Abstract: This paper proposes a simple and efficient generalized method of moments(GMM) estimation for a model with non-ignorable missing data. In contrast to the existing the GMM estimation with a fixed number of moments, we allow the number of moments to grow with the sample size and use optimal weighting. Hence, our estimator is efficient, attaining the semiparametric efficiency bound derived in the literature. Existing semiparametric estimators estimate an efficient score. However, this approach is either locally efficient, or it suffers from the curse of dimensionality and the bandwidth selection problem. In contrast, our estimator does not suffer from these problems. Moreover, the proposed estimator and its consistent covariance matrix are easily computed using commercially available GMM packages. We propose two data-driven methods to select the number of moments. A small-scale simulation study reveals that the proposed estimator outperforms existing alternatives in finite samples.

Key words and phrases: Generalized method of moments, non-ignorable nonresponse, semiparametric efficiency.