OSIPP Discussion Paper: DP-2019-E-010

How general is managerial human capital? : Evidence from the
Retention of Managers after M&As
September 25, 2019

Kenjiro Hirata*
Faculty of Economics, Kobe International University

Ayako Suzuki**
School of International Liberal Studies, Waseda University

Katsuya Takii***
Osaka School of International Public Policy, Osaka University【 Keywords 】 Tenure; Managerial Skill; Managerial Turnover after M&As; Selection Bias; Cox
Proportional Hazards Model【JEL Codes】G34; J41; J63【Abstract】This paper investigates the transferability of managerial experience by
examining how managers' tenures in target firms influence their probability ofretention as board members after mergers or acquisitions in Japanese firms. It develops
a general equilibrium model that distinguishes several hypotheses on managerial
experiences based on the coefficients of tenure on separation, given several data
limitations.

In particular, the paper provides a novel method to correct for selection

biases by utilizing the timing of selection in a selected sample, which does not require arandom sample from the population.

Our results suggest that Japanese firms value

both target firm-specific and general human capital after M&As and that experience as
an employee increases firm-specific skills, but at the expense of the accumulation ofgeneral skills.

However, experience as a board member does not have this effect.

We would like to thank Boyan Jovanovic, Kei Kawai, Ryosuke Okazawa, David Yermack, and seminar
participants at the APL Seminar, the Asset Pricing Workshop, the Kansai Labor Workshop, and theMonetary Economics Workshop for their helpful comments. In addition, we thank Yoko Kitagawa forher assistance in the construction of the data. Financial support from the Japanese Ministry of
Education, Culture, Sports, Science and Technology (a Grant-in-Aid for Scientific Research 18330051,
21243024, 25245040, 18H03636) is gratefully acknowledged.
* Email: khirata@kobe-kiu.ac.jp** Email: a-suzuki@waseda.jp*** Email: takii@osipp.osaka-u.ac.jp

1

Introduction

How general is managerial human capital? Market-based views on managerial compensations
explain high CEO compensation in the U.S. as resulting from the competition to employ scarcemanagerial talent (e.g., Gabaix and Landier, 2008; Terviö, 2008). However, the validity of these
theories critically depends on the answer to this question. This question is also related to thesensitivity of managerial turnover to poor performance by a …rm (e.g., Eisfeldt and Kuhnen,2013). Thus, it is one of the most important empirical questions in the literature on corporate
governance.
The empirical studies on the retention of managers after M&As may provide some evidence
to assist in answering this question. Although several theories of takeovers presume that top
managers in a target …rm must be replaced after a takeover1 , there is increasing evidence thatthe retention of a management group is important to the new …rm2 . This evidence suggeststhat there are important skills held by executives of a target …rm that a new management groupin an acquiring company cannot easily replace.
Interestingly, the existing literature …nds that the tenure of a CEO does not have any
signi…cant e¤ect on his/her probability of retention after takeover (e.g., Buchholtz et al., 2003;
Wulf and Singh, 2011). Given that experience in a …rm is assumed to result in the developmentof …rm-speci…c skills, the lack of such an e¤ect places doubt on the hypothesis that …rm-speci…cskills are required to manage a newly merged …rm after a merger and acquisition (M&A).
It appears that managers’tenures may have a negative impact on their retention rate after
an M&A. If it is expected that managers with long tenures will have di¢ culty in adapting to
the new environment— because the smaller number of …rms in which their experience is gained
reduces their ability to improve their general human capital— a newly merged …rm may notwant to employ a manager with a long tenure (e.g., Buchholtz et al., 2003).

Therefore, this

could o¤set the positive e¤ect of tenure on the retention rate.
This paper examines how the tenure of managers in‡uences the retention rate of a management group after M&As in Japanese companies during the period 1990–2006. It attempts to1
Some research considers takeovers as a disciplinary device (e.g., Martin and McConnell, 1991). Alternatively,
Shleifer and Summers (1988) argue that a takeover causes a breach of trust with stakeholders and transfers rent
from them to shareholders. Jovanovic and Rousseau (2002) emphasize that a takeover can reallocate capital tobetter manage a …rm. All of these theories presume that top managers in a target company must be replaced
after a takeover.
On the other hand, the synergy view of takeovers, which is supported by McGuckin andNguyen (1995) and Matsusaka (1993), does not predict the replacement of top managers.
2
Matsusaka (1993) …nds that the retention of managers in a …rm targeted for takeover increases the bidder’s
return, and Cannella and Hambrick (1993) and Zollo and Singh (2004) …nd that the departure of executives fromacquired …rms is harmful to postacquisition performance.

2

separate the two di¤erent hypotheses regarding the e¤ect of tenure on separation probability.
We show that negative and positive e¤ects of tenure on the managers’separation rate coexist
in the case of Japanese M&As.
The main challenge to achieving our goal is developing a way to cope with the limitationsof the data.

Ideally, we need a fairly rich dataset, which includes the random assignmentof target managers and their history afterward, including not only their career paths, butalso wage payments and obtained skills.

Unfortunately, it is not possible to obtain suchdata for Japanese …rms. These data restrictions force us to develop a model that can extract
meaningful information from the restricted dataset. We develop a general equilibrium modelthat is designed to analyze the separation of target-…rm managers after M&As. We show that
our structural model can be approximately estimated by a strati…ed Cox proportional hazards
model.
Equipped with the constructed theoretical model, we conduct survival analyses of Japanese
titled directors, who are considered to be the top executives in Japanese companies3 . Because
the Japanese promotion system is known to encourage investment in …rm-speci…c human capital, we expect that the advantages and disadvantages of long tenure can be more accurately
measured and investigated in Japanese companies than is the case for other countries.
Our empirical analyses show that an increase in a manager’s tenure as an employee in atarget company increases both the probability of being appointed to the board in a merged …rmand the subsequent separation probability after this appointment. However, a longer tenure
as a board member within the target …rm does not have any signi…cant impacts on either
appointment probability or separation probability.

Through the lens of our theory, we caninterpret these …ndings as follows: 1) Japanese …rms after M&As value both the target …rmspeci…c human capital and the general human capital of managers; 2) experience as an employee
increases …rm-speci…c skills, but at the expense of the accumulation of general human capital;and 3) Experiences as a board member are likely to be more general than those as an employee.
There have been many attempts to understand the retention of managers after M&As4 .
3Comparing U.S. CEOs and Japanese presidents, Kaplan (1994) argues that, because decisions in a Japanese…rm are made on a consensus basis, it is important, for the sake of accurate comparison, to include other directors,
not only presidents. Saito and Odagiri (2008) argue that, because there is heterogeneity among directors, not
all directors are important decision makers and, therefore, they choose to focus on directors with titles as theimportant decision makers in Japanese …rms. We follow Saito and Odagiri (2008) and identify directors withtitles as the relevant executives in the sample target …rms.
4
Walsh (1988), Walsh (1989), and Walsh and Ellwood (1991) investigate several factors that in‡uence theturnover of top managers after M&As. More recently, Wulf (2004), Hartzell et al. (2004), and Bargeron et al.
(2009) focus on the power of target CEOs to negotiate bene…ts, which includes a position in a new …rm, as an
expense borne by shareholders. Finally, Mateos de Cabo et al. (2014) investigate how individual characteristics,
including gender or membership of a minority group, in‡uence appointments to directorships after M&As.

3

However, to the best of our knowledge, this is the …rst paper that constructs a structural modelof managers’retention after M&As. Without a structural model, it is di¢ cult to disentangle theseveral mechanisms underlying the causal e¤ects of tenure on the separation of target managers
after M&As, which is the main purpose of this paper.
In contrast to the standard structural estimation approach of, for instance, Rust (1987)
and Hotz and Miller (1993), we do not attempt to estimate all structural parameters, instead
focusing on particular parameters of interest, namely the coe¢ cients of the e¤ects of tenure on
the separation rates. Our model is designed to clarify the conditions under which we can obtain
economically meaningful interpretations from these parameters. Given the data limitations that
we face, this strategy allows us to utilize weaker parametric assumptions for our identi…cation,
resulting in greater transparency of the source of variations for the identi…cation. In particular,
we show that, without making any parametric assumptions on the dynamics of productivity after
M&As that are unrelated to human capital accumulation, we can estimate the coe¢ cients oftenure by using the strati…ed Cox proportional hazards model5 .
Our model attempts to overcome several data limitations. First, because we cannot observeskills, we must di¤erentiate two di¤erent hypotheses regarding the length of tenure and theseparation probability of managers.

Our identi…cation strategy is built on the recognition

that, although target-speci…c human capital is important as an input for current production,
employment of managers with the ability to learn in a new environment is an investment in
future production. More concretely, on the one hand, because managers in an acquiring …rm
do not have much knowledge of the target …rm’s organization, the acquirer initially regards the
speci…c skills held by the target-…rm managers as highly valuable in managing and restructuring
the target …rm. On the other hand, because target managers accumulate knowledge of the new…rm over time, the di¤erence between the amount of knowledge accumulated by a manager who
learns quickly and one who is a slow learner becomes larger as time goes by6 . It is shown that5
Similar to our empirical strategy, Chetty (2009) and Heckman(2010) discuss the bene…ts of estimating wellfocused parameters rather than full structural parameters.
6This intuition may not be true if the amount of total knowledge that must be learned is so little that a quick
learner can immediately understand everything and if an acquiring …rm can wait until a slow learner catches up.
However, this case is less likely to be important for our empirical studies. First, the literature on the learning
curve (e.g., Jovanovic and Nyarko, 1995) suggests that a rise in productivity continues for a long time, especially
if tasks are complex, which is likely to be the case for management jobs. Second, as most …rms are subject toseasonal events, it is less likely that every operation can be understood without spending at least one year in
the …rm. Therefore, we focus on one year as the period over which extensive learning occurs in our empirical
study. Third, because, as Kaplan (1994) argues, the decisions in many Japanese …rms (the focus of our empiricalstudies) are made on a consensus basis, it is important to learn what people think about a particular strategy. As
suggested by the literature on higher-order beliefs, learning about the beliefs of other people on random objects
is more di¢ cult than learning about the random objects themselves (see Veldkamp, 2011). Hence, it is likelythat a target-…rm manager needs time to learn the consensus views held by the managers in the new company.

4the timing of separation re‡ects the relative importance of each type of human capital.
This seemingly intuitive argument requires nontrivial theoretical consideration of learning
capability. Although the argument in the previous paragraph implicitly assumes that a newly
merged …rm is willing to employ managers with high learning ability, this may not be true.
Because the ability to learn in a new environment is a general ability, the market competition
can raise the compensation of able managers, which may make the …rm reluctant to employ
them. Therefore, the validity of the above argument depends on the structure of the external
labor market for managers. Because we developed a general equilibrium model, we can discuss
how the frictions in the managerial external labor market in‡uence the coe¢ cients of the e¤ectsof tenure on the separation probability.
In addition, the coe¢ cients of the e¤ects of tenure might be in‡uenced by the second data
problem: the lack of compensation data for Japanese managers.

It is not obligatory for

publicly traded companies to provide information on the compensation of managers in Japan.
As suggested in the literature (e.g., Wulf, 2004, Hartzell et al., 2004, and Bargeron et al., 2009),
this might cause several biases if managers in target …rms can negotiate the compensation andseverance pay in the newly merged …rm during the process of an M&A. Our theoretical modelshows that if it is impossible to make a complete contract on treatment of the new managers
in the new …rm during the M&A and there are some explicit or implicit transfers after the new…rm starts as a result of ex post bargaining, then the separation probability does not depend
either on the compensation or on the severance pay of managers. That is, the model provides
a theoretical condition under which we can extract meaningful information from the coe¢ cientsof the impact of tenure on the separation rate even when compensation data are not available.
Finally, because managers in a target company are not randomly assigned, the coe¢ cient oftenure can be contaminated by another e¤ect. If a talented person is promoted to a management
position faster than is usually the case, the short tenures observed in our data may simply
indicate that a manager has a high unobserved ability.
In order to deal with these selection biases, we propose a novel method to extract information
about the unobserved heterogeneity of workers from the data on managers.

Intuitively, if atalented person is promoted to a management position faster, the length of tenure prior to
becoming a manager must contain useful information about their unobserved ability.

Weutilize this information to identify and control for unobserved ability to estimate the causale¤ects of tenure.
Finally, there is no economic reason for an acquiring …rm to keep a slow learner until they start to catch up.

