Department of Social Systems and Management
Discussion Paper Series

No.1280

Employment Protection and Incentives:
Severance Pay vs. Procedural Inconvenienceby
Kyota EGUCHI

September 2011

UNIVERSITY OF TSUKUBA
Tsukuba, Ibaraki 305-8573
JAPANEmployment Protection and Incentives:
Severance Pay vs. Procedural Inconvenience *Kyota Eguchi**
University of Tsukuba
Department of Social Systems and Management

May 2011
2011/05/23* I am grateful to Ryo Kambayashi, Ryoichi Imai, Masaru Sasaki, Hideshi Itoh, Takashi Shimizu,

and the seminar participants at the Search Theory Workshop, the Law and Economics Workshop,
Tohoku University, Nihon University, the Contract Theory Workshop, Nanzan University, andTokei-kenkyu-kai. This research was partially supported by Grant-in-Aid for Scientific Researchfrom the Japanese Ministry of Education, and the Japan Securities Scholarship Foundation. Anyerror, if present, is entirely mine.
JEL Classification Numbers: J64, J65, K31** 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

Employment Protection and Incentives:
Severance Pay vs. Procedural Inconvenience
Abstract
I consider the effects of employment protection (EP) on workers’ incentives and thelabor market with search friction. EP is categorized into severance pay and proceduralinconvenience. Severance pay is merely a transfer of money from firms to dismissed
employees, while procedural inconvenience yields a wasteful cost. This difference is
crucial to workers’ incentives because severance pay is a benefit for shirking employees.
Although it appears to negatively affect workers’ incentives, EP, particularly proceduralinconvenience, has a positive effect on incentives if EP is not severe. An optimalbalance exists between severance pay and procedural inconvenience.
JEL Classification Numbers: J64, J65, K31
Key words: Employment protection, Incentives, Commitment, and Efficiency wage.

2

1. Introduction
In general, it is believed that an employment protection (EP) policy is a major
cause for the poor performance of labor markets in European countries; however, thevast literature on EP has shown conflicting results regarding crucial factors such as
unemployment rates and social welfare. The ambiguous results can be applied to verify
the effect of EP on incentives of workers.
EP is often assumed to negatively affect workers’ incentives. A leading theory,
the efficiency wage model, holds that the threat of dismissal is a driving force inworkers’ incentives. If shirking workers are unlikely to be fired because of EP
provisions, EP has a disincentive effect. However, EP can have a positive effect onworkers’ incentives. Even if a worker works hard, his/her performance or the state ofaffairs of his/her firm may be very poor in uncertain situations, resulting in doubts
regarding the firm’s ability to maintain the employer-employee relationship. When
workers who make credible efforts are easily fired because of bad business conditions,they realize that they cannot recover the cost of their efforts; thus, they are discouraged.
Because a firm’s decision regarding the dismissal of an employee tends to be based on
ex post optimization, credible job security should be provided in such conditions. A
significant function of EP is that it serves as a commitment device for job security. Thus,
it has a commitment effect. The objective of this paper is to consider the effects of EP on
the incentives of workers and the labor market with search friction and to show whether
the commitment effect overrides the disincentive effect.
While the disincentive effect of EP has often prevailed, the commitment effecthas generally not been given serious consideration, except in some recent studies
regarding skill formation. Suedekum and Ruehmann (2003) and Belot, Boone, and vanOurs (2007) indicate that the introduction of severance pay (SP) as a type of EP
encourages workers to make a human investment, because SP gives workers some of
the rent that drives skill formation. Booth and Zoega (2003) suggest that firing policies
tend to be excessively implemented because firms are not concerned about the humancapital lost when workers quit and move to another industry.1
Although previous studies generated insightful results, they are limited topartial equilibrium models. They, therefore, exclude the effects of EP on firms’ entry
level in terms of the general equilibrium. As a recent study by Demougin and Helm
1

Some studies show that unions function as commitment devices: Booth and Chatterji (1998) showthat unions’ bargaining power enhances skill formation and improves social welfare; Eguchi (2002)
also points out the significance of unions as commitment devices for job security. Piccirilli (2010)
analyzes the effect of employment protection when unions can commit future wages.
3

