ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E16-1

The Effects of Skill-biased Partial Labor
Reforms on the Macroeconomic Outcomesby
Ching-Yang Lin

February 2016

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITYThe Eﬀects of Skill-biased Partial Labor Reforms on
the Macroeconomic Outcomes∗
Ching-Yang Lin†
January, 2016

Abstract
Over the past decades several governments have implemented similar labor reforms
by increasing the flexibility of hiring unskilled temporary workers, but leaving the skilledworkers under the protection of the indefinite-term contract. This paper argues that
this type of partial reform may lead to dampened eﬀects and unintended consequences.
To assess this argument, I examine and compare the eﬀects of two diﬀerent types ofpartial reform in the context of the framework of Hopenhayn and Rogerson (1993).
In addition to workers’ heterogeneity in skill, my model considers the search frictions
and workers’ decision on labor market participation. The numerical results indicatethat reducing the employment protection legislation (EPL) on unskilled workers brings
about small eﬀects on improving output, productivity, and welfare, though reducing
the income inequality. In comparison, reducing the EPL of skilled workers significantly
improves the conditions of macroeconomic aggregates.

∗
I am grateful for the research support under Grants-in-Aid for Scientific Research No.25780195 and theEconomic Research Center of Nagoya University.
†
International Development Program, International University of Japan. Email address: clin@iuj.ac.jp1

1

Introduction

Policymakers have been viewing liberalizing the labor market—through easing the use of temporary contracts or reducing the employment protection legislation (EPL)—as the panacea
to improve labor market performance and revive macroeconomic activities. By reducing
firms’ labor adjustment cost, this type of policy reform encourages firms to hire new workers, even in the face of uncertainty; on the other hand, it also induces firms to fire unneeded
workers, allowing production factors to be allocated more eﬃciently. The overall eﬀects leadto a rise in firms’ productivity and output.
In theory, there is consensus on the above-mentioned benefits, but in practice, there are
doubts about its eﬀectiveness and fairness. When it comes to the practical implementation,
the labor reform is usually shaped into a type of partial reform. That is, not all but only
a specific group of workers’ employment conditions are altered. For instance, as argued inprevious studies, there exists discrepancy in the employment conditions of the newly hired
workers and currently employed workers. The partial reform leads to a two-tier labor market,
which comes with myriad social and economic problems. (Blanchard and Landier (2002),
Saint-Paul (2002) and Bentolila et al. (2012))
In this study I follow this strand of this study to revisit the question: how good (bad)a partial reform is. In contrast with previous studies, I explore the eﬀects of a skill biased
reform, whose influences only placed a specific skill group of workers (for instance, workers
with the college degree). For instance, when the government eases the restrictions on the useof temporary contracts, evidence suggest that these temporary contracts are usually used forthe employment of unskilled workers. For the skilled workers, however, their employments
remain protected by the permanent contracts.1
Under this situation, we may have to consider the following possibilities:
1. Since skilled and unskilled workers make diﬀerent contributions in production, thepolicy eﬀects of a reform that targets to liberalize the employment of unskilled workers
will be diﬀerent from the policy eﬀects of another policy that targets to skilled workers.
2. Because the influences of on turnovers, flows, and wages across workers’ types are
diﬀerent, a policy reform may generate considerable distribution eﬀects.
These concerns imply that a skilled biased partial reform may lead to not only dampened
eﬀects but also unintended consequences. To explore this argument, I construct a theoretical1

the permanent contracts: the open-ended contracts subject to mandatory payments. Evidence: In Belotet al. (2007) Table 1 shows that in most countries the share of temporary jobs among those with a higheducation is substantially lower than among those with a low education. Other studies include: Gebel andGiesecke (2011)Kahn (2007) )2

