Department of Social Systems and Management
Discussion Paper Series

No.1281

Employment Protection Legislation and Cooperation
under Relational Contracts

byKyota EGUCHI

September 2011

UNIVERSITY OF TSUKUBA
Tsukuba, Ibaraki 305-8573
JAPANEmployment protection legislation and cooperation
under relational contracts*
Kyota Eguchi**
University of Tsukuba
Department of Social Systems and Management
September 20112011/09/25

Abstract
In this paper, I argue how employment protection legislation (EPL) influences relational
employment contracts. Firing costs caused by EPL are categorized into two kinds:
procedural inconveniences (negotiation costs) and severance pay. I focus on theminimum value of the discount factor that sustains mutual cooperation under trigger
strategies, and show that a hike in firing costs first enhances and then dampens
cooperation. Additionally, a hike in severance pay leads to moral hazard for workers.
EPL processes, especially procedural inconveniences such as negotiations with unions,can enhance cooperative employment relationships as long as they are not large.
Moderate, not overly strict, EPL is supportive of cooperative employment relationships.
JEL Classification Numbers: J41, J53.
Key Words: Relational contract, Incentives, Cooperation, and Minimum discount factor* An earlier version of this paper was presented at the 16th World Congress of the International

Economic Association at Tsinghua University, Beijing, in 2011. I am grateful for Ryo Kambayashi,
Hideshi Itoh, and the seminar participants at the Contract Theory Workshop and the Law andEconomics Workshop. This research was partially supported by Grant-in-Aid for Scientific
Research of the Japanese Ministry of Education, and the Japan Securities Scholarship Foundation.
Naturally, any errors are mine alone.
** Correspondence: Kyota Eguchi, University of Tsukuba, Department of Social Systems andManagement, 1-1-1, Tennou-dai, Tsukuba, Ibaraki 305-8573, Japan.
e-mail: eguchi@sk.tsukuba.ac.jp
11. Introduction
Numerous studies have focused on the effects of employment protection
legislation (EPL) on the economy, especially from macroeconomic perspectives.
However, they have provided ambiguous results. Bertola, Boeri, and Cazes (2000) cite
the complexity of social institutions as the main reason for the ambiguity. Difficulties
posed by social institutions include industrial relationships with central or local wage
bargaining, safety nets such as unemployment insurance, the structure of internal andexternal labor markets, and so on. These factors differ from country to country and are
influenced by different historical and regional backgrounds. Further supporting thisview, recent studies by Aghion, Algan, Cahuc, and Shleifer (2010), Aghion, Algan, andCahuc (2011), and Blanchard and Philippon (2006) point out that state regulation oflabor markets is negatively correlated with the quality of industrial relationships. In
countries with strict labor regulations such as France and the southern European
countries, the quality of industrial relationships is poor. In contrast, in the Nordic
countries where moderate regulations exist, cooperative and trusting industrial
relationships have been established. These studies imply that microeconomic
perspectives on industrial relationships are crucial to evaluate the effects of EPL.
Since conflictual employment relationships are likely to lead to poor
performance, it is vital to identify how good employment relationships are associatedwith strict and moderate EPL. Strict EPL seems to be unnecessary if good relationships
have been established; labor market regulations can be substituted for trusting
relationships. However, this does not mean that EPL is not needed at all. EPL may
support good and trusting relationships. This study aims to consider how EPL influencesa cooperative employment relationship.
A good relationship makes it possible to enhance cooperation between a firm
and a worker through an implicit relational contract mechanism. A relational contract
mechanism is especially crucial when behaviors of firms and workers are not verifiable.
When verifiable observations are less accurate at measuring contributions of workers, as
Baker (1992) (2002) reveals, it is not beneficial to evaluate workers’ contributions withthem. As the well-known multitask principal-agent model of Holmstrom and Milgrom(1991) shows, if firms are tempted to base the remuneration of workers on verifiable but
inappropriate observations, it does not necessarily bring firms the most benefits. Given
the reality of multitasking, as Brown (1990) points out, firms are likely to adopt implicit
relational contract mechanisms rather than high-powered incentive schemes based only2

on verifiable observations. The appropriate motivation of workers can be developedwith a relational contract mechanism.
Long-term employment relationships that are formed through a relational
contract can induce workers to pay more attention to unverifiable but essential work.
EPL can help to support long-term employment relationships; thus, it may enhance good
employment relationships. In contrast, the efficiency wage model of Shapiro and Stiglitz(1984), a leading theory, holds that the threat of dismissal is a driving force in worker
incentives. EPL may provide a negative impact because shirking workers are not likely
to be fired or punished. Therefore, it is important to analyze both the positive andnegative effects within the relational contract framework.
In this paper, I consider an employment relationship with a firm and a worker.
A firm offers a remuneration package consisting of an explicit-contract basic wage andan implicit-contract bonus. Since the worker’s performance is not observed by a third
party, the firm cannot make an explicit-contract wage conditional on the worker’s
performance. The basic wage must be paid regardless of the worker’s performance; thus,
the firm does not offer incentives to the worker. An implicit-contract bonus can be a
driving force to encourage the worker. However, the implicit bonus payment is under
the control of the firm, and thus the firm may not pay the bonus even if the worker has
shown good performance. This is a typical hold-up problem whereby the firm does not
pay any positive bonus and therefore the worker makes no effort if they play the
one-shot game.
To enforce the implicit bonus and encourage the worker to show good
performance, a repeated employment relationship must be formed. It is well establishedthrough the folk theorem that the firm and the worker will engage in cooperative
behaviors when they emphasize more on mutual future benefits; that is, their discountfactors are sufficiently high.1 In this paper, to examine how EPL enhances cooperation,
I analyze the effect of EPL on the minimum value of discount factors that sustain
mutual cooperation under trigger strategies. Although trigger strategies are restrictive,
they make it possible to derive the minimum value of discount factors for mutual
cooperation. The approach is similar to Baker, Gibbons, and Murphy (1994), who
consider the relationship between subjective but correct performance measures and1

