New methods in moment based econometric models
The goal of this research project is the development of new methods for moment-based econometric models. Two fundamental issues are addressed: the finite sample properties of and the nonparametric inference for moment-based methods. Moment-based methods such as the Generalized Method of Moments (GMM) and the Efficient Method of Moments (EMM, or Indirect Inference, II) are at the core of modern Econometrics. The GMM was proposed by Hansen (1982) and Hansen and Singleton (1982) to estimate semiparametrically structural models formulated by Euler equations. Since these pioneering works, the GMM experienced a phenomenal diffusion, with application to all fields of Economics and Finance. At the root of this success of GMM are its generality and the estimation principle based on orthogonality conditions, which incorporates in a natural way the restrictions delivered by modern economic theory. The EMM/II was introduced by Gallant and Tauchen (1996) and Gourieroux, Monfort and Renault (1993) to estimate parametric models with an intractable likelihood. Since many models in Economics and Finance fall in this class, such as models with latent variables or continuous-time models, the EMM/II is also an estimation principle that has found a broad application in empirical Economics and Finance. Despite the large diffusion of moment based approaches, several fundamental open issues remain, which are key for the successful application of these methods. This project addresses two of them. First, several contributions have emphasized a poor finite-sample performance of moment-methods like the GMM. This shortcoming is a serious limitation for applications in which the available data samples are small, as for instance in Macroeconomics. Second, the estimation of functional parameters defined by conditional moment restrictions is an open problem in the GMM. This extension aims at estimating and testing models that exploit exclusively the restrictions implied by economic theory, without introducing parametric assumptions. Applications of these methods include the nonparametric instrumental varables estimation and the nonparametric identification of preferences. This project contributes to the above open issues of moment-based econometric methods by pursuing the three following research directions. (1) We study information-theoretic approaches to indirect estimation and inference in moment-based models, in order to improve the finite sample properties of statistics based on the EMM/II. (2) We study a new class of statistics for testing parametric hypotheses in a GMM context, which are designed to have better higher-order asympotic properties. (3) We study a new class of nonparametric minimum distance estimators, for the estimation of functional parameters defined by conditional moment restrictions.