On the Convergence Criterion in Three-Period-Lived Overlapping Generations Models

This article considers a three-period-lived pure exchange overlapping generations economy and clarifies the role of market complementarities in the scope for Kehoe & Levine's convergence criterion in order to reduce the size of continuation equilibria and establish uniqueness and determinacy. The argument is based upon the price-relatedness of dated goods and the way the law of demand, gross substitutability and the scope for asymmetric complementarities come into play when three periods lifespans are considered. The nature of these restriions is clarified in the context of stationary economies and the way it relates to equilibrium continuation and Kehoe & Levine's determinacy is made precise. A detailed articulation between complementarities and determinacy is finally provided in the context of Samuelson intermediate economies. The key role of dated goods spaced one period apart and entering in an additive way is emphasised in the determinacy result while the importance of asymetric complementarities between isolated goods spaced two periods apart is also pointed out.