model. Using the calibrated model, I conduct simulations to quantitatively assess the eﬀects
of skill-biased partial reforms.
My model is on the basis of the framework developed by Hopenhayn and Rogerson (1993),
which provides an environment to study the extent to which the distortions in productionin the presence of firing cost. I incorporate workers’ heterogeneity by embedding the Krusell
et al. (2000) style capital-skill complementary production function. This function specificallycharacterizes the role of each production factors—including skilled and unskilled workers,
and two types of capital—and the relationship (substitutability) among them. We can thus
explore how the distortion might be amplified (or alleviated) by these factors.
The model considers both the search frictions and workers’ labor market participation
decision. While the participation decision is often abstracting from the flow approach tomodeling labor markets, it is crucial in studying the policy eﬀects on labor market outcomes.
As Pries and Rogerson (2009) suggests based on cross country data, that “diﬀerences inlabor market participation are often larger than diﬀerences in unemployment rates”. Thislarge diﬀerence may be caused by the labor policy. Moreover, by considering labor market
participation decision, the model prediction on policy eﬀects precludes the case Ljungqvist(2002) suggests, that those three major frameworks’ predictions on the policy eﬀect hinges oneach models’ assumption on the labor market structure. In my model’s setting, the worker’s
decision on market participation, one of the key element determining the policy eﬀects,
are responsive to the equilibrium wage, probability of being dismissed, and the severance
payment, all of which are aﬀected by policy.
When using simulations to conduct policy experiment, I consider two types of partial
reform: (1)A reform that reduces only firms’ firing cost of the unskilled worker, keeping
skilled workers’ firing cost remaining the same (henceforth, L-reform), and (2)A reform that
reduces the firing cost of the skilled worker, keeping unskilled workers’ firing cost remaining the same (henceforth, H-reform). In practice, it may be unusual to see a labor reform
explicitly aiming at a specific skill group. But a skill biased reform may occur under the
influence of labor provision or due to firms’ response to the reform. For instance, the temporary contracts are usually restricted to the employment of the young and the long-term
unemployed, while a large share of this group members is unskilled. Another situation isthat firms tend to use the inferior temporary contract, which provides less job security, tohire those less competitive unskilled workers but use the permanent contract for those skilledworkers. Thus we can categorize as follows: a policy that eases the use of temporary contract
can be regard as an L-reform, while a policy that reduces the employment protection forpermanent employees—most likely reduces the skilled workers’ firing cost—is equivalent to3

an H-reform.2
The main findings are as follows: (1) Both reforms increase aggregate output and firms’
productivity, due to a more eﬃcient allocations of production factors. More eﬃcient production and less labor adjustment cost also make wages to rise. Since the eﬀects on wages
are strong, even though reforms lead to a higher probability of being dismissed, workers’
welfare and job participations rate still increase. Moreover, there is an interesting pattern,that both reforms generate the strongest positive eﬀects when the labor market is sclerotic.
Those eﬀects, however, are diminishing. The benefits turn to be negligible when the EPL ismoderate. (2) Both reforms do not necessarily raise the employment. The combined eﬀects
of the increases in workers’ labor participate rates and firms’ firing rates constitute an interesting equilibrium outcome: In a labor market with strong EPL, the reform tends to increase
the aggregate employment; but if the EPL are initially moderate in the labor market, thereform may reduce the aggregate employment. (3) Comparing both reform, I find that thepositive eﬀects on output, productivity, employment and welfare of H-reform is more thanfour times that of the L-reform. On the other hand, because H-reform raises skilled workers’
wages, it intensifies the income inequality. And for the same reason, L-reform reduces theincome inequality.
These finding concludes two important policy implications. First, a reform is most eﬀective when conducted in a sclerotic labor market caused by strong EPL and high labor firingcost. Second, a H-reform, the reform that aims to reduce skilled workers’ firing cost, canlead to stronger favorable eﬀects.
Related literature This study extends the analysis of the literature that explores theeﬀects of a partial labor reform—mostly implemented through the liberalization of temporary
contracts. The core idea is that this type of reform divides the labor market into two tiers: thecurrently employed workers and the newly hired workers. The diﬀerence of these two groups
lies in the contract type. The focus are mainly centering on the labor market performance andworkers welfare. (Saint-Paul (2002), Cahuc and Postel-Vinay (2002), Blanchard and Landier(2002), Belot et al. (2007) and Faccini (2014)) Blanchard and Landier (2002) explicitly points
out that such partial reform generates perverse eﬀects—higher unemployment rates and lower
workers’ welfare. This result is mainly caused by the high turn over rates and low payment
of entry-level jobs (temporary employment) due to the labor reform.
2
A good example of H-reform and L-reform is the experiences in Spain during the 80s and 90s. In
the 80s, Spanish government initiated a series of policy reforms to liberalize the use of temporary contracts.
Bentolila et al. (1994) report that unskilled workers are over-represented in this temporary employment. The
reform during this period can be regarded as an L-reform. During the 90s, Spanish government conducted
another reform, which intends to reduce the temporary employment by reducing the EPL of those permanent
employed workers. This reform can regarded as H-reform. (See and Bentolila et al. (1994) for detail)4In contrast to these existing theoretical studies, this article provides an alternative viewto explore the eﬀects of skill biased labor reform. This perspective is motived by empiricalevidence. As reported in several empirical studies, most reforms have generated unbalanced
eﬀects on skilled and unskilled workers. (Kahn (2007), Kahn (2010) and Gebel and Giesecke(2011)) Most of the temporary jobs are used to hire the unskilled workers. And as I haveconcluded from the numerical experiments, there indeed exists large discrepancy between
two diﬀerent types of partial reforms. Moreover, the model implies that most of the existingreforms (the L-reform) would fail to achieve its expected results.
The model’s prediction on the negative eﬀects of EPL on productivity is consistent withmost of the empirical evidence. (eg:Jahn et al. (2012), Cappellari et al. (2012), Hirsch
and Mueller (2012) total productivity Autor et al. (2007)) Regarding the eﬀects of EPL on
employment, empirical results are mixed. While our model also shows the possibilities ofboth positive eﬀects and negative eﬀects. In terms of inequality, our models that H-reform
intensifies the inequality. This is consistent with Jahn et al. (2012) reported.
The paper is organized as follows: Section 2 describes the model economy and defines theequilibrium. Section 3 describes the calibration procedures, including the way of selecting
the parameters. In section 4, I report the simulation results and the policy implications.
Section 5 concludes.

