Econometric methods for Moment Restriction Models and Mixtures

该项目由两部分组成。第一部分是矩条件模型的估计。提出了一种新的估计方法，它具有渐近的极小极大效率性质。第二部分探讨了有限混合模型的非参数可辨识性，并开发了半参数估计器。第一部分的目的是提供一种估计矩条件模型的方法，在目前的应用文献中，矩条件模型通常是用广义矩方法(GMM)来估计的。这项研究的动机是最近的担忧，即在经验相关的数据生成过程中，转基因技术的表现可能存在问题。传统的局部一阶效率理论在分析这一问题时作用有限。建议的这一部分利用大偏差原理(LDP)发展了矩条件模型的全局一阶效率理论，这是概率论中的一个主要主题。然后提出了一种新的估计量，它在大偏差意义下达到了渐近的极小极大有效界。新的估计器使用Owens经验似然作为一个关键因素，实际上，它可以被解释为传统经验似然估计器的粗化版本。初步的模拟结果表明，新方法的性能优于竞争估计器，尽管项目中将进行更多的实验研究。计划了该方法在面板数据模型中的实证应用以及该方法的进一步理论扩展。第二部分考虑有限混合模型。有限混合模型允许应用研究人员以一种方便和可解释的方式处理参数变化，例如未观察到的异质性或未观察到的区域。然而，现有的关于有限混合模型的文献主要集中在参数模型上。提出的研究发展了有限混合的非参数辨识理论，其中混合模型的组分被非参数处理。虽然少数研究已经成功地处理了这类模型，但它们需要更多的参数，例如对称分布或每个观测单元的多个独立观测。这项研究采用了一种与这些研究截然不同的方法，并表明通过使用协变量中的变量来进行非参数识别是可能的。针对半参数有限混合模型，提出了一种新的估计算法。将探讨这些结果的概括，包括它们对动态模型的扩展。拟议活动的广泛影响拟议活动的结果的更广泛影响包括以下内容。首先，该项目将制作向公众开放的计算机程序。例如，对极大极小估计的研究将为新的方法产生计算机软件。作为一个副产品，这项工作将包括开发一个可靠的程序来实施经验似然方法，这在实践者中引起了极大的关注。这将使广泛的社区受益。第二，研究生将直接和间接地得到拟议项目的支持。过去的NSF资助使研究生能够以研究助理的身份参与PI的项目。这为他们提供了资金支持以及学习最先进的计量经济学和编程技能的机会。拟议的项目将继续支持研究生，并为他们提供论文研究和早期职业发展所需的技能和知识。第三，本项目的计量经济学方法将用于分析实证经济问题。这包括新的极小极大估计方法在收入动态模型中的应用，这些模型具有重要的政策含义。预计拟议的方法将使人们对与广大受众高度相关的经济问题有新的认识。

This project consists of two parts. The first part is concerned with estimation of momentcondition models. A new estimation method that achieves an asymptotic minimax efficiencyproperty is proposed. The second part explores nonparametric identifiability for finite mixturemodels, and develops a semiparametric estimator.Intellectual merit of the proposed activitiesThe first part aims at providing a method for estimating moment condition models, whichare usually estimated by the Generalized Method of Moments (GMM) in the current appliedliterature. This research is motivated by the recent concerns that the performance of GMMmay be problematic under empirically relevant data generating processes. The conventionallocal first-order efficiency theory is of limited use for analyzing this problem. This part of theproposal develops a global first-order efficiency theory for moment condition models using thelarge deviation principle (LDP), which is a major subject in probability theory. It then proposesa new estimator that achieves the asymptotic minimax efficiency bound in a large deviationsense. The new estimator uses Owens empirical likelihood as a crucial ingredient; indeed, itcan be interpreted as a robustified version of the conventional empirical likelihood estimator.Preliminary simulation results imply that the new method outperforms competing estimators,though more experimental studies will be undertaken in the project. Empirical applications ofthe method to panel data models and further theoretical extensions of the method are planned.The second part considers finite mixture models. Finite mixture models allow appliedresearchers to deal with parameter variations, such as unobserved heterogeneity or unobservedregimes, in a convenient and interpretable way. The existing literature on finite mixture models,however, focuses on parametric models. The proposed research develops nonparametricidentification theory for finite mixtures, where components of a mixture model are treatednonparametrically. While a few studies have succeeded in treating such models, they demandspecifications such as symmetric distributions or multiple independent observations from eachobservation unit. This research takes an approach that is very different from these studies andshows that nonparametric identification is possible by using variations in covariates. It also proposesa new estimation algorithm for a semiparametric finite mixture model. Generalizations ofthese results, including their extensions to dynamic models, will be explored.Broader impacts of the proposed activitiesThe broader impacts of the results from the proposed activities include the following. First,the project will produce computer programs that will be made accessible to public. For example,the research on minimax estimation will yield computer software for the new procedure. Thiseffort, as a byproduct, will include developing a reliable program for implementing empiricallikelihood methods, which have been attracting a great deal of attention among practitioners.This will benefit a broad range of communities. Second, graduate students will be supporteddirectly and indirectly by the proposed project. Past NSF support enabled graduate students toparticipate in projects of the PI as research assistants. This provided them with financial supportas well as opportunities to learn state-of-the-art econometrics and programming skills. Theproposed project will continue to support graduate students and provide them with the skills andknowledge necessary for their thesis research and early career development. Third, econometricmethodologies from this project will be used to analyze empirical economic problems. Thisincludes applications of the new minimax estimation method to models of income dynamics,which have important policy implications. The proposed methods are expected to shed newlight on economic problems that are highly relevant to a broad audience.