(2011) analyzed an incentive problem from the perspective of the search model, I focus
on incentive problems of workers rather than on skill formation. I consider, from theviewpoint of the general equilibrium, the effects of EP on the incentives of workers andlabor markets with search friction, in particular, wage level, likelihood of firing,
employment, unemployment rate, inflows and outflows of unemployment, and social
welfare. Furthermore, my infinitely long-term model enables the analysis of EP’s
effects under short- or long-term economic shocks.
In the literature on EP, EP has been treated as a firing cost that firms incur
upon firing workers. In this paper, firing costs are categorized into SP and proceduralinconvenience (PI). Both increase the cost of firing for firms; thus, some studies
consider SP as a firing cost, while others investigate PI. Although the effects of SP and
PI have probably been separately investigated, I compare the effect of SP along with PI
and show an optimal balance between SP and PI. SP is merely the transfer of moneyfrom a firm to a fired employee, while PI, for example, providing sufficient advancenotice or negotiations with a union, leads to a transaction cost. It seems that SP is better
than PI, but SP can be a benefit for a shirking employee and may damage workers’
incentives. This difference is significant.
Punishment schemes for shirking employees are critical with regard to their
incentives. In the context of EP, one crucial issue is whether shirking employees are
eligible for SP. Dismissals are therefore categorized into two types of cases: in the caseof redundancy, when firms fire workers because of bad financial health, the workers are
eligible; in the case where disciplinary action is taken and workers are fired on the
grounds of poor performance or unprofessional conduct, they are not eligible.
When EP provides benefits only for diligent employees in the case of
redundancy, it is unlikely to cause a negative effect on workers’ incentives because only
diligent employees are protected, the shirking ones are not. In this case, if monitoring
devices work effectively, the negative effect of EP on incentives is unlikely to appear.
Thus, Boeri and Jimeno (2005) indicate that EP can be exempted for small companies
when shirkers can be easily identified in small companies. Fella (2000) compares SPwith PI by using the efficiency wage model with a monitoring device and shows that SP
generates a positive effect when the monitoring device effectively functions.
My purpose, however, is to consider a situation in which no monitoring device
is available and all fired employees receive SP. In this situation, EP is expected to be
the cause of employee moral hazard; however, it will be shown that EP can generate apositive impact on employee incentives and the economy through the commitment4

effect.2 According to my computer simulation, the negative effect of SP is apparent
when SP is not low. The impact of PI is not significant when SP is low or high.
However, when SP is in the middle range, PI intensifies the commitment effect,encourages workers to work hard, and improves social welfare. If credible job security
is provided to an employee through PI, a firm can lower wages in exchange for high job
security, thus reducing the cost of retaining an employee. When PI is moderately severe,it boosts market tightness and reduces the unemployment rate. The positive effect of PI
appears when SP is in the middle range; thus, an optimal balance exists between SP andPI.
The result of numerical illustration indicates that an extensive relaxation in theprovisions of EP as well as very severe EP reduces employees’ incentives. This result isalso similar with those of studies that accept the positive effect of a firing tax without
explicit concerns regarding employee incentives, such as Ljungqvist and Sargent (1998)(2007), Rogerson and Schindler (2002), Pissarides (2001), and Blanchard and Tirole(2008).
This paper is organized as follows. Section 2 presents a Mortensen–Pissarides
matching model with an incentive problem and considers the effects of SP and PI as EP
categories. I also conduct a computer simulation in Section 3 to investigate the effects
of SP and PI. Finally, Section 4 presents the conclusions.

2. The Model
1. Employment contract
A firm with a job vacancy is randomly matched to an unemployed worker inthe labor market. After matching, the employed worker is required to make an effort toachieve high productivity, and the effort cost c is borne by the employee. Productivity pof an employee who makes an effort is stochastically determined to be p  [0 , p ] . The
density and distribution functions are denoted as ( p ) and  ( p ) , respectively. In the2