2

The model

My model is built on the framework developed by Hopenhayn and Rogerson (1993).3 The
main feature of this class of models is the resource misallocation due to the adjustment cost.
In the model firms (or establishments) reallocate their employment level in response to theidiosyncratic productivity shock each period. A dismissal cost leads firms to fire or hire lessworkers than they do in the environment without the dismissal cost, creating distortion in
the allocations and reducing eﬃciency in aggregate level, such as jobs flow, employment,
output and labor productivity.
The main concern of this study is to examine the impacts of a partial reform, a reformtargeting to liberalizing the employment of a specific type of worker. Thus I incorporate
workers’ heterogeneity and explicit model their roles in the production. Moreover, to comprehensively look at the policy eﬀects on labor market performance, a worker’s decisionon labor market participation and the search friction are both considered. For simplicity,
we assume the interest rate is exogenously given. I will evaluate the policy eﬀects focus
on the stationary equilibrium, where, except for the interest rates, wages, allocations and3

My model also extends several settings in Alvarez and Veracierto (2001).

5

distributions of variables are endogenously determined.

2.1

Workers’ problem

The economy is populated by a measure one of workers, categorized by two types: theskilled and the unskilled. The fractions of workers who are skilled φ and unskilled 1 − φ areexogenously given. Workers are risk neutral, with discount factor equal to β. In addition toskill level, each worker diﬀers in their preference for working, characterized by a parameterb. Time is discrete. A worker’s life expectancy is finite. Each period a worker may die withprobability θ. Once a worker dies, he will be replaced by another new born worker withidentical skill level and preferences.
A worker’s objective is to maximize his expected lifetime value, by choosing whether or
not to participate in the labor market. If a worker choose not to participate in the labormarker, he will receive b, derived from engaging in non-market activities (such as doinghousework, or taking care of children). We assume b is drawn from an uniform distribution
between [0, Bi ], i ∈ [l, h]. Hereafter the subscript h and l represent for the variables for theskilled and unskilled workers.
The labor markets are segregated by skill level. A worker can only participate in thelabor market according to his skill level. For a type i worker (i ∈ {h, l}), once deciding toparticipating in the market, he starts from the unemployed state. Each period an unemployed worker may find a job with probability fi , an exogenous job finding rate, and being
employed. An employed worker receives wage wi , determined in the market, in each period
until separated from the job. A worker may separate from a job for two reasons: (1) he is
fired by the firm (2) the firm dies. If fired by the firm, a worker receives a severance payments
ϵi wi , representing ϵi periods of wage wi .4 In the latter situation, a worker receives nothing.
After separating from the job, the worker transits to the unemployed state, until receiving
another job oﬀer.
A worker’s value of being employed Ji and unemployed Ui are given by
Ji = wi + β̄ {de Ui + κi (ϵi wi + Ui ) + (1 − de − κi )Ji } ,(1)

Ui = β̄ {fi Ji + (1 − fi )Ui } .

(2)where β̄ = β(1 − θ), κi is the probability of a worker being fired by the firm and de is theprobability firm dies. The probability κi and de will be further explained in firm’s problem.
4

Technically, this severance payment is a transfer from the government and is financed by a firing tax
imposed on firms. This prevents a wage re-negations between firms and workers and the misallocation
implied in the model issue will not occur. (See ... for detail)6

A worker chooses whether or not to participate in the market by comparing the value
from non-market activity b/(1 − β̄) and the expected value derived from labor market U.
Therefore, there exits a threshold value b∗ , such that a worker decides to participate in thelabor market if his utility b is greater than b∗ . Solving equation (1) and (2), we obtainb∗i = (1 − β̄)U =!

