Statistical Inference For Panel Data Partially Linear Single-Index Model With Spatiotemporal Dependence

In the last dozen years or so,with the world economic integration and the globalization degree unceasing deepens,the economic ties between countries,provinces,cities,and smaller regions will be continue to close,and the spatial relevance of various economic phenomena and their economic data is also becoming stronger.Therefore,different individuals often contain unobservable and time-invariant spatial heterogeneity information,and there will also be serial correlations between the same individuals at different times.In the process of solving practical problems,traditional panel data models usually assume that the samples are independent of each other.However,if the individual heterogeneity,spatial correlation and serial correlation of the panel data are not considered,for one thing,the information behind the data will be wasted;for another thing,the estimated values of the parameters in the model will not be able to maintain the original consistency and efficiency,and it will weakens the interpretation and prediction ability of the panel data model.In actual application,many economic phenomena cannot be explained by parametric regression models alone.This requires the use of non-parametric regression models.However,when non-parametric regression models are extended from one element to multiple elements,it often leads to the problem of "dimensionality disaster".The semi-parametric regression model can not only achieve the purpose of data dimensionality reduction,but also retain the advantages of non-parametric smoothness.Partially linear single-index model considers that the relationship between the response variable Y and the p-dimensional explanatory variable X is linear,and the qdimensional explanatory variable Z is projected to a one-dimensional linear space,and fit a one-variable function.Compared with other forms of semiparametric regression models,this model has a variety of degenerate forms and is more applicable.There are abundant researches on panel data models at home and abroad,but there are few studies that consider the temporal and spatial correlation,and there is no literature that considers temporal and spatial correlation in the partial linear singleindex model of panel data.This article discusses the statistical inference of some linear single-index models of time-space-related panel data.The main contributions are as follows:First,this paper proposes a partial linear single-index model of panel data that considers spatio-temporal correlation at the same time.Spatial error correlation and serial autocorrelation are considered in the error term.The core of this paper is to consider the spatiotemporal covariance matrix during the estimation procedure,and propose the weighted correction GEE of the corresponding parameter components and the weighted local least squares estimation of the unknown connection function to improve the effectiveness of the estimation of the unknown parameter component and the non-parametric connection function.Next,this paper gives the asymptotic properties and proofs of the estimators.Second,this article gives simulation results of the estimated parameter vectors,unknown connection function,spatial lag parameter,autocorrelation coefficient,individual effect variance and the model disturbance variance under different timespace spans and the degree of time-space correlation.It can be seen from the simulation results that the estimation results can meet the consistency,and the parameter component and the unknown connection function estimator are more effective when considering the time-space correlation than when the time-space correlation is not considered.Third,on the basis of Kottaridi and Stengos(2010),the model proposed in this paper is used to study the economic development impact of 27 OECD member countries.The study found that the fixed capital formation ratio and urbanization rate have positive effects on per capita GDP growth rate.For every 1% increase in the fixed capital formation ratio and urbanization rate,the per capita GDP growth rate will grow2.60% and 0.19%,respectively.Moreover,the growth rate of population,the proportion of foreign direct investment and human capital can promote the growth rate of per capita GDP.In addition,the parameter estimation that considers spatio-temporal correlation has a smaller standard error and shorter confidence interval than that without considering spatio-temporal correlation,and the unknown connection function has a smoother and gentler fitting curve and a narrower confidence band.