a logarithmic expression (log (wi,t )) on the interaction terms ofthe two-year-joined dummy variables (Yearjoined19XX−YY), which takes 1 if worker i joinedi· log (wi,t−1 ),the ironworks in 19XX or 19YY, and the first-lagged terms (Yearjoined1928−29i
1930−31
Yearjoinedi· log (wi,t−1 ), etc.), controlling for years of schooling (S ≡ Schooli ), years
of total experience in the labor market (tT ≡ TotExperiencei,t ), tenure at the ironworks
5

See Nakabayashi (2013), Table 1.

10

(te ≡ Tenurei,t ), their squared terms, and growth in the real gross national product as a representative variable of exogenous shocks. Then, for all cohorts, cohort effects are significant.
Furthermore, significant non-parallel wage curves are observed, even between adjacent cohorts. This indicates that the cohort effects should be considered when examining Prediction
1.
INSERT Table 1 HERE

4 Empirical results
4.1 Standard test of employer learning
Before estimating equation (7), we describe the benchmark results for equation (5). Table 2 gives the results of the random effect estimation regressing the logarithm of the real
wages (log (wi,t )) on relative height when employed by the firm (Heighti );6 years of schooling (Schooli ); total experience in the labor market (tTi,t = TotExperiencei,t ); tenure at thefirm (tei,t = Tenurei,t ), their squared terms; the interaction term between relative height andtotal labor market experience (Heighti · TotExperiencei,t ), the interaction between relative
height and tenure (Heighti · Tenurei,t ); the interaction between years of schooling and totallabor market experience (Schooli · TotExperiencei,t ); the interaction between years of schooling and tenure (Schooli · Tenurei,t ); the dummy variables for completing in-house training
programs, namely the Development Center for Youth (Training1927−35, operated in 1927–35),
i,tSchool of Youth (Training1935−48,
operatedin
1935–48),Development
Center for Techniciansi,t1935−46(Trainingi,t, operated in 1939–46), and Development Center (Training1946−73, operated
i,t
in 1946–73), which takes 1 when and after worker i completes a program; and the interactionof these dummy variables with tenure (Training1927−35· Tenure, Training1935−48· Tenurei,t ,
i,ti,t1935−46
1946−73
7
Trainingi,t· Tenurei,t , Trainingi,t· Tenurei,t ). We control for the potential impact
of extended compulsory schooling using the postwar-education generation dummy variable(Postwari ), which takes 1 if worker 1 is twelve years or older in 1947, when the US-led
education reform was implemented.
INSERT Table 2 HEREIn Table 2, the coefficient of tenure (Tenurei,t ), controlling for total labor market experience (TotExperiencei,t ), implies that the return on firm-specific skill is considerable.
Then, the interaction of years of schooling with total labor market experience after graduation(Schooli · TotExperiencei,t ) has significant negative coefficient in specifications 2-1 and 2-3,
as does the interaction of years of schooling with tenure (Schooli · Tenurei,t ) in specifications
2-2 and 2-4. The employer learning effect is clearly observed.
6

To control for improved nutrition throughout the period, we use relative as compared to the national average height, provided by the Ministry of Education’s statistics for estimation. Thus, (employee i’s observedheight)/(national average height at employee i’s age in the year of i’s joining) is used as i’s “height (Heighti ).”7
The information on height, weight, and lung capacity is not included in the wage records of the employees
who joined the firm before 1939.

11

Along with years of schooling, proxies for abilities observable to the employer are physiological characteristics, such as height. Physical strength was important for blue-collar workers, and height is a good proxy of such physical strength. Indeed, with regard to height, theemployer learning effect is observed. The interaction terms of relative height with both total labor market experience and with tenure (Heighti · TotExperiencei,t , Heighti · Tenurei,t ,respectively) have negative coefficients in specifications 2-3 and 2-4.

4.2 Learned abilities and acquired skills in the internal labor market
Next, we examine equation (7) and Prediction 1. A straightforward specification without
control for the cohort effect by the random effect estimation is presented in specifications 3-1
and 3-2 in Table 3. After controlling for the changes in return on schooling using the interaction term between the year dummy variables and years of schooling (Year19XX · Schooli ),specification 3-1 regresses the logarithm of real wages (log (wi,t )) on years of schooling(Schooli ), labor market experience after graduation and before employment with the firm (tpi =PreExperiencei ), tenure after employment with the firm (Tenurei,t ), their squared terms,
the interaction between years of schooling and previous labor market experience (Schooli ·PreExperiencei ), and the interaction between years of schooling and tenure (Schooli ·Tenurei ).
Then, the interaction between years of schooling and previous labor market experience (Schooli ·PreExperiencei ) has a strictly greater coefficient than that between years of schooling andtenure (Schooli · Tenurei,t ) has, implying that Prediction 1 holds: β̂4 > β̂5 .
Specification 3-2, in addition to specification 3-1, controls for marginal decreases in the
returns on previous labor market experience and tenure in their interactions with years ofschooling (Schooli · PreExperience2i , School · Tenure2 ). Then, the interaction between yearsof schooling and previous labor market experience (Schooli · PreExperiencei ) has a positivecoefficient and the interaction between years of schooling and tenure (Schooli · Tenurei,t ) has
a negative coefficient. Hence, Prediction 1 holds: β̂4 > β̂5 .
Specifications 3-3 and 3-4, in addition to specifications 3-1 and 3-2 respectively, control
for cohort effects by inserting interactions between the two-year-joined dummy variables and·Schooli , etc.) as regressors.
·Schooli , Yearjoined1932−33
years of schooling (Yearjoined1930−31ii
In specification 3-3, as in specification 3-1, both the interactions of years of schooling with previous labor market experience and with tenure (Schooli · PreExperiencei , Schooli · Tenurei,t ,respectively) have negative coefficients. However, the former is strictly greater than the latter.
In specification 3-4, as in specification 3-2, the former has a significant positive coefficientand the latter has a significant negative coefficient. Thus, Prediction 1 holds: β̂4 > β̂5 .
INSERT Table 3 HERE

