Econometric Methods for Models with Covariate Adaptive Randomization and Partial Identification

本研究开发了新的计量经济学方法，以解决经济学和其他社会科学几个领域的应用研究人员最近面临的两类问题。首先，发展经济学家经常采用随机对照实验，使用协变量自适应随机化来“平衡”观察到的潜在协变量的影响。标准推理方法通常用于此设置，但它们可能产生无效的结果。鉴于此，研究的第一部分开发了既有效又易于实现的新型推理方法。其次，部分识别模型已广泛用于劳动经济学和产业组织中，以纳入缺失数据或多重均衡，但文献没有充分解决如何测试力矩条件子集的有效性。因此，研究的第二部分开发了一种新的方法来解决这个问题。特别是，本项目中考虑的假设检验也可以用来评估某个工具变量在具有矩等式和不等式的模型中是否有效。本研究为两个计量经济模型的分析提供了新的理论和方法。前两个项目研究使用协变量自适应随机化的随机对照实验中对平均治疗效果的推断。第一个项目考虑有多种处理的实验，分配不一定均匀地分布在对照组和处理组之间。该项目提出了基于回归的推理方法，这些方法被证明是有效的，具有优异的功率特性，并且易于实现。第二个项目考虑在小组或集群层面进行的任务实验，例如，教室，村庄等。每个群体中个体之间的统计依赖性要求开发新的方法。最后，第三个项目考虑了由矩等式和不等式定义的部分识别模型中的推理问题。在这种情况下，目标是测试力矩条件子集的有效性，同时保持其余条件的有效性。本课题开发了一种新的基于自举的方法，该方法被证明是有效的，并且具有良好的功率性能。

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.