Galdon-Sanchez and Guell (2003) also focus on the situation in which the court is unable todistinguish between the cases of redundancy and disciplinary action. In their model, firms allege thatworkers have been fired for disciplinary reasons even if the opposite is true. Hence, the fired workers
do not receive SP because of the firms’ moral hazards. In the situation where firms’ moral hazard
regarding firings is pervasive, some regulations that inhibit firms from easily firing employees arelikely to provide positive effects on the economy. In contrast, I consider a situation in which thecourt makes no distinction between cases of redundancy and disciplinary dismissal and I focus on
the employee moral hazard. Firms have to pay SP to all fired employees, including shirking
employees.
5case of a shirking employee, the density and distribution functions are similarly denotedby  S ( p ) and  S ( p ) , respectively. The effort cost of a shirking employee is zero. It
is assumed that the first-order stochastic dominance holds, i.e.,  ( p )   S ( p ) forp  [0 , p ] , with strict inequality for a set of values of p with possible probability.
A wage is specified when a firm is matched to a worker. The wage is notconditional on either the worker’s behavior or on his/her productivity p, and the wage
cannot be changed once it is specified. This setting is identical to the Shapiro andStiglitz (1984) efficiency wage model.
The chronology of the actions of a worker and a firm is as follows:[1] When a firm is matched to a worker in the labor market, wage w is specified.
[2] The worker chooses whether or not to make an effort.
[3] Productivity p  [0 , p ] of the worker is observed.
[4] The firm makes a decision regarding the dismissal after the revelation of
productivity p. If an employee is fired, he/she receives SP, is transferred to theunemployment pool, and gets reservation wage w . The firm firing the employee postsa job vacancy in the labor market. On the other hand, if a worker retains employment in
the firm, he/she produces output of value p and receives wage w.
[5] In the next period, the fired worker and the firm that dissolved the match search for a
new job match in the labor market. On the other hand, if both the employee and the firmthat maintain the match repeat the same process: a new wage is specified, the employee
chooses whether or not to make an effort, and then the value of his/her productivity is
stochastically determined. Each period’s productivity is independent of past periods.
2. Employment protection
When a firm fires an employee, the firm bears firing cost f. After p is revealed,
the firm’s current profit is either p  w if the firm maintains the match or  f if thefirm fires the employee.
Firing cost f borne by the firm consists of two factors, s and z, given asf  s  z , where s denotes a monetary transfer such as SP, and z denotes PI such asadministrative costs for notification and certification or negotiation with unions. PI is asocially wasteful transaction cost. SP is always given to all fired employees, including
shirkers. SP and PI are social rules and are exogenously determined by the government.3
3

Although SP is a lump-sum transfer, studies have been conducted on the effect of SP proportional
to wages. Staffolani (2002) analyzes SP related to wages in the Shapiro–Stiglitz efficiency wage
model and shows that increase in SP is likely to increase employment when increase in SP reduces
wages. Goerke (2006) compares a lump-sum type of SP with an earnings-related type of SP
regarding employment levels and points out that a lump-sum type of SP has a larger effect on
6

3. Matching technology
The Mortensen-Pissarides-type matching function is given by m  m (u , v ) ,where u is the unemployment rate and v is the vacancy rate, denoted as the number ofvacant jobs as a fraction of the labor force. The vacancy-unemployment ratio v/u or v-u
ratio, indicating market tightness, is denoted as  . The matching function is assumed tou 
be a constant return to scale, that is, q()  m  , 1 , where q (  ) denotes thev 

probability with which a job vacancy will be matched to an unemployed worker.
Clearly, q '()  0 . Similarly, the probability with which the unemployed worker will
be matched to a job vacancy is given by q () .
In the labor market, all unemployed workers are considered identical regardlessof their past behaviors, because their past behaviors are not noted. Hence, the matchingprobability is equivalent among the unemployed. Similarly, all job vacancies in themarket are identical for the unemployed.
4. Incentive compatibility
As I show later, an employee is fired in the case of p  [0 , pˆ ) , where
threshold p̂ is endogenously determined. A diligent worker who makes an effort isfired with probability  ( pˆ ) . If a diligent worker is fired for low productivity, he/she

receives SP from his/her firm and is transferred to the unemployment pool. His/her
expected current payoff is given by  ( pˆ )( s  w)  (1   ( pˆ )) w  c .
If an employee shirks work, he/she is fired with probability  S ( pˆ ) . The
expected current payoff of a shirking employee is  S ( pˆ )( s  w)  (1   S ( pˆ )) w .
Because the court cannot distinguish between a diligent employee and a shirking one,firms have to pay SP even to shirking employees. No monitoring technology isavailable to firms.
The present discounted value of the payoff of a diligent or shirking employee isdenoted as EN or ES, respectively. I apply a discrete-time model; thus, the present
discounted value of a diligent employee’s payoff is given as
E N   ( pˆ )( s  w)  (1  ( pˆ )) w  c 

1
( pˆ )U  (1  ( pˆ )) E ,1 r...(1)

where E  max{E N , E S } , r is the time preference rate, and U is the present discounted
increasing employment levels than an earnings-related type.
7

value of the payoff to the unemployed. Similarly, the present discounted value of ashirking employee’s payoff is given by
E S   S ( pˆ )( s  w)  (1   S ( pˆ )) w 1 S ( pˆ )U  (1   S ( pˆ )) E .
1 r...(2)

