Estimation And Application Of Spatial Lag Threshold Models

At present,the theory and method of linear parameter spatial econometric model have been systematic and complete,and have been widely used in many fields of research such as modern economics,management,sociology,environmental science and geography.The linear parameter spatial econometric model usually pre-sets the model form.The advantage is that the statistical inference is relatively simple,the estimation convergence speed is fast,the problem is easy to explain,and it is predictable.However,in the real complex economic problems,the influencing factors with truncation(jumping)characteristics are widespread,and the traditional linear parameter spatial econometric models are often difficult to meet the needs of practical research problems.In order to overcome this limitation,we need to develop a theory and method that can describe the spatial econometric model with splitting features.In the existing econometric models,the threshold regression is worth learning from.The advantage of the threshold regression is that it can accurately represent non-linear features such as asymmetry,aggregability,and jump phenomena in the data,but its disadvantage is that it cannot describe the spatial correlation between the economies.Along with faster diffusion and deeper integration of economy,science,and culture,spatial correlation is ubiquitous among economies.Besides,ignoring spatialcorrelations may introduce bias to some estimators.Therefore,in order to solve the problems above,this paper attempts to construct several new spatial lag threshold regression models,systematically study their theory and method,and apply them to solve economic problems.The models are characterized by the integration of exogenous threshold features and spatial correlation into the linear parameter regression models.The shortcomings are complemented in the model design.As are the extension of both the threshold models and the linear parameter spatial econometric models in their respective fields,the proposing new models will have wider adaptability.Whether it is theoretical analysis or empirical application,the study of spatialthreshold model is still at the initial stage.Existing studies have only considered the threshold effect for spatial term with the cross-sectional data,and we have not yet found relevant research in which spatial data have time dimension or threshold effects are introduced to the exogenous explanatory variables.In order to fill gaps in the existing research,we establish three new spatial lag threshold regression models:a spatial lag threshold regression model based on cross-sectional data,a spatial lag threshold panel model with fixed effects,and a spatial lag threshold panel model with random effects.This paper presents quasi-maximum likelihood estimation(QMLE)methods for the above three models correspondingly,and systematically studies the large sample property and small sample performance of the estimator,and finally,applies the estimation method to investigate the local government's taxation strategy and its influencing factors.The research content and results can be summarized as follows:First,we study the estimation of the spatial lag threshold model based on cross-sectional data.On the basis of the spatial lag regression model with exogenous explanatory variables and cross-section data,we introduce a threshold structure for exogenous variables.It not only considers the spatial correlation features of the dependent variables,but also effectively captures the asymmetric effects of the independent variables on the dependent variables in different regions.To estimate the unknown parameters,we constructed a QMLE method,and proved the large sample property of estimators under certain assumptions.At the same time,we apply Monte Carlo simulation method to study the small sample property,which is desirable as in the results.Second,we study the QMLE of the the spatial lag threshold panel models(SLTPM).We consider two kinds of panel models:the SLTPM with fixed effect and the SLTPM with random effect.The advantage of a panel data model is that it reduces the influence of the colinearity on the estimation by using the individual dimension and time dimension information.Besides,we construct the QMLEs for both models.Under certain assumptions,we give the large sample properties of the parameter estimators and prove them.Moreover,we apply Monte Carlo simulation method to study small sample property.The result of the numerical simulation shows that the constructed method has good performance in the case of small sample.Third,in empirical application,this paper applies the theoretical model to the study of the local government's taxation strategy and its influencing factors.Based on the tax competition theory,this paper analyzes the relationship between the average tax rate of industrial enterprises and the level of industrial agglomeration,the capital stock and the market liquidity in 280 cities in China from 1999 to 2008,and adopts the SLTPM with fixed effect for empirical analysis.The results show that the influencing factors such as tax competition and economic agglomeration are shown in the city as a unit of local government.After research,we found that China's tax competition is not race-to-the-top,nor race-to-the-bottom.Despite the failure to collect taxes on agglomeration,China's local governments still have the ability to raise actual tax levy on high-region-adhesive corporations,in which way this country could avoid the blind competition.We believe that the tax competition between China's local governments is a policy-led game between the government and enterprises.The research method of this paper has some popularization value for the theoretical study of spatial econometric model with splitting data in other forms.The corresponding estimation technology has certain application value in social science and other social disciplines.