Age-Specific Labour Market Effects of Employment Protection: A Numerical Approach

Abstract

The particular situation of the youngest and oldest individuals on the labour market motivates age-specific labour market analysis. One topical case is employment protection for older workers. The effect of employment protection on the total number of jobs is ambiguous. The positive effect of lower job destruction is counteracted by the negative effect of lower job creation. This ambiguity carries over to the more specific case of age-related employment protection. Numerical analysis can be illuminating when countervailing effects produce an ambiguity. In this paper, I present a numerical model based on the theoretical set-up of Chéron et al. (Econ J 121:1477–1504, 2011). Simulations performed with the model highlight age-specific effects of general employment protection measures and effects of measures targeted at particular age-groups on workers outside the target group. Firing taxes and hiring subsidies have age-specific consequences because employment and unemployment rates vary over the lifecycle. Positive effects of employment protection for the target group can be outweighed by negative effects for other workers.

Appendices

Appendix 1: The Model of Chéron et al. (2011)

In contrast to the numerical model of this paper, the original model of CHL (2011) works with a continuous distribution of productivities. Crucial for the working mechanism are reservation productivities $R_{i}$ (for ongoing jobs) and $R_{i}^{0}$ (for new jobs), which generate transitions according to the productivity distribution function G.

The model has T age classes, indexed by $i\in \left\{ 1,\ldots ,T\right\}$. At age $i=1$, workers enter the labour market and are unemployed with certainty ($u_{1}=1$), age $i=T-1$ is the last period when workers are active on the labour market, in period T, they retire with certainty.

The probability of an unemployed worker of age i to be employed at age $i+1$ is

$$\begin{aligned} jc_{i}\equiv p(\theta )\left[ 1-G(R_{i+1}^{0})\right] , \end{aligned}$$

where p is the matching rate generated by the matching function for unemployed workers, u, and vacancies, v:

$$\begin{aligned} p(\theta )=M(u,v)/u \end{aligned}$$

The job destruction rate for employed workers is given by¹⁵

$$\begin{aligned} jd_{i}=G(R_{i}) \end{aligned}$$

The resulting labour market flows generate the following age-profile of unemployment:

$$\begin{aligned} u_{i+1}=u_{i}\left\{ 1-p(\theta )\left[ 1-G(R_{i+1}^{0})\right] \right\} +G(R_{i+1})(1-u_{i}) \end{aligned}$$

for¹⁶ $\forall i\in (1,T-2)$ and the initial condition $u_{1}=1$. Adding up gives the overall level of unemployment:

$$\begin{aligned} u=\sum _{i=1}^{T-1}u_{i} \end{aligned}$$

Note that the unemployed of period $T-1$ are part of the unemployment pool and can be matched with a vacancy, even if the do not start working because they are about to reach the retirement age.

The expected value of a vacant position is¹⁷

which, using the zero-profit condition $V=0$, can be written as

Bellman equations for the values of the different labour market states are formulated in the usual, recursive manner. This gives

for the value of a filled new job (with outsider wage $w_{i}^{0}(\epsilon )$) for $\forall i\in (1,T-1)$,

for the value of a filled continued job (with insider wage $w_{i}^{0}(\epsilon )$) and

for the values of insiders, outsiders and unemployed workers, respectively. The final conditions are ${\mathcal {W}}_{T}={\mathcal {U}}_{T}$ (exogenous).

Wages are determined by Nash bargaining with bargaining power $\gamma$ of the worker

$$\begin{aligned} {\mathcal {W}}_{i}^{0}(\epsilon )-{\mathcal {U}}_{i}= & {} \gamma \left[ J_{i}^{0}(\epsilon )+H_{i}+{\mathcal {W}}_{i}^{0}(\epsilon )-{\mathcal {U}}_{i}\right] \\ {\mathcal {W}}_{i}(\epsilon )-{\mathcal {U}}_{i}= & {} \gamma \left[ J_{i}(\epsilon )+F_{i}+{\mathcal {W}}_{i}(\epsilon )-{\mathcal {U}}_{i}\right] \end{aligned}$$

Appendix 2: Pitfalls of Pre-determined Productivity Bin Boundaries

In a straightforward numerical implementation of the CHL set-up we can discretise the productivity space into bins of equal size and calculate the value functions for each of these bins. An earlier version of this paper was actually based on this straightforward implementation (with 30 equal-distant bins). However, the discretisation produces non-continuous reactions that make the results difficult to interpret. This appendix illustrates the pitfalls and motivates the approach with endogenous bin boundaries used in the main text (Sect. 3.4).

Figure 9 shows the employment effects of a uniform firing tax in the model with pre-determined bin boundaries. In contrast to the main text, the level of the tax is chosen particularly low (0.01, i.e. 1 % of the maximum production per worker and period) in order to highlight the resulting interpretation problems. The no-policy situation (solid line) is rather close to the model with endogenous bin boundaries (Fig. 1). The employment rate is first increasing, reaches a steady-state value of slightly higher than 70 % after the age of 30 and finally declines because of the end-game effect.

Fig. 9

Employment effects of a small firing tax

As in the main text, a uniform firing tax (dashed line in Fig. 9) has an employment-increasing effect in general. However, the age-specific pattern that emerges is irritating. For age groups between 25 and 50, employment increases considerably, significantly more that what one might have expected as a reaction to the small policy impulse. For workers above age 50, in contrast, the employment effect is hardly noticeable.

This strange age-pattern in the employment effect is an artefact of the productivity discretisation. With discrete productivity (in roughly 3 %-points steps when there are 30 bins), any policy will either have a negligible effect¹⁸ (if the reservation productivity does not shift by at least one productivity bin) or a significant effect (if it does). This is highlighted in Fig. 10, which shows the pattern of the reservation productivity with and without the firing tax.

Fig. 10

Reservation productivity with small firing tax

The solid line depicts the reservation productivity in the “no policy” case (where the lines for hiring and firing coincide). It is constant until age 55 and then sharply increasing. In the case with the firing tax, the reservation productivity for hiring remains unchanged. This outcome is not unexpected; however, because of general equilibrium feedback, it is not obvious either. The changes take place in the reservation productivity for firing, which in general declines. The changes are in line with the discrete structure of the productivity bins. For the age groups below 50 and above 60, the reservation productivity declines by exactly one bin width (3 %-points), for the age groups in-between, it does not change at all.

Patters of this sort are, even if qualitatively enlightening, quantitatively unconvincing. They produce spurious jumps in the age-specific effects of a uniform policy, depending solely on the coincidental closeness of the reservation productivities to the bin boundaries. Therefore, the model in the main text has been modified to include endogenously adjusting bin boundaries.

Fig. 11

Employment effects of a small firing tax

Figure 11 shows the age-specific employment effects of a small firing tax (0.01) in this modified model. In both respects that were unsatisfactory in the model with fixed bin boundaries, the situation is improved:

• The employment effects are small and in the order of magnitude of the policy shock analysed.

• The age-pattern of employment effects is smooth, as one would expect with a policy that is not targeted to specific age groups.

• The pattern of reservation productivities (Fig. 12) is smooth as well. In both the no-policy and the firing-tax scenario the end-game effect sets in gradually, not abruptly as in Fig. 10.

Fig. 12

Reservation productivity with small firing tax