Non-parallel wage curves in Table 1 suggest the necessity to control for different effectsof learning in different cohorts when checking the robustness of the results in Table 3. Thus,
Table 4 regresses the logarithm of real wages (log (wi,t )) on years of schooling (Schooli ); previous labor market experience (PreExperiencei ); tenure (Tenurei,t ); their squared terms, and,motivated by Table 1, the interaction terms of the two-year-joined dummy variables, years ofschooling, and previous labor market experience (Yearjoined1936−37·Schooli ·PreExperiencei ,Yeearjoined19ii
12

Schooli · PreExperiencei , etc.), and the interaction of the two-year-joined dummy variables,
years of schooling, and tenure (Yearjoined1936−37· Schooli · Tenurei , Yearjoined1938−39·iiSchooli · Tenurei , etc.) to control for the cohort effects on learning. Possible marginal decreases in the interaction terms of previous labor market experience and tenure with years ofschooling are controlled for by the interaction of their squared terms with years of schooling (Schooli · PreExperience2i , Schooli · Tenure2i,t ) in specification 4-1 and by the interaction of their squared terms with squared years of schooling (School2i · PreExperience2i ,School2i · Tenure2i,t ) in specification 4-2. In addition, changes in the return on schooling overtime are controlled for using the interaction between the year dummy variable and years ofschooling (Year19XX · Schooli ). Since cohorts that contain two or more employees who had
acquired positive previous labor market experience include only those who joined in 1934 orlater, the sample cohorts are restricted to this period, and the control two-year-joined dummy
variable is Yearjoinedi1934−35 . Then with the exception of the only nonsignificant cohort 1936–
37 in specification 4-1 and of those 1936–37, 1938-39, and 1940-1941 in specification 4-2, theinteractions years of schooling with previous labor market experience in all significant cohorts
have positive positive coefficients and the interactions with tenure in all cohorts have negative
coefficients. Therefore, we still have β̂4 > β̂5 and Prediction 1 holds, even after controllingfor different learning curves in different cohorts.
INSERT Table 4 HERE
While the regression of wages on the interaction term between years of schooling andtotal labor market experience (Schooli · TotExperiencei,t ) in specifications 2-1 and 2-3 inTable 2 suggests that the employer learning hypothesis holds, the results in Table 3 indicate that the effect should be divided into before and after gaining employment with the firm
(Schooli · PreExperiencei , Schooli · Tenurei,t ). In the mid-career recruiting market, workers
were expected to have experience complementary to their schooling before gaining employment with the firm. After gaining employment with the firm, the complementarity was lessvalued and the employer learning process was more strongly observed. While the learning
process differs in different cohorts, as shown in Table 4, the same tendency is still obvious
after controlling for the difference due to cohort effects.
Table 4 also shows that the absolute value of the negative coefficient of the interaction
between years of schooling and tenure (Schooli · Tenurei,t ) increases as the cohort nears theend of the covered period. Since the marginally decreasing return in a better match in thelabor market or that in investment in firm-specific skill is captured by the interaction term
between years of schooling and tenure squared (Schooli · Tenure2i,t ) in specification 4-1 andby that between squared years of schooling and tenure squared (School2i · Tenure2i,t ), the result
is thought to come from the learning process. The greater absolute value of the negative
coefficients for cohorts closer to the end suggest that the employer learning effect had a larger
impact in the earlier tenure in the internal labor markets. Faster learning in the earlier career
stages have been reported for the United States and Germany as well (Lluis (2005); Gibbons,Katz, Lemieux and Parent (2005) and Lange (2007)).

