本文關(guān)鍵詞： 面板數(shù)據(jù) 分位數(shù)回歸 Copula函數(shù) 非線性　出處：《山東大學(xué)》2017年博士論文　論文類型：學(xué)位論文

【摘要】：面板數(shù)據(jù)模型是現(xiàn)代計(jì)量經(jīng)濟(jì)學(xué)中的重要組成部分,隨著計(jì)量經(jīng)濟(jì)學(xué)理論的迅速發(fā)展,無論是在發(fā)達(dá)國家還是在發(fā)展中國家,基于面板數(shù)據(jù)的理論研究日益增多,其應(yīng)用領(lǐng)域也越來越廣泛。傳統(tǒng)的面板數(shù)據(jù)分析方法存在一定的局限性:一方面,傳統(tǒng)的面板數(shù)據(jù)模型構(gòu)建多數(shù)基于均值回歸模型的基本假設(shè),回歸結(jié)果僅能反映均值附近數(shù)據(jù)之間的結(jié)構(gòu)關(guān)系,對上尾和下尾處變量關(guān)系的刻畫并不準(zhǔn)確;另一方面,傳統(tǒng)的面板數(shù)據(jù)模型假設(shè)誤差項(xiàng)服從正態(tài)分布,當(dāng)所獲得的樣本數(shù)據(jù)不滿足經(jīng)典假設(shè)時(shí),例如存在尖峰或者厚尾時(shí),其估計(jì)結(jié)果往往不再具有優(yōu)良性和穩(wěn)健性。分位數(shù)回歸方法的提出恰好可以彌補(bǔ)傳統(tǒng)模型的缺陷,Koenker(2004)首次將分位數(shù)回歸方法應(yīng)用于面板數(shù)據(jù)模型,提出了面板數(shù)據(jù)分位數(shù)回歸方法,這一方法是對傳統(tǒng)面板數(shù)據(jù)分析方法的有力補(bǔ)充和擴(kuò)展,既可以充分利用面板數(shù)據(jù)大樣本特征,又可以精確地描述自變量對于協(xié)變量條件分布變化的影響,同時(shí)放寬了對誤差分布假設(shè)的限制,提高了模型的解釋能力,其估計(jì)量的穩(wěn)健性和有效性更強(qiáng)。近年來,國內(nèi)外關(guān)于面板數(shù)據(jù)分位數(shù)回歸模型的研究逐漸展開,研究方向主要包括:對固定效應(yīng)或隨機(jī)效應(yīng)面板數(shù)據(jù)分位數(shù)回歸模型的模型構(gòu)建、模型求解、參數(shù)檢驗(yàn)、漸進(jìn)性等問題的研究;關(guān)于動(dòng)態(tài)面板分位數(shù)回歸模型的研究;關(guān)于非線性面板分位數(shù)回歸模型的研究;關(guān)于面板分位回歸模型的非參數(shù)估計(jì)、半?yún)?shù)估計(jì)方法的研究;關(guān)于刪失面板分位回歸模型、分層面板分位回歸模型、面板數(shù)據(jù)自回歸分位模型等擴(kuò)展模型的研究等等。通過梳理面板數(shù)據(jù)分位數(shù)回歸模型的發(fā)展過程,并對研究現(xiàn)狀進(jìn)行分析發(fā)現(xiàn):一方面固定效應(yīng)或隨機(jī)效應(yīng)面板數(shù)據(jù)分位數(shù)回歸模型的求解方法并不唯一,對現(xiàn)有方法進(jìn)行改進(jìn)或者探索新的求解方法可能簡化模型估計(jì)過程,提高模型估計(jì)能力;另一方面,關(guān)于面板數(shù)據(jù)非線性分位數(shù)回歸技術(shù)的研究比較缺乏,與基于時(shí)間序列的非線性分位數(shù)回歸方法相比,前者在模型構(gòu)建、模型求解、參數(shù)檢驗(yàn)和估計(jì)量性質(zhì)等方面的研究仍處于起步階段,有待進(jìn)一步發(fā)展。本文首先對面板數(shù)據(jù)分位數(shù)回歸方法的發(fā)展過程、研宄現(xiàn)狀和應(yīng)用情況進(jìn)行了綜述,梳理了國內(nèi)外已有研究內(nèi)容和待研究之處,為明確研究方向奠定了基礎(chǔ)。然后從模型構(gòu)建、參數(shù)估計(jì)、參數(shù)檢驗(yàn)等方面分別對分位數(shù)回歸模型和面板數(shù)據(jù)分位數(shù)回歸模型進(jìn)行了闡述,介紹了面板數(shù)據(jù)模型的懲罰分位回歸法、兩階段分位回歸法以及動(dòng)態(tài)面板數(shù)據(jù)模型的工具變量分位數(shù)回歸法。最后基于面板數(shù)據(jù)分位數(shù)回歸模型的研究現(xiàn)狀,對模型構(gòu)建和模型求解從三個(gè)方面進(jìn)行了有益的探討。主要研究內(nèi)容包括:1.考慮到現(xiàn)有固定效應(yīng)面板分位回歸模型的求解存在無法估計(jì)個(gè)體效應(yīng)、計(jì)算復(fù)雜等問題,探索一種新的求解方法。