This paper addresses the question of when is unemployment insurance likely to be most valuable. Bailey (1978) showed that the extent of individual savings affects the value of UI. More recently, a literature has emerged that studies explicitly how well households can smooth consumption against transitory fluctuations in income, particularly those fluctuations that result from unemployment: there is limited value from UI providing risk,pooling across individuals if unemployment is transitory. However, we show in this paper that UI can still play a role in smoothing consumption when a lack of liquidity means it is costly for individuals to smooth consumption over time. In particular, the value of UI depends on how difficult it is for the unemployed to access credit markets and on the cost of saving. We provide empirical evidence that indicates substantial heterogeneity both in access to credit markets and in the cost of saving. The aim of this paper is to show the implications of these differences in the cost of self insurance for the effects of UI, and to provide a framework for showing how these differences can affect optimal replacement rates.
Differences in the cost of accumulating liquid assets arise for many reasons. First, some individuals are already accumulating illiquid saving for retirement, paying a retirement with, olding tax, and this makes liquid saving more costly. This highlights the interaction between different social insurance programs: forced illiquid saving for retirement may make the liqudity provided by UI more beneficial. Second, more generally, consumption needs differ over the life cycle, reflecting for example the presence of children, and this leads to differences in the cost of forgoing consumption in order to save. Third, individuals differ in their expected income growth, and particularly for those who expect the fastest growth, a need to save for precautionary reasons operates against the desire to smooth consumption. Finally, individuals may differ in their impatience or willingness to be exposed to consumption fluctuations. These sources of heterogeneity in the cost of saving, and also differences in individuals access to credit, will lead to differences in the amount of savings, and hence in the value of UI.
We explore these issues by constructing a three,period life,cycle consumption model, extending Bailey (1978). In our model, job loss is exogenous, the unemployed can invest in subsequent earnings capacity, insurance is partly from public unemployment insurance and partly from private savings. We introduce (i) a retirement savings motive and the possibility of forced retirement saving, (ii) variation in age at job loss, and (iii), the possibility of borrowing constraints. We use this framework to illustrate the connections between credit market imperfections, the cost of precautionary saving and the role of UI. We are able to show theoretically that in the presence of borrowing constraints, UI may have a benefit that derives from providing liquidity that enables smoothing consumption over time, in addition to the benefit in the Bailey model (the latter derives from smoothing over states and from pooling across individuals). Further, the liquidity provided by UI to credit constrained individuals allows those individuals to spend longer unemployed searching for a suitable job: durations could be inefficiently short in the absence of UI.
As one might expect, these liquidity benefits can raise the optimal replacement rate. On the other hand, when the retirement savings motive is strong and there is only limited illiquid retirement saving, self,insurance is less costly because retirement savings can also serve as a buffer stock to smooth consumption and the liqudity benefit of UI is less important. In our framework, we show that optimal replacement rates may vary substantially with the strength of the retirement saving motive, age at job loss and access to credit (from less than 20 percent to almost 60 percent). Lentz (2009) shows a similar result in an infinite horizon framework: optimal benefit rates are sensitive to the rate of return on savings , a high rate of return makes it attractive to hold wealth and hence self,insurance is not costly.
In the next section we present some emprical evidence on variation in asset holdings and in access to credit. This is indicative of the extent of self,insurance and the heterogeneity in the cost of self,insurance that motivates our analysis. In section III we develop our life,cycle framework. Section IV outlines the implications of our model for consumption smoothing, asset accumulation and duration of unemployment. Section V shows how optimal levels of unemployment benefit might vary with access to credit and the extent of other savings motives. Section VI concludes.
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