Optimal unemployment benefits financing scheme and aggregate fluctuations. Julien Albertini1 Xavier Fairise2 Juin 2008 First draft Abstract The aim of this paper is to feature the optimal unemployment benefits financing scheme in the presence of search externalities and aggregate fluctuations. In this work, we consider a simple unemployment insurance system that combines both a lump-sum tax and a layoff tax to finance unemployment benefits. In particular, we assume that the layoff tax is a function of the expected fiscal cost of an unemployed worker. Numerical simulations show that this unemployment insurance system is welfare enhancing and can reduces the cost of aggregate fluctuations. In our model, the optimal financing scheme is defined as the Ramsey equilibrium. We show that it allows to implement the Pareto allocation. Furthermore, the first-best allocation features (i) a layoff tax that is close to the expected fiscal cost of an unemployed worker and (ii) an average replacement rate that is reduced but still remains positive. The second-best allocation exhibits similar features but strongly affects labor market dynamic.

Keys-words : DSGE models, matching, firing tax, experience rating.

JEL Classification : E61; E65, J41.

Centre d’Études des politiques Économiques de l’Université d’Evry (EPEE), [email protected], Université d’Evry, bd François Mitterand, 91025 Evry Cedex. 2 Centre d’Études des politiques Économiques de l’Université d’Evry (EPEE), [email protected], Université d’Evry, bd François Mitterand, 91025 Evry Cedex. 1

Introduction An original feature of the US labor market is the unemployment insurance system by which individual employers’ contribution rates are varied on the basis of firms’ history of layoff. This system, known as experience rating (ER thereafter), has been designed to “encourage employers to stabilize employment” and to “equitably allocate the costs of unemployment ” 3 . It is often argued that an higher payroll taxes-indexation lowers the incentive for firms to lay off during economic downturns and to hire during booms. These commonly mentioned hypothesis highlight the need to study the effect of unemployment insurance from a dynamic perspective. We tackle this issue to features the optimal unemployment benefits financing scheme. However, we consider instead a simple unemployment insurance system that combines both a lump-sum tax and a layoff tax to finance unemployment benefits4 . Our paper aims to answer the following questions : How layoff taxes affect labor-market dynamics ? What is the optimal unemployment-benefits financing scheme in presence of search externalities and aggregate fluctuations ? Is this system welfare enhancing ? The first theoretical paper that deals with experience rating is due to [Feldstein 1976]. His work investigates the role of unemployment insurance programs in magnifying temporary layoffs (which are frequent in the US). He finds that unemployment insurance subsidies5 play a major role in reducing employment instead hours. The reason is that firms pay less than the full cost of layoffs. [Topel 1983], [Topel 1983] and [Topel and Welsh 1980] agree with the Feldstein’s view and argue that an imperfect experience rating system may account for as much as 30 percent of all spells of temporary layoffs in United States. However, other researchers such as [Burdett and Wright 1989] and [Marceau 1993] argued that a less-thanfull indexation is preferable. [Anderson 1993] and [Anderson and Meyer 2000] survey unemployment insurance (UI thereafter) in United States; they conclude that ER is likely to give an incentive for employers to make an effort to reduce temporary layoffs. The contribution of [Card and Levine 1994] is of particular interest because they estimate6 the impact of such a system on temporary layoffs and unemployment at different periods of the economic cycle. They find a strong negative relation between the degree of ER and the rate of temporary layoff, with a stronger impact during economic downswings. They show that increasing the degree of ER reduce both the number of temporary layoffs during recessions, and According to the definition provided by the Employment and Training Administration (ETA). 4 Layoff taxes can be viewed as an ersatz of experience rating because they compel firms to contribute to the benefits payments they create through their firing decisions. We discuss later the differences between the system we use and the current regulations. 5 The experience rating system is said to be perfect when an employer pays for the entire cost of unemployment benefits that are perceived by his ex-employees. When it is imperfect, an employer who fires a worker obtain an implicit subsidy which is financed through others firms. 6 With the help of individual data over the period 1979 - 1987 for 36 states and five sectors. 3

1

the number of hirings during booms. In the last half-decade, there have been several works that analyze the consequences of introducing an experience rating system in Europe. In their report on employment protection in France, [Blanchard and Tirole 2004] and [Cahuc 2003] take inspiration from the US unemployment insurance. Both recommend to make firms responsible of their layoff decisions and to reduce the strictness of employment protection legislation. They plaid in favor of an experience rating system rather than a mutual insurance system. Using [Mortensen and Pissarides 1999] tractable framework, [Cahuc and Malherbet 2004] incorporate a simplified ER system and some features of rigid continental European labor market to evaluate its impact on equilibrium unemployment. They show that ER reduces unemployment rate for the low-skilled workers and can improve their welfare in the presence of high minimum wages, a strict employment-protection legislation and temporary jobs. In a recent study, [L’Haridon and Malherbet 2008] look on the consequences of reforming employment protection in European labor markets. They show that such a reform reduce unemployment, job creation and job destruction variability by about 22%, 14% and 42% respectively. There is a rich litterature that address labor-market institutions issues from a business cycles perspective like [Joseph, Pierrard, and Sneessens 2004], [Algan 2004], [Veracierto 2007] and [Zanetti 2007]. Most of them agree to say that employment protection in the form of an exogenous firing cost is likely to reduce job-flows volatility. However, none of them consider the firing cost as a layoff tax and do not make the link with unemployment benefits. The paper of [Blanchard and Tirole 2008] is of particulary interest. They emphasis the need to study labor market institutions together. Indeed, they focus on the optimal architecture of unemployment benefits and employment protection. In a static model, they show that employment protection is likely to be efficient in the form of a layoff tax whose level correspond to unemployment benefits. In this line of research, [Cahuc and Zylberberg 2007] conclude that the optimal layoff tax is equal to the social cost of job destruction when the government provides a public unemployment insurance and aims at redistributing incomes. This social cost corresponds to the sum of unemployment benefits and payroll taxes (which represent a fiscal losses). However, as they underline in conclusion, their analysis remains incomplete in some directions. They do not considers dynamic effects of labor markets institutions nor aggregate productivity shocks. We take on this task to study the properties of an optimal financing scheme. We use a dynamic stochastic general equilibrium model with labor market frictions and endogenous job destructions. We consider a simple unemployment insurance system as in [Cahuc and Malherbet 2004]. In particular, we assume that the layoff tax is a function of the expected fiscal cost of an unemployed worker. Numerical simulations show that experience rating is welfare enhancing and can reduces the cost of aggregate fluctuations. In our model, the optimal 2

financing scheme is defined as the Ramsey equilibrium. We show that it allows to implement the Pareto allocation. Furthermore, the first best allocation features (i) a layoff tax that is close to the expected fiscal cost of an unemployed worker and (ii) an average replacement rate that is reduced but still remains positive. The second best allocation exhibits similar features but strongly affects labor market dynamic.

1

The economic environment and the model

Following [Den Haan, Ramey, and Watson 2000], our model includes Non-Walrasian labor market with endogenous job destruction in the spirit of [Mortensen and Pissarides 1994]. According to [Shimer 2005], we focus on workers flows between employment and unemployment. Workers “out of the labor force” are thus not taken into account. Time is discrete and our economy is populated by ex ante homogeneous workers and firms. Endogenous separations occur because of firms specific productivity shocks. There are search and matching frictions in the labor market, wages are determined through a Nash bargaining process. There is no other market failures.

