Identifiability and estimation of two-sample data with nonignorable missing response.

Nonignorable missing data presents a great challenge in statistical applications, since the observed likelihood is not identifiable without any further restrictions. In this paper, we make inference about the differences between the corresponding parameters of two independent samples with nonignorable missing renponse. To address the identifiability issue, we consider a parametric propensity model and utilize group label information as an instrument. Two-step generalized method of moments is applied to estimate the parameters of the propensity based on the instrumental estimating equations, and then population parameters are estimated based on the inverse probability weighting with the estimated propensity. The asymptotic properties of the resulting estimators are established. The finite-sample performance of the differences for the population means, distribution functions and quantiles is studied through simulations, and an application to Korean Labor and Income Panel Study (KLIPS) data set is also presented. [ABSTRACT FROM AUTHOR]