A Simple and Efficient Estimation Method for Models with Nonignorable Missing Data

摘要

This paper proposes a simple and efficient estimation procedure for the modelwith non-ignorable missing data studied by Morikawa and Kim (2016). Theirsemiparametrically efficient estimator requires explicit nonparametricestimation and so suffers from the curse of dimensionality and requires abandwidth selection. We propose an estimation method based on the GeneralizedMethod of Moments (hereafter GMM). Our method is consistent and asymptoticallynormal regardless of the number of moments chosen. Furthermore, if the numberof moments increases appropriately our estimator can achieve the semiparametricefficiency bound derived in Morikawa and Kim (2016), but under weakerregularity conditions. Moreover, our proposed estimator and its consistentcovariance matrix are easily computed with the widely available GMM package. Wepropose two data-based methods for selection of the number of moments. A smallscale simulation study reveals that the proposed estimation indeed out-performsthe existing alternatives in finite samples.