LABOR MARKET INSTITUTIONS ANDEMPLOYMENT FLUCTUATIONS IN DYNAMIC
GENERAL EQUILIBRIUM MODELS
Toyoki Matsue
January 2017
Discussion Paper No.1701

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANLABOR MARKET INSTITUTIONS ANDEMPLOYMENT FLUCTUATIONS IN DYNAMIC
GENERAL EQUILIBRIUM MODELS

Toyoki Matsue
January 2017

ABSTRACTLabor market reforms have been undertaken to eliminate labor market rigidities in European
countries since 1970s. The important features of the reforms are the reduction in adjustment costs
and the introduction of fixed-term contracts (FTC). In recent years, the substantial decreases inunemployment rates have not been observed. On the other hand, some empirical studies point out
employment fluctuations become more volatile after the reforms. This paper presents two types ofdynamic general equilibrium models and analyses effects of the key features of the reforms: One is
the model with FTC and the other is the model with indefinite-term contracts (ITC). In the modelwith ITC, total employment and new hiring do not behave cyclically if an expected shock takes
place. However, in the model with FTC, the shock causes the cyclical behavior of employment.
Moreover, a reduction in adjustment costs amplifies fluctuations in both of the models. In the labormarket literature, a number of studies point out importance of trade unions in European countries.
This paper also analyses effects of union influence, and indicates that the stronger union influenceleads to larger employment fluctuations.

Keywords: employment fluctuations, fixed-term contracts, trade unions, labor market reforms
JEL Classifications numbers: E24, J30, J51, J63*Reseach Fellow, Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada-ku, Kobe
657-8501, Japan; toyoki.matsue@port.kobe-u.ac.jp. The author wishes to thank Prof. Tamotsu Nakamura
and participants at the KMSG conference for their valuable comments.

11. INTRODUCTION
Labor market institutions are one of the most influential factors in macroeconomic dynamics. For a
persistent high unemployment rate in the European countries, labor market reforms have been
undertaken to eliminate the labor market rigidities since 1970s. Faccini (2013) and Giannelli et al.
(2012) point out that important features of the reforms are reduction in adjustment costs andintroduction to fixed-term contracts (FTC).1 However, substantial decreases in unemployment rates
were not observed. Alonso-Borrego et al. (2005) and Jiménez-Rodríguez and Russo (2012) indicatethat employment fluctuations become more volatile after the reforms. Moreover, De Serres andMurtin (2013) and OECD (2012) show that increase in the share of FTC amplifies the employment
fluctuations.
In the dynamic labor demand literature, adjustment cost models are widely used.2 In the models,
it can be considered that indefinite-term contracts (ITC) are assumed. Matsue and Nakamura (2016)
and Matsue (2016) create two types of dynamic labor demand models: One is a model with FTC andthe other is a model with ITC. They show that the FTC and ITC models are different in terms ofproperty of employment dynamics. In the ITC model, total employment and new hiring do not
behave cyclically if an expected productivity shock takes place, while the shock causes the cyclicalbehavior of employment in the FTC model.
Layard et al. (2005) discuss an importance of trade union in the European labor market. Union
membership ratio and coverage ratio are proxy variables for influence of trade union on wage settingor union power. The union membership ratio has been recently declining in European countries,
whereas the union coverage ratio is still high, as shown in OECD (2015). Booth (2014) argues, using
French data, that the coverage ratio is a better measure of union influence than union membership
ratio.
A relationship between union influence and unemployment rates has been investigatedextensively in the research of business cycles. Faccini and Bondibene (2012) and Gnocchi et al.
(2015) analyze a relationship between some labor market institutions and cyclical behavior ofunemployment rates for OECD countries. Faccini and Bondibene indicate that increase in the
coverage ratio amplifies cyclical fluctuations of unemployment rates, whereas Gnocchi et al. do notshow statistically significant results about this relationship.
First, we present two types of dynamic general equilibrium models and compare dynamics of1

Jiménez-Rodríguez and Russo (2012) precisely study the regulations about FTC of recent years for
major European countries.
2
Hamermesh and Pfann (1996) thoroughly explain the property of the adjustment cost model.

