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A simple and efficient estimation method for models with nonignorable missing data

Authors: Chunrong Ai , Oliver Linton and Zheng Zhang
Date: 10 January 2018
Type: cemmap Working Paper, CWP02/18
DOI: 10.1920/wp.cem.2018.0218

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 non-parametric 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 fi nite samples.

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