A Search Model of the Lost Generation
Ryoichi Imai∗
Kyushu University(Tentative draft, not to be quoted)
February 2, 2009

Abstract
We study the eﬀects of labor market policies on the employment distribution in a search-theoretic model of dual labor markets with regularand non-regular jobs. The labor market is dual in the sense that the senior market is separated from the junior one. The regular jobs are charged
with payroll and income taxes, while the non-regular jobs with only income
tax. In this frame work, the policies protecting the employee’s gain havesome aggregate eﬀects into the same directions, while the tax policies workwith negative feedbacks between sectors. A replacement of payroll tax withincome tax, keeping tax wedge constant, does not aﬀect the creation ofregular jobs, while it reduces the creation of non-regular jobs.
∗

Kyushu University International Student Center, Higashi-ku Hakozaki 6-10-1, Fukuoka 8128581, Japan. e-mail: imryoichi@isc.kyushu-u.ac.jp

11. Introduction
We entered society after the collapse of the bubble. I call this thepost-bubble generation. Many of us will continue to live in the faceof humiliation. By contrast, many of those of the “economic growth
age generation” will continue to live comfortably. This after all is themeaning of “a peaceful society.”...........Right after the collapse of the bubble, both enterprises andworkers were thinking only about how to escape the collapse. Companies planned to reduce personnel and labor unions dropped their base-up
demands and prioritized restructuring. Both agreed that it was necessary to reduce to the minimum the hiring of new workers. Enterprises
cut new hires and tried avoid hiring regular employees. They did so byusing agency workers, part-timers and arbeiters.
Society sympathized with middle aged and older workers who were
spared restructuring and ignored freeters who could not get regular jobs
and were pushed to low-wage work. Because they were not employedfrom the start, staying unemployed was not considered a problem.
..........In that unequal society in which the haves and the have nots
are deeply divided and there is no mobility between them, war ceases
to be taboo. Far from it. The anti-war peace slogan is the very thingthat is understood as the arrogance of the haves, which keeps us lockedin poverty throughout our lives.
Tomohiro Akagi (2007):“War is the Only Solution.
A 31-year-old freeter explains
the plight and future ofJapan’s marginal workers.”
The conflict of interests between generations has been a serious issue of thelabor market in the OECD countries. Many economists and policy analysts pointout that the deregulation on labor contracts and working condition developped
in the last few decades has created a huge gap in compensation, other fringebenefits, and the access to social security between the generations before andafter the deregilation. In this paper, I construct a search model of dual labormarkets separated markets between junior and senior workers.
It is widely recognized that the employment opportunites for young workers
have been deteriorating in the last few decades. Of course, the stagnant economic
growth is a major reason of the low employment opportunities for the youth.
However, it is increasingly recognized that market institutions and policies are
crucial to the long-run labor market performance. There are many plausible stories
in which the labor market policies and institutions aﬀect youth unemployment.
First, taxation on employment such as income and payroll taxes might increase
youth unemployment by reducing the business’ incentive to create jobs. Second,
government regulation on working conditions such as hours and intensity may
increase hiring costs for firms directly and indirectly: It might prevent employers from allocating labor input eﬀectively, and increase the unit labor costs bystrengthing the workers’ bargainig power in wage nagotiations. Third, a stronger
enforcement of employment protection legislation (EPL) might prevent eﬃcientjob destruction and produces more mismatches between jobs and workers: EPL
might induce firms to hold old workers with low productivity and prevents themfrom creating vacancies for talented, young workers.
Tax wedge is a key determinant of long-run labor force participation andworking hours in the neo-classical growth model. Prescott (2002, 2004), AlesinaGlaeser-Sacerdote (2006), Coenen-McAdam-Straub (2008) and others, argue thatthe high tax wedge in Europe is the major cause of its low labor-market participation and low output per workers relative to the US, while the negative supply
eﬀect is reported to be relatively small by Nickel (2003). In the search-theoretic
analysis of the labor market, however, much work have not yet been done on the
tax and subsidy policies except for Mortensen-Pissarides (2003).
In the present paper, the labor market is “dual” in the sense that the job market for workers with previous job experiences is separated from the one for thosewith no experiences. It becomes increasingly diﬃcult for new school graduates tofind adequate and stable jobs in the OECD countries. The longer they stay inthe unemployment pool, the more likely they become unemployable, since firms
are less willing to hire workers who have been spending so much time in the poolof the unemployed. Unemployed workers might loose their employablity because
their trainability deteriorates as time goes on. The gap in job opportunities among
workers are anlyzed by various authors, focussing on the skill-biased technologicalprogress. As is in Saint-Paul (1996), Acemoglu (1999), Albrecht-Vroman (2002),

