The Research Of Heterogeneous Panel Quantile Regression Model And Its Application

In the era of big data,technologies such as the Internet,cloud computing and artificial intelligence are developing rapidly,and data are increasingly characterized by diversity,magnanimity and high dimensionality.With the increasing availability of data,data in the socio-economic field has been more widely used,which brings challenges and provides a broader development space for economics research.In traditional economics research,researchers usually explore the laws of economic operation based on the assumption of homogeneity.Although this modeling approach can simplify parameter estimation and statistical inference,it ignores the potential heterogeneity in the data and is insufficient to reveal the interactions among economic variables comprehensively and precisely.This problem has become more prominent in the era of big data,and a large number of empirical studies have shown that the homogeneity assumption is no longer sufficient for the analysis of heterogeneous data.Therefore,how to deal with the complex data in the socio-economic field and to explore and analyze the heterogeneity embedded in it has become one of the most important research topics in the field of economics and data science at present.In the relevant discussions of this issue,heterogeneous panel data models and panel quantile regression models have received a lot of attention from scholars both at home and abroad.Among them,research on heterogeneous panel data models can be divided into three categories,including panel data models with group structures in the individual dimension,panel data models with structural breaks in the time dimension,and panel data models with two-dimensional heterogeneity.On the basis of different heterogeneity settings for the models,researchers have also carried out research on parameter estimation,asymptotic properties and finite sample properties.The study of panel quantile regression models with fixed effects or random effects mainly includes the model construction,parameter estimation,parameter test,and asymptotic properties.Dynamic panel quantile regression models,censored panel quantile regression models,and hierarchical panel quantile regression models are also discussed.Through the combing and analysis of related studies,it is found that most of the integrative analysis methods of heterogeneous panel data models are based on the mean reversion assumption,while extending the existing methods to panel quantile regression models can portray the effect of regression variables in the entire conditional distribution of the dependent variable more comprehensively.However,there is a lack of research in this area,and the discussion of the model needs to be deepened.By reviewing the development process and existing research on heterogeneous panel data models and panel quantile regression models,this study identifies specific research directions and paths.From the aspects of model construction and parameter estimation,this paper firstly introduces the panel quantile regression model and its two main estimation methods:penalized quantile regression and two-stage quantile regression,and describes the setting methods of different types of heterogeneous panel data models and the corresponding integrative analysis methods;then,the study provides insight into the heterogeneous panel quantile regression model from three perspectives:1.Constructing a panel quantile regression model with group structures in the coefficients of explanatory variables.By introducing the penalty term into the minimum weighted absolute distance objective function,the study proposes a integrative analysis method that can simultaneously estimate the coefficients of explanatory variables and identify the unknown group structures;explores the statistical and finite sample properties of the parameter estimators based on the regularization assumption;applies the method to empirical analysis based on CFPS household consumption panel data to achieve automatic grouping of heterogeneous consumers in China objectively and analyze the heterogeneous consumption behavior of different groups of consumers;2.Constructing a panel quantile regression model with unknown multiple structural breaks in the coefficients of explanatory variables.Based on the penalized minimum weighted absolute distance objective function,the study proposes an integrative analysis method that can simultaneously perform parameter estimation and structural breaks identification,proves the asymptotic properties of the parameter estimator;and verifies the finite sample properties of the estimation method by Monte Carlo simulation,and the automatic identification of structural breaks of the environmental Kuznets curve was achieved using the method;3.Constructing a panel quantile regression model with two-dimensional heterogeneous block structures for model coefficients.The study proposes a double integrative analysis method based on a double penalized minimum weighted absolute distance objective function and performs model coefficient estimation and block structure identification,explores the statistical properties and finite sample properties of the parameter estimators,and applies the method to achieve automatic identification of the two-dimensional heterogeneous structure of economic development in China.The innovation of this paper contains:1.A penalty integrative analysis method is proposed by extending the C-Lasso method for panel quantile regression model with group structure in the coefficients of the explanatory variables.Unlike traditional approaches based on panel data models and mean reversion hypothesis,this paper identifies the group structures at different quartiles and uses this result to provide an integrated analysis of the interactions between variables across the conditional distribution.It can be demonstrated that the parameter estimates have good statistical and finite sample properties,and accelerates the operations by designing iterative algorithms.2.A penalized quantile regression method is proposed for the panel quantile regression model with unknown multiple structural breaks of the explanatory variables.Compared with the existing structural breaks identification methods,this paper incorporates the differences in the coefficients of explanatory variables at different time points,introduces the concave integrative penalty function into the objective function,and the estimation method is universal,taking the mean-reversion phenomenon into account.In addition,an improved ADMM algorithm is proposed for parameter estimation and structural breaks identification,which reduces the time complexity of the algorithm and proves that the estimators are consistent based on the regularity condition.3.A double penalty integrative analysis method is proposed for the panel quantile regression model with two-dimensional heterogeneity of the model coefficients.Compared with the traditional two-dimensional heterogeneity model setting methods,our method is based on a sparsity approach,assuming the existence of block structures of model coefficients containing multiple heterogeneous structures with generality.A double integrative analysis method is proposed based on a double penalized minimum weighted absolute distance objective function.Parameter estimation and block structure identification are performed simultaneously,and it is demonstrated that the estimation method can consistently estimate the model coefficients and improve the computational speed by improving the ADMM algorithm.In summary,this paper extends the analytical methods of heterogeneous panel data model and panel quantile regression model by constructing a heterogeneous panel quantile regression model and proposing the corresponding parameter estimation methods.This method is used to analyze the hot issues in the socio-economic field and realize the automatic identification of heterogeneous structures in different dimensions,which enriches the research methods of heterogeneity analysis in terms of theory and application.However,there are still some problems that deserve in-depth research and improvement in the future.For the new models and methods,further exploration of robust estimation methods is needed,including exploring the asymptotic properties of the estimators in theory and analyzing the heterogeneity embedded in frontier problems in application,so as to improve the theoretical and applied results of econometric models and estimation methods.