Econometric Methods for Models with Covariate Adaptive Randomization and Partial Identification

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This research develops new econometric methods to address two types of problems recently faced by applied researchers in several areas of economics and other social sciences. First, development economists often employ randomized control experiments using covariate adaptive randomization to "balance" the impact of the underlying observed covariates. Standard inference methods are typically used in this setting, but they can produce invalid results. In light of this, the first part of the research develops novel inference methods that are both valid and easy to implement. Second, partially identified models have been widely used in labor economics and industrial organization to incorporate missing data or multiplicity of equilibria, but the literature has not adequately addressed how to test the validity of a subset of the moment conditions. The second part of the research thus develops a new method to address this problem. In particular, the hypothesis test considered in this project can be also used to evaluate whether a certain instrumental variable is valid or not in a model with moment equalities and inequalities.This research develops new theories and methods for analyzing two econometric models. The first two projects study inference on the average treatment effect in randomized control experiments that use covariate adaptive randomization. The first project considers experiments in which there are multiple treatments, and the assignment is not necessarily evenly distributed among the control and the treatment groups. The project proposes regression-based inference methods that are shown to be valid, to have excellent power properties, and to be easy to implement. The second project considers experiments with assignment occurring at a group or cluster level, e.g., classroom, village, etc. The statistical dependence among individuals within each group requires developing new methodologies. Finally, the third project considers an inference problem in a partially identified model defined by moment equalities and inequalities. In this context, the goal is to test the validity of a subset of the moment conditions, while maintaining the validity of the remaining ones. This project develops a new bootstrap-based method that is shown to be valid and has good power properties.