Job Flows and Unemployment in an Equilibrium Unemployment Model
with Firm-Specific Skill Training
by
Hiroaki Miyamoto ∗
Graduate School of Economics, Keio University
2-15-45 Mita, Minatoku, Tokyo 108-8345, Japan
and
Yoshimasa Shirai
Faculty of Economics, Keio University
2-15-45 Mita, Minatoku, Tokyo 108-8345, Japan.
June, 2003
Abstract
We introduce productivity enhancing firm-specific skill training into the labor
search model in which the firm-specific skill training intensity and the job destruction
rate are endogenously determined. It is shown that the higher the intensity of firm
specific-skill training, the lower the rates of unemployment, job creation, and job
destruction. The model of the paper provides a theoretical framework to understand
the peculiarity of Japanese labor market often mentioned; that prevalently low rates
of unemployment, job creation, and job destruction in Japan are due to its training
system that promotes workers to acquire firm-specific skills.
JEL classification numbers: E24, J41, J64.
∗
Phone: +81-42-584-6119, Fax: +81-42-584-6119. E-mail adress: [email protected]
1
Introduction
Until early 1990’s both job creation and destruction flows and unemployment rate in Japan
had been significantly low compared to other OECD countries.1
2
A number of empirical
researches conjecture that these peculiarly low rates of job flows and unemployment in
Japan are due to the extensive firm-specific skill accumulation made by Japanese workers.3
In this paper, we incorporate firm-specific skill training of the workers into the model of
endogenous job creation and destruction with equilibrium unemployment developed by
Mortensen and Pissarides (1994)4 in order to see what influence it has on the relationship
between unemployment rate and job creation and job destruction flows.
Following Mortensen and Pissarides, there is a continuum of jobs. A job is a pair of a
worker and a firm and produces a unit of differentiated goods at each moment of time. The
1
Job creation and destruction rates in Japan were 8.1% and 7.2% during the period of 1986-1991 and
were 7.4% and 7.9% during the following period of 1991-1994. They were 13% and 10.4% in the U.S.
(1984-1991), 14.5% and 11.9% in Canada (1983-1991), 13.9% and 13.3% in France (1984-1991), 11.9% and
11.09% in Italy (1984-1993), 8.7% and 6.6% in U.K. (1985-1991). Sources: OECD Employment Outlook
(1987, 1994), Contini et al. (1995), and Higuchi (2002). Genda (1998) further takes a look at job creation
and destruction rates in Japan for the period of 1991 to 1995. Furthermore, Genda(1999) points out that
both rates of job creation and destruction in Japan are lower than those of other OECD countries.
2
The unemployment rate in Japan was about 2.6% from 1981 to 1997. During approximately same
period (1982-1997), those of the U.S., the U.K., France, and Germany were respectively 6.7%, 9.5%, 10.3%,
and 6.6%. Source: OECD Employment Outlook
3
It is often pointed out that the importance of firm-specific skill investment in Japanese firms which
takes the form of on-the-job training. See Mincer and Higuchi (1988), Hashimoto and Raisian (1985)
(1992), and Koike (1984) (1988). They offer conjectures that low unemployment rate is due to the extensive
firm-specific skill investment made in Japan which makes firms refrain from firing workers easily. Genda
et al. (2001) informally suggests a possible mechanism that accounts for the low rates of job creation and
destruction in Japan in terms of firm-specific skill training given to workers: because costs of training are
sunk, it makes costly for firms to fire employees and create new jobs. The higher costs of hiring and firing
tend to reduce the rates of job creation and destruction.
4
They are motivated by the empirical evidence that there is a co-existence of large job creation and
job destruction flows at all phases of business cycles in many countries. See Davis and Haltiwanger (1990)
and Davis, Haltiwanger and Schuh (1996).
1
productivity of goods produced by each job consists of two components: the first is subject
to idiosyncratic risk which realizes according to Poisson arrival frequency and drawing from
common distribution. The second is subject to the level of firm-specific skill training given
to workers at the time of formation of a job. The higher the training level is, the higher
this component of productivity becomes. This second component of productivity is the
new ingredient introduced in our analysis. The level of the firm-specific training given to
the worker is determined at the moment when a job is formed with its cost and expected
benefit in consideration.
