Collaborative Research: Extending the Scope of Inference in Partially Identified Models

当采样过程和维持的假设将感兴趣的参数的值限制在称为识别集的集合中时，模型被称为部分识别，该集合小于参数的逻辑范围，但可能大于单个点。当强有力的、通常不切实际的假设被更弱、更可信的假设取代时，经济模型中自然会出现部分认同的模型。部分辨识模型自提出以来，在经济学和其他社会科学的许多领域中越来越流行，本研究的目的是扩大部分辨识模型的推理范围，分为三个相关的研究项目。第一个项目研究了当我们考虑到模型规范中的小错误(即局部错误规范)的可能性时，在矩不等式模型中的推理的文献中常用的几个置信集的行为。这个项目的动机源于这样一个事实，即计量经济学模型只是对潜在的利益现象的近似，因此本质上是错误的。文献中有不同的推理过程，在正确的模型规范的假设下，它们在渐近大小和功率特性方面进行了比较。该项目提出了渐近置信度的偏差大小作为选择竞争推理方法的标准，并应用该标准来比较临界值和测试部分识别模型中构建信任集所使用的统计量。因此，应用研究人员将意识到这些错误造成的问题，并将能够选择将这些问题降至最低的方法。第二个项目解决了对感兴趣的参数向量存在多维置信度集的模型中的推理。在展示结果时，研究人员通常求助于使用所识别的集合在其每个单独坐标中的投影，从而生成多维超矩形。虽然研究人员通常非常了解原始置信集的性质，但对这些超矩形的性质知之甚少。该项目的目的是填补这一空白。第三个项目提出了一种基于具有未知/未知函数的矩等式的部分识别模型的推理方法，而不是现在标准的推导矩不等式限制的方法。该方法可以处理不容易建立在矩不等模型中的模型(例如，回归模型中缺少协变量)。该方案中的三个项目的动机是应用研究人员在使用部分识别的模型时所面临的问题。这项建议的最终目的是让应用研究人员和政策制定者更好地了解这些模型的统计特性。例如，在分析政策建议的数据时，研究人员通常会做出假设，以简化分析和结果的阐述。这项建议旨在帮助研究人员选择对这些假设不那么敏感的工具。此外，这些项目的实施需要开发计算经济学家和计算机科学家感兴趣的计算工具。最后，这项研究议程的发展被纳入针对对计量经济学感兴趣的研究生甚至优秀本科生的课程课程。

A model is said to be partially identified when the sampling process and the maintained assumptions restrict the value of the parameter of interest to a set, called the identified set, which is smaller than the logical range of the parameter but potentially larger than a single point. Partially identified models arise naturally in economic models when strong and usually unrealistic assumptions are traded by weaker and more credible ones. Since their relatively recent introduction, partially identified models have become increasingly popular in many areas of economics and other social sciences.The objective of this research proposal is to extend the scope of inference in partially identified models and it is divided into three related research projects. The first project studies the behavior of several confidence sets commonly used in the literature on inference in moment inequality models when we allow for the possibility of making small mistakes in the specification of the model (i.e. local misspecification). The motivation for this project stems from the fact that econometric models are only approximations to the underlying phenomenon of interest and are therefore intrinsically misspecified. There are different inference procedures available in the literature that have been compared in terms of asymptotic size and power properties under the assumption of correct model specification. This project proposes the amount of distortion to asymptotic confidence size as a criterion to choose among competing inference methods, and applies this criterion to compare across critical values and test statistics employed in the construction of confidence sets in partially identified models. As a result, the applied researcher will be aware of the problems caused by these mistakes and will be able to choose a methodology that minimizes these problems.The second project addresses inference in models where there is a multi-dimensional confidence set for a parameter vector of interest. At the time of the presentation of the results, researchers typically resort to the use of a projection of the identified set in each of its individual coordinates, generating a multi-dimensional hyper-rectangle. While researchers typically know the properties of the original confidence sets very well, little is known about the properties of these hyper-rectangles. This project has the objective of filling in this void.The third project proposes an inference approach for partially identified models based on moment equalities with unknown/unidentified functions as opposed to the now standard approach of deriving moment inequality restrictions. The approach can handle models that are not easily framed into moment inequality models (e.g. missing covariates in a regression model).The three projects in this proposal are motivated by problems that applied researchers face when working with partially identified models. The ultimate objective of this proposal is to provide applied researchers and policy makers with a better understanding of the statistical properties of these models. For example, when analyzing data for policy recommendations, researchers typically make assumptions to simplify the analysis and the exposition of the results. This proposal aims to help the researcher choose tools that are less sensitive to those assumptions. Furthermore, the implementation of these projects requires developing computational tools that will be of interest to computational economists and computer scientists.Finally, the developments of this research agenda are incorporated into the curriculum of courses targeted to graduate students interested in econometrics and even outstanding undergraduate students.