Recursive Equilibrium in Stochastic Overlapping - Generations Economies

THE OVERLAPPING-GENERATIONS (OLG) model, introduced first by Allais (1947) and Samuelson (1958), is one of the two major workhorses for macroeconomic and financial modeling of open-ended dynamic economies. Following developments in the study of two-period economies, the OLG model has been extended to cover stochastic economies with production and possibly incomplete financial markets. As is the consensus, in dynamic economies the general notion of competitive equilibrium à la Arrow and Debreu, which allows for prices and allocations to depend on histories of arbitrary length, is not always fully satisfactory for a variety of reasons. Among them, it is worth recalling at least the following two. First, from a theoretical viewpoint, when prices have unbounded memory, the notion of rational expectations equilibrium is strained because of the complexity of the forecasts and the expectations coordination involved. Second, the ensuing large dimensionality of the allocation and price sequences strains the ability of approximating solutions with present-day computers through truncations, rendering this general notion of equilibrium not very useful for applied, quantitative work, even in stationary Markovian environments. Duffie, Geanakoplos, Mas-Colell, and McLennan (1994) gave a general theorem for the existence of stationary Markov equilibria for OLG economies with associated ergodic measure.2 While these equilibria help bypass the two above-mentioned issues, they are still quite complicated as the state space contains a number of past and current endogenous variables. Therefore, the conceptual issue of whether it is possible to find simpler equilibria—stationary Markov equilibria based on a minimal state space—remains open.