5Compared with the standard sample selection models that have appeared in econometrics
textbooks (e.g., Wooldridge, 2002; Cameron and Trivedi, 2005), our approach has three advantages. First, because we utilize the timing of selection in a selected sample to correct for
selection bias, we do not need to access a random sample from the population.

We are notaware of any other papers that provide a tractable method to correct a selection bias inherent
to personnel data using only the selected sample. Second, because the timing of observations
is generally di¤erent from the timing of promotions, we can …nd several exclusive variables thatare required to identify parameters and obtain reliable estimates.

Finally, although a stan-

dard two-step estimator makes distributional assumptions to correct selection biases, we relyon an extreme value theory to obtain robust results against misspeci…cations of distributional
assumptions. Gabaix and Landier (2008) argue that an extreme value theory can provide a niceapproximation for the upper tail of a large class of continuous distributions. We apply theirargument and derive an explicit solution to the conditional expectation of unobserved ability
under a selected sample, which is used to determine unbiased estimates of parameters under aselected sample.
The methodology developed in this paper may be applicable to a broader literature than thatof managerial retention after M&As. Although it is recognized that the characteristics of CEOschange the strategies of …rms (e.g., Bertrand and Schoar, 2003), researchers face di¢ culties in
examining the causal role of CEO characteristics in a …rm because publicly available data on top
managers typically involve selected samples. We propose a method to deal with this problem.
Moreover, our methodology can be applied to data on internal promotions, when researchers
are not able to access data on employees’whole careers. We hope that this novel approach canhelp researchers struggling with data limitations to evaluate the role of leaders.
In addition to our methodological contribution to the literature, our results contribute toseveral streams of literature, including those on managerial compensation and Japanese M&As.
We clarify the contribution of our results to these …elds in Section 8.
The paper is organized as follows. Section 2 presents a general equilibrium model of theseparation of target managers after M&As. It shows how target …rm-speci…c human capital andgeneral human capital can in‡uence the separation decision after M&As. Section 3 links thelength of tenure and each type of human capital and provides a number of testable conditions
that distinguish several hypotheses on the skill contents of managerial experiences in a …rm
based on the evidence of the e¤ect of tenure on separation probability. Section 4 introduces
our empirical model and discusses how to correct a selection bias using our selected dataset.

6Section 5 describes our Japanese dataset and Section 6 presents our estimation model and our
results, interpreted through the lens of our theory. Section 7 discusses whether the moral hazardof managers could in‡uence the interpretation of our results. Section 8 relates our results toseveral streams of literature that cover managerial compensation and Japanese M&As. Section
9 concludes the paper.

2

A General Equilibrium Model of Managerial Separation after
M&A

In this section, we construct a general equilibrium model that is designed to examine theseparation of target managers after M&As using the following procedure. First, we discuss theassumptions on the production functions, which describe how target …rm-speci…c human capitaland general human capital in‡uence the production process.

Second, using the production

functions, we model the separation of a manager from a target …rm after an M&A by taking theoutside values of managers as given.

Third, we model an external managerial labor market,

which allows us to determine the outside values of the managers.

Finally, we show how

our structural model can be approximately represented by the proportional hazards modeland discuss how target …rm-speci…c human capital and general human capital in‡uence theparameters of the proportional hazards model.

Target Firm-Speci…c Human Capital vs. General Human Capital: Suppose that whena …rm is merged with another …rm, managers from the target …rm must learn new skills and/or
new routines to manage the merged …rm in its new environment. We assume that all learning
takes place at time t = 0 and that normal …rm operations start after time t = 1, where theanalysis time t is the length of time of operation after the year in which the new …rm wascreated by the M&A. Assume that a manager in a target …rm has general human capital hG
and human capital speci…c to the target …rm, hT . Suppose that the productivity of the manager
with human capital h = hG ; hT

is described by pt (h):pt (h) = fGs hG + fT s hT + (t : X) ;s = l if t = 0;
= n if t

1;

7

where the vector X includes any variables that can be controlled for in our empirical study and(t : X) captures the transitional dynamics of productivity after the M&A that is unrelated tohuman capital accumulation.
The production technologies fGs and fT s depend on the state s. We use s = l to denote alearning state, whereas s = n denotes the normal operation state. We assume that fGs hG
and fT s hT00 and fGnhG

0 for any s 2 fn; lg and hG and hT . We also assume that fT0 l hT
0
fGl
hG

0

fT0 n hT0.

The assumption of fT0 n hT

fT0 l hT means that an increase in the target …rm-speci…chuman capital can initially increase bene…ts. When a merger occurs, managers in the acquiring…rm do not have enough knowledge about the target …rm.

Hence, initially, the …rm-speci…cknowledge relating to the target …rm must be more valuable. The assumption of fT0 n hT
fT0 l hT captures this e¤ect.
0hG
The assumption of fGn

0
hG
fGl

0 may require more explanation. We assume thatfGn hG = fGl hG + hN and hN = g hG , where hN is new …rm-speci…c human capital andg hG is a learning function. We also assume that g hG

0 and g 0 hG00h G + g hG
hG = fGlassumptions, it can be shown that fGn

The assumption of g 0 hG

1 + g 0 hG

0. Under these
0
hG .
fGl

0 attempts to capture the idea that general human capitalcan improve the speed of learning. Nelson and Phelps (1966) consider that education increases
the speed of technology adoption because educated people are better able to understand newtechnology. Schultz (1975) argues that human intelligence can be used to interpret new information and adapt to a new environment, and refers to such intelligence as entrepreneurial
ability. Gibbons and Waldman (2006) construct a model of promotion in which education can
increase learning capability, arguing that this concept has signi…cant empirical support.

We

attempt to incorporate this idea in our model.

The Separation of a Manager from a Target Firm after an M&A: Now, we constructa model of managerial separation.

The present value of the expected pro…t sequences from

employing a particular manager, Jt (h) at t

1, can be described as follows:

2

n
o 3
^ l hG + Pt+1 + "t+1 max Jt+1 (h) ; J^0 Pt+1
I Wt+1 (h) W5;hi
Jt (h) = pt (h) wt + E" 4
^ l hG + Pt+1 + "t+1
+ 1 I Wt+1 (h) W
J^0 Pt+1
where wt is the manager’s compensation at time t, Pt+1 is the severance pay at time t + 1,
8

< 1 is a discount factor, "t is the sum of any idiosyncratic random bene…ts that the manager
can obtain if he/she leaves the …rm at time t, E" [ ] is the expectation operator with respect
to "t+1 , J^0 is the present value of the expected net pro…t sequences from employing a new^ l hG are the present values of the sum of the expected income
manager, and Wt (h) and W‡ows when a manager stays and when he/she leaves the …rm at time t, respectively. Note thatwhen managers stay in the same …rm, their value functions depend on both target …rm-speci…chuman capital and general human capital, h, whereas when they leave, their value functions
depend only on their general human capital, hG .
We assume that …rms review their managers every period.

Assuming that the manager^ l hG + Pt+1 (h) + "t+1 = 1, the …rm hasW

prefers to stay, which means that I Wt+1 (h)to decide whether to retain the manager as a board member. If it retains the manager, it expects
to obtain Jt+1 (h) in future from the manager. However, if it …res the manager, the …rm must…nd a new manager and receives J^0 .

Because the …rm must pay severance pay Pt+1 in thecase of separation, it must incur Pt+1 . Because a …rm is assumed to maximize its pro…t, theno^ l hG + Pt+1 (h) + "t+1 ,expected pro…t would be max Jt+1 (h) ; J^0 Pt+1 . If Wt+1 (h) < W
the manager leaves, irrespective of the …rm’s decision and, therefore, the …rm receives J^0 Pt+1 .

Similarly, the present values of the sum of the expected income ‡ows of managers in the…rm at the analysis time t, Wt (h), can be described as follows:2

Wt (h) = wt + E" 4no 3
^ l hG + Pt+1 + "t+1
Pt+1 max Wt+1 (h) ; W
5;
0
l
G
^
^
I Jt+1 (h) J
Pt+1
W h + Pt+1 + "t+1

I Jt+1 (h)
+ 1

J^0

When a manager stays in a …rm, in every period that follows, he/she reassesses and decides whether to stay with the …rm or leave. If the manager stays, he/she expects to obtain^ l hG + Pt+1 + "t+1 . Hence, if
Wt+1 (h). If the manager leaves, he/she expects to obtain W
a …rm decides to continue employing the manager, I Jt+1 (h) J^0 Pt+1 = 1, the expectedno^ l hG + Pt+1 + "t+1 . If the …rm decides to …re the manvalue must be max Wt+1 (h) ; W
ager, I Jt+1 (h)J^0

Pt+1 = 0, the manager must leave and receive the outside bene…ts of^ l hG + Pt+1 + "t+1 , irrespective of his/her own decision.
W
We assume that:wt = wtc + wtn ;where wtc is the contracted compensation, whereas wtn 2 R is the negotiable compensation. As
9suggested in the literature (e.g., Wulf, 2004, Hartzell et al., 2004, and Bargeron et al., 2009), amanager may control the sale of the …rm and refuse to take a deal in the M&A process unlesshe/she is personally promised something in return, such as a position on the board of the new…rm. As a result of this negotiation, a target-…rm manager and the acquiring …rm may write
an explicit contract on (wtc ; Pt ) before the new …rm starts its operation. However, we consider
that the contract in the real world is far from complete and that it leaves room for negotiabletransfers wtn after the new …rm starts. We consider that wtn can be a negative implicit transfer
because it may involve harassment and mental pressure. We show that the existence of wtn
makes the separation decision independent of (wtc ; wtn ; Pt ).
We de…ne the joint surplus of the manager and the new …rm by St (h)J^0Jt (h) + Wt (h)^ l hG . The proof of the following proposition is provided in the Appendix.
W

Proposition 1 Suppose that the manager and the …rm can negotiate wtn 2 R at the beginningof time t. The separation occurs at time t if and only if St < "t and the dynamics of St can be
described by:
St (h) = pt (h)where b hG = (1b hG +[St+1 + E" [I ("t+1 > St+1 (h)) ("t+1

St+1 (h))]] ;

(1)

h
i
^ l hG + J^0 is the sum of the average expected ‡ow bene…ts received) W

by both a manager and a …rm from the outside market.

Proposition 1 shows that the separation decision does not depend on (wtc ; wtn ; Pt ), and that it
depends only on the joint surplus of the target manager and the merged …rm, St . This means
that, although the negotiation during an M&A may result in a complicated compensation
scheme and severance pay, it does not in‡uence the separation decision as long as a …rm and amanager can ‡exibly negotiate the ex post transfer.
In addition, Proposition 1 shows what determines the joint surplus. For any t, maintaining the relationship brings a joint instantaneous surplus of pt (h)(1^ l hG) J^0 + W.

If they maintain their relationship, the manager and …rm can enjoy St+1 (h) in the next period.

However, if the instantaneous random bene…ts from the outside market happen to begreater than the joint surplus, "t+1 > St+1 (h), then they will decide to separate and obtain
the additional value of "t+1

St+1 (h).

Because they can separate only when the random

bene…ts are large enough to exceed the joint surplus, the possibility of separation simply provides each party with the additional value arising from separation. This e¤ect is captured by
E" [I ("t+1 > St+1 (h)) ("t+1

St+1 (h))].
10

Assume that "t is exponentially distributed with a parameter . The separation probability,
qt , is shown to be a function of St , as follows:qt (h) = E" [I ("t > St (h))] = e

St (h):

This suggests that increases in the joint surplus, St , reduce the probability of separation.
Given this distributional assumption, the expected gain from separation is shown to be
proportional to the separation probability.
E" [I ("t+1 > St+1 (h)) ("t+1

St+1 (h))] =qt+1 (h):Inserting the expected gain from separation into the dynamics of the joint surplus, we canrewrite equation (1) and summarize how the two types of human capital in‡uence the separation
probability using the following equations:qt (h) = e

St (h)St (h) = pt (h)b hG +"

St+1 (h) +e

St+1 (h)#:Note that both target …rm-speci…c and general human capital in‡uence the separation
through an increase in productivity, pt (h). The general human capital has additional e¤ects
on the separation through a change in outside value, b hG . Therefore, without knowing thestructure of function b hG , we cannot make any clear theoretical prediction on the impacts ofgeneral human capital on the separation probability.

