The Research On The Theoretic Essence Of GMM And Its Extension Of The Method

An important developing direction of Econometrics should be the innovation of econometric threories and methods. That is also to say the improvement of statistical inference methods in econometric model. This dissertation is basically theoretical researches about GMM in the methodology of Econometrics.Generalized Method of Moments is the important innovation of methods in econometrics analysis. Theoretically, GMM is only based on moment conditions for parameter estimating and testing, not considering model specification or specification errors. So GMM has a very strong motivation in methodology research.GMM is an impotant and popular method in modern econometrics analysis. It has a big value in theory and practice. GMM shows more general in method system of estimation and inference. Estimating method such as OLS, IV,2SLS, 3SLS, even ML can all be regarded as special case of GMM; some important testing methods such as LR, Wald, LM are also essencially connecting with GMM distance test. In other words, GMM has deeper theoretical background and wider application prospects.This dissertation does research and discovery by focusing on the following three aspects:the throught idea and theoretic essence of GMM; the improvement of small sample properties of GMM estimator, and the extension of GMM method; the GMM method in panel data model.About the throught idea and theoretic essence of GMM, the dissertation presents researching and analyzing from two points of estimating and testing. The main contents and character of this aspect are to show deeply the theoretic essence and logic sequence of ideas of GMM by strictly mathematical proof. In aspect of the improvement of small sample properties of GMM estimator and the extension of GMM, the main research objects and conclusions are that the GEL (Generalized Empirical Likelihood) estimators have smaller high order bias than GMM estimator. It also says that GEL estimators are more efficient. This means that in applications, especially in the cituation of small sample case, GEL method is a good alternative and improvement of GMM. GEL estimators are extension of GMM estimator.About the GMM method in panel data model, this dissertation presents the using conditions, applying effects of GMM; and the efficiency of GMM in theoretic analysis in panel data model.The framework, structure and contents of this dissertation are followed:Chapter 1:Preface. It describes roughly the researching background, purpose and construction, contents and character, and logical relation of this dissertation.Chapter 2:Basic Theory and Summarizing Statement of Literatures. This chapter states and analyzes some important fundamental theories and some relative classic literatures. It includes the general theories and methods of GMM; typical problems of GMM; the relationship of GMM estimator and IV estimator, the relationship of GMM estimator and 2SLS estimator; convergence modes and stochastic orders; statement and analysis on improvement of small sample properties of GMM estimator; statement on extension of GMM method; summarizing statement of GMM method in panel data model.Chapter 3:The Throught Idea and Theoretic Essence of GMM. This chapter shows deeply the inner essence and logic sequence of ideas of GMM in theory by strictly mathematical proof. It includes the relationship of GMM andχ2 statistic; the relationship of GMM test and LR, Wald, LM tests. The conclusions display that the ideas of GMM andχ2 statistic are the same in theoretic origin; and LR, Wald, LM tests are special cases of GMM distance test under certain conditions. This chapter probes and demonstrates the generality and superiority of GMM method from two points of estimating and testing. Also this chapter shows the advantage of GMM by analyzing a real case. Chapter 4:The Extension of GMM Method. Baced on discussing about the small sample properties and/or asymptotic properties of estimators, also about evaluating criterions and using conditions, this chapter focuses on the extension of GMM method with considering the improvement of small sample properties of GMM estimator and summarizing relative literatures. The key is the development and evolvement from GMM to GEL. And it also demonstrates that, from the view of high order asymptotic bias, GEL method is indeed the improvement and the extension of GMM method. And by simulation, this chapter still compares the estimating biases, mean square errors of GMM estimators and GEL estimators.Chapter 5:The GMM Method in Panel Data Model. Despite it has an important application in regular cross section data or time series data, GMM method has the important theoretic meaning and researching value in panel data model. According to some relative literatures, this chapter mainly researches and analyzes theoretic method and application of GMM in panel data model, and organizes and refines ideas of GMM in panel data model.Chapter 6:Concluding Remarks. This chapter sums up the dissertation and points out the further research directions.About highlights of this dissertation, the author concludes as followed:(1) This dissertation shows deeply the inner essence and logic sequence of ideas of GMM in theory by strictly mathematical proof.(2) This dissertation shows the development and evolvement from GMM to GEL. And it also demonstrates that GEL method is indeed the improvement and the extension of GMM method.(3) This dissertation shows the advantage of GMM and/or GEL by analyzing a real case and by simulation. It is to make the system of GMM theory and method tending to perfection. The value of this dissertation is to seek a direction of method innovation and provide deeper theoretic foundation for application.