Collaborative Research: Asymptotic Properties for Partially Identified Models

项目：经济学项目负责人：Molinari， francescate题目：合作研究：部分识别模型的渐近性质理论模型的采样过程和维持的假设与一组参数向量一致的情况很常见，而不是单一参数向量。这些计量经济模型被称为部分识别模型。然后，经济分析的重点就变成了兴趣参数向量的一组可接受值。然而，尽管这些模型中的识别关注的是集合而不是单点，但迄今为止，估计和推理依赖于为点识别模型设计的技术。这是因为计量经济学家缺乏易于操作的工具来估计和测试具有确定参数的模型。不幸的是，当经济学家试图分析日益复杂的社会现象时，他们遇到了部分确定的集合模型。本研究将提供一种方法来扩展从单值对象到集值对象到估计和假设检验的概念转变。pi提出的方法是基于最初由经济理论家引入的数学工具，并在最近的数学和统计文献中进行了深入研究，尽管没有在计量经济学文献中使用。这项研究的结果应该允许经济学家以一种完全类似于对点识别模型进行估计和测试的方式对部分识别模型进行估计和测试。这是对经济科学的巨大贡献。部分识别模型在最近的理论和实证经济学中无处不在。例子包括对英国拍卖不完全模型的理论研究，对具有多重均衡的寡头垄断进入模型的实证研究，以及考虑就业构成的男女工资分布变化的实证研究。本研究的结果将为估计和测试这些模型提供一个方法框架，并提供软件，在无法完全识别时应用该方法进行估计和推断。这项研究的结果将使研究人员（理论和实证）能够研究迄今为止仅在理论层面分析的日益复杂的现象。基于这些研究的政策将更加现实。

Proposal No: 0617482Institution: Cornell University-EndowedNSF Program: ECONOMICSPrincipal Investigator: Molinari, FrancescaTitle: Collaborative Research: Asymptotic Properties for Partially Identified Models It is common to have situations in which the sampling process and the maintained assumptions of a theoretical model are consistent with a set of parameter vectors, rather than a single parameter vectors. These econometric models are called partially identified models. The focus of the economic analysis then becomes the set of admissible values for the parameter vector of interest. However, while identification in these models focuses on sets and not on single points, estimation and inference have so far relied on techniques designed for point identified models. This is because econometricians have lacked tractable tools to estimate and test models with set identified parameters. Unfortunately, as economists attempt to analyze increasingly complex social phenomena, partially identified set models are being encountered. This research will provide a methodology to extend the conceptual shift from single valued to set valued objects to estimation and hypothesis testing. The methodology the PIs propose is based on mathematical tools that were originally introduced by economic theorists, and are intensely researched in the recent mathematical and statistical literature, although not used in the econometrics literature. The results of this research should allow economists to conduct estimation and testing for partially identified models in a way that is completely analogous to how estimation and testing are conducted for point identified models. This is a huge contribution to economic science. Partially identified models are ubiquitous in the recent theoretical and empirical economics. Examples include theoretical studies of incomplete models for English auctions, empirical studies of oligopoly entry models with multiple equilibria, and of the changes in the distribution of male and female wages accounting for employment composition. The results of this research will provide a methodological framework for estimating and testing these models as well as provide software to apply this ethodology to conduct estimation and inference when full identification is not available. The results of this research will allow researchers (both theoretical and empirical) to investigate increasingly complex phenomena that had hitherto only been analyzed at the theoretical level. Policies based on such studies will be more realistic.