As a job continues to produce goods, the first component of the productivity may fall
below a reservation threshold level at which the firm decides that it is better off to destruct
the job and post a vacancy afresh. If the second component of the productivity is high,
this threshold level of the first component of the productivity is low; in other words if the
level of firm-specific training given to the worker is high, the job becomes more resistant
to negative idiosyncratic shocks. This implies that an economy which tends to have high
level of firm-specific skill training shows low rate of job destructions. As in the original
Mortensen and Pissarides’ model, the low rate of job destruction is accompanied with low
rate of job creation and unemployment.
Furthermore, we show that the parameters such as unemployment subsidy (or employment protection) and aggregate productivity have no direct effect on training intensity.
This implies that we can decompose the factors that determine job flow rates and unem2
ployment rate into those of firm-specific skill training, unemployment subsidy and aggregate productivity. This observation facilitates us to explain the differences in job flow rates
among OECD countries by the differences in employment policies and agents’ behavior on
firm specific training.
In seeing the effect of firm-specific skill training to unemployment rate, Higashi (2002)
developed a model of on the job search with firm-specific skill investment on workers’
side. The aim of his paper is to explain low unemployment rate due to the small intensity
of on the job search when workers are making more firm-specific skill investment. The
present paper rather put emphasis on the endogenous determination of job flow rates and
unemployment rate and effect of firm-specific skill training on these rates.
The paper is organized as follows: The model is presented in Section 2. In section 3,
steady state equilibrium of the model is characterized. We carry out comparative statics
on the parameter of firm-specific cost function and unemployment subsidy (or aggregate
productivity of jobs) and show implications of the model in section 4. Section 5 concludes.
2
2.1
The Model
The Environment
Consider an economy consisting of a continuum of workers normalized to one and a large
number of identical risk-neutral firms. Time is continuous. All agents are infinitely lived
and maximize the present discounted value of their income stream with discount rate
3
r. Upon entering the labor market, each firm has one job that can be either filled and
producing or vacant and searching for a worker. A worker can be either employed and
producing or unemployed and searching for a job. When a firm with vacant job and a
searching worker meet and start producing, it is said that job creation takes place. On the
other hand, it is said that job destruction takes place when a filled job separates and stop
producing. When job destruction takes place, the firm can either reopen a job as a new
vacancy or withdraw from the labor market while the worker becomes unemployed.
A filled job produces output per unit of time and we denote the productivity of filled
job by p(x + t), where p is general productivity parameter which is common to all producing jobs, x is an idiosyncratic productivity specific to each job, and t is the enhanced
productivity due to firm-specific skill training given to the matched worker. We assume
that x=1 when a job is created. The idiosyncratic shocks hit a filled job with Poisson arrival rate λ. Each shock causes a change in firm-specific productivity x which takes value
in the range [0, 1] and it is distributed according to the c.d.f G(x). Facing the changed
productivity x, the firm with a filled job has to choose either continuing to produce at the
new productivity or closing the job down and separate from the worker. Each firm chooses
the reservation value R and destroys the job if the firm-specific productivity falls below it.
The reservation productivity is chosen as to maximize the firm’s present value. When the
filled job is destroyed, the firm leaves the labor market or reopens a new vacant job and
the worker moves into an unemployment pool and search for another job. On the firm’s
4
side, it incurs a vacancy cost pγ per unit of time while posting its vacancy. While worker
being unemployed, he/she receives unemployment subsidy z per unit of time.
At the moment of vacant job being filled, the firm decides the level of firm-specific
skill training t, incurring the cost pC(t, κ) which is twice differentiable and increasing with
respect to t and a cost parameter κ. We also assume that the marginal cost of firm-specific
skill training is increasing with respect to cost parameter. Firm-specific skill training will
increase worker’s productivity only with the current employer. Our assumption on the
function C(t, κ) are the followings;
Assumption 1 Ct (t, κ) > 0, Cκ (t, κ) > 0, Ctt (t, κ) ≥ 0, and Ctκ (t, κ) ≥ 0.
