This project consists of two parts. The first part is concerned with estimation of moment condition models. A new estimation method that achieves an asymptotic minimax efficiency property is proposed. The second part explores nonparametric identifiability for finite mixture models, and develops a semiparametric estimator. Intellectual merit of the proposed activities The first part aims at providing a method for estimating moment condition models, which are usually estimated by the Generalized Method of Moments (GMM) in the current applied literature. This research is motivated by the recent concerns that the performance of GMM may be problematic under empirically relevant data generating processes. The conventional local first-order efficiency theory is of limited use for analyzing this problem. This part of the proposal develops a global first-order efficiency theory for moment condition models using the large deviation principle (LDP), which is a major subject in probability theory. It then proposes a new estimator that achieves the asymptotic minimax efficiency bound in a large deviation sense. The new estimator uses Owens empirical likelihood as a crucial ingredient; indeed, it can 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 of the 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 applied researchers to deal with parameter variations, such as unobserved heterogeneity or unobserved regimes, in a convenient and interpretable way. The existing literature on finite mixture models, however, focuses on parametric models. The proposed research develops nonparametric identification theory for finite mixtures, where components of a mixture model are treated nonparametrically. While a few studies have succeeded in treating such models, they demand specifications such as symmetric distributions or multiple independent observations from each observation unit. This research takes an approach that is very different from these studies and shows that nonparametric identification is possible by using variations in covariates. It also proposes a new estimation algorithm for a semiparametric finite mixture model. Generalizations of these results, including their extensions to dynamic models, will be explored. Broader impacts of the proposed activities The 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. This effort, as a byproduct, will include developing a reliable program for implementing empirical likelihood 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 supported directly and indirectly by the proposed project. Past NSF support enabled graduate students to participate in projects of the PI as research assistants. This provided them with financial support as well as opportunities to learn state-of-the-art econometrics and programming skills. The proposed project will continue to support graduate students and provide them with the skills and knowledge necessary for their thesis research and early career development. Third, econometric methodologies from this project will be used to analyze empirical economic problems. This includes applications of the new minimax estimation method to models of income dynamics, which have important policy implications. The proposed methods are expected to shed new light on economic problems that are highly relevant to a broad audience.
