A Sparsity-Based Model of Bounded Rationality
52 Pages Posted: 8 Mar 2011 Last revised: 18 Mar 2012
Date Written: December 1, 2011
This paper proposes a model in which the decision maker builds an optimally simplified representation of the world which is "sparse," i.e., uses few parameters that are non-zero. Sparsity is formulated so as to lead to well-behaved, convex maximization problems. The agent's choice of a representation of the world features a quadratic proxy for the benefits of thinking and a linear formulation for the costs of thinking. The agent then picks the optimal action given his representation of the world. This model yields a tractable procedure, which embeds the traditional rational agent as a particular case, and can be used for analyzing classic economic questions under bounded rationality. For instance, the paper studies how boundedly rational agents select a consumption bundle while paying imperfect attention to prices, and how frictionless firms set prices optimally in response. This leads to a novel mechanism for price rigidity. The model is also used to examine boundedly rational intertemporal consumption problems and portfolio choice with imperfect understanding of returns.
Keywords: anchoring and adjustment, inattention, boundedly rational dynamic programming, price rigidity, hedging demand, sparse representations, L1 minimization, dictionaries
JEL Classification: D03, D8
Suggested Citation: Suggested Citation