2these two models: One is the model with FTC and the other is the model with ITC. Similarly to the
dynamic labor demand models, total employment and new hiring do not behave cyclically if an
expected productivity shock takes place in the model with ITC, while the shock causes the cyclicalbehavior of employment in the model with FTC. Zipperer and Skott (2011) exhibit cyclicalemployment trend with short-run cycles in French and Spanish economies, which is consistent withsimulation results in this paper.
Second, this study analyzes relationship between union influence and employment dynamics inthe models by using simulation analysis. The simulation results show that the stronger union
influence on wages leads to larger employment fluctuations in both the FTC and ITC models. The
strong union influence puts an upward pressure on wage rates. Then, firms need to adjust its
employment significantly when the productivity shock takes place. This is consistent with the resultsof Faccini and Bondibene (2012).
Third, this study examines relationship between elasticity of wage with respect to employment
rate and employment dynamics. The higher elasticity of wage with respect to the employment rate
leads to smaller employment fluctuations in both the FTC and ITC models. The firms do not need toadjust employment largely because wage varies significantly when the elasticity of wage withrespect to the employment rate is high.
The rest of this paper is organized as follows. Section 2 sets up the general equilibrium models.
Section 3 discusses the property of the models with simulation analysis. Section 4 investigates theinfluence of the labor supply side on employment fluctuations. Section 5 concludes the paper.

2. MODEL
Consider two types of dynamic general equilibrium models: One is the model with fixed-term
contracts (FTC) and the other is the model with indefinite-term contracts (ITC). The difference
between the two models is only the types of contracts. In the dynamic labor demand literature,adjustment cost models are widely used. In this study, the ITC model is the extension of theadjustment cost model.

2.1 FTC model
Let us set up the model with FTC. Firms plan their production during the finite time period T , andthey produce homogeneous goods. The objective function is as follows:

3

T

max
ht , Kt  [( A L ) K   w L  (r   )K  ( 2)h ] ,
1
t

t

t

t

t

t

t

t

2
t

(1)

t 0

where 0    1 is discount factor,

At is positive productivity parameter, Lt is total

employment, ht is new hiring, and K t is capital. Moreover, wt is wage rate, rt is rental priceof capital, and ( 2)ht2 , where   0 is labor adjustment cost function. Suppose that a firm makes
an agreement for an FTC with labor, in which the term of contracts is two periods. The total
employment is as follows:

Lt  ht 1  ht 2 .

(2)Then, h2 , h1 , and K 0 are given. It is assumed that the firm hires constant LT  0 as given.
Additionally, KT  0 is given. The firm decides ht from period 0 to T  3 and K t fromperiod 1 to T  1 . The first-order conditions are as follows:
t 1

t 1

s t

s t

  sAsls 1    s ws   t 1ht 1 , t  1, 2,, T  2 ,(1   )lt  rt   , t  1, 2,, T  1 ,where lt  At Lt Kt .

(3)
(4)

Similar to Blanchard (1997), suppose that the wage setting equation is as follows:L 
wt    t  ,
N

(5)

where N denotes labor force in this economy that is assumed constant,  is wage at zero
unemployment, and   1 is wage elasticity with respect to employment rate Lt N . 3 It is
assumed that Lt  N to analyze employment fluctuations. The increase in  exerts an upward
pressure on the wage rate.4 Hence,  could be interpreted as a union influence on wage. Equation(5) is transformed as follows:l 
wt    t  ,
 nt 

(6)

where nt  At N Kt . From equations (3) and (6), we obtain the following equation:t 1  A l
s

 1

s s

s t



t 1

l 

   s    t 1ht 1 .
 ns 
s t



s

(7)

Equation (7) is rewritten as follows:3

In the wage setting equation, it is assumed that the wage is an increasing function of the employment
rate. Adachi and Nakamura (2015) point out that this relationship is justified by wage bargaining theory
or efficiency wage theory. The wage bargaining theory and efficiency wage theory are thoroughly
discussed in Layard et al. (2005).
4
Blanchflower and Bryson (2002), and Nickell (1997) point out that the union puts an upward pressure
on the wage rate.

4

1

lt At lt 1   2 At 1lt11   2 (lt 1 nt 1 )  ht 1  

 ,
nt 



(8)

which is employment rate. Then, unemployment rate is as follows:

N  Ltl 1 t .
N
nt(9)Households own firms, and they save and invest a fixed fraction s of production Yt :I t  sYt , 0  s  1 .

