تاثیرات استحقاقی مجدد روی بیمه بیکاری وابسته به مدت زمان در یک تعادل تطبیقی تصادفی

In the context of a standard equilibrium matching framework, this paper considers how a duration-dependent unemployment insurance (UI) system affects the dynamics of unemployment and wages in an economy subject to stochastic job-destruction shocks. It establishes that re-entitlement effects induced by a finite duration UI program generate intertemporal transfers from firms that hire in future booms to firms that hire in current recessions. These transfers imply a net hiring subsidy in recessions which stabilizes unemployment levels over the cycle.

This paper considers a matching equilibrium where the aggregate economy is subject to stochastic job-destruction shocks. Workers when laid-off are entitled to unemployment benefits for a fixed term, say 6 months, after which they receive no further benefits from the government. Since Mortensen (1977) we know that such duration-dependent unemployment benefit schemes generate re-entitlement effects: becoming re-employed implies the worker (eventually) requalifies for full unemployment insurance (UI). This paper considers the impact of such re-entitlement effects on hiring incentives over a (stochastic) business cycle. We show that in a non-competitive labour market, re-entitlement effects generate an intertemporal transfer from future hiring firms to current hiring firms. Such transfers are employment stabilizing over the cycle – they imply a net hiring subsidy in recessions. An important insight for our results is that in a non-competitive labour market, the joint value of a worker–firm match is increasing in the level of UI benefits. This occurs because the UI system credibly raises the worker's reservation wage when laid-off which subsequently forces the worker's next employer to offer a higher hiring wage. By extracting more rents from an outside party (the next hiring firm) the UI system increases the joint value of a current match. The issue then is who enjoys those additional rents? Clearly if the worker has all the bargaining power, those rents go into the worker's pocket and the current employer does not benefit. Less obviously, those rents also go into the worker's pocket if UI payments are constant with duration. In that case increasing the level of UI payments is not unlike increasing the value of leisure while unemployed. This automatically leads to higher negotiated wages and all firms are worse off. But suppose instead UI payments are duration dependent – for example suppose UI payments cease after 6 months unemployment. This introduces re-entitlement effects – the unemployed worker whose UI entitlement has expired can only become re-entitled to future UI through re-employment. Re-entitlement effects allow the current hiring firm to expropriate at least part of those third party rents. The mechanism is most easily understood by assuming firms have all the bargaining power and so hire unemployed workers at their reservation wage. Consider then an unemployed worker whose UI entitlement has expired. Having no further UI entitlement this worker can be hired at a relatively low wage. The current hiring firm offers that worker a wage which reflects that, by becoming employed, the worker also becomes re-entitled to UI. But consider what happens when that worker is laid-off at some future (random) date because of a job-destruction shock. In the next unemployment spell, UI re-entitlement implies that worker then has a relatively high reservation wage (at least at first while his UI entitlement has not expired). Thus, the next hiring firm may have to pay a relatively generous wage to compensate for any foregone UI payments. But the assumption that firms have all the bargaining power implies the current hiring firm extracts those expected future rents through a lower hiring wage. Thus, re-entitlement effects imply a transfer of rents from an (as yet unknown) future hiring firm to the current hiring firm. Such re-entitlement effects do not necessarily reduce unemployment. When a firm hires a worker who is entitled to receive further UI, the higher wage that needs to be offered is essentially a transfer to the worker's previous employer; the previous employer paid a lower wage reflecting this potential outcome. Of course by becoming fully re-entitled to UI in the future, the current firm offers a lower wage reflecting those future rents. But discounting implies those expected rents from future employers are worth less than the (average) transfer paid to previous employers. Thus, a more generous UI scheme yields higher unemployment rates in a steady state. Outside of steady state the analysis is more complicated. The paper identifies this transfer effect using a standard equilibrium matching framework where firms are subject to idiosyncratic job-destruction shocks which evolve stochastically over time. In the Conclusion we provide a back-of-the-envelope calculation for the US economy which suggests that the net transfer to firms hiring in recessions may be as high as 6 weeks UI. This works out as a 1.5% wage subsidy. This is clearly not a huge amount but being a targeted hiring subsidy it yields a significant stabilizing effect on employment over the cycle. Simulations formally establish that a reduction in the duration of UI (tied to a compensating increase in the level of benefits so that the budget balancing tax is held constant) implies a reduction both in the average unemployment level and in the variance of unemployment over time. The existing literature on duration-dependent UI systems has several strands. The optimal UI literature (e.g. Shavell and Weiss, 1979 and Hopenhayn and Nicolini, 1997) designs UI programs which insure employed workers against