Markov-Chain Approximations for Life-Cycle Models

Abstract

Non-stationary income processes are standard in quantitative life-cycle models, prompted by the observation that within-cohort income inequality increases with age. This paper generalizes Tauchen (1986), Adda-Cooper (2003), and Rouwenhorst’s (1995) discretization methods to non-stationary AR(1) processes. We evaluate the performance of these methods in the context of a canonical finite-horizon, income-fluctuation problem with a non-stationary income process. As a special case, we also examine relative performance when innovations to the persistent component of earnings are modeled as draws from a mixture of Normal distributions. We find that the generalized Rouwenhorst’s method performs consistently better than the others even with a relatively small number of states.