Sparse Dynamic Programming and Aggregate Fluctuations

This paper proposes a way to model boundedly rational dynamic programming in a parsimonious and tractable way. It first illustrates the approach via a boundedly rational version of the consumption-saving life cycle problem. The consumer can pay attention to the variables such as the interest rate and his income, or replace them, in his mental model, by their average values –this way using a "sparse" model of the world. Endogenously, the consumer pays little attention to the interest rate but pays keen attention to his income. This helps resolve some extant puzzles in consumption behavior, especially the tenuous link between interest rates and consumption growth. The model is then applied to a Merton-style portfolio choice problem. This problem is usually quite complex and formidable. We see how a sparse agent will handle the problem, and will have a simpler solution to it: the agent may for instance pay limited or no attention to the varying equity premium and hedging demand terms. Finally, the paper studies the impact of bounded rationality on macroeconomic outcomes, in a prototypical DSGE model with one variable, capital. We find that in general equilibrium, bounded rationality leads to more persistent shocks, and to larger aggregate fluctuations.