  This paper proposes a simple and efficient estimation procedure for the model
with non-ignorable missing data studied by Morikawa and Kim (2016). Their
semiparametrically efficient estimator requires explicit nonparametric
estimation and so suffers from the curse of dimensionality and requires a
bandwidth selection. We propose an estimation method based on the Generalized
Method of Moments (hereafter GMM). Our method is consistent and asymptotically
normal regardless of the number of moments chosen. Furthermore, if the number
of moments increases appropriately our estimator can achieve the semiparametric
efficiency bound derived in Morikawa and Kim (2016), but under weaker
regularity conditions. Moreover, our proposed estimator and its consistent
covariance matrix are easily computed with the widely available GMM package. We
propose two data-based methods for selection of the number of moments. A small
scale simulation study reveals that the proposed estimation indeed out-performs
the existing alternatives in finite samples.