The Model of the Managerial Labor Market: We model an external labor market andendogenize b hG

= (1^ l hG + J^0 .
) W

Suppose that an external managerial labormarket is segregated by the type of worker hG . A …rm can …nd a worker with hG by paying ahiring cost F hG such that:nJ^0 = max J^l hG
hG

11

F hG

o

where:J^l hG= fGl hGw
^ l hG +J^n hG= fGn hGw
^ n hG +hiq^J^l hG + (1 q^) J^n hG ;ihq^J^l hG + (1 q^) J^n hG :q^ is the separation probability, and w^ s hG and J^s hG are the compensation for a manager
and the present value of the expected pro…t sequences from employing a manager who has ageneral skill hG at the state s; respectively.

We assume that F hG

0 and F 0 hG

0.

These assumptions imply that it is di¢ cult to …nd a manager and even more di¢ cult to …nd an
able manager. Similar to the situation for a new …rm after an M&A, there is a learning state
and a normal operation state for the production function. In contrast to the situation for the
new …rm after an M&A, productivity does not depend on fT s hT and(t : X). This meansthat target-…rm speci…c human capital is useless and there is no transition dynamics after an
M&A for the …rms that do not experience M&As. As a result, the environment is stationary
and the separation probability q^ does not depend on t.
Suppose that managerial talent is a scarce resource and all …rms competitively post an initial
wage to attract a manager as long as pro…ts are positive.

Because of the price competition,J^0 = 0 at the equilibrium. Hence, for all hirable hG , J^l hG = F hG and, therefore:w^ l hG = fGl hG +(1q^) J^n hG

F hG :(2)

Similarly, the present values of the sum of the expected income ‡ows of a manager who has^ s hG are described as follows:a general skill hG at the state s: W
^ l hGW= w^ l hG +^ n hGW= w^ n hG +hi^ l hG + (1 q^) W^ n hG
q^W
h
i
l
G
n
G
^
^
q^W h + (1 q^) W h^ n hGWe de…ne the surplus under a normal operation as S^n hG = J^n hG + W(3)(4)^ l hG .
W

Then, it is shown that:S^n hG = fGn hG
Note that S^n hG

fGl hG + F hG0:0 means that there is a surplus that managers and …rms can share. Hence,

they can adjust w^ n hG to maintain their relationship. Note also that S^n hG

120 as long as

learning increases productivity fGn hG = fGl hG + g hG
cost F hG

fGl hG and there is a hiring

0.

Because J^0 = 0 at the equilibrium, b hG = (1^ l hG .
)W

Substituting equation (2)into equation (3), we can derive:b hG = fGl hG

F hG +q^) S^n hG :(1

Using this result, we can summarize the separation probability derived from our generalequilibrium model of the managerial separation after an M&A in the following proposition.
Proposition 2 The separation probability of a target manager after an M&A is characterized
by the following equations:
St (h)

qt (h) = e
St (h) =s(h) + (t : X) +"(1

St+1 (h) +e

St+1 (h)#where:n(h)fT n hT + [1l(h)fT l hT + F hGS^n hG= fGn hGq^)] S^n hG(1q^) S^n hG

fGl hG + F hG :The proposition shows that not only the production function but also the hiring cost functionin‡uences the separation productivity of the target manager after an M&A.

Proportional Hazard Model of Separation: We show how our structural model can beapproximately represented by the proportional hazards model. The advantage of the proportional hazards model is that we do not need any parametric assumption on the basic hazard
and, therefore, the model does not make any assumptions on the shape of the hazard over time.
It is shown that without making any assumption on(t : X), we can conduct our empiricalanalysis.
We assume that after the merger, a new …rm faces a transition period and eventually converges to an operation state that is similar to those of other …rms that did not experience an
M&A. We derive an approximate solution of St (h). We decompose X and
13(t : X) into twoparts: X = (XZ ; XV ), v s (XV ) and z (t : XZ ) so thats = fl; ng.

(t : X) = v s (XV ) + z (t : XZ ) ; where
St+1 (h)Taking a …rst-order approximation of e

derive an approximate solution of St (h) for t

St+1 (h) = q^, we canaround e

1:

n

St

(h) + Z (t : XZ )
V)
n
(h) =
1
(1 q^)1X
Z (t : XZ ) =[ (1 q^)] z (t +n (h) + v n (X: XZ ) +=0

where ^ (^q) =1 ln q^

^ (^
q)
1

(1

;

q^)

q^.

Similarly, the present value of the stream of instantaneous joint surpluses at time 0, S0 canbe expressed as:
S0 =l(h) + v l (XV ) + z (0 : XZ ) +

e

S1 +

S1

:

Therefore, using the same approximation, we can show that:
S0
where

(h) =

l (h)

(h) +

n (h) + v l (XV)n(h) + Z (0 : XZ ) ;v n (XV ).

The following proposition summarizes the results.
Proposition 3 Separation probability can be estimated using the following proportional hazards
model:
qt = B (t : XZ ) e [ (h)I(t=0)+n (h) + v n (X )
V
n
(h) =
;
1
(1 q^)n (h)]

where:(h) = fGl hGnfGn hG + fT l hT(h) = fT n hT + [1B (t : XZ ) = e(1

fT n hT + v l (XV )q^)] fGn hG

v n (XV ) ;fG0 hG + F hG;

Z(t:XZ ) and I (t = 0) = 1 when t = 0 and I (t = 0) = 0 otherwise.

We assume that the acquiring …rm appoints the manager in the target …rm to the board
14

of the new …rm at the beginning of t = 0.
manager is equivalent to 1

Because the probability of being appointed aq0 , investigating the separation probability in the initial period

provides information about the appointment probability as well. As we discussed, we derive
the basic hazard B (t : XZ ) as a function of z (t +parametric assumption on z (t +: XZ ).

Therefore, without making any: XZ ) ; we can conduct the estimation of this proportional

hazards model.
Let us examine how target …rm-speci…c and general human capital in‡uence the parametershi@ n (h)@qt=
q
for anyon the proportional hazards model. Because, for x = G or T , @h
x
t
@hx
h
i
n
@
(h)
@ (h)
@q0
t
1 and @h
, we can analyze the impact of human capital on
x = q0@hx + @hx
the separation rate by @

n (h)

@hx

, @

(h)

@hx

and @

[

n (h)](h)+@hx, where x = G or T . We canobtain the following proposition.
Proposition 4 The impacts of target …rm-speci…c human capital and general human capitalon the proportional hazards model can be analyzed by the following equations:
1. The impacts of target …rm-speci…c human capital:
n (h)

@

@hT
@

@

[

(h)
@hT
(h) + n (h)]@hT=

fT0 n hT
(1 q^)

10

fT0 l hT"

fT0 n hT

=

0
fGn
hG

0
hG + F 0 hG
fGl

=

0
fGl
hG

0
fGn
hG

=

fT0 l hT +

=

(1
1

0

q^) fT0 n hT
(1 q^)#

0

2. The impacts of general human capital:
n (h)

@

@hG
@
@

[

(h)

@hG
(h) + n (h)]@hG=F 0 hG

00

0

The …rst result in Proposition 4 shows that a rise in hT increasesn (h) and(h)+n (h),

and, therefore, always decreases the separation probability of managers. That is, because target…rm-speci…c human capital always improves productivity, fT0 l hT
rise in hT also increases(h) and, therefore, lowers

0 and fT0 n hT(h). This is because we assume

that the target …rm-speci…c human capital is initially more important, fT0 l hT

15

0. A

fT0 n hT .

The impacts of general human capital are more complicated. Because of the competition
for general human capital, a rise in this type of human capital increases not only productivity,
but also the cost of employing managers.

Therefore, how general human capital in‡uences

the separation probability appears to be unclear. However, the second results in Proposition
4 provide clear theoretical predictions.

That is, a rise in hG increasesn (h) andn (h), and, therefore, always decreases the separation probability of managers.

increases
F 0 hG(h) +n (h) and, therefore, reduces q(h) +A rise in hG

0 if it is di¢ cult to …nd more able managers

0. If the costs of …nding talented managers are the same as those of …nding ordinary

managers, there are no bene…ts from employing managers with high general human capital
because the competition for talent forces …rms to pay high compensation rates for talented
managers. The bene…ts of having managers with high general human capital increases in thelater period if employing someone with high learning capability can be considered an investment0hG . If managers have a greater ability to learn in the new environment, this
fGn

0
hG
fGl

skill increases the …rm’s future outputs. However, it does not increase the initial output during
a learning period. Because(h) simply re‡ects the initial instantaneous output, net of the

future instantaneous output yielded by the manager, the impact of learning ability on
is negative.

(h)This unique prediction helps us to separate general learning ability from target…rm-speci…c skills.

3

Tenure and Separation Probability

In this section, we explain how we utilize the timing of separation to obtain information to
distinguish two hypotheses on managerial experiences in a …rm (i.e., an increase in target …rmspeci…c human capital and a reduction in the general ability to learn in a new environment) fromthe coe¢ cients of the e¤ect of tenure on separation probability. For this purpose, we propose
testable hypotheses to interpret the relationship between tenure and separation probability.
Taking a …rst-order approximation, it is shown that:n(h) = ~ T hT + ~ G hG + ~ 0X XV ;(h) =where ~ T =fT0 l hT

fT0 n (hT )1 (1 q^)

fT0 n hT00, ~ G = fGn

0,0
G = fGn

hG

Th

hG

T

Gh

0
fGl

hG

0
fGl
hG

16

G

+

(5)

0
X XV ;+ F0
0, andhGX =(6)@v n (XV )@XV

0, ~ X = 1@v l (XV)@XV(1 q^) ,V)@v n (X
@XV

.

T

=

Let

b and

e denote the manager’s tenure as a board member and as an employee in thetarget …rm, respectively. Following the tradition of labor economics, we assume that the target…rm’s …rm-speci…c human capital is an increasing function of these tenures.
hT =We assume that

x

0+

b b+

e e:

0 for x = b or e, which means that increases in both types of tenuresassist in the accumulation of …rm-speci…c human capital.
On the other hand, as hG is a general skill, labor economists typically assume that hG
increases not only as a result of experience in the target …rm, i.e., as a result of both
but also as a result of the duration of other experiences,o.

hG = ! 0 + ! b b + ! e e +where ! x
and

b and

e,

Therefore, we have:o+;0 (x = b; e) are the parameters that capture the importance of tenure for learning
0 is the parameter that captures the importance of other experiences.

This model

generalizes the standard assumption, in that it allows for di¤erent experiences to vary in theire¤ectiveness in accumulating general human capital. Estimating

o by

o =a

b

e , where

a is the manager’s age when the M&A takes place, we can rewrite hG as a function of tenures
and age:hG = ! 0 + (! bThe parameters ! x)

b + (! e

)

e+

a+ :

(x = b; e) capture the relative productivity of tenure for the accu-

mulation of general human capital compared with other experiences. Buchholtz et al. (2003)
argue that longer tenure may hamper the accumulation of general skills that are needed foradaptation to a new environment. This implies that ! x< 0. Although this might be areasonable assumption, we also allow for the possibility that ! x> 0: i.e., that experience ina target …rm can assist in improving general human capital. Several studies on spin-o¤ e¤ects
suggest that previous experience in incumbent …rms can be an important source of experience inestablishing new …rms (e.g., Klepper, 2001). It would be possible to apply a similar reasoning
in this context. This possibility is captured by ! x

17

> 0.

The following proportional hazards model can be derived:[

qt = B (t : XZ ) en(h)I(t=0)+n (h)];(h) = ~ T hT + ~ G hG + ~ 0X XV
(h) =

Th

T

Gh

hT

b b+

e e;

=

hG = (! b

)

G

+

0
X XV

b + (! e

)

e+

a+ :

Using this derived hazard function, the theoretically predicted e¤ects of tenure on separation
probability are summarized as follows:n (h))

d(

d x
d(

(h))
d x

@[

(

(h) +
@ x

n (h))]=[~ T x + ~ G (! x

)] ;

(7)

=

[ T x

)] ;

(8)

=

[(~ T +G (! xT ) x + (~ G

G ) (! x

)] ;

(9)

where x = b or e.
Investigating equations (7), (8), and (9) provides the following propositions that we wish to
reject in our empirical study.