(10)

Suppose that equation for capital dynamics with depreciation rate  is as follows:

Kt 1  Kt  I t  Kt .

(11)

From equations (10), (11), and the production function, the capital dynamics is as follows:

K t 1  slt K t  (1   ) K t .

(12)

The equilibrium is determined by equations (2), (7), (12), the initial conditions, and termination
conditions. Now, consider the steady state: ht 1  ht  h , Lt 1  Lt  L , and Kt 1  Kt  K , thatis lt 1  lt  l , nt 1  nt  n . Further, it is assumed that At 1  At  A , then equations (2), (7), and(12) are transformed as follows:
1
h L,
2

(13)
1

 (1   )  ( L N )  h  1l ,(1   )A



(14)

1

  l   .
s

(15)

Equation (13) indicates that the new hiring is as much as the labor that leaves a job in the steadystate. From equation (11), the investment equal to the depreciation at the steady state. In addition, theinvestment is determined as a fixed fraction s of production. Hence, l is determined by savingrate and depreciation rate as shown in equation (15). From equations (13)–(15), we obtain the steadystate values h* , L* , and l * . Moreover, from l  AL K , equation (15) is transformed as follows:1 s 
K    AL .
 

(16)

If we substitute L* into equation (16), we obtain the steady state value K * .

2.2 ITC model
To understand the role of FTC, the FTC model should be compared with a labor adjustment costmodel, that is, the ITC model in this study. The labor adjustment cost model is widely used in the5dynamic labor demand literature. It is assumed that employees leave their job by a fixed fraction

0    1 of total employment. The employment dynamics is as follows:
Lt  (1   ) Lt 1  ht 1 ,(17)

where  is turnover rate. The firm optimizes objective function (1), subject to the constraint ofequation (17), where the initial conditions ( L0 , K 0 ) and the terminal conditions ( LT , K T ) are
given. The firm decides ht from period 0 to T  2 and K t from period 1 to T  1 . The
first-order conditions are as follows:At lt 1   (1   )ht 1  wt  ht , t  1, 2,, T  1 ,

(1   )lt  rt   , t  1, 2,, T  1 .

(18)
(19)

Similar to the FTC model, consider the employment rate. From equations (6) and (18), we obtain as
follows:l 
 nt 



At lt 1   (1   )ht 1    t   ht .

(20)

Transform equation (20), then the employment rate is obtained as follows:1

lt At lt 1  (1   )ht 1  ht  

 .
nt 



(21)

Unemployment rate is obtained by substituting equation (21) into equation (9). The householdbehavior is the same with the FTC model. Hence, the equilibrium is determined by equations (12),(17), (20), the initial conditions, and termination conditions. At the steady state, equations (12), (17),and (20) are as follows:h  L ,

(22)
1
1

h 

  ( L N )  1   (1   )
l

A



,

(23)

1

  l   .
s

(24)

Equation (22) shows that the new hiring is as much as the labor that leaves a job in the steady state.
From equations (22)–(24), we obtain the steady state values h* , L* , and l * . From l  AL K ,equation (24) is rewritten as follows:1 s 
K    AL .
 

(25)

Then, by substituting L* into equation (25), we obtain the steady state value K * . Compare
equations (13)–(15) with equations (22)–(24); if   0 and   1 2 , then the steady state values
between the two models are the same.
63. MODEL PROPERTIES
Now, we analyze effects of an expected productivity shocks on employment by running somesimulations. The shocks are either temporary or permanent, which decreases one percent of the total
employment. Similar to Matsue and Nakamura (2016) and Matsue (2016) that are dynamic labordemand models, the ITC model does not show cyclical employment behavior, while the FTC modelshows it regardless of the shock type.

