Self-insurance vs. self-financing: A welfare analysis of the persistence of shocks

We study the welfare cost of market incompleteness in a generalized Bewley model where idiosyncratic risk takes the form of entrepreneurial productivity shocks. Market incompleteness in our framework has two dimensions. First, in the Bewley tradition, only a limited set of instruments for consumption smoothing is available. Second, entrepreneurs' capital rental is subject to collateral constraints. As is well known, it is harder to self-insure against more persistent shocks, and the welfare cost of missing consumption insurance increases with shock persistence. On the other hand, with collateral constraints, an increase in shock persistence leads to better allocation of production factors through entrepreneurs' self-financing, and the welfare cost of imperfect capital rental markets decreases with shock persistence. The overall welfare cost of market incompleteness can be increasing, decreasing, or even non-monotone in shock persistence, depending on the relative strengths of its two components-the cost of missing insurance and the cost of imperfect capital markets.