Stochastic Overlapping Generations Models

In this chapter, we introduce both idiosyncratic and aggregate uncertainty into the OLG model. The methods that we will apply for the computation of these models are already familiar to you from previous chapters and will only be modified in order to allow for the more complex age structure of OLG models. In particular, we will apply the log-linearization from Chapter 2, the algorithm for the computation of the stationary distribution from Chapter 7, and the Algorithm by Krusell and Smith (1998) from Chapter 8 for the solution of the non-stochastic steady state and the business cycle dynamics of the OLG model.

In the following, we will first introduce individual stochastic productivity in the standard OLG model, and, then, aggregate stochastic productivity. In the first section, agents have different productivity types. Different from the traditional Auerbach-Kotlikoff models, agents are subject to idiosyncratic shocks and may change their productivity types randomly. As a consequence, the direct computation of policies and transition paths is no longer feasible. As an interesting application, we are trying to explain the empirically observed wealth heterogeneity. In the second section, we introduce aggregate uncertainty and study the business cycle dynamics of the OLG model.