Finally, the present discounted value of the unemployed is given as
U  w

1
q() E  (1  q())U  .
1 r...(3)

where the reservation wage for the unemployed w indicates the value of leisure.
Incentive compatibility (IC) and individual rationality (IR) are given by
E  E and E  U , respectively. Wage w should be more than reservation wage w ;otherwise, no worker would be willing to search for a new job. It holds from w  w
that E S  U , because a shirker receives a higher wage w or reservation wage w withs upon being fired. This indicates that E  U always holds and IR is slack, providedNS

E N  E S holds. Therefore, it is sufficient to focus on the constraint E N  E S . The
following condition is introduced on the basis of E N  E S and E  U : (r  q()  1)( w  w)  (r  q()) s  S
IC ( w)   ( ( pˆ )  ( pˆ ))  c .
r  q()   S ( pˆ )...(4)

If constraint (4) is satisfied, IC and IR hold. Because a firm is willing to minimize thewage, constraint (4) is binding at the equilibrium.
5. Dismissal
The present discounted value J of a firm matched to a worker is as follows:p

J   ( pˆ ) f   ( p  w)( p)dp pˆ

1( pˆ )V  (1  ( pˆ )) J  .
1 r

The present discounted value V of a job vacancy is V  k 1
q() J  (1  q())V  ,1 rwhere k is the job vacancy cost. From the free entry and exit condition on job vacancies,
8V  0 . Hence, I obtain J J (1  r )kJ; thus,. Further, J is defined as J 
q()
1 r



p
1
( p  w)( p)dp  ( pˆ ) fr  ( pˆ ) pˆ   q(k)  .

...(5)

If a firm fires an employee, the present discounted profit is –f, given that V = 0. On theother hand, if the firm maintains the match, the present discounted profit is given bykp w
. Hence, the threshold is given byq()pˆ  w  f 

k
.
q()

…(6)

The threshold depends on the wage and the firing cost. Decrease in wage or increase in
the firing cost reduces threshold p̂ . Note that the threshold is given after the wage has
been specified and the effort cost has been sunk. An employee and a firm can consider
threshold p̂ upon being matched. A firm, therefore, minimizes the wage subject toconstraint (4) and threshold (6) by using backward induction.
Threshold p̂ must be positive to maintain an employee’s incentive, i.e.,pˆ  0 . If pˆ  0 holds, an employee is never fired; thus, constraint (4) on incentives isnever satisfied. The absence of the threat of dismissal motivates an employee to shirk.
This is the common result of the efficiency wage model.
6. Beveridge curve
Constraint (4) on incentives, the present discounted value of a firm’s profit
given by (5), and the threshold of dismissal given by (6) specify search equilibriumuand the job destruction rate is  ( pˆ ) .
( , w) . The job creation rate is q ()1 uFrom the steady state condition in terms of job flow, the job creation rate should beequivalent to the job destruction rate. Thus, the equilibrium unemployment rate is given
as the Beveridge curve byu

( pˆ ).
( pˆ )  q()…(7)9

7. Search equilibrium
Although unstable equilibria can exist in my model, it is reasonable to focus on
stable equilibria. In a match, it is assumed that the adjustment of the entry or exit of job
vacancies in the market is slower than the wage adjustment. In addition, a firm is too
small to influence market tightness  , and the firm minimizes the wage given market

tightness, subject to constraint (4) on incentives. Constraint (4), therefore, is binding at
all times, even if the economy is not in the search equilibrium. The locally stablecondition of equilibria is given by

ICw

kq '
 IC Jw  0 ,q2

where ICw ...(8)JIC ( w)IC ( w).
, IC , and Jw 
w
w


The search equilibria are represented by the points of intersection in Figure 1.4
The wage is adjusted more smoothly than the entry or exit of job vacancies; therefore,
the economy is almost always on the IC curve of constraint (4). In Figure 1, point A on
IC ( w)  c , which is near equilibrium E1, is below the JC curve of (5); hence, theexpected profit of a job vacancy at point A is positive, causing more job vacancies in themarket. The economy will be distant from equilibrium E1; therefore, equilibrium E1 isunstable, while equilibrium E2 is stable. Although I do not explicitly consider transition
dynamics, my focus is limited to the equilibrium satisfying the locally stable condition(8).
First, I consider how the change in the relative share of SP affects the economy
given a constant level of firing cost, that is, f  f .
Proposition 1
Assume that the share of SP increases given a constant level f of the firing cost.

