Markov-Chain Approximations for Life-Cycle Models

Non-stationary income processes are standard in quantitative life-cycle models. Their approximation is key for numerical implementations. We develop methods to apply standard discretization algorithms within non-stationary life-cycle settings and assess their relative performance. In one extension we also examine income processes in which shocks to earnings are modeled as draws from a mixture of Normal distributions and describe simple and tractable approaches to numerically model non-Normal earnings distributions.

With
Giulio Fella, Jutong Pan

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 and 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 life-cycle,income-fluctuation problem with a non-stationary income process. We also examine the case in which 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.

DRAFT (PDF)

Citation

@techreport{fgp2018approximations,
  title={Markov-Chain Approximations for Life-Cycle Models},
  author={Fella, Giulio and Gallipoli, Giovanni and Pan, Jutong},
  year={2018},
  note = {Working Paper},
  institution={UBC, Vancouver School of Economics}
}