具有截面相关的变系数面板数据模型的估计及应用
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摘要
本文建立了一类变系数面板数据模型.此模型假设自变量的系数是某一平滑变量的未知函数,允许自变量,平滑变量和误差项存在通过共同因子结构引入的截面相关.由于一些共同因子的不可观测性,本文采用局部线性共同相关效应估计方法对未知的函数进行估计并给出了估计量的渐近性质.蒙特卡罗模拟结果表明该估计方法具有良好的小样本性质.利用1990-2012年中国省级面板数据,本文对我国外商直接投资与经济增长之间的关系进行了实证分析,结果表明:外商直接投资和经济增长之间存在明显非线性关系,各省份不同的初始经济水平会导致外商直接投资对经济增长的影响不同.
In this paper, we propose a varying-coefficient panel data model. This model assumes the coefficients of explanatory variables to be unknown functions of certain smooth variables and allows for cross-sectional dependence among explanatory, smooth variables and error terms through a common factors structure. The local linear common correlated effect estimation technique is applied to estimating the varying coefficients, and the asymptotic property for the proposed estimator is established. Meanwhile,Monte Carlo simulations demonstrate good finite sample performance for this estimator. Furthermore, we examine the relationship between foreign direct investment(FDI) and economic growth by using China's provincial level data in the period from 1990 to 2012. Our empirical findings verify the existence of a significant nonlinear relationship, and show that the impact of FDI on economic growth depends on the level of initial economic conditions in different regions.
In this paper, we propose a varying-coefficient panel data model. This model assumes the coefficients of explanatory variables to be unknown functions of certain smooth variables and allows for cross-sectional dependence among explanatory, smooth variables and error terms through a common factors structure. The local linear common correlated effect estimation technique is applied to estimating the varying coefficients, and the asymptotic property for the proposed estimator is established. Meanwhile,Monte Carlo simulations demonstrate good finite sample performance for this estimator. Furthermore, we examine the relationship between foreign direct investment(FDI) and economic growth by using China's provincial level data in the period from 1990 to 2012. Our empirical findings verify the existence of a significant nonlinear relationship, and show that the impact of FDI on economic growth depends on the level of initial economic conditions in different regions.
引文
[1]Anselin L. Spatial econometrics:Methods and models[M]. Dordrecht:Kluwer Academic, 1988.
[2]Anselin L, Le Gallo J, Jayet H. Spatial panel econometrics[M]. 3rd ed. The Econometrics of Panel Data, 2008:625-660.
[3]Bai J. Panel data models with interactive fixed effects[J]. Econometrica, 2009, 77(4):1229-1279.
[4]Moon H R, Weidner M. Dynamic linear panel regression models with interactive fixed effects[R]. Cemmap Working Paper, No. CWP63/13, 2013.
[5]Moon H R, Weidner M. Linear regression for panel with unknown number of factors as interactive fixed effects[J].Econometrica, 2015, 83(4):1543-1579.
[6]Song M. Asymptotic theory for dynamic heterogeneous panels with cross-sectional dependence and its applications[R]. Mimeo Working Paper, 2013.
[7]Pesaran M H. Estimation and inference in large heterogeneous panels with a multifactor error structure[J].Econometrica, 2006, 74(4):967-1012.
[8]Westerlund J, Urbain J P. Cross-sectional averages versus principal components[J]. Journal of Econometrics,2015, 185(2):372-377.
[9]Holly S, Pesaran M H, Yamagata T. A spatio-temporal model of house prices in the USA[J]. Journal of Econometrics, 2010, 158(1):160-173.
[10]Hjalmarsson E. Predicting global stock returns[J]. Journal of Financial and Quantitative Analysis, 2010, 45(1):49-80.
[11]陈浪南,苏海峰.人民币汇率变动对中国出口的非对称影响研究[J].系统工程理论与实践,2014, 34(9):2212-2219.Chen L N, Su H F. The asymmetric impacts of RMB exchange rate on China's exports[J]. Systems Engineering—Theory&Practice, 2014, 34(9):2212-2219.
[12]Cai Z, Li Q. Nonparametric estimation of varying-coefficient dynamic panel data models[J]. Econometric Theory,2008, 24(5):1321-1342.
[13]Li D, Chen J, Gao J. Non-parametric time-varying coefficient panel data models with fixed effect[J]. The Econometrics Journal, 2011, 14(3):387-408.
