Collaborative Research: Asymptotic Properties for Partially Identified Models

提案编号：0617482机构：康奈尔大学-EndowedNSF计划：经济学首席研究员：Molinari，FrancescaTitle：合作研究：部分识别模型的渐近性质通常有这样的情况，即采样过程和理论模型的维护假设与一组参数向量一致，而不是单个参数向量。这些计量经济学模型被称为部分识别模型。然后，经济分析的焦点变成了感兴趣的参数向量的容许值的集合。然而，虽然这些模型中的识别集中在集合而不是单个点上，但估计和推断迄今为止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处理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，以扩展从单值到集值对象的概念转变，估计和假设检验。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进行估计和测试的方式，是完全类似于如何估计和测试点识别模型进行部分识别模型。这是对经济科学的巨大贡献。 部分可识别模型在现代理论经济学和经验经济学中普遍存在。例子包括不完全模型的理论研究，英国拍卖，寡头垄断进入模型与多重均衡的实证研究，并在男性和女性的工资分配占就业构成的变化。这项研究的结果将提供一个方法框架，估计和测试这些模型，以及提供软件，应用这种方法进行估计和推理时，不能完全识别。这项研究的结果将使研究人员（包括理论和经验）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.