1.1

The labor market

Search process and recruiting activity are costly and time-consuming for both, firms and workers. To produce, a firm needs to hire one worker, thus, each firm offers one job. A job may either be filled and productive or unfilled and unproductive. To fill its vacant job, the firm posts a vacancy and incurs a cost κ. Workers are ex ante identical, they may either be employed or unemployed. Unemployed workers are engaged in a search process. The number of matches Mt is given by the following Cobb-Douglas matching function : Mt = χ(1 − Nt )ψ Vt1−ψ with ψ ∈]0, 1[, χ > 0

(1)

with Vt the vacancies and 1 − Nt the unemployed workers. The labor force is normalized to 1, the number of unemployed workers Ut thus satisfied Ut = 1−Nt . The matching function (1), satisfying the usual assumptions, is increasing, concave and homogenous of degree one. A vacancy is filled with probability qt = Mt /Vt . Let θt = Vt /(1 − Nt ) be the labor market tightness, the probability an unemployed worker finds a job is θt qt = Mt /(1 − Nt ). It is useful to rewrite these probabilities as follows :

3

qt = χ θt qt = χ

 

1 − Nt Vt Vt 1 − Nt

ψ

1−ψ

(2) (3)

At the beginning of each period, separations occur for two reasons. Firstly, some separations occur at an exogenous rate ρx . Secondly, firms productivity is subject to idiosyncratic shocks i.i.d. drawn from a time-invariant distribution G(.) defined on [0, ε]. If the firm specific productivity component εt falls below an endogenous threshold εt , the job is destroyed and the employment relationship ceases. Endogenous separations occur at rate : ρnt = P (εt < εt ) = G(εt )

1.2

(4)

The sequence of events

At each date, a firm is characterized by its specific productivity level εt drawn from the distribution G(.). The firm productivity is also subject to an aggregate productivity shock zt . The production level is given by : yt = zt εt

(5)

We now describe the sequence of events and the labor market timing, we mainly follow [Zanetti 2007]. Employment in period t has two components : new and old workers. New employment relationship are formed through the matching process. Matches formed at period t − 1 contribute to period t employment. New jobs begin with the highest productivity level ε, thus, all the new employment relationship are productive (at the first period). Let NtN = Mt−1 denote the new employment relationships. At the beginning of period t, Nt−1 jobs are inherited period t − 1 and ρx Nt−1 jobs are exogenously destroyed. Then after, idiosyncratic shocks are drawn and firms observe their specific component εt . If the specific component is below the threshold εt , the employment relationship is severed. Otherwise, the employment relationship goes on. A fraction ρnt of the remaining jobs (1−ρx )Nt−1 is destroyed. The number of continuing employment relationships is thus given by NtC = (1 − ρx )(1 − ρnt )Nt−1 and the total separation rate is defined as follows : ρt = ρx + (1 − ρx )ρnt

(6)

Finally, the employment law of motion is described by the following equations : 4

N Nt+1 = Mt Nt = NtC + NtN Nt = (1 − ρx )(1 − ρnt )Nt−1 + NtN

1.3

(7) (8) (9)

The large family

To avoid heterogeneity, we suppose that infinitely lived households are members of a large family. There is a perfect risk sharing, family members pool their incomes (labor incomes and unemployment benefits) that are equally redistributed. Following [Algan 2004], the large family assumption allows to assess the own impact of layoff taxes on the cost of aggregate fluctuations. Contrarily to [Andolfatto 1996] the large family model allows to distinguish unemployed workers and tenured workers trajectories. The dynamic optimization problem of the large family consists of choosing a consumptions sequence {Cs }∞ t maximizing the expected intertemporal utility : max Et Ct

∞ X

β s−t

s=t

(Cs + (1 − Nt )h)1−σ 1−σ

(10)

subject to the budget constraint : − Ct − Tt + Nt w¯t + (1 − Nt )bt + Πt = 0 (λt )

(11)

β ∈]0, 1[ is the discount factor and σ ∈]0, 1[∪]1, ∞[ is the intertemporal elasticity of substitution. h denotes unemployed workers home production. Family consumption is thus the sum of the total home production (1 − Nt )h and of the market consumption goods Ct . bt is the unemployment benefit perceived by an unemployed worker and wt denotes the average wage. Finally, the large family receives instantaneous profits for an amount Πt . The optimality condition of the above optimization problem writes : (Ct + (1 − Nt)h)−σ = λt

1.4

(12)

Firms and workers behaviors

As previously said, new jobs (filled in t − 1) begin with the highest idiosyncratic productivity ε¯ in t. Two different values, for filled jobs and for employed workers, must be distinguished. The expected values of a new jobs JtN (¯ ε) and of continuing jobs Jt (εt ) are :

5

JtN (¯ ε)

  Z ε¯ λt+1 x Jt+1 (˜ ε)dG(˜ ε) = zt ε − + βEt (1 − ρ ) λt εt+1   n E N − ρt+1 (F + τt+1 ) + ρt+1 Vt+1 wtN (¯ ε)

  Z ε¯ λt+1 x Jt (εt ) = zt εt − wt (εt ) + βEt Jt+1 (˜ ε)dG(˜ ε) (1 − ρ ) λt εt+1   n E N − ρt+1 (F + τt+1 ) + ρt+1 Vt+1

(13)

(14)

Endogenous separations are costly. A firm that terminates an employment relationship has to support a cost F induced by the employment protection legislation and to pay a firing tax τtE . Two wages must then be distinguished. New jobs begin with the highest specific productivity level and obviously no separation occurs. New jobs are always productive at their beginning and new jobs wages7 do not take into account separation costs. Conversely, old jobs do not continue (recall the decision to continue is taken after observing the specific productivity shock) if their specific productivity level is below a threshold εt . The continuing job wages take into account separation costs. Equations (13) and (14) only differ by the wage value. The continuing job wage take into account separation costs VtN denotes the present value of a vacant job. It can be written in the following manner :   λt+1 N N N Vt = −κ + βEt qt Jt+1 (ε) + (1 − qt )Vt+1 (15) λt where κ represent a vacant job cost Consider now workers and let WtN (¯ ε) and Wt (εt ) respectively denote the present value of a new matched worker and the present value of an old matched worker :   Z ε¯ λt+1 N N x (1 − ρ ) Wt+1 (˜ ε)dG(˜ ε) + ρt+1 Ut+1 (16) Wt (¯ ε) = wt (¯ ε) + βEt λt εt+1   Z ε¯ λt+1 x Wt (εt ) = wt (ε) + βEt (1 − ρ ) Wt+1 (˜ ε)dG(˜ ε) + ρt+1 Ut+1 λt εt+1

(17)

Unemployed workers are engaged in a search process and the present value U of an unemployed worker satisfies :   λt+1 θt q(θt )Wt+1 (ε) + (1 − θt qt )Ut Ut = bt + h + βEt (18) λt 7

The wage bargaining process will be described latter

6

An unemployed worker enjoys at time t a return composed of an unemployment benefit bt and of a home production h.

