در تعادل جستجو کار با مزایای بیکاری درون زا

This paper develops an on-the-job search model with wage posting where unemployment benefits are proportional to past wages. We emphasize that this contributes to increasing the reservation wages of unemployed workers and introduces a feedback effect of the distribution of wages on the distribution of unemployment benefits. We show that the model predictions are consistent with some stylized French facts and quantify the impact of inefficient rejections of low-wage offers by the unemployed. We find that, by reducing the indexing of unemployment benefits to previous earnings and increasing lump-sum transfers, it is possible to increase both employment and welfare.

In their seminal paper, Burdett and Mortensen (1998) (BM henceforth) not only show that pure wage dispersion can exist at equilibrium with the on-the-job search, but also that the interplay with unemployment benefits dispersion gives rise to “inefficient unemployment” according to BM's definition. This means that some unemployed workers reject low-wage offers, which pushes up the unemployment rate. Although this dispersion of the unemployment benefits (UB) does not reflect any heterogeneity of workers' ability, these job rejections are unambiguously inefficient. The distribution of UB should therefore collapse to a mass point. However, it is obvious that there is also an insurance motive for the UB system because consumption-smoothing raises the well-being of risk-averse workers.1 This argument favors the indexing of UB to previous earnings, which would lead to a dispersed distribution of UB. From another standpoint, Marimon and Zilibotti, 1999 and Acemoglu and Shimer, 2000 argue that a generous UB system can be considered as a subsidy to the search activity; this allows workers to find high productivity jobs and contributes to raising output and welfare. Overall, the indexing of UB to previous earnings introduces a trade-off between inefficient unemployment on the one hand, and insurance/subsidy motives on the other hand. The aim of this paper is to quantitatively analyze this trade-off by extending the BM framework to allow UB to be proportional to past wages. In most OECD countries (see OECD (1994)), the UB distribution is not a mass point. UB systems therefore differ according to average replacement rates but also according to the heterogeneity of the unemployment compensations. The UB system typically embodies two components: a “Beveridge” component (lump-sums) associated with redistribution, and a “Bismarck” component associated with the insurance i.e. the UB indexing to previous earnings. The extent of this indexing differs largely across countries (between 57.4% and 75% of gross wages in France, 60% of the net wages in Germany, 40% of gross wages in Italy…). Moreover, the UK, Australia and New Zealand are noticeable exceptions where there are only lump-sum transfers (the “Beveridge” component). The first goal of this paper is to show how the on-the-job search equilibrium with endogenous wage dispersion is affected by endogenous unemployment benefits. Secondly, this paper aims at showing the main trade-offs behind the definition of an optimal UB system in the context of the on-the-job search equilibrium. Previous works in line with BM assumed that the dispersion of unemployed reservation wages is exogenous. This implies that the position of workers within the unemployment distribution does not depend on the worker's career and his previous wage earnings (see, e.g. Bontemps et al., 2000 and Postel-Vinay and Robin, 2002). Unemployed benefits/reservation wages dispersion modifies the shape of the wage distribution, but the latter has no feedback effect on the distribution of the unemployed. In this paper, we emphasize that the proportionality of UB to past wages implies an unexplored argument for the job search decision of the unemployed which raises their reservation wages. An unemployed worker indeed expects that if he accepts a wage equivalent to his benefits, this can imply lower unemployment compensation in the future event of the job's destruction; he would earn only a fraction of the accepted wage. Endogenous UB dispersion then introduces additional restrictions on the job contact rates: the probability of the worker accepting a wage offer now depends only on the wage dispersion and no longer on an ad-hoc distribution of the UB. From the empirical point of view, a first objective is to assess the on-the-job search model's performance as regards its ability to replicate not only the distribution of wages but also the distribution of UB. As can be seen from Table 1 and Fig. 6 in Appendix A, the heterogeneity of UB is high in France.2 More precisely, the dispersion is relatively higher for unemployed incomes than for wage earnings: the coefficient of variation is larger for UB than for wages, whatever the skill of the workers. Fig. 1 examines the value of the earnings decile over average earnings (both for wages and unemployment benefits)3 and then shows that both for low-skilled and medium-skilled workers the distribution of UB is unambiguously flatter than the distribution of wages. Numerical experiments based on the French low-skilled labor market show that our model allows a good fit of both distributions (wages and unemployment benefits). It implies a large right-hand tailed of the UB distribution, which is in some extent the outcome of job rejections by the unemployed. This suggests, therefore, that to explain a worker's upward mobility along the wage distribution during his career it could be worthwhile to consider indexing of UB to previous earnings (see Burdett et al., 2009 and Bagger et al., 2006 for alternative explanations of this mobility4). Because the dispersion of the UB is endogenous, our model is a useful tool to examine the impact of reforming the UB system, on unemployment, productivity and welfare. First, our model is well-suited to quantify the potential extent of inefficient unemployment. Moreover, because we consider endogenous productivity dispersion, as was first suggested by Mortensen (2000)5 to generate the observed hump-shaped wage distributions,6 our model also allows us to deal with the productivity argument discussed in Marimon and Zilibotti, 1999 and Acemoglu and Shimer, 2000. Finally, we introduce risk-aversion in order to take into consideration the insurance motive related to the UB system. Our quantitative analysis is based on the French low-skilled full-time labor market. We find that the impact of job-offer rejections on the unemployment rate is not very large but significant, around one percentage point. This gives an assessment of the inefficient unemployment for low-skilled workers in France. We then show that the optimal UB system for this population would correspond to a “Beveridge” system with only lump-sum transfers without any indexing of the UB to previous earnings. The remainder of the paper is as follows. The first section presents the model. The second section is devoted to calibration, model assessment and policy analysis. The last section concludes.