Estimating and Testing for Smooth Structural Changes in Moment Condition Models

Numerous studies have been devoted to estimating and testing for moment condition models. Most of the existing studies assume that structural parameters are either fixed or changed abruptly over time. This study considers estimation of and testing for smooth structural changes in moment condition models where the data generating process is assumed to be locally stationary. A novel local generalized method of moment estimator and its boundary-corrected counterpart are proposed to estimate the smoothly changing structural parameters. Consistency and asymptotic normality are established, and an optimal weighting matrix and its consistent estimator are obtained. In particular, a consistent nonparametric test is proposed to check both smooth changes and abrupt breaks in structural parameters. The test is asymptotically pivotal and does not require prior information about the alternative. A Monte Carlo study is performed to illustrate the merits of the proposed test. In an empirical application, we document the time-varying features of the risk aversion parameter in an asset pricing model, which are consistent with business cycles and financial crisis.