3.1 Property of FTC model
In this section, we consider fluctuations in employment for an expected productivity shocks with the
FTC model. We set the parameter values as shown in Table 1.5 In the beginning of planning period,
the economy is at the steady state. Then, it is assumed that the total employment is 100 ( L0  100 ).
Thus, half of L0 is the new hiring at period  1 and the other half is the new hiring at period  2( h1  h2  50 ). Suppose that the shocks take place at period 15, and T  50 Here, negative
shocks to productivity are expected, which decreases one percent of the total employment at period
15. We assume two types of shocks: one is a temporary shock and the other is permanent shock. The
former takes place at period 15 and then it returns at period 16. The latter takes place at period 15
and then stays at that level forever. The initial productivity level A0 is chosen by having

L0  100 .6 The initial capital K 0 is chosen by substituting A0 and L0  100 into equation (16).
If the shock is temporary, the terminal conditions are L50  100 and K 50  K 0 . If the shock ispermanent, the terminal condition is L50  99 . In addition, the terminal condition K 50 is chosen
by substituting L50  99 and A50 into equation (16). Then, similar to the initial condition, A50
is chosen by substituting L  99 and h  49.5 into the equation given by (14) and (15) (seefootnote 5).
[Table 1 about here]
Figures 1 and 2 show the simulation results with the temporary shock. The solid lines show the
optimum paths when the negative shock takes place, while the dotted lines show the optimum paths
when no shock takes place. These figures show that the fluctuations are cyclical even if the firm does
not incur the adjustment costs.
We set the parameters  and  that are in the wage setting equation to the same values in
Blanchard (1997). The parameters  and s are the same values used in Novales et al. (2010) chapter
2.
5

From equations (14) and (15), we have A  [(1   ) ( L N )  h] [(1   ) (s  )6(1 ) ].

Substitute L  100 and h  50 into this equation, then the initial productivity level with FTC case is
obtained.

7

If the negative shock takes place at period 15, the firm decreases new hiring at periods 13 and 14( h13 and h14 ) in order to adjust total employment at period 15 ( L15 ). Then, the firm faces lessemployment than the optimum employment at periods 14 ( L14 ) and 16 ( L16 ). Therefore, it increases

h12 and h15 to avoid falling into the condition, because L14  h13  h12 and L16  h15  h14 . These
decisions cause increase in the total employment at periods 13 and 17. Hence, the firm decreases
new hiring at periods 11 and 16. These decisions are repeated throughout the planning period. Then,the employment and the new hiring behave cyclically. With the adjustment cost case, the behavior issmaller than the no adjustment cost case. This is because the adjustment costs play a role insmoothing the labor adjustments.
[Fig. 1 about here][Fig. 2 about here]
With the permanent shock cases, similar to the temporary cases, the cyclical behavior is observed
as shown in Figures 3 and 4. If the negative permanent shock takes place at period 15, the firm
decreases h13 and h14 in order to decrease L15 . Then, the firm increases h12 and h15 in order
to avoid less employment. After that, as is the case with the temporary case, the new hiring isadjusted by avoiding overemployment and underemployment within the planning period. In the FTCmodel, the shock causes the cyclical behavior of employment in not only the temporary case but also
the permanent case. Moreover, cyclical behavior of capital and production are observed.
[Fig. 3 about here][Fig. 4 about here]

3.2 Property of ITC model
To compare with the FTC model, let us consider the ITC model. The assumptions about the shocks
are similar to the case with the FTC model. Table 1 shows the parameter values.
In the beginning of the planning period, the economy is at the steady state. Then, it is assumed
that L0  100 . In order to compare with the FTC model, at the steady state, half of the total
employment leaves the job at the end of the period (   0.5 ). Then, equation (13) is equal toequation (22). Moreover, the new hiring and total employment between the two models with noadjustment costs are the same at the steady state.

A0 is chosen by having L0  100 .7 K 0 is chosen by substituting A0 and L0  100 into
7

From equations (23) and (24), we have A  [ ( L N )  1   (1   )h] [ (s  )(1 ) ].

Substitute L  100 and h  50 into this equation, then the initial productivity level with ITC case is
obtained.

8equation (25). If the shock is temporary, the terminal conditions are L50  100 and K 50  K 0 . If
the shock is permanent, the terminal condition is L50  99 . Moreover, the terminal condition K 50
is chosen by substituting L50  99 and A50 into equation (25). Then, similar to the initialcondition, A50 is chosen by substituting L  99 and h  49.5 into equations (23) and (24) (seefootnote 6).
Figures 5 and 6 show the simulation results with temporary shocks. The solid lines show the
optimum paths when an anticipated negative shock takes place, while the dotted lines show the
optimum paths when no shock takes place.
In the ITC case, preparing for the negative shock at period 15, the firm decreases the new hiring
at period 14 in order to decrease the total employment at period 15. The adjustment cost makes thefluctuations smooth. Different from the FTC case, these figures do not show the cyclical behavior.
[Fig. 5 about here][Fig. 6 about here]
With the permanent shock cases, similar to the temporary cases, the cyclical behavior is notobserved in Figures 7 and 8. Further, the fluctuations are smooth if the firm incurs the adjustment
costs.
[Fig. 7 about here][Fig. 8 about here]