Bull (1987) and Macleod and Malcomson (1989), seminal studies on the relational contract theory,
analyzed what type of contracts can implement cooperation continuously. Levin (2003) consideredan optimal relational contract in the constrained situation in which players confront asymmetric andunverifiable information.
3

objective but distortionary ones under trigger strategies. They show a complementary
relationship between subjective and objective performance measures to implement
cooperative behaviors.
Firing costs that firms bear are categorized into two kinds: one is a monetarytransfer such as severance pay and the other is a procedural inconvenience such asproviding advance notices or negotiations with unions. Although both increase the firing
cost for firms, monetary transfer is limited to earnings for workers, but proceduralinconvenience results in wasteful loss. Monetary transfer seems to be better, but it also
benefits shirking workers and may dampen worker incentives. This difference is crucial
in the analysis of the effects of EFL.
The main conclusion of this study is that as the firing cost increases, theminimum discount factor that sustains mutual cooperation first decreases, and thenincreases. In other words, initially EPL enhances industrial relationships and supports
cooperative employment relationships, but as it is strict, it eventually dampens
relationships. EPL plays a positive role in deterring the firm from exploiting output
without paying a bonus. However, EPL can also have a negative effect on worker
incentive. When EPL is moderately strict, the former positive effect on industrial
relationships overrides the latter negative one. In contrast, in the case of strict EPL, thepositive effect is dominated by the negative one. Moreover, it will be shown that, as thefraction of monetary transfer in the firing cost increases, a cooperative employment
relationship is unlikely to be sustained. Therefore, we conclude that moderate EPL
enhances mutual cooperation, and negotiation with unions is more crucial thanseverance pay.
This paper contributes to the literature on the effect of EPL on incentives. As
the efficiency wage model suggests, EPL seems to have a disincentive effect. However,it has also been shown that EPL can provide a positive effect on incentives by several
studies such as Fella (2000), Galdon-Sanchez and Guell (2003), Suedekum andRuehmann (2003), Belot, Boone, and van Ours (2007), and Demougin and Helm (2011).
Although the theoretical frameworks of these studies differ, they are limited to one-shot
relationships in which EPL plays a significant role as a kind of commitment device. In
contrast, I focus on the effects of EPL on the sustainability of cooperative employment
relationships through a relational contract, and show that cooperative relationships canbe built with appropriate EPL.
This paper is organized as follows. Section 2 presents the structure of an
infinitely repeated game model in which a firm and a worker play trigger strategies.
4

There are two phases: cooperative and punishment. First, I consider the punishment
phase in section 3. Next, in sections 4 and 5, I show equilibrium remuneration and theeffects of EPL on cooperation after and before establishing a relationship, respectively.
Finally, section 6 presents the conclusions.

2. Model1. ModelI consider an employment relationship between a firm and a worker. A firm
requires a worker to make an effort to produce a high output. If a worker bears the effort
cost of ȝ, he produces the output of y = 1 over the effort cost ȝ. If he shirks his work, heproduces nothing, y = 0. I assume that the worker’s contribution is observable to thefirm, but is too complex and subtle to be verified by a third party, and so cannot be thebasis of an enforceable contract. The output is subjectively assessed inside theemployment relationship.
Remuneration consists of a basic wage w and an implicit-contract bonus b. A
firm offers a worker a remuneration package, p { ( w , b) . The firm can decide on abasic wage and a bonus freely as long as it is non-negative. The firm must pay the basic
wage w regardless of the worker’s performance whenever he is employed. The basic
wage is always enforced by a third party, such as a court. On the other hand, the third
party cannot require that any implicit-contract bonus be fulfilled. The bonus can be paid
after the worker’s performance is revealed. Profit of the firm in a period is given byS y  w  b if the firm pays the bonus.
The employment relationship can be infinitely repeated, and a worker and afirm play trigger strategies. Therefore, the worker and the firm begin to cooperate andthen continue cooperating unless either of them defects. If either of them deviates fromcooperation, they refuse to cooperate forever after.2
2. Timing of behaviors
Here, the timing of events within each period is considered. Formally, eachperiod t is divided into four subperiods; t0 in which the firm offers a remuneration

2

The trigger strategies have the virtue of being simple to analyze. As a result, I do not consider an
optimal punishment scheme and renegotiation, which are beyond my focus in this paper.
5

package pt( wt , bt ) to the worker; t1 in which the worker decides on quitting (qt = 0)or not (qt = 1); t2 in which the worker makes a decision on his output, yt = 0 or 1, if heremains in the firm; and t3 in which the firm pays the basic wage and gives, or does not
give, the bonus. Then, the next period comes, and the same behaviors are repeated if theemployment relationship continues. The timing of the behaviors is summarized in figure
1.
The firm makes a decision on a bonus payment after observing the worker’s
behavior. The employment relationship can be dissolved in subperiod t1 of a period t; aworker can quit after observing a remuneration package pt( wt , bt ) and before

generating output in the period. The firm commits a basic wage in subperiod t0, thenpays it in subperiod t3. This indicates that the firm has to pay the basic wage after the
production process has been completed in subperiod t2, but does not have to pay before
it has been completed. In other words, if the worker quits the firm in subperiod t1, theworker cannot get the basic wage wt but the gets outside wage w .
3. Firing cost
The firm bears firing cost f caused by EPL when an employment relationship isbroken off. The firing cost consists of an administrative cost, which is a sociallywasteful transaction cost such as procedural inconveniences, and a monetary transfer
such as severance pay. On the discussion of EPL, it seems to be natural that firms bear afiring cost whenever they fire workers, but firms do not bear this cost when workers
leave their jobs voluntarily. However, we must realize that firms are willing to pretend
not to fire workers and avoid a firing cost if workers quit voluntarily. In fact, firms can
induce workers to leave by lowering their remuneration. This seems to be the voluntary
turnover of workers, but in essence they are fired. If this was not accepted as firing but
instead as voluntary turnover, EPL would not function. It would just be a veil. In thispaper, to consider the effect of EPL, it is assumed that a firm has to bear the firing cost
regardless of the reasons of why a worker quits his firm, involuntarily or voluntarily.
The firm must incur the firing cost whenever the employment relationship is dissolved.
Once an employment relationship has been established, the firm has to bear thefiring cost upon dissolving the employment relationship. In contrast, in the beginning of
period 1, the employment relationship has not been established yet; thus, the firm does
not incur the firing cost when the worker rejects the firm’s offer. As I show later, this6

