Paper

Abstract: The thesis of this essay is that, in heterogeneous agent macroeconomics, the assumption of rational expectations about equilibrium prices is unrealistic and should be replaced. Rational expectations imply that decision makers forecast equilibrium prices like interest rates by forecasting cross-sectional distributions. This leads to an extreme version of the curse of dimensionality: dynamic programming problems in which the entire distribution is a state variable ("Master equation" a.k.a. "Monster equation"). Frontier computational methods struggle with these infinite-dimensional Bellman equations, making it implausible that real-world agents solve the associated decision problems. These difficulties also limit the applicability of the heterogeneous-agent approach to central questions in macroeconomics -- those involving aggregate risk and non-linearities such as  financial crises. This troublesome feature of the rational expectations assumption poses a challenge: what should replace it? I outline three criteria for alternative approaches:  (1) computational tractability, (2) consistency with empirical evidence, and (3) (some) immunity to the Lucas critique. I then discuss several promising directions, including temporary equilibrium approaches, incorporating survey expectations, least-squares learning, and reinforcement learning.

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