job creation is endogenous in this paper, althoug skill formation is not formallyanalyzed.
The situation becomes even worse, because the junior unemployed are usually
excluded from the social security system. Eligibility for unemploment insurance
benefits is often restricted to the unemployed with suﬃciently long tenure atprevious full-time jobs.
In the present model, there are two types of jobs, good and bad, following theterminology of Accemoglu (2001). The good job is more productive than the badone. The labor market is frictional, and each worker-firm pair produces a match
surplus, to be shared by them through the Nash bargaining. Workers employedat the good job is more protected by law than workers employed at the bad job.
Therefore a larger share of match share goes to the former than to the latter.
However, the bad job has its own advantage over the good one, which is charged
not only with income tax but also with payroll tax, while the bad job is charged
only with income tax. Job vacancies are created endogenously by entrepreneurs,
who consider the productivity gap, the legal protection, and the tax burden at
once. Young workers enter the economy as “good” unemployed, who can be hired
at both the good and bad jobs. However, a random shock deteriorates them tobad workers, who can be hired only at the bad job. I share a similar intuition
with Moen (2003) on the externality that the good jobs impose on the bad jobs.
In Moen, workers are heterogeneous, while workers are homogeneous and jobs areheterogeneous in this paper.
The main results of the paper are as follows. I interpret the workers’ bargaining
power in the surplus division as the degree of employee protection by law. The
good job is more protected by law and then the larger share of the match surplus
goes to the employee, while a zero or only fixed amount of the surplus is obtainedby he employee at the bad jobs. The diﬀerence of the bargaining power between
the jobs types distinguishes my paper from Acemoglu (2001), in which the worker’s
share is identical in both types, and the fraction of the good job is always too low,
since the wage is not equated between the types due to the constant sharing of
the match surplus. That is, the wage at the good job is too high, while the wage
at the bad job is too low. Acemoglu does not discuss the overall eﬃciency ofjob creation. In the present paper, however, the worker’s bargaining power isβ ∈ [0, 1] in the good job but zero in the bad job. Therefore there are too manyvacancies of the bad job, while the eﬃciency of the good job sector depends onthe comarison of the worker’s share with the elasticity of the matching function.
The eﬀects of taxation are even more complicated with the interation between

the sectors. The labor market tightness in the good job sector is determined solely
by the tax wedge, and is not aﬀected by the ratio of payroll tax to income tax.
However, the labor market tightness in the bad job sector is aﬀected by the tax
wedge in the good job sector as well as by the income tax in the bad job sector.
The higher tax wedge with constant income tax reduces employment in the good
sector, while it increases employment in the bad sector, since the latter is exempt
from payroll tax.
The goal of this paper is to explore the impacts of the labor market policies on
the welfare of the young unemployed, good or bad. The welfare of the unemployed
is a weighted average of the discounted present values of the upcoming states of
the good and bad employment. A rise in the employee’s gain increases the values,
and reduces the chances, of being employed. Therefore its impacts on the welfareof the employed are mixed and ambiguous. It should be noted that the eﬀects of
employee protection are not restricted to the sector where the policy is imposed,
but spread to the whole economy with a positive feed back in values, and a negative
feed back in propabilities: More protection of the good job employees improves thevalue of the bad job employment through the consideration of future job prospects.
More protection of the bad job increases the value of being unemployed, which
results in the rise of the threat point in the wage bargaining of the good job.
However, the employee protection reduces job creation in the bad jobs as well as
in the good jobs.
However, tax reforms aﬀect the creation of both the jobs in opposite directions. A reducing tax wedge with constant income tax rate increases the good job
creation and reduces the bad job creation, with increasing values of filled jobs inthe both sectors. However, a replacement of payroll tac with income tax underconstant tax wedge reduces the bad job creation, with no eﬀects on the good jobs.
Therefore the bad unemployed workers suﬀer welfare reduction. If the increasing
tax base asscoated with a rise in income tax rate enables the government to reduce
the tax wedge under a given tax revenue, it alleviates the welfare loss and mightyield a slight gain, depending on the parameters. On the contrary, a tax reform
into the opposite direction improves the welfare. The governemnt should replace
income tax with payroll tax, if the tax wedge is constant.
The paper is organized as follows. The next section presents the simple model.
which is esential to the complete analysis. In section 3, the simple model isextended to the full model, and the implications of the labor market policies andinstitutions on the young unemployed are explored. More detailed discussions arepresented in section 4. Section 5 concludes the paper.

