Estimation and inference in models with multiple behavioural equilibria

TL;DR

This paper introduces estimation and inference techniques for macroeconomic models with multiple equilibria, using constant-gain learning and addressing complex convergence behaviors.

Contribution

It develops new methods for consistent estimation and inference in models with multiple equilibria, including confidence bands and handling mixed convergence rates.

Findings

Methods perform well in finite samples

Confidence bands effectively capture equilibrium uncertainty

Monte Carlo simulations validate the approach

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.