The …rst proposition below shows the set of conditions underwhich a newly merged …rm does not value any speci…c skills of employees in the target …rm
and/or any ability to learn in a new environment, and under which a market friction does notdepend on the general human capital.
Proposition 5 We assume that0
1. Suppose that fGlhGx

0 for both x = b and e.

0fGn
hG and F 0 hG

fT0 n hT = fT0 l hT = 0, and, therefore, ~ T =0 and, therefore, ~ G
T

G

0.

If

= 0, then, for both x = b and e, we

have:
sign

d(

n (h))

d x

=

sign

d(

(h))
d x

= sign

@[

(

(h) +
@ x

n (h))]:(10)

2. Suppose that fT0 l hT

fT0 n hT

0 and, therefore,

18

T

~T

0.

0
0
(a) If fGl
hG = fGnhG and, therefore,

G = 0, then, for both x = b and e, we have:

d(

(h))
d x

(b) If F 0 hG = 0 and, therefore, ~ G
@[

0

(11)

G = 0, then, for both x = b and e, we have:

(

(h) +
@ x

n (h))]000(c) If fGl
hG = fGnhG and F 0 hG = 0 and, therefore, ~ G =(12)

G = 0, then, for bothx = b and e, we have:d(n (h))

d x

0;

d(

(h))
d x

0;

@[

(

(h) +
@ x

n (h))]

0:(13)

The intuition behind equation (10) in Proposition 5 is explained as follows. If target …rmspeci…c human capital does not increase productivity, fT0 n hT = fT0 l hT = 0, an increase intenure in‡uences the separation probability only because it can change the learning capabilityof managers. If ! x, where x = b or e, because an increase in tenure assists in improving

general human capital relative to other work experience, it increases the productivity of the
manager in the newly merged …rm and, therefore, lowers the separation probability at all times.
However, because learning takes time, the bene…ts from a general skill that improves the learning
capability are not initially realized. Hence, the initial products of tenure, net of future products,
are negative and the coe¢ cient of the interaction with the t = 0 dummy must be positive.
However, if ! x, the opposite mechanism occurs.

Because an increase in tenure reduces

the experiences that improve general skills in this case, it simply lowers the productivity of the
manager in a merged company and, therefore, increases the separation probability at all times.
However, because the initial productivity of the manager after the M&A is not subject to thisnegative e¤ect, the initial products of tenure, net of future products, are positive. Therefore,
the coe¢ cient of the interaction with the t = 0 dummy must be negative.

Hence, for bothcases, equation (10) must be satis…ed.
Similarly, we can explain the intuition behind equations (11) (12) and (13) in Proposition 5 as00follows. If there are no bene…ts from learning capability fGl
hG = fGnhG , an improvementin general human capital does not cause any productivity di¤erence between the initial period
and the later period. Because the human capital speci…c to the target …rm possessed by thetarget-…rm manager is more important before the managers in the acquiring …rm learn the same19

skills, it would be more highly valued at t = 0.

Therefore, the coe¢ cient of the interaction

with the t = 0 dummy must be negative. Equation (11) shows this condition.
If the cost of hiring a new manager does not depend on the general human capital of the
manager, F 0 hG = 0, as a result of market competition, there are no bene…ts from employing
a manager with high general human capital. Therefore, as an increase in tenure raises target…rm-speci…c human capital, it certainly lowers the initial separation probability. Equation (12)shows this condition.
0
0
If there are no bene…ts from learning capability fGl
hG = fGnhG , and the cost of hiring

a new manager does not depend on the general human capital of the manager, F 0 hG = 0,
an increase in tenure changes the separation probability only because it can raise the humancapital speci…c to the target …rm.

In addition to this, for the reason explained above, thecoe¢ cient of the interaction of tenure with the t = 0 dummy must be negative. Equation (13)summarizes these conditions.
Note that Proposition 5 requires that equations (10) and (11) are jointly satis…ed by thecoe¢ cients for both the tenure as a board member, x = b, and the tenure as an employee, x = e.
Because an acquiring …rm does not care about how a target manager obtains a skill, if the skills
are not pro…table within the merged …rm, the coe¢ cients of tenure as a board member and as
an employee will be in‡uenced in a similar way. In other words, if the derived conditions are
not satis…ed for either x = b or x = e, we can reject the hypotheses in Proposition 5.
On the other hand, the di¤erence between the coe¢ cients for the two types of tenure, x = b
and x = e, provides us with information about the di¤erences in skills obtained as a result ofexperience gained as a board member or as an employee. The following proposition summarizes
the hypotheses about speci…c human capital and experience that we wish to reject.
Proposition 6 Suppose that fT0 l hT0that fGlhG0
fGn
hG and F 0 hG

fT0 n hT0, and, therefore,

0 and, therefore, ~ G

G

T

~T

0. Suppose0.

If

x = 0, whichmeans that experience gained during x, where x = b or e, does not raise human capital speci…cto the target …rm, then:
sign

d(

n (h))

d x

=

sign

d(

(h))
d x

= sign

@[

(

(h) +
@ x

n (h))]:(14)

Equation (14) looks very similar to equation (10). The only di¤erence is that Proposition
5 requires that equation (10) must be jointly satis…ed for both x = e and x = b, whereas
Proposition 6 states that we can separately use equation (14) for x = e and x = b.
20

The

intuition behind equation (14) is the same as that behind equation (10). However, by separately
applying the same logic to the coe¢ cients for the tenure as a board member and the tenure as
an employee, we can determine di¤erences in skills obtained from experience as a board member
compared with experience as an employee.
Finally, the following proposition summarizes the hypotheses about general human capitaland experience that we wish to reject.
Proposition 7 Suppose that fT0 l hT

fT0 n hT0that fGlhG

0 and, therefore, ~ G

1. If ! x0fGn
hG and F 0 hG

0, and, therefore,
G

T

~T

0. Suppose0.

, which means that a long tenure during x, where x = b or e, does not hamper

the accumulation of general human capital relative to other experiences, then:d(n (h))d x
2. If ! x

0;

@[

(

(h) +
@ x

n (h))]

0:, which means that a long tenure during x, where x = b or e, does not assist in

the accumulation of general human capital relative to other experiences, then:
d(

(h))
d x

If ! x0:, an increase in tenure assists in the accumulation of general human capital. Be-

cause an increase in tenure also increases valuable human capital speci…c to the target …rm, along tenure is valued by the newly merged …rm and, therefore, it lowers the separation probability at all times.
However, if ! x, the opposite e¤ect occurs. Because the human capital speci…c to thetarget …rm is initially more highly valued, and because limited learning abilities do not initiallycause any problem, the initial value of tenure is larger than its subsequent value. Therefore,
a de…nite prediction of our theory is that the coe¢ cient of tenure interacted with the t = 0
dummy must be negative. Equipped with the theoretical predictions outlined in this section,
we now conduct our empirical study.

4

Dealing with Unobserved Heterogeneity

Suppose that XV can be decomposed into the characteristics of the target-…rm manager andthose of the …rm to which the manager belongs. To analyze the determinants of the retention
21

rate of target managers in a newly merged …rm, we use the following strati…ed Cox proportional
hazards model, which summarizes our theory:^ (t : XZ;f ) e
qf jt = B

where

[

f j I(t=0)+

fj

]

fj

= ~ b b;f j + ~ e e;f j + ~ 0D XD;f;j + ~ 0F XF;f +~fj=

b b;f j +e bf;j +0
D XD;f;j +fj

0
F XF;f +b;f j is the jth person’s tenure as a board member at …rm f ,fj;

e;f j is the jth person’s

tenure as an employee at …rm f , the vector XD;f;j contains any other target-…rm manager
characteristics of the jth person in …rm f , including the jth person’s age when …rm f was taken
over, and the vector XF;f contains any characteristics of the f th …rm that can in‡uence theproductivity of managers. Finally, the vector XZ;f contains any …rm-level variables that can^ (t : XZ;f ) contains B (t : XZ;f ) and some constant terms.
in‡uence baseline hazard and B
This equation depends on the individual unobserved heterogeneity of a manager j at …rmf,

fj.

Without controlling forf j , our estimates might be biased.

3, we focus on titled directors in Japanese companies.

As explained in footnote

However, talented workers may be

appointed to titled director positions with less experience than less talented workers. Hence,f j andb;f j can be correlated.

In order to deal with this bias, we estimate unobserved abilities from our data and control
for them in our survival analysis. The following argument explains how to estimate

fj.

Suppose that a person is appointed to a management position (titled director) in Japan if
and only if:^ f j t^h

H0 Nh f; t^ ;^ f j t^
h

(1

(15)

^
!) hTfj t^ + !hG
fj t^
where hTfj t^ and hG
f j t are the target …rm-speci…c human capital and the general humancapital of a person j at the f th …rm in calendar year t^, ! is the weight on the general humancapital and H0 Nh f; t^ is the level of human capital required for appointment to a managerial
position, where H is a parameter vector and a vector Nh f; t^ summarizes the conditions thatin‡uence the required level of human capital of …rm f in calendar year t^.
^ f j t^ , we can …nd the parameters
From the de…nition of h

22

0,

b,

e , ando to describe thefollowing human capital accumulation function:^ f j t^ =
h
where

b;f j

0+

b b;f jt^ +e e;f j +o o;f j + ! f j ;(16)t^ is the tenure as a board member of person j at …rm f in calendar year t^ ando;f j is the jth person’s length of experience before joining …rm f .

Combining equations (15)and (16), when an employee j is appointed to an executive position, the following equality mustbe satis…ed:~ = H , ~0 =where H~~ 0 Nh f; t^jt^j = Hb;f j

, ~e =, ~o =~

0~e e;f j! fj

o o;f j

~fj ;

(17)

b

, and t^j is the calendar year whenemployee j is appointed to an executive o¢ cer position.

This equation implies that, after

b

0
b

e
b

o
b

controlling for several observable variables,
means that

b;f j

t^j

, ~fj =t^jb;f j

is negatively correlated with ~ f j . Thispotentially contains useful information about ~ f j .

Let us de…ne a function R such that:
R f; j; t^~ 0 Nh f; t^
H

~

~

0

e e;f j~o o;f j

b;f j

t^ :

~ ~ 0 , ~ e , and ~ o , we can estimate ~ j from the following:
Given the estimates of H,~ f j = R f; j; t^j :~ ~ 0 , ~ e , and ~ o . However, this is not easyHence, we seek to obtain unbiased estimators of H,
because we can observe only a selected sample.
We de…ne the deviation of the unobserved ability from the …rm-level average in year t^ forthe observed sample, "f j t^ , as follows:"f j t^~fj

E ~ f j jIb = 1; f; t^ = R f; j; t^j

E ~ f j jIb = 1; f; t^ ;where Ib is the dummy variable that equals one if and only if a person is a titled director and isincluded in our sample and, therefore, E ~ f j jIb = 1; f; t^ is the conditional expectation of ~ f j ,given all relevant information at the f th …rm in year t^ for the observed sample. Then, equation(17) can be rewritten as follows:b;f j~ 0 Nh f; t^jt^j = H~0~e e;f j~o o;f j23

E ~ f j jIb = 1; f; t^"f j t^ ; 8t^:

(18)

Note that E "f j t^ jIb = 1 = 0 by construction. Note also that the deviation of the unobserved
ability from the conditional expectation of ~ f j at the f th …rm in year t^ for the observed sample,"f j t^ , is uncorrelated with …rm-level variables. Hence, we expect to satisfy an orthogonality
condition that E "f j t^ Nf jIb = 1 = 0 for the vector of …rm-level variables Nf for any t^.
Therefore, if we know a functional form of E ~ f j jIb = 1; f; t^ , we can obtain unbiased estimates~ ~ 0 , ~ e , and ~ o from a generalized method of moments (GMM) estimation, using …rm-levelof H,

variables from the sample of titled directors as its instruments.
In order to implement this idea, we need to estimate E ~ f j jIb = 1; f; t^ . Because we use
the sample of titled directors at target …rms in the year when an M&A occurs, equation (15)^ f j t^m
implies that Ib = 1 if and only if hf^m
H0 Nh f; t^mf , where tf is the calendar year

in which the M&A occurs for target …rm f .

Using equation (16) and a function R f; j; t^ ,^ f j t^mhf

H0 Nh f; t^mcan be rewritten as a condition for ~ f j as follows:f
Ib = 1 if f ~ f jfor any f and j.