Proposition 1
In the ITC model, the total employment and new hiring do not behave cyclically if an expected
shock that is either temporary or permanent takes place. However, in the FTC model, the shockcauses the cyclical behavior of employment even if the firm does not incur any adjustment costs.
The FTC and ITC models are different about the property of employment dynamics.

4. LABOR SUPPLY AND EMPLOYMENT FLUCTUATIONSIn this section, we run some simulations to analyze an effect of labor supply side on employment
dynamics in the models. That is, a relationship between union influence  and employment
dynamics, and a relationship between elasticity of wage with respect to employment rate  andemployment dynamics. These parameters are included in the wage setting function. Additionally, we
assume that the firm incurs adjustment costs   0.01 . The other parameters about the simulations

9

are the same in the Table 1.

4.1 Relationship between union influence and employment dynamics
We analyze a relationship between union influence  and employment dynamics in the FTC modeland the ITC model. Suppose that an expected negative shock to productivity takes place at period 15,
which decreases one percent of the productivity at period 15. The shock is temporary, i.e. the level ofproductivity decreases at period 15 and then it returns at period 16. In the beginning of the planning
period, the economy is at the steady state.
First, let us consider the FTC case. Figure 9 shows the simulation results for the FTC model. The
solid lines show the difference between the optimum paths of employment when the negative shock
takes place and the optimum paths when no shock takes place, while the dotted lines show thechanges in optimum paths when no shock takes place. A0 is chosen by having L0  100 . Hence,
the level of A0 is different depending on the level of  .8 The cyclical behavior is observed near
the shock period when   0.35 , while it is observed widely when   2 . The four figures in
Figure 9 show that the stronger union influence leads to larger cyclical behavior.
[Fig. 9 about here]
In this model, we assume N  Lt  U t and the unemployment rate is defined as equation (9),where N is constant. Thus, the stronger union influence leads to the large cyclical behavior ofunemployment rate. This result is consistent with the empirical results in Faccini and Bondibene(2012). The increase in  puts upward pressure on the wage rate. Hence, the firm adjusts
employment significantly when the productivity shock takes place.
Next, Figure 10 shows the simulation results with the ITC model. It is assumed that the economy
is at the steady state in the beginning of the planning period. Then, we set the steady state value of
employment is L0  100 .9 Suppose that the anticipated temporary shock takes place at period 15.
The solid lines and the dotted lines mean the same as in Figure 9. Similar to the FTC case, the four
figures in Figure 10 show that the stronger union influence leads to larger employment dynamics.
Meanwhile, the cyclical behavior is not observed.

From equations (14) and (15), we have A  [(1   ) ( L N )  h] [(1   ) (s  )8(1 ) ].

Substitute L  100 and h  50 into this equation, then the initial productivity level with FTC case is
obtained. If we assume a large  , we have a large initial productivity level.
9

From equations (23) and (24), we have A  [ ( L N )  1   (1   )h] [ (s  )(1 ) ].

Substitute L  100 and h  50 into this equation, then the initial productivity level with ITC case is
obtained. Similarly to the FTC case, if we assume a large  , we have a large initial productivity level.

10[Fig. 10 about here]

Proposition 2
Suppose that an expected temporary productivity shock takes place. Then, the stronger the union
influence on wage leads to larger employment fluctuations in both the FTC and ITC models.

4.2 Relationship between elasticity of wage with respect to employment rate and employment
dynamics
We analyze a relationship between elasticity of wage with respect to employment rate  andemployment dynamics in the FTC model and the ITC model. It is assumed that an expected negative
shock to productivity takes place at period 15, which decreases one percent of the productivity atperiod 15. Moreover, the shock is temporary. The assumption of the simulations is the same as in theprevious section, except for the assumption about the elasticity of wage with respect to employment
rate  .10 Figure 11 shows the simulation results with the FTC case.
[Fig. 11 about here]
It shows that the increase in  causes the decrease in employment fluctuations. Suppose that theelasticity of wage with respect to the employment rate is high. Then, the firm does not need to adjust
employment largely because the wage varies significantly when the shock takes place.
Figure 12 shows the simulation results with the ITC case. As is the case with FTC, the higher
elasticity of wage with respect to the employment rate leads to smaller employment fluctuations.
[Fig. 12 about here]

Proposition 3
Suppose that an expected temporary productivity shock takes place. Then, the higher elasticity ofwage with respect to the employment rate leads to smaller employment fluctuations in both the FTC
and ITC models.