1.5 1.5.1

Decision rules and wage setting Decision rules

There is a free entry condition, thus, firms open vacancies up to the value of a vacant job be zero, that is : VtN = 0

(19)

At equilibrium, all profits opportunities from new jobs are exhausted. The job destruction rule is determined through the endogenous specific productivity threshold. The job becomes unprofitable if the specific productivity component falls below the threshold εt . It is better to dismiss the worker and to pay the firing tax τtE and the cost F if εt < εt . This rule writes : Jt (εt ) + F + τtE = 0

(20)

εt is the critical value of the idiosyncratic productivity below which a job becomes unprofitable and the separation takes place. 1.5.2

Wage setting mechanism

At equilibrium, filled jobs generate a return (the value of the job plus the corresponding employed worker value) greater than the sum of values of a vacant job and of an unemployed worker. The net gain issued from a filled job is the total surplus of the match. In our model, we have to distinguish two surplus, the surplus of a new job and the surplus of a continuing job, that is : StN (¯ ε) = JtN (¯ ε) − VtN + WtN (¯ ε) − Ut N St (εt ) = Jt (εt ) − Vt + Wt (εt ) − Ut + F + τtE

(21) (22)

Note that in equation 22, the surplus increase with F + τtE because continuing the employment relationship allows to save firing costs amount. The two wages are determined through an individual Nash bargaining process between a worker and a firm who share the total surplus. Each participant threat point corresponds to the value of the alternative option, that is the value of being unemployed or the value of a vacant job. The outcome of the bargaining process is given by the solution of the following maximization problems :

7

wtN (¯ ε) = arg max (WtN (¯ ε) − Ut )1−ξ (JtN (ε) − VtN )ξ

(23)

wt (εt ) = arg max (Wt (εt ) − Ut )1−ξ (Jt (εt ) − VtN + F + τtE )ξ

(24)

wtN (¯ ε) wt (εt )

where ξ ∈]0, 1[ and 1 − ξ denote the bargaining power of firms and workers respectively. Using the free entry condition, the optimality conditions of the above problems may be written as follows :
ξ WtN (ε) − Ut = (1 − ξ)JtN (ε) (25) ξ (Wt (εt ) − Ut ) = (1 − ξ)(Jt (εt ) + F + τtE )

(26)

Using equations (13) to (18) to substitute values in (25) and (26) by their expression, wages8 are given by :  
λt+1 x N E wt (¯ ε) = (1 − ξ) zt ε + κθt − β(1 − ρ )Et (F + τt+1 ) λt + ξ(bt + h) (27)  
λt+1 E x E (F + τt+1 ) wt (εt ) = (1 − ξ) zt εt + κθt + F + τt − β(1 − ρ )Et λt + ξ(bt + h) (28) The structure of the wage equations is the same as in the standard matching theory. It contains the weighted contribution of both parties. Both equations take into account the expected firing costs (F and τtE ). During the bargaining, firms internalized that hiring a worker may be costly if the job is destroyed. The burden of the expected firing costs is thus subtracted from the worker’s contribution to firm’s output. Equations (27) and (28) differ because of the firing costs. Concerning an old job, firing costs should be paid in case of separation. Each party may use the cost of layoffs as a threat.

1.6

Job creation and job destruction

Job creation is driven by the free entry condition. At the equilibrium, all gain opportunities generated by a vacancy are equal to zero Vt = 0. Using equations (13) — (15), (19) and the two wage equations (27) and (28), the job creation condition may be rewritten as follows :   κ λt+1 E = ξβEt zt+1 ε − zt+1 εt+1 − F − τt+1 (29) qt λt 8

See appendix for the derivation of wage equations.

8

The expected gain from hiring a new worker is equal to the expected cost of search (which is κ times the average duration of a vacancy 1/qt ). It defines the relationship between the labor market tightness and the threshold value of idiosyncratic productivity. The threshold value of the productivity component is determined through condition (20). To obtain it, substitute equation (28) in (14) and set εt = εt . After some algebra, one gets : ξ(zt εt + F + τtE − bt − h) − (1 − ξ)θt κ ( !) Z ε λt+1 E +β(1 − ρx )ξEt (zt+1 ε − zt+1 εt+1 )dG(ε) − F − τt+1 = 0 (30) λt εt+1

This equation teaches us that the critical value of a job productivity depends on the reservation wages and on firing costs. It states that higher firing costs lower the reservation productivity because separations are more costly.

1.7

The unemployment insurance fund budget constraint

We follow [Cahuc and Malherbet 2004] to represent an experience rating system. An unemployed worker receives a benefit bt . Unemployment benefits are financed through a layoff tax and a lump sum tax paid by the large family. The experience rating tax is paid by employers when an endogenous separation occurs. Experience rating system is said to be complete or perfect when unemployment benefits are financed only by firing taxes i.e. Tt = 0. In that case, firms are fully liable for their layoff decisions. On the contrary, if τtE is equal to zero, unemployment insurance is fully financed by the lump-sum tax. Therefore, the cost of unemployment benefits are fully shared like in Continental Europe. We impose the unemployment benefits may not be financed by debt. The unemployment insurance fund budget constraint is thus balanced every period : = (1 − Nt ) bt {z } | Unemployment benefits

Tt + (1 − ρx ) ρnt Nt−1 τtE |{z} | {z } Lump sum Experience tax rating part

where w¯t represents the average wage of the economy. It is given by : Z ε NtN N Nt−1 wt = w (¯ ε) + (1 − ρx ) wt (ε˜t ) dG(ε˜t ) Nt t Nt εt

(31)

(32)

The sequences followed by Tt , τtE and bt may be chosen following different ways, provided they satisfy the above budget constraint. Our aim is to evaluate 9

some rules close to the US labor market institutions and to study their optimality. In the following paragraph, we consider a system in which taxes and benefits are set according to rules close to the US labor market ones. 1.7.1

Experience rating system

An unemployed worker receives a benefit bt equal to a proportion of the average wage w t , that is : bt = ρR w t

(33)

ρR < 1 is the average replacement rate. The experience rating system works as follows : the lay off tax is proportional to the expected fiscal-cost of an unemployed worker Qt+1 . Let e > 0 be the experience rating index (ERI), the firing tax τtE satisfies : τtE = eQt

(34)

where Qt = bt + βEt

λt+1  θt qt × 0 + (1 − θt q(θt ))Qt+1 λt

(35)

The above equation recursively determines the expected cost of an unemployed worker. The lay off tax corresponds to a share of the expected fiscal cost of an unemployed worker paid by the firm. The higher the ERI, the higher the firm contribution to the unemployment insurance. Substituting equation (34) in equation (35) provides : Tt = (1 − Nt )bt − (1 − ρx )ρnt Nt−1 eQt

(36)

Its a very simple way to represent the US experience rating system. Its consistency may be questionable considering the complexity of current regulations. However, our representation may be viewed as an approximation of the US unemployment insurance system. As emphasized by [Cahuc and Malherbet 2004] and [L’Haridon and Malherbet 2008], it is a convenient mean to make firms contribute to the fiscal cost they induce. It is also a satisfactory rule because it embodies some important features such that : • For all e > 0, an increase of endogenous separations raises the fiscal cost and compels the employer to pay more layoff expenditures. • The higher the experience rating degree, the lower the mutual part of the unemployment benefits. Then, firing tax is increasing in e and decreasing in Tt . 10

• If Tt = 0, Firms are fully liable for their layoff decisions. They thus pay the entire expected cost of benefits perceived by the unemployed workers. • The experience rating tax is increasing in the replacement rate and decreasing in the labor market tightness. The first one raises the expected fiscal cost of an unemployed worker while the second moves it in the opposite direction, indeed, it reduces the average unemployment duration.

