Analysis of panel data with informative missing responses

Missing responses is a common problem existing in panel data collection. In some studies, one can argue that the missingness does not depend on unobserved responses given all observed information. However, in many other studies, the missing pattern is more likely to be dependent on the unobserved responses. When this dependence is indirect through some panel level random effects, it is called ``informative missingness''. Some parametric and semi-parametric estimation methods have been proposed in the literature for informative missing responses, where the estimation processes are mainly likelihood-based. In this thesis work, we proposed a semi-parametric method to solve this estimation problem. Because no specific distribution assumption is needed in our method, this method can be easily employed in practice without worrying about model mis-specification and struggling with maximization of complicated likelihoods. The estimation process contains two steps as we partition the parameters into two parts based on their relationship to the random effects. Parameters not related to random effects are estimated first, with the introduction of a linear transformation. In the second stage, these parameters are replaced by their estimates, and the remaining parameters can be estimated. Grouping of panels may be necessary if some panels do not have enough observation. The resulting estimators are proved to be unbiased and asymptotically normal. Simulation studies comparing our estimator to some other existing estimators are conducted, which shows advantage of our methods under certain informative missingness setting. This proposed method is applied to a real data examples: the Health and Retirement Study.