From equations (14) and (15), we have A  [(1   ) ( L N )  h] [(1   ) (s  )10(1 ) ].

Substitute L  100 and h  50 into this equation, then the initial productivity level with FTC case is
obtained. Moreover, in the ITC case, from equations (23) and (24), we haveA  [ ( L N )  1   (1   )h] [ (s  ) (1 )  ] . Substitute L  100 and h  50 into thisequation, then the initial productivity level is obtained. If we assume a high  , a small initial
productivity level is obtained, because we suppose that L  N .
11

5. CONCLUDING REMARKS
Unemployment and employment dynamics have been studied in many theoretical and empiricalanalyses. The labor market institutions are one of the most influential factors in macroeconomic
dynamics. This study analyzes the impact of labor market institutions on employment fluctuations by
employing two types of dynamic general equilibrium models: One is the model with fixed-term
contracts (FTC) and the other is the model with indefinite-term contracts (ITC). The FTC model and
ITC model have different properties in terms of employment dynamics. In the ITC model, the total
employment and new hiring do not behave cyclically if an expected shock takes place, while theshock causes the cyclical behavior of employment in the FTC model. Moreover, the reduction in
adjustment cost amplifies the fluctuations in the models.
The union influence in the labor market is important because the union coverage ratio is still at ahigh level. This study also analyzes the relationship between the union influence and employment
dynamics in the models with simulation analysis. The simulation results show that the stronger union
influences on wage leads to larger employment fluctuations in both the FTC and ITC models. The
strong union influence puts upward pressure on the wage rate. Then, the firm needs to adjust its
employment significantly when the productivity shock takes place, which is consistent with theresults of Faccini and Bondibene (2012). In this case, the cyclical behavior is observed only in the
FTC model.
Further, this study analyzes additional influence of the labor supply side on employment
fluctuations. The higher elasticity of wage with respect to the employment rate leads to smaller
employment fluctuations in both the FTC and ITC models. The firm does not need to adjust its
employment largely because the wage varies significantly when the elasticity of wage with respect tothe employment rate is high.
Nevertheless, the FTC model in this study is restricted to a simple case in which the term ofcontracts is only two periods. Hence, it is necessary to analyze a more general case. Moreover, themodels could be extended to consider the endogenous labor supply and intertemporal optimizationof consumption. Further investigation of these issues remains to be undertaken.

12

REFERENCES
Adachi, H. and Nakumura, T. (2015). ‘Growth and Fluctuations in Demand-Constrained Economies:
A Medium-Run Macroeconomic Analysis, in: Adachi, H., Nakamura, T. and Osumi, Y. (Eds.),
Studies in Medium-Run Macroeconomics: Growth, Fluctuations, Unemployment, Inequality and
Policies’, World Scientific Publishing Co. Pte. Ltd.
Alonso-Borrego, C., Fernández-Villaverde, J. and Galdón-Sánchez, J. E. (2005). ‘Evaluating labormarket reforms: a general equilibrium approach’, NBER Working Paper, No. 11519.
Blanchard, O. J. (1997). ‘The medium run’, Brooking papers on economic activity, 2, pp.89–158.
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UK and the US revisited’, NBER Working Paper, No. 9395.
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pp.53–58.
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Faccini, R. and Bondibene, C. R. (2012). ‘Labour market institutions and unemployment volatility:
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Giannelli, G. C., Jaenichen, U. and Villosio, C. (2012). ‘Have Labor Market Reforms at the Turn of
the Millennium Changed the Job and Employment Durations of new Entrants? A Comparative
Study for Germany and Italy’, Journal of Labor Research, 33, pp.143–172.
Gnocchi, S., Lagerborg, A. and Pappa, E. (2015). ‘Do labor market institutions matter for businesscycles?’, Journal of Economic Dynamics & Control, 51, pp. 299–317.
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Jiménez-Rodríguez, R. and Russo, G. (2012). ‘Aggregate employment dynamics and (partial) labour
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Layard, R., Nickell, S. and Jackman, R. (2005). Unemployment: Macroeconomic performance andthe labour market, Oxford University Press Inc., New York.
Matsue, T. (2016). ‘Fixed-term contracts as a source of labor demand fluctuations’, mimeo,
Kobe University.
Matsue, T. and Nakamura, T. (2016). ‘Fixed-term contracts and the cyclical behavior of labor13demand’, mimeo, Kobe University.
Nickell, S. (1997). ‘Unemployment and labor market rigidities: Europe versus North America’,
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Novales, A., Fernández, E. and Ruiz, J. (2010). Economic Growth: Theory and Numerical Solution
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14

