An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse
An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse
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DOI：
10.5705/ss.2012.074
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发表时间：
2014-07
影响因子：
1.4
通讯作者：
Sheng Wang;J. Shao;Jae Kwang Kim
中科院分区：
文献类型：
--
作者：
Sheng Wang;J. Shao;Jae Kwang Kim
当研究变量 y 和协变量 x 的联合分布是非参数且以 y 和 x 为条件的无应答概率具有参数形式时，考虑基于不可忽略的无应答数据的估计。即使 y 和 x 的联合分布是参数化的，基于观测数据的可能性也可能无法识别。我们表明，可以通过利用无响应工具来克服这一困难，无响应工具是与 y 相关但与 y 和 x 条件下的无响应概率无关的辅助变量。在某些条件下，我们可以应用广义矩法（GMM）来获得无响应概率和 y 和 x 的非参数联合分布中的参数估计量。建立了 GMM 估计量的一致性和渐近正态性。还介绍了模拟结果以及对韩国劳工和收入小组调查数据集的应用。
Estimation based on data with nonignorable nonresponse is considered when the joint distribution of the study variable y and covariate x is nonpara- metric and the nonresponse probability conditional on y and x has a parametric form. The likelihood based on observed data may not be identifiable even when the joint distribution of y and x is parametric. We show that this difficulty can be overcome by utilizing a nonresponse instrument, an auxiliary variable related to y but not related to the nonresponse probability conditional on y and x. Under some conditions we can apply the generalized method of moments (GMM) to obtain es- timators of the parameters in the nonresponse probability and the nonparametric joint distribution of y and x. Consistency and asymptotic normality of GMM es- timators are established. Simulation results and an application to a data set from the Korean Labor and Income Panel Survey are also presented.