Statistical Inference For Spatial Panel Semi-parametric Durbin Model

Spatial econometrics is a subject that studies whether there is economic development relationship between regions and adjacent regions.In the analysis of economic problems,people tend to build linear or nonlinear parameter models to explain the relationship between variables,but the premise of this kind of modeling is to set up the relationship of variables in advance.Since the distribution of most variables in reality is unknown,the correlation between variables may not be simply expressed in linear form or parameterized nonlinear form,so such linear or nonlinear parametric models are at most approximate descriptions of real stochastic systems,and there may be large model setting errors in the actual estimation.If there is a non-parametric relationship between economic variables,the statistical inference method of parameter models established based on the classical hypothesis often lacks robustness,cannot meet the actual needs of applied research,and cannot capture the real relationship between variables.Therefore,a semi-parametric Durbin model is proposed to describe the complex relationships among variables flexibly.The main contributions of this paper can be summarized as the following two points:First,this paper introduces the classical spatial econometric model and semi-parametric model.Then the process of combining the Durbin model with the semi-parametric model(single index model,variable coefficient model)is discussed in detail.The model proposed in this paper mainly uses the maximum likelihood estimation method of cross section and the local estimation method commonly used for semi-parameters,uses maximum likelihood estimation to avoid the endogenous problem caused by the spatial lag factor,and finally solves the parameters in the model through nonlinear optimization,and gives the detailed parameter estimation process and asymptotic properties.At the same time,numerical simulation is carried out for the two models with different spatial weights,independent variables satisfying different distributions,different time dimensions and independent variable dimensions,indicating that the model proposed in this paper has a good estimation effect when dealing with complex variables.Secondly,this paper studies the problems between industrial development level and regional economic growth.First of all,through the analysis found that level of industrial development and economic growth between the obvious spatial dependence,the study found that the industrial development level of regional economic growth have more significantly improve effect,further studies have found that if not considering the spatial effect between different regions,the estimated results will be significantly overvalued.