13

4.3 Employer learning for better trainee selection
Employers statistically discriminate when hiring. Then having hired, they begin to privately
learn about employees’ abilities and assign them to notches in the basic wage ladder based on
their own private learning and employees’ skill acquisition in the previous period. This is theprimary channel of employers’ learning and employees’ skill acquisition. Both employers’
learning and employees’ skill acquisition are factored in when upgrading basic wages, but do
not directly interact with each other.
There is another channel, in which learning might directly affect skill acquisition: In-housetraining programs in which decisions on who acquires what skills is made by the employer, notthe employees. If, when making a decision on trainee selection, an employers uses employee
information that he/she has learned privately since hiring, the in-house training program might
improve efficiency by more than if selection was based only on information available in themarket. If the employer does not use information he/she learned privately, internal training
programs supplied by the employer would not outperform human resource allocations attainedby the market. Thus, we next focus on in-house training programs provided by the case firm.
In the sample period, the firm operated four consecutive programs: The Development
Center for Youth operated from 1927 to 1935 (Training1927−35 );the School for Youth operated
from 1935 to 1948 (Training1935−48 ); the Development Center for Technicians operated from
1939 to 1946 (Training1939−46 ); and the Development Center operated from 1946 to 1973
(Training1946−73 ).
Regulations behind the programs differed before and after the education reform in 1947.
From 1926 to 1935, the government requested that major firms have a Development Center for Youth (Training1927−35 ). In 1935, the program was extended to a School for Youth(Training1935−48 ). From 1939, major firms were required to have a School for Youth (Training1935−48 ).
Before 1947, secondary schooling was not mandatory, and the Development Center for Youth(Training1927−35 ) and School for Youth (Training1935−48 t) were designed to complement shorter
schooling. The Development Center for Technicians (Training1935−48 ) was not required bylaw and was operated according to the firm’s own training plan.
The regulatory requirement was abandoned when junior high school became compulsory
in 1947 and the School for Youth (Training1935−48 ) was abolished. The firm’s original Development Center for Technicians (Training1939−46 ) program was reorganized as the Development Center (Training1946−73 ).
The Development Center for Youth (Training1927−35 ) and School for Youth (Training1935−48 )offered a program of three days a week for four years, 800 hours in total. The Development
Center for Technicians (Training1939−46 ) offered a full-time program for three years, 6,453
hours in total. The Development Center (Training194673 ) offered a program of three days aweek before 1950, and six days a week from 1950, for two years. From 1963, only highschool graduates were admitted as trainees.
Table 5 presents the estimated probabilities of acceptance to the in-house training programs, namely the School for Youth (Training1935−48 ), the Development Center for Technicians (Training1939−46 ), and the Development Center (Training1946−73 ), given age (Age),years of schooling (School), previous labor market experience (PreExperience), and their14

squared terms. We assume that cohorts who joined the firm two years before introductionof a new program or later and until the year when the program was amended or abandoned
were eligible to apply for the new program. Then, the sample period is defined as the one
during which the relevant program was operated and the sample cohorts are defined as those
who joined the firm from two years before the introduction of the relevant program to the year
194673
when the program ended. For the Development Center (Trainingdc), since high school
graduation became an explicit condition to be accepted as a trainee from 1963, the sample
period and cohorts are defined as being until 1962. For the earliest program, the Development
Center for Youth from 1927 to 1935, the data set does not include sufficient cross-sections.
INSERT Table 5 HERE
For schooling, the results are opposite for the School for Youth (Training1935−48 ) and forthe Development Center (Training1946−73 ). In the former case, as required by regulations,employees with less schooling were more likely to be accepted. In the latter case, better
educated employees were more likely to be accepted.
Next, we examine whether information learned privately by the employer was used fortrainee selection in the post-1947 program, which was not motivated by the government
regulations. In Table 6, specification 6-1, as a benchmark regresses the logarithm of thereal wage (log (wi,t))) on tenure (Tenurei,t ), its squared term, the interaction term of yearsof schooling, previous labor market experience, the Development Center dummy variable(Schooli · PreExperiencei · Training1946−73), and the interaction term of years of schooling,i,ttenure, and the Development Center dummy variable (Schooli · Tenurei,t · Training1946−73).
i,tThen, specification 6-2, as an inquiry on learning in trainee selection, regresses the logarithm of the real wage (log (wi,t ))) on tenure (Tenurei,t ), its squared term, the interaction
term of years of schooling, previous labor market experience, and the probability of being accepted by Development Center estimated by specification 5-3 in Table 5 (Schooli ·PreExperiencei · E[Training1946−73 ]), and the interaction term of years of schooling, previous labor market experience, and the estimated probability of being accepted by Development
Center (Schooli · Tenurei,t · E[Training1946−73]). We also control for the Development Centeri1946−73
dummy variable (Trainingi,t), its interaction with tenure (Training1946−73· Tenurei,t ) ini,t
specification 6-1, and the estimated probability of being accepted by the Development Center(E[Training1946−73 ]), its interaction with tenure (E[Training 1946−73 ] · Tenurei,t ) in specification 6-2. We also control for the interactions of years of schooling with the year dummy
variable (Schooli · Year19XX ) in both specifications.
INSERT Table 6 HEREFirst in specification 6-1, the benchmark specification, the coefficient of Schooli ·PreExperiencei ·Training1946−73
is positive, while that of Schooli ·Tenurei,t ·Training1946−73
is negative, whichi,ti,tis consistent with Prediction 1, β̂4 > β̂5 .
Next, in specification 6-2, after inserting the estimated E[Training1946−73 ] for the observed
Training1946−73, the coefficient of Schooli · PreExperience i · E[Training1946−73 ] is negative,i,t15

