| Since the 1950 s,more and more scholars have found that these research objects have spatial correlation(spatial spillover effect)or heterogeneity,such as the housing price of a city,in the research of regional science,energy economy,environmental science,urban and real estate economics,economic geography and other fields.Concretely speaking,rapid rise will usually lead to the rise of housing prices in surrounding cities;the development of innovation ability in a region will generally affect the innovation ability of surrounding areas;the evaluation of energy efficiency,energy consumption structure and energy development level among regions also show obvious spatial correlation and heterogeneity;financial agglomeration on the region.There are spatial spillover effects in regional economic growth.However,the traditional econometric models fail to take spatial factors into account,so they can not satisfy the needs of these models.Based on this reality,spatial econometric models emerge as the times require,and have been rapidly developed and widely used.Spatial econometrics is a theory to study the interaction of social and economic phenomena among different spatial regions.Since the introduction of spatial theory into the study of economic theory,the theory of spatial econometrics has developed rapidly and been widely used.It has quickly become an important branch of modern econometrics,and the important theoretical and practical results have greatly enriched eonometric system.The emergence of semi-parametric,variable coefficients and geographically weighted spatial econometric models provid several important choices to the application of spatial econometric models for the researchers.Compared with the traditional parametric spatial econometric models,the semi-parametric spatial econometric model not only considers the linear effect of the explanatory variables,but also considers the nonlinear effect of the explanatory variables,which is more practical in application.Geographically weighted spatial econometric model is simple and feasible,which can directly and intuitively depict the spatial non-stationarity.In addition,the estimation results of the model coefficients have a clear analytical expression and can be visually displayed on the geographical graph.The variable coefficient spatial econometric model contains more significance than the geographically weighted spatial econometric model.At present,the semi-parametric,variable coefficient and geographic weighted spatial econometric models are far inferior to the traditional spatial econometric models in both theory and application.Therefore,it is of great theoretical significance to study semi-parametric,variable coefficient and geographically weighted spatial econometric models from estimation methods,asymptotic properties and so on.The main contents of this study are as follow:Firstly,based on the maximum likelihood estimation(MLE)method and kernel estimation method,we derive the estimates of parameters and non-parameter part of semi-parametric spatial econometric model(spsar).The estimation of the spatial regression coefficient is achieved by optimizing the log likelihood function.In addition,under suitable conditions,we derive the limit distributions of the estimators of parameters and nonparametric components in the model.In comparison with the existing results,our approach has several advantages.First,The semiparametric spatial econometric model not only considers the linear function of partially explaining variables,but also takes account of the nonlinear effects of the explanatory variables in the other part,which is more practical in the application.Second,our estimation is based upon likelihood function,as a result,we can have an analytic form for our estimators,and it is easy to implement in practice.Third,we can obtain the limiting distributions of our estimators under relatively simple conditions.Secondly,when censored data appear in the semi-parametric spatial econometric model,a new data analysis strategy is proposed.On the basis of reasonable processing of censored data,by properly using instrumental variables and kernel estimators,we give a simple estimation procedure for computation.In the case of known and unknown distribution of truncated variables,the estimates of parametric and nonparametric parts are given respectively.Compared with the case of complete data,we only add a few assumptions and still obtain the asymptotic normality and consistency of the estimator.We extend the research of semi-parametric spatial econometric model from complete data to censored data,which provides more possibilities for the application of the model.Thirdly,We study the geographically weighted spatial autoregressive model with spatial autoregressive structure for random perturbation terms.Using the tool variable method,weighted least squares method and generalized moment estimation method,we derive the estimates of variable coefficient part,constant coefficient part and spatial autoregressive coefficient of the model respectively.In this case,we do not need the normal distribution assumption of the random perturbation terms.The analytical expression of parameter estimation can also be obtained.Furthermore,under some common conditions,we also give the large sample properties of the estimators.Fourthly,we use local polynomials,instrumental variables,weighted least squares and generalized moment estimation to estimate the semi-parametric partially linear variable coefficient spatial autoregressive model.In addition,based on the prior information of constant coefficients and the linear constraints,the Bayesian estimation and the linear constrained estimation of the parameters of the semi-parametric partially linear variable coefficients spatial autoregressive model are given respectively,and then the estimation of the variable coefficients are derived.In short,based on the detailed interpretation of spatial econometrics model,three kinds of more practical spatial econometric models are studied.In addition to the estimation of the model,the large sample properties of the estimator are studied based on appropriate assumptions and the characteristics of the estimator. |
