APPENDIX Development of the Model
The rate at which vacant jobs and unemployed workers meet is determined by the simple matching function m(v,u), where m is a first degree homogeneous matching function and v and u represent the number of vacancies and unemployed workers respectively, normalized by the fixed labor force size.
Vacancies are filled at the rate: q(θ)=m(v, u)/v=m(1, u/v); θ=v/u and q’(θ) < 0
If Cobb-Douglas m(v, u) = v1-α uα and q(θ)=(v1-α uα)/v = (u/v)-α = θ-α
The rate at which workers find job is: γ (θ) = m(v,u)/u = m(v/u, 1) = θq(θ); γ’(θ) > 0
Job creation is defined by the number of matches: m(v,u)=vq(θ).
Each job is characterized by a fixed irreversible technology and produces a unit of a differentiated product whose productivity is p + σε. The productivity is made up of an aggregate component p, common to every job, and a job specific component ε.31 The parameter σ reflects dispersion, and increases in σ representing a symmetric mean preserving spread in the job-specific shock distribution or equivalently an increase in productivity variance.
The process that changes the idiosyncratic component of prices ε is Poisson with arrival rate equal to λ. When there is a change in ε, the new value of the job specific productivity ε is a drawing from the fixed distribution F(ε), which has finite upper support εu, lower support ε1 and no mass point other than at the upper support εu. This way of modeling implies a memoryless but persistent idiosyncratic productivity. The persistence of any given productivity ε is 1 /λ.
The model assumes that firms have the option to select the best productivity in the market, and create jobs at the upper support p + σεu. Once a job is created, however, the firm has no choice over its productivity. Filled jobs are said to be fully operative if the idiosyncratic productivity is above some critical value εd, while they are said to be idle if the job specific productivity is below εd. Therefore, the rate at which jobs turn idle is λF(εd), while idle jobs get firing permissions and leave the market at rate s. The parameter s summarizes EPL in the model as s →∞ EPLs are eliminated. Finally, idle jobs are subject to idiosyncratic uncertainty and can return fully operational at rate λ(1-F(εd)).
The model assumes that employers capture all the rents associated with a job-worker match by paying workers the common alternative value of their time, b.
The unknowns of the model are the number of job vacancies v and unemployment u, which determine, through the matching technology, job creation, and the critical value for the idiosyncratic component of productivity, εd, that induces idle job.
The asset valuation of a filled job, conditional on an idiosyncratic productivity ε is:
where J(.) is the value of a job, r is the exogenous interest rate, p + σε - b are operational profits at idiosyncratic productivity ε. Apart from the flow-term p + σε - b, Eq. (1) involves two capital gain terms. At rate λ the firm loses its current asset value J(e) and draws a new ε from the productivity distribution. At rate s firing permissions arrive and the firm gets an option to destroy the job. Since a destroyed job has zero value, the max operator in Eq. (1) captures the idea that a firm will keep running a job as long as its value is positive. It follows that an operational job is a positively valued job that ignores firing permissions while an idle job is a negatively valued job that is destroyed when permissions arrive. Differentiating Eq. (1) with respect to e, it shows that J(.) is a piece-wise increasing function of ε and its derivative reads:
If we define the reservation productivity εd as:
J(εd) = 0,
making use of Eqs. (1) and (3), after an integration by parts, the expected value of a job in Eq. (1) reads:
The last term of Eq.(4) is the value (negative)of an idle job and is a measure of expected firing costs. As the average waiting time goes to zero (s → ∞), the second term on the right hand side of Eq.(4) vanishes, firing is always possible and it is accomplished as soon as the value of the job is negative. To obtain the cut off value εd, below which the firm will accept firing permission, we make use of Eq.(4) and we evaluate Eq.(1) at J(.)=0. The reservation productivity solves:
Eq.(5) is one of the key equations of the model and uniquely determines the reservation productivity as a function of the parameters r, λ, p, s, b, σ and the productivity distribution F(e). The left hand side of Eq.(5) is the profit from the marginal operational job. In an economy with no firing constraints (s → ∞), the second term of the right hand side vanishes, the marginal profit is negative and there is voluntary labor hoarding in equilibrium. When firing is instantaneous (s → ∞) but hiring is costly, the firm will hoard labor up to the level in which current losses compensate savings of hiring costs if conditions improve. The presence of firing delays increases, through the last term in Eq. (5), the value of the marginal profits. As the average waiting time for firing permissions increase, a job will be kept running in bad times for a longer period of time because of exogenous constraints and there will be institutional labor hoarding. Since the firm anticipates firing restrictions when conditions are bad, in Eq.(5) the firm reduces the extent of voluntary labor hoarding. As s falls, it is possible that firing restrictions become so high that the firm will accept firing permissions at a positive profit per period.