1.8 1.8.1

The equilibrium The aggregate resource constraint

The aggregate output Yt is obtained through the sum of individual productions : Z ε¯ Yt = (1 − ρx )Nt−1 zt εedG(e ε) + NtN zt ε (37) εt

The aggregation of the individual profits provides the amount of profits Πt received by the large family, that is : Πt = Yt − wt Nt − κVt − (F + τtE )(1 − ρx )ρnt Nt−1

The above equation together with equations 11 and 31 gives the aggregate ressource constraint : Yt = Ct + κVt + F (1 − ρx )ρnt Nt−1 1.8.2

(38)

Definition of the equilibrium

Definition 1 For given lump sum tax rate Tt and firing tax τtE processes, and for a given exogenous stochastic process zt , the competitive equilibrium is a sequence of prices and quantities Nt , NtN , NtC , Ct , Vt , εt , θt , λt , qt , wt , wtN , Yt , ρnt , Mt and bt satisfying equations (1)-(4), (7)-(9), (12), (27), (29)-(32), (37) and (38). If taxes and benefits are set as described in subsection 1.7.1, the equilibrium definition writes as follows : Definition 2 (Experience rating system) For given parameters ρR and e and for a given exogenous stochastic process zt , the competitive equilibrium is a sequence of prices and quantities Nt , NtN , NtC , Ct , Vt , εt , θt , λt , qt , w t , wtN , Yt , ρnt , Mt , bt , τtE , Tt and Qt satisfying equations (1)-(4), (7)-(9), (12), (27), (29)-(32), (37), (38) and (33) - (35).

11

1.8.3

The Ramsey allocation

As shown by equation (31), unemployment benefit may be financed through two ways : an experience rating tax (τtE ) and a lump-sum tax (Tt ). The lumpsum tax adjusts to equilibrate, at each date, the unemployment benefit fund. As the Hosios condition is not satisfied, the decentralized equilibrium of the economy without unemployment benefit and taxes is not optimal. Our aim is to determine an optimal unemployment benefit financing scheme and to compare the equilibrium allocation obtained with the Pareto allocation. The Ramsey policy is the taxation policy under commitment maximizing the intertemporal welfare of the representative household. Definition 3 (The Ramsey allocation) The Ramsey equilibrium is a sequence of prices, quantities and taxes Nt , NtN , NtC , Ct , Vt , εt , θt , λt , qt , w t , wtN , Yt , ρnt , Mt , bt , Tt , τtE maximizing the representative agent life-time utility :

Et

∞ X j=0

βj

(Ct+j + (1 − h)Nt+j )1−σ 1−σ

subject to the equilibrium conditions (1)-(4), (7)-(9), (12), (27), (29)-(32), (37) and (38) and given the exogenous stochastic processes zt . 1.8.4

The Pareto allocation and the equivalence with the Ramsey allocation

Consider equations (29) and (30), suppose the Hosios condition (ξ = 1 − ψ) be satisfied and set the unemployment benefit and taxes equal to 0. One gets the following equations : −


κ Vt λt + βEt λt+1 zt+1 ε − yt+1 εt+1 − F = 0 1 − ψ Mt

ψ Vt λt (zt εt + F − h) − κ λt 1 − ψ 1 − Nt   Z ε +β(1 − ρx )Et λt+1 (zt+1 εe − zt+1 εt+1 )dG(e ε) − F =0

(39)

(40)

εt+1

Definition 4 (The Pareto allocation) For a given exogenous stochastic process, the Pareto allocation is a sequence of quantities Nt , NtN , Ct , Vt , εt , λt , Yt , ρnt , Mt satisfying equations satisfying equations (1),(4), (7), (9), (12), (27) and (37)(39). Result 1 (The Pareto allocation implementation) The optimal unemployment benefit financing scheme [definition 3] allows to implement the Pareto allocation. 12

Proof See appendix. The above result provides a simple way to determine the taxes and unemployment benefit processes implementing the Pareto allocation. The equilibrium values of Nt , NtN , NtC , Ct , Vt , εt , θt , λt , qt , Yt , ρnt and Mt are determined using equations (1)-(4), (7)-(9), (12) and (37)-(39). The exogenous stochastic process being given. The processes followed by the taxes and unemployment benefits Tt , τtE and bt are then easily deduced from equations (29)-(31). Finally, wt and wtN are provided by equations (27) and (32). If the Hosios condition is not satisfied, that is if 1 − ψ 6= ξ, the equilibrium is not a Pareto optima. Comparison of equations (29) and (30) with equations (39) and (40) allows to see how the firing tax τtE works to restore Pareto optimality. To simplify, consider these equations at the steady state and suppose the Hosios condition be satisfied. One has : κ V ξ − (1 − ψ) β M ξ(1 − ψ) κ V ξ − (1 − ψ) V ξ − (1 − ψ) + κ b = (1 − β(1 − ρx )) β M ξ(1 − ψ) 1 − N ξ(1 − ψ)

τE =

It immediately follows that τ E = 0 and b = 0, this is obvious since there is no distortion. Suppose now that 1 − ψ < ξ, that is the bargaining process is in the favor of firms. The firing tax τ E and the unemployment benefit b are positive. The labor market is characterized by trade externalities. A greater number of vacancies increases the probability an unemployed worker finds a job and reduces the probability a firm fills a vacancy. Similarly, a greater number of unemployed increases the probability a firm fills a vacancy and reduces the probability a worker finds a job. If the bargaining power of workers 1−ξ is weak, that is less than ψ, the wage is low and firms post a lot of vacancies. In this case, without taxes and benefits, there are congestion externalities caused by searching firms posting a great number of vacancies, unemployment is below its optimal level. There exits a firing taxes and unemployment benefits scheme allowing to ensure optimality. Firing taxes reduce job creation, there are less searching firms. Unemployment benefits allow to strengthen the threat point of workers. Wage is thus set at a higher level, which reduces job creations. The optimal unemployment benefit financing scheme works like the Hosios condition. The negative intra-group externalities and the positive inter-group externalities just offset. The distorsion comes from a too strong firms bargaining power and firing taxes allow to ensure optimality. Conversely, if the bargaining process is at the advantage of workers, that is if 1 − ψ > ξ, firing taxes must be negative.