Increase in the share of SP boosts the wage, the threshold of dismissal, and theunemployment rate. It also reduces the market tightness.
The proof is provided in the appendix. When the stringency of EP is fixed, thatis, f  f , a firm incurs the same firing cost f  f regardless of the share of SP.
4

The IC curve, constraint (4), may have a downward or upward slope. The slope of the IC curve isirrelevant to the result only if stable condition (8) holds.
10Because a shirking employee is entitled to receive SP whenever he/she is fired, SPdiscourages an employee from delivering the required effort. A high wage offer istherefore necessary to maintain the employee’s incentives, which reduces the firm’s
profit from the match. This is the disincentive effect, which causes firms with vacancies
to exit the market, thereby reducing market tightness.
Because the total firing cost does not change, the JC curve of (5) does not shift.
On the other hand, increase in the share of SP shifts the IC curve of constraint (4)upward, thereby increasing the wage and reducing market tightness (Figure 2a).
Moreover, the job destruction rate depends on threshold p̂ , which is increased byincrease in wage w and decrease in market tightness  . Therefore, the job destruction
rate clearly increases, resulting in increase in the unemployment rate, as mentioned in(7). The Beveridge curve (7) shifts because of increase in the job destruction rate  ( pˆ ) ,as shown in Figure 2b. In addition, the JC curve in Figure 2b shifts clockwise becauseof decrease in market tightness  . Increase in the share of SP, therefore, shifts theequilibrium from E1 to E2 (Figure 2b). Because market tightness decreases, theunemployment rate unambiguously increases.
In contrast, if the share of PI increases, the wage decreases and market
tightness increases. In addition, the threshold of dismissal and the unemployment rate
decline.

3. Numerical Illustration
Proposition 1 holds only when the total firing cost is fixed. This situation,
however, is restrictive. The total effect of the firing cost is ambiguous from thetheoretical perspective; hence, I conduct a computer simulation on the searchequilibrium.
The equilibrium is characterized by constraint (4) and the zero profit conditionof vacancy (5) along with threshold (6). A baseline situation is given in Table 1. I
11
consider the case in which productivity is uniquely distributed, that is, ( p)  .
p 100
Furthermore, the productivity density function of a shirking employee is given by1S ( p) for p  [0, 10] and  S ( p )  0 for p  [10 , 100] . The distributions of10
the productivity of employees satisfy the first-order stochastic dominance. In thebaseline situation, a unique search equilibrium exists.
11

Figure 3a shows the curve of  S ( p )   ( p ) in the simulation. The curve firstincreases, then decreases. Whether the curve increases or decreases is crucial for
considering the effect of firing cost on incentives. When a high firing cost deters a firmfrom firing an employee, threshold p̂ of dismissal decreases. The effect on incentives
depends on the value of  S ( pˆ )   ( pˆ ) . If decrease in p̂ lowers the value of S ( pˆ )   ( pˆ ) , constraint (4) on the incentive of the employee will be tight; thus, theeffect of firing cost on incentives is likely to be negative. In contrast, if decrease of p̂caused by high firing cost increases the value of  S ( pˆ )   ( pˆ ) , the effect can bepositive.
Figure 3b shows the curve of  S ( pˆ )   ( pˆ ) when the distribution functions
are normal with the expectation values 1 and 0 and the common variances are equal to 1.
The curve is smoother than, but is similar to, that of Figure 3a. Although the distributionfunctions in the baseline seem to be restrictive, the result of this simulation is not
greatly influenced by the setting of the distribution functions.
1. Wage and market tightness
Proposition 2
In this simulation, the following points are considered:[1] As Figure 4 shows, the wage initially increases and then decreases with respect to s(SP), given a level of z (PI).
[2] The influence of PI on the wage is not significant when SP is low. When SP is in the
middle range, for example, s = 25, increase in PI lowers the incentive-compatible wage.
[3] As Figure 5 shows, increase in SP decreases market tightness.
[4] Increase in PI also results in decrease in market tightness when SP is either low orhigh. However, when SP is in the middle range, for example, approximately s = 25, PI
may increase market tightness. However, if PI is excessively severe, for example, z = 12,
market tightness is reduced.