2. The Model
Before presenting the model, I would like to define the labor market policies andinstitutions explored in this paper.
In the present paper, I discuss the two types of taxation on employment. One ispayroll tax, and the other is income tax. Let w be the pre-tax instaneous wage paid
to the employee, and τ p and τ e be the payroll and income tax rates respectively.
Then the eﬀective instantaneous cost of hiring an employee is (1 + τ p )w, and theeﬀective compensation fro an employee is (1 − τ e )w. The tax wedge is defined asω=

1 + τp> 0,
1 − τeand is the well-known measure of labor-market distortion. In the present model,
income tax is identical to consumption tax, since there is no saving.1
Employment protection legislation (EPL) is not explicitly modelled in thispaper, since job destruction is exogenous here. I consider the situation in which
the government’s regulation on working hours and environments is reflected by
the worker’s bargaining power β in the Nash wage bargaining. It is widely knowthat a simple transfer of income within a match such as severance pay does not
aﬀect the threshold productivity of job destruction. See. for instance, Cahucand Zilberberg (2004).2 However, EPL aﬀects the threat points of the bargaining
participants and tends to reduce firms’ entry. I abstrac the model from thesedetails and adopt a simple ‘reduced form’ approach to treat β as the measure of
employment protection.
We start the analysis with a simple model, in which there is no deteriorationof unemployed workers’ quality. The transition of agents is illustrated in Figure
1.
Time is continuous. Agents discount the future with discount rate r. There are
numerous workers and firms. The population on the worker is normalized to one.
The population of firms is determined by the zero-profit condition. Per unit time,δ workers enter the economy, and they die at Poisson rate δ. Thus the workers’
population is kept at unity. There are three states of workers: Unemployed,
1

An interesting politico-economic analysis of the replacement of income tax with consumption
is presented by Rios-Rull et al (2006).
2
Saint-Paul (1995) argues that severance payment should be considered in the employer’s
match payoﬀ, while it should no be included in that of the employee, since the transfer ofseverance payment occurs only when one side of them voluntarily destroys the match. Theneven a simple transfer aﬀects the match surplus and aﬀects the threshold match productivity.

δ

eG

δ

αG
σG

u

αG s
σB

δ

αB

eB

Figure 1: The Simple Modelδemployed at a good job, and employed at a bad job. The value functions of thesethree states are denoted by U, WG , and WB , respectively, and satisfy the following
Bellman equations.
rU = z + b + αG (WG − U) + αB (WB − U) − δU
rWG = (1 − te )wG + σ G [U − WG ] − δWG
rWB = (1 − te )wB + sαG (WG − WB ) + σ B [U − WB ] − δWB(1)

An unmeployed worker consumes home-production output z, and receives unemployment insurance benefit b. At Poisson rate αG , he is employed by a good
employer, while employed by a bad employer at Poisson rate αB . While employed,a workers receives wage wG (wB ), which is taxed at income tax rate τ e . A good(bad) job is destroyed by an exogenous shock that comes at rate σ G (σ B ), andσ G < σ B . An employee at a bad job is engaged in on-the-job search for a good
employment, of which the good job chance comes at Poisson rate sαG , where s
stands for the relative advantage of disadvantage of on-rhe-job search.
A firm creates a vacancy for a good or bad job when it enters the economy.
The value of a firm with a vacancy is denoted by Vi , i = G, B, while the value of a
firm employing a worker is denoted by Vi , i = G, B. c denotes the instantaneous
cost of maintaining a vacancy. A firm with a good (bad) vacancy hires a worker
at rate ϕG (ϕB ). A good job yields output yG and a bad job yields yB (< yG ).
A payroll tax is charged on all the good jobs at rate tp , while no payroll tax ischarged on a bad job. Both jobs are destroyed by an exogenous shock (at rate
σ G or σ B ) and by the employee’s death (at rate δ). A bad job is destroyed more
often than a good job, then σ G < σ B . In addition, a bad job is destroyed by theemployee’s quit that occurs rate sαG . The value functions satisfy the following
Bellman equations.
rVG
rVB
rJG
rJB