[14]Sun Y, Carroll R, Li D. Semiparametric estimation of fixed-effects panel data varying coefficient models[M].Advances in Econometrics, 2009, 25:101-129.
[15]Cai Z, Chen L, Fang Y. Semiparametric estimation of partially varying-coefficient dynamic panel data models[J].Econometric Reviews, 34(6-10):695-719.
[16]Cai Z, Chen L, Fang Y. Semiparametric quantile panel data models with an application to estimating the growth effect of FDI[R]. Working Paper, 2017.
[17]Su L, Jin S. Sieve estimation of panel data models with cross section dependence[J]. Journal of Econometrics,2012, 169(1):34-47.
[18]Huang X. Nonparametric estimation in large panels with cross-sectional dependence[J]. Econometric Reviews,2013, 32(5-6):754-777.
[19]Su L, Zhang Y. Nonparametric dynamic panel data models with interactive fixed effects:Sieve estimation and specification testing[R]. Working Paper, Singapore Management University, 2013.
[20]Kottaridi C, Stengos T. Foreign direct investment, human capital and non-linearities in economic growth[J].Journal of Macroeconomics, 2010, 32(3):858-871.
[21]Nunnenkamp P. To what extent can foreign direct investment help achieve international development goals?[J].The World Economy, 2004, 27(5):657-677.
[22]Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models[J].Bernoulli, 2005, 11(6):1031-1057.
[23]Karabiyik H, Urbain J P, Westerlund J. CCE estimation of factor-augmented regression models wit more factors than observables[R]. Working Paper, 2014.
[24]Hansen B E. Uniform convergence rates for kernel estimation with dependent data[J]. Econometric Theory, 2008,24(3):726-748.
[25]Cai Z, Fan J, Yao Q. Functional-coefficient regression models for nonlinear time series[J]. Journal of the American Statistical Association, 2000, 95(451):941-956.
[26]费宇,王江.FDI对我国各地区经济增长的非线性效应分析[J].统计研究,2013,30(4):70-75.Fei Y, Wang J. The non-linear effects of FDI on regional economic growth in China[J]. Statistical Research, 2013,30(4):70-75.
[27]Park J H, Prime P B. Export performance and growth in China:A cross-provincial analysis[J]. Applied Economics, 1997, 29:1353-1363.
[28]Berthelemy J C, Demurger S. Foreign direct investment and economic growth:Theory and application to China[J]. Review of Development Economics, 2000, 4(2):140-155.
[29]Cai Z, Fang Y, Xu Q. Inferences for varying-coefficient panel data models with cross-sectional dependence[R].Working Paper, 2018.
1.这里为了简化符号,我们假设d=1.本文的研究可以容易地推广到U_(it)是多维向量的情况.由于非参数估计存在“维度诅咒”问题,在实际应用中d一般小于等于3.
2.这里为了简化符号,我们仍然使用ε_i~*表示经过Taylor展开近似之后的新误差项.
3.这里为了简化符号,我们对不同的横截面个体i使用相同的核函数k(·).
4.为了解决可能出现的不可观测共同因子个数大于解释变量个数的情况,Karabiyik等~([23])提出了组合增广CCE(combination-augmented CCE)估计量,其做法是在回归时加入{Z_(1t),…,Z_(Nt)}的多个线性组合.
[2]Anselin L, Le Gallo J, Jayet H. Spatial panel econometrics[M]. 3rd ed. The Econometrics of Panel Data, 2008:625-660.
[3]Bai J. Panel data models with interactive fixed effects[J]. Econometrica, 2009, 77(4):1229-1279.
[4]Moon H R, Weidner M. Dynamic linear panel regression models with interactive fixed effects[R]. Cemmap Working Paper, No. CWP63/13, 2013.
[5]Moon H R, Weidner M. Linear regression for panel with unknown number of factors as interactive fixed effects[J].Econometrica, 2015, 83(4):1543-1579.
[6]Song M. Asymptotic theory for dynamic heterogeneous panels with cross-sectional dependence and its applications[R]. Mimeo Working Paper, 2013.
[7]Pesaran M H. Estimation and inference in large heterogeneous panels with a multifactor error structure[J].Econometrica, 2006, 74(4):967-1012.
[8]Westerlund J, Urbain J P. Cross-sectional averages versus principal components[J]. Journal of Econometrics,2015, 185(2):372-377.
