The Trouble with Rational Expectations in Heterogeneous Agent Models: A Challenge for Macroeconomics

2025-08-28

AI Summary

Rational expectations in heterogeneous-agent macroeconomic models induce a “curse of dimensionality”: equilibrium price predictions require the entire cross-sectional distribution as a state variable, rendering the Bellman equation infinite-dimensional and computationally and cognitively intractable—severely limiting applicability to aggregate risk and nonlinear crisis analysis. Method: We systematically critique the theoretical and empirical deficiencies of rational expectations and propose an alternative expectation paradigm grounded in three criteria: computational feasibility, empirical consistency, and partial immunity to the Lucas critique. This framework integrates temporary equilibrium, survey-based expectations, least-squares learning, and reinforcement learning. We employ dynamic programming, master equation modeling, and behavioral–machine learning hybrid methods. Contribution/Results: We formally establish the fundamental infeasibility of rational expectations in high-dimensional heterogeneous environments and deliver the first analytically rigorous yet numerically tractable framework for heterogeneous-agent macroeconomics—opening a viable path for modeling systemic risk and crises.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Rational expectations in heterogeneous agent models are unrealistic
• It causes computational intractability due to infinite-dimensional state variables
• This limitation restricts macroeconomic analysis of crises and risk

Innovation

• Replace rational expectations with alternative approaches
• Address curse of dimensionality in heterogeneous models
• Explore tractable computational methods like reinforcement learning