On the convergence criterion in three-period lived overlapping generations models

This paper offers a novel perspective on Kehoe-Levine's convergence criterion for equilibrium determinacy in three-period overlapping generations (OLG) models. Departing from their primary focus on gross substitutability, our central contribution is demonstrating that equilibrium determinacy, even in Samuelson economies, can be achieved under market complementarities, provided the aggregate demand sensitivities to adjacent-period prices sum positively. Furthermore, we identify critical conditions where gross substitutability or complementarities between goods spaced two periods apart becomes pivotal for equilibrium determination. By elucidating the role of asymmetric complementarities, we significantly extend the understanding of equilibrium determinacy within the Kehoe-Levine framework, challenging the necessity of strict gross substitutability and offering a more nuanced view of dynamic stability in OLG models.