difference is crucial.
When the employment relationship is broken off, the firm bears firing cost f,which consists of a monetary transfer kf and administrative cost (1-k)f, where k( 0 d k d 1 ) is a parameter representing the fraction of the monetary transfer in the firingcost. The firing cost and the fraction of the monetary transfer are exogenously given as asocial rule in the economy.3
In the incumbent period in which the employment relationship is broken off,
payoffs of the firm and the worker are íf and kf  w , respectively.4 Since the worker
rejects the offer before producing output, the worker works outside the firm and gets theoutside wage w in addition to the severance pay kf. Then, in the next period or later,
payoffs of the firm and the worker are 0 and w , respectively.
4. Trigger strategies
Let at denote an outcome of these decisions in period t: at = {pt, qt, yt, bt}. The
histories that are common knowledge to the firm and the worker are given by,h (t 0 )( a1 , a2 , ... , at 1 ) , where h(10 )1h (t )

h(t )  { pt } ,h(t 2 )

h(t 1 )  {qt } ,h (t 3 )h(t 2 )  { yt } .

I,

0The firm and the worker can observe all of their behaviors; they do not face any
problems caused by asymmetric information. I focus on the subgame perfect Nashequilibrium of this model. In the repeated game with perfect information, there are twophases under trigger strategies: cooperative and punishment. In the cooperative phase,
the worker produces high output and the firm pays the bonus. I denote the outcome of aperiod t that belongs to the cooperative phase as,

3

In the real world, the fraction of the monetary transfer and administrative cost in the firing cost
tend to be dependent on the history and quality of employment relationships. Fired workers may
receive generous severance pay at a low administrative cost under good employment relationships.
In contrast, it may take a long time to reach an agreement between firms and fired workers underpoor relationships. In this case, the administrative cost is likely to be large. Thus, this model can beapplied to various situations by appropriate adjustment of the parameters.
4 In period 1, the current payoffs of the firm and the worker are 0 and w , respectively, when theworker rejects the firm’s offer because the employment relationship has not been established.
7

at­a1* { {( w1* , b1* ) , 1, 1, b1*} if t 1,®
¯ a* { {( w *, b*) , 1, 1, b*} if t 2,3,...

Formally, the trigger strategy of the firm is as follows:pt (h(t ))­ ( w1* , b1* ) ,°®( w *, b*) ,° ( w , 0) ,¯ dbt (h(t 3 ))­ b1* , if h(13 ) {( w1* , b1* ) , 1, 1},°3*® b *, if t t 2 and h(t ) (a1 , a *, ..., a *, {( w *, b*) , 1, 1}),
° 0, otherwise.
¯

0

if t 1,
if t t 2 and h(t 0 )otherwise;(a1* , a *, ..., a*),The trigger strategy of the firm indicates that in period 1, the firm offers the
remuneration package (w1*, b1*). Then, if the worker accepts the firm’s offer and theoutput of the worker is y = 1, the firm pays the bonus b1*. Otherwise, the firm does not.
In period t (= 2, 3,…), if the outcome of all t í 1 preceding periods has been in thecooperative phase, the firm offers the remuneration package (w*, b*) and pays thebonus. Otherwise, the firm offers a different remuneration package pt( wd , 0) .

Similarly, the trigger strategy of the worker is defined as follows:qt (h(t1 ))­1, if h(11 ) {( w1* , b1* )} or w1 t w,°
°1, if t t 2, and®
1*° [1] h(t ) (a1 , a *, ..., a *, {( w *, b*)}) or [2] wt t (1  G)kf  w,
° 0, otherwise;¯

yt (h(t 2 ))­ 1, if h(12 ) {( w1* , b1* ) , 1},°
2*® 1, if t t 2 and h(t ) (a1 , a *, ..., a *, {( w *, b*) , 1}),
° 0, otherwise.
¯

The trigger strategy of the worker indicates that in period 1, the worker accepts the8firm’s offer and generates high output if the remuneration package (w1*, b1*) is offered.
In period t (= 2, 3,…), if the outcome of all t í 1 preceding periods has been in thecooperative phase, the worker remains in the firm and makes an effort to generate
output. Otherwise, the worker will shirk his work duties or quit the firm.
Note that in the punishment phase the worker is willing to remain in the firm
when the basic wage offered is equivalent to or more than his alternative payoff. The
alternative payoff depends on whether the employment relationship has been established.
Once the relationship has been established, the worker is willing to remain in the firm in
the punishment phase if the basic wage offer is equivalent to or more than w  (1  G)kf ,which is the average payoff per period that the worker receives by quitting. When therelationship has not been established in period 1, the worker will accept the firm’s offer
if a basic wage offer is equivalent to or more than the outside wage w . As I show in thenext section, when the firing cost is huge, the firm is willing to maintain theemployment relationship even if the worker will not produce anything.

3. Punishment phase
The behaviors of the firm and the worker in period 1 depend largely on their
expected future behaviors; thus, I proceed to consider period 2 or later. First, I have todeliberate the punishment phase, where the worker does not produce anything and thefirm does not pay any bonus.
The punishment phase will continue forever once either the firm or the worker
deviates from the cooperative phase.5 In the punishment phase, the firm can choose twostates, “firing” and “dead wood,” through the basic wage offer. “Firing” means
dissolving the employment relationship by offering a basic wage lower than theworker’s alternative payoff. In contrast, “dead wood” indicates continuing therelationship by offering a basic wage sufficient enough to maintain the relationship. The
firm realizes that the worker generates no output; he is nothing but “dead wood.”However, the firm will maintain the employment relationship in the punishment phasewhen the firing cost f is very large. To make the worker remain in the firm, a basic wage
plays a significant role. It can deter the worker from quitting the firm, but a bonus offer

