Nonparametric Instrumental Variable Estimation using Complex Survey Data

The literature on nonparametric instrumental variable (IV) methods has been growing, and while the mathematics behind these methods are highly technical, researchers believe that these methods will soon emerge as viable alternatives to parametric approaches. The difficulty of these methods stems from the fact that the nonparametric instrumental variable estimator is the solution to a ill-posed inverse problem. The ill-posed inverse problem is solved by using regularization methods. Therefore there are two steps for solving the nonparametric (IV) problem: estimating conditional means and regularization. When analysis is performed using complex survey data, one must also consider the sampling design. When endogeneous sampling is present, traditional estimation methods will be inconsistent. I extend the theory of nonparametric IV models to account for sample design by estimating the conditional mean functions using a probability weighted local constant estimator.