طراحی بیمه بیکاری: القاء حرکت و آموزش مجدد

Evidence suggests that unemployed individuals can affect their job prospects by undertaking a costly action like deciding to move or retrain. Realistically, such an opportunity only arises for some individuals and the identity of those may be unobservable ex ante. The problem of characterizing constrained optimal unemployment insurance in this case has been neglected in previous literature. We construct a model of optimal unemployment insurance where multiple incentive constraints are easily handled. The model is used to analyze the case when an incentive constraint involving moving costs must be respected in addition to the standard constraint involving costly unobservable job-search. Absent wealth effects on behavior, we derive closed-form solutions showing that when the moving/retraining incentive constraint binds, unemployment benefits should increase over the unemployment spell, with an initial period with low benefits and an increase after this period has expired.

An important feature of the modern welfare state is the existence of an extensive unemployment insurance (UI) system. It is now well established that the design of the unemployment insurance affects the incidence of unemployment by distorting the incentives of unemployed to search for a job (see, e.g., Holmlund, 1998 for a survey). This has motivated a growing literature on how the UI system should be designed to make an optimal trade-off between providing good insurance, on the one hand, and not distorting the incentives too much, on the other. The key informational friction in this literature is that search activity cannot be monitored, so sufficient search incentives must be provided. The contribution of this paper is twofold. The first contribution is to focus on an important informational friction that has been largely neglected in the literature. We will consider the case when individuals who become unemployed have different opportunities to find a new job. However, we assume that the insurer cannot (perfectly) observe these differences. Specifically, we assume that some, but not all, unemployed can increase the probability of being hired by undertaking a costly investment, e.g., by retraining or moving to a location with better employment prospects. Under the realistic assumption that the insurer is unable to observe who has this option, an incentive problem arises and failure to take this into account may lead to sub-optimal UI-design. One direct way of mitigating the problem would be to offer subsidies to moving or retraining. While we will discuss this case at the end of the paper, our main case is when full cost-compensation is not feasible, for example because the insurer cannot fully distinguish voluntary and involuntary job-separations. Although an empirical investigation is outside the scope of this paper, we argue that the consequences of not providing reasonable incentives for people to move or retrain may be of substantial quantitative importance. For instance, Bartel (1979) documents that the proportion of geographical mobility in the U.S. caused by the decision to change jobs is one-half of all migration decisions for young workers and one third of all migration decisions for workers aged above 45. Furthermore, geographical mobility is substantially lower in continental Europe, and Hassler et al. (2005) document in panel-data a negative correlation between geographical mobility and UI-generosity as well as between mobility and aggregate unemployment rates. Other empirical documentations of the link between unemployment and geographical mobility are DaVanzo (1978), Pissarides and Wadsworth (1989) and McCormick (1997). The second contribution of our paper is more methodological. Search incentives and incentives to move are generally not independent and should therefore be jointly analyzed. The reason why moving incentives are not included in the standard analysis is that multiple incentive constraints with different characteristics are difficult to analyze. Including both search and moving/retraining incentive constraints complicates the analysis, since it is difficult to evaluate which of many constraints are binding, in particular when unemployment benefits are allowed to be non-constant. Suppose, for example, that the benefit schedule contains x tiers, so that the benefit level b is an element of B≡{b1,b2,…,bx}B≡{b1,b2,…,bx}. The incentive constraint for an individual at a particular tier then depends on benefits in all tiers that the individual could eventually end up, in general all elements of B. The methodological contribution of the paper is to show that the problem of finding the optimal benefit structure can be formulated in such a way that all incentive constraints are linear and parallel or independent of each other. It is then immediate to check which constraints are binding and optimal benefits can easily be characterized, both graphically and analytically. We will provide analytical expressions for the (constrained) optimal benefit schedule and, in particular, focus on the issue of whether benefits should increase or decrease over time. Our model easily lends itself to allowing multiple incentive problems and adding, for example, a moral hazard problem in job-retention effort as in Wang and Williamson (1996) should be straightforward. There exists an extensive literature on the optimal design of social insurance schemes under moral hazard. In one line of research, the question is how to optimally set a time invariant benefit level in a two state setting (e.,g., employment and unemployment) where an individually costly and unobserved action (job search) determines the transition probability from one of the states. A seminal contribution is Baily (1978), who uses a two period model to derive a formula for the optimal benefit level that only depends on three parameters: the degree of risk aversion, the consumption-smoothing