Insurance in human capital models with limited enforcement

This paper develops a tractable human capital model with limited enforceability of contracts. The model economy is populated by a large number of long-lived, risk-averse households with homothetic preferences who can invest in risk-free physical capital and risky human capital. Households have access to a complete set of credit and insurance contracts, but their ability to use the available financial instruments is limited by the possibility of default (limited contract enforcement). We provide a convenient equilibrium characterization that facilitates the computation of recursive equilibria substantially. We use a calibrated version of the model with stochastically aging households divided into 9 age groups. Younger households have higher expected human capital returns than older households. According to the baseline calibration, for young households less than half of human capital risk is insured and the welfare losses due to the lack of insurance range from 3 percent of lifetime consumption (age 40) to 7 percent of lifetime consumption (age 23). Realistic variations in the model parameters have non-negligible effects on equilibrium insurance and welfare, but the result that young households are severely underinsured is robust to such variations.