13

1.8.5

The Second best allocation

The equilibrium allocation (definition 1) is defined conditionally to the unemployment benefits financing scheme (equations (33) - (36)). This unemployment benefits financing scheme is a proxy of the American system. The key parameters, that is the replacement rate ρR and the ERI e, are set by the authorities. Thereafter, quantitative evaluations are made using a benchmark calibration based on US data, but there is no reason these two parameters be optimal. Here, we define a second best allocation where ρR and e are chosen to maximize the conditional welfare. Given initial conditions N−1 and N0N and given parameters ρR and e, let et and N et the consumption and employment equilibrium denote respectively by C allocation. The conditional welfare under the equilibrium allocation writes : f R , e; N−1 , N0N ) = E0 W(ρ

∞ X

βt

t=0

et + (1 − N et )h)1−σ (C 1−σ

Optimal values for ρ∗R and e∗ are obtained solving the following problem : f R , e; N−1 , N N ) {ρ∗R , e∗ } = arg max W(ρ 0 ρR ,e

The second best allocation is given by definition 2, knowing that ρR = ρ∗R and e = e∗ . 1.8.6

The welfare costs

In order to compare the different alternative allocations with the Ramsey allocation, we compute their welfare costs. We evaluate the fraction of the consumption stream from an alternative policy needed to be added to achieve the Ramsey allocation welfare. Let W0∗ be the conditional welfare under the Ramsey allocation and let Cta and Nta denote an alternative allocation. The welfare cost Ψ is obtained by solving the following equation : W0∗ = E0

∞ X

βt

t=0

[(1 + Ψ) (Cta + (1 − Nta )h)]1−σ 1−σ

Ψ can be written as follows :

Ψ =



W0∗ W0a

with : 14

1  1−σ

−1

(41)

W0a = E0

∞ X t=0

βt

(Cta + (1 − Nta )h)1−σ 1−σ

Ψ is numerically computed using a second order approximation (see [SchmittGrohé and Uribe 2004]).

2

Quantitative evaluation of the model

2.1

Calibrating and solving the model

The benchmark calibration is based on US data. We follow [Shimer 2005] to set the labor market parameters. His approach concerns only transitions between employment and unemployment and start from a simple measure of the job finding and separation probabilities. The institutional context of the labor market is characterized by an experience rating system described previously. This last one exhibit a low level of replacement rate compare to European labor markets. The model is calibrated according to quarterly frequencies over the period 1951Q12005Q4. Baseline parameter are reported in table 1. We set the discount factor to 0.99 to have an annual steady state interest rate close to 4%. The relative risk aversion coefficient is set to 1.5 according to [Kydland and Prescott 1982]. The capital depreciation rate δ is equal to 0.025, which implies an annual rate of 10%. The aggregate productivity shock follows a first order autoregressive process : log zt+1 = ρz log zt + εzt+1 . ρz corresponds to the autocorrelation coefficient; it is equal to 0.95 as in [Den Haan, Ramey, and Watson 2000]. ǫzt+1 is a random variable whose realization are i.i.d. from a time-invariant Gaussian distribution with mean zero and standard deviation σz = 0.007. The elasticity of the production function with respect to capital is calibrated to one-third. The distribution G(.) of idiosyncratic productivity shock is iid and log-normal with mean zero and whose upper bound is equal to 95 percentile as in [Zanetti 2007]. Following [Shimer 2005], total separations from employment to unemployment represent by around about 3.48 percent of employment size on average. We suppose as is [Den Haan, Ramey, and Watson 2000], [Zanetti 2007] and other that exogenous separations are two times higher than endogenous ones. Consequently, ρx = 0.0234 and ε is fixed in such a way that ρn ≡ 1/2ρx = 0.0117 at the steady state. We keep the traditional value of 0.5 for the workers bargaining power. We still follow the Shimer’s approach to set the elasticity of matching function with respect to unemployment : ψ = 0.7. The steady state unemployment rate U is calibrated to 5%9 and therefore N=0.95. At the steady state, the number 9

Which is closed to the statistics from the BLS on the period 1951-2005.

15

of match must be equal to the number of separation: M = ρN. Following [Andolfatto 1996], the rate at which a firm fills a vacancy is 0.9. We can deduce the number of vacancy V = M/qt and a job finding rate of about 0.65, which is closed to the observed empirical value compiled by Shimer (0.61). Then, it takes a little bit more than one and a half quarter on average for an unemployed to find a job. χ is calculated in such a way that M = χ(1 − N)ψ V 1−ψ . Statistics from the Census Bureau of labor show that the average ERI across states and over the period 1988-2007 is about 0.65. The US net replacement rate exhibit a ratio of 0.32 according to OECD (1994). The remaining parameters κ and h are only determined by solving the system of three equations (29), (30) and (32) in three unknowns (κ, h and w). ¯ So, κ represent 8% of average wage which is broadly consistent with empirical finding. Finally we set σε to catch up with the observed cyclical properties of labor market outcomes. Variables Discount factor Risk aversion Capital depreciation rate Production elasticity Autocorrelation coefficient Std. dev. of aggregate shock Std. dev. of idiosyncratic shock 95 percentile upper bound Matching elasticity Total separation rate Exogenous separation rate Endogenous separation rate Worker bargaining power Replacement rate Experience rating index Vacancy cost Firing cost

Symbol β σ δ α ρz σz σε ε¯ ψ ρ ρx ρn ξ ρR e κ F

Value 0.99 1.5 0.025 0.33 0.95 0.007 0.092 1.2384 0.7 0.0348 0.0234 0.0117 0.5 0.32 0.65 0.08 0

Table 1: Baseline parameters. We solve the model with a second-order perturbation method. State variables are Nt , NtN and zt . Changing parameters lead up to a new steady state. It is calculated by a Newton algorithm with a Gauss-Chebyshev quadratures to solve integrals for which we use 100 nodes to compute the grid.

16

2.2

The optimal labor market policy

The optimal labor market policy (first-best allocation) solve a Ramsey problem subject to competitive equilibrium condition10 . It exhibit two features : (i) A layoff tax that is slightly lower than the fiscal cost of an unemployed worker and (ii) an average replacement rate that is one third lower. The second best allocation is defined through the two institutional parameters (e and ρR ) that maximize the large family welfare. It displays similar features but strongly affects labor market dynamics. The experience rating index appear to be a tiny bit lower than the Ramsey allocation as well as replacement ratio. The steady state effects and welfare comparisons are reported in table 2.

Experience rating index Replacement rate Output Consumption Employment Welfare Welfare cost Workers flows rate

Benchmark economy 0.6500 0.3200 100.00 100.00 100.00 100.00 0.2644 3.48 %

1st best allocation Pareto Ramsey 0 0.9745 0 0.2186 101.93 101.81 102.52 100.13 0.0000 2.38 %

Second best allocation 0.9662 0.2161 101.94 101.81 102.52 100.13 0.0003 2.38 %

Table 2: Optimal labor market policy. Output, consumption, employment and welfare have been standardized. e and ρR have been recalculated when we compute the Ramsey. Percentage welfare losses are relative to the Ramsey allocation. Optimal financing schemes (first and second-best) sharply depart from the benchmark one. Labor market failures are strongly reduced when the second best allocation is implemented. In the first-best and the second-best allocation, the layoff tax is close to the expected fiscal cost of an unemployed worker. In the Ramsey allocation, equilibrium worker flows are reduced by around 30%. As mentioned [Algan 2004] and [L’Haridon and Malherbet 2008], turnover costs introduce a labor hoarding phenomena. As long as firing is costly, firms prefer continue the relation with a low productivity level than pay for the layoff tax. They cut back the reservation productivity to reduce endogenous separations. The reservation productivity falls up to a point where endogenous separations are close to zero. Then, ins and outs of employment are almost only governed by exogenous separations. In that case, an higher index doesn’t reduce labor market flows anymore11 . Output and employment increase by 1.93% and 1.81% We solve the model with a second-order approximation method around the steady state to make welfare comparisons. 11 The reason come from the reservation productivity. When τ E increase, ε strongly decreases 10

17

respectively. The welfare is enhanced by 0.13% compare to the benchmark. The welfare loss (Ψ) of the benchmark economy is of about 0.26% relative to the optimal policy. The alternative policy (second-best) displays a very weak loss (0.0003%). In order to scrutinize the effects of the unemployment insurance, we compute the conditional welfare as a function of our two institutional parameters (figure 1) in the second-best allocation. Figure 1 depicts a dome-shaped surface. The replacement rate seems to have an higher impact on welfare than the experience rating index. A maximum is reached when the replacement rate is equal to 0.2161 and the experience rating index to 0.9662. To clarify, we set ρR to its optimal value and vary the experience rating index (figure 2). We do the same exercise when e is imposed and ρR varies. In both cases, the welfare depicts a hump-shaped curve with a peak corresponding to the optimal second-best policy. The mean level of consumption and employment seems to vary in the same direction when we change the level of an institutional parameters. Since the collective utility function is increasing in Ct and decreasing in Nt , the overall effect on welfare is ambiguous. Finally, we compute alternative labor market policy and calculate welfare losses. Results are reported in table 3.

