Econometric Methods for Models with Covariate Adaptive Randomization and Partial Identification

这项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，发展经济学家经常使用随机化控制实验，使用协变量自适应随机化来“平衡”潜在观察到的协变量的影响。在此设置中通常使用标准推理方法，但它们可能会产生无效结果。有鉴于此，研究的第一部分开发了既有效又易于实现的新的推理方法。其次，部分识别的模型已被广泛应用于劳动经济学和产业组织，以纳入缺失数据或多重均衡，但文献没有充分讨论如何检验矩条件的子集的有效性。因此，本研究的第二部分提出了一种解决这一问题的新方法。特别是，本文所考虑的假设检验也可以用来评估某个工具变量在含有矩等式和不等式的模型中是否有效。本研究为分析两个计量经济模型提供了新的理论和方法。前两个项目研究在使用协变量自适应随机化的随机对照实验中对平均处理效果的推断。第一个项目考虑了有多个处理的实验，分配不一定在对照组和处理组中均匀分配。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，具有良好的功率特性，并且易于实现。第二个项目考虑了在小组或群组一级进行分配的实验，例如教室、村庄等。每个小组内个人之间的统计依赖需要开发新的方法。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，目标是测试矩条件的一个子集的有效性，同时保持其余条件的有效性。本项目开发了一种新的基于Bootstrap的方法，该方法被证明是有效的，并且具有良好的功率特性。

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.