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

TL;DR

This paper introduces a GMM-based estimation method for models with non-ignorable missing data that is simpler, more efficient, and easier to compute than existing semiparametric estimators, achieving optimality under weaker conditions.

Contribution

The paper develops a GMM-based estimator for non-ignorable missing data models that is consistent, asymptotically normal, and can attain semiparametric efficiency with appropriate moments, simplifying computation.

Findings

The proposed GMM estimator outperforms existing methods in finite samples.

It achieves the semiparametric efficiency bound with increasing moments.

The estimator and covariance matrix are easily implemented using standard GMM software.

Abstract

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.