ρR ρR ρR ρR ρR ρR

= 0.10 = 0.15 = 0.20 = 0.25 = 0.30 = 0.35

e = 0.5 0.0473 0.0357 0.0902 0.3297 0.9166 1.2827

e = 0.7 0.0453 0.0204 0.0130 0.0410 0.1273 0.3572

e = 0.9 0.0448 0.0176 0.0018 0.0082 0.0671 0.3425

e = 1.1 0.0448 0.0177 0.0019 0.0081 0.0670 0.3462

e = 1.3 0.0450 0.0180 0.0023 0.0084 0.0673 0.3502

Table 3: Welfare loss. All welfare losses are relative to the optimal Ramsey allocation.

It is shown that if the government imposes a replacement ratio, there is an experience rating degree that minimize the welfare loss. However, alternative policies are always welfare detrimental. In our calibration, we assume that the worker bargaining power (1 − ξ) is lower than its efficient value: ψ. Consequently, the first-best allocation features a positive layoff tax that offset congestion externalities. What happened in the opposite case i.e. if the bargaining process is in the favor of workers ? We compute the optimal layoff tax when ξ varies from 0.1 to 0.9. The result is plotted in figure 6. The greater the firms bargaining power the higher the layoff tax. When 1−ξ = ψ, the Hosios condition is satisfy and τ E = 0. When 1−ξ > ψ, to balance the job destruction rule (30). According to the shape of the distribution, a small negative change in ε lead to an important decrease of the endogenous separation rate G(ε). These results remain virtually unchanged with a capital accumulation or/and a uniform distribution.

18

the layoff tax become negative. In other words, the competitive economy does not yield enough job destructions.

2.3

Impulse response function analysis

Let us now investigate how changes in the degree of experience rating affect aggregate fluctuations. We simulate a one percent negative aggregate productivity shock and compute impulse response functions (see Fig. 3-5) for the benchmark economy (e = 0.65) and the two optimal allocations. Under the optimal policies significatively, shocks propagation is drastically affected. The quantitative impact of the productivity shock exhibit wide differences among the three economies. The adjustment path is roughly similar between the benchmark and the Ramsey but strongly differs from the second-best economy. We first discuss the benchmark and the Ramsey out-of-steady-state dynamics. On impact, firms post fewer vacancy while the size of unemployment increase with a one-lag period, reproducing the Beveridge curve. As a consequence, the labor market tightness and the number of match jumps below their steady state level. As in [Den Haan, Ramey, and Watson 2000], the increase in unemployment after the shock drives new matches above their initial level (known as the "echo effect"). The jump in the reservation productivity raises the job separation rate. The number of old workers is reduced as well as total employment. Output and consumption decline following the shock and return gently to their equilibrium. In the Ramsey allocation, the jump of separation rate is seven times lower than the benchmark while the initial increase of reservation productivity is two times higher. The reason is that the steady states reservation productivity is located on the bottom of the distribution (see [Zanetti 2007]). The slope of the distribution is nearly horizontal. Therefore, a shift of εt doesn’t generate a strong increase of endogenous separations. The initial fall of the hiring rate is widely reduced in the optimal policy. This is consistent with the most common admitted hypothesis according to which a high index lowers hirings during booms ([Card and Levine 1994]). The drop of vacancies and the labor market tightness are almost three times weaker. Consumption and output decline with a more pronounced hump-shaped adjustment in the benchmark case. The layoff tax and the lump-sum tax appear counter-cyclical. This is consistent with the employers’ contribution rate fluctuations observed over the period 1950-2007 in the US12 . On impact, unemployment benefits are reduced according to their wage indexation. The layoff tax jump above its steady state level to offset the effect on job destruction. The lump-sum tax diminishes to balanced the unData construct by the US department of labor (DOL) relates a negative correlation between GDP and contribution rates with a one-year lag. As mentioned [Fougère and Margolis 2000], it can be justify by the fact that contribution rates are set according to the trust funds of the previous years. Our model fail to reproduce this stylized fact because taxes are both forward looking variables and jump following the shock. 12

19

employment insurance trust funds. However, UI’s expenditures goes up because unemployment increases with a one-lag period. Consequently, the lump-sum tax increases to balance the budget and follows the same adjustment path as unemployment. Since unemployment is persistent and recruitment is a time-consuming activity, the fiscal cost of an unemployed worker remains high. Taxes slowly converge to their equilibrium value. In the Ramsey allocation, it is shown that taxes jump in the opposite direction. The initial fall of unemployment benefits is more pronounced. One can explain it by the weak increase of unemployment and the strong effect on wages. As a consequence, UI’s expenditures goes down following the shock. Taxes have to decrease to balanced the unemployment insurance trust funds. We now focus on the second-best allocation dynamic. Propagation mechanisms appear to be widely affected as well as adjustment paths. Indeed, the fall of hirings is more pronounced but converge without overtaking the steady state. Following the negative aggregate shock, the reservation productivity jumps below its initial value, diminishing endogenous separations. This can be explained by the rise in the cost of separations. As long as it remains high, it dissuades firms from pin up the critical value of the idiosyncratic productivity. Firms cut back vacancies during the recession rather than firing an inefficient worker. Then, the effect of the aggregate shock translate into the job posting activity. This, in turn, magnifies the initial effect on vacancies while it dampens unemployment fluctuations.