=
=
=
=

−c + ϕG η G [JG − VG ]−c + ϕB η B [JB − VB ]yG − (1 + tp )wG + (σ G + δ)[VG − JG ]yB − wB + (σ B + δ + sαG )[VB − JB ](2)

where αG , αB , ϕG , and ϕB are the functions of the labor market tightness, θGand θB , and dereived from a standard CRS matching technology, satisfying
ϕG =

αG
,
θG

ϕB =

αB
.
θB

Note that the concavity of the matching function implies
α0G (θG ) > 0,
ϕ0G (θG ) < 0,

α0B (θB ) > 0
ϕ0B (θB ) < 0.

η G and η B are the probabilities that the job applicant is employable. Note thatηG =u + seB, η B = 1.
u + eB

We consider such a situation that an on-the-job searcher is not more likely to bematched for employment. Therefore s ≤ 1 and η G ≤ 1, while everyone is hired
once he meets an employer and η B = 1. In order to make the analysis tractable,
I assume that s = 1 and η G = 1. Later I will present some numerical excercisesby allowing for the case s < 1.
The worker and the firm in a filled job bargain over the wage. The wage
bargaining is forward-looking: The worker’s threat point is U, the value of unemployment. In a good job, the worker takes fraction β of the surplus, while theworker in a bad job takes a certain reservation value, h, which reflects the degreeof legal protection of the bad job.
WG − U = β[WG − U + JG − VG ],WB − U = h.
Each firm chooses its type when it enters the economy. Creating a good job
costs k, while creating a bad one costs nothing. Then the job choice condition is
given by:
V = max{VG − k, VB }or equivalently,

The entry condition is:

VG − k = VB .

(3)

VB = 0(4)

We solve the model as follows. First we solve the value functions of incumbent
workers,
rU = z + b + αG (WG − U) + αB (WB − U) − δU
rWG = (1 − te )wG + σ G [U − WG ] − δWG
rWB = (1 − te )wB + sαG (WG − WB ) + σ B [U − WB ] − δWBto obtain
DG ≡ WG − U,DB ≡ WB − U.

Second, with (3) and (4). we solve the firm’s value functions,
rk
0
rJG
rJB

=
=
=
=

−c + ϕG η G [JG − k]−c + ϕB η B JB
yG − (1 + tp )wG + (σ G + δ)[k − JG ]yB − wB − (σ B + δ + sαG )JB

to obtain the reduced forms of ϕG , ϕB , JG , and JB , as functions of wages, wG
and wB . Note thatEG ≡ JG − k, EB ≡ JB .
Third, we find the wages to solve the Nash bargaining:
DG = β(DG + EG ),DB = h.

We substitute the reduced forms of the wages into the expressions of ϕG and ϕB
obtained at the the second step. To obtain clear analytical results, we assume
h = 0. The labor market tightness in the good job sector, θG , is implicitly
determined byϕG (θG ) = ΛG ,
(5)
where
ΛG =
and

(rk + c)[(r + δ + σ G )(1 − β + βω) + αG (θG )]η G (1 − β){yG − rk − ω[b + z]}

1 + tp1 − teis the tax wedge. The left-hand side of (5) is decreasing in θG , while the righthand side is increasing in θG . Therefore the equilibrium is uniquely determined.
Note that ΛG does not depend on tp or te , but only on ω, the tax wedge. Hence
we have obtained the well-known irrelevance proposition: any tax reform which
does not aﬀect the tax wedge is irrelevant for the good job employment. The
determination of the labor market tightness is illusrtaed in Figure 2.
It is straightforward to see thatω=dΛG
(rk + c){(r + δ + σ G )(1 − β)(b + z) + (yG − rk)[r + δ + σ G + αG (θG )]}
=
> 0.
dω
[rk − yG + ω(b + z)]2 (1 − β)η G

