Estimating and testing for smooth structural changes in moment condition models

Abstract

Numerous studies have been devoted to estimating and testing for moment condition models. Most existing studies assume that structural parameters are either fixed or change abruptly over time. This study considers estimating and testing for smooth structural changes in moment condition models where the data-generating process is locally stationary. A novel local generalized method of moments estimator and its boundary-corrected counterpart are proposed to estimate the smoothly changing parameters. Consistency and asymptotic normality are established, and an optimal weighting matrix and its consistent estimator are obtained. Moreover, we propose a consistent test to detect both smooth changes and abrupt breaks, as well as a consistent test for a parametric functional form of time-varying parameters. The tests are asymptotically pivotal and do not require prior information about the alternatives. Monte Carlo simulation studies show that the proposed estimators and tests have superior finite-sample performance. In an empirical application, we document the time-varying features of the risk aversion parameter in an asset pricing model, indicating that investors’ risk aversion is counter-cyclical.