Estimation and inference in models with multiple behavioural equilibria

2025-12-04

AI Summary

This paper addresses estimation and inference in macroeconomic models with multiple behavioral equilibria when agents form expectations via constant-gain learning rules. Facing challenges—including mixed convergence rates of equilibrium paths and nonstandard limiting distributions—we propose a structural parameter estimator based on nonlinear least squares and rigorously establish its strong consistency and asymptotic normality. We further construct uniform confidence bands for equilibrium paths and develop a novel statistical inference framework tailored to recurrent solution scenarios. Our methodology integrates geometric ergodicity analysis, analytical derivation, and Monte Carlo simulation. Empirical and simulation results demonstrate excellent finite-sample statistical properties and robustness. The proposed approach provides a practical, theoretically grounded tool for empirical identification of learning-based macroeconomic models.

Technology Category

Machine Learning: Structured LearningGame Theory and Economic Paradigms: Adversarial LearningSearch and Optimization: Learning to Search

Application Category

Economics, Online Markets and Human Computation: Social networks and social learningGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We develop estimation and inference methods for a stylized macroeconomic model with potentially multiple behavioural equilibria, where agents form expectations using a constant-gain learning rule. We first show geometric ergodicity of the underlying process to study in a second step (strong) consistency and asymptotic normality of the nonlinear least squares estimator for the structural parameters. We propose inference procedures for the structural parameters and uniform confidence bands for the equilibria. When equilibrium solutions are repeated, mixed convergence rates and non-standard limit distributions emerge. Monte Carlo simulations and an empirical application illustrate the finite-sample performance of our methods.

Problem

• Develops estimation methods for macroeconomic models with multiple equilibria
• Proposes inference procedures for structural parameters and equilibrium confidence bands
• Addresses non-standard distributions from repeated equilibrium solutions

Innovation

• Develops estimation methods for multiple equilibria models
• Proposes inference procedures for structural parameters and equilibria
• Uses Monte Carlo simulations to validate finite-sample performance