5

Under the trigger strategies, players never return to the cooperative phase. In section 6, I mention acase in which they can return to the cooperative phase.
9cannot because it is not credible for the worker in the punishment phase.
The firm is willing to continue employing the worker as dead wood in thefpunishment phase when it holds that f t ¦ Gi wd , where the discount factor denoted as
i 0

G (d 1) is common for the worker and the firm. On the other hand, the worker will
f

f

i 0

i 0

remain in the firm when it holds that kf  ¦ Gi w d ¦ Gi wd . If the two inequalities holdsimultaneously,
G  G1 (k , f ) { 1 w,(1  k ) f

…(1)the employment relationship continues even in the punishment phase. The firm willoffer the minimum value of the basic wage if it is willing to maintain the employment
relationship: wdw  (1  G)kf . Otherwise, the firm will offer a basic wage strictly lessthan w  (1  G)kf , for example, wd

0 ; thus, the worker quits and the employment

relationship is broken off. The behaviors in the punishment phase, therefore, depend on
the strictness of EPL.
Lemma 1
The trigger strategies of the firm and the worker are the best responses to theirpartners’ strategies toward each other in the punishment phase. The outcome of a period

t

in

the

punishment

phase

is

at

{ pt , qt , yt , bt } {(0, 0) , 0, 0, 0}

at{( w  (1  G)kf , 0), 1, 0, 0} .

of

G t G1 (k , f ) ,and [2] in the case of

G  G1 (k , f ) ,

[1]

in

the

case

The proof is given in the Appendix. Condition (1) shows that, as the firing cost
increases, the employment relationship is likely to continue in the punishment phase.
Moreover, as the fraction of the monetary transfer in the firing cost increases, firing
tends to be conducted. When the fraction of the monetary transfer is high, the firm has
10to pay a high basic wage to maintain the relationship. Thus, the firm is likely to induce
the worker to quit.

4. After establishing a relationship
1. Incentive conditions of a worker
Next, I consider incentive compatibilities of a firm and a worker to keep thecooperative phase in period 2 or later. Then, we will return to period 1.
First, I analyze the incentive compatibilities of a worker in the cooperative
phase. A firm has to offer an equilibrium remuneration package (w*, b*) that satisfies
the incentive compatibilities of a worker to maintain the cooperative phase. The
incentive compatibilities of a worker in subperiod t1 and t2 are given by
f

f

i 0

i 0

WIC-q: ¦ Gi ( w * b * P) t kf  ¦ Gi w ,  ͐(2)f
f§·
WIC-y: ¦ Gi ( w * b * P) t w * G ¨ kf  ¦ Gi w ¸ .
i 0
i 0
©
¹

 



͐(3)

The left-hand sides of WIC-q and WIC-y indicate the present value of the worker’s total
payoffs in period t in the cooperative phase. The right-hand side of WIC-q mentions thepresent value of the worker’s total payoffs when the worker rejects the remuneration
package and quits the firm in subperiod t1. The right-hand side of WIC-y indicates thepresent value of the worker’s total payoff when the worker engages in shirking behavior.
A shirking worker receives the current basic wage w* because the worker has alreadybeen employed in period t. However, the bonus is not paid in subperiod t3.
As mentioned, in the punishment phase, a firm can choose between two states,
firing or dead wood. However, the present value of the worker’s total payoff is notaffected by the firm’s decision in the punishment phase because the firm is willing tooffer the minimum basic wage to keep the worker as dead wood.
The two constraints of WIC-q and WIC-y must be satisfied to prevent theworker from deviation. Since the firm is willing to minimize the remuneration cost, thebasic wage w* should be lower than w  (1  G)kf :11

w* d w  (1  G)kf .

…(4)In this case, WIC-y is slack as long as WIC-q holds. Thus, WIC-q is binding at theequilibrium:w * b* P  w  (1  G)kf .

…(5)To implement and keep the cooperative phase, the firm is willing to offer the
remuneration package ( w *, b*) satisfying (4) and (5).
2. Incentive conditions of a firm
Next, I consider the incentive compatibilities of the firm to pay the implicit

bonus. The firm makes a decision on the bonus after observing the behavior of theworker. Even if the worker produces positive output, the firm can breach the implicit
promise on the bonus. It is necessary to check whether the firm is willing to pay thebonus b* to keep the cooperative phase.
The firm makes a decision on a remuneration package in subperiod t0 and thebonus payment in subperiod t3. The firm’s incentive compatibilities in period t (= 2,3,…) are given, respectively, as follows:
fw ½­
FIC-p: ¦ Gi (1  w * b*) t  min ® f , kf ¾,
1 G ¿
¯
i 0

…(6)

f
w ½
­
FIC-b㸸 ¦ Gi (1  w * b*) t 1  w * G min ® f , kf ¾.
1 G ¿¯i 0

͐(7)The left-hand side of FIC-p and FIC-b indicates the present value of the firm’s total
payoffs in the cooperative phase. The right-hand side of FIC-p indicates the firm’s
payoff when the firm deviates from the equilibrium remuneration package. The outcome
depends on the strictness of EPL. In the case of firing, the firm bears the firing cost f.
On the other hand, in the case of dead wood, the firm keeps on paying the basic wage ina period equivalent to w  (1  G)kf ; thus, the present value of the total wage cost is
kf 

w
.
1 G

The right-hand side of FIC-b is the payoff of the firm when the firm does not
12

pay the bonus b*. The firm can swindle the output, but has to pay the basic wage w*.
Then, the punishment phase starts from the next period.
Lemma 2
FIC-p holds as long as FIC-b does.

The Proof is easy and given in the Appendix. FIC-p is slack, and thus I focus only on
FIC-b.
3. Equilibrium remuneration package
It is well established by the folk theorem that cooperation between a firm and aworker can be implemented and continued when the discount factor is sufficiently high.

By considering the trigger strategies, I can derive the minimum value of the discountfactor, G , to sustain the cooperative phase. Higher w* reduces the right-hand side of
FIC-b and makes FIC-b less tight. As the right-hand side of FIC-b is smaller, thediscount factor for cooperation dwindles. Therefore, the minimum discount factor isderived under the remuneration package by w* w  (1  G)kf and b* P .
Lemma 3The minimum discount factor for cooperation is given under the remuneration
package: w* w  (1  G)kf and b* P .

