Estimation and Inference in Adaptive Learning Models with Slowly Decreasing Gains
Alexander Mayer · EUR Research Repository (Erasmus University Rotterdam) · 2022
An asymptotic theory for estimation and inference in adaptive learning models with strong mixing regressors and martingale difference innovations is developed. The maintained polynomial gain specification provides a unified framework which permits slow convergence of agents' beliefs and contains recursive least squares as a prominent special case. Reminiscent of the classical literature on co-integration, an asymptotic equivalence between two approaches to estimation of long-run equilibrium and short-run dynamics is established. Notwithstanding potential threats to inference arising from non-standard convergence rates and a singular variance-covariance matrix, hypotheses about single. as well as joint restrictions remain testable. Monte Carlo evidence confirms the accuracy of the asymptotic theory in finite samples.