Differentiating Eq.(5) with respect to s and rearranging, yields:
Thus ∂∊d/∂s ≤ 0: an increase in the average waiting time of permission (fall in s) increases the productivity at which the firm takes advantage of firing permissions. This is consistent with the firm anticipating long waiting time when conditions worsen.
The reservation productivity falls with p, the common productivity. Differentiating Eq.(5) with respect to (p-b) and rearranging, yields:
Thus ∂∊d/∂p ≤ 0: as the productivity increases the firm will find it profitable to keep a job operational for a higher range of productivities. The effect of other parameters on the reservation productivity is ambiguous. Higher discount rate r reduces the flow of income from the job and makes labor hoarding less profitable. This would reduce εd. But simultaneously, the higher discount rate reduces expected firing costs and makes autonomous labor hoarding profitable. Similar arguments hold for changes in the arrival rate of idiosyncratic shocks. Higher λ corresponds to an increase in the arrival rate of productivity shocks. On the one hand the reservation productivity tends to decrease since the firm expects the duration of adverse conditions to be shorter. At the same time, the probability of facing a firing procedure is higher and the net effect depends mainly on the distribution F(.).
68. Job creation comes through the posting of vacancies. When creating a job, we assume the existing technology is fully flexible and the productivity distribution is common knowledge. This implies that new firms have the option to select the best productivity in the market and job creation takes place at the upper support of the distribution (εu). A posted vacancy yields an asset return of -c per period, c being the constant cost of hiring, and a probability q(θ) of being filled with a job created at the upper support of the distribution. The vacancy asset valuation is:
With free entry into the job market, there are, in equilibrium, zero expected profits (V=0) (Pissarides, 1990) and the value of a job equals the expected searching costs:
where the value of a job at the upper support of the distribution is obtained subtracting Eq.(5) from Eq.(1) and reads:
Eq.(9) is the job creation condition and uniquely determines the vacancy unemployment ratio θ as a function of the parameters r, λ, c, the matching function q(.), the upper support of the distribution εu and the reservation productivity εd.
Differentiating Eq.(11) with respect to common productivity p, yields
and, making use of the facts that ∂∊d/∂p < 0 and q’ (.) < 0, ∂θ/∂p > 0. Higher common productivity, increasing the flow of future profits, increases job creation at given unemployment Conversely, higher job security provisions reduce the expected value of a job and reduce the profitability of new jobs. Job creation at given unemployment falls. Differentiating Eq.(11) with respect to s,
making use of ∂∊d/∂s < 0 Eq.(13) implies that ∂θ/∂s>0.
To close the model, we need to introduce unemployment. With a fixed labor force, a worker can be either unemployed or employed. If employed, a worker can be attached to a fully operational (ε ≥ εd) or to an idle job ε< εd. Normalizing variables in terms of a constant labor force, the relationship among different labor force status is:
where u is the unemployment rate, ni is the employed idle capacity, and nj is the employed operational rate. In an interval dt, the outflow rate (job creation) corresponds to the number of matches per unemployed times the number of unemployed, while the inflow rate (job destruction) corresponds to the fraction of workers in the idle state whose employers obtained firing permission.
where 6 q(θ) is the job finding rate. Eq. (15) defines unemployment variation as the difference between job destruction and job creation. Simultaneously, there are a number of fully operational jobs that are hit by a shock below the reservation productivity and enter the idle state. The outflow from the idle state corresponds to the idle jobs that have obtained firing permissions plus those idle jobs that, hit by a positive productivity shock, return to be fully operational. The inflow into the idle state is given by the operational jobs hit by a shock below the reservation productivity. The change in the idle rate is:
In steady state equilibrium, the unemployment rate and the employment composition between idle and operational jobs is constant. From Eqs. (15) and (16) it follows that unemployment and the idle rate are constant if the inflow rate is equal to the outflow rate. Steady state idle rate is:
and steady state equilibrium unemployment is:
In steady state, the system is recursive and it reduces down to four equations. Eq.(5) uniquely determines the reservation productivity εd, while Eq.(11), given εd, uniquely determines the vacancy/unemployment ratio θ. Given θ and εd, Eq.(17) and (18) simultaneously determine unemployment and the idle rate. Finally, given the unemployment rate, θ determines vacancies.
