Search and matching in the labor market without unemployment insurance

We study the differences between complete and incomplete markets against idiosyncratic shocks in a search model of the labor market in which the distribution of idiosyncratic uncertainty is determined endogenously. We show that in addition to the usual wealth effect at high levels of wealth, costly search introduces a wealth effect at low levels of wealth such that poor agents may find it optimal not to look for a job. We find conditions under which the long run equilibrium is such that there is no production with incomplete market. This equilibrium is at odds with the one obtained under the assumption of complete markets. It is also at odds with the equilibrium one would obtain under the usual assumption in the literature that idiosyncratic uncertainty is ``policy invariant" (or invariant to the market arrangement). In the second part of the paper we use numerical methods to obtain quantitative predictions of the model under a less stringent assumption such that the probability of finding a job may be positive even if search effort equals zero.