A feature of our model is that despite the dynamic nature of the decisions, the analysis can be carried out in a static model. We prove this by fully analyzing a dynamic model of search with precautionary savings, and establishing that all the qualitative results are the same as in a static model. Since the equilibrium of the static model is equivalent to the solution of a constrained maximization problem and can be analyzed diagrammatically, it can easily be used for other applications.

Our model is closely related to the general equilibrium search literature (e.g. Diamond, 1982, Mortensen, 1982, Pissarides, 1990) and to the wage posting models of Peters (1991) and Montgomery (1991). We extend these papers by including risk-aversion and capital investments. In the process, we also generalize the efficiency results of Hosios (1990), Moen (1997), and Shimer (1996).

Perhaps the most surprising result of our analysis is that an appropriate level of UI restores the economy to the output maximizing allocation. We are aware of no other paper that has obtained this result, although others have also demonstrated that unemployment benefits may improve the allocation of resources in search models (Diamond, 1981; Acemoglu, 1997; Marimon and Zilibotti, 1997). However, because these papers assume risk-neutrality, UI is simply a subsidy to search.

In contrast, we work with a model in which UI reduces output when workers are risk-neutral, demonstrating that the role of UI is not to subsidize search, but to undo the distortions introduced by uninsured risks. Many of our results, including the comparative static results with respect to attitudes towards risk and the finding that UI is the right instrument to achieve productive efficiency, rely explicitly on our modeling of risk-aversion.

Our model also implies that the impact of UI on search behavior crucially depends on the wealth level of individuals, an empirical prediction that distinguishes our mechanism from models in which unemployment benefits are simply a subsidy to search. legitimate payday loans