Nonparametric and Robust Methods in Econometrics

该项目由两部分组成。第一个是关于随机系数离散选择模型。第二部分研究了力矩限制模型的稳健有效估计。该项目的第一部分旨在为非参数随机系数二次选择模型开发一种新的估计量。随机系数二元选择模型在应用经济分析中有着广泛的应用。它们为在未观察到的异质性存在的情况下对经济决策进行建模提供了一个自然而方便的框架。通常，研究人员对误差项和随机系数分布进行参数分布假设，然后应用最大似然估计器(MLE)，通常使用计算成本较高的数值或模拟方法。这项研究的目标是提供一种计算上有吸引力的非参数估计量，以避免特殊的分布假设。所得到的估计器既不需要数值优化，也不需要基于数值或模拟的积分，并且具有理想的收敛速度和渐近正态性质。项目的第二部分涉及矩限制模型的稳健估计。该模型是半参数且无分布的，因此施加了温和的假设。然而，可以合理地预期，观测值的概率律可能与矩限制模型所模拟的理想分布有一些偏差。因此，明智的做法是寻求对产生观测值的概率度量中的微小扰动具有健壮性的估计和测试程序。主要结果表明，本项目中的矩约束最小Hellinger距离估计(MHDE)具有最优的极小极大稳健性质。此外，当模型假设成立时，它仍然是半参数有效的。为它们的实现提供了方便的数值算法。考虑将结果扩展到时间序列数据。拟议活动的更广泛影响包括以下几个方面。首先，该项目旨在开发对经济学各个领域的应用研究人员以及社会科学其他学科的应用研究人员有用的工具。例如，随机系数离散选择模型在许多领域都很重要，包括营销学、政治学和其他社会科学。同样，稳健估计方法涉及矩约束模型，因此适用于经济和金融中的许多模型。这两个项目开发了实用的算法，这将使程序成为从业者可行的工具。其次，该项目将为拟议的程序生成用MatLab编写的计算机程序，并将免费向公众提供。此外，稳健估计程序项目还包括在STATA中开发一套程序。为矩约束MHDE、EL和其他矩条件模型的最新方法提供STATA代码，对应用研究人员有潜在的好处。第三，拟议的活动预计将通过拟议补助金资助的研究助学金为研究生提供教育福利。我之前由国家科学基金会提供的助学金资助了一些研究生。这种支持给了他们宝贵的机会来发展他们在不同领域的技能，包括计算机编程和研究规划，事实证明这对发展他们自己的论文主题很有帮助。这些经验将对他们在学术界或公共部门的研究生涯产生宝贵的影响。这个项目使研究生能够参与到计划中的项目中，这将促进他们的学位论文研究。

This project consists of two parts. The first is concerned with random coefficients discrete choice models. The second explores robust and efficient estimation of moment restriction models. The first part of the project aims at developing a new estimator for a nonparametric random coefficient binary choice model. Random coefficient binary choice models are widely used in applied economic analysis. They offer a natural and convenient framework for modeling economic decision making in the presence of unobserved heterogeneity. Typically researchers make parametric distributional assumptions on the error term and the random coefficients distribution, then apply the maximum likelihood estimator (MLE), often with numerical or simulation methods that can be computationally costly. The goal of the proposed research is to provide a computationally attractive nonparametric estimator that avoids ad hoc distributional assumptions. The resulting estimator requires neither numerical optimization nor numerical or simulation-based integration, and has desirable properties in terms of its rate of convergence and asymptotic normality properties.The second part of the project is concerned with robust estimation of a moment restriction model. The model is semiparametric and distribution-free, therefore imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution as modeled by the moment restriction model. It is then sensible to seek estimation and testing procedures that are robust against slight perturbations in the probability measure that generates observations. The main result shows that an estimator, termed the moment restriction minimum Hellinger distance estimator (MHDE) in this project, possesses optimal minimax robust properties. Moreover, it remains semiparametrically efficient when the model assumptions hold. Convenient numerical algorithms for implementing them are provided. Extensions of the results to time series data are considered.The broader impacts of the proposed activities include the following. First, the project aims at developing tools that are useful for applied researchers across a wide range of fields in economics but also in other disciplines in social science. For example, random coefficient discrete choice models are important in many areas including marketing, political science and other social sciences. Likewise, the robust estimation method is concerned with moment restriction models and therefore applicable to numerous models in economics and finance. The two projects develop practical algorithms, which will make the procedures feasible tools for practitioners. Second, the project will yield computer programs for the proposed procedures, written inMATLAB, and they will be made freely available to the public. Also, the project for the robust estimation procedure includes the development of a suite of programs in STATA as well. Providing STATA codes for the moment restriction MHDE, EL and other recent methods for moment condition models is potentially beneficial for applied researchers. Third, the proposed activities are expected to provide educational benefits to graduate students through research assistantships supported by the proposed grant. My previous grants provided by the NSF supported a number of graduate students. This support gave them valuable opportunities to develop their skills in various areas including computer programing and research planning, which proved helpful in developing their own thesis topics. These experiences will have invaluable impacts on their research careers in academia or the public sector. This project enables graduate students to participate in the planned projects, which will promote their dissertation research.