The implicit bonus is the driving force for the worker’s incentive, but is
independent of the firing cost. The firing cost influences the basic wage only.
Substituting the remuneration package into FIC-b, the minimum discount factor G isderived. In the case of firing, G t G1 (k , f ) , FIC-b turns into a quadratic condition:g ( k , f ) { G 2 (1  k ) f  G ^1  w  (1  k ) f `  P d 0 . Then, we denote a smaller solution ofg (k , f ) 0 as G2 (k , f ) . Clearly, the quadratic condition holds under G t G2 (k , f ) ;thus, the minimum discount factor for cooperation is given by G

G 2 ( k , f ) . Similarly,

in the case of dead wood, G  G1 (k , f ) , FIC-b becomes a simple condition: G t P .
13

Thus, the minimum discount factor is given by G

P . The results are summarized asfollows:
Proposition 1w,(1  k )(1  P)

[1] In the case of firing, which occurs under 0  f dG

G2 (k , f ) {1  w  (1  k ) f ^1  w  (1  k ) f `  4(1  k ) f P
2

2(1  k ) f[2] In the case of dead wood, which occurs under f !
[3] In the case of k 1 or f

0 , it holds that Gw, G(1  k )(1  P)

.

P.

P
.
1 w

The Proof is given in the Appendix. The minimum discount factor for cooperation isdrawn as the red bold curve shown in figure 2. The case of k 1 or f 0 gives a
corner solution. Therefore, attention is given to the interior solution under 0 d k  1
and f ! 0 throughout this paper.
4. Effects of EPL
The effect of the firing cost on the minimum discount factor is given as

follows:
Proposition 2[1] In the case of firing, a hike in the firing cost decreases the minimum discount factor

for cooperation. An increase in the fraction k of the monetary transfer in the firing costraises the minimum discount factor.
[2] In the case of dead wood, a hike in the firing cost or fraction k of the monetarytransfer does not affect the minimum discount factor for cooperation.
The Proof is shown in the Appendix. As figure 2 indicates, in the case of firing, theminimum discount factor dwindles as the firing cost increases. This means that the14

firing cost deters the firm and the worker from deviating. In other words, the firing cost
plays a significant role in enforcing the implicit bonus b* and enhancing cooperation.
w, the firm is willing toWhen the firing cost exceeds the critical level: f(1  k )(1  P)
maintain the employment relationship even in the punishment phase. In the case of deadwood, a hike in the firing cost does not affect the minimum discount factor forcooperation.
A hike in the firing cost f means an increase in the administrative andnegotiation costs of firing. The ex post rent of the employment relationship is increased
by a hike in the firing cost. Thus, it gives the firm and the worker more incentives tomaintain the cooperative relationship. This generates the positive effect and motivation
to decrease the minimum discount factor for cooperation. On the other hand, an increasein fraction k of the monetary transfer decreases the administrative cost, which decreases
the ex post rent of the employment relationship. Thus, it gives a negative effect on theircooperation.
When the firing cost is large, the firm will continue employing the worker as
dead wood in the punishment phase; thus, the firm does not bear the large firing costdirectly. The firing cost does not influence all of the ex post rent of the employment
relationship if it exceeds the critical point. While a hike in the firing cost raises the
remuneration that the worker can receive, in the case of dead wood, it is just an issue ofthe distribution of the rent between the firm and the worker. As lemma 3 indicates, thebonus is independent of the firing cost and monetary transfer. Once the employment
relationship has been established, the worker can always receive the benefit of themonetary transfer through the basic wage specified by lemma 3. Thus, the firing costand monetary transfer are not directly associated with behaviors of the firm and theworker when the punishment phase is the case of dead wood.
As mentioned above, a huge firing cost does not influence the minimum valueof the discount factor for cooperation once the employment relationship has been
established. However, a huge firing cost will have an influence if the relationship has
not been established. This is the next issue to consider.

5. Before establishing a relationship
1. Incentive conditions in period 1
15

I have considered the periods (t = 2, 3,…) after the employment relationshiphas been established, where the firm bears the firing cost f and the worker receives themonetary transfer kf whenever the worker quits (or is fired by) the firm. In contrast, thefirm does not have to bear the firing cost in period 1 when the worker rejects the firm’soffer because the employment relationship has yet to be established. The difference is
crucial between the before and after period of establishing the relationship. Now, wereturn to period 1.
The minimum value of the discount factor G , which sustains mutual
cooperation after establishing the relationship in period 2 or later, has been shown inproposition 1. It is needed to consider whether the discount factor also satisfies the
incentive compatibilities of the worker and the firm before establishing the relationship.
Unless it did, the employment relationship would not be established or the cooperative
phase would not begin in period 1 under the discount factor G ; thus, a discount factor
higher than G would be needed to implement cooperation from period 1.
The incentive compatibilities of the worker in subperiod 11 and 12 are given,
respectively, as follows:
WIC-1-q: w1*  b1*  P Gw( w * b * P) t
,
1 G
1 G

WIC-1-y: w1*  b1*  P Gw ·§( w * b * P) t w1*  G ¨ kf 
¸. 
1 G
1 G ¹
©

 

͐(8)

 ͐(9)

When the worker rejects the firm’s offer in period 1, the worker receives only theoutside wage w , thereby, as shown on the right-hand side of WIC-1-q, the present
value of the total payoff isw. In contrast, the right-hand side of WIC-1-y (9) is1 Gsimilar, except w1* and w*, to that of WIC-y (3) because the production process has
finished and the employment relationship has been established.
If w1* d w  Gkf , WIC-1-y is slack as long as WIC-1-q holds. Since the basic
wage w1* in period 1 is non-negative, WIC-1-y is slack in the case of w t Gkf . In thiscase, using lemma 3, WIC-1-q requires w1*  b1* t P  w  Gkf . Since the firm is willingto minimize the remuneration, the optimal remuneration package in period 1 is given by16

w1*  [0 , w  Gkf ] and w1*  b1*

P  w  Gkf .

