Reseach On Theory And Applicaton Of Semiparametric Econometric Panel Data Model

The research of semiparametric econometric panel data model is one of the most leading subjects in econometrics, combined with the advantages of the parametric panel data model and nonparametric panel data model. Not only aviod the so called “curse of dimensionality” of nonparametric model, but also compared with the traditional linear panel data model, semiparametric model has better adaptability and modeling capabilities. Now this model has been applied into many fields, such as statistics for management, econometrics and financial risk, and has been become a powerful tool for dealing with multiple regressions.In the reality economic life, in addition to sample information, we may have some prior information about the parameter vectors of the model; it can make the estimation results better if we take this priori information into consideration in our estimation procedure. However, the estimation procedure for semiparametric panel data with constraints has not yet been put forward.Therefore, there are great realistic significance and practical value in researching the constrained estimations of parametric and nonparametric in semiparametric model under the constrained conditions. In addition, as data collection is more and more easily, this leads to the database scale, more complexity. Such as various types of trade transaction data, gene expression data and multimedia data, etc., their dimensions can often reach hundreds of thousands, or even higher. It is because of universal existence of high-dimensional data, these Highlights the significance and value of the research on this new type of data mining. However, the classical statistical measurement analysis method is hard to processing. Therefore, it is an unceasing exploratory subject for us to study the problem of variable selection for high dimensional panel data model, and it is also one of major concern in this study.This paper carries out a series of studies center on the semiaprametic panel econometric models. Considering the parameters have linear constraints, we proposed a constrained least square estimation method for the semiparametric partially linear panel data with fixed effects, and proved that the parameter estimation and the nonparameter estimation are both follow the asymptotic normal distribution. The proposed approach is examined by many simulation analyses using simulated data and repeated trials, our results show that in the presence of constraints, the constraint estimate is better than the estimate, which ignores the constraints. Partilly linear varying coefficient panel data model is another common model in semiparametric model, it is also the generalization of partilly linear panle data model. The main characteristics of this model are that part of the independent variable is linear correlation with dependent variable, while the other part of the independent variable is nonlinear By combining with the profile least-square method, local linear estimation theory and Lagrange multiplier method, we propose the corresponding estimation procedures to obatin the estimators of parametric part and nonparametric part in partially linear varying-coefficient panel data with fixed effects under unrestricted and restricted condition. In addition, to reduce the model misspecification, many variables are introduced in the model before carry out the data analysis. However, most of these variables are actually redundant, so in order to improve the prediction precision of the model, we need to eliminate the unnecessary variables from the model, i.e., we need to consider variable selection for the model. We construct the semiparametric adaptive Lasso penalty function for fixed-effects partially linear varying coefficient errors-in-variables models, this method can simultaneously select significant variables and estimate unknown parameters. Then, under certain regularity conditions and with appropriate selection of the tuning parameters, we demonstrate that the proposed procedure performs as well as an oracle procedure. Moreover, a modified LARS algorithm is proposed to obtain the solutions for the object function. Simulation results show that the penalized least squares estimators perform well in model selection and parameter estimation.The models mentioned above are applied to the study the income elasticity of health care spending. We consider the relationship between per capita HCE and per capita GDP for 42 African countries over the period 1995–2009. To facilitate comparison, this paper also providers the results obtained from the parameter model and variable coefficient model, and 42 African countries are divided into two categories according to the division of the World Bank, then we consider the relationship between per capita HCE and per capita GDP under the condition of different income levels. Our results show that the income elasticity is less than 1, so health expenditures increase more slowly than income.