纵向数据下半参数工具变量模型的二次推断函数估计及应用

发布时间：2018-03-01 19:08

本文关键词： 纵向数据半参数模型工具变量 B-样条二次推断函数估计　出处：《重庆工商大学》2016年硕士论文　论文类型：学位论文

【摘要】：随着社会的发展以及统计学在各个领域中的应用,分析的实际问题变得越来越复杂,在建立统计模型时,线性回归模型已不再满足实际需求。统计模型已经由线性回归模型发展到半参数回归模型。半参数回归模型既含参数分量又含非参数分量,能够更好的寻找数据的内在规律。当解释变量是外生变量时,大量文献已讨论了半参数回归模型的统计方法和理论,也将该模型推广到了纵向数据的情形。但是当解释变量是内生变量时,已有的统计方法和理论不再适用。如何解决纵向数据下半参数回归模型中内生解释变量的问题和组内相关问题是本文的核心。本文考虑纵向数据下半参数工具变量模型中兴趣参数的估计,提出了三步估计过程。首先,利用B-样条方法逼近半参数模型中的非参数分量,将半参数回归模型转化为参数模型。其次,为了处理内生变量,通过引入工具变量,将内生变量分解,利用外生变量部分对模型进行估计。然后,先假定参数已知,估计非参数分量。最后,为了得到参数分量有效的估计,利用二次推断函数方法构造兴趣参数的目标函数。在一些正则条件下,证明了所得估计的相合性与渐近正态性。为了讨论所得估计的有限样本性质,对本文提出的方法进行了模拟研究。模拟研究表明所提出的估计方法有效地消除了内生变量的影响,而且无论工作相关矩阵是否正确指定,所得估计的效率都被提高。最后将所提出的估计方法应用于探究贸易开放与经济增长的关系中,选取国外市场接近度作为工具变量。结果表明实际产出与对外贸易开放度存在显著正相关关系,时间对实际产出的影响存在非线性关系。
[Abstract]:With the development of society and the application of statistics in various fields, the practical problems of analysis become more and more complicated. The statistical model has been developed from the linear regression model to the semi-parametric regression model. The semi-parametric regression model contains both parametric and non-parametric components. When explaining that variables are exogenous variables, a large number of literatures have discussed the statistical method and theory of semi-parametric regression model. The model is also extended to the case of longitudinal data, but when it is explained that the variable is an endogenous variable, The existing statistical methods and theories are no longer applicable. The core of this paper is how to solve the problem of endogenous explanatory variables and intra-group correlation in the semi-parametric regression model of longitudinal data. Estimation of parameters of interest in quantitative models, In this paper, a three-step estimation process is proposed. Firstly, the nonparametric components of the semi-parametric model are approximated by the B-spline method, and the semi-parametric regression model is transformed into a parametric model. Secondly, in order to deal with the endogenous variables, the tool variables are introduced. The endogenous variables are decomposed, and the model is estimated by the exogenous variables. Then, the parameter is known and the nonparametric component is estimated. Finally, in order to obtain the effective estimation of the parameter component, The objective functions of parameters of interest are constructed by using the quadratic inference function method. Under some regular conditions, the consistency and asymptotic normality of the obtained estimates are proved. The simulation results show that the proposed estimation method can effectively eliminate the influence of endogenous variables, regardless of whether the working correlation matrix is correctly assigned. The efficiency of the resulting estimates has been improved. Finally, the proposed estimation method is applied to explore the relationship between trade openness and economic growth. The results show that there is a significant positive correlation between actual output and foreign trade openness, and there is a nonlinear relationship between time and actual output.
【学位授予单位】：重庆工商大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1;F752;F124.1

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