Optimal Allocations in Growth Models with Private Information

This paper considers a class of growth models with idiosyncratic human capital risk and private information about individual effort choices (moral hazard). Households are infinitely-lived and have preferences that allow for a time-additive expected utility representation with a one-period utility function that is additive over consumption and effort as well as logarithmic over consumption. Human capital investment is risky due to idiosyncratic shocks that follow a Markov process with transition probabilities that depend on effort choices. The production process is represented by an aggregate production function that uses physical capital and human capital as input factors. We show that constrained optimal allocations are simple in the sense that individual effort levels and individual consumption growth rates are history-independent. Further, constrained optimal allocations are the solutions to a recursive social planner problem that is simple in the sense that exogenous shocks are the only state variables. We also show that constrained optimal allocations can be decentralized as competitive equilibrium allocations of a market economy with a simple tax- and transfer scheme. Finally, it is always optimal to subsidize human capital investment in the market economy.