Table 1
Parameters in the simulationsParameter in production function

0.64



Discount factor

0.99



Elasticity of wage with respect to employment rate

1.0

Depreciation rate

0.25



Turnover rate

0.50



Wage at zero unemployment

0.35



Adjustment cost

0.0 or 0.01s

Saving rate

0.30

N

Labor force

110.0

15

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period59.7

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period50

CapitalProduction

59.6

59.5

59.4

0

0

49.5

49

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 1. FTC model with   0 (temporary shock).

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period0

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period90

107.3

Production

Capital

107.2

107.1

89

107

106.9

0

88

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 2. FTC model with   0.01 (temporary shock).

16

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period59

58

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period50

Production

Capital

60

0

0

49

48

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 3. FTC model with   0 (permanent shock).

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period90

108

Production

107

Capital

0

106

89

88

105
0

87

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 4. FTC model with   0.01 (permanent shock).

17

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period59.7

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period50

CapitalProduction

59.6

59.5

59.4

0

0

49.5

49

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 5. ITC model with   0 (temporary shock).

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period90

107.6

CapitalProduction

107.4

107.2

107

0

0

89

88

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 6. ITC model with   0.01 (temporary shock).

18

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period59

58

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period50

Production

Capital

60

0

0

49

48

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 7. ITC model with   0 (permanent shock).

50.5

New hiring

Employment

100

99.5

50

49.5

99

49
0

5 10 15 20 25 30 35 40 45 50
Period108

5 10 15 20 25 30 35 40 45 49
Period0

5 10 15 20 25 30 35 40 45 50
Period90

Production

107

Capital

0

106

89

88

105
0

87

5 10 15 20 25 30 35 40 45 50
Periodwith shock

without shock

Fig. 8. ITC model with   0.01 (permanent shock).

19

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

0

5

10

without shock

15

20

25 30
Periodwith shock(a)   0.35

35

40

45

50

without shock(b)   1.0

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

without shock

0

5

10

15

20

25 30
Periodwith shock

35

40

45

without shock(d)   2.0(c)   1.5

Fig. 9. Union influence and employment fluctuations (FTC model).

20

50

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

0

5

10

without shock

15

20

25 30
Periodwith shock(a)   0.35

35

40

45

50

without shock(b)   1.0
0.1

0

0

-0.1

-0.1

%

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

0

5

10

15

20

25 30
Periodwith shock

without shock(c)   1.5

35

40

45

without shock(d)   2.0

Fig. 10. Union influence and employment fluctuations (ITC model).

21

50

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

0

5

10

without shock

15

20

25 30
Periodwith shock

35

40

45

50

without shock(b)   1.5(a)   1.0

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

without shock

0

5

10

15

20

25 30
Periodwith shock(c)   2.0

35

40

without shock(d)   3.0

Fig. 11. Elasticity of wage with respect to employment rateand employment fluctuations (FTC model).

22

45

50

0.1

0

0

-0.1

-0.1

%

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

0

50

5

10

15

20

25 30
Periodwith shock

without shock(a)   1.0

35

40

45

50

without shock(b)   1.5

0

0

-0.1

-0.1

%

0.1

%

0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
0

5

10

15

20

25 30
Periodwith shock

35

40

45

50

without shock

0

5

10

15

20

25 30
Periodwith shock(c)   2.0

35

40

without shock(d)   3.0

Fig. 12. Elasticity of wage with respect to employment rateand employment fluctuations (ITC model).

234550