while that of Schooli · Tenurei,t · E[Training 1946−73 ] is positive, which contradicts the theoretical prediction. Furthermore, in specification 6-4, after controlling for marginal decreases
in the interactions of tenure and previous work experience with years of schooling by theirsquared terms, the coefficients of both Schooli · PreExperiencei · E[Training1946−73 ] andSchooli · Tenurei,t · E[Training 1946−73 ] are negative. That is, the employer learning effectis mostly absorbed by the expected probability of being accepted as trainees.
This result indicates that the firm utilized information learned privately after hiring whenselecting trainees and, hence, on average, the trainee selection process absorbs the employer
learning effect, which would have appeared otherwise. Thus, overall, we can see that the inhouse training program capitalized on information learned privately inside the internal labormarket and, in this sense, likely improved efficiency. The information about abilities learned
faster in earlier career stages was exploited efficiently for better training.

5 Discussion: A source of the mixed picture
We conjectured theoretically that, in the market, young workers are expected to have work experience complementary to schooling in the cross-sectional dimension. This complementarityof acquired skills in the cross-sectional distribution could hide the employer learning effect in
the longitudinal dimension.
Then, we have empirically shown that the employer learning effect in the longitudinal
dimension is dominated by the cross-sectional complementarity expectation and is hidden
for previous labor market experience before workers gained long-term employment with thecase firm. We then showed that the employer learning effect is clearly observed once theygained long-term employment. At the same time, the employer learning effect is more weakly
observed in the latter stages of workers’ internal careers. Furthermore, the case firm drew on
information learned privately in the earlier internal career stages to screen potentially morecompetent employees as trainees for their in-house training program.
While this research addresses a Japanese experience, we believe that our results have relevance to labor markets in other developed economies. For example, the complementarity
effect between schooling and work experience is also reported for young US workers in asimilar to our results (Habermalz (2006)). Then, recent empirical research found that internal
labor markets are still a widely used incentive device in the United States (Ben-Ner, Kongand Lluis (2012)). Given these related findings, internal labor markets that affect both thedirection of workers’ skill acquisition and the speed of employers’ learning still seem to beprevalent in developed economies. In addition, and the diversity of their forms might explain
the puzzling heterogeneity of workers’ skill acquisition and employers’ learning among developed economies. For instance, the schooling and training system in Germany (Pischke andvon Wachter (2008)) might explain a puzzling result of employer learning observed in intrafirm wage dynamics in the country (Lluis (2005)). Our study suggest a viewpoint for further
comparative studies on such diversity of firm organizations.

16

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Appendix I: Proof
Proof of Lemma 1. For worker i + 1 who is promoted in his/her third period, we have
wi+1,2,t (Si+1 , ηi+1,t ) = d2 + c2

k(d1 − d2 ) − c1 (φL f (2) + bSi+1 f (2))
+ G(Si+1 ),k(c2 − c1 ) − c1

wi+1,2,t (Si+1 , ηi+1,t ) − wi,2,t (Si , ηi,t )c1 c2 (bSi+1 f (2) − bSi f (1)) c1 c2 φL (f (2) − f (1))−
+ G(Si+1 ) − G(Si ).
=−k(c2 − c1 ) − c1k(c2 − c1 ) − c1
For worker i + 1 who is not promoted in his/her second or third period, we have
wi+1,1,t (Si+1 , ηi+1,t ) = d1 + c1 (φL + bSi+1 )f (2) + G(Si+1 ),
wi+1,1,t (Si+1 , ηi+1,t ) − wi,1,t (Si , ηi,t )=c1 (bSi+1 f (2) − bSi f (1)) + c1 φL (f (2) − f (1)) + G(Si+1 ) − G(Si ).
Suppose that Si+1 > Si . The term (bSi+1 f (2) − bSi f (1)) has a positive multiplier if work
experience and schooling are complements and a negative multiplier if they are substitutes
in the cross-sectional dimension i = 1, 2, . . . , n. Since k > c1 /(c2 − c1 ), c1 > 0 >−c1 c2 / [k(c2 − c1 ) − c1 ], which implies that work experience and schooling are expected tobe complements for non-promoted workers and substitutes for promoted workers.

Appendix II: Data sources
Wages and workers’ characteristics

Original wage records of the case firm in Japan.

19Series of national data Consumer prices (to deflate nominal wages): Nippon Tokei Kyokai(Japan Statistical Association), ed (1988), p.362. National average height: the School Health
Statistics surveyed by the Ministry of Education, Science, Sports and Culture (http://www.estat.go.jp/). Real gross national product: Ohkawa, Takamatsu and Yamamoto (1974), pp. 232(1885-1929) – 233 (1930–70); to connect series before and after 1955, when governmental
statistics are not continuous, a deflator from Ohkawa, Noda, Takamatsu, Yamada, Kumazaki,
Shinomiya and Minami (1967), p. 134, is used.

