Research On Semi - Parameter Space Econometric Model

Traditional spatial econometric models base on linear hypothesis where the parameters are strictly limited. However, the real spatial data are very complex and usually have their own characteristics. The old models have been unsuitable for most occasions. Thus, in order to solve practical problems, proposing new ideas to improve the previous models is becoming a hot space in econometric models researching today.Partially linear models is a class of semi-parametric models, which put non-parametric part into linear models to make them more flexible. Varying coefficient models is a popular class of non-parametric models, and their theoretical properties have been studied in depth. This article combined both partially linear idea and varying coefficient idea with traditional spatial autoregressive models to deduce partially linear spatial autoregressive models, varying coefficient spatial autoregressive models and partially varying coefficient spatial autoregressive models. On one hand, the newly three models change the traditional linear models to non-parametric or semi-parametric models, which greatly enhancing the flexibility of the ordinary linear models and also make them universal. On the other hand, the newly introduced three models still maintain the basic shape of the linear model, which is easy to be understood and interpreted. Specifically, the work in this article has the following aspects:First, variable selection should be done as to the linear part of partially linear spatial autoregressive models. The more the variables are, not only the complexity and difficulty of computing increase, and the accuracy of the model may be affected. Thus, unimportant variables should be eliminated. This article chose a popular method in recent years for the linear part. The results of simulation study shows that screening effect is very obvious, not only to the exclusion of less important variables, but also improve the ability for the key variables to explain the model.Second, a new method to test the spacial correlation is proposed for varying coefficient spatial autoregressive model. Only with a spatial correlation, data can be fitted by spatial autoregressive models. Therefore, testing the spatial correlation is essential. Previous studies only aimed at a particular index, which is hard to calculate and has many restrictions. Learning from other models, this article put forward a new idea to test spatial correlation, which not only gives a specific form of the test statistic, and also gives the verification of the significance of the testing method by numerical simulation. Cases analysis, by using of the Boston housing data, obtained some useful results.Third, the research of partially varying coefficient spatial autoregressive models. In practice studies, not all factors are considered as constant (ie, the traditional linear model). Similarly, in the study of varying coefficient models,we can not believe that all the coefficients exist as functions. Some factors are changing, but others are not. In view of this situation, this article presented partially varying coefficient spatial autoregressive models. Maximum likelihood method, the local polynomial estimation method and nonlinear optimization methods were used for estimating spatial lag coefficient, constant coefficient and variable coefficient functions. Since there is a linear part in partially varying coefficient spatial autoregressive models, variable selection was also considered.