β̄fi wi 1 + β̄κi ϵi"

1 − β̄ + β̄(fi + de + κi )(3),

A worker’s decision rule can be expressed as an indicator function I(b). Ip (b) = 1 if b > b∗ ,and Ip (b) = 0 otherwise. The proportion of workers who participate in the labor market willbeb∗
P rob(b < b∗ ) = i .
(4)BiEquation (3) and (4) imply that the job participation rate is increasing in the job finding
rate fi , wage wi severance payment level ϵi , and decreasing in job destruction rate di anddismissal rate κi .

2.2

Firms’ problem

There are a continuum of heterogenous finite-lived firms (establishments) in the markets.
All firms follow the production function, as introduced by Krusell et al. (2000), which nests
three production factors: capital equipment k, skilled worker h and unskilled worker l in a
CES functional form, given by
F (k, h, l) = A

#$

!

ρ

ρ

µ (λk + (1 − λ)h )

1
ρ

"σ

+ (1 − µ)lσ% 1 &γσ.

Each firm diﬀers in its productivity A. The productivity changes over period, following afirst-order Markov process T . We assume A ∈ [AG , AB , 0] and AG > AB > 0. The AG andAB represents a good and a bad state. With probability de , the firm fall into the state A = 0.
The firm dies and all its hired workers become unemployed.
The parameter σ and ρ govern the elasticity of substitution between unskilled worker,
capital equipment and labor (σ and ρ < 1). The parameter µ and λ governs the income
share. The original setup in Krusell et al. (2000) incorporates another production factor
called the capital structure, and these total four production factors make up a constantreturns to scale production function. Unlike Krusell et al. (2000) that capital structure canbe decided by firms, we assume that the capital structure acting as a fixed cost Ψ that thefirm pays for when entering the market. Thus in our case the parameter γ is less than one.

7

Furthermore, we assume at any point of time, there exists many potential entrants.
Each period firms decide the production factors after observing the shock A. Firms rent
the capital equipments in the market with a fixed rental rate r + δ, where r is the interest
rate and δ is the depreciation rate.5 Firms hire skilled and unskilled workers, taking as given
the wage rates wh and wl . A firm can hire workers up to the amounts it needs before theproduction starts, although it takes time for a worker to find a job. When firing a worker,
firms subject to a firing cost ϵi wi . This ϵi wi will transfer to the worker as the severance
payment. Firms also need to consider that each period a worker may leave the job withexogenous probability θ (due to death). Let h−1 and l−1 stand for the employment level inthe last period and h and l stand for the employment decision in the current period. Thenthe total cost a firm spends on firing each type of workers (or to speak in a boarder way,
adjusting the labor force) Di can be expressed as,
Dh = ϵh wh max(0, (1 − θ)h−1 − h) + ϵl wl max(0, (1 − θ)l−1 − l).
A firm’s problem is to maximize the expected present value of profit streams, given by
V (A, h−1 , l−1 ) = max F (k, h, l) − wh h − wl l − Dh (h, l, h−1 , l−1 )h,l,k
1
EV (A′ , h, l|A).
−(r + δ)k +1+r
It is clear that a firm’s decision on {k, h, l} are functions of state variables {A, h−1 , l−1 }.
Three state variables give rise to higher complexity in numerical analysis and diﬃculty inexpiation. Therefore, we simplify the analysis by examining the policy eﬀects of ϵi separately.
That is, each time we focus on the eﬀects of a change of dismissal cost on one particularkind of labor, given the other dismissal cost be 0. Then we compare the consequences on
those variables of interest of these two policies. In the following illustration, we concentrateon the case where the dismissal cost is imposed on the skilled worker h ( ϵh > 0 and ϵl = 0).
If there is no dismissal cost, the firm’s problem is static. i.e. the state variable h−1 has
no influence on firm’s decision making. The firm simply chooses {k, h, l} such that the firstorder conditions (FOCs) of each factors hold. The firms decision rule is a set of allocations{k(A), h(A), l(A)}.
When ϵh > 0, the firm’s employment policy function becomes a kinked function, as
described in studies of the labor adjustment cost. (for example, see (Cooper and Willis,
5Here we abstract the details of the capital market. However, this can be easily modeled as the following
way: there is a competitive capital rental market where capital-rental firms use output goods Y to produce
capital equipments K via the production function K = Y and rent for the goods-producing firms. Under
the no arbitrage condition, the equilibrium rental rate of capital equals to r + δ.

