Nonparametric and Robust Methods in Econometrics

Yale University, New Haven CT

Investigators

Abstract

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.