The rate at which vacant jobs and unemployed workers meet is determined by the
matching function M(u, v), where u and v represent the number of unemployed workers
and vacancy respectively. The matching function M(u, v) is continuous, differentiable,
and constant return to scale in its two arguments. We define θ = v/u as a measure of the
tightness of the labor market. The rate at which a vacant job is matched with a worker
per unit of time is M(u, v)/v = M(1/θ, 1) ≡ q(θ) where q (θ) < 0 and its elasticity strictly
between -1 and 0. The absolute value of this elasticity is denoted η. In a similar way,
the rate at which an unemployed worker is matched per unit of time is M(u, v)/u = θq(θ)
where d[θq(θ)]/dθ > 0. The elasticity of θq(θ) is 1 − η > 0. In steady-state, the inverse
of the transition rate, 1/q(θ) and 1/θq(θ), are the expected duration of a vacancy and an
5
unemployment, respectively.
We assume that wage is determined by Nash bargaining at each moment of time, where
the worker has bargaining power β.
2.2
The Value Functions
The filled job with idiosyncratic productivity x and worker with firm-specific skill level t
produces p(x + t) per unit of time, and the employed worker is paid the wage w(x) per unit
of time. When the idiosyncratic shocks arrive to jobs at Poisson rate λ, the firm-specific
productivity changes from its initial value x to some new value s ∈ [0, 1] according to the
c.d.f. G(s). If the new value s is larger than the reservation value R, the firm continue to
produce at the new productivity, but stop to produce if s < R.
The value of a filled job, the present discounted value of expected profit from a filled job
with idiosyncratic productivity x, is denoted by J(x) and satisfies the following Bellman
equation,
rJ(x) = p(x + t) − w(x) + λ
1
R
J(s) dG(s) + λG(R)V − λJ(x)
(1)
where V is the asset value of a vacant job.
The value of the employed worker with idiosyncratic productivity x is denoted by W (x)
which is defined as
rW (x) = w(x) + λ
1
R
W (s) dG(s) + λG(R)U − λW (x).
6
(2)
Now we consider the value of a vacant job V . Although all jobs are created at maximum
idiosyncratic productivity, x = 1, the expected profit of a new match will be different from
J(1), as generally defined in equation (1), because there exists the training cost which
is sunk at the moment of job creation. Therefore, we introduce the notation J0 for the
expected profit of a new match to the firm. Hence we have,
rV = −pγ + q(θ)[J0 − V − pC(t, κ)]
(3)
Moreover, the value of an unemployed worker U is defined by,
rU = z + θq(θ)[W0 − U]
(4)
where W0 is the value of the worker at the moment of job creation.
Given the starting wage w0 , the initial value of the filled job and the worker respectively
satisfy
(r + λ)J0 = p(1 + t) − w0 + λ
1
R
J(s) dG(s) + λG(R)V
(5)
and
(r + λ)W0 = w0 + λ
1
R
W (s) dG(s) + λG(R)U.
(6)
The wages are determined through the Nash bargaining between worker and employer
over the share of expected future joint income W + J. The starting wage is determined by
the following equation
w0 = argmax(W0 − U)β (J0 − V − pC(t, κ))1−β
7
(7)
where β is a parameter which indicates the bargaining power of worker and is of value
between 0 and 1. Similarly, the continuing wage rate after the arrival of firm-specific shock
satisfies
w(x) = argmax(W (x) − U)β (J(x) − V )1−β .
(8)
The solution to these optimization problems (7) and (8) must satisfy the following
first-order conditions respectively,
(1 − β)(W0 − U) = β(J0 − V − pC(t, κ))
(9)
(1 − β)(W (x) − U) = β(J(x) − V ).
(10)
and
When an idiosyncratic shock arrives, the firm has the choice of either continuing to
produce at the new productivity or closing the job down. The optimal decision of the firm
is that the firm should continue to produce if J(x) ≥ 0, and stop to produce and separate
from worker if J(x) < 0. Hence, the reservation value R is determined by following
condition,
J(R) = 0
(11)
In the equilibrium all profit opportunities from new jobs are exploited so that we have,
V = 0.
8
(12)
The level of training t is chosen by firm to maximize the present-discounted value of
their expected income at the moment of job creation. The optimal level of t satisfies
d
[J0 − V − pC(t, κ)] = 0.
dt
(13)
Finally, the steady-state unemployment rate is determined by equating the flow into
unemployment with the flow out of it. Thus
u=
λG(R)
.
