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This paper employs a dynamic general equilibrium model to design and evaluate long-term unemployment insurance plans (plans that depend on workers' unemployment history) in economies with and without hidden savings. We show that optimal benefit schemes and welfare implications differ considerably in these two economies. Switching to long-term plans can improve welfare significantly in the absence of hidden savings. However, welfare gains are much lower when we consider hidden savings. Therefore, we argue that switching to long-term plans should not be a primary concern from a policy point of view. Journal of Economic Literature Classification Numbers: J65, D82.

An important adverse effect of unemployment insurance is the disincen- tive to find/maintain a job. 2 Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997) suggest that a possible remedy is switching to long-term contracts where benefit payments depend on workers’ unemployment his- tory. In particular, Hopenhayn and Nicolini (1997) show, by simulating a search-theoretic model, that switching from the current U.S. unemployment insurance system to the optimal one may reduce the cost of the system by 30%. The optimal plan they propose provides a declining benefit path to create intertemporal incentives. It punishes workers (agents) for con- tinued unemployment and creates incentives to find a job. A maintained assumption in these papers is that consumer/workers cannot save or, alter- natively, that any savings they undertake are perfectly monitored and thus completely controlled by the insurance provider. The main contribution of our paper is to study long-term unemployment insurance plans by relaxing the assumption that agents’ savings can be perfectly monitored. Thus, we consider “hidden savings.” We believe that introducing hidden savings is important for at least two reasons. First, it is not realistic that perfect mon- itoring is available at zero cost. Second, and more important, if savings can- not be monitored, the incentives of consumer/workers change significantly. Suppose that we apply the unemployment insurance system suggested by Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997) to our econ- omy where agents have hidden savings. Then the agents would be tempted to cheat: they would try to get a higher net present value transfer from the unemployment insurance system and would deal with any implied increase in risk by self-insuring using their hidden savings. Thus, in an economy with hidden savings—where agents can self-insure—the government-provided insurance may be less important and may change in nature. We find that indeed it is important to consider hidden savings in the analysis. The nature of the optimal unemployment insurance plans dif- fers significantly from the ones suggested by Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997): the benefit path is not necessarily declin- ing. We also find that the role of history dependence of unemployment insurance plans is not as important quantitatively as the earlier studies sug- gest. Our analysis, in fact, also suggests that unemployment plans that are designed ignoring agents’ ability to save secretly could cause an increase in unemployment and be harmful to the economy.The model we study is different from the models analyzed in the cited papers in several aspects. First of all, we do not look at fully optimal dynamic contracts since they are difficult to characterize when agents have hidden savings. However, we consider a broad set of history-dependent unemploy- ment insurance plans. Second, we focus on the moral hazard problem based on unobservability of job refusals as opposed to the job-search effort as in Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997). Third, we insist on budget balance of the unemployment insurance system. That is, there is a feedback of the benefit part of the system to the tax on the labor income of employed agents. Therefore, we choose a dynamic general equi- librium model for our analysis. We study an extension of the model with incomplete markets analyzed in Hansen and Imrohoroglu (1992). To understand the role of hidden savings, we also consider a variant of our model in which we shut down the savings channel. The economy consists of ex-ante identical agents who derive utility from consumption and leisure. Agents are subject to unemployment risk: at the beginning of each period, they are offered an employment opportu- nity with a certain probability. They can partially insure themselves against the possibility of income loss by saving through non-interest-bearing assets. Agents also have access to an unemployment insurance system financed by the government through proportional taxes. The system distinguishes agents according to their unemployment history: agents are offered differ- ent benefit levels, depending on how long they have been unemployed. We introduce moral hazard to the model by assuming that government mon- itoring of insurance claimants is imperfect; i.e., the government monitors only a certain fraction of the claimants. Therefore, agents who are not qualified (who refuse job opportunities) can collect benefits with a positive probability. We refer to imperfect government monitoring as moral hazard, because ineligible agents are more likely to take advantage of the unem- ployment insurance system when the government monitors a small fraction of claimants. In this framework, our objective is to compute the unemployment insur- ance (UI) plans that maximize the steady-state equilibrium welfare. One should consider all possible employment histories to find “the” optimal UI plan in the context of dynamic contracting literature. However, due to the computational complexity of this problem, we restrict our attention to a certain degree of history dependence. The unemployment insurance plans that we consider focus only on the most recent unemployment spell and distinguish agents with respect to the number of periods they have been unemployed consecutively up to “ T ” periods. We allow the benefit levels to be flexible for T periods and thereafter the benefit level is held constant. We increase T up to a point beyond which increasing T does not improve wel- fare significantly. We refer to the plan that maximizes steady-state