Bentolila, S., and G. Saint-Paul, 1994. “The Macroeconomic Impact of Flexible Labor Contracts, with an Application to Spain”. European Economic Review, Vol.36, No. 5.
Bertola, G., and S. Bentolila, 1990. “Firing Costs and Labor Demand: How Bad is Eurosclerosis?”. Review of Economic Studies, No. 57.
Burda, M., 1992. “A Note on Firing Costs and Severance Benefits in Equilibrium Unemployment” Scandinavian Journal of Economics, No. 94.
Elmeskov, J., J.P. Martin, and S. Scarpetta, 1998. “Key Lessons for Labor Market Reforms: Evidence from OECD Countries’ Experiences”. Swedish Economic Policy Review, Vol. 5, No. 2.
Fanizza, D., 1996. “Employment Cycles in Search Equilibrium”. Journal of Economic Dynamics and Control, No. 20, Elsevier Science.
Kugler, A.D., and G. Pica, 2004. “Effects of Employment Protection and Product Market Regulations on the Italian Labor Market”. Center for Economic Policy Research, Discussion paper No.4216.
Millard, S., 1996. The Effect of Employment Protection Legislation on Labor Market Activity: A Search Approach” Bank of England Working Paper.
Millard, S., and D. Mortensen, 1997. “The Unemployment and Welfare Effects of Labor Market Policy: A Comparison of the US and UK”. In Unemployment Policy: Government Options for the Labor Market, Edited by Dennis J. Snower and Guillermo de la Dehesa. Cambridge University Press.
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- Export Citation
)| false Millard, S., and D. Mortensen, 1997. “ The Unemployment and Welfare Effects of Labor Market Policy: A Comparison of the US and UK”. In Unemployment Policy: Government Options for the Labor Market, Edited by Dennis J. Snower and Guillermo de la Dehesa. Cambridge University Press.
Mortensen, D. and C. Pissarides, 1994. “Job Creation and Job Destruction in the Theory of Unemployment”. Review of Economic Studies, Vol. 61.
Pissarides, C., 1999. “Policy Influences on Unemployment: The European Experience”. Scottish Journal of Political Economy, Vol. 46, No. 4.
The authors of this paper are Taline Koranchelian and Domenico Fanizza.
The law does not require tax payments when firing employees, neither severance payments are high by international standards.
The World Bank estimated the elasticity of employment to GDP growth to 0.5 during 1994-2001.
The main reforms included:
Introduction of two categories of fixed-term contracts, determinate and indeterminate period of time. Fixed-term contracts are permitted for a maximum of four years, subject to the agreement of the parties.
Introduction of part-time work. Part time is defined as less than 70 percent of the normal hours. It is based on two principles: freedom of choice for employees and equal treatment with full-time employees.
These reforms stipulated that the complete process, from initial application for downsizing to a final decision of the Commission du controle des licenciements, should take a maximum of 33 days, unless the parties agree to an extension.
This includes job turnover from closures and firm contraction. Data cover the 1980s and early 1990s for 16 OECD countries.
In the case of licienciement abusif for fixed-term (CDD) employees, payment should equal the remaining part of the contract.
See appendix for the description of the complete model and the characterization of equilibrium.
σ reflects dispersion and is common to every job. It is a normalizing parameter useful for the simulations.
As Diamond (1971) has shown, this outcome is an equilibrium in a wage setting game played among employers when workers have only the power to accept or reject offers and workers search sequentially at some positive costs. Given this outcome, workers have no incentive to search on the job and their parameters, other than b, do not affect the equilibrium. Alternatively, if we allowed a continuously renegotiated Nash bargain between the firm and the worker, the wage would be higher than the worker reservation utility in operational jobs, where the surplus from the match is positive. But the presence of firing restrictions, would force the firm to pay the worker even when the job is idle and the worker’s participation constraint is binding. This would force idle firms to offer the worker his reservation utility b, exactly as in the present model. Thus, a continuously renegotiated bargain would only affect the wage of operational jobs, leaving unchanged the behavior of idle jobs, the distinctive feature of this model. To keep track of such bargains would be analytically tedious and would not change the qualitative results of the paper.
σreflects dispersion and is common to every job. It is a normalizing parameter useful for the simulations.