Existence of Recursive Constrained Optima in the Heterogeneous Agent Neoclassical Growth Model
32 Pages Posted: 1 Aug 2017 Last revised: 31 Mar 2019
Date Written: November 15, 2017
Recently, macroeconomists have begun to study optimal policy in heterogeneous agent models with incomplete markets, or Aiyagari-Huggett models. A natural way to formulate an optimal policy problem in the model is by using a constrained planner (Davila , 2012), a planner who cannot complete markets but must improve welfare subject to agents' budget constraints. Despite the relevance of the constrained planner to understanding optimal macroeconomic policy, existence of constrained optima has not been verified. This paper proves existence of recursive constrained optima in the standard Aiyagari-Huggett model. A key challenge the proof overcomes is non-compactness of feasibility correspondences in the constrained planner's dynamic optimisation problem, brought on by the infinite dimensional structure of the Aiyagari-Huggett model.
Keywords: Neoclassical Growth Models, Incomplete Markets, Heterogeneous Agents, Constrained Planner, Dynamic Optimisation, Recursive Policies, Infinite Dimensional State-Space
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