8

0.030

Employment policy function − AB

Employment policy function − AG
ε=6
ε=12
no dismissal cost

1.0
h

0.020
0.005

0.6

0.010

0.8

0.015

h

0.025

1.2

ε=6
ε=12
no dismissal cost

0.00

0.01

0.02
h−1

0.03

0.0

0.5

1.0

1.5

h−1

Figure 1: Employment policy function2009)) In Figure 1 we show some typical shapes for the firm’s demand functions for skilledworkers h, under diﬀerent productivityAB (the left plot) and AG (the right plot). In eachplot, the black cross denotes the firm’s choice when there is no dismissal cost, the (blue) realline is the firm’s demand function when dismissal cost is low (ϵ = 6) and the (red) dotted lineis the firm’s demand function when dismissal cost is high (ϵ = 12). We can find the general('
patterns of a firm’s decision: for each productivity Ai , there exists an interval hAi , h̄Ai . If

h−1 lies in this interval, the firm will not do anything. Since a fraction of workers θh−1 hasleft, the employment level is the workers remain staying in the firms (1 − θ)h−1 . If h−1 ismore (less) than the upper bound h̄Ai (lower bound hAi ), then the firm fires (hire) workers
up to the upper bound (lower) bound.
This kind of decision rule allow firms to reduce the labor adjustment costs. Firms tend to
employ an average level of workers. In each plot the first kink point, located at left bottomside of the figure, indicates the employment level of a firm’s just newly entering the market.
When facing a high productivity (as shown in the right plot), the firm hires less workers
than it does if there is no dismissal cost, denoted by the symbol X. 6 By doing so this firm
can reduce the possible dismissal payment if the state changes in the future. The eﬀect getsstronger as the dismissal cost increases. This figure demonstrate how resources might be
6

We also notice that the firm hires more workers when facing a low productivity shock. But this is driven
by diﬀerent reason: the equilibrium wage is lower under the high adjustment cost. Since firms with low
productivity do not need to consider the firing cost, they hire more workers given the low marginal cost oflabor.

9misallocated in the presence of adjustment cost. Since the choice h(A, h−1 ) enters into the
FOCs of other production factors, this decision rule implies that not only h deviates to the
optimal level, but also other production factors.

2.3

Equilibrium

Firstly, I introduce the measures and conditions required for define the equilibrium.
Free entry condition and the distribution of firms
When a new firm enters the market, it starts with zero employment level, that h−1 and l−1
equals 0. Assume that the new entry firm’s productivity level may be AG or AB with equal
probability. Thus, the free entry condition can be expressed as,
11
Ψ = V (AG , 0, 0) + V (AB , 0, 0) ,
2
2

(5)

where the right hand side is the expected value of a newly created firm. Under this condition,in every period there will be M firms entering the market. Let Ω(h−1 , l−1 , A) represent the
distribution of firms across states. Then, the following condition holds,′Ω(h, l, A ) =1Ω(h−1 , l−1 , A)P rob(A′ , A) + M × If (h, l),2h=h(h−1 ,l−1 ,A),l=l(h−1 ,l−1 ,A))

where P rob(A′, A) is the probability of a state A transit to state A′ , If (h, l) is an indicatorfunction, that If (h, l) = 1 if both h and l are equal to 0, and If (h, l) = 0 otherwise.
Labor Markets
In equilibrium, the number of employed workers ni equals the total employments by firms.
This relationship can be described by,nh =)h(h−1 , l−1 , A)Ω(h−1 , l−1 , A))l(h−1 , l−1 , A)Ω(h−1 , l−1 , A)

h−1 ,l−1nl =

h−1 ,l−1

Let ei denote the number of workers participating in the labor markets. The value of ei isdetermined by the fraction of the labor force i and the fraction of workers participating in10

the markets. That is,eh = φP rob(bh < b∗h )(6)el = (1 − φ)P rob(bl < b∗l )(7)

Let ui denote the number of unemployed workers. In the equilibrium, the following condition
hold for both h and l,
ei = ni + ui

(8)

The unemployments uh and ul can be solved by considering the workers flows in the equilibrium. The inflows to unemployments equals the outflows to employments. That is(ei − ui )si = ui fi
ei si
ui =
fi + si(9)where si = de + (1 − de )θ + κi is the gross job separation rate. The probability of a worker
being fired in the beginning of the period κh can be expressed asκh =*h−1 ,l−1 max (0, (1 − θ)h−1 − h(h−1 , l−1 , A)) Ω(h−1 , l−1 , A)*

h−1 ,l−1 (1 − θ)h−1 Ω(h−1 , l−1 , A)

(10)and κl can be defined in the similar way.
With above equilibrium conditions, the stationary competitive equilibrium can be defined
as follows: there exit (1) a set of time invariant variables: employments ni , unemployments
ui , the workers who participate in the markets ei and number of new entry firms M, (2)a set of decision rules {k(A, h−1 , l−1 ), h(A, h−1 , l−1 ), l(A, h−1 , l−1 ), Ih (b), Il (b)}, (3) a set ofprices {wh , wl }, and (4) a time invariant distribution of firms Ω(h−1 , l−1 , A), such that thefollowing conditions hold.
1. Given prices, the policy functions {k(A, h−1 , l−1 ), h(A, h−1 , l−1 ), l(A, h−1 , l−1 )} solve
each firm’s problem.
2. Given prices, the decision rule Ii (b) solves workers problem
3. The time invariant measures and variables Ω(h−1 , l−1 , A), ni , ui , ei are consistent withfirms’ and workers’ decision rules.
4. Market clearing condition (8) holds.