layoff risk. There are no re-entitlement effects in those papers as they consider an individual looking for work during a single spell of unemployment. Using a sequential search framework Mortensen (1977) and van den Berg (1990) ask how a duration-dependent UI program affects reservation wages given an exogenous distribution of wages. Those papers show that the re-entitlement effect reduces reservation wages at long unemployment durations. Albrecht and Vroman (2005) extend that approach by instead supposing UI payments expire according to a Poisson process (rather than after a deterministic period of time). This simpler framework allows them to identify a steady-state wage posting equilibrium. Equilibrium is characterized by a two-point wage distribution where workers whose UI payments have expired have a lower reservation wage. As this reservation wage depends on re-entitlement effects, re-entitlement effects lead to lower posted wages. Perhaps the closest literature is the equilibrium matching literature with duration-dependent UI. This literature has two strands. Millard and Mortensen (1997), Davidson and Woodbury (1997), Cahuc and Lehmann (2000), Fredriksson and Holmlund (2001), Coles (2006) suppose wages are determined by Nash bargaining where the worker's threatpoint is the value of being laid-off. This bargaining approach much simplifies the analysis as it implies all workers negotiate the same wage. Assuming workers are strictly risk averse, these papers then consider the optimal (duration-dependent) UI program taking into account that the UI program distorts wages and hence job creation rates by firms. Note however that this Nash bargaining approach rules out any re-entitlement effects on wages – although unemployed workers whose UI payments have expired have low reservation wages, they negotiate the same high wage consistent with being fully entitled to receive UI.1 Perhaps Cahuc and Lehmann (2000) provide the best motivation for this approach – they assume union wage bargaining where wages are negotiated by insiders (whose threatpoint is the value of being laid-off) and new employees (outsiders) must be hired at the union wage. Coles and Masters, 2004 and Coles and Masters, 2006 instead assume hiring wages are determined by strategic bargaining between the hiring firm and the unemployed worker and so depend on the worker's remaining entitlement to further UI. The bargaining approach used here is closely related. Coles and Masters (2006) show that for sensible parameter values, UI payments around the one-year duration mark distort (average) hiring wages the most. With the exception of Millard and Mortensen (1997), the above papers only consider steady state and so do not identify the stabilization mechanism identified in this paper. Millard and Mortensen (1997) assume Nash bargaining which rules out re-entitlement effects on wages. Following Mortensen and Pissarides (1994) there is also a rapidly growing literature which describes equilibrium matching when the economy is subject to aggregate productivity shocks. The aim of this literature is to determine whether this matching approach can fit the business cycle data. Shimer (2005) argues that the standard Nash bargaining approach implies wages are too procyclical. The resulting variation of vacancies over the cycle is then too small. This occurs as the assumed worker bargaining threatpoint – the value of being unemployed – moves a lot over the cycle. Of course, it is well known that different bargaining games imply different Nash bargaining structures (e.g. Binmore et al., 1986). For example, if search is costly and so while bargaining the worker does not search for outside opportunities (the worker expects to reach immediate agreement tomorrow and so there is little gain to search), the worker's equilibrium threatpoint while bargaining is simply the value of leisure. This immediately implies wages move less over the cycle (e.g. Hall and Milgrom, 2005). Our bargaining approach is closely related to this latter approach – the unemployed worker's threatpoint here is not the value of continued search, it is the value of leisure augmented by additional UI payments received from the government (if entitled). See Mortensen and Nagypal (2005) for a mini survey of this rapidly burgeoning literature. Finally, it is worth pointing out that the wage effects considered here are not unrelated to the on-the-job search approach (e.g. Postel-Vinay and Robin, 2002a, Postel-Vinay and Robin, 2002b and Cahuc et al., 2006) and the investment literature (Acemoglu, 1997 and Acemoglu and Pischke, 1999). In the on-the-job search approach, an employed worker can obtain outside job offers which trigger Bertrand competition between his current employer and the outside firm. Such competition yields significant wage increases. When hiring an unemployed worker, the hiring firm offers a low starting wage reflecting these expected future wage gains. The same mechanism occurs here where re-entitlement to UI implies the worker can extract more rents from the next hiring firm and so the current hiring firm extracts those rents through offering a lower wage. Acemoglu (1997) points out that with job-destruction shocks, ex post wage bargaining implies the worker's next employer will extract part of the rents which accrue to general human capital investment. As that employer is not identified at the time when training takes place, this market failure leads to too little training. Our point is that a UI system generates the opposite transfer effect. Should the worker be laid-off in the future, then being entitled to receive UI payments increases the worker's reservation wage when next employed, and the worker extracts greater rents from his next future employer.

