Human Capital Risk and Limited Commitment

This paper analyzes a general equilibrium model with limited commitment and production. There are a large number of infinitely-lived, risk-averse agents who invest in physical and human capital, and production exhibits constant-returns-to-scale with respect to these two input factors. Preferences allow for a time-additive expected utility representation with constant relative risk aversion. There is a government that can insure agents against idiosyncratic human capital risk subject to a sequential participation constraint. For a general Markov process over idiosyncratic and aggregate shocks, we show that simple recursive equilibria exist and provide a general characterization of these equilibria. In equilibrium, the participation constraint i) may bind for agents receiving a negative labor income (human capital) shock and ii) the participation constraint either binds for all wealth levels or does not bind at all. For a calibrated version of the model economy, human capital risk generates substantial consumption volatility and has significant welfare consequences.