Estimators Of Spatial Probit Models With Skew Normal Error Terms:a Monte Carlo Study

With the continuous development of the social economy and the intensification of the globalization process,We are facing unprecedented challenges while gaining huge development opportunities in the econometric system.On the one hand,the range of the econometric system can be applied has been rapidly expanded and more and more socioeconomic laws have been revealed and studied because the collection of data is getting easier and easier.On the other hand,the difficulty of parametric estimation and model fitting in the traditional econometric model system has gradually emerged with the continuous increase in the amount of data and the continuous enrichment of data types.How to expand the applicable scope of the model and make the best of its own advantages is one of the problems that need to be solved in the current econometric system research.In the context,it is significant to combine the spatial discrete model with skew normal distribution and study the spatial Probit model with skew normal error terms and its properties in this paper.Firstly,the relevant important properties of the skew normal distribution are introduced.And then the normal Probit model with skew normal error terms and the spatial Probit model with skew normal error terms are proposed.Next,the maximum likelihood method of estimating the normal Probit model with skew normal error terms and the EM algorithm,the Gibbs algorithm,the generalized moment method of estimating the spatial lag Probit model with skew normal error terms are presented.Finally,the properties of estimators with the maximum likelihood method,the EM algorithm,the Gibbs algorithm and the method of estimating the Probit model with normal error terms are investigated by using Monte Carlo simulation,followed by an empirical application about the carbon intensity data of 30 provinces in China in 2014.The result of Monte Carlo simulation shows that the performance of the maximum likelihood estimation is better than the method of estimating the normal Probit model with normal error terms for the normal Probit model with skew normal error terms.As for the spatial lag Probit model with skew normal error terms,the EM algorithm performs best for low spatial lag coefficient such as 0 or 0.1,while the method of estimating the spatial lag Probit model with normal error terms performs best for medium and high spatial lag coefficient such as 0.45 or 0.8.In addition,the result of empirical application shows that the energy consumption intensity has significant impact for the determination of the carbon intensity level.But the spatial lag effect based on the common boundary has little impact on the carbon intensity of 30 provinces in China.