This paper has shown that when UI payments are duration dependent, re-entitlement effects in a non-competitive economy generate transfers from firms that hire in the future to currently hiring firms. Using an equilibrium matching framework, simulations find that a switch from a pure UA system to a pure 6-month UI system lowers both average unemployment and the variance of unemployment over the cycle. A simple back-of-the-envelope calculation illustrates the potential magnitude of this stabilization effect. Suppose that the UI program stops payments after 26 weeks of unemployment. Further suppose the business cycle is a two-state phenomenon – the economy is either in recession with an average duration of unemployment equal to 18 weeks, or in a boom with an average duration of 8 weeks where each state is equally likely [i.e. the average spell is 13 weeks over the cycle]. In the recession, the mean remaining UI entitlement of a currently unemployed worker is 12 weeks more UI. Reflecting the worker's option value of remaining unemployed, the (average hiring) wage depends on the annuitized value of that remaining entitlement. But that hiring wage also reflects the worker's re-entitlement to future UI. Suppose then that when laid-off in the future, that layoff occurs in a boom. With average unemployment spells of 8 weeks in a boom, the mean remaining UI entitlement of a currently unemployed worker is 18 weeks. Hiring firms in booms offer higher wages to compensate for that entitlement, but those rents are essentially a transfer to the worker's previous employer. In this example, re-entitlement effects imply an average transfer of 18-12=618-12=6 weeks UI from firms that hire in booms to firms that hire in recessions. Assuming a 50% replacement rate and annuitizing over an average employment spell of around 4 years (e.g. Cole and Rogerson, 1999) yields a 1.5% wage subsidy. This is not a huge amount. Indeed the simulations show that average hiring wages do not move much over the cycle – hiring wages in the conditional steady state with low job-destruction rates are only 1.2% higher than in the conditional steady state associated with high job-destruction rates. Indeed the average employee wage hardly changes over the cycle. Nevertheless, being a targeted hiring subsidy in recessions, simulations show that these transfers are effective in stabilizing employment levels over the cycle. For ease of exposition the paper has assumed the business cycle is driven by variations in job-destruction rates (e.g. Davis and Haltiwanger, 1992 and Mortensen and Pissarides, 1994). Shimer (2005) challenges this view of the cycle. As our back-of-the-envelope calculation reveals, however, what is important for our argument is that the average duration of unemployment is higher in recessions. Introducing productivity shocks complicates our model as renegotiation constraints might bind; e.g. the wage is renegotiated should productivity p<wp<w. Of course when hiring, the firm and worker anticipate such renegotiations and, as the firm has all the bargaining power, the starting wage adjusts so that the firm still extracts all expected rents (see Postel-Vinay and Robin, 2002a and Postel-Vinay and Robin, 2002b for related arguments). Although wages then evolve stochastically during the lifetime of the job, the above insights continue to hold: re-entitlement effects imply a net subsidy to firms who hire in recessions. Typically UI systems define compensation in terms of replacement rates rather than a b(.)b(.) paid to all. Given the model generates equilibrium wage dispersion, an extended model with UI payments defined as replacement rates, would also generate dispersion in the level of UI received (while entitled). This extension much complicates the model as negotiated wages depend on current UI received (and continuing entitlement), while current UI received depends on previous wage agreements. Identifying a stochastic matching equilibrium involves solving this additional fixed point problem. Nevertheless, the insights of the model provided here remain appropriate. Should a firm/worker pair negotiate a higher wage, the higher UI received when laid-off allows the worker to extract greater rents from the next employer. An extended boom therefore gradually raises average wage levels which has long run repercussions as those workers eventually become laid-off through idiosyncratic job-destruction shocks. The same applies in an extended recession. But it is not clear how these wage effects affect economic stability over the cycle as average employment spells exceed business cycle frequencies.