ΛG

ω↑

ϕG (θ G )
θG
Figure 2: The Determination of θG
that is, ΛG shifts up as the tax wedge increases, which reduces the tightness in
the good job sector, as is illusrated in Figure 2.
Let us turn our attention to the bad job employment. We obtain
1= ΛB ,
ϕB (θB )(6)

where the expression of ΛB is too complex to be presented here. Note that theleft-hand side of (6) is increasing in θB , and its right-hand side is not aﬀected byθB , and then the solution is unique. It is straightforward to see thatdΛB
(1 − s){(r + δ + σ G )(b + z)(1 − β) + (r + σ G + αG )(yG − rk)}αG βη B=>0dω(1 − te )[(r + δ + σ G )(1 − β + βω) + αG βω][r + δ + σ B + sαG (θG )]c
Then a rise in the tax wedge in the good job sector increases the entry into thebad job sector, as is illustrated in Figure 3.
Consider the replacement of payroll tax with income tax, which is identical toincreasing income tax rate te for a given tax wedge. We have−(b + z){(r + δ + σ G )[β(ω − 1) + 1] + αG (θG )(1 − s)β(yG − rk)]}η B
dΛB
< 0.
=
dte
(1 − te )2 {(r + δ + σ G )[β(ω − 1) + 1] + αG (θG )βω]}[r + δ + σ B + sαG (θG )]c1
ϕ B (θ B )

ω↑

ΛB

τe ↑

θB
Figure 3: The Determination of θBThat is, a rise in the income tax shifts the ΛB locus down, and decreases θB .
Therefore a replacement of payroll tax with income tax decreases the entry into
the non-regular sector as is illustrated in Figure 3, while it does not aﬀect thejob creation in the regular sector. The comparative statics are summarized in thefollowing proposition.
Proposition 1. In the simple model of dual labor markets, we have the following.
1. In the good sector, the labor market tightness and the job creation are solely
determined by the tax wedge. A rise in the tax wedge reduces the good job
creation.
2. In the bad job sector, the labor market tightness is determined not only by
the tax wedge but also by the income tax rate. A rise in the tax wedge shifts
employment from the good to the bad sector.
3. A tax-wedge neutral replacement of payroll tax with income tax does not
aﬀect the good job creation, while it reduces the bad job creation.
The interpretation of the last result in the proposition is straightforward. Increasing income tax with no change in the tax wedge does not change the tax
burden on the good job sector, while it increases the burden on the bad job sector. Then the economy is more distorted after the reform. Due to the reductionin the bad job creation, in order to make the same tax revenue, the government
might need to raise the income tax rate, which makes the situation even worse.
Increasing income tax rate is compensated by a reduction in the payroll tax ratewith no substantial eﬀect in the good sector. In the bad sector, increasing tax
revenue with the income tax rise is partially oﬀset by the reduction of job creation.
Given tax wedge, a tax reform to substitute payroll tax with income tax has noeﬀect on the good job creation, while it reduces the bad job creation because thebad job creation is more distorted by the reform. Therefore, a wedge-neutral tax
reform to replace payroll tax with income tax might yield a government surplus
or deficit, depending on the extent to which the reduction in job creation is compensated by the larger tax base. If the reduction in the labor market tightness isrelatively small, the government would obtain a surplus. In other words, the governemnt can reduce the tax wedge on the good job by further reducing the payroll
tax rate to finance the fixed expenditure. On the contrary, if the job creation in
the bad job sector is suﬃciently elastic to the income tax rate, a revenue-neutralreform requires a higher tax wedge in the good job sector. Futhermore, a simple(not wedge-neutral) replacement of payroll tax with income tax raises tax wedge,
and even reduces the labor market tightness in the good job sector.3

3. The Extended ModelIn the simple model, the unemployed worker’s quality does not deteriorate. The
labor market is integrated over the two types of jobs, and all the unemployedworkers are endowed with equal job opportunities. In this section I will extend
the model to introduce a true duality into the labor market as follows. Once theunemployed worker’s quality deteriorates, he can no longer apply for the goodjob, and is allowed to apply only for the bad job. In other words, good workers
are entitled to apply both the good and bad jobs, while bad workers are allowed
to apply only for the bad jobs. Another source of duality is the access to social
security. All the unemployed workers with previous good or bad job experiences
can receive the unemployment benefit, while all the workers with no previous
job experience is not eligible for the unemployment benefit. The labor market isdivided by the workers’ history with or without job experiences. Once workers are
hired, they are promoted to the upper market in which they are protected by thegovernment’s social security program, and would never go back to the pool of theunemployed with no legal protection. The simple model is a world of workers withprevious job experiences, who are legally protected and allowed to obtain a partof job match surplus. The extended model has the simple model as a submarket,
which does not depend the rest of the labor market.
Time is continuous. There are numerous workers and firms. There are two
types of jobs: good and bad, which are endogenously created. The workers’
population is normaliezed to one, while the firms’ poluation is determined by entry
and exit. Workers are either employed or unemployed. Per unit time, δ workers
enter the economy, while each worker dies at Poisson rate δ, so the population is
kept at unity. The new workers are good in the sense that they can be employed3