結(jié)合最優(yōu)化理論,運(yùn)用多維無約束極值問題中的模式搜索法迭代求解未知參數(shù),得出未知參數(shù)的數(shù)值解。通過隨機(jī)生成的面板數(shù)據(jù)進(jìn)行蒙特卡洛模擬,將模式搜索法與其它分位數(shù)回歸方法進(jìn)行比較研究。使用固定效應(yīng)面板分位回歸模型對我國金融發(fā)展與經(jīng)濟(jì)增長之間的非線性關(guān)系進(jìn)行了實(shí)證研究。2.由于隨機(jī)效應(yīng)面板數(shù)據(jù)模型中存在截面內(nèi)相關(guān)現(xiàn)象,結(jié)合Copula相關(guān)函數(shù),對隨機(jī)效應(yīng)面板分位回歸模型的求解進(jìn)行了研究。借助分位數(shù)回歸與ALD分布的關(guān)系,提出了帶有Copula相關(guān)結(jié)構(gòu)的隨機(jī)效應(yīng)面板分位回歸模型的極大似然估計(jì)求解法。通過蒙特卡洛數(shù)值模擬對估計(jì)量的無偏性和有效性進(jìn)行檢驗(yàn),并利用這一方法對我國通貨膨脹對經(jīng)濟(jì)增長的影響效應(yīng)進(jìn)行了實(shí)證分析。3.鑒于線性分位數(shù)回歸模型的局限性,將Copula分位回歸曲線應(yīng)用于面板數(shù)據(jù),對面板數(shù)據(jù)非線性Copula分位數(shù)回歸模型的構(gòu)建和求解進(jìn)行了研究。通過生成帶有Clayton Copula相關(guān)結(jié)構(gòu)的隨機(jī)面板數(shù)據(jù),進(jìn)行蒙特卡洛模擬實(shí)驗(yàn),結(jié)果證明當(dāng)變量間存在非線性相關(guān)關(guān)系時(shí),非線性Copula分位回歸對數(shù)據(jù)關(guān)系的擬合效果更好。應(yīng)用這一模型,使用35個(gè)大中城市的面板數(shù)據(jù),對我國房價(jià)和物價(jià)相關(guān)性進(jìn)行了實(shí)證分析。研究工作的創(chuàng)新之處包括:1.針對現(xiàn)有固定效應(yīng)面板分位回歸模型求解中存在的問題,提出了一種固定效應(yīng)面板分位回歸模型的求解方法——模式搜索法。根據(jù)最優(yōu)化理論中的模式搜索法原理編寫算法步驟及程序代碼,在Matlab環(huán)境下實(shí)現(xiàn)對未知參數(shù)的求解。該方法與現(xiàn)有方法相比其優(yōu)勢在于,算法的實(shí)現(xiàn)過程較為簡單,并且估計(jì)過程中可以同時(shí)得到自變量系數(shù)和個(gè)體固定效應(yīng)的估計(jì)值。2.基于分位數(shù)回歸與ALD分布之間的關(guān)系,通過引入Copula相關(guān)結(jié)構(gòu),提出了隨機(jī)效應(yīng)面板分位回歸模型的極大似然求解法。構(gòu)造帶有相關(guān)結(jié)構(gòu)的極大似然函數(shù),結(jié)合約束優(yōu)化理論中的坐標(biāo)輪換法進(jìn)行迭代求解,計(jì)算未知參數(shù)的數(shù)值解。這一方法不僅能處理隨機(jī)效應(yīng)面板數(shù)據(jù)的截面內(nèi)相關(guān)性問題,而且可以有效減少估計(jì)量的均方誤差。3.將Copula分位數(shù)回歸曲線應(yīng)用于面板數(shù)據(jù),提出了面板數(shù)據(jù)的非線性Copula分位回歸模型。模型求解可通過啟用Matlab優(yōu)化工具箱并調(diào)用fmincon函數(shù)來完成。當(dāng)面板數(shù)據(jù)模型中存在非線性相關(guān)關(guān)系時(shí),Copula分位數(shù)回歸的擬合效果更好,預(yù)測準(zhǔn)確度更高。本文通過對面板數(shù)據(jù)分位數(shù)回歸模型的研究,在模型構(gòu)建和參數(shù)求解方面做出了有益的補(bǔ)充,但是仍存在值得探索和改進(jìn)之處。對于新方法求解得到的估計(jì)量,需要對其參數(shù)檢驗(yàn)及漸進(jìn)性質(zhì)等方面做進(jìn)一步的理論探討,進(jìn)一步完善估計(jì)方法的理論體系。
[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硶榪涜榪唬姹傝В,璁＄畻鏈煡鍙傛暟鐨勬暟鍊艱В.榪欎竴鏂規(guī)硶涓嶄粎鑳藉鐞嗛殢鏈烘晥搴旈潰鏉挎暟鎹殑鎴潰鍐呯浉鍏蟲，

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