θq(θ) + λG(R)
(14)
In this model, the empirical job creation rate is defined as the ratio of number of
jobs created to existing number of jobs, i.e., m(u, v)/(1 − u) = θq(θ)u/(1 − u). The job
destruction rate is defined as the ratio of total destruction to employment, λG(R).
3
Steady State
A steady-state equilibrium is a profile {u, θ, R, t, w0, w(x), J0, J(x), V, W0 , W (x), U} which
satisfies the value equations (1),(2),(3),(4), (5), and (6), the wage equation (7) and (8), the
reservation value condition (11), the free entry condition (12), the optimal level of training
condition (13), and the stationary condition (14).
The free entry condition (12) together with equation (3) implies,
J0 =
pγ
+ pC(t, κ).
q(θ)
(15)
From (9) and (15), the value of unemployment U can be rewritten as
rU = z +
βpγθ
.
1−β
9
(16)
By substituting J(x) and W (x) given by equations (1) and (2) into the sharing rule
(10), and by imposing the equilibrium condition V = 0, we obtain
w(x) = βp(x + t) + (1 − β)rU.
(17)
The wage is a weighted average of the net out of the job match and the worker’s flow
value of unemployment. Substituting the value of unemployment U into (17), we get an
expression for wage w(x),
w(x) = βp(x + t) + (1 − β)z + βpθγ.
(18)
Substitution of the wage equation (18) into (1) yields
(r + λ)J(x) = p(1 − β)(x + t) − (1 − β)z − βpθγ + λ
1
R
J(s) dG(s).
(19)
Evaluating (19) at x = R and by noting (11), we know that the last three terms of the
right hand side of equation (19) can be expressed as −p(1 − β)(R + t). Substituting this
again into (19), we obtain
J(x) =
p(1 − β)(x − R)
.
r+λ
(20)
Substiution of J(x) given by (20) into (19) leads to
(r + λ)J(x) = p(1 − β)(x + t) − (1 − β)z − βpθγ +
p(1 − β)λ 1
(s − R) dG(s).
r+λ
R
(21)
We can derive the starting wage in a similar manner as we did in obtaining the continuing wage. Using equations (9),(15),(16),(5), and (6), we obtain the starting wage rate,
w0 = βp(1 + t) − β(r + λ)pC(t, κ) + (1 − β)z + βpθγ.
10
(22)
A starting wage equation differs from a continuing wage one. Because training cost is
incurred at the creation of the match, it is shared between worker and employer. The
starting wage is reduced by the worker’s share of training cost β(r + λ)pC(t, κ). But once
job is created, the training cost is sunk and as such does not influence in the continuing
wage.
Substituting (20) and (22) into (5) and subtracting the equation (21) evaluated at
x = R from it, we get
J0 =
p(1 − β)(1 − R)
+ βpC(t, κ).
r+λ
(23)
Making use of equation (15) and (23), we drive the following equilibrium relationship
between the labor market tightness and the reservation productivity,
(1 − R)
γ
= (1 − β)
− C(t, κ) .
q(θ)
r+λ
(24)
We refer to this as the job creation condition. The job creation condition (24) states that
the expected vacancy cost, the left side of (24), equals to the firm’s share of the expected
net surplus from a new job match, the right hand side of (24).
The reservation threshold equation is derived from (21) by evaluating it at x = R,
λ
p R+t+
r+λ
1
R
(s − R) dG(s) = z +
βpγ
θq(θ).
(1 − β)q(θ)
(25)
We refer to this as the job destruction condition. The left side of (25) is the marginal
value (in terms of output) of continuation of the job under the reservation value R. The
11
first and second terms are the current productivity gain, and the third term is the option
value of retaining an existing job. On the right-hand side of (25) is the marginal value
of destruction (or the marginal opportunity cost of continuation) of a job which consists
of the value of unemployment compensation z and the second term which is equal to the
5
expected gain for the workers being hired again.
Equation (25) says that the optimal
reservation value R should be set so as to equalize marginal benefit of continuation and
destruction of the job.
Finally, by substituting equations (12), (20) and (22) into (5), the condition (13) can
be rewritten as,
Ct =
1
,
r+λ
(26)
which determines the equilibrium level of training. Condition (26) states that in equilibrium the optimal amount of training is such that the marginal cost of training is equal to
the expected gain from marginal increase in training. Note that equilibrium training level
does not depend on other endogenous variables.