Let τ p and τ e be the payroll and income tax rates respectively. Then the tax wedge is1+τ
written as 1−τ pe . With a simple replacemnt of payroll tax with income tax, the income tax rates
is raised by ² and the payroll tax rate is reduced by the same amount. Then the tax wedge
increase since
1 + τp − ² 1 + τp²(τ p + τ e )=−> 0.
1 − τe − ² 1 − τe
(1 − τ e − ²)(1 − τ e )not only at bad jobs but also at good jobs. They become bad workers at Poisson
rate λ. Bad workers are so in the sense that they can be hired only at bad jobs.
The good unemployed can find an employment opportunity at good jobs at rate
αG (θG ) and at bad jobs at rate αB (θB ), where θi , i = G, B, is the labor-market
tightness of the good (bad) job sector. An employee at a bad job is engaged inon-the-job search for a good job. He is employed by a good employer at Poisson
rate αG (θG )s, where q ∈ [0, 1]: It is less often for an employee at a bad job tobe employed at a good job than for a good unemployed worker. As is found by
Nakajima (2008), on-the-job search is not so eﬀective as oﬀ-the-job search. A
filled job is destroyed by a shock at rate σ G or σ B . A bad job is destroyed more
often than a good job, then σ G < σ B . Once a job is destroyed, a worker goes tothe same unemployment pool, u, no matter if they were employed at a good or
bad job. They resume employement at a good job with Poisson rate αG (θG ), andat a bad job with Poisson rate αB (θB )f .
I introduce some minor parameters to match the model to the real labor market
in the numerical exceicises. Good unemployed workers with no job experiences,always accept a good job oﬀer, while accepting a bad one with probability f ∈[0, 1]. Bad workers receive no good job oﬀer, and a bad job oﬀer with probability
αB (θB )q where q ∈ [0, f ]. That is, a bad worker is no more likely to be employed
at a bad job than a good worker. The transition of workers is illustrated in Figure
4.
The good job is distinct from the bad job in the three senses. First, theformer is more productive than the latter, that is, yG > yB . Second, the former
is destroyed less often than the latter, that is, σ G < σ B . Third, the former ischarged on not only with income tax but also with payroll tax, while the latter ischarged on only with income tax. Let tp and te denote the payroll and income tax
rates respectively. All the unemployed workers with no previous job experiences
receive instantaneous income z, while the unemployed with job experiences receive
unmployment benefit b in addition to z.
The extended model is identical to the simple model except for the two additional value functons. The value functions of the good unemployed UG , the bad
unmployed UB , satisfy the following Bellman equations.
rUG = z + αG (WG − UG ) + f αB (WB − UG ) + λ(UB − UG ) − δUG
rUB = z + qαB (WB − UB ) − δUB
The Bellman equations for U, WG , WB are identical to (1).

(7)

δ

δ

eG

αG
αG s

uG

δ

σG
σB

eB

αB f

λ

αG

α Bq

αB

δ

uB

u

δ
Figure 4: The Extended ModelδFirms create good or bad job vacancies when they enter the economy. Creatinga good job vacancy costs k, while creating a bad job costs nothing. They pay
instantaneous vacancy cost c. A firm with a vacancy meet a job-seeking worker at
Poisson rate ϕi (θi ), i = G, B. The firm hire him with probability η i , i = G, B.
Both ϕi (θi ) and η i are endogenously determined in the model. The employer
of a filled good (bad) job pays wage wG (wB ) to the employee and payroll tax
tp wG (tp wB ) to the government. A filled job is destroyed by an exogenous shockthat comes at Poisson rate σ G (σ B ) and the employee’s death that comes at rate
δ. In addition, a bad job is destroyed as the employee quits to switch to a good job
at rate sαG . The Bellman equations for the firms are identical to the the firms’
value functions satisfy are identical to (2), except for the hiring probabilitues:
ηG =uG + seB + u
f uG + quB + u, ηB =
uG + eB + u
uG + uB + u