2.4

Conclusion

In this paper, we use a DSGE model to study the optimal unemployment benefits financing scheme. We investigate how search and matching frictions influence the optimal policy. We show that unemployment benefits and layoff taxes allow to implement the Pareto allocation. In other words, the policy instruments mentioned above can offset congestion externalities caused by matching frictions. In our dynamic model, the Ramsey problem display a time-consistent policy. We show that layoff taxes can decrease unemployment rate and improve welfare when they are used to finance unemployment benefits. The basic idea is that firms internalize the cost of their firing decision. It is fund that layoff taxes give a financial incentive for employers to stabilize their employment. Indeed, an optimal combination of unemployment benefits and layoff taxes reduces the cost of aggregate fluctuations. It is shown that layoff taxes induce a labor hoarding phenomena by increasing the cost of separations. However, they do not represent a simple firing cost like employment protection legislation. They are also a fiscal instrument which can be used by policy maker in order to counterbalance excess of layoffs. However, the model can be developed in several directions. First, throughout this paper we deals with a simple unemployment insurance system as a proxy 20

of current regulations. While our model of unemployment insurance borrowed from [Cahuc and Malherbet 2004] preserve several assumptions, the experience system in force exhibit wide differences. Employer contribution rates depend on the firms’ unemployment history and unemployment benefits that are perceived by its ex-employees. Here we consider a combination of a layoff tax and a lumpsum tax which are forward looking variables. Therefore the model does not take into account lagged periods following shocks and assumes a quarterly frequency13 To catch up with current regulations it will be worth introducing the formula provided by [Topel 1983] and [Anderson 1993] and measuring the marginal tax cost. Second, it will be worth introducing wage rigidities as in [Shimer 2005] to match the business cycle. Moreover, as highlighted [Cahuc and Malherbet 2004] and [Joseph, Pierrard, and Sneessens 2004] the effects of firing costs on labor market outcomes are ambiguous in the presence of a minimum wage. As in [Den Haan, Ramey, and Watson 2000] and [Algan 2004], a capital accumulation can be consider to have a more realistic fluctuation of output and employment. Heterogeneities ex-ante among firms and workers is also an interesting issue ([Pissarides 1994] and [Krause and Lubik 2006]) that may help to explain the effects of unemployment insurance on labor market outcome. The question one can ask is what are the consequences of an imperfect experience rating system when labor turnover is heterogenous among firms. It will be worthwhile to measure the effect of the implicit subsidy finance through other firms as in [Feldstein 1976] and others. Another interesting issue is to introduce an imperfect insurance system in an economy populated by a continuum of ex-ante homogenous workers. This method used in heterogenous-agent models can be helpful to generate different labor market trajectories. Associated to an experience rating system that record unemployment history will be complex to solve but will be a rigorous approximation of the current unemployment insurance system.

13

while employers’ contribution rates are revised every year.

21

A

Proof of result 1

Let’s write the lagrangian of the Ramsey allocation problem :

L = E0

∞ X t=0

β

t



(Ct + (1 − Nt )h)1−σ 1−σ

 
Vt e + κ − βξλt+1 (zt+1 ε − zt+1 εt+1 − F − τt+1 Mt  Vt 2 + Ωt λt ξ (bt + h − zt εt − F − τte ) + (1 − ξ)κλt 1 − Nt !! Z ε e − β(1 − ρx )ξλt+1 zt+1 (ε − εt+1 )dG(ε) − F − τt+1 Ω1t

εt+1

+ +

Λ1t (Yt − Ct − κVt − F (1 − ρx )ρnt Nt−1 ) N Λ2t (−Nt+1 + Mt ) + Λ3t (−Nt + (1 − ρx )(1

− ρnt )Nt−1 + NtN )   Z εt 4 ϕ 1−ϕ 5 n + Λt (−Mt + χ(1 − Nt ) Vt ) + Λt −ρt + dG(ε) 0 ! Z ε

+ Λ6t

εdG(ε) + NtN zt ε

−Yt + (1 − ρx )Nt−1 zt

εt


 + Λ7t (Ct + (1 − Nt )h)−σ − λt + Λ8t (−(1 − Nt )bt + Tt + (1 − ρx )ρnt Nt−1 τtE )

The optimality conditions with respect to Tt , bt and τtE write :

∂L = Λ8t = 0 ∂Tt ∂L = Ω2t λt ξ − Λ8t (1 − Nt ) = 0 ∂bt ∂L = Ω1t−1 ξλt − Ω2t−1 λt ξ + Ω2t−1 (1 − ρx )ξλt + Λ8t (1 − ρx )ρnt Nt−1 = 0 ∂τtE It immediately follows that Ω1t = Ω2t = Λ8t = 0 ∀t. The others optimality conditions may then be written as follows :

22

∂L ∂Ct ∂L ∂λt ∂L ∂Yt ∂L ∂Vt ∂L ∂ρnt ∂L ∂Nt

= (Ct + (1 − Nt )h)−σ − Λ1t − Λ7t σ(Ct + (1 − Nt )h)−σ−1 = 0

(42)

= −Λ7t = 0

(43)

= Λ1t − Λ6t = 0

(44)

= −Λ1t κ + Λ4t χ(1 − Nt )ϕ (1 − ϕ)Vt−ϕ = 0

(45)

= −Λ1t F (1 − ρx )Nt−1 − Λ3t (1 − ρx )Nt−1 − Λ5t = 0

(46)

= −βEt Λ1t+1 F (1 − ρx )ρnt+1 − Λ3t + βEt Λ3t+1 (1 − ρx )(1 − ρnt+1 ) Z ε 4 ϕ−1 1−ϕ 6 − Λt χϕ(1 − Nt ) Vt + βEt Λt+1 (1 − ρx )zt+1 εdG(ε) εt+1

+

Λ7t σh(Ct

+ (1 − Nt )h)

−σ−1

− h(Ct + (1 − Nt )h)−σ = 0

∂L = −Λ2t + βEt Λ3t+1 + βEt Λ6t+1 zt+1 ε = 0 N ∂Nt+1 ∂L = Λ2t − Λ4t = 0 ∂Mt ∂L = Λ5t − Λ6t (1 − ρx )Nt−1 zt εt = 0 ∂εt

(47) (48) (49) (50)

The system formed by equations 42 — 50 seems untractable. However, it can easily be showed that it reduces to the equations system defining the Pareto allocation. It immediately follows from equation 43, 42 and 44 that Λ7t = 0, Λ1t = (Ct + (1 − Nt )h)−σ = λt and Λ6t = λt . >From equations 45, 46, 49 and 50, is is easily deduced that : κ Vt λt 1 − ϕ Mt = (1 − ρx )Nt−1 λt εt = −λt F − λt zt εt = Λ4t

Λ4t = Λ5t Λ3t Λ2t

Substituting in equations 47 and 48 provides :

23

κ Vt λt − βEt {λt+1 (zt+1 (ε − εt ) − F )} = 0 1 − ϕ Mt ϕ Vt λt (zt εt + F − h) − κ λt 1 − ϕ 1 − Nt ( !) Z ε (ε − εt+1 )dG(ε) − F +β(1 − ρx )Et λt+1 zt+1 =0 −

εt+1

The above equations are exactly equations 40 and 39. We thus have verified that the Ramsey allocation corresponds to the Pareto one.

24

References Algan, Y. (2004): “La protection de l’emploi : des vertus stabilisatrices ?,” working paper. Anderson, P. (1993): “Linear Adjustment Costs and Seasonal Labor Demand: Evidence from Retail Trade Firms,” Quarterly Journal of Economics, 108(4), 1015–1042. Anderson, P., and B. Meyer (2000): “The Effects of the Unemployment Insurance Payroll Tax on Wages, Employment, Claims and Denials,” Journal of Public Economics, 78(81-106). Andolfatto, D. (1996): “Business cycles and labor market search,” The american economic review, 86(1), 112–132. Blanchard, O., and J. Tirole (2004): “Protection de l’emploi et procédure de licenciement,” in Rapport pour le Conseil d’Analyse Economique. La documentation française. (2008): “The joint design of unemploymment insurance and employment protection. A First Pass,” Journal of European Economic Association, 6(1), 45–77. Burdett, K., and R. Wright (1989): “Optimal Firm Size, Taxes and Unemployment,” Journal of Public Economics, 39, 275–287. Cahuc, P. (2003): “Pour une meilleure protection de l’emploi,” Document de travail 63, COE. Cahuc, P., and F. Malherbet (2004): “Unemployment compensation finance and labor market rigidity,” Journal of Public Economics, 88, 481–501. Cahuc, P., and A. Zylberberg (2007): “Optimum income taxation and layoff taxes,” Journal of Public Economics, Forthcoming. Card, D., and P. Levine (1994): “Unemployment insurance taxes and the cyclical and seasonal properties of unemployment,” Journal of Public Economics. Den Haan, W., G. Ramey, and J. Watson (2000): “Job Destruction and Propagation of Shocks,” American economic review, 90(3), 482–498. Feldstein, M. (1976): “Temporary Layoffs in the Theory of Unemployment,” Journal of political economy, 84(5), 937–957.

