Penalized Quadratic Inference Function Estimation Of Partially Linear Spatial Error Panel Regression Models

In the study of practical problems,there is usually spatial correlation among the observed values of the research objects in different units,such as regional economy,commodity prices,digital inclusive finance,agricultural green development,environmental pollution,meteorological factors,ground motion parameters,and even criminal activities.In addition,due to the complexity of practical problems,the main influencing factors of these research objects may have both linear and nonlinear effects on them.It is an important research work with significant theoretical and practical value to accurately characterize the interrelationships and mechanisms between variables using spatial regression models.Spatial econometrics has been formed since the 1970s and its theory and methods have been further enriched and improved.Among them,the parametric spatial regression models have the characteristics of simple structure,easy theoretical derivation and easy interpretation,but such models require a preset model form,and mis-specification of the model form may lead to inconsistency in estimation and bias in conclusion.Nonparametric spatial regression models can study the common nonlinear characteristics between economic variables,and the fitting of this nonlinear relationship is data-driven.However,these models often face the problem of"curse of dimensionality".Therefore,scholars have applied"dimensionality reduction"techniques such as single index,varying coefficient,and additive models to nonparameter spatial regression models,and further extended them to partially linear semiparameter spatial regression models.This kind of model is more flexible in form setting,effectively avoids the"curse of dimensionality",and can study the linear and nonlinear relationship between variables at the same time.In recent years,with the extensive application of panel data analysis in many fields such as economy,management,ecology,geography,medicine and environmental science,more and more literatures have proposed to use semiparametric spatial regression model to model panel data and conduct statistical inference research.Intra-individual correlation and cross-section heterogeneity are important characteristics of panel data,and how to reasonably describe the error structure of semiparametric spatial panel regression model is one of the important issues worth studying.At present,the research on semiparametric spatial regression models at home and abroad is still in the ascendant stage.Based on the existing research results,this thesis proposes two types of four semiparametric spatial error regression models for panel data.The advantages of these four models are:（1）They can reflect both linear and nonlinear relationships between variables;（2）They can effectively avoid the risk of mis-specification of parameter spatial regression models and overcome the"curse of dimensionality"problem of non-parameter spatial regression models;（3）In the setting of the regression error term,the spatial effect of data between different units is investigated by introducing its spatial lag term;（4）In the setting of the residual error term,it is allowed to have relevant structure within the individual;（5）By adding individual effects to the model,the influence of cross-sectional heterogeneity in panel data is considered.On the basis of systematic summary,sorting out and review of existing relevant literature,this thesis has completed the following main research contents:（1）Four partially linear spatial error panel regression models are proposed,including fixed effects partially linear single index spatial error panel regression models,random effects partially linear single index spatial error panel regression models,fixed effects partially linear varying coefficient spatial error panel regression models,and random effects partially linear varying coefficient spatial error panel regression models;（2）The estimators of unknown parameters and functions of the above four models are estimated based on their specific characteristics;（3）The large sample properties of the estimators of the four models are proved by mathematical demonstration method;（4）Monte Carlo numerical simulation method is used to investigate the finite sample performance of estimators under different spatial error correlation coefficients,sample sizes,and residual error correlation structures;（5）The estimation techniques acquired are applied respectively to the analysis of the influencing factors of provincial digital economy development and PM_2.5 pollution in China.The main research results of this thesis are summarized as follows:（1）According to the specific characteristics of the four new models proposed,the penalty quadratic inference function estimation of unknown parameters and functions is obtained by combining the ideas of B-spline function,SCAD penalty function and quadratic inference function;（2）Under some regular assumptions,it is proved that the parameter estimators satisfy consistency and asymptotic normality,and the nonparametric estimators have optimal convergence rate.（3）Monte Carlo numerical simulation results show that the estimation methods constructed for the four new models have good performance in the case of finite samples.（4）（1）The analysis results of the influencing factors of provincial digital economy development in China show that there is error spatial autocorrelation in China’s inter-provincial digital economy development data;Scientific and technological investment,economic development level,human capital and resident income have significant positive linear effects on digital economy development;Advanced industrial structure,opening up to the outside world and innovation output will show different degrees of nonlinear characteristics on digital economy development with the improvement of economic development level.（2）The analysis results of the influencing factors of provincial PM_2.5 pollution in China show that there is error spatial autocorrelation in China’s inter-provincial PM_2.5 pollution data;Population size,energy intensity,urbanization level,temperature and wind speed have significant positive linear effects on PM_2.5;Precipitation and humidity have significant negative linear effects on PM_2.5;The comprehensive factors of economic growth,energy consumption structure,industrialization level and possession of civil vehicles have obvious nonlinear effects on PM_2.5;The impact coefficients of economic growth,energy consumption structure,industrialization level and possession of civil vehicles on PM_2.5 show different degrees of nonlinear change with the increase of per capita GDP.The combination of theoretical demonstration,simulation investigation and empirical analysis is the research feature of this thesis.The models studied not only enriche and improve the theoretical system of semiparametric spatial regression models,but also provide new theoretical guidance tool for the study of practical socioeconomic problems,which have theoretical significance and application value.