q and s are exogenously given, while f is chosen by the good worker unemployed
as follows.
⎧
⎫
⎧
⎫
⎨ > ⎬
⎨ =1
⎬
∈ (0, 1)f
if min[WB − UG , WB − U ] = 0
⎩
⎭
⎩
⎭
<
=0
That is, the good unemployed accepts a bad job if it yields a positive gain.
The wage bargaining and the vacancy creation are similar to those of thesimple model with relevant notation changes. We assume that the wage bargaining
is forward-looking. That is, the worker’s threat point is U, the value of theunemployed with previous job experiences.
WG − U = β[WG − U + JG − VG ],WB − U = h.
The matching technology exhibits the CRS:
m(uG + eB + u, vG )= m (1, θG )uG + eB + um(uG + uB + u, vB )αB (θB ) == m (1, θB )uG + uB + u
αG (θG ) =

where
θG =

vG
vB
, θB =
uG + eB + u
uG + uB + uO

ϕG and ϕB are defined as
ϕG (θG ) =αG (θG ),θG

ϕB (θB ) =αB (θB )θB

Note that the concavity of the matching function implies
α0G (θG ) > 0,
ϕ0G (θG ) < 0,

α0B (θB ) > 0
ϕ0B (θB ) < 0.

That is, the tighter the market is, the more often the worker meets a firm with avacancy, and the less often the firm meets a worker.
We solve the model recursively: First, we solve the market for the workers
with previous experiences, (1) and (2). Then we substitute the solution into (7)to obtain the whole equilibrium. We finally obtain the labor market tightness θG
in the good job sector implicitly by
ϕG (θG ) = ΛG ,where ΛG is identical to the expression obtained in (5):ΛG =(rk + c)[(r + δ + σ G )(1 − β + βω) + αG (θG )]η G (1 − β){yG − rk − ω[b + z]}

and1 + tp1 − teis the tax wedge. Here we assume h = 0; the non-regular employment is notprotected by law, in order to make the analysis tractable. The labor market
tightness θB in the bad job is determined by
ω=

1
= ΛB
ϕB (θB )The expression for ΛB is identical to the one in (6).
The extended model has a recursive structure and the firm section and theexperienced section are independent of whatever occurs to workers with no experience. Therefore we obtain the same analytical results obtained in Proposition
1.
The property of the senior market is identical to the simple model. Our interest
rests on the impacts of the labor market policies on the junior market. The value

functions of the junor workers are weighted average of the value functions of thegood and bad employment, and can be written as(r + δ + qαB )αG WG + [f qαB + λq + f (r + δ)]WB + (qαB + λ + r + δ)z,(r + δ + qαB )(αG + f αB + λ + r + δ)z + qαB WB=.
r + δ + qαB

UG =
UB

Note that a rise in WG is assoiciated with a decline in αG (θG ), while a rise in WB
is assiciated with a decline in αB (θB ). That is, the more attractive a job is, themore diﬃcult it is to get it. Therefore a rise in WG or WB increases both UG and
UB , while the increasing value is partly cancelled by the associated reduction in
the labor market tightness.
β, ω, τ e , h, s, q are the policy or institutional variables in this model. β isthe bargaining power of workers reflecting the government’s regulation on various
working conditions. ω is the tax wedge determining the eﬃciency of the good job.
A tax reform to replace payroll tax with income tax under a constant tax wedge
is captured by a rise in τ e . The protection of the bad job is reflected by h. s isa measure of the easiness of on-the-job search. q is the degree of disadvantage ofthe bad unemployed relative to the good unemployed. (θG , θB , WG , WB ) is a setof variables keen to our interests. These policy variables pin down the equilibrium
values of them.
The whole system is reduced to the two equations, (5) and (6), which determineθG and θB . The reduced forms of WG and WB are complex. However, the partial
derivatives of them with respect to thse policy variables are obtained as follows.
∂WG(r + δ + αG )(r + δ + σ G )[yG − rk − ω(z + b + αB h)]>0=∂β(r + δ)[something]2∂WB(r + δ + σ G )[yG − rk − ω(z + b + αB h)]αG>0=∂β(r + δ)[something]2
A rise in the worker’s bargaining power tends to increase not only the value of agood job employee but also that of the bad job employee.
∂WG
∂WB
=
= 0.
∂s
∂s
A rise in the eﬀectiveness of on-the-job search does not aﬀect WG or WB . On-the
job search increaes the continuation value of the match bu reduces its current