This implies that increase in SP damages an employee’s incentives when SP is low. As
a result, increase in SP increases the wage required to maintain workers’ incentives.
High SP leads to small market tightness, which results in a high cost of shirking
behavior by employees. In this situation, decline of market tightness influences theworker’s incentive more than the wage. Therefore, as Figure 4 shows, the wage
decreases after SP exceeds a particular level, approximately s = 23.
On the other hand, increase in PI positively affects the incentives of employees.
12Because PI deters a firm from frequently firing employees, a diligent employee, the one
who can be fired but who is less likely to be fired than a shirking one, benefits from theresultant high job security, and the low wage is sufficient to maintain the incentive in
exchange for high job security. This is the positive commitment effect.
2. Threshold of dismissal and unemployment rate
Proposition 3
In this simulation, the following points are considered:[1] As SP increases, as shown in Figure 6, initially an employee is more likely to be
fired and then is less likely to be fired.
[2] Increase in PI does not significantly affect the threshold of dismissal when SP is low.
However, increase in PI reduces the threshold significantly when SP is high.
[3] As Figure 7 shows, the unemployment rate tends to be increased by increase in SP,
while the unemployment rate is decreased by a hike of SP when SP is in the middle
range and PI is moderate.
[4] Increase in PI reduces the unemployment rate when SP is in the middle range.

From (7), the unemployment rate depends on market tightness and the threshold ofdismissal. Because increase in SP decreases market tightness (Proposition 2 [3]), theunemployment rate increases when SP increases the threshold of dismissal. On the other
hand, when SP is high, the threshold of dismissal reduces as SP increases. If this result
dominates the reducing effect of market tightness, the unemployment rate decreases
with respect to SP. In fact, at approximately s = 25 and z = 2 or z = 4, increase in SP
reduces the unemployment rate.
When SP is in the middle range, Propositions 2 [4] and 3 [2] indicate that as PI
increases, market tightness improves and the threshold of dismissal decreases, resulting
in reduction in the unemployment rate. The effect of PI in reducing the unemployment
rate appears when PI is in the appropriate range. If PI is severe, for example, z = 12, theeffect disappears; that is, severe PI causes increase in the unemployment rate. Moreover,when SP is low or high, the influence of PI on the unemployment rate is comparatively
small. The positive effect of PI on the unemployment rate clearly appears when SP is
appropriately given; thus an optimal balance exists between SP and PI.
In this model, the equilibrium inflows to unemployment, which is equivalent to
the outflows from unemployment at the equilibrium, is given by the likelihood of
dismissal  ( pˆ ) . Figure 6 shows that increase in PI reduces the inflows to13unemployment. This indicates that PI has a negative effect on the reallocation of thelabor force, which is similar to the results in the literature on EP. Consistent with theliterature, the simulation shows that the speed of the inflows to and outflows fromunemployment is not significantly associated with the unemployment rate.
3. Social Welfare
As the same situation is repeated in every period on the equilibrium path, it issufficient to consider the social welfare level in one period. Social welfare in one period
is given by



p



   p( p )dp   ( pˆ )( w  z )  c (1  u )  uw  k u .
pˆFigure 8 shows the level of social welfare.
Proposition 4
When SP is in the middle range, appropriate PI improves social welfare through thepositive commitment effect.

As shown in Figure 8, social welfare improves gradually with respect to SP
when SP is low. Although the effect of SP seems to be positive, this positive effect onsocial welfare may be due to the elimination of the negative search externality. Thus, it
can be inferred that social welfare improves if EP solves the search externality.
I can infer the effect of the search externality on the basis of previous studies.
When the bargaining power of an employee is weak compared to the elasticity of thematching function, as the Hosios (1990) condition shows, the unemployment rate isexcessively low from the perspective of efficiency. In this case, social welfare improves
if a policy or an institutional device increases the unemployment rate. In my model, thelevel of SP is relevant to the bargaining power of an employee because high SP
increases the ex post rent E-U of an employee. High SP is relevant to the case in which
an employee has a strong bargaining power in the textbook model. This implies thatsocial welfare increases with respect to SP when SP is low, as shown in Figure 8. The
effect of improving social welfare is attributed in part to the elimination of the negative
search externality.
In the textbook model of Pissarides (2000), the efficient level of bargaining
power is uniquely determined by the Hosios condition. When the bargaining power of14