benefit of UI, and the elasticity of unemployment duration to the benefit rate. Chetty (2006) shows that a generalized formula, including also the degree of prudence, is applicable in a surprisingly more general and dynamic setting, provided the focus is on time invariant benefits and two states. Given these results, empirical analysis on the sensitivity of consumption and unemployment duration to the benefit level, like for example David Card and Weber (2007), can then be used to “calibrate” the formula for the optimal benefit level and no direct evidence on, for example, the ability the individual has to self-insure, is needed. The generality of this approach of course comes at a cost—it is not enough to consider the change in consumption as unemployment is entered and how this is affected by changes in UI. Rather, it is the sensitivity of lifetime average total consumption to UI benefits that must be estimated. However, Shimer and Werning(2007) recently show that the reservation wage of individuals can be used as an alternative summary measure of worker utility. Arguably, this is easier to measure since it can be observed without access to panel data. Our work is closely related to this line of research in the sense that a key variable of focus is how much the individual decides to change her consumption when her labor market status changes. In principle, the previous analysis could allow for a moving choice that affects the duration of unemployment. We add to this by allowing heterogeneity among unemployed and show that this has implications for the optimal time profile of benefits. Empirical work on how the time profile of benefits affects unemployment duration and consumption should therefore be valuable. By allowing time varying benefits and our work is related to the line of papers following the influential papers by Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997). Here, the focus is on the optimal time profile of benefits chosen by a planner who can control consumption of the individual but not her search intensity. A key result here is that the optimal trade-off between insurance and incentive provision implies that consumption should fall over time as long as the individual remains unemployed. A standard interpretation of this result is that unemployment benefits should fall over time. However, this interpretation relies on the assumption that the insurer can perfectly control individual consumption by determining the benefit levels. In a recent line of papers (e.g., Pavoni, 2006, Arpad and Pavoni, 2005, Werning, 2002 and Shimer and Werning, 2005), the individual is allowed to make her own consumption decisions by allowing access to a perfect market for saving and borrowing. Then, as assets are run down during an unemployment spell, consumption falls over time by choice of the individual also with constant benefits. In fact, under constant absolute risk-aversion, there is no need to affect the rate of decline of consumption and a constant benefit level is optimal if the moral hazard problem is stationary (see Werning, 2002 and Shimer and Werning, 2005). The fact that our model easily and analytically can handle several incentive constraints hinges on the absence of wealth effects, which is due to some key assumptions. First, we follow the papers mentioned above by assuming access to a safe bond. Second, we assume constant absolute risk-aversion.1 The absence of wealth effects on incentives implies that we can induce people to voluntarily move or retrain, as well as to search for a job, using simple benefit schemes with a limited number of benefit levels that are independent of the full employment history of the agent. With decreasing absolute risk aversion or financial frictions, it could be the case that unemployed individuals do not retrain or move until they have run down their assets to some critical level and then decide to move. A similar case could arise if unemployed individuals learn about their prospects over time, starting their unemployment spell with optimistic beliefs and then turn more pessimistic. Clearly, this would not only complicate the analysis but could also alter our results regarding the optimal time-profile of benefits. Regarding our assumption of access to a market for borrowing and saving, we want to stress that there is empirical evidence indicating that precautionary saving is used to self-insure against unemployment risk. Using PSID, Gruber (1997) finds that, in the absence of UI, consumption falls by only 22% when an individual becomes unemployed, showing that individuals are able to smooth consumption also when there is no UI. Similarly, Engen and Gruber (2001) show that UI crowds out financial savings, indicating that households use financial markets to self-insure against unemployment risk.2 It is nevertheless clear that neither of the key assumptions is perfectly realistic and a quantitative analysis might require wealth effects, either because of non-constant absolute risk aversion and/or because of variations in the bite of liquidity constraints. However, we hope that illustrating a mechanism not previously explored in the literature might provide guidance for future quantitative work. We return to this issue in the conclusion. The paper is structured in the following way. The model is presented in Section 2, where the relevant value functions are derived in Section 2.1. The formal optimality problem is defined and solved in Section 3. In Section 3.1, we show the methodology in the simplest case with a constant benefit level and in Section 3.2, we allow time varying benefits. In Section 4, the optimal insurance scheme is characterized under different assumptions on search and moving costs. Section 5 relaxes some of the assumptions in the previous section and Section 6 concludes. Some proofs are given in the main text, others in the appendix and the remaining ones are available from the authors upon request.

