A Study Of GMM Estimation And Their Applications For Factor Models

In recent years,econometrician and statistician based on the idea about factor analysis to establish exact factor model,approximate factor model and dynamic factor models to solve the problems caused by general high dimensional data models and to identify the common driving factor of higher dimensional random variables,so as to ensure that there is no significant loss of information after 'dimensionality reduction'.Particularly,the dynamic factor models have been widely used in study of economic cyclical fluctuations analysis,monetary policy research and core inflation rate estimation.Under the background,this paper studies GMM estimation method and statistic properties of a class of approximate factor models and the dynamic factor models.In order to identify common factors that driving all kinds of listed companies' growth and China's macroeconomic fluctuations,the paper builds approximate factor model and dynamic factor model to carry on the empirical analysisOn the basis of the comprehensively and systematically combing the existing literature,this paper clarifies the classification of factor model and develops the way and the direction of estimation method.It focuses on the generalized moment estimation method and its statistical properties of factor model.This paper proposes a kind of GMM method which regard to approximate factor model and dynamic factor models that the idiosyncratic components are cross-sectional correlation.It also studies asymptotic properties and the finite sample properties of the common factors and factors' loading GMM estimators.In addition,by using the Monte Carlo simulation method this paper compares and analysis the differences of principal component estimation method,maximum likelihood estimation method and the GMM estimation methods.In empirical research,this paper deeply researches common factor which drives listed companies' growth and China's macroeconomic fluctuations based on the domestic economic background and data and comprehensively referenced existing research domestic and overseas.This paper's main contents and conclusions and innovation can be summarized as follows:Firstly,the paper first present the generalized method of moments estimation of the common factors vector and the factor loadings matrix for a class approximate factor models when the idiosyncratic components are cross-sectional correlation;this method generalizes the maximum likelihood estimation method of Doz et al.(2012);secondly,respectively to study the asymptotic properties of generalized method of moments estimation of model parameters and statistical properties of finite sample,under the appropriate conditions,it is proved that the GMM estimators of parameters are consistency and the asymptotic normal distribution.Secondly,the paper first present the generalized method of moments estimation of the dynamic factors vector and the factor loadings matrix for a class dynamic factor models when the idiosyncratic components are cross-sectional correlation;the method studied dynamic factor model GMM estimation under the framework of time domain analysis,which is complementary to the existing estimates method;secondly,respectively to study the asymptotic properties of generalized method of moments estimation of model parameters and statistical properties of finite sample,under the appropriate conditions,it is proved that the GMM estimators of parameters are consistency and the asymptotic normal distribution.Thirdly,this paper structures a dynamic factor model aiming to identify common factors that driving the growth of all kinds of listed companies in our country and its diversity,according to quarterly data on the six industry growth rate of listed companies in our country.The study finds significant difference in common factors sequences that drive industries profit growth.It means that the growth rates of total profit differs in industries;prosperity indexes is also an important factor which influences the company's total profit growth rate.The industries at stage of high growth,have wide marketing prospect and capacity.The industry profit growth is faster and factor loading is bigger.Fourth,In order to identify the driving factors of China's macroeconomic fluctuations,the paper builds dynamic factor model to carry on the empirical analysis by selecting the 1978-2014,42 dimensions annual macroeconomic sample data sets,according to the particularity of China's economy.We conclude five potential factors driving macroeconomic fluctuations,including the first four main factors respectively reveals the driving major sources of China's economic cycle fluctuation,these factors namely industrial production factor,foreign direct investment factor,equipment utilization factor,total factor productivity factor and a potential unrecognized factor.In addition,we discuss the harmonizing macroeconomic fluctuations in economic policy choices.Finally,this paper further discusses direction of dynamic factor models' identification,testing about the number of common factors and evaluation.