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Open AccessOA2025
The Trouble with Rational Expectations in Heterogeneous Agent Models: A Challenge for Macroeconomics
This essay argues that rational expectations about equilibrium prices in heterogeneous agent models leads to an extreme curse of dimensionality, making it implausible that real-world agents solve such problems. It proposes three criteria for alternative approaches and discusses promising directions including temporary equilibrium, survey expectations, least-squares learning, and reinforcement learning.
Benjamin Moll· Economic Journal· 2025· DOI 10.1093/ej/ueaf104
The core problem
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 (the 'Master equation' or '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?
Innovation
The essay employs a theoretical and computational critique of the rational expectations assumption in heterogeneous agent models. It analyzes the implications of rational expectations for the dimensionality of dynamic programming problems, specifically the emergence of infinite-dimensional Bellman equations where the cross-sectional distribution of agents serves as a state variable. The author evaluates the computational feasibility of solving such problems using frontier methods and assesses the limitations for addressing aggregate risk and non-linearities. The methodology includes a conceptual framework for evaluating alternative approaches based on three criteria: (1) computational tractability, (2) consistency with empirical evidence, and (3) (some) immunity to the Lucas critique. The essay then surveys and discusses several promising directions that meet these criteria.
Introduction
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 (the 'Master equation' or '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?
Why it matters
The essay proposes three criteria for alternative approaches to replace rational expectations: computational tractability, consistency with empirical evidence, and some immunity to the Lucas critique. It then discusses several promising directions that satisfy these criteria. These include temporary equilibrium approaches, which allow for non-market-clearing and adaptive behavior; incorporating survey expectations to capture real-world forecasting behavior; least-squares learning, where agents update their beliefs based on past data; and reinforcement learning, where agents learn optimal policies through trial and error. Each of these approaches offers a way to model expectations that is more computationally feasible and empirically grounded than rational expectations, while being less vulnerable to the Lucas critique. The essay concludes by highlighting the need for further research to develop and integrate these alternatives into heterogeneous agent macroeconomics.
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