an employee is very weak, as the bargaining power increases, social welfare improves
initially and then declines. If the search externality is only crucial to social welfare, thesocial welfare curve should be mound shaped with respect to SP. In contrast, in mymodel, the social welfare curve is comparatively complex as shown in Figure 8. Thus,
the result that PI improves social welfare in the middle range of SP is not caused by theeffect of eliminating the search externality.
4. Long-term shock
The discount rate in this numerical illustration is 0.0125, which indicates thatthe model uses quarterly periods. Even if the productivity of an employee is low, he/she
is unlikely to be fired if the bad financial situation continues only for a quarter. By
considering the vacancy cost, a firm would be inclined to retain an employee if the low
productivity is expected for only a short period. In contrast, if the low productivity
persists for a long time, the firm would be unwilling to retain the match, and thus thematch is likely to be dissolved.
To examine the long-term low productivity situation, I implement a numericalillustration with a high discount rate. For example, consider the case of r = 0.1, whichindicates that the low productivity situation continues for approximately 2-4 years. A
high discount rate naturally increases the threshold of dismissal as well as theunemployment rate. However, in the middle range of SP, a more severe PI, z = 8,
reduces the unemployment rate in the case of r = 0.1 to a greater extent than in the caseof r = 0.0125. The difference in the unemployment rate between z = 8 and z = 4 isdenoted as u  u z 8  u z  4 as shown in Figure 9a. To reduce the unemployment rate,
PI is more effective in the case of r = 0.1 than in the case of r = 0.0125.
Similarly, the difference in social welfare    z 8   z  4 is represented in
Figure 9b. The social-welfare-improving effect is larger in the case of r = 0.1 than in thecase of r = 0.0125. Thus, the positive effect of PI is not necessarily smaller when low
productivity persists for a long time.

4. Discussion and Conclusion
I examined the efficiency wage model with matching technology to analyze theeffects of EP on workers’ incentives. EP generates two effects: the disincentive effectand the commitment effect. If the latter dominates the former, EP improves social
welfare. I also examined the differences between SP and PI. Although SP seems better
15

than PI from the perspective of social welfare, SP is an earning for shirking employees,
and thus its effects on employee incentives may be negative compared with the effect ofPI.
Similar to the results of previous studies regarding EP, my results on the effectsof EP were theoretically ambiguous. I therefore conducted a computer simulation andobtained the following results: [1] SP tends to increase the unemployment rate. [2] PI
does not have a significant effect on the economy when SP is low or high; however,when SP is in the middle range, it decreases the threshold of dismissal and theunemployment rate, improving social welfare. [3] Very severe PI negatively affects
employee incentives. Therefore, it is necessary to design EP appropriately.
In this model, increase in PI reduces the inflows to and outflows fromunemployment. Consistent with the literature, the speed of the inflows to and outflows
from unemployment is not significantly associated with the unemployment rate.
I have not considered workers’ bargaining power explicitly in this paper.
Rocheteau (2001) focuses on incentives and the bargaining power of employees,
concluding that a firm inflexibly sets the wage, similar to the efficiency wage model,
when employees’ bargaining power is weak. If employees’ bargaining power is strong,
the wage and the threshold of dismissal are determined through labor-management
negotiations. Therefore, my model, in which firms control the wage and the threshold ofdismissal, applies to the case of employees with weak bargaining power. However, thisdoes not indicate that my model is irrelevant to the situation where employees’
bargaining power is strong. The degree of employment protection tends to be associatedwith employees’ bargaining power and industrial relationships. Stringent EP is relevant
to bargaining power; thus, this study is not quite different from studies regarding EP andindustrial relationship such as Belot and van Ours (2001) (2004) and Garibaldi andViolante (2005).
I considered the case in which the wage is flexibly decided during theformation of employment contracts but is inflexible ex post. Empirically, the issue ofthe degree of wage flexibility has been controversial. Differences in views on
macroeconomic policy often stem from differences in views regarding the extent towhich the wage is flexibly adjusted. As Pissarides (2009) indicates, the wage of a newmatch relevant to the external wage of outsiders is comparatively flexible, but thecontinuous wage of an existing match is comparatively inflexible. As a result, thesetting of the model is consistent with the real world.
Bewley (1999) conducted interviews with over 200 business people, including
firm managers, lawyers, and consultants; Campbell and Kamlani (1997) conducted16

investigations on firm managers. These studies suggest that wages are inflexible
because a wage cut seriously damages motivation. Furthermore, according to behavioral
science, some psychological factors deter firm managers from decreasing wages. A
well-known psychological effect—the money illusion—makes wage declines lesspreferable than increases. Kahneman, Knetsch, and Thaler (1986) and Agell andBennmarker (2007) report that workers tend to prefer constant nominal wages with
inflation over nominal wage decline without inflation, even if both result in identicalamounts of real wages. In addition to these studies, experimental studies such as that by
Fehr and Falk (1999) show wages to be inflexible in the case of excessive labor supply
and involuntary unemployment. The experimental studies indicate that firm managers
experience difficulty adjusting wages downward.5 Therefore, my setting in which thewage is flexibly decided during the formation of employment contracts but is inflexible
ex post is not unrealistic.

