The Research Of Integrative Analysis In Heterogenous Panel Data Model And Its Application

In the reality of economy,there exist obvious differences in the characteristics of economic entities and their behaviors.Classical economic theories,considering the simplification and technical limitations,set up economic entities with homo-geneity and rationality,assuming that there is no difference between economic entities.Under this assumption,the economic theories aim to reveal the laws and characteristics of real-world economic.However,these researches are based on model singularization or homogeneity,assuming the data all come from the same regression model.Although the assumption of homogeneity helps simpli-fy the estimation parameter and statistical inference to a large extent,ignoring the heterogeneity of data may not be able to fully discover the characteristics of economic operations,and even draw some wrong conclusions.In recent years,due to the development of technologies,such as the storage of data and the analysis of big data,many economic data sets have significant the features of big data,such as,large sample and high dimensions.Relevant economic empirical research has found different conclusions from the hypothesis of homogeneous economic entities in classical economic theory.How to deal with the heterogeneity in the data has become one of the urgent problems to be solved in the current regression analysis.With the application of machine learning and other methods in statistics and econometrics,heterogeneous data models,espe-cially heterogeneous panel data models,have received extensive attention and research from many scholars.Panel data integrates cross-sectional data and time series data,and individual effects or time effects can characterize unobserved heterogeneity.However,the time effect is homogeneous in the individual dimen-sion,and the individual effect term is homogeneous in the time dimension,or the slope coefficient is homogeneous in the classic panel data model,that is,it does not change with the individual or the time dimension,which is called ho-mogeneous panel data model.On the basis of the rich research of homogeneous panel data model,a large number of scholars have studied the heterogeneous panel data model and the existing research can be divided into model with time dimensional heterogeneity,model with individual dimensional heterogeneity and two-dimensional heterogeneity model.It can also be divided into model with complete heterogeneity and model with partial heterogeneity or sparse according to the characteristics.This dissertation expands the existing research,sets up three heterogeneous panel data models that are more in line with economic re-ality,and proposes corresponding meothd of parameters' estimation,and then studies the statistical properties of estimators.The thesis first reviews the background of research,developmental process and research status of the heterogeneous panel data model,and combs the existing research on the heterogeneous panel data model by domestic and foreign scholars and lays the foundation for the direction of research in this dissertaion.Subse-quently,the heterogeneous panel data model was briefly introduced in terms of the classification of the heterogeneous panel data model,the setting of the model aand the corresponding parameter estimation methods.Based on the research sta-tus and existing problems,the existing heterogeneous panel data model research will be expanded from three aspects to supplement the existing models,providing a theoretical basis for heterogeneous economic data,and analyzing economic data sets and Its economic practical problems,which has important theoretical and practical significance.The content of this dissertation mainly includes:1.Establishing an panel data model with interactive effect,multiple unknown heterogeneous change points in the slope coefficient,and proposing a integrative analysis based on penaltied least square method to estimate the coefficients of model and heterogeneous sparse structure of coefficients simultaneously.Explor-ing the asymptotic properties of estimator in large samples and limited sample;2.Establishing a panel data model with individual and time two-dimensional heterogeneous sparse coefficients,and proposing a double integrative analysis method based on the penaltied least square method to estimate the model co-efficients and the two-dimensional heterogeneous sparse structure of coefficients,and exploring asymptotic properties in the large sample and limited sample of the estimator,using the proposed model and parameter estimation method to estimate the heterogeneous coefficient of the Solow economic growth model;3.Establishing a nonstationary panel data model with interactive effects,unknown structural breaks in both slope coefficients and factor loadings,and complete individual heterogeneity,and proposing a method of estiamting the structural change point based on the least squares method,and then estimating the coefficients of regressors in the model.Under the assumption of regulariza-tion,the large sample asymptotic properties and the limited sample properties of parameter estimators are explored.The innovations of this dissertation include:1.Aiming at the interactive effect panel data model with unknown heteroge-neous structural change points in the slope coefficient,a fusion penalty analysis method is proposed.Compared with the setting of existing research models,the setting of explanatory variable heterogeneity structure change point is more re-alistic,and it also includes the situation of coefficient state recovery,which is more general.Compared with the existing penalty least squares structure change point estimation method,this dissertation proposes a penalty term for the fusion penalty sum of different explanatory variables.Compared with the traditional least squares structure change point estimation method,parameter estimation and structure change point identification can be performed at the same time,and it is also suitable for the situation that the slope coefficient structure change point does not exist;2.For the panel data model with two-dimensional heterogeneity in coefficients,a panel data model with block-like heterogeneity in coefficients is constructed,and a two-dimensional fusion penalty analysis method is proposed.Compared with the existing two-dimensional heterogeneous panel data model,this dissertation assumes that the coefficients have a sparse structure of individual and time di-mensions,and proposes that the coefficients have a block-like sparse structure.This setting is general,and it also contains many irregular sparse settings in line with economic reality.On this basis,this dissertation proposes a double fusion analysis method to reveal the heterogeneous structure of coefficients,and proves the Oracle nature of coefficient estimators.In addition,this dissertation opti-mizes the model algorithm in the objective function solving algorithm,which improves the calculation speed of the algorithm;3.Aiming at the interactive effect panel data model with structural change points for slope coefficients and factor loads,this dissertation extends the research of existing scholars and extends it to non-stationary data.In view of the existing literature considering the structural change point of the factor model,a simple joint estimation method with the structural change point of the slope coefficient and the factor load is proposed,and the consistency of the estimator of the slope coefficient and the structural change point of the factor load is verified.In addition,there are still some unsolvable problems in the research process,which are worthy of further research in the future,such as the robust estima-tion and inference of the integrative method,and the convergence speed of the structure change point estimation in the structure change point model.In re-sponse to these problems,we will explore more robust heterogeneous structure identification methods and establish a new theoretical framework to obtain the convergence rate of structural change points in the future of research.