This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the ﬁrst step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identiﬁcation tests for the second step GMM that properly reflect the ﬁrst-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the ﬁrst step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.
Chen, Xiaohong and Liao, Zhipeng, "Sieve Semiparametric Two-Step GMM under Weak Dependence" (2015). Cowles Foundation Discussion Papers. 2449.