R f; j; t^mf ;This means that the observed sample is considered to be drawn from anupper-tailed distribution of ~ f j and that:E ~ f j jIb = 1; f; t^m
f = E ~ f j j~ f jhWe need to estimate E ~ f j j~ f j^m
R f; j; t^mf ; f; tf :ito obtain unbiased estimators of the; f; t^m
R f; j; t^mff

parameters. The standard two-stage estimator in Heckman (1979) uses a random sample fromthe population to estimate selection equations, the parameters of which are used to constructihm , by assuming that ~^an inverse Mills ratio to estimate E ~ f j j~ f j R f; j; t^m;f;t
f j isffdrawn from a normal distribution. Typically, exclusive variables are needed for the estimationof selection equations to obtain reliable estimates.
Unfortunately, a random sample from the population is not available in our case. However,
h
i
m ,
^
note that our conditional expectation of unobserved ability, E ~ f j j~ f j R f; j; t^m
;
f;
t
f
f
is a function of R f; j; t^mf , which is determined by the parameters of our structural equation~ ~ 0 , ~ e , and ~ o . Therefore, it might be possible to jointly estimate the parameters on(18), H,the conditional expectation of unobserved ability with equation (18) using the GMM. This ispossible because, although we have only a selected sample, the timing of selection is di¤erent
across individuals, which gives us information about selection equations. In addition, the timing^of observations, t^mf , is generally di¤erent from the timing of promotions, tj . Therefore, we can24

…nd several exclusive variables that are needed to identify parameters and to obtain reliable
estimates.
The remaining concern is determining what is a plausible distribution of ~ f j . Gabaix andLandier (2008) argue that an extreme value theory can provide a nice approximation for theupper tail of a large class of continuous distributions, including uniform, Gaussian, exponential,
lognormal, Weibull, Gumbel, Fréchet, Pareto, stretched exponential, and log-gamma distributions.

More speci…cally, suppose that ~ is drawn from a distribution function F (~ ), whereF 0 (~ ) is di¤erentiable in a neighborhood of the upper bound of its support
there exists= lim ~ !

d 1 F (~ )d~ F 0 (~ ) and2 R [ f+1g, and< 1. We de…ne F (~ ) = 1 F (~ ) and Q (x) = F

1 (x).

Gabaix and Landier (2008) apply an extreme value theorem and show that there exists aand0such that:

Q0 (x)

0x

1.

Our appendix proves the following lemma.
1 , where
0, and that there exists a Q (0) =Lemma 8 Suppose that Q0 (x) =0xihlim"!0 Q (") + 0 " and Q (0) < 1. Then, for any small xp , we have:E [ jxxp ] =

Q (0) + Q (xp ):+1

The assumption in Lemma 8 requires that the ability distribution has a …nite upper bound,Q (0). Gabaix and Landier (2008) provide empirical evidence that supports this assumption
using data on U.S. compensation of CEOs.
We assume that a function Q may di¤er across …rms f and across years t^, Q x : f; t^ ,and that Q 0 : f; t^m=f

0Nf; t^mf , where Nf; t^ is a vector of variables that in‡uencea potential upper bound of talent in …rm f in calendar year t^. Let us choose xp so thatnom . Then, fxm^^xp = F R f; j; t^m
:
f;
t
x
g
=
~
R
f;
j;
t
and Q xp : f; t^m
=
p
fj
f
f
f
f
R f; j; t^m
Therefore, we can estimate the conditional expectation of ability in each …rm
f .
h
i
m by:
^
E ~ f j j~ f j R f; j; t^m
:
f;
t
f
f
E ~ f j j~ f j^m
R f; j; t^mf : f; tf =0N

f; t^m+ R f; j; t^m
f
f
+1

:

~ ~ 0 , ~ e , and ~ o using the GMM based on
In sum, we can obtain unbiased estimates of H,
25

the following orthogonality condition:
0 = E "f j t^mf Nf jIb = 1 ;"f j t^mf~~ 0 Nh f; t^H

R f; j; t^where Nf = Nh f; t^j , Nh f; t^m,Nfof the …rm-level averages of

b;f j

t^ ,

f; t^m+ R f; j; t^mf
f

0N= R f; j; t^jf; t^m;fe;f j ; and

e

+1
~
e;f j

f

t^m
;
f

~

0

(19)
;

(20)

o o;f j

b;f j

t^ ;

(21)

t^j

, whereft^ is the vectorfo;f j in year t^.

Using the estimated parameters,~ ~ 0 , ~ e , and ~ o , we can estimate ~ f j by:H,~ f j = R f; j; t^j .

(22)

Using ~ f j , we can estimate:^ (t : XZ;f ) e
qf jt = B[

f j I(t=0)+

fj

]

(23)

fj

0
0
+
~fj ;
= ~ b b;f j t^m
f + ~ e e;f j + ~ D XD;f;j + ~ F XF;f +fj=where ~ + = !b ~ andb b;f j

+ =

5

Data

5.1

Firm-level data

b

!

t^m
f +

e e;f j +0
D XD;f;j +

0
+
~fj ;
F XF;f +

(24)
(25)

.

Below, we test the propositions outlined in the previous sections, focusing on M&As during
the period 1990–2006 in Japan. We identify Japanese M&As in this period from the Delistingdataset, which is manually constructed from various sources of information, including Kaisha
Nenkan 1969–2006, Kaisha Shikiho 2000–2006, and Tosho Yoran 1972–1973 and 1975–2007.
This dataset contains information on delisted …rms in exchange markets throughout Japan
from 1968 to 2007.

The information includes the stock code and name of the delisted …rm,the listed market, dates of listing and delisting, the reason for delisting, and the name and thestock code of the new …rm, when the reason given for delisting was a merger or an acquisition.
From the database, we selected those …rms that had been delisted because of a “merger”or26

Figure 1: Number of M&As each year during the period 1990–2006

a “full-ownership acquisition” during the sample period7 . When the …rms that were delisted
as the result of M&As involve a consolidation of assets and liabilities under a company with astock code, we can observe who is retained in the new …rm after the M&A as a board member.
We select these types of delisted …rms, and refer to them as “target …rms”. In most M&As,
one of the merging …rms survives as the same …rm with the same stock code. In other cases,
mergers result in a new company with a new stock code. Our dataset includes both cases, andwe refer to the postmerger …rms in both cases as “new …rms” in this paper. When we discuss
surviving …rms with the same stock codes after M&As, we refer to them as “acquirers”and werefer to all premerger …rms that transacted with target …rms during M&As as “other merged…rms”.
Our sample contains 344 M&A cases, comprising 123 mergers and 221 full-ownership acquisitions. Only mergers between listed …rms are included. Figure 1 depicts the number ofsample M&As over the study period. We can see that the number of M&As rapidly increased
after 1998.
The exchanges on which the target …rms are listed include the Tokyo, Osaka, Nagoya, andother local stock exchanges, as well as emerging and over-the-counter markets. However, we
exclude cases in the JASDAQ market because director-level data for these …rms are available
only after 2000.
We merge data on …rm characteristics for the target …rms and the new …rms with the above
7

Other reasons given for delisting include “stock transfer”, “bankruptcy”, “insolvency”, “window-dressing
settlement”, and “business suspension”. There was a single case of stock transfer in our sample, but we excluded
it because the target …rm was in the JASDAQ market.

27

M&A data. The data on …rm characteristics are from the Nikkei NEEDS database. We …rst
merge the three-digit Nikkei industry code for each target and new …rm.
Table 1 presents the numbers of target and new …rms in our sample, based on a two-digit
industry classi…cation8 .

The second column shows the number of target …rms by industry,whereas the third column shows the number of new …rms by industry.

The fourth column

shows the number of M&A cases where the target and new …rms are from the same industry.
We can see that M&As within the same industry occurred most often in the electronics industry.
Industry
Food
TextilePulp
ChemicalPharmaceutical
Petroleum
RubberCeramic
Iron ore
Nonferrous metal and metal
Machinery
Electronics
Shipbuilding
Automobile
Transport machinery
Precision instruments
Other manufacturers
Marine products
MiningConstruction
Trade
RetailOther …nancial businesses
Real estate
Rail and bus
Land transportation
Marine transportation
Air transportation
Telecommunications
Electricity
ServiceTotal

No. of target …rms
15
7
13
19
6
3
2
14
7
15
24
27
0
9
6
2
10
1
4
26
43
27
2
11
2
2
7
1
4
0
35
344

No. of new …rms
16
8
13
21
3
6
1
13
13
18
24
46
1
9
0
2
9
0
2
26
32
31
4
1
12
4
6
3
2
2
15
344

Both
14
5
10
14
2
3
1
10
7
10
16
24
0
4
0
1
6
1
2
16
22
21
2
1
2
2
6
1
2
0
13
218

Table 1: Numbers of mergers and acquisitions by industry
8
We exclude …nancial institutions such as banks, stock companies, and insurance companies because of thedi¤erence in accounting systems.

28

Next, we merge the …nancial characteristics in the Nikkei NEEDS database with our sample.
More speci…cally, we merge operating income, sales, number of full-time employees, personnel
expenses, total assets, and the stock share of the top ten stockholders for each target …rm.
These variables are explained in detail below. We also merge operating income, total assets,
and the stock share of the top ten stockholders of the acquirer of the target …rm in the year
prior to the M&A if there is a surviving …rm with the same stock code. For cases of M&As
without any surviving …rm, we use the average value of these variables for all other merged…rms instead to represent those of the acquirer.

5.2

Personnel data

Next, we merge the …rm-level data with the director-level data. The data for board members aretaken from the Directors data published by Toyo Keizai. This database contains informationon the directors of all listed …rms in Japan from 1990 to 2007. The information includes thetitle, the date the person entered the …rm, and a personal history of the board member, alongwith the name and date of birth.
Because we are interested in the retention of Japanese executives after M&As, we focus ouranalysis on directors with titles in the sample target …rms9 . Therefore, our sample comprises
all directors with titles at target …rms in the year of the M&A10 . As explained in footnote
3, following the arguments by Kaplan (1994) and Saito and Odagiri (2008), we consider titleddirectors to be the top executives in Japanese companies. In the following sections, we analyze
whether executives in target …rms are retained as board members in the new …rms after M&As.
We have 1520 observations (titled directors) for 343 targets, with an average of 4:43 titleddirectors per target. We specify the date of birth, title, the date a person entered the …rm, andher/his history as a board member. We also identify the number of other …rms (including thetarget …rm itself) in which target-…rm managers served as board members in the year of the
M&A.
From the Directors data, we determine whether a target manager was retained as a board
member (with or without a title) in the new …rm after the M&A and, if so, how many years
he/she stayed on the board after the M&A11 . In addition, we identify whether a target-…rm
9

Auditors are excluded.
More precisely, titled directors who served in their positions until a year before the M&A are also included
in our sample because of a gap between the M&A date and the recording date for the Directors data. We assume
that titled target directors who resigned their positions more than a year before the M&A did so for reasons
other than the M&A, and we exclude them from our sample.
11
We consider the target manager to have been retained even if he/she becomes a director with a di¤erent
title in the new …rm or if the manager loses his/her title in the new …rm. In addition, in the cases where an
1029manager served as a board member of the acquirer before the M&A.
Table 2 provides summary statistics of the managers’ retention characteristics.

The …rst

variable (retained ) takes a value of one if the target manager became a board member of the new…rm after the M&A and is zero otherwise. The second variable (years of survival if retained )is the number of years that the retained target manager served as a board member of the new…rm after the M&A. The table shows that only 38:7% of the target managers were retained asboard members after M&As and that the retained managers kept their positions for an averageof less than …ve years.
Variable
Retained
Years of survival if retained

No. of observations

Mean

S.D.

Min.

Max.

1520
588

0:387
4:117

0:487
2:190

0
1

1
16

Table 2: Characteristics of target directors

5.3
5.3.1

Empirical speci…cation
GMM estimation

Using the dataset explained above, we …rst conduct a GMM estimation using equations (19),(20), and (21) to obtain the unobserved individual ability de…ned in equation (22).
The summary statistics of the variables used in the GMM estimation can be found in Table
3. The …rst four variables are those of the manager’s tenure history, which determine his/herhuman capital at t^j and t^m
f as in equation (16).

