We develop a general equilibrium model of search and matching with risk-averse agents and incomplete insurance. Firms make irreversible investments and post wages. Workers optimally search among posted wages. There is an unavoidable risk for workers in this frictional economy as they may suffer unemployment. When workers are more risk-averse, wages and unemployment decrease, and firms invest less. The reason is that risk-averse workers wish to avoid the risk of unemployment, and in response, the labor market offers its own version of insurance, an equilibrium with higher employment but lower wages. In a frictional market, when the unemployment risk of workers is reduced, the vacancy risk of firms increases, implying lower utilization of their ex ante investment. Anticipating this, firms reduce their capital-labor ratio review.
UI encourages workers to apply to high wage jobs with high unemployment risk. The impact of UI on worker and firm behavior is driven by a form of moral hazard. Because the insurers cannot directly control workers’ actions, the increased utility of unemployment induces them to search for higher wage jobs. Firms respond by creating high wage jobs, with greater unemployment risk and greater capital-labor ratios, enabling workers to seek riskier opportunities.
Next, we investigate how risk-aversion and UI affect the level of output. We find that the decentralized equilibrium fails to maximize output as long as workers are risk-averse. This is because when opening low wage jobs with lower unemployment risk, firms are creating high vacancy risk for themselves, and so prefer to reduce their ex ante investments. This moves the economy away from “productive efficiency” and reduces net output. We show that there always exists a level of incomplete UI which ensures productive efficiency and maximizes output.
Hence the title of our paper: “Efficient” Unemployment Insurance. Although an allocation that maximizes output does not maximize ex ante utility, i.e. is not optimal, our results imply that moderate UI not only creates risk-sharing benefits, but also increases the level of output. As a result, an economy with optimal UI may have higher output than an economy with no UI.
This contrasts with existing results on optimal insurance which emphasize risk-sharing/output (equity/efficiency) tradeoffs. In our basic model, this contrast is sharp because conventional moral hazard is absent — UI does not reduce search effort. We show, however, that even when search effort is endogenous, UI continues to increase the level of output for plausible parameter values.