Econometric methods for Moment Restriction Models and Mixtures

本项目由两部分组成。第一部分是关于矩条件模型的估计。提出了一种新的估计方法，该方法具有渐近极大极小效率性质。第二部分探讨了有限混合模的非参数可辨识性，并给出了一个半参数估计。第一部分旨在提供一种估计力矩条件模型的方法，在当前的应用文献中，这些模型通常是由广义矩法（GMM）估计的。这项研究的动机是最近的关注，gmm的性能可能是有问题的，在经验相关的数据生成过程。传统的局部一阶效率理论对这一问题的分析作用有限。本部分利用大偏差原理（LDP）建立了力矩条件模型的全局一阶效率理论，这是概率论中的一个重要课题。然后提出了一个新的估计量，该估计量在大偏差意义下实现了渐近极大极小效率界。新的估计器使用欧文斯经验似然作为关键成分；事实上，它可以被解释为传统经验似然估计的鲁棒化版本。初步的模拟结果表明，新方法优于竞争的估计方法，尽管在项目中将进行更多的实验研究。该方法在面板数据模型中的实证应用和进一步的理论扩展是计划的。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机制。然而，现有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物的非参数识别理论，其中混合模型的组成部分被非参数化处理。虽然一些研究已经成功地处理了这种模型，但它们要求规范，如对称分布或来自每个观测单元的多个独立观测。本研究采用了一种与这些研究非常不同的方法，并表明通过使用协变量的变化可以进行非参数识别。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。建议活动的更广泛影响建议活动的结果的更广泛影响包括：首先，该项目将制作对公众开放的计算机程序。例如，对极大极小估计的研究将产生用于新程序的计算机软件。这个努力，作为副产品，将包括开发一个可靠的程序来实现经验似然方法，这已经在实践者中引起了大量的关注。这将使广泛的社区受益。其次，研究生将直接或间接地得到拟议项目的支持。过去NSF的支持使研究生能够作为研究助理参与PI的项目。这为他们提供了经济支持，以及学习最先进的计量经济学和编程技能的机会。该计划将继续支持研究生，为他们的论文研究和早期职业发展提供必要的技能和知识。第三，将使用本项目的计量经济学方法来分析实证经济问题。这包括将新的极大极小估计方法应用于收入动态模型，这具有重要的政策意义。预计拟议的方法将为与广大受众高度相关的经济问题提供新的思路。

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.