[9]Holly S, Pesaran M H, Yamagata T. A spatio-temporal model of house prices in the USA[J]. Journal of Econometrics, 2010, 158(1):160-173.
[10]Hjalmarsson E. Predicting global stock returns[J]. Journal of Financial and Quantitative Analysis, 2010, 45(1):49-80.
[11]陈浪南,苏海峰.人民币汇率变动对中国出口的非对称影响研究[J].系统工程理论与实践,2014, 34(9):2212-2219.Chen L N, Su H F. The asymmetric impacts of RMB exchange rate on China's exports[J]. Systems Engineering—Theory&Practice, 2014, 34(9):2212-2219.
[12]Cai Z, Li Q. Nonparametric estimation of varying-coefficient dynamic panel data models[J]. Econometric Theory,2008, 24(5):1321-1342.
[13]Li D, Chen J, Gao J. Non-parametric time-varying coefficient panel data models with fixed effect[J]. The Econometrics Journal, 2011, 14(3):387-408.
[14]Sun Y, Carroll R, Li D. Semiparametric estimation of fixed-effects panel data varying coefficient models[M].Advances in Econometrics, 2009, 25:101-129.
[15]Cai Z, Chen L, Fang Y. Semiparametric estimation of partially varying-coefficient dynamic panel data models[J].Econometric Reviews, 34(6-10):695-719.
[16]Cai Z, Chen L, Fang Y. Semiparametric quantile panel data models with an application to estimating the growth effect of FDI[R]. Working Paper, 2017.
[17]Su L, Jin S. Sieve estimation of panel data models with cross section dependence[J]. Journal of Econometrics,2012, 169(1):34-47.
[18]Huang X. Nonparametric estimation in large panels with cross-sectional dependence[J]. Econometric Reviews,2013, 32(5-6):754-777.
[19]Su L, Zhang Y. Nonparametric dynamic panel data models with interactive fixed effects:Sieve estimation and specification testing[R]. Working Paper, Singapore Management University, 2013.
[20]Kottaridi C, Stengos T. Foreign direct investment, human capital and non-linearities in economic growth[J].Journal of Macroeconomics, 2010, 32(3):858-871.
[21]Nunnenkamp P. To what extent can foreign direct investment help achieve international development goals?[J].The World Economy, 2004, 27(5):657-677.
[22]Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models[J].Bernoulli, 2005, 11(6):1031-1057.
[23]Karabiyik H, Urbain J P, Westerlund J. CCE estimation of factor-augmented regression models wit more factors than observables[R]. Working Paper, 2014.
[24]Hansen B E. Uniform convergence rates for kernel estimation with dependent data[J]. Econometric Theory, 2008,24(3):726-748.
[25]Cai Z, Fan J, Yao Q. Functional-coefficient regression models for nonlinear time series[J]. Journal of the American Statistical Association, 2000, 95(451):941-956.
[26]费宇,王江.FDI对我国各地区经济增长的非线性效应分析[J].统计研究,2013,30(4):70-75.Fei Y, Wang J. The non-linear effects of FDI on regional economic growth in China[J]. Statistical Research, 2013,30(4):70-75.
[27]Park J H, Prime P B. Export performance and growth in China:A cross-provincial analysis[J]. Applied Economics, 1997, 29:1353-1363.
[28]Berthelemy J C, Demurger S. Foreign direct investment and economic growth:Theory and application to China[J]. Review of Development Economics, 2000, 4(2):140-155.
[29]Cai Z, Fang Y, Xu Q. Inferences for varying-coefficient panel data models with cross-sectional dependence[R].Working Paper, 2018.
1.这里为了简化符号,我们假设d=1.本文的研究可以容易地推广到U_(it)是多维向量的情况.由于非参数估计存在“维度诅咒”问题,在实际应用中d一般小于等于3.
2.这里为了简化符号,我们仍然使用ε_i~*表示经过Taylor展开近似之后的新误差项.
3.这里为了简化符号,我们对不同的横截面个体i使用相同的核函数k(·).
4.为了解决可能出现的不可观测共同因子个数大于解释变量个数的情况,Karabiyik等~([23])提出了组合增广CCE(combination-augmented CCE)估计量,其做法是在回归时加入{Z_(1t),…,Z_(Nt)}的多个线性组合.