This dissertation consists of three chapters, each of which proposes methods to deal with the "many moments" problem in a different model. Chapter I develops shrinkage methods for solving the "many moments" problem in the context of instrumental variable estimation. The procedure can be...

In this paper, we propose a doubly robust method to present the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of...