θG
θB
WG
WB

β
−
−
+
+

s
0
−
0
0

h
−
−
+
+

ω
−
+
−
−

τe
0
−
0
0

Table 1: Comparative Statics
value, therefore, a rise in s does not change WB .
αB [(1 − β)(r + δ + σ G ) + ω(σ G − δ)]
∂WG
=
>0
∂h
(r + δ)[(1 − β)(r + δ + σ G ) + ω(r + σ G + αG )]∂WB
r + δ + αB
βωαG αB
=
−
>0
∂h
r+δ
(r + δ)[(1 − β)(r + δ + σ G ) + ω(r + σ G + αG )]A rise in the worker’s gain at the bad job increases the welfare of the value not
only of the bad but also good employee. A similar result is pointed by Acemoglu(2001) as the eﬀect of minimum wage.
The derivatives of WG and WB w.r.t. ω are complex. However, we obtain
∂WG
µ∂ω
¶
r + δ + αG ∂WB=αG∂ω∝ β(rk − yG )(r + σ G + αG ) − (1 − β)(r + δ + σ G )(z + b + αB h) < 0
The larger tax wedge on the good job sector with a constant income tax rate andan increasing payroll tax rate, reduces the values of the employed workers, withthe larger extent for the good job employee. On the contrary, we have
∂WG
∂WB
=
= 0.
∂τ e
∂τ e
The replacement of payroll tax with income tax has no direct eﬀect on the valuesof the employed. However, it has indirect eﬀects through the firms’ entry.
The eﬀects of policy changes are listed in Table 1.
The policy implications are summerized as follows.
1. A rise in the general protection of the good job increases the welfare of bothtypes of jobs, while it reduces the availability of jobs. Its overall eﬀects onthe welafare of the junior unemployed are ambiguous, since they can gethigher job welfare with lower probabilities.
2. On-the-job search does not aﬀect the employees’ values and the labor market
tightness in the good job sector. However, it reduces the creation of the badjobs. Then the over all eﬀects on the junior unemployed tend to be negative.
3. A stronger protection of the bad job employees increases the values of bothtypes of jobs, while it reduces the creation of them. Again the overall eﬀects
on the welfare of unemployed are ambiguous.
4. A higher tax wedge on the good job reduces the value of the employees
of both types and the creation of the good jobs. However it increases thecreation of the bad jobs, since it is associated with a constant income tax
rates and an increasing payroll tax rates. It also reduces the values of theemployees at both types of jobs. The overall eﬀects on the junior employed
might be negative.
5. A tax reform to replace payroll eax with income tax under constant tax
wedge reduces the creation of the bad jobs, while the employees’ values andthe labor market tightness of the good job are not aﬀected. The overall
eﬀects on the junior unemployed might be slightly negative.
A rise in the employee’s gain (β and h) increases the values, and reduces the
chances, of being employed. Therefore its impacts on the welfare of the employed
are mixed and ambiguous. It should be noted that the eﬀects of employee protection are not restricted to the sector where the policy is imposed, but spread to
the whole economy with a positive feed back in values, and a negative feed backin propabilities: More protection of the good job employees improves the value ofthe bad job employment through the consideration of future job prospects, while
it reduces the job creation in both the sectors. More protection of the bad job
increases the value of being unemployed, which results in the rise of the threat
point in the wage bargaining of the good job. However, it also reduces job creation
not only in the bad jobs but also in the good jobs.
However, tax reforms aﬀect the creation of both the jobs in opposite directions. A reducing tax wedge with constant income tax rate increases the good job
creation and reduces the bad job creation, with increasing values of filled jobs inthe both sectors. However, a replacement of payroll tac with income tax underconstant tax wedge reduces the bad job creation, with no eﬀects on the good jobs.

Therefore the bad unemployed workers suﬀer welfare reduction. If the increasing
tax base asscoated with a rise in income tax rate enables the government to reduce
the tax wedge under a given tax revenue, it alleviates the welfare loss and mightyield a slight gain, depending on the parameters. On the contrary, a tax reform
into the opposite direction improves the welfare. The governemnt should replace
income tax with payroll tax, if the tax wedge is constant.

4. Discussion
To be completed. The social optimum and numerical examples.

5. Conclusion
To be Completed

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