5
6
The second term of the right hand side can be decomposed into three parts, pγ/q(θ), β/(1 − β), and
θq(θ). The first part is gain for the firm becoming filled job from vacant job (take a look at equation
(15)). Multiplying the second part to it makes the gain for the worker becoming employed (take a look at
equation (9)). Finally, multiplying to it the third part makes it the expected gain for the workers to be
hired again. Since the gain for the firm by destruction of the job is zero, the right hand side of equation
(25) represents the gain from destruction of the job for the firm and worker together.
6
One might wonder why equilibrium training level does not depend on other endogenous variables. The
reason for this comes from our assumption that training level t and firm specific productivity x affects
production linearly and independently and that the cost of training is sunk at the moment of job match
when training level is determined. The former assumption implies that the contribution of training t for
the firm is expected value of training to the production pt/(r + λ). And the latter assumption implies that
agent only takes into account this expected benefit due to training pt/(r + λ) against its cost pC(t, κ).
12
The system of equations (24), (25), and (26) determine the endogenous variables θ, R,
and t. We can obtain the steady-state equilibrium unemployment rate from equation (14).
4
Comparative Statics
In this section, we state comparative statics results with respect to κ and z/p.
We start by seeing the effect of change in parameter κ for the firm-specific training cost
function. Totally differentiating (26), we obtain dt/dκ = −Ctκ /Ctt < 0. Substituting this
into totally differentiated equations (24) and (25), we obtain


(θ)
− γq
q(θ)2
βγ
− (1−β)
(1−β)
r+λ
r+λG(R)
r+λ

dθ 
dκ
dR
dκ

=
(1 − β)
Ct CCtκ
tt
Ctκ
Ctt

− Cκ 
where the determinant for the matrix on the left hand side is given by,
∆=−
βγ
γq (θ) r + λG(R)
> 0.
+
q(θ)2
r+λ
r+λ
We can solve for dθ/dκ and dR/dκ respectively as,
1−β
Ct Ctκ
dθ
Ctκ
=
(r + λG(R))
− Cκ −
dκ
(r + λ)∆
Ctt
Ctt
1−β
=
(r + λ)∆
r + λG(R)
Ctκ
−1
− (r + λG(R))Cκ
r+λ
Ctt
and
γ
q (θ) Ctκ
dR
Ctκ
=
β Ct
− Cκ −
.
dκ
∆
Ctt
q(θ)2 Ctt
13
(27)
If the sign of the square bracket term for the expression dR/dκ becomes positive and hence
dR/dκ itself becomes positive. A sufficient condition for dR/dκ to be positive is given by,
Assumption 2 Ctk (t, κ)/Cκ (t, κ) ≥ Ctt (t, κ)/Ct (t, κ)7 .
Now turning to the effect on unemployment, utilizing above results we can differentiate
(14) and obtain (under assumption 2),
du/u
= (1 − u) ΓR εRκ − ( − η(θ))εθκ > 
dκ/κ
(28)
where ΓR = G (R)R/G(R) ≥0 the elasticity of G with respect to R, εRκ = (dR/dκ)(κ/R) >
0 (under assumption 2) the elasticity of R with respect to κ, and εθκ = (dθ/dκ)(κ/θ) < 0
the elasticity of θ with respect to κ. The results are summarized in the following proposition.
Proposition 1 Under Assumption 1, an exogenous increase (decrease) in parameter κ
for the firm-specific cost function reduces (increases) training intensity t and labor market
tightness θ. Under Assumptions 1 and 2, an exogenous increase (decrease) in firm-specific
cost function increases (reduces) reservation productivity level R and unemployment rate
u.
The intuition for proposition 1 is as follows; the lower the cost of firm-specific skill
training, the higher the intensity of firm-specific skill training which in turn makes the
7
Assumption 2 can be interpreted as elasticity of marginal cost for firm-specific training being smaller
than the elasticity of Ck (the marginal increase in cost with an increase in cost parameter) with respect
to training level t. Examples of the cost function that satisfies all properties given in this assumption are
C(t, κ) = κt2 /2 and C(t, κ) = κet .
