面板数据分位数回归模型求解及应用研究

发布时间：2018-01-22 09:00

  本文关键词： 面板数据 分位数回归 Copula函数 非线性　出处：《山东大学》2017年博士论文　论文类型：学位论文

【摘要】：面板数据模型是现代计量经济学中的重要组成部分,随着计量经济学理论的迅速发展,无论是在发达国家还是在发展中国家,基于面板数据的理论研究日益增多,其应用领域也越来越广泛。传统的面板数据分析方法存在一定的局限性:一方面,传统的面板数据模型构建多数基于均值回归模型的基本假设,回归结果仅能反映均值附近数据之间的结构关系,对上尾和下尾处变量关系的刻画并不准确;另一方面,传统的面板数据模型假设误差项服从正态分布,当所获得的样本数据不满足经典假设时,例如存在尖峰或者厚尾时,其估计结果往往不再具有优良性和稳健性。分位数回归方法的提出恰好可以弥补传统模型的缺陷,Koenker(2004)首次将分位数回归方法应用于面板数据模型,提出了面板数据分位数回归方法,这一方法是对传统面板数据分析方法的有力补充和扩展,既可以充分利用面板数据大样本特征,又可以精确地描述自变量对于协变量条件分布变化的影响,同时放宽了对误差分布假设的限制,提高了模型的解释能力,其估计量的稳健性和有效性更强。近年来,国内外关于面板数据分位数回归模型的研究逐渐展开,研究方向主要包括:对固定效应或随机效应面板数据分位数回归模型的模型构建、模型求解、参数检验、渐进性等问题的研究;关于动态面板分位数回归模型的研究;关于非线性面板分位数回归模型的研究;关于面板分位回归模型的非参数估计、半参数估计方法的研究;关于删失面板分位回归模型、分层面板分位回归模型、面板数据自回归分位模型等扩展模型的研究等等。通过梳理面板数据分位数回归模型的发展过程,并对研究现状进行分析发现:一方面固定效应或随机效应面板数据分位数回归模型的求解方法并不唯一,对现有方法进行改进或者探索新的求解方法可能简化模型估计过程,提高模型估计能力;另一方面,关于面板数据非线性分位数回归技术的研究比较缺乏,与基于时间序列的非线性分位数回归方法相比,前者在模型构建、模型求解、参数检验和估计量性质等方面的研究仍处于起步阶段,有待进一步发展。本文首先对面板数据分位数回归方法的发展过程、研宄现状和应用情况进行了综述,梳理了国内外已有研究内容和待研究之处,为明确研究方向奠定了基础。然后从模型构建、参数估计、参数检验等方面分别对分位数回归模型和面板数据分位数回归模型进行了阐述,介绍了面板数据模型的惩罚分位回归法、两阶段分位回归法以及动态面板数据模型的工具变量分位数回归法。最后基于面板数据分位数回归模型的研究现状,对模型构建和模型求解从三个方面进行了有益的探讨。主要研究内容包括:1.考虑到现有固定效应面板分位回归模型的求解存在无法估计个体效应、计算复杂等问题,探索一种新的求解方法。结合最优化理论,运用多维无约束极值问题中的模式搜索法迭代求解未知参数,得出未知参数的数值解。通过随机生成的面板数据进行蒙特卡洛模拟,将模式搜索法与其它分位数回归方法进行比较研究。使用固定效应面板分位回归模型对我国金融发展与经济增长之间的非线性关系进行了实证研究。2.由于随机效应面板数据模型中存在截面内相关现象,结合Copula相关函数,对随机效应面板分位回归模型的求解进行了研究。借助分位数回归与ALD分布的关系,提出了带有Copula相关结构的随机效应面板分位回归模型的极大似然估计求解法。通过蒙特卡洛数值模拟对估计量的无偏性和有效性进行检验,并利用这一方法对我国通货膨胀对经济增长的影响效应进行了实证分析。3.鉴于线性分位数回归模型的局限性,将Copula分位回归曲线应用于面板数据,对面板数据非线性Copula分位数回归模型的构建和求解进行了研究。通过生成带有Clayton Copula相关结构的随机面板数据,进行蒙特卡洛模拟实验,结果证明当变量间存在非线性相关关系时,非线性Copula分位回归对数据关系的拟合效果更好。应用这一模型,使用35个大中城市的面板数据,对我国房价和物价相关性进行了实证分析。研究工作的创新之处包括:1.针对现有固定效应面板分位回归模型求解中存在的问题,提出了一种固定效应面板分位回归模型的求解方法——模式搜索法。根据最优化理论中的模式搜索法原理编写算法步骤及程序代码,在Matlab环境下实现对未知参数的求解。该方法与现有方法相比其优势在于,算法的实现过程较为简单,并且估计过程中可以同时得到自变量系数和个体固定效应的估计值。2.基于分位数回归与ALD分布之间的关系,通过引入Copula相关结构,提出了随机效应面板分位回归模型的极大似然求解法。构造带有相关结构的极大似然函数,结合约束优化理论中的坐标轮换法进行迭代求解,计算未知参数的数值解。这一方法不仅能处理随机效应面板数据的截面内相关性问题,而且可以有效减少估计量的均方误差。3.将Copula分位数回归曲线应用于面板数据,提出了面板数据的非线性Copula分位回归模型。模型求解可通过启用Matlab优化工具箱并调用fmincon函数来完成。当面板数据模型中存在非线性相关关系时,Copula分位数回归的拟合效果更好,预测准确度更高。本文通过对面板数据分位数回归模型的研究,在模型构建和参数求解方面做出了有益的补充,但是仍存在值得探索和改进之处。对于新方法求解得到的估计量,需要对其参数检验及渐进性质等方面做进一步的理论探讨,进一步完善估计方法的理论体系。
[Abstract]:The panel data model is an important part in Modern Econometrics, with the rapid development of econometric theory, whether in developed countries or in developing countries, more theoretical research increased based on panel data, its application is more and more widely. The traditional panel data analysis method has some limitations: on the one hand, to construct a panel the traditional data models based on the most basic assumptions mean regression model, the regression results can reflect the structural relationship between the mean near data, on the tail and tail of characterizing variables is not accurate; on the other hand, the traditional panel data model assumes that the error obeys normal distribution, when the sample data is not obtained meet the classic assumptions, such as the peak or thick tail, the estimation results are often no longer has excellent performance and robustness. The method of quantile regression. That just can make up for the shortcomings of the traditional model, Koenker (2004) for the first time the quantile regression method is applied to the panel data model, the panel data quantile regression method, this method is a powerful supplement and extension of traditional analysis method of panel data, which can make full use of the panel data of large sample characteristics, and can be accurate to describe the influence of independent variables on covariate distribution conditions, at the same time to relax the assumptions of the error distribution, improve the explanatory ability of the model, the estimation of the validity and robustness is stronger. In recent years, the domestic and foreign research on panel data quantile regression model gradually developed, the main research direction includes: construction, points quantile regression model of fixed effects or random effects panel data model to solve the model, parameter test, study on progressive issues; on the dynamic panel quantile regression model The type of research; research on nonlinear panel quantile regression model; nonparametric estimation of panel quantile regression model, the method of research on semi parametric estimation; censored panel quantile regression model and hierarchical panel quantile regression model and panel data of quantile autoregressive model and extended model development