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Fougère, D., and D. Margolis (2000): “Moduler les cotisations employeurs à l’assurance chomage: les experiences de bonus-malus aux Etats-Unis,” Revue Française d’Economie, 15, 3–76. Joseph, G., O. Pierrard, and H. Sneessens (2004): “Job turnover, unemployment and market institutions,” Labour economics, 11(4), 451–468. Krause, M., and T. Lubik (2006): “The Cyclical Upgrading of Labor and On-the-Job Search,” Labour Economics, 13(4), 459–477. Kydland, F., and E. Prescott (1982): “Time to build and aggregate fluctuations,” Econometrica, 50, 1345–1371. L’Haridon, O., and F. Malherbet (2008): “Employment protection reform in search economies,” European economic revew, Forthcoming. Marceau, N. (1993): “Unemployment Insurance and Market Structure,” Journal of Public Economics, 52, 237–249. Mortensen, D., and C. Pissarides (1994): “Job creation and job destruction in the theory of unemployment,” The review of economic studies, 61(3), 397– 415. (1999): “Job reallocation, employment fluctuations and unemployment,” in Handbook of Macroeconomics, vol. 1, chap. 18, pp. 1171–1228. Elsevier Science, New York. Pissarides, C. (1994): “Search Unemployment with On-the-Job Search,” Review Economic Studies, 61, 457–475. Schmitt-Grohé, S., and M. Uribe (2004): “Solving dynamic general equilibrium models using a second-order approximation to the policy function,” Journal of economic dynamics and control, 28, 755–775. Shimer, R. (2005): “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” American Economic Review, 95(1), 25–49. Topel, R. (1983): “On Layoffs and Unemployment Insurance,” American economic review, 73(4), 541–559. Topel, R., and F. Welsh (1980): “Unemployment Insurance: Survey and Extensions,” Economica, 47, 351–379. Veracierto, M. (2007): “On the Short-Run Effects of Labor Market Reforms,” Journal of Monetary Economics, 54(4), 1213–1229. Zanetti, F. (2007): “Labor market institutions and aggregate fluctuations in a search and matching model,” working paper 333, Bank of England. 26

Figure 1: Conditional welfare.

27

0.05

0.5 0 % Dev.

% Dev.

0

−0.05

Employment −1.5

0.9

1 1.1 1.2 1.3 Experience rating index

−2 0.1

1.4

Consumption

0.15

0.2 0.25 0.3 Replacement rate

0.35

0.15

0.2 0.25 0.3 Replacement rate

0.35

−201.5 Conditional Welfare

Conditional Welfare

−201.5805

−201.581

−201.5815

−201.582 0.8

−1

Employment Consumption

−0.1

−0.5

−201.6 −201.7 −201.8 −201.9 −202 0.1

1 1.2 Experience rating index

Figure 2: Optimal policy. Effect of changing institutional parameters on consumption, employment and welfare.

28

0.2 1 % Deviation

% Deviation

0 −0.2 −0.4

Consumption

−0.6 Output

−0.8 0

5

New workers

0.5 0 Old workers

−0.5 −1

10 15 Time : Quarters

20

25

30

0

5

10 15 Time : Quarters

20

25

30

20

25

30

20

25

30

1.5 2 1

0

% Deviation

% Deviation

Unemployment

Vacancy

−2

Tightness

−4 −6 −8

0.5

Job destruction rate

0 −0.5

Job creation rate

−1 0

5

10 15 Time : Quarters

20

25

30

0

5

10 15 Time : Quarters

0.3

2 Lump sum tax

1

% Deviation

% Deviation

1.5 Layoff tax 0.5 0

Benefits

0.2 Threshold

0.1 0

−0.5 −1 0

5

10 15 Time : Quarters

20

25

30

−0.1

0

5

10 15 Time : Quarters

Figure 3: Impulse response functions. One percent negative aggregate productivity shock simulated on the benchmark economy (e = 0.65, ρR = 0.32).

29

0.2 0.2

−0.2 −0.4

New workers

0.1 % Deviation

% Deviation

0

Consumption

−0.6

Output

0 Old workers

−0.1 −0.2 −0.3

−0.8 0

5

10 15 Time : Quarters

20

25

−0.4

30

0

5

10 15 Time : Quarters

20

25

30

20

25

30

20

25

30

1 0.2 Unemployment % Deviation

% Deviation

0.5 0 Vacancy

−0.5 −1

Tightness

−1.5 −2

0

5

10 15 Time : Quarters

0

Job destruction rate

−0.1 −0.2 −0.3

20

25

−0.4

30

0

Job creation rate 0

5

10 15 Time : Quarters

0.5 Lump sum tax

−0.5

% Deviation

% Deviation

0.1

Layoff tax −1 −1.5

Benefits

0.4 0.3 Threshold

0.2 0.1 0

−2 0

5

10 15 Time : Quarters

20

25

30

−0.1

0

5

10 15 Time : Quarters

Figure 4: Impulse response functions. One percent negative aggregate productivity shock simulated on the Ramsey allocation.

30

0.2

0.5 0

0

Old workers

% Deviation

% Deviation

−0.5 −0.2 Consumption

−0.4 −0.6

−1

New workers

−1.5 −2 −2.5

Output

−3

−0.8 0

5

10 15 Time : Quarters

20

25

30

0

5

10 15 Time : Quarters

20

25

30

10 15 Time : Quarters

20

25

30

20

25

30

0 Unemployment

−0.5 % Deviation

% Deviation

0 −2

Vacancy −4

Tightness

−6

Job destruction rate

−1 −1.5 −2 −2.5 Job creation rate

−3

−8 0

5

10 15 Time : Quarters

20

25

30

0

5

3 0.05 0

Layoff tax

% Deviation

% Deviation

2 1 Lump sum transfer 0

−0.05

Threshold

−0.1 −0.15 −0.2

Benefits

−0.25

−1 0

5

10 15 Time : Quarters

20

25

30

0

5

10 15 Time : Quarters

Figure 5: Impulse response functions. One percent negative aggregate productivity shock simulated on the second-best allocation (e = 0.9662, ρR = 0.2161).

31

0.4 0.2 0

Layoff tax

−0.2 −0.4 −0.6 −0.8 −1 −1.2 0.1

0.2

0.3

0.4 0.5 0.6 Firms bargaining power

0.7

0.8

0.9

Figure 6: The optimal layoff tax. The optimal layoff tax is obtained by varying the firms’ bargaining power in the Ramsey allocation.

32