Tenure as a board member,b;f jt^ , isthe manager’s length of tenure after he/she became a board member in the target …rm. We
calculate tenure as a board member in the years t^j and t^mf from the target manager’s history asa board member in the target …rm. Tenure as an employee,

e;f j , is the manager’s length oftenure as an employee in the target …rm, which is calculated by determining the tenure before
he/she became a board member, and outside experience,o;f j , is calculated from the manager’sage (calculated from the date of birth) minus his/her entire period of tenure in the target …rm.
For the variables that determine the human capital level required for appointment to a
managerial position (a titled director position), Nh f; t^ , we use Negative operating income,Direct, No. of employees, Wage, Median tenure as a titled director, and Median age at t^mf .
The summary statistics of these variables in the years t^j and t^mf are shown in rows 7 to 16 inother merged …rm of an M&A survives as the new …rm and the manager of the target …rm was also a director
in this other merged …rm and continues to be a director in the new …rm, we consider this manager to have beenretained.

30

the table12 . Negative operating income is an indicator variable that takes a value of one if theoperating income of the target …rm is negative and is zero otherwise.

Kaplan (1994) showsthat, if the operating income is negative, then the current managers are likely to be dismissed.
Because a …rm must replace managers with new appointees for an exogenous reason in this case,the required level of human capital would be lower than is usually the case for appointments.
Therefore, we expect a negative impact from negative operating income on the required level ofhuman capital.
Direct is an indicator variable that takes a value of one if the manager is hired from outside
the …rm.

We control for this variable because the required human capital level may di¤erdepending on whether the manager is selected from among the employees of the …rm or is hiredfrom outside. We control for the number of employees to estimate the required human capitallevel because more employees may mean there is more intense competition to become a manager
on the board. Therefore, we expect that the number of employees will have a positive e¤ect on
the required human capital level. Similarly, a higher average wage may imply that employees ofthe …rm have a higher average human capital level. Therefore, a greater level of human capital
may be required for appointment to a titled director position. The average wage is calculatedusing the number of employees and the personnel expenses of the target …rm.
We include the median length of tenure as a titled director within a …rm and consider theturnover rate of titled directors to be low if the tenure length as a titled director is high, on
average.

In such cases, it is more di¢ cult to become a titled director.

We also control the

median value of age in the merger year. If a …rm has the high median age, it is likely that the…rm set a high requirement to become a titled director. Therefore, we expect its coe¢ cient tobe positive.
For a variable in a vector N

f; t^mf , we assume that the potential highest level of ability

in a target …rm depends on the …rm’s size.

We use the sales volume of the target …rm as aproxy for the target …rm’s size. The summary statistics for the sales volume are shown in row
18 of the table. The next three variables in Table 3 represent the instrumental variables forthe endogenous variables in the model, that is, the instrumental variables for tenure as a board
member at t^m
f , tenure as an employee, and outside experience. We use the target …rm’s median
12

More speci…cally, we calculate the values of these variables immediately before the years t^j and t^m
f , except
for Direct, which takes the same value for these two years. For median tenure as a titled director, we calculate
the median tenure of all the titled directors of …rm f , excluding that of the target manager. The tenure of eachtarget manager is calculated on a monthly basis and then expressed in years. When we use the variables from
Nikkei NEEDS, we use the published data for the latest …scal year to t^j : In some cases, especially for variables
at t^j , the …nancial data are not available. In these cases, we use the data for the year nearest to t^j :31

value at t^mf for these variables as instruments.

5.3.2

Survival analysis

Once we obtain the unobserved individual ability, ^ f j , from the GMM estimation, we analyze
the determinants of the retention of target-…rm managers after M&As. We utilize the strati…ed
Cox proportional hazards model in equations (23), (24), and (25), which requires us to specify
the vector XD;f;j of target-…rm manager characteristics other than tenure at the time of the
M&A, the vector XF;f that in‡uences the productivity of managers, which includes the target…rm characteristics and the transaction characteristics suggested by Wulf and Singh (2011)13 ,and the vector XZ;f , which contains any variables that in‡uence the baseline hazard.
For the variables in the vector XD;f;j , we use the manager’s age at the time of the M&A(Age), the number of …rms in which the target manager served as a board member (No. of …rms
as a board member ), whether the target manager was a board member in the acquirer before
the M&A (Board member in the acquirer before the M&A), and whether the target manager
was the president or chairman of the board of directors (Upper ). These variables are calculated
from the Directors data, as explained in the previous section.

We include the target …rm’s

performance as a manager characteristic to measure the manager’s ability. To represent thetarget …rm’s performance, we use the return on assets (ROA) in the year prior to the M&A,
where the ROA is de…ned as operating income divided by assets, measured using the deviationfrom the industry median. Note that this measure is at the …rm level, even though we consider
it as a manager characteristic, as suggested by Wulf and Singh (2011).
The target …rm’s characteristics in XF;f include …rm size and the board size of target…rms.

To control for the target …rm’s size and its board size, we include the logarithm of

the target …rm’s assets in the year prior to the merger (Log target assets) and the number ofboard members (Board size). The previous literature has considered the target …rm’s size tobe important because larger and more complex …rms may require managers with unique skills,
which may increase the retention rate of managers (Finkelstein and Hambrick, 1989)14 .

We

13Wulf and Singh (2011) investigate the determinants of target CEO retention rates. Our analysis di¤ers in that
we include other directors with a title. As for the determinants of CEO retention rates, Wulf and Singh (2011)
consider target-…rm characteristics, CEO characteristics, transaction characteristics, and acquirer governancecharacteristics. They also include variables such as target-…rm CEO compensation and the number of days as
CEO until completion of the merger. Unfortunately, these variables are not available for our chosen context.
However, we are able to include more detailed director characteristics because of the richness of our personnel
data.
14
The models regarding span of control (e.g., Lucas, 1978; Rosen, 1982) predict that a large …rm should be
operated by a talented person. Recent assignment theories of managerial compensation (e.g., Terviö, 2007;32

Variable
Tenure as a board member at t^j (years)
Tenure as a board member at t^mf (years)Tenure as an employee (years)
Outside experience (years)
Age (years)
Variables in Nh f; t^ , for t^ = t^j ; t^mf
Negative operating income at t^j
Negative operating income at t^mf
DirectNo. of employees at t^j (1000)
No. of employees at t^mf (1000)
Wage at t^j (million yen)
Wage at t^mf (million yen)Median tenure as a titled director at t^j (years)
Median tenure as a titled director at t^mf (years)(yearsold)Median age of titled directors at t^mf
Sales (1000 million yen)
f

;

f

Mean

S.D.

Min.

Max.

2:70
8:50
11:82
40:35
60:67

2:91
7:41
13:59
15:62
5:54

0:00
0:25
0:00
15:17
35:08

20:92
56:42
43:17
71:17
90:92

1520
1520
1520
1520
1520
1520
1519
1520
1520
1520

0:15
0:21
0:20
1:70
1:53
4:25
5:03
4:89
4:61
55:35

0:36
0:41
0:40
2:65
2:24
3:37
3:89
4:00
3:19
4:34

0:00
0:00
0:00
0:006
0:006
0:08
0:21
0
0:50
27:58

1:00
1:00
1:00
23:87
16:35
28:39
25:57
33:17
24:67
69:17

1520

146:78

256:950:68

2877:40

1520
1520
1520

7:48
10:84
40:20

4:17
12:17
13:66

0:25
0:00
20:42

32:42
35:83
68:42

1520
1520
1520
1520

1:14
0:15
0:31
0:00

0:51
0:35
0:46
0:06

1:00
0:00
0:00
0:43

10:00
1:00
1:00
0:52

1520
1520
1520
1520
1520
1520
1520
1520

11:07
5:77
6:89
0:27
0:48
0:61
0:00
7:09

1:35
2:73
1:35
0:23
0:50
0:49
0:06
1:56

6:92
1:00
8:39
0:00
0:00
0:00
0:68
8:89

14:61
15:00
0:14
0:99
1:00
1:00
0:60
0:00

f; t^mf

Variables in N

t^m
f

No.

1520
1520
1520
1520
1520

t^j

(instrumental variables)

Median value of tenure as a board member at t^mf (years)
Median value of tenure as an employee (years)
Median value of outside experience (years)
Manager characteristics
No. of …rms as a board member
Board member in the acquirer before the M&A
Upper
Target ROA
Firm characteristics
Log target assets
Board size
Log stock share of top 10
Target …rm’s relative size in assets
RelatedAcquisition

Acquirer or others ROA
Log top 10 share of acquirer or others
Table 3: Summary statistics

33

include the board size of the target …rm because an increase in the number of managers may
reduce the productivity of managers in a target …rm.
Our theory is based on the presumption that there are some explicit or implicit transfers thathave to be negotiated after the M&A. Although we believe that this is a plausible assumption,some may argue that this may not be true. If so, the initial contracts resulting from the exante strategic bargaining during the M&A can in‡uence the separation probability. To estimate
the importance of ex ante strategic bargaining, Bargeron et al. (2009) control for a measure of
the ownership structure, speci…cally, the level of insider ownership in a target …rm. Following
this idea, we include the logarithm of the stock share of the top 10 stock holders (log stock
share of top 10 ) in XF;f , so that we can minimize the bias even if our assumptions are notvalid. We expect that the impact of strategic retention would be smaller if the value of thisvariable were larger because large shareholders have more incentive to monitor managers undera concentrated ownership structure.
The transaction characteristics in XF;f include the relative size of the target …rm. If the …rm
is large, the postmerger integration may be more di¢ cult and, therefore, we would expect thelikelihood of manager retention to be higher (Zollo and Singh, 2004). To measure relative …rm
size, we calculate the ratio of the target …rm assets to the acquirer assets if there is a surviving…rm with the same stock code.

For cases of M&As without any surviving …rm, we use thetotal assets of all other merged …rms in place of the acquirer assets.

Following the previous

literature, including Walsh (1989) and Buchholtz et al. (2003), we include a dummy variable
that represents whether the target and the new …rm operate in the same industry as a transaction
characteristic. More speci…cally, we create an indicator variable that is equal to one if the newand target …rms operate in the same three-digit Nikkei industry code (i.e., medium industry
classi…cation) and is zero otherwise (Related ).

We also include a full-ownership acquisition

dummy to observe whether mergers and full-ownership acquisitions have di¤erent e¤ects on theretention rate (Acquisition).
We control for the governance characteristics of the other merged …rms. Speci…cally, we
control for the ROA and the stock share of the top 10 stock holders of the acquirer if there isa surviving …rm with the same stock code. For cases of M&As without any surviving …rm, we
use the average value of these variables for all other merged …rms in place of the acquirer values(“Acquirer or others ROA” and “Log top 10 share of acquirer or others”).
Gabaix and Landier, 2008) make this assumption and …nd that this model can quantitatively explain the relation
between CEO compensation and …rm size. If this prediction is correct, the size of a …rm can also be considered
as a manager characteristic.

34

The summary statistics of these variables, which appear exclusively in the strati…ed Cox
proportional hazards estimation, are shown in the last two groups in Table 3. In addition tothese variables, we need tenure as a board member at t^m
f , tenure as an employee, and age, forwhich summary statistics are shown in the …rst group of the table. Tenure and age variables
are calculated as explained above.
In addition, for the vector XZ;f in equation (23), we include two-digit industry codes for a
new …rm and a target …rm and the year of the M&A. This means that we allow the baseline
hazard functions to di¤er for these groups. Finally, we construct an initial dummy that assigns
a value of one for the initial year (t = 0) and zero for any other separation time15 .

6

Results

Table 4 shows the results of our GMM estimation using equations (19), (20), and (21). In addition to the variables explained in the previous section, we include two-digit industry dummiesand decade dummies in Nh f; t^jand Nh f; t^m: We select a group of exogenous variablesfso that the estimation passes the over-identi…cation test and use them as instruments, alongwith the instruments for the endogenous variables. The instrument variables we used are listed
under Table 4.
We can see in Table 4 that the signs of the coe¢ cients of the variables in the R function
in equation (20) are all as expected.

