EFFICIENT UNEMPLOYMENT INSURANCE: A Model of Job Search 7

Worker Heterogeneity

We have simplified our analysis by assuming that all workers have the same level of assets, the same utility function, and receive the same level unemployment benefits. Our results generalize to an environment in which workers differ with respect to all of these features. In particular, suppose that there are 5 = 1,2,.. .,5 types of workers, where type s has utility function ua, after-tax asset level As, and unemployment benefit zs. Let U now be a vector in R5, and assume, for simplicity, that zs < z for all s. Then:
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This proposition states that any triple {А*,го*, g*} that is part of an equilibrium maximizes the utility of one group of workers, subject to firms making zero profits. In other words, the market endogenously segments into S different submarkets, each catering to the preferences of one type of workers, and receiving applications only from that type. The proof of the proposition is analogous to Proposition 1, and is omitted other.

We can repeat the analysis of Proposition 2 for each submarket. If workers of type s axe more risk-averse or receive less UI, their submarket will create lower wage jobs with shorter queues and less investment, but the rest of the submarkets will be unaffected. This result crucially depends on the assumption that workers observe all posted wages, and so can choose to ignore the presence of other submarkets.

This analysis predicts that a group of workers with higher UI will apply for higher wage jobs with longer queues and suffer longer unemployment spells. This prediction is verified empirically (Ehrenberg and Oaxaca, 1976; Katz and Meyer, 1990). This analysis also shows that (except in the case of constant absolute risk aversion), workers’ asset levels will systematically affect their search behavior, and will alter the impact of UI. This last prediction distinguishes the model from one in which UI is simply a subsidy to search by risk-neutral workers.