14
productivity of the job higher and reduces the reservation productivity level of job destruction R. The job creation and destruction rates are given by θq(θ)u/(1 − u) and
λG(R) respectively and they equalize in steady state as described in equation (14). The
job destruction rate is increasing with respect to R. The lower reservation productivity
reduces the job destruction and creation rates and these lead to tighten the labor market
on the employers’ side (reduction of θ) and to lower unemployment rate. These effects conform to the labor market facts peculiar to Japanese economy until early ’90s, that extensive
firm-specific skill training makes firms resistant to firing workers in the face of negative
idiosyncratic shocks and it reduces job destruction and creation rates and unemployment
rate.
Furthermore we can understand why Assumption 2 is needed as a sufficient condition
for the comparative statics result on R by looking at figure 1. Given equilibrium training
intensity determined by equation (26), the locus of the pairs of θ and R that satisfies the
job creation condition (24) is a downward sloping curve over θR-space. This is denoted
as JC curve. On the other hand, the locus of the pairs of θ and R that satisfies the job
destruction condition (25) is an upward sloping curve over θR-space, denoted as JD curve.
The intersection of JC and JD curve determines the equilibrium pair of θ and R. With an
increase in κ, JD’ curve shifts left. However, the shift in JC curve is not clear in general.
If JC curve shifts leftward with an increase in κ, it is not clear whether R increases or
decreases. Under Assumption 2, it can be seen that JC curve shifts rightward. With an
15
increase in κ, the second term of the right hand side bracket of equation (24) increases
under Assumption 2. For given value of R, the left hand side of equation (24) must also
increase by an increase in θ. This rightward shift in JC curve to JC’ assuring the increase
in R with an increase in κ as equilibrium point moves from E to E’. One might worry that
the rightward shift of JC curve would lead to the increase in θ, but one can see in equation
(27) that this rightward shift of JC curve in not large enough in general to increase θ
compared to the original equilibrium point E. The first term of the bracket in the right
hand side of equation (27) is the effect of rightward shift in JC curve on θ that tend to
increase it. The second term is the effect of leftward shift in JD curve on θ that tend to
decrease it. The latter effect always dominates the former in general as it can be seen in
the second line of equation (27).
[Figure 1.]
The effects of changes in labor market tightness and reservation productivity level on
unemployment rate can be understood by seeing equations (14) and (28) in figure 2. The
system of equations (24), (25), and (26) determine θ, R, and t. On the space of u and v,
the possible pair of u and v satisfying the equilibrium value of θ can be described as a ray
starting from origin (the θ line). The pair of u and v that satisfies equation (14) for a given
value of R can be drawn as a curve B1 convex to the origin and tangent to the u-axis at
point 1. This is a Beveridge curve. The intersection of curve B1 and line θ pins down the
16
equilibrium value of u and v. With the reduction of cost parameter κ, θ increases and R
decreases. The increase in θ turns the ray θ counter clockwise to the ray θ . The decrease
in R turns the Beveridge curve from B1 to B’1 clockwise. Both the effects of θ and R
tend to decrease unemployment rate from equilibrium point E to E’. The effect of change
in cost parameter κ to v is ambiguous. The movement of curve B1 and ray θ depends
on the elasticities εRκ and εθκ respectively. As it can be seen in equation (28), the higher
the absolute values of elasticities of R and θ with respect to κ, the higher the elasticity of
unemployment rate with respect to κ.
[Figure 2.]
Let us turn to the comparative statics for real unemployment subsidy z/p. Again
totally differentiating the system of equations (24), (25), and (26) and rearrangement of
them yields,


(θ)
− γq
q(θ)2
βγ
− (1−β)
(1−β)
r+λ
r+λG(R)
r+λ


dθ
d(z/p)
dR
dd(z/p)
=
0
1
and dt/d(z/p) = 0. The solution to dθ/d(z/p) and dR/d(z/p) are given by,
dθ
1−β
=−
<0
d(z/p)
(r + λ)∆
and
dR
γη
=
> 0.
d(z/p)
∆θq(θ)
17
As to the effect on unemployment rate, by totally differentiating (14) and using above
results, we obtain
du/u
= (1 − u) ΓR εR,(z/p) − ( − η(θ))εθ,(z/p) > 
d(z/p)/(z/p)
(29)
where εR,(z/p) = (dR/d(z/p))((z/p)/R) < 0 and εθ,(z/p) = (dθ/d(z/p))((z/p)/θ) > 0. The
results are summarized as follows;
Proposition 2 An exogenous increase (decrease) in real unemployment subsidy z/p reduces (increases) labor market tightness θ, and increases (reduces) reservation productivity
level R and unemployment rate u. However, it does not affect firm-specific skill training
intensity t.