That is, a higher number of employees, higher wages,

higher median tenure as a titled director, and higher median age seem to make it more di¢ cultfor a director to be appointed as a titled director, whereas poor performance of the current
management makes it easier. The coe¢ cient of Direct is negative, indicating that the humancapital level required to be appointed to a titled director position is lower for managers fromoutside the …rm. The coe¢ cients for Direct, Wage, and Median age are statistically signi…cant.
The results show that the coe¢ cients for both tenure as an employee and outside experience
are positive, implying that these variables raise individuals’human capital. However, because
the values of these coe¢ cients are smaller than one, their e¤ect on human capital is smaller
than that of tenure as a board member, i.e., experience as a board member seems to be more
important for promotion to a management position than is experience as an employee.
15We

We expand our data in order to include this time-varying covariate. More speci…cally, each observation of
titled directors who are retained in the new …rms is expanded to two observations, one for the initial year andthe other for the following years. Therefore, we have 2018 observations in total, as seen in our later estimation of
the Cox proportional hazards model, comprising 588 observations with an initial dummy value of zero and 1520
observations with an initial dummy value of one.

35

estimate 1=( + 1) and obtain a value such that 0 < 1=( + 1) < 1 without imposing any
restrictions on estimation.

This is consistent with the assumption of> 0 in Lemma 8.

The coe¢ cients of the variables that a¤ect the manager’s human capital are all statisticallysigni…cant.

f; t^mf

The coe¢ cient of sales that appears in N

is positive and signi…cant,

implying that, as the company size grows, the potential highest level of ability increases.
Using the estimated parameters, we obtain the unobserved ability, ~ f j , for each manager inour sample from equation (22). Table 5 shows the summary statistics for individual unobserved
ability, whereas Figure 2 represents the kernel density estimate of the estimated unobserved
ability.
Variable
Negative operating income
DirectNo. of employees
WageMedian tenure as a titled director
Median age
Constant ( ~ 0 )Tenure as an employee ( e )Outside experience ( ~ o )1=( + 1)
Sales
Industry code dummy
Decade dummy
Number of observations

Coef.

Std. Err.

0:636
1:964
0:000
0:242
0:025
0:801
73:183
0:400
0:382
0:663
0:000

0:404
1:030
0:000
0:049
0:028
0:253
13:474
0:230
0:224
0:051
0:000
Yes
Yes

1519

Instruments for the equation: negative operating income, direct, no. of employees,
wage, median tenure as a titled director, median age as a titled director,
median tenure as a board member, median tenure as an employee, medianoutside experience, sales, and decade and industry dummy for both t^j and t^mfTable 4: GMM estimation

~fj

Obs.

Mean

Std. Dev.

Min.

Max.

1520

6:606

5:104

44:191

5:654

Table 5: Estimated unobserved skill
Tables 6 and 7 show the results of our strati…ed Cox proportional hazards model estimation
using equations (23), (24), and (25).

All results pass the test of the proportional hazards

assumption, based on the test of nonzero slope in a generalized linear regression of the scaled
Schoenfeld residuals on a natural log of the analysis time at the 5% level. For equations (1) and(3), the standard errors are obtained using 1000 bootstrap samples.
Speci…cation (1) in Table 6 is our benchmark speci…cation. The result for speci…cation (1)
36

0

.02

.04

Density
.06

.08

.1

Kernel density estimate

-40

-20

0

20

kai_iv2
kernel = epanechnikov, bandwidth = 0.8012

Figure 2: Kernel density of estimated unobserved skill

shows that the coe¢ cient of tenure as a board member is not signi…cant, whereas the coe¢ cientof tenure as an employee is positive and signi…cant. The coe¢ cient of tenure as a board member
with an initial dummy is not signi…cant, whereas the coe¢ cient of tenure as an employee withan initial dummy is negative and signi…cant. The sum of tenure as a board member and thatwith an initial dummy is negative, as is the sum of tenure as an employee and that with an
initial dummy. A Wald test shows that the latter summed variable is statistically signi…cant,whereas the former is not. The results indicate that, whereas the tenure as a board member has
no impacts on the separation probability after M&As, irrespective of timing, a longer tenure
as an employee increases the separation rate and the probability of appointment as a board
member in a new …rm, with statistical signi…cance.
The coe¢ cient for age is positive and signi…cant, whereas that for age with an initial dummyis negative and signi…cant. The sum of these variables is positive. Therefore, older managers
are less likely to be retained either in the initial year after an M&A or in the years after.
Because many other control variables are insigni…cant in Speci…cation (1), we suspect that
there may be some multicollinearity among variables. Hence, we drop the variables with initial
dummies for which both the level and interaction terms are insigni…cant in Speci…cation (1).
The result is shown as Speci…cation (3) in Table 7. It is shown that the results on tenures are
the same and, therefore, are robust.
The coe¢ cients of many other control variables become signi…cant in Speci…cation (3).
Speci…cally, the coe¢ cient of board size is positive and signi…cant. This may imply that the
productivity of managers decreases with the number of managers. The results also indicate that37

managers who serve as board members in di¤erent companies have a lower separation rate. We
can see that managers who were in the acquirer before the M&A and managers who belonged
to a target …rm in the same industry as the new …rm are likely to be retained on the board of
the new …rm. This may imply that acquirer-speci…c knowledge and industry-speci…c knowledge
are appreciated by the new …rm. We can also see that the target managers are less likely tobe retained in cases of acquisition and that higher-level managers (Upper ) are more likely to beretained.
Speci…cations (2) and (4) are the same as Speci…cations (1) and (3), respectively, exceptthat the former do not include the estimated unobserved skill, ~ f j : We can see that theestimated coe¢ cients for Speci…cations (2) and (4) are almost the same as those for (1) and (3),respectively, except for the coe¢ cients on tenure as a board member and its interaction term.
The Wald test for the sum of the coe¢ cients of tenure as a board member and its interaction
term become negative and signi…cant in both (2) and (4), implying that longer board experiences
increase the appointment probability of a board member in a new …rm. However, this seems
to re‡ect a selection bias resulting from an unobserved skill because these e¤ects of board
experiences disappear in (1) and (3), where we control for unobserved skills.
Now, we wish to interpret the results using our theory.
to interpret the results of our estimation.

We …rst apply Proposition 5

Because the conditions in Proposition 5 must be

satis…ed by the coe¢ cients of both tenure as a board member and tenure as an employee, if thecoe¢ cients of either type of tenure can reject the conditions, then the corresponding hypothesis
in Proposition 5 is rejected.

First, let us test hypotheses 1 and 2 in Proposition 5 using

the result for tenure as an employee. Our estimated results on the coe¢ cient of tenure as an
employee, the coe¢ cient of tenure as an employee with the initial dummy, and the sum of thesetwo coe¢ cients correspond to @[n (h)]

@ e

; @[

(h)]
@ e

; and @[

(

(h)+
@ e

n (h))]; respectively. Ourestimated coe¢ cients are all statistically signi…cant and the signs we obtained are @[0;@[

fT0 n hT(h)]@ e< 0; and @[= fT0 l hT

(

(h)+
@ e

n (h))]< 0.

n (h)]@ e>Hence, they de…nitely reject hypothesis= 0 in Proposition 5. Therefore, the evidence suggests that new …rms

value …rm-speci…c human capital.

Although the directions of the coe¢ cients cannot reject00
hypotheses fGl
hG = fGnhG and F 0 hG = 0 separately, they can reject the joint hypotheses00
of fGlhG = fGnhG and F 0 hG = 0 in Proposition 5. This suggests that a new …rm values

general human capital either because new …rms appreciate learning capability or because it ismore di¢ cult to hire managers with higher general human capital.

38

(1)
Variable
Coef.
Std. Err.
1: Tenure as a board member
0:006
0:024
2: Tenure as an employee
0:011
0:007
3: Tenure as a board member
initial dummy
0:012
0:024
4: Tenure as an employee
initial dummy
0:014
0:007
Age
0:112
0:031
Board size
0:097
0:081
No. of …rms as a board member
0:166
0:215
Board member in the acquirer before the M&A
0:106
0:479
Acquisition
0:025
0:797
Target ROA
11:913
7:626
Related
0:117
0:562
Target …rm’s relative size in assets
0:990
0:530
Log target assets
0:026
0:216
Upper
0:277
0:198
Log stock share of top 10
0:460
0:355
Acquirer or others ROA
3:164
6:143
Log top 10 share of acquirer or others
0:134
0:265
~fj
0:044
0:039
Age
I (t = 0)
0:072
0:031
Board size
I (t = 0)
0:073
0:082
No. of …rms as a board member
I (t = 0)
0:293
0:248
Board member in the acquirer before the M&A
I (t = 0)
0:114
0:482
Acquisition
I (t = 0)
0:729
0:819
Target ROA
I (t = 0)
11:813
7:691
RelatedI (t = 0)
0:383
0:577
Target …rm’s relative size in assets
I (t = 0)
0:210
0:567
Log target assets
I (t = 0)
0:012
0:220
Upper
I (t = 0)
0:007
0:207
Log stock share of top 10
I (t = 0)
0:504
0:357
Acquirer or others ROA
I (t = 0)
5:533
6:241
Log top 10 share of acquirer or others
I (t = 0)
0:161
0:269
~fj
I (t = 0)
0:037
0:039
Wald Test
Coef.
Chi2(1)
1+3
0:006
1:28
2+4
0:003
2:71
Number of observations
2108
Strati…ed by year, acquirer industry code, and target industry code.

Table 6: Strati…ed Cox proportional hazards model estimation

39

(2)
Coef.

Std. Err.

0:010
0:011
0:002
0:014
0:100
0:105
0:179
0:108
0:003
11:335
0:034
0:942
0:066
0:264
0:455
2:214
0:092

0:009
0:005
0:010
0:005
0:016
0:049
0:137
0:308
0:495
3:860
0:374
0:433
0:133
0:132
0:194
3:368
0:162

0:061
0:080
0:281
0:116
0:702
11:198
0:300
0:257
0:054
0:017
0:503
4:636
0:120

0:017
0:051
0:184
0:312
0:525
3:910
0:388
0:464
0:138
0:143
0:200
3:577
0:165

Coef.

Chi2(1)

0:008
0:003
2108

5:31
3:74

(3)
Variable
Coef.
Std. Err.
1: Tenure as a board member
0:002
0:022
2: Tenure as an employee
0:010
0:006
3: Tenure as a board member
initial dummy
0:005
0:022
4: Tenure as an employee
initial dummy
0:013
0:006
Age
0:116
0:026
Board size
0:036
0:020
No. of …rms as a board member
0:358
0:094
Board member in the acquirer before the M&A
0:229
0:074
Acquisition
0:579
0:156
Target ROA
0:466
1:000
Related
0:244
0:106
Target …rm’s relative size in assets
1:016
0:437
Log target assets
0:036
0:053
Upper
0:279
0:059
Log stock share of top 10
0:009
0:057
Acquirer or others ROA
1:223
1:439
Log top 10 share of acquirer or others
0:028
0:047
~fj
0:036
0:033
Age
I (t = 0)
0:076
0:026
Board size
I (t = 0)
No. of …rms as a board member
I (t = 0)
Board member in the acquirer before the M&A
I (t = 0)
Acquisition
I (t = 0)
Target ROA
I (t = 0)
RelatedI (t = 0)
Target …rm’s relative size in assets
I (t = 0)
0:294
0:484
Log target assets
I (t = 0)
Upper
I (t = 0)
Log stock share of top 10
I (t = 0)
Acquirer or others ROA
I (t = 0)
Log top 10 share of acquirer or others
I (t = 0)~fj
I (t = 0)
0:027
0:034
Wald Test
Coef.
Chi2(1)
1+3
0:006
1:18
2+4
0:003
2:95
Number of observations
2108
Strati…ed by year, acquirer industry code, and target industry code.

Table 7: Strati…ed Cox proportional hazards model estimation

40

(4)
Coef.

Std. Err.

0:016
0:010
0:007
0:012
0:107
0:039
0:361
0:232
0:578
0:463
0:252
1:006
0:040
0:275
0:008
1:370
0:035

0:009
0:005
0:010
0:005
0:016
0:046
0:082
0:064
0:139
4:068
0:097
0:374
0:049
0:133
0:195
1:219
0:043

0:069

0:017

0:289

0:414

Coef.

Chi2(1)

0:009
5:58
0:003
4:08
2108

Next, we separately investigate the role of tenure as a board member and that of tenure
as an employee after M&As. Let us …rst apply Proposition 6 to the estimated results for thetenure as an employee. It shows that the evidence for tenure as an employee, @[
@[

(h)]
@ e

< 0; and @[

(

(h)+
@ e

n (h))]n (h)]@ e> 0;< 0; rejects the hypothesis that experience as an

employee does not increase …rm-speci…c skills ( e = 0). Similarly, applying Proposition 7, theevidence for tenure as an employee, @[rejects the hypothesis that ! e >n (h)]@ e> 0, @[(h)]@ b< 0; and @[

(

(h)+
@ e

n (h))]< 0;, although we cannot reject the hypothesis that ! e <.