and so on. The process of combing through panel data quantile regression model, and the current research situation of analysis: a method for solving the fixed effects or random effects panel data quantile regression model is not only, the existing methods of improvement or explore new methods for solving the simplified model estimation process, improve the model estimation ability; on the other hand a comparative study of the panel data, the lack of nonlinear quantile regression method, and nonlinear time series quantile regression method based on the constitutive model in comparison. The construction, solving the model, parameter estimation and the test of the nature of the research is still in its infancy, needs further development. Firstly, the development process of quantile regression for panel data, research status and applications are reviewed, combed the domestic and foreign existing research content and the research, laid the foundation for clear research direction. Then from the model, parameter estimation, test parameters were quantile regression model and panel data quantile regression model is discussed in this paper, introduces the panel data model to punish the quantile regression method, two stage quantile regression method and dynamic panel data model ivqr method finally. Based on the research status of panel data quantile regression model, to explore the beneficial model and solving the model from three aspects. The main research contents include: 1. According to the existing fixed effect panel quantile regression model is unable to estimate individual effects, the computational complexity of problems, explore a new method to solve the problem. With the optimization theory, using multidimensional unconstrained extremum problem in iterative pattern search method to solve the unknown parameters, the numerical solution of the unknown parameters. Monte Carlo simulation was performed by the panel randomly generated data, the pattern search method of comparative study with other quantile regression method. Using the fixed effects panel quantile regression model, the nonlinear relationship between financial development and economic growth in China, makes an empirical study on.2. due to the presence of section related to the phenomenon of random effect panel data model, combined with the Copula correlation function of the study of the random effect panel quantile regression model. With the help of solving relationship of quantile regression and ALD distribution, put forward with Copula The maximum likelihood random effect panel closed structure of quantile regression estimation method. Through Monte Carlo simulation test without bias and the validity of the estimator, and on China's inflation on economic growth. The empirical analysis of the.3. in view of the limitations of linear quantile regression model using this method. The Copula quantile regression curve applied to panel data, constructing and solving the nonlinear Copula regression model for panel data quantile is studied. With random Clayton panel data of Copula related structures generated by Monte Carlo simulation, experimental results show that, when there is a nonlinear relationship between variables, nonlinear Copula quantile regression on the data relations the fitting effect is better. The application of this model, using panel data of 35 large and medium-sized city, on China's housing prices and price correlation The empirical analysis. The research work includes: 1. innovation for the existing fixed effect panel in a regression model in solving problems, put forward a kind of fixed effect panel quantile regression model, the solving method of pattern search method. According to the pattern search optimization theory in the principle of preparation steps and algorithm of cable code implementation to solve the unknown parameters in the Matlab environment. The method is compared with the existing methods of its advantages, the realization process of the algorithm is simple, and the estimation process can be obtained simultaneously estimate the coefficient of the variables and individual fixed effect value of the relationship between.2. and quantile regression based on the distribution of ALD, by introducing the Copula structure, is proposed the maximum likelihood method of random effect panel quantile regression model is constructed. With the maximum likelihood function structure, combined with the constrained optimization theory of coordinate wheel 鎹㈡硶杩涜�岃凯浠ｆ眰瑙�,璁＄畻鏈�鐭ュ弬鏁扮殑鏁板�艰В.杩欎竴鏂规硶涓嶄粎鑳藉�勭悊闅忔満鏁堝簲闈㈡澘鏁版嵁鐨勬埅闈㈠唴鐩稿叧妫�

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