average utility as the optimal UI plan. We use a variant of the evolutionary algo- rithms suggested by Gomme (1997) to compute the optimal UI plans. This algorithm reduces computation time drastically and makes it possible to solve otherwise infeasible optimization problems. In this study, we analyze unemployment insurance in two different eco- nomic environments. In the first economy, agents have hidden savings and in the second, they do not. Our analysis suggests that optimal benefit paths differ remarkably in these two economies. In general, the optimal bene- fit levels are significantly higher and the optimal unemployment insurance plan implies a declining benefit path when there are no savings. However, when agents have hidden savings, the optimal benefit path is not necessar- ily declining. Depending on the degree of moral hazard, the benefit path can be nonmonotonic or even increasing. Yet, the optimal unemployment insurance plan implies a declining consumption path as Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997) argue. We also show that wel- fare implications of long-term plans are different in these two economies. Our experiments suggest that long-term plans can improve welfare sig- nificantly in economies without savings. For example, the welfare gain of switching to long-term plans is 2.0133% of consumption. 3 Yet, the welfare gains are much lower if we consider savings in the analysis. The welfare gain varies between 0.0325% and 0.1840%, depending on the degree of moral hazard. An important result of our analysis is that the welfare gains of switch- ing to unemployment insurance plans that depend on the unemployment history are quite small when agents have hidden savings. Even if the govern- ment can monitor a large fraction of unemployment claimants, the welfare gains are as low as 0.06%. We show that our conclusion is not affected by plausible variations in parameters. Given our results and the fact that long-term unemployment insurance plans are hard to administer in prac- tice, we argue that switching to long-term plans perhaps should not be a primary concern from a policy point of view. Finally, our findings reveal that unemployment insurance plans, designed ignoring agents’ ability to save privately, could be harmful to the econ- omy. When we apply the optimal plan from the economy without savings to our economy with hidden savings, a quite drastic increase in unemploy- ment results. This is because this plan critically uses history dependence; in particular, it applies high benefit rates in the first few periods upon job loss. Thus, any recently separated workers with access to hidden sav- ings would choose to turn down new job offers, collect the high benefit, and use hidden savings to smooth consumption. This example also reveals the importance of taking into account the general equilibrium effects in the design of unemployment insurance plans: the lower the employment rate is, the higher the tax rate on labor income of the employed should be in order to balance the budget of the unemployment insurance system. This feedback—which indeed is present in real life—exacerbates the neg- ative effects of improperly designed unemployment insurance systems on the economy. Hansen and Imrohoroglu (1992) is the first study that analyzes the wel- fare effects of the unemployment insurance system in a general equilibrium environment with moral hazard and savings. They concentrate on constant benefit schemes and argue that it is almost impossible to insure agents for high degrees of moral hazard. We generalize their result by showing that more complicated unemployment insurance plans do not provide much bet- ter insurance when agents have hidden savings. Long-term unemployment insurance plans in environments where agents have hidden savings are also studied by Wang and Williamson (1999). They evaluate alternative unemployment insurance schemes in a dynamic economy with unobservable job-search and job-retention effort. Their main concern is to study the welfare implications of long-term plans and experience rating. They, too, report small welfare gains from switching to long-term plans. It is noteworthy that they reach a similar conclusion to ours by using a different framework. However, they do not specifically ana- lyze how savings affect the nature and the role of long-term unemployment insurance plans. The plan of the paper is as follows. In Section 2, we describe the econ- omy. Section 3 discusses the calibration. Section 4 explains the algorithm used in the numerical solution. Section 5 discusses calculation of welfare gains. In Section 6, we present our results. Section 7 provides an example regarding the importance of hidden savings. Section 8 presents our conclu-sions.

We have studied short-term and long-term unemployment insurance plans in economies with and without savings. We find that welfare implica- tions change notably when we consider savings. Although long-term plans can improve welfare significantly in economies without savings, our experi- ments suggest that welfare gains are much lower when hidden savings are taken into account. Potential welfare gains of long-term plans depend on the degree of moral hazard. However, for a wide range of moral hazard values, we find that the welfare gains of long-term unemployment insurance plans are close to 0. Our conclusion is not affected by plausible variations in parameters, including the coefficient of relative risk aversion and the weight of leisure in the utility function. We recognize that our results are not strictly comparable to those of the dynamic contracting literature since our plans do not keep track of the entire unemployment history of workers. One might argue that contracts that depend only on the most recent unemployment spell and distinguish agents up to four periods can be considered short-term contracts. However, we have shown that these contracts, in fact, improve welfare considerably in economies without savings. This result suggests that the small welfare gains we obtain with hidden savings are not a consequence of limited his- tory dependence but rather a consequence of hidden savings. Given these results, as well as the fact that long-term unemployment insurance plans are hard to administer in practice, switching to long-term plans may not be a desirable policy.