The results consistently show that longer tenure as an employee of a target …rm hampers theaccumulation of general human capital relative to other experiences.
On the other hand, the relevant coe¢ cients for tenure as a board member are not statisticallysigni…cant, and we are not able to reject the hypothesis that experience as a board member
does not increase …rm-speci…c skills and does not have a larger in‡uence on the accumulation ofgeneral human capital relative to other experiences. Without rejections of any null hypotheses,
we cannot make a strong argument in relation to the e¤ects of experience as a board member.
However, our result seems to be consistent with the argument that managerial experience does
not involve …rm-speci…c human capital and does not hamper the accumulation of general humancapital. Hence, it is likely that experiences as a board member are more general than those as
an employee.
In summary, we can interpret our results as follows. 1) After an M&A, Japanese …rms value
both the target …rm-speci…c human capital and the general human capital of managers.

2)

Experience as an employee increases …rm-speci…c skills, but at the expense of the accumulationof general human capital. 3) Experiences as a board member are likely to be more general thanthose as an employee.

7Discussion

In this section, we discuss whether the moral hazard of managers could in‡uence our interpretation. In line with the literature, including Wulf (2004), Hartzell et al. (2004), and Bargeron etal. (2009), we note that managers with long tenures in target …rms may become very powerful
and attempt to protect “their position” as much as possible in the event of M&As.
As this paper shows, as long as ex post bargaining is possible without any costs, we do
not need to be concerned about this possibility. In fact, although we control for a measure of
the ownership structure using the logarithm of the stock share of the top 10 stock holders, it

41

does not have any signi…cant impacts on the separation rate. This strongly suggests that theentrenchment story may not be a serious problem for M&As in the Japanese context.
Of course, this may not be taken as conclusive evidence to justify our presumption. If theex post negotiation is costly, these managers would remain very powerful in the initial period
and the acquiring …rms would …nd it di¢ cult to …re them. However, eventually, the power ofthese managers would be eroded such that, …nally, it would become possible for the new …rms
to …re them. Thus, this kind of entrenchment story may be able to explain the coe¢ cient oftenure in our survival analysis.
To the extent that the power of these managers is the source of their productivity, there
is no reason to distinguish their power from their target …rm-speci…c skills. In this case, theabove story can be consistent with the story that we have presented. However, it is possiblethat a powerful manager could be unproductive. Unfortunately, we do not have conclusive
evidence that can reject this kind of entrenchment story.

Nevertheless, there are at least

three reasons to consider that the entrenchment of powerful but unproductive managers is notimportant for our results. First, the entrenchment argument is consistent with our coe¢ cient oftenure as an employee, but it is inconsistent with the coe¢ cient of tenure as a board member.
These results are peculiar because we would expect that tenure as a board member would
be a more appropriate measure of power in a …rm than tenure as an employee.

Second,because it is impossible, in reality, to write an explicit contract for all possible contingencies,
powerful managers should anticipate that they will eventually lose their power.
not theoretically clear why they would initially agree to a merger.

If so, it is

Most mergers in Japanare friendly and, therefore, if the managers are very powerful, they could potentially oppose
them. This suggests that managers do not possess the degree of power required to support
the entrenchment argument. Finally, senior people typically have more authority in Japanesesociety than do younger people. Hence, it is possible that power in a …rm could be captured byage rather than tenure. In fact, the coe¢ cient of age is signi…cantly positive, the interaction with
the initial dummy is signi…cantly negative, and the sum of the two coe¢ cients is signi…cantly
positive, which indicates that senior managers are less likely to be appointed as board membersof a new …rm. This is to be expected when these managers are less productive, despite theirpower in the initial years. Therefore, we expect that, after controlling for age, the entrenchment
story will have little e¤ect on the coe¢ cient of tenure.

42

8Contribution of Our Results to the Literature

In addition to our methodological contributions to the literature, our results have a numberof important implications for several streams of literature, including those on managerial compensation and Japanese M&As.

This section discusses how our results contribute to these…elds.
First, evidence about the transferability of managerial skills between Japanese …rms canprovide a useful basis and comparison for the discussion of sources of high compensation for
U.S. CEOs.

As Bertrand (2009) and Frydman and Jenter (2010) show, some researchersconsider the high compensation of U.S. CEOs to be the result of powerful managers setting
their own pay rates, whereas others consider it to be the result of a competitive market for
managerial talent. One of the key presumptions behind the market-based view (e.g., Gabaix
and Landier, 2008; Terviö, 2008) is that important managerial skills are transferable across…rms.

Indeed, Murphy and Zábojn k (2004) and Frydman (2005) argue that a rise in theimportance of a CEO’s general skills relative to his/her …rm-speci…c skills can explain not only
the increase in CEO compensation but also the increase in the turnover rate that has occurredsince 1970. Kaplan et al. (2012) investigate a proprietary dataset for executives and provide
evidence that general skills are important managerial skills.

Our results, focusing on theJapanese context, provide evidence that complements this U.S.-based literature; we …nd thatexperiences as a board member in a target …rm are likely to be more general than those gained
as employees, even though the promotion structure of Japanese …rms is considered to facilitate
the accumulation of …rm-speci…c skills to a particularly large extent (e.g., Mincer and Higuchi,1988).
It should be noted that Japanese managers receive far less cash compensation than do their
U.S. counterparts16 and that Japanese CEOs have very long tenures at their …rms relative toCEOs in U.S. …rms17 . This suggests that, even if experience as a board member in Japan istransferable across …rms, such an appointment does not immediately imply high compensation
and a high turnover rate. Accounting for the di¤erences in the market for managers between
the U.S. and Japan is beyond the scope of this paper. However, together with our evidence that16
Kaplan (1994) shows that U.S. o¢ cers earned 13.5 times the average compensation of other employed males,
whereas the ratio for Japanese executives is only 4.8. Moriguchi and Saez (2008) show that, whereas the wage
income share of the top 1% of wage earners in the U.S. rose exponentially from 5% to 12% between 1970 and
2005, the share in Japan has remained nearly constant at around 5% during this period.
17

Kaplan (1994) shows that the average tenure of a president in a Japanese …rm is 34.3 years, whereas that ofa U.S. CEO is 26 years.

43experience gained as an employee is …rm speci…c and is required to manage a newly merged…rm, a plausible conjecture is that Japanese managers must conduct both tasks that needmanagerial skills and tasks that require an understanding of employees’ speci…c skills18 , and,
therefore, there are barriers to the division of labor and the creation of a market for managerial
skills in Japan.
Finally, this is the …rst paper that examines the retention of managers after M&As using
a Japanese dataset. The number of M&As in Japan has dramatically increased since the late
1990s. Although there are several attempts to understand Japanese M&A waves (e.g., Fukao et
al. 2005), few papers investigate the separation of workers after M&As. Notable exceptions are
Kubo (2004) and Kubo and Saito (2012), which analyze the e¤ect of mergers on employment
and wages. In particular, Kubo (2004) analyzes the personal characteristics of employees who
separated from …rms before and after mergers using …rm personnel data.

However, neither

work discusses the retention of top managers. Although the impacts of mergers on employees
are interesting in their own right, the reasons for the separation of managers from the boardsof newly merged …rms would di¤er from the reasons for the separation of employees. Hence,the evidence in our paper provides valuable new information to understand how Japanese …rms
adapt to merger waves.

9

Conclusion

This paper examines how the tenure of managers in‡uences the retention rate of management
groups after M&As in Japanese companies. It develops a general equilibrium model of managerial separation after M&As that distinguishes several hypotheses about the e¤ect of tenure
on separation, given several data limitations. Our empirical results show that acquiring …rms
obtain bene…ts from skills that are speci…c to the target …rm and from skills that are speci…cto the new …rm, which must be acquired by managers from the target …rm following an M&A.
We also show that experience as an employee in a target …rm, prior to becoming a manager,increases valuable speci…c skills but at the expense of the accumulation of managers’ generalhuman capital.
Because the data available to many researchers have several limitations, we develop a modelthat can extract meaningful information from this restricted dataset. The development of themodel results in several methodological contributions, which can be applicable to the broader
18
In fact, Jacoby (2005) compares Japan’s internal labor market with the U.S. internal labor market andhighlights the stronger role of personnel departments in Japan.

44

literature. In particular, we provide a novel method to correct for selection biases by utilizing
the timing of selection in a selected sample, which does not require a random sample from the
population.
Of course, the development of the model is based on several assumptions. Hence, we do notclaim to provide conclusive evidence on the retention rate of managers after M&As. However,
because the importance of human capital in understanding the retention of managers cannot bedenied, we believe that our results provide a reasonable explanation of the otherwise puzzlingevidence on the retention rate of managers after M&As. Moreover, because our model is ‡exible
and amendable, it can provide a sound basis for the development of a more complete theory ofretention in the future.

10

Appendix

The Proof of Proposition 1:Note that, if both the …rm and the manager prefer to maintainPt and Wt (h)^ l hG + Pt + "t ), they can do so.
WHowever, if one party prefers to walk away, Jt (h) < J^0^ l hG + Pt + "t , thenPt or Wt (h) < W

the relationship at time t, (Jt (h)J^0they must separate from each other. This implies that they can maintain their relationship at
t if and only if:
St (h)Wt (h)^ l hG
W

Pt

"t :

(26)

Applying equation (26) to the de…nition of St , the dynamics of St can be expressed as:
St (h) = pt (h)(12+ Et 4 h^ l hG) J^0 + W
St+1 (h) +1

I St+1 (h)Hence, wtn cannot in‡uence St (h).

Wt+1 (h)^ l hGW

We claim that if St (h)…nd wtn and, therefore, Wt to satisfy equation (26).
^ l hGW

Pt+1

Suppose that St (h)Then, Jt (h)We de…ne Wt hG such that Wt hG

St (h)^ l hG + J^0
W t hG + W

J^0^ l hGW

St+1 (h))"t .

If Wt (h)Pt and the worker receives^ l hG + Pt + "t > Wt (h).
W

Pt .

Hence, both parties have

incentives to renegotiate and choose Wt hG to avoid separation.
Wt (h)("t+1

On the other hand, if

Pt > St (h), then the separation occurs, the …rm obtain J^0^ l h G + Pt + " t .
worker receives W

We de…ne Wt (h)455"t , it is mutually bene…cial to

Pt < "t , then separation occurs, the …rm obtains J^0^ l h G + Pt + " t .
W

"t+1

i

3

^ l hG + Pt .
St (h) + W

Pt andThen,Wt (h)^ l hG + Pt + "t and J (h)Wt^ l hG + J^0 = J^0
Wt (h) + W

St (h)

Pt .

Hence, both parties have incentives to renegotiate and choose Wt (h) and avoid separation.
Therefore, as long as St (h)"t , the parties will avoid separation. However, when St (h) < "t , itis impossible to satisfy equation (26) and they must separate. The desired result is immediate.
The Proof of Lemma 8:De…ne F (~ ) = 1

E [ j"xF (~ ) and Q (x) = F
R (")

(xp )

xp ] =F0 ( )dF (Q ("))
R (")

(xp )

=

1 (x). Then:

F (Q (xp ))F0 ( )dF (Q (xp )) F (Q ("))
R xp
00
" Q (x) F (Q (x)) Q (x) dx
xp "
R xp
" Q (x) dx
:
xp "

=
=

Because the top x percent position of Q (x) can be approximated by Q0 (x) =" ]0 [x. Hence:show that Q (x) = Q (")
R xp"

E [ j"xxp ] =Q (")
xp= Q (") +Because

0"

[

" ]

0 x

"

h

dx

+1
0 xp

(xp

h
0 and there exists a …nite Q (0) = lim"!0 Q (") +

0x

" +1

i

") ( + 1)0"i:, we can derive:

0 xp
xp ] = Q (0)and( + 1)
h
i9
8
<
" =
0 xp
Q (xp ) = lim Q (")= Q (0)"!0 :;E [ jxCombining the two equations, we can derive:E [ jxxp ] =

Q (0) + Q (xp )
:
+1

46

0 xp

:

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