This thesis develops several Generalized Method ofMoments (GMM) estimators for analysing Not Missing at Random (NMAR) data, which is commonly referred to as the self-selection problem in an economic context. We extend the semiparametric estimation procedures of Ramalho and Smith (2003) to include the case where the missing data mechanism (MDM) depends on both a continuous response variable and covariates. Within this framework, it is possible to avoid imposing any assumptions on the missing data mechanism. We also discuss the asymptotic properties of the proposed GMM estimators and establish the connections of them to the GMM estimators of Ramalho and Smith and to the pseudolikelihood estimators of Tang, Little and Raghunathan (2003). All of the aforementioned estimators are then compared to other standard estimators for missing data such as the inverse probability weighted and sample selection model estimators in a number of Monte Carlo experiments. As an empirical application, these estimators are also applied to analyse the UK wage distribution. We found that, in many circumstances, our proposed estimators perform better than the other estimators described; especially when there is no exclusion restriction or other additional information available. Finally, we summarise that, since the true MDM is unlikely to be known, several estimators which impose different assumptions on the MDM should be used together to examine the sensitivity of the outcomes of interest with respect to the assumptions made and the estimation procedures adopted
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