Econometric methods for Moment Restriction Models and Mixtures

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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.