20

Appendix III Definition and descriptive statistics of variables.
Variable

Kurtosis

Numberofobservations

2.447566.7437

23,1200.0406-0.47506.6180

16,63713.0000
5.00008.1126
1.61940.3644
1.18812.54974.335623,12023,1201.00000.00000.3846

1.66153.760623,12042.0000

0.00008.53400.31592.520523,12035.0000

0.00005.1436

0.76893.439323,12037.7500

0.00006.93910.61562.751523,1201.00000.00000.030832.3714 1,048.9100

23,120Standard
Skewness
deviation

MeanMedian Maximum Minimum

3.57823.370072.0600

0.34001.96500.99571.00001.10000.800030.5638 30.0000
8.7093 8.0000

55.0000
15.0000

0.18050.000015.8309 15.0000
TotExperience Years of total labor market experience: AgeSchool).
Years of previous labor market experience prior joining the firm:
PreExperience AgeSchool+Tenure. Every sample employee had worked at
6.3631 6.0000
the firm until the last year of his record.
10.0591 9.0000
TenureTenure: (years after employed by the firm).
=1
ifcompleted
Development
Centerfor
Youth(operatedfrom
1927
0.0010 0.0000
Training1927 35
to 1935), and 0 otherwise.

w
HeightAge
SchoolPostwarDefinition
Real daily wage: yen per day.
Relative height when employed by the firm: (observedheight)/(national average height at his age in the year).
Age.
Years of schooling.
Postwar education generation dummy variable: =1 if 12 years old or
younger in 1947, and 0 otherwise.

Training1935 48=1 if completed School for Youth (operated from 1935 to 1948), and0 otherwise.

0.04190.00001.00000.00000.20044.572021.9034

23,120Training1939 46=1 if completed Development Center for Technician (operated from
1939 to 1946).

0.05130.00001.00000.00000.22054.070017.5646

23,120Training1946 73=1 if completed Development Center (operated from 1946 to 1973),
and 0 otherwise.

0.12570.00001.00000.00000.33162.2577

6.097023,120

Yearjoined19XX Y

2-year-joined dummy variable: =1 if joined the firm from 19XX to
19YY(=19XX+1), and 0 otherwise.

Year dummy variable: =1 if the year is 19XX, and 0 otherwise.
Year19XX
GNP
Real gross national product.
Sources : See Appendix II.

Table 1 Cohort effect on wage curves.

TotExperiencei , t 2
Tenurei , t
Tenurei , t 2

1 1
panel extended generalized least squares
log(w i , t )random effectpooled (no year dummies inserted)coefficientt statistic-0.0781-2.2423 **0.03585.0124 ***-0.0015-4.0319 ***0.011215.7277 ******-0.0001-7.8801
0.012513.2765 ******0.000411.3815

Yearjoined1930 31i ･log(w i , t 1)

0.435915.0252***0.475532.3269***

0.505342.7458***

0.521857.3005***

0.565092.1537***

0.5815102.6212***

0.601797.8593***0.625390.2239***0.664282.7922***0.6853168.9371***

0.7132134.0633***

0.748868.2213***0.774685.3240***0.7629152.6817***

0.7967107.5379***

0.803677.0475***

0.821966.1291***0.853257.0154***0.8847
Yes

28.1190***

Estimation method
Dependent variable
Cross-section
Period (year)
Independent variables
Constant
Schooli
Schooli 2
TotExperiencei , t

Yearjoined1932 33i ･log(w i , t  1)

Yearjoined1934 35i ･log(w i , t  1)
Yearjoined1936 37i ･log(w i , t  1)
Yearjoined1938 39i ･log(w i , t  1)
Yearjoined1940 41i ･log(w i , t  1)
Yearjoined1942 43i ･log(w i , t  1)
Yearjoined1944 45i ･log(w i , t  1)
Yearjoined1946 47i ･log(w i , t  1)
Yearjoined1948 49i ･log(w i , t  1)

Yearjoined1950 51i ･log(w i , t  1)
Yearjoined1952 53i ･log(w i , t  1)
Yearjoined1954 55i ･log(w i , t  1)
Yearjoined1956 57i ･log(w i , t  1)
Yearjoined1958 59i ･log(w i , t  1)
Yearjoined1960 61i ･log(w i , t  1)
Yearjoined1962 63i ･log(w i , t  1)
Yearjoined1964 65i ･log(w i , t  1)
Yearjoined1966 67i ･log(w i , t  1)
ΔGNP
cross-sections included
periods included (years)
included observations
adjusted R2
F statistic

1,555

40 (1930 69)

21,5620.8936
6,962.4719 ***Notes : The control cohort dummy variable is Yearjoined1928 1929. *** and **respectively denote significance at the 1- and 5-percent levels.