Otherwise, in the case of w  Gkf , WIC-1-y is more crucial than WIC-1-q because
WIC-1-q is slack. From lemma 3, WIC-1-y becomes b1* t P . The firm is unwilling to
pay a positive basic wage in period 1, w1*

0 . The results are summarized as follows:

Lemma 4The optimal remuneration package in period 1 is given by[1] in the case of w t Gkf , w1*  [0 , w  Gkf ] and w1*  b1*[2] in the case of w  Gkf , w1*

0 and b1*

P  w  Gkf

P.

Once the employment relationship has been established, the firm has to incur the firing
cost when the worker quits (is fired by) the firm. Thus, the worker has an opportunity toreceive the monetary transfer kf whenever he quits. The firm must compensate theworker with the transfer to keep the worker employed. The firm and the worker
anticipate the situation after the relationship has been established; thus, in period 1, thefirm is willing to take back the entire rent that the worker will receive in period 2 orlater. The case [1] in lemma 4 means that in period 1 the firm can take all rents, which
the worker will receive in period 2 or later, by lowering the remuneration in period 1.
On the other hand, in case [2] in lemma 4, the firm can absorb a part of the rent.
The following result is easy to introduce from lemmas 3 and 4:
Proposition 3[1] In the cooperative phase, the optimal basic wage in period 1 is lower, but in period 2or later it is higher than the outside wage: w1*  w d w * .
[2] An optimal bonus is equivalent to the effort cost in any period of the cooperative
phase: b1*

b* P .
17

Proposition 3 shows that the worker receives the rent through the basic wage in period 2or later, and that the firm takes back the entire or a part of the rent by lowering the basic
wage in period 1. The gap in the basic wage between in periods 1 and 2 or later is given
by kf or (1  G)kf . Therefore, EPL increases the gap in the basic wage before andafter establishing the relationship.
2. Minimum discount factor for cooperation
The incentive compatibilities of the firm in period 1 are given by

FIC-1-p: 1  w1*  b1* 

G(1  w * b*) t 0 ,1 G

FIC-1-b: 1  w1*  b1* Gw ½­(1  w * b*) t 1  w1*  G min ® f , kf ¾.
1 G
1 G ¿¯

We have to deliberate whether the minimum discount factor G for cooperation fromperiod 2 satisfies FIC-1-p and FIC-1-b.
When b1*

b* P is offered, FIC-b holds if and only if FIC-1-b does. Thismeans that FIC-1-b always holds as an equality under G G because FIC-b holds as anequality under G G from the definition of G . Thus, it is sufficient to consider
whether the other constraint, FIC-1-p, holds under G G . If it holds, the discount factor
G is also the minimum value for cooperation from period 1, which is denoted as G * .
Lemma 5w ½­
It holds that G* G when 1 t G min ® f , kf 
¾ does.
1 G ¿¯

The lemma indicates that the minimum discount factor G for cooperation in period 2or later, which is specified in proposition 1, satisfies FIC-1-p and FIC-1-b when theabove condition holds. Note that FIC-1-b always holds as an equality under G G .
When the condition in lemma 5 holds, the right-hand side of FIC-1-b is non-negative byoffering w1* , appropriately. Thus, FIC-1-p holds under G
18

G.

w ½
­
Since G min ® f , kf 
¾ increases with respect to G , there is a value of1 G ¿¯Ĝ such that Gˆ min ­® f , kf  w ½¾ 1 . Thus, the condition in lemma 5 is replaced as
1  Gˆ ¿¯follows:w ½­
G d Gˆ , where Ĝ satisfies Gˆ min ® f , kf 
¾ 1.
1  Gˆ ¿¯

…(10)I present a sufficient condition, w t Gkf , under which condition (10) holds. As
lemma 4 shows, when w t Gkf holds, the firm can absorb all of the rent, which theworker will receive in period 2 or later, by lowering the basic wage sufficiently inperiod 1.6 The present value of the firm’s total profit is equivalent to the total net
benefit generated by the employment relationship,

1 P  w, which is always positive1 G

for any discount factor given in the assumption of the model. Therefore, the minimum
discount factor G * for cooperation from period 1 is equivalent to the discount factor

G from period 2 or later. The effect of EPL shown in proposition 2 is also applied fromperiod 1.7
Finally, I consider the case in which condition (10) does not hold under G

G.

Proposition 4
When condition (10) does not hold, the minimum discount factor that sustains mutual

cooperation from period 1 is given by

kf  w  (kf  w) 2  4kf (1  P)
G* G3 (k , f ) {
! G.
2kf

The condition (10) holds if w t Gkf does; however, the opposite is not true. Even if the firmcannot absorb all of the worker’s rent, FIC-1-p may hold under G G .
7 In this model, the basic wage and bonus have been assumed to be non-negative. Without theassumption of limited liability, firms could take all benefits of workers by sufficiently negative wage
offers; thus, the discount factor G is applied from period 1: G* G .
196

The Proof is in the Appendix. When condition (10) does not hold, the discount factor

G * for cooperation from period 1 is more than G . As the folk theorem shows, asufficiently high discount factor that satisfies all incentive conditions from period 1
always exists. This case is likely to occur when kf is huge.
Condition (10) indicates that when both k and f are sufficiently large, thediscount factor G does not satisfy the incentive compatibilities of the firm in period 1.
When the fraction of monetary transfer, k, is small, the discount factor G satisfies the
incentive compatibilities of the firm in period 1 even if the firing cost f is huge. In fact,as lemma 4 shows, in the case of k 0 , the firm can take back all of the rent, which theworker receives in period 2 or later. Hence, the minimum discount factor G * forcooperation from period 1 is equivalent to G .
3. Effects of EPL
The effect of the firing cost is given as the following proposition:
Proposition 5[1] When condition (10) does not hold, it holds that G* G3 (k , f ) . A hike of f or k
increases G * .
[2] Otherwise, G* G holds. The effect of the firing cost is given as shown inproposition 2.
The Proof is in the Appendix. Finally, I consider the effect of the firing cost on theminimum value of the discount factor that sustains mutual cooperation from period 1.
Proposition 6
As the firing cost increases given a particular level of the fraction of monetarytransfer, the minimum value of the discount factor G * that sustains mutual cooperationfrom the period 1 decreases first, then increases.
The shape of the minimum discount factor G * that sustains mutual cooperation fromperiod 1 is dependent on the parameters, as shown in figures 3 and 4. Regardless of thecases shown in figure 3 or 4, as the firing cost increases, the minimum discount factor
G * decreases first, then increases.
20

