Estimation And Application Of A Class Of Generalized Spatial Lag Semi-parametric Varying-Coefficient Panel Models

Firstly,we construct a class of generalized spatial lag semi-parametric varying-coefficient panel models,including:(static)generalized spatial lag semiparametric varying-coefficient panel model with random effects,(static)generalized spatial lag semi-parametric varying-coefficient panel model with fixed effects,space-time dynamic semi-parametric varying-coefficient panel model with random effects and space-time dynamic semi-parametric varying-coefficient panel model with fixed effects.The above four models not only contain the spatial lag terms of observable dependent variables Y and the unobservable error term ?,but also the semi-parametric varying-coefficient part is added to describe the nonlinear relationship,which increases the flexibility and applicability of the model,and also overcomes the "Dimension Curse" problem of nonparametric models.In addition,the space-time dynamic model adds time lag Y-1 and the space-time lag WY-1 based on spatial lag term,which is the most general form of the model.Then,the profile maximum likelihood method is used to construct the estimators of the parametric and non-parametric coefficients respectively,and it is proved that the estimators have good large sample properties,satisfying the consistency and asymptotic normality under certain regular conditions.After that,the Monte Carlo numerical simulation is used to test the finite sample properties of the estimators.The specific results are as follows:(1)In(static)generalized spatial lag semi-parametric varying-coefficient models,the estimators have good small sample properties,and the estimation accuracy increases with the increase of the sample size.The selection of the spatial weight matrix has no significant difference on the estimator's performance,but under the Case weight matrix,when the sample sizes are the same,the estimated deviations of the spatial correlation coefficients ? and ? increase with the increase of the spatial structure complexity M.(2)In the space-time dynamic semi-parametric varying-coefficient models,the estimators also have good small sample properties.The estimation accuracy increases with the increase of sample size,and the choice of spatial weight matrix does not make any significant difference in the performance of estimators.However,when the Case weight matrix is selected,the estimation error of spatial lag coefficient ?,? and space-time lag coefficient ? increases with the increase of spatial complexity M.Finally,the relationship between China's provincial corruption,trade openness and economic growth is analyzed by using(static)generalized spatial lag semi-parametric varying-coefficient models,and the relationship between China's provincial foreign direct investment,intellectual property protection and economic growth is analyzed by using the space-time dynamic semi-parametric varying-coefficient panel models.The empirical study explores the spatial and non-linear dynamics of the relevant economic variables in depth and further confirms the rationality and applicability of the theoretical models.The results show that:(1)regional economic growth is significantly related in space;(2)the path of regional corruption affecting economic growth is a nonlinear function of trade openness;(3)the path of regional FDI on economic growth is a nonlinear dynamic function of the level of intellectual property protection.(4)The regional economic growth is convergent.It can be concluded that these generalized spatial lag semi-parametric varying-coefficient panel models established in this paper have theoretical innovation and application feasibility:On the one hand,they expand the form and structure of the existing spatial panel models,have more generalized model meanings,and improve the flexibility and explanatory power;On the other hand,they make up for the vacancy of the nonlinear and dynamic spatial panel models,greatly enrich and expand the scope of empirical research.