Table 2 Skill elements and employer learning effect in wage determination.
2 2
2 3
2 4
2 1
Estimation method
panel extended generalized least squares
log(w i , t )Dependent variable
Cross-section
random effect
Period (year)
pooled (no year dummies inserted)
Independent variables
coefficient t statisticcoefficient t statisticcoefficient t statisticcoefficient t statistic
Constant-1.3797 -17.6256 *** -1.0374 -13.7473 *** -8.2014 -11.2220 *** -7.9041 -10.3975 ***Heighti
12.3992
8.5047 *** 13.2281
8.7190 ***
***
***
2
-5.4457-7.4297-6.1167-8.0237
HeigtiSchooli
0.1904 12.3740 ***0.13959.1231 ***0.16178.9997 ***0.08684.8363 ***
***
***
***
2
-0.0064-8.5673-0.0050-6.5236-0.0051-5.8399-0.0024-2.7609 ***Schooli
***
***
***
***
Postwari
0.4703 57.5718
0.4937 60.3669
0.4932 62.4583
0.5166 64.0350
TotExperiencei , t
0.0587 30.7057 ***0.0412 35.8644 ***0.1274 20.6904 ***0.0296 25.5080 ***
***
***
***
***
2
-0.0003-8.7299-0.0002-6.7225-0.0002-6.9956-0.0002-5.6679
TotExperiencei , t
Tenurei , t
0.0870 77.4515 ***0.0922 46.6436 ***0.1356 103.5312 ***0.2114 28.8327 ***
***
***
***
***
2
-0.0015 -37.4222-0.0015 -36.9969-0.0030 -54.7404-0.0030 -54.5433
Tenurei , t
Heighti ･TotExperiencei , t-0.0018 -11.5768 ***-0.0759 -12.3038 ***Heighti ･Tenurei , t-0.0616-8.6816 ******Schooli ･TotExperiencei , t-0.0024 -16.2488
Schooli ･Tenurei , t-0.0006-3.1841 ***-0.0016-9.2743 *********-0.8494-5.0896-0.8338-4.9526
Training1927 35i , t****
1927 35
0.02212.4901
0.02122.3904Training
i , t ･Tenurei , t******-0.1644-7.6893-0.1707-7.8796
Training1935 48i , t******
0.00755.64220.00765.7226
Training1935 48i , t ･Tenurei , t******-0.2251 -11.2331-0.2305 -11.3440
Training1939 46i , t******
0.01078.62920.01098.7899Training1939 46i , t ･Tenurei , t******
0.1539 13.0095
0.1372 11.5120
Training1946 73i , t******-0.0067-6.1725-0.0056-5.1606
Training1946 73i , t ･Tenurei , t
1,558
1,558
1,246
1,246
cross-sections included
periods included (years)
41 (1929 69)
31 (1939 69)
41 (1929 1969)
31 (1939 69)
23,21023,210
16,637
16,637
included observations
0.77300.77450.86400.8639adjusted R2
4,922.0817 ***4,964.6115 ***9,609.0120 ***9,599.4685 ***F statistic
Notes : *** and ** respectively denote significance at the 1- and 5-percent levels. The information about physiologicalcharacteristics is not included in the wage records of the employees who joined the firm before 1939.

Table 3 Detection of employer learning effects in previous experience and tenure.
3 2
3 3
3 4
3 1
Estimation method
panel extended generalized least squares
log(w i , t )Dependent variable
Cross-section
random effect
Period (year)
pooled (no year dummies inserted)
Independent variables
coefficient t statisticcoefficient t statisticcoefficient t statisticcoefficient t statistic
***
***
***
-0.4701 -18.9872-0.6386 -14.8029-0.6996 -15.7167 ***Constant-0.6740 -15.2121
***
***
***
Schooli
0.0957
11.1396
0.053811.74410.1212
12.19210.1204 11.9630 ***
***
***
***
2
-0.0059 -14.4278-0.0038 -17.7145-0.0056 -13.9784-0.0054 -13.6782 ***Schooli
***
***
***
***
PreExperiencei
0.030618.45450.01989.21050.029517.9188
0.01343.6080PreExperiencei 2
Tenurei , t
Tenurei , t 2
Schooli ･PreExperiencei
Schooli ･Tenurei , t
Schooli ･PreExperiencei 2***-11.0913
157.6259 ******-52.9482***-2.6272-78.3730 ***Schooli ･Tenurei , t 2
Year19XX･Schooli

Yes

Yearjoined19XX YYi ･

No

No

1,558
41 (1929 69)
23,1200.9766
20,076.5892 ***0.00040.1246-0.00190.0007-0.0071-0.0001
0.0001***

3.171463.1873 ******-23.6766***
2.9480-31.2024 ******-6.8403
14.0995 ***Yescross-sections included
periods included (years)
included observations
adjusted R2
F statistic-0.0004
0.1093-0.0007-0.0004-0.00541,558
41 (1929 69)
23,1200.9687
14,300.3232 ***-0.0002
0.1092-0.0006-0.0010-0.0075***-5.2303157.2888 ******-47.8240***-6.2116-34.1524 ***

***

Yes

3.249284.6012 ******-29.9396**
2.1320-40.1782 ******-4.231321.6793 ***
Yes

Yes

Yes

1,558
41 (1929 69)
23,1200.9771
14,741.6266 ***0.00060.1427-0.00210.0009-0.0114-0.0001
0.0002

1,558
41 (1929 69)
23,1200.9776
14,624.3724 ***Notes : *** and ** respectively denote significance at the 1- and 5-percent levels. Control year dummy variable for Year19XX･
School is Year1929. Control 2-year-joined dummy variable for Yearjoined19XX-YY･School is Yearjoined1928-1929.