11

3

Quantitive analysis

I choose the U.S. economy statistics as the calibration targets. Although we are interested in
the implications of labor reforms that usually conducted in European countries, it is easier tocalibrate the model parameters in a laissez-faire benchmark economy, and the U.S economy
is the most closer to this case.
I choose the model period to be one month. There three groups of parameters. First
group contains parameters whose values can be directly followed from the existing literature.
Table 1 reports the values and sources of these parameters. I set the interest rate equal to0.0033, which yields 4% a year. The discount factor β is 0.9967, allowing the conditionβ(1 + r) = 1 holds. I use the elasticity parameters in production function, including ρ =−0.495, σ = 0.401, capital structure’s share of income 1 − γ = 0.117 and annual depreciation
rate of capital equipment δ = 0.125 estimated by Krusell et al. (2000); I use the monthly job
finding rate for skilled workers and unskilled workers are the estimates reported in Hagedorn
et al. (2010).7 Using the CPS 2012 and the education based classification, I compute thefraction of skilled worker φ = 0.415, and the labor force participation rates of the skilled andunskilled workers.8 The labor force participation rates allow us to pin down Bh and Bl , theparameters associated with the distribution of utility derived from non-market activities.
The second group are parameters in the transition matrix T and [AG , AB , 0]. Suppose T
follows the form⎡⎤
ρa1 − ρa − πd πd ⎥⎢⎢⎥T = ⎢ 1 − ρa − πdρaπd ⎥ ,
⎣

0

0

1

⎦

where πd id the firm’s death rate the ρa is the persistence parameter. I normalize AB = 1,
and use the following three observations reported (Davis and Haltiwanger, 1992) to pin down
AG , ρa and πd :In a year,
1. 2% of the firms die.
2. The job creation rate is 9.2%
3. 80% of the newly created jobs are from the existing firms.
I obtain AB = 1.7037 , de = 0.0018 and ρa = 0.9917. Noted that, since the model period
is one month, to compute the moments in our model comparable with the data report, I
7

These estimates are obtained using the CPS data, based on Shimer (2012) two state model.
The skilled workers includes the individuals in the following education attainment group: associate’s
degree, bachelor’s degree, master’s degree, professional degree, and doctoral degree.
812

Table 1: Parameters value
Parameter
r
β
1−γ
ρ
σ
δ
fh
fl
φ
de
Bh
Bl

meaning
Real interest rate
Discount factor
Share of capital structure
Elasticity of substitution between k and l
Elasticity of substitution between k and h
Depreciation rate
Job finding rate of skilled worker
Job finding rate of unskilled worker
Fraction of labor in skilled sector
workers’ death rate
Upper bound of h’s non-employment utility
Upper bound of l’s non-employment utility

Value
0.00330.99670.117-0.4950.401
0.0125/12
0.36180.41850.415
0.0021
4.091
3.047

Source and Target
Annual interest rate 4%
β = 1/(1 + r)
Krusell et al. (2000)
Krusell et al. (2000)
Krusell et al. (2000)
Krusell et al. (2000)
Hagedorn et al. (2010)
Hagedorn et al. (2010)
CPS 2012
40 years working periods
h’s job participation rate 0.75
l’s job participation rate 0.51

simulate model for 12 periods and calculate these moments. For instance, when calculating
the newly crated jobs, I sum up all the jobs created by firms who exist in the first period
and still survive after 12 periods. (This parameters are independent of the values reported
in the first group. So when conducting the sensitive analysis by adjusting ρ or σ, I can still
keep these values. )The last group the parameters in the production function governing the shares {µ, λ} ofincome contributed by each factor. Having the parameter pinned downed in the previous
steps, together with the two conditions: (1) the labor share of output 70% and the wage
ratio between skilled and unskilled worker 1.9846 solve λ = 0.778 and µ = 0.521.