In this paper, we have argued that there are reasons to believe that an important informational problem associated with unemployment insurance has been neglected in the previous literature. This problem stems from the fact that unemployed individuals sometimes have the option of making an investment that could increase their chances of finding a job. Examples of such investments are retraining and moving to another location. Since it is reasonable to assume that it is difficult or impossible to observe who has these options, the UI system should give incentives for people to take advantage of any reasonable option to increase their labor market prospects. If such options arrive at a reasonably high rate or exist already at the onset of the unemployment spell, this can have important qualitative implications for how the UI system should be designed. By deriving graphical and analytical closed-form solutions, we have shown how a simple UI system should be constructed to provide sufficient incentives to move or retrain without excessively reducing the insurance value of the unemployment benefits. Unless the hiring rates of long-term unemployed are very low and search costs too high, this requires an initial period of relatively low benefits. The intuition here is straightforward, by setting initial benefits at a low level, individuals with good opportunities to get new jobs are induced to exploit these and quickly leave the pool of unemployed. On the other hand, individuals with worse opportunities value insurance against long-term unemployment more than insurance against short-term unemployment. The value of the UI system can therefore be maintained by providing more generous benefits for long-term unemployment, calling for an upward sloping benefit profile. We have assumed that individuals can self-insure via unobservable savings, i.e., that individual consumption is unobservable or, for some other reason, non-contractable. If, in contrast, the insurer has control over the consumption of the individual, it is well known that a downward sloping path of consumption (and benefits, if the individual has no other income) provides the best trade-off between good search incentives and insurance. In a working paper version of this paper (Hassler and Rodríguez Mora, 2003), we analyze the case when individuals have no access to a market for saving and borrowing. In this case, we show that it is optimal to have constant benefits if the moving constraint binds while search constraints are slack. The reason for this is that there is no point in punishing unsuccessful search by reducing consumption as the unemployment spell continues if the search constraints are slack anyhow. With savings, the downward sloping consumption profile is achieved voluntarily as individuals deplete their assets. This is true in general but under CARA preferences, the downward slope of consumption that is optimal with search moral hazard is achieved with constant benefits. Under the perhaps more realistic assumption of constant relative risk-aversion, the analysis is greatly complicated by the fact that search incentives would depend on asset holdings. Shimer and Werning(2007) show that the behavior of an unemployed individual with CRRA preferences is similar to that of an individual with CARA preference if they have the same riskaversion and access to a riskless bond. However, with CRRA preferences, the degree of riskaversion changes with individual asset holdings. Therefore, incentive compatibility would not in general be consistent with benefits that are independent of individual asset holdings. However, the intuition for the results in this paper does not appear to be related to such effects. In our model, the preference for increasing benefits arises from the need to separate between the two types of workers and the fact that individual assets are depleted during unemployment (which is true for general specifications of utility, in particular for CRRA, as shown in e.g., Hassler and Rodríguez Mora, 1999). Both mechanisms are likely to be present also under more general preference specifications. However, since search incentives in general depend on asset holdings and the duration of unemployment is likely to be correlated with the individual's asset holdings, unobservability of the latter may have consequences for optimal benefit time profiles. For example, if the search incentives are reinforced as wealth is depleted and individuals with long unemployment spells are likely to have less wealth, this might strengthen the case for increasing benefits. On the other hand, with wealth effects present, it could also be the case that individuals with opportunities to move do not do so until their assets are run down sufficiently. An initial period of low benefits may then not be sufficient to separate individuals who can move from those who cannot and upward sloping benefits could be suboptimal. We have argued that under some circumstances, upward sloping benefits could be optimal, challenging the conventional wisdom that benefits should fall over the unemployment spell. We finally want to provide some word of caution. Neither the assumptions we have used nor the ones used to derive the conventional wisdom are perfectly realistic. The incentive problems operating during an unemployment spell are specific to the individual, time varying and wealth dependent. The moving costs is not a constant, but rather specific to the particular moving opportunity and finding a moving opportunity may require costly search, blurring the difference between the two types of incentive constraints analyzed in this paper. Furthermore, the market for borrowing and saving is neither perfect nor non-existent and CRRA is probably a better description of preferences than CARA, implying wealth effects on incentives. All this implies that incentive constraints are heterogeneous, partly determined by unobserved individual characteristics and state variables. Therefore, a quantitative analysis must recognize the possibility that some incentive constraints should optimally be violated. The social cost of this depends on the number of people for whom the constraint is violated. Finding the optimal benefit system then requires information on the distribution of the unobserved individual characteristics and how the evolution of partly endogenous state variables depend on the characteristics of the UI-system. This is left to future research.