As the firing cost increases, the ex post rent of the employment relationshipincreases given a particular fraction k of the monetary transfer. Thus, it reduces theminimum discount factor for cooperation and makes the firm and the worker more
motivated to cooperate. This is the positive effect of EPL to enhance cooperation.
However, when the firing cost is huge, the monetary transfer that the worker can receiveis large. Thus, the firm has to offer a big remuneration to keep the worker’s incentive,
which discourages the firm from employing the worker. This is the negative effect,
which is likely to appear when the fraction of the monetary transfer is high. The
negative effect caused by strict EPL requires a higher discount factor for cooperation.
Therefore, as shown in figures 3 and 4, there is an appropriate strictness in EPL in the
middle range.

6. Conclusion and Discussion
I have considered the effect of firing costs on the minimum discount factor forcooperation: [1] A hike in the firing cost first decreases the minimum discount factor,
and then increases it and [2] A hike in the fraction of the monetary transfer increases theminimum discount factor. These results show that procedural inconveniences such asproviding advance notices or negotiations with unions can enhance a cooperative
employment relationship as long as they are not strict. In contrast, monetary transfers
such as severance pay dampen cooperation because they discourage workers’ incentive.
The above results are explained intuitively as follows. The existence ofprocedural inconveniences increases the ex post rent generated by the relationshipbetween a firm and a worker; thus, their motivation for cooperation is enhanced. As aresult, the minimum discount factor for cooperation decreases. On the other hand, a hikein the firing cost increases the severance pay that workers receive when they leave theirfirms. This makes the moral hazard problem of workers more serious; thus, firms are
required to pay high remuneration. The effect is negative. As the firing cost increases,
the positive effect is likely to be dominated by the negative one; thus, an appropriate
level for the firing cost exists in the middle range.
Although I have focused on an employment relationship from a microeconomic
perspective, this result is associated with macroeconomic views. From the perspectiveof macro search models, the effect of EPL has been controversial. When EPL is strict,the effect of EPL is likely to be negative and to worsen unemployment rates. However,21

when EPL is moderate, it is not always negative. A similar result is obtained from both
macroeconomic and microeconomic perspectives.
In this paper, the subgame perfect Nash equilibrium under the trigger strategies
has been considered. Although it has the virtue of being simple to analyze, thepossibility of renegotiation is ignored. An optimal punishment scheme is also beyond
the focus of this paper, but infinitely repeated punishment seems to be unrealistic.
However, it is not essential to the results. Suppose that the punishment phase continues
for a particular s ( t 1 ) period. Even if they deviate from the cooperative phase, they canreturn from the punishment phase in s periods. As s increases, punishment is severe, and,thus, the minimum discount factor for cooperation decreases. As long as s is positive,that is, the punishment phase exists, the results in this paper hold. Clearly, when thepunishment phase continues infinitely, the minimum discount factor for cooperation isminimized.8
The above situation, in which firms and workers can return to the cooperative
phase from the punishment one, is also associated with the macroeconomic searchmodel. In the Mortensen- and Pissarides-type search model, firms and workers can find
new partners from the unemployment pool. Although I have not considered themacroeconomic search mechanism, the main result of this study is consistent with thoseof the macroeconomic perspectives and is not much influenced by the assumption of thetrigger strategies.

8This is the principle of Abreu (1988).
22

Appendix
Proof of lemma 1
A firm and a worker play their trigger strategies in period t (t = 2, 3,…).

[1] The best response of the worker to the firm in the punishment phase is as follows:x

In subperiod t2, the worker will not produce positive output given the history ofh(t 2 ) z ( a1* , a *, ..., a *, {( w *, b*) , 1}) because the worker realizes that he cannot

receive any bonus, and that his payoff is not influenced hereafter by generating highoutput.
x

In subperiod t1, the worker will remain in the firm, qt = 1, if the basic wage offer isequivalent to or more than his alternative payoff, w  (1  G)kf . He gets themonetary transfer kf in the incumbent period and the outside wage w hereafter if
he quits; thus, his average payoff in a period is given by w  (1  G)kf . If the firmpays the basic wage or a higher wage, it is more optimal for the worker to remain
than to quit. Otherwise, the worker will quit the firm, qt = 0.
Therefore, the trigger strategy of the worker is the best response to the firm in thepunishment phase.
[2] The best response of the firm to the worker in the punishment phase is as follows:x

In subperiod t3, zero bonus payment, bt = 0, is optimal for the firm given the historyof h(t 3 ) z ( a1* , a *, ..., a *, {( w *, b*) , 1, 1}) because a positive bonus does not
induce the worker to produce positive output hereafter.

x

In subperiod t0, given the history of h(t 0 ) z (a1* , a *, ..., a*) , the firm anticipatesthat no output is produced by the worker. In the case of G t G1 (k , f ) , the zero
remuneration package ( wt , bt ) (0, 0) is optimal for the firm to induce the worker
to quit. In the other case of G  G1 (k , f ) , the firm will avoid breaking off theemployment

relationship;

thus,

the

remuneration

package( wt , bt ) ( w  (1  G)kf , 0) is optimal. The basic wage is the minimum payment tomaintain the relationship.
23

Therefore, the trigger strategy of the firm is the best response to the worker in thepunishment phase.
Accordingly, the outcome of a period t in the punishment phase isat{(0, 0) , 0, 0, 0} in the case of G t G1 (k , f ) or at{( w  (1  G)kf , 0) , 1, 0, 0}

in the case of G  G1 (k , f ) .‫ڦ‬

Proof of lemma 2

FIC-b is written as follows: b * Gw ½­(1  w * b*) t G min ® f , kf 
¾ . Thus,
1 G
1 G ¿¯

it holds that1w ½ b*w ½­­(1  w * b*) t  min ® f , kf t  min ® f , kf 
¾
¾.
1 G
1 G ¿ G
1 G ¿¯¯This indicates that FIC-p always holds as long as FIC-b does. ‫ڦ‬Proof of proposition 1[1] In the case of G t G1 (k , f ) , FIC-b becomes (1  w * b*) t (1  G)(1  w*)  G(1  G) f .
Substituting the remuneration package specified by lemma 3, it holds thatg ( k , f ) { G 2 (1  k ) f  G ^1  w  (1  k ) f `  P d 0 .

