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

协作研究：扩展部分识别模型的推理范围

• 批准号: 1123586
• 负责人: Ivan Canay
• 金额: $ 17.18万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1123586&HistoricalAwards=false
• 关键词: Collaborative; Research; Extending; Scope; Inference

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.

当采样过程和保持的假设将感兴趣的参数的值限制为一个集合（称为已识别集合）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。在经济模型中，当强有力的、通常不切实际的假设被较弱的、更可信的假设所取代时，部分可识别的模型自然会出现。部分可辨识模型自引入以来，在经济学和其他社会科学的许多领域越来越受欢迎。本研究计划的目标是扩展部分可辨识模型的推理范围，分为三个相关的研究项目。第一个项目研究了在矩不等式模型的推理文献中常用的几个置信集的行为，当我们允许在模型的规范中犯小错误（即局部错误）的可能性时。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利息的基本现象的近似，因此本质上是错误的。有不同的推理程序，在文献中已经比较了渐近的大小和权力的性质下，假设正确的模型规格。本计画提出以渐近置信度的失真量作为选择竞争性推论方法的准则，并应用此准则比较部分辨识模型中构造置信集时所使用的临界值与检验统计量。因此，应用研究人员将意识到这些错误所造成的问题，并将能够选择一种方法，最大限度地减少这些问题。第二个项目地址在模型中的推理，其中有一个多维的信心集的参数向量的兴趣。在呈现结果时，研究人员通常会使用已识别集合在其每个单独坐标中的投影，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属性，但对这些超矩形的属性知之甚少。本项目的目标是填补这一空白。第三个项目提出了一种推理方法，部分识别模型的基础上的矩等式与未知/未识别的功能，而不是现在的标准方法，推导矩不等式的限制。该方法可以处理那些不容易被构建成矩不等式模型的模型（例如，回归模型中缺少协变量）。该提案中的三个项目是由应用研究人员在使用部分识别模型时面临的问题所激励的。这项建议的最终目标是为应用研究人员和决策者提供更好地了解这些模型的统计特性。例如，在分析数据以提出政策建议时，研究人员通常会做出假设，以简化分析和结果的说明。该建议旨在帮助研究人员选择对这些假设不太敏感的工具。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，这个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设置。