Table 4 Detection of employer learning effects in previous experience and tenure with controlling for cohort effects.
4 1
4 2
Estimation method
panel extended generalized least squares
log(w i , t )Dependent variable
Cross-section
random effect
Period (year)
pooled (no year dummies inserted)
Independent variables
coefficient t statisticcoefficient t statistic-0.3901 -9.2345 ***Constant-0.6047 -14.6739 ******Schooli
0.0866 10.7921
0.04205.1172 *********-0.0063 -16.1554-0.0040 -10.1654
Schooli 2******
PreExperiencei
0.01154.30580.01435.3403***20.00138.79100.0000 -0.2235
PreExperiencei******
Tenurei , t
0.0867 87.6503
0.0852 86.2228
***
***
2
0.00013.0339-0.0005 -15.3233
Tenurei , t1936 37
previous experience Yearjoined-0.0001 -0.3144-0.0004 -0.9107
i ･Schooli ･PreExperiencei**
1938 390.00072.02910.0004
1.1647
Yearjoined
i ･Schooli ･PreExperiencei**
1940410.00082.36740.00041.2302･School･PreExperience
Yearjoined
i
i
i
***
***
1942 430.00164.60010.00133.7370
Yearjoined
i ･Schooli ･PreExperiencei******
1944 450.00143.47600.00112.6563
Yearjoined
i ･Schooli ･PreExperiencei******
1946 47
0.00369.37560.00328.3964
Yearjoined
i ･Schooli ･PreExperiencei******
0.0034 11.2480
0.0030 10.0146
Yearjoined1948 49i ･Schooli ･PreExperiencei******
0.0032 10.2964
0.00289.1290
Yearjoined1950 51i ･Schooli ･PreExperiencei******
1952 530.00468.79950.00428.1084
Yearjoined
i ･Schooli ･PreExperiencei******
1954 55
0.00498.40890.00477.9865
Yearjoined
i ･Schooli ･PreExperiencei******
0.00299.67020.00258.4724
Yearjoined1956 57i ･Schooli ･PreExperiencei******
0.00195.84960.00154.7576
Yearjoined1958 59i ･Schooli ･PreExperiencei******
0.00237.38980.00196.2218
Yearjoined1960 61i ･Schooli ･PreExperiencei******
1962 63
0.00289.07090.0024
7.8368
Yearjoined
i ･Schooli ･PreExperiencei******
0.0043 14.0531
0.0039 12.8821
Yearjoined1964 65i ･Schooli ･PreExperiencei******
0.00387.58790.00356.9848
Yearjoined1966 67i ･Schooli ･PreExperiencei******
1936 37
tenure-0.0011 -12.0123-0.0011 -12.2029
Yearjoined
i ･Schooli ･Tenurei , t******-0.0011 -14.1849-0.0011 -13.9519
Yearjoined1938 39i ･Schooli ･Tenurei , t******-0.0011 -14.2744-0.0011 -13.3863
Yearjoined1940 41i ･Schooli ･Tenurei , t******-0.0012 -14.1783-0.0012 -13.3786
Yearjoined1942 43i ･Schooli ･Tenurei , t******-0.0012 -12.4599-0.0011 -11.5020
Yearjoined1944 45i ･Schooli ･Tenurei , t******
1946 47-0.0008 -7.5235-0.0008 -6.9188
Yearjoined
i ･Schooli ･Tenurei , t******1948 49
-0.0023 -23.9710-0.0022 -22.7975
Yearjoined
i ･Schooli ･Tenurei , t******
195051-0.0022 -19.5376-0.0021 -18.6083
Yearjoined
i ･Schooli ･Tenurei , t******
1952 53
-0.0022 -11.6990-0.0021 -11.0768
Yearjoined
i ･Schooli ･Tenurei , t******-0.0021 -13.2253-0.0020 -12.4992
Yearjoined1954 55i ･Schooli ･Tenurei , t******
1956 57
-0.0027 -17.9852-0.0026 -16.9971
Yearjoined
i ･Schooli ･Tenurei , t******
1958 59
-0.0026 -14.1252-0.0025 -13.3082
Yearjoined
i ･Schooli ･Tenurei , t******
1960 61-0.0031 -12.6286-0.0029 -12.0812
Yearjoined
i ･Schooli ･Tenurei , t******
1962 63-0.0039 -11.4366-0.0038 -10.9617
Yearjoined
i ･Schooli ･Tenurei , t******
1964 65
-0.0052 -10.1331-0.0051 -9.7979
Yearjoined
i ･Schooli ･Tenurei , t******
1966 67
-0.0081 -8.8014-0.0080 -8.7226
Yearjoined
i ･Schooli ･Tenurei , t***
2-0.0003 -15.4276
Schooli ･PreExperiencei***
220.0000 -13.9982
Schooli ･PreExperiencei***-0.0001 -36.8799
Schooli 2･Tenurei , t 2***0.0000 -38.1034
Schooli ･PreExperiencei 2
19XX
Yes
Yes
Year
･Schooli
1,551
1,551
cross-sections included
36 (1934-69)
36 (1934-69)
periods included (years)
joined in 1934-67
joined in 1934-67
cohorts included
22,92822,928included observations
2
0.9767
0.9767
adjusted R
12,793.6875 ***12,799.9763 ***F statistic
Notes : Control 2-year-joined dummy variable is Yearjoined1934 1935 and control year dummy variable for interaction
1934
with schooling is Year . *** and ** respectively denote significance at the 1-percent and 5-percent levels.