 …(A1)

Note that in the case of G 1 , it holds that g (k , f ) 1  P  w  0 .
In the case of k z 1 and f z 0 , (A1) becomes a second-order inequality withrespect to G . Then, I denote a smaller solution of g (k , f ) 0 as G2 (k , f ) :24

G2 (k , f ) {1  w  (1  k ) f ^1  w  (1  k ) f `  4(1  k ) f P
2

2(1  k ) f.

Thus, when G t G2 (k , f ) , the inequality (A1) holds as shown in figure A-1. The
minimum value of the discount factor is given by G
must satisfy G 2 (k , f ) t G1 (k , f ) { 1 [2]Similarly,

in

the

G 2 ( k , f ) . In addition, G2 (k , f )w
w. The range is 0  f d.
(1  k ) f(1  k )(1  P)

case

of

G  G1 (k , f )

,

FIC-b

turns

to

(1  w * b*) t (1  G)(1  w*)  G(1  G)kf  Gw . Substituting the remuneration package
specified by lemma 3, it is obtained that G t P . Thus, the minimum value of the
discount factor is given by G
range is f !

P . In addition, it must satisfy P  G1 (k , f ) . Thus, thew.
(1  k )(1  P)

[3] In the case of k 1 and f
discount factor is given by G

0 , (A1) turns to G t

P. Thus, the minimum
1 w

P
.‫ڦ‬
1 w

Proof of proposition 2[1] In the case of G t G1 (k , f ) , differentiating g (k , f ) with the firing cost f:
wg (k , f )G(1  G)(1  k )  0 . This means that the smaller solution of g(k, f) = 0 is
wf

reduced by a hike of f .
wg (k , f )Gf (1  G) ! 0 .
wkThis indicates that the smaller solution of g (k , f ) 0 is raised by an increase of the

Next, differentiating g (k , f ) with respect to k,

fraction of the monetary transfer.
[2] In the case of G  G1 (k , f ) , the minimum discount factor G is equivalent to P .
25Thus, it is not affected by a hike of f or k. ‫ڦ‬Proof of proposition 4

When the condition (10) does not hold, FIC-1-p does not hold under G

G . Inthis case, w  Gkf holds. Thus, as lemma 4 shows, the optimal remuneration packagein the period 1 is ( w1* , b1* )(0 , P) . Substituting the remuneration packages ( w1* , b1* )and (w*, b*) shown in lemma 3 into FIC-1-p, the following inequality is derived:h(k , f ) { G2 kf  G(kf  w)  1  P t 0 .

…(A2)

Under G 1 , (A2) becomes h(k , f ) 1  P  w ! 0 ; thus, (A2) holds. Then, I denote alarger solution of h(k , f ) 0 as G3 (k , f ) , where

G3 ( k , f ) {kf  w  (kf  w) 2  4kf (1  P).
2kf

Therefore, when G t G3 (k , f ) , (A2) holds (figure A-2). The minimum discount factor
for cooperation from period 1 is given by G* G3 (k , f ) .‫ڦ‬

Proof of proposition 5

Differentiating h(k , f ) with respect to f,wh(k , f )wfGk (1  G)  0 . This indicatesthat G3 (k , f ) increases with respect to f. Similarly, differentiating h(k , f ) withrespect to k,wh(k , f )wkGf (1  G)  0 . Thus, G3 (k , f ) increases with respect to k. ‫ڦ‬
26

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28

t0 : The firm offers a remuneration package, pt = (wt , bt).
t1 : The worker remains or quits, qt {0, 1} .
the worker remains:

the worker quits:t2 : The worker produces
output or not, yt  {0, 1} .

The employment
relationship is broken off;
hence, the firm bears thefiring cost f in period t (= 2,
3,...).

period t
t3 : The firm pays the basic
wage, and makes a decisionon the bonus payment.

t + 10 : The firm offers a new
remuneration package, pt +1 = (wt + 1, bt + 1).
࣭    ࣭    ࣭

Figure 1
Timing of behaviors

29

In period t (= 2, 3,...), thefirm and the worker get thepayoffs íf and kf  w ,respectively. (Note that inperiod t = 1, the firm and theworker get the payoffs 0 and
w , respectively.)
From period t + 1, the firm
and the worker get thepayoffs 0 and w forever,respectively.
࣭    ࣭    ࣭į1

G1 (k , f )firingP1 w

į2 (k, f)dead wood

P

O

w
1 k

w
(1  k )(1  P)f

Figure 2
In a period t (= 2, 3,…), the red curve indicates the minimum discount factor for mutual

cooperation under the trigger strategies of the firm and the worker. In the case of

G  G1 (k , f ) , the worker remains as dead wood in the firm in the punishment phase. In
the case of G t G1 (k , f ) , the worker quits (is fired by) the firm in the punishment
phase.

30į
1

G1 (k , f )P1 w

į2 (k, f)

G3 ( k , f )

P

G*
Ĝ

O

w
1
(1  k )(1  P)

1  P  Pw
k P(1  P)f

Figure 3
A case of the minimum discount factor G * for cooperation represented by the red bold

curve

31

į
1

G1 (k , f )

P
1 w

G*

į2 (k, f)

1 k  Pwk

G3 ( k , f )

P
Ĝ

O

1

wk
1 k  Pf

Figure 4
Another case of the minimum discount factor G * for cooperation represented by the

red bold curve32

g (k, f)PO

G2 (k , f )1

Figure A-1
The curve of g (k, f)

33

Gh (k, f)1 P
GG3 ( k , f )O

1Figure A-2
The curve of h (k, f)

34

G