4

Results and discussion

The simulations focus on the eﬀect of a decrease in ϵh and ϵl , representing a policy intended
to increase labor market flexibility. I examine the responses of the economy to two typesof reform: A H-reform and a L-reform. H-reform represents a reduction of firing cost ofhigh skilled workers (ϵh ), while L-reforms represents a reduction of firing cost of high skilledworkers (ϵl ).
The simulation begins with a highly protected labor market, characterized by a large ϵ(ϵ = 20). Then I examine the responses of variables of interest as ϵ declines, representing theliberalization of labor market. Notice that, when a H-reform is conducted, the other labormarket (unskilled workers’ market) is assumed to be perfectly flexible. The same assumption
applies to L-reform.
13Figure 2 to 4 display the results for the rage where ϵ decreases from 20 to 0. In eachfigure, the y axis represents the percentage deviation to laissez-faire steady state ϵi = 0.
The real blue line represents results of H-reform, and the dotted black line represents theresults of L-reform.

4.1

Main results

Figure 2 displays the responses of macroeconomic aggregates. The figure shows that output
and labor productivity (calculated by y/(h + l)) increases as ϵ declines. To reduce ϵh from 20
to 0 induce the labor productivity to rise by 1.2 % and output by 1.9%. The explanation forthis is the resource misallocation led by the adjustment cost (severance payment). As shownin Figure 1, firms tend to maintain employment staying at an average level to prevent a
future adjustment cost. When adjustment cost is high, such tendency gets stronger, leading
to a larger deviation to the optimal employment level. Less eﬃcient production leads tolower profit, implying less active firms in the market (as shown in the plot with title M).
Moreover, since some proportions of output spent for the adjustment cost, resulting smaller
share to pay for workers and capital, workers’ wages and capital employment all declines(as shown in the plots Wh , Wl and capital). When market turns to be more flexible, i.e.ϵ
decreases, all the distortions mentioned above decline. I also note that the marginal benefit
from reducing ϵ is diminishing. In particular, except for the wages, the eﬀects turn to bevery small when ϵ is smaller than 10.
One clear pattern for all the plots in Figure 2, that the responses to H-reform are muchlarger than the responses to L-reform. For output and productivity, by reducing each ϵfrom 20 to 0 , the benefit from H-refrom is around four times higher than that from Lreform. The economic force at work is clear: that the magnitude of a firm’ misallocationon the employment in response to its firing cost, causing a eﬃciency and output loss, is
proportional to the marginal contribution of this resource. The diﬀerence of responses toϵh and ϵl is driven by the productivity diﬀerence of workers’ skill. (i.e the contribution on
produciton)
Figure 3 displays the responses of labor market performance to the partial reforms. We
first note that the separation rates rise as ϵ declines. The changes in the separation rates isgoverned by a firm’s decision on firing κ. We have learnt that firms is more willing to adjust
employment, including firing workers in the downturn, when ϵ is small, and his explains theobserved pattern. The two plots in the second row show that the probability of a worker
to choose to participate in the labor market increases as ϵ declines. As noted in Eq. (4),this probability is increasing with wage w and severance payments ϵ, decreasing with the14

firing rate κ. When ϵ is large, in the range [10,20], the eﬀects of the rise of wage dominates.
As ϵ move to the moderate range, [0, 10] , the eﬀects of the rise in separation rate and thedecline in severance payments becomes stronger. In particular, it is shown in the responseof unskilled workers’ participation rate declines, though a small level, as ϵ shifts from 10 to0.
The equilibrium employment is the consequence of the workers’ decisions on labor market
participation and the firms’ firing decision. The former governs the ins of workers to theemployment while the latter determines the outs. Some interesting findings are (1) An Lreform reduces the employment of unskilled workers but raises the employment of skilledworkers. Both impacts are small, less than 0.1%. (2) When an H-reform is conducted in avery rigid labor market ϵ ∈ [10, 20], the employment of skilled workers largely rises; while thereform slightly lowers the employment in a moderate protected market ϵ ∈ [0, 10] (3) The
eﬀects of H-reform is much stronger than L-reform. In particular, a partial reform intending
to liberalize the labor market of the skilled workers causes even large impacts on rising theemployment of unskilled workers.
Figure (4) shows the consequences of labor reforms on various welfare indexes. The twoplots in the first row shows the eﬀects of reform on a worker’s value in the unemployment
state U. The value U is one suitable measure of welfare, since it represents the thresholdfor individuals to decide whether to participate in the labor market, indicating the average
lifetime value staying in the labor market. The responses of U indicate that the a partial
reforms on the skilled worker can improve all workers welfare. The reason is identical to
the responses of labor market participation rate, that the policy improves the production
eﬃciency, raising the wages paid to workers and the value staying in the labor market.
The remaining two plots in the Figure (4) show the responses of income inequality,
measured by GINI coeﬃcient, and the responses of the ratio of employment between l and h.
The impacts on inequality come from two sources: the wage gap and the relative proportions
between these two types of workers. We have learnt that when ϵh declines, skilled workers’
wage largely increases, so as the wages gap. Meanwhile, firms rises their demand for the
relative cheaper unskilled workers as substitutes, increasing the relative size of the poor in
the economy. Both forces intensify the income inequality, as we see in the plot. The same
explanation can be applied to the partial reform on the unskilled worker reducing the income
inequality: wage gap and the size of the poor both declines. This is the only significant andpositive eﬀects brought by this partial reform.