Table 5 Probability of acceptance as a trainee for in-house training programs.
5 1
5 2
Estimation method
binary probit
binary probit
1935 48
Dependent variable
Training
Training1939 46
marginal
marginal
Independent variables coefficient z statisticcoefficient z statistic
effecteffectConstant-5.5027 -2.9138 ***-34.4557 -5.3953 ***Age
0.7384 5.1269 *** 0.0009
3.2124 5.8500 *** 0.0000-0.0159 -4.8545 ***-0.0821 -5.5880 ***Age2***
School-0.8331 -3.2905-0.00100.5146 0.6187
0.00000.0414 3.1259 ***-0.0181 -0.4422
School2
PreExperience-0.1676 -4.4759 *** -0.0002-0.8942 -7.0762 *** 0.0000
2

***

***

5 3
binary probit
Training1946 73
marginal
effectcoefficient z statistic-21.0175 -20.4493 ***0.0968 3.0832 ***-0.0029 -4.5522 ***4.5331 22.8440 ***-0.2445 -23.7262 ***-0.4530 -37.0305 ******0.00340.1592-0.0159

0.0077 2.5979
0.0721 6.5262
0.0203 24.1173
PreExperience
periods included (years)
13 (1936 48)
8 (1939 46)
17 (1946 62)
cohorts included
joined in 1933 48
joined in 1937 46
joined in 1944 62
1,822
844
12,741included observations-342.6259-137.5664-2,769.0706
Log likelihood
0.09570.41210.4700
McFadden R2******
72.4878
192.8855
4,911.9308 ***LR statistic
Notes : Marginal effects are calculated by mean values of independent variables. *** and ** respectively denote significance at the 1and 5-percent levels.

Table 6 Employer learning for trainee selection.
6 2
6 3
6 4
6 1
Estimation method
panel extended generalized least squares
Dependent variablelog(w i , t )Cross-section
random effect
Period (year)
pooled (no year dummies inserted)
Independent variables
coefficient t statisticcoefficient t statisticcoefficient t statisticcoefficient
Constant-0.0368-8.0315 *** -0.1534 -31.4632 *** -0.1269 -28.3160 *** -0.1713
Tenurei , t
0.0926 125.9735 ***0.0809 111.8764 ***0.0843 121.1516 ***0.0811
2
***
***
***
-0.0008 -18.9280-0.0009 -22.1007
0.000816.3695-0.0006
Tenurei , t
Schooli ･PreExperiencei ･Training1946 73i , t
1946  73

Schooli ･Tenurei ･Trainingi,tSchooli ･PreExperiencei ･E[Training1946 73]
Schooli ･Tenurei ･E[Training1946 73]

0.00185.8888 ***0.0004

1.3816-0.0034***-0.0018-2.6263 ***-4.6671-0.0002-13.5066 ***0.00039.9936 ***0.001576.6054 ***0.001229.3802 ***Schooli 2･PreExperiencei 20.000032.5343 ***0.000023.4869 ***0.0000-7.4097 ***-10.6473 ***-0.0419-19.6426 ***-52.2662 ***
Yes
1,229
 (1946  62)
1944 62
12,741
0.9786
26,423.3359 ***-0.00992

Schooli ･Tenurei , t 2
1946  73

Trainingi,tTraining1946 73i , t ･Tenurei , t

0.0556
0.03380.0000-77.0932 ***8.0619***0.04837.6216***5.3983***0.01762.9762 ***E[Training1946 73]-0.0242

E[Training1946 73]･Tenurei , t-0.0114

Schooli ･Year19XX
cross-sections included
periods included (years)
cohorts included
included observations
adjusted R2
F statistic

Yes
1,229
 (1946  62)
1944 62
12,741
0.9731
20,962.8151 ***t statistic-36.9536 ***117.1807 ***-10.2334 ***

Yes
1,229
 (1946  62)
1944 62
12,741
0.9782
23,774.2416 ***-26.4809 ***
Yes
1,229
 (1946  62)
1944 62
12,741
0.978424,055.6607 ***Notes : E[Trainingdc1946 73] is estimated by specification 5 3 in Table 5. ***, ** and * respectively denote significance at the 1-, 5-, and 10-percent
levels. Control year dummy variable for School･Year19XX is Year1946.