This result is basically the same as the one they obtained in Mortensen and Pissarides
(1994) and Ch.2 of Pissarides (2000). Notable point to make in proposition 2 is the independency of firm-specific skill training intensity from unemployment subsidy and aggregate
productivity. This implies that we may decompose the factors that explain the unemployment rate into firm-specific skill training and real employment subsidy. If we were to
carry out regression of unemployment rate by training intensity, and real unemployment
subsidy, the model suggests that the latter two can be treated as independent variables.
These results can be easily understood by looking at Figure 1. An increase in real unemployment subsidy only shifts JD curve to JD’ curve, since the term z/p only shows up in
job destruction condition (25). This moves equilibrium point from E to F unambiguously.
18
Moreover, if we add a firing cost8 pF into the model á la Mortensen and Pissarides
(1999) and carry out the comparative statics in term of pF , we obtain the similar results as
those in Proposition 2 namely Proposition 2’; higher firing cost leads to smaller job creation
and destruction rates and the firm-specific skill training intensity is independent from the
change in firing cost pF . Several empirical studies have tried to explain the differences
in job creation and destruction rates among OECD countries in terms of institutional
difference of recruitment and firing practices among those countries by looking at an index
called employment protection. Employment protection index accounts for how difficult
for the firms in that country to fire workers. Firing cost F can be thought of as this
employment protection index. In case of Japan, employment protection index are not
significantly high compared to other OECD countries so that it cannot be considered as
a significant factor to account for the low rates of job creation and destruction in Japan.
On the other hand as pointed out in Blanchard and Portugal (2001), an extremely high
employment protection is responsible for the low rates of job creation and destruction in
Portugal. Combining the results of Proposition 1 and 2’, we may explain that low rates
of job creation and destruction in Japan and in Portugal are due to high firm-specific skill
training intensity and high employment protection respectively.
8
They assume that the firing cost pF is incurred to the firm at the time of job destruction. In the
context of our model, it enters into the fourth term of the right hand side of equations (1) and (5) that it
becomes λG(R)[V − pF ], the term (J(x) − V ) of equations (8) and (10) becomes (J(x) + pF − V ), and
equation (11) becomes J(R) + pF = 0.
19
5
Concluding Remarks
In this paper we built a model that conforms to a seemingly peculiar labor market fact
in Japan that the low job flow rates and unemployment rate coexists without having
definite high unemployment subsidy or employment protection compared to other OECD
countries. The key ingredient was the low cost of firm-specific training that allows the
firms to give more training to workers and enhance the productivity of the jobs. This
makes rates of job destruction and creation rates low and also unemployment rate low. The
model shows that the effect of firm-specific training is independent from the factors such as
employment protection or unemployment subsidies. The model suggests that incorporation
of firm-specific skill in international comparison of job flow rates and unemployment rate
would become much consistent. Empirical investigation incorporating the firm-specific
skill training is needed as a future research in order to test this implication.
20
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21
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22
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23
JD R ✻
JD
❅
I
❅
✠
r
F
Er r
E
JC JC
✲
Figure 1: The effect of increase in κ on θ and R.
24
θ
v ✻
B
B
✠
ppp
p
pp
ppp
ppp
p
pp
ppp
ppp
p
pp
ppp
p θ
❅
I
❅
❅
✚
✚
pp p
✚
p
✚
ppp
✚
pp p p p
✚
pp
✚
pp p p p
✚
✚
pp
pp p p p
✚
p
✚
rE
prp p ✚
pp p p p E
✚
pp
✚
pp p p p
✚
✚
pp
pp p p p
✚
p
✚
ppp
pp p p p ✚✚
ppp ✚
pp p p ✚
pp✚
r
r
pp
ppp
0
u
u
θ
r
1
✲
u
Figure 2: The effect of decrease in κ to unemployment rate
25