15

4.2

Robustness check

To check the robustness of the results, I conduct three additional experiments: (1) To fix
agents’s labor force participation rate (2) To assume the job finding rate to be convex tofirm’s hiring. (3) To change the capital-skill complementarity property in the production
function.9 The responses of policy on productivity and output are quantitatively similar
to the baseline case, the response on the use of production factors, prices and inequality
is qualitatively consistent to the baseline case. These experiments support the conclusiondrawn from the baseline simulation.

5

Conclusion

I constructed a model to evaluate the policy eﬀects of partial reforms on macroeconomic
aggregates. The partial reform refers to those labor reforms that intend to increase thelabor market flexibility, implicitly and unintentionally targeting to a specific labor market
compose by unskilled workers, perhaps due to the political concern. The numerical results
indicate that this kind of partial reform can only give rise to limited improvements on the
output, labor productivity, labor force participation rate and workers’ welfare, though it does
eﬀectively reduce the income inequality, by rising unskilled workers’ wage. In comparison,
if the partial reform can instead aim at the skilled worker, the resulting eﬀect is muchlarger, and consistent with the policymaker’s intension. This conclusion is in line withseveral previous studies, for instance Blanchard and Landier (2002) and Bentolila and Bertola(1990); Bentolila et al. (2012), that ”a partial reform may be a very poor substitute forbroader reform”, even though the focus of this study look at diﬀerent perspective. Another
implication drawn by our simulation is that a reform attains the strongest eﬀects when thelabor market is extremely rigid. Moreover, the eﬀects diminishes and turns to be negligible
quickly.
The current model has been simplified in several dimensions, so that there exists several
potential extensions. For instance, one may attempt to explore the partial eﬀects under theenvironment both firing costs are imposed on skilled and unskilled workers. (i.e. a complete
sclerotic labor market). Another extension is to relax the assumption on the exogenous job
finding rate. Given that a high protection reduces firm’s hiring, it is nature to think theprotections may also lower the job finding rate. This perspective has not well captured in
the current model, but may provide a more comprehensive understudying of the impact ofpolicy reforms on labor market performance.
9

The results of these experiment do not report here.

16

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18

Output
2.0

1.5

Productivity
H−reform
L−reform

0.0

0.0

0.5

0.5

1.0

1.0

1.5

H−reform
L−reform

15

10

5

0

20

15

10

ε

ε

wh

wl
12

12

20

0

5

0

5

0

H−reform
L−reform

0

0

2

2

4

4

6

6

8

8

10

10

H−reform
L−reform

5

15

10

5

0

20

15

10

ε

ε

Capital

Number of Firms
3.5

20

3.0

H−reform
L−reform

0.0

0.0

0.5

0.5

1.0

1.5

1.0

2.0

2.5

1.5

H−reform
L−reform

20

15

10

5

0

20

ε

15

10

ε

Figure 2: Responses of partial reform for macroeconomic aggregates19H−reform
L−reform

H−reform
L−reform

6

l ’s Job Separation Rate

0

0

2

1

4

2

6

3

8

4

5

10

12

h ’s Job Separation Rate

15

10

5

0

20

15

10

5

ε

ε

h ’s Job Participation Ratel ’s Job Participation Rate

0

1.0

20

0.8

H−reform
L−reform

0.0

0.0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

H−reform
L−reform

15

10

5

0

20

10

ε

Employment of h

Employment of l

H−reform
L−reform

5

0

5

0

H−reform
L−reform

0.0

0.0

0.1

0.2

0.2

0.4

0.3

0.4

0.6

0.5

15

ε

0.8

20

20

15

10

5

0

20

ε

15

10

ε

Figure 3: Responses of partial reform for workers
20l ’s Welfare
1.0

h ’s Welfare

0.8

H−reform
L−reform

0.0

0.0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

H−reform
L−reform

15

10

5

0

20

15

10

ε

ε

employment Ratio l/hGini (workers)

5

0

5

0

15

0.3

20

H−reform
L−reform

−15

−10

−0.1

−5

0.0

0

0.1

5

10

0.2

H−reform
L−reform

20

15

10

5

0

20

ε

15

10

ε

Figure 4: Responses of partial reform for welfare indicators21