Collaborative Research: Identification in incomplete econometric models using random set theory

合作研究：使用随机集理论识别不完全计量经济模型

• 批准号: 0922373
• 负责人: Patrick Bayer
• 金额: $ 21.43万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-15 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0922373&HistoricalAwards=false
• 关键词: Collaborative; Research; Identification; incomplete; econometric

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This project would contribute to the literature on identification and inference in incomplete econometric models. An econometric model may be incomplete when, for example, sample realizations are not fully observable, or when the model asserts that the relationship between the outcome variable of interest and the exogenous variables is a correspondence rather than a function. In these cases, the sampling process and the maintained assumptions are consistent with a set of values for the parameter vectors (or statistical functionals) characterizing the model. This set of values is the sharp identification region of the models parameters. When the sharp identification region is not a singleton, the model is partially identified. The investigators use the tools of random sets theory to study identification in incomplete econometric models. These tools are especially suited for partial identification analysis, because they provide conditional and unconditional .probability distributions and expectations for random sets, that allow researchers to characterize the identified features of a model in the space of sets, in a manner which is the exact analog of how this task is commonly performed for point identified models in the space of vectors. The methodology that the investigators aim to develop focuses on a specific class of incomplete models, for which it provides a computationally tractable characterization of the sharp identification region. An incomplete model belongs to the class treated in the proposed research, if it predicts a convex set of conditional probability distributions of outcomes given covariates, rather than a single conditional probability distribution. Examples of models in this class include: static, simultaneous move finite games of complete information in the presence of multiple mixed strategy Nash equilibria; and polychotomous choice models with interval regressor data. These examples are explicitly analyzed in the proposal. A computationally tractable characterization of the sharp identification region of the parameters of models in this class was considered unattainable in the related literature.Partially identified models are ubiquitous in the recent theoretical and empirical literature in economics. Although it sometimes is easy to characterize their identification region explicitly, there exist many important problems in which a tractable characterization is difficult to obtain. It may be particularly difficult to establish sharpness, that is, to show that a conjectured region contains exactly the feasible parameter values and no others. Basing inference on a conjectured region which is not sharp may significantly weaken the ability of the researcher to make useful predictions, and to test for model misspecification. The intellectual merit of this proposal is twofold: (1) To provide a methodological framework to obtain a computationally tractable characterization of the sharp identification region of a model; (2) To provide practitioners with ready to use software to apply this methodology and conduct estimation and inference when point identification is not available.Broader impacts: The proposed methodology for characterization and computation of the sharp identification region enables practitioners to evaluate the credibility of existing policy studies, and compare the results of different approaches to policy research, by addressing both the identification aspects, as well as the statistical inference aspects of the problem. This research program aims to integrate teaching and research through research experience for undergraduates, the use of graduate assistants, and the instruction of a graduate course on inference in partially identified models using random sets theory.

该奖项是根据2009年的《美国回收与再投资法》（公法111-5）资助的。该项目将有助于对不完整的计量经济学模型的识别和推断的文献。例如，当样本实现不完全观察时，或者该模型断言感兴趣的结果变量与外源变量之间的关系是对应关系，而不是函数时，计量经济学模型可能是不完整的。 在这些情况下，采样过程和维护的假设与表征模型的参数向量（或统计函数）的一组值一致。这组值是模型参数的尖锐识别区域。当尖锐的识别区域不是单胎时，该模型会被部分识别。研究人员使用随机集理论的工具来研究不完整的计量经济学模型中的识别。这些工具特别适合部分识别分析，因为它们为随机组提供了条件和无条件的。概率分布和期望，从而使研究人员能够以集合空间中模型的已确定特征来表征该任务在该任务中通常如何在vectors space dissedical模型中执行该任务的确切类似物。 研究人员旨在发展的方法侧重于一类特定类别的不完整模型，为此提供了对尖锐识别区域的计算典型表征。一个不完整的模型属于拟议研究中处理的类，如果它预测了给定协变量的结果的有条件概率分布，而不是单个条件概率分布。此类模型的示例包括：在存在多种混合策略纳什均衡的情况下，静态，同时移动完整信息的有限游戏；以及带有间隔回归数据的多重调节选择模型。这些示例在提案中明确分析。在相关文献中认为该类别的模型参数的尖锐识别区域对尖锐的识别区域的计算障碍表征被认为是无法实现的。在最近的理论和经济学文献中，在经济学的最新理论和经验文献中均无处不在。尽管有时很容易明确地表征其识别区域，但是很难获得可拖动的表征的许多重要问题。建立清晰度可能特别困难，即表明猜想的区域完全包含可行的参数值，而没有其他参数值。基于不锐利的猜想区域的推断可能会显着削弱研究人员做出有用预测并测试模型错误指定的能力。该提案的智力优点是双重的：（1）提供一个方法学框架，以获得模型的尖锐识别区域的计算典型表征； （2）为实践者提供准备使用软件来应用这种方法，并在无法获得点识别时进行估计和推断。Boader的影响：尖锐识别区域的表征和计算的拟议方法，使实践者能够评估现有政策研究的可信度，并通过解决识别方面的识别方面，并将其解决方面的识别方面的问题，以及统计学上的分类，并将其比较。该研究计划旨在通过针对大学生的研究经验，研究生助理的使用以及使用随机集理论的部分识别模型进行推断的研究生课程来整合教学和研究。