Appendix
Proof of Proposition 1

IC ( w)
 0 holds at thewequilibrium. The proof is as follows. Assume that ICw  0 . In this situation, a firm can
Because constraint (4) is binding at the equilibrium, ICw 

reduce the wage further provided constraint (4) is satisfied, thus increasing the firm’s
profit. This contradicts the notion that the original wage maximizes the firm’s profit.
Hence, at the equilibrium ICw  0 holds.
Next, I conduct comparative statics regarding the search equilibrium withrespect to s subject to df  ds  dz  0 , as follows:

5

Recently, the relationship between wage rigidity and the matching model has been a widely
discussed issue. Shimer (2005) indicates that the Mortensen–Pissarides matching model can hardly
explain the volatility of unemployment and vacancies; Hall (2005) shows that introducing wage
rigidity in the model improves its suitability.
While Mortensen and Nagypal (2007) and Pissarides (2009) mention that wage rigidity improves
the model’s power of explanation, they argue that the model does not require wage rigidity.
According to them, the power of explanation improves if other factors such as hiring or firing costs,
demand shocks, and on-the-job search behavior are considered in the typical model. In addition, as
Kennan (2010), Moen and Roser (2007), and Brugemann and Moscarini (2007) analyze the issue,
asymmetric information, such as adverse selection and moral hazard, magnifies the volatility inunemployment and vacancies.
17 kq '
 dw / ds 
1

q2



kq
'
 d  / ds  IC
 IC Jw   Jw
w
q2

 IC   ICs ,  J sICw IC ( w)r  q(){ S ( pˆ )  ( pˆ )}  0Sˆsr  q()   ( p)1  ( pˆ )
 0,Using the locally stable condition (8) and Jw  
r  ( pˆ )
where

ICs 

and

J
0 .
Js 
s

 kq 'ICs 
 dw / ds 12qholds.
 d  / ds  IC kq '  IC J   J IC 
w
 w 
w
s 
q2

Hence,dwddpˆ
 0 and 0 . The results lead to 0 from (6), andds f  f
ds f  f
ds f  fthus, it holds from (7) thatdu
 0 .■
ds f  f18

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21

w

E1
A
IC: IC ( w)  c

E2

JC: J O

Figure 1
Equilibrium E1 is unstable but E2 is stable.

22

k
q()

w

E2

IC’
IC
JC

E1

2

O



1

Figure 2a
Search equilibrium

v

JC

JC’

E2

E1

BC’

2

1

BC

u

Figure 2b
Search equilibrium23 S ( p)  ( p)

10

O

100

Figure 3a
The curve of  ( p )   ( p ) in the base line caseS

FS p-Fp

0.35
0.30
0.25
0.20
0.15
0.10
0.05
-3

-2

-1

1

2

3

4

Figure 3b
The curve of  ( p )   ( p ) in the normal distribution case
S

24

p

wage
51.5

z=2

51.0

z=4
50.5

z=8
z=12

50.0

49.5

0

5

10

15

20

Figure 4: Wage

25

25

30

35

s

tightness : q
2.0

1.5

z=4
z=8

1.0

z=2

z=12

0.5

0.0

20

25

30

Figure 5: Market Tightness

26

35

s

threshold : `p
z=2
15

z=4
z=8

10

z=12

5

0

0

5

10

15

20

25

Figure 6: Threshold of Dismissal

27

30

35

s

u
0.25

0.20

z=12
z=2

0.15

z=4

0.10

z=8
0.05

0.00

0

5

10

15

20

25

Figure 7: Unemployment Rate

28

30

35

s

welfare
23.0

z=8
22.5

z=4

z=12

22.0

21.5

z=2

21.0

0

5

10

15

20

Figure 8: Welfare

29

25

30

35

s

Du
0.06

0.04

r=0.0125

0.02

0.00

5

10

15

20

25

30

35

s

30

35

s

- 0.02- 0.04r=0.1- 0.06- 0.08Figure 9a
Effect of long-term shock on the unemployment rate

DW
1.5

r=0.1

1.0

r=0.0125

0.5

0.0

5

10

15

20

25

- 0.5

- 1.0

Figure 9b
Effect of long-term shock on social welfare30

Table 1
Values of Parameters
Parameters
range of state

Valuesp  [0, 100]

1
for p   0, 100
100

density function of diligent
workers( p ) 

density function of shirking
workers

 1
for p   0, 10 ( p )   10
 0 for p  10, 100

reservation wagew  10interest rater  0.0125

effort costc  25vacancy cost

k=5
m  0.7(uv) 0.5

Smatching function31