Estimating and Testing for Smooth Structural Changes in Moment Condition Models

Numerous studies have been devoted to estimating and testing of moment condition models. Most of the current literature assumes that structural parameters are either fixed or changed abruptly. This paper considers the estimating and testing for smooth structural changes in moment condition models where the underlying data generating proces is assumed to be locally stationary. A local generalized method of moment (LGMM) and its boundary corrected counterpart are proposed to estimate the smoothly changing structural parameters. The consistency and asymptotic normality are established. An optimal weighting matrix and its estimator are obtained. In particular, a nonparametric test is proposed to check both smooth changes and abrupt breaks of the structural parameters. The proposed nonparametric test statistic is shown to follow a standard normal distribution asymptotically. A Monte Carlo study illustrates the merits of the proposed test. In an empirical application, we document the time-varying property of the risk aversion parameter in an asset pricing model