Robust Estimations For Panel Data Models

In the field of econometrics,panel data are extremely important.In the macroeco-nomic research,panel data models are widely used in the test of exchange rate determi-nation theory and the theory of convergence of transnational economic growth,and in the analysis of industrial structure and technology innovation.In the study of microeco-nomics,panel data models are widely used in the analysis of enterprise cost,employment,household consumption and so on.With the wide application of the panel data models in the economic fields,some limitations of traditional analysis methods for panel data are gradually highlighted.First of all,for panel data models,researchers always make the assumption that the error term follows normal distribution.However,it is difficult to satisfy this assumption in the real world,so estimates obtained by the traditional estimator may be biased or even invalid.Second,in the process of data collection,data are probably contaminated for some reasons,which means that there exists outliers in the data set.Since traditional methods are sensitive to outliers,the estimates may differ largely from the true value,so the analysis of economic problems may be unreasonable.Scholars have done a lot of work for these limitations,such as constructing the robust estimation for panel data models and studying the quantile regression models of panel data.However,these methods still have some shortcomings.Firstly,the robust estima-tions for panel data models are usually constructed by Huber loss function which can reduce the effects of outliers.Unfortunately,it has two shortcomings:the robustness is weak and the effectiveness is low which means the variance of the estimator is large.Sec-ondly,if there exists endogeneity in the quantile regression model of the panel data,the existing instrumental variable method is complex and needs to estimate a large number of redundant parameters.This doctoral dissertation proposes a more robust and more effective method(ESL-EL)for mean regression models of panel data,and generalizes it to complex panel data models such as the generalized linear models and partially linear models.In addition,for the quantile regression models of panel data with endogeneity,we propose a two stage instrumental variable estimator(2S-IVFEQR),which can greatly reduce the com-putational complexity.Then the new estimator is generalized to the quantile regression model for dynamic panel data.The dissertation is divided into seven chapters.In chapter one,we introduce the background,significance and contents of the research.In chapter two,we introduce the references of robust estimations for panel data and instrumental variable quantile regression for panel data.In chapter three,we introduce the classical estimations for panel data models and empirical likelihood.A robust estimator named ESL-EL is pro-posed in chapter four.The statistical properties and robustness of the new estimator are studied.We also compared our method with classical robust estimators by Monte Carlo simulations.In chapter five,the ESL-EL method for generalized linear models and partially linear models are proposed and their properties are studied.A new two-stage instrumental variable quantile regression(2S-IVFEQR)is proposed in chapter six.The new method is computationally easy and is less biased for long panel data models.In chapter seven,we summarize the main research results of the dissertation,put forward the problems to be solved,and look?forward?to?the?prospects?of?the?future?research.The main innovations of this paper include:1.A robust estimation method(ESL-EL)is proposed for mean regression model-s of panel data such as linear regression models,generalized linear models,partially linear models respectively.Specifically,we introduce the exponential squared function as the loss function to limit the effects of the outliers,and combine it with the classi-cal generalized estimating equations(GEE)as well as the empirical likelihood method(EL)to construct the ESL-EL estimator.We also study the large sample properties and the robustness indicators of the new estimator,such as the asymptotic distribution,the breakdown point and the influence function.We implement the algorithm by R language,and study the finite sample properties of the new estimator by Monte Carlo simulations.2.We construct robust empirical likelihood ratio functions for the above mean regres-sion models respectively and derive their asymptotic distributions for further statistical inference.Empirical likelihood inference can avoid the calculation of some redundant parameters(such as the variance of the estimator,the variance of error terms,etc.),which greatly reduces the computational complexity.Furthermore,the shape of the confidence region is determined by the data,which improves the accuracy of statistical inference.Through the Monte Carlo simulation,we find that the performance of the new method is as well as the performance of GEE method and traditional robust method in the case of no outliers.When there are a proportion of outliers in the data,the new approach performs much better than the others,namely,the coverage probabilities is closer to the confidence level and the width of the confidence interval is smaller.3.A two-stage instrumental variable estimator(2S-IVFEQR)is proposed for the quantile regression models of panel data.In the first stage,the fixed effects are estimated and eliminated in the model.In the second stage,we estimate the common parameters by using IVQR approach directly.Compared with the traditional IVQR estimator for panel data,the new estimator greatly reduces the computational complexity,and performs much better for the long panel data models.In addition,for the quantile regression models with dynamic panel data,we use the second order lagged explained variable as the instrumental variable,and use the 2S-IVFEQR to construct the estimator.The ESL-EL estimation can be generalized to many models,such as single index models,varying coefficient,models,generalized partially linear models,generalized addi-tive models and so on.In real data analysis,our method receives the same result with classical method if there are not any outliers.Moreover,if there are outlies in the data,our estimates is more close to the real parameters.Thus,using our methods can get more scientific conclusions in real data analysis.