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A Negishi Approach to Recursive Contracts

Econometrica 2022 90(6), 2821-2855 open access
In this paper, we argue that a large class of recursive contracts can be studied by means of the conventional Negishi method. A planner is responsible for prescribing current actions along with a distribution of future utility values to all agents, so as to maximize their weighted sum of utilities. Under convexity, the method yields the exact efficient frontier. Otherwise, the implementation requires contracts be contingent on publicly observable random signals uncorrelated to fundamentals. We also provide operational first‐order conditions for the characterization of efficient contracts. Finally, we compare extensively our approach with the dual method established in the literature.

Do not Blame Bellman: It Is Koopmans' Fault

Econometrica 2024 92(1), 111-140 open access
We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.