Unemployment Insurance in an Economy with a Hidden Labor Market

This paper considers the problem of optimal unemployment insurance in a moral hazard framework. Unlike existing literature, unemployed workers can secretly participate in a hidden labor market; as a consequence, an endogenous lower bound for promised utility preventing "immiserization" arises. Moreover, the presence of a hidden labor market makes possible an extra deviation and therefore hardens the provision of incentives. Under linear cost of effort, we show that the optimal contract prescribes no participation in the hidden labor market and a decreasing sequence of unemployment payments until the lower bound for promised utility is reached. At that moment, participation jumps and unemployment payments drop down to zero. For the case of non-linear effort cost we calibrate the model to Spain. As in the linear cost of effort, this exercise reproduces no participation and decreasing payments during the initial phase of unemployment. After around three years of unemployment, the contract prescribes a jump in participation and an abrupt decline in unemployment payments. To the best of our knowledge, this is the first paper justifying an abrupt drop in unemployment payments. In addition, the quantitative analysis suggests that in an environment in which agents differ in separation rate, the hidden labor market reinforces the benefits from a type-dependent unemployment system.