Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function. As both the time series length T and the cross-sectional size N tend to infinity, the resulting estimator of the parameter vector is asymptotically normal with a root-(NT) convergence rate. Meanwhile, the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root-(NTh) convergence rate. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method are applied to a CPI data set as well as an input–output data set.

[1]  T. Subba Rao.  Nonlinear time series: Semiparametric and Nonparametric methods , 2010 .

[2]  Zhengyan Lin,et al.  Statistical inference in partially time-varying coefficient models , 2011 .

[3]  Zhijie Xiao,et al.  A Semiparametric Panel Model for Unbalanced Data with Application to Climate Change in the United Kingdom , 2010 .

[4]  Dale J. Poirier,et al.  Intermediate Statistics and Econometrics: A Comparative Approach , 1995 .

[5]  Yong Zhou,et al.  Series Estimation in Partially Linear In‐Slide Regression Models , 2011 .

[6]  Peter C. B. Phillips,et al.  Trending time series and macroeconomic activity: Some present and future challenges , 2000 .

[7]  A. Ullah,et al.  Profile likelihood estimation of partially linear panel data models with fixed effects , 2006 .

[8]  Jiti Gao,et al.  Non�?Parametric Time�?Varying Coefficient Panel Data Models with Fixed Effects , 2011 .

[9]  Liangjun Su,et al.  Sieve estimation of panel data models with cross section dependence , 2012 .

[10]  Su Liangjun.  Pro fi le Likelihood Estimation of Partially Linear Panel Data Models with Fixed , 2005 .

[11]  Jiti Gao,et al.  A NEW DIAGNOSTIC TEST FOR CROSS-SECTION UNCORRELATEDNESS IN NONPARAMETRIC PANEL DATA MODELS , 2010, Econometric Theory.

[12]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[13]  Jiti Gao,et al.  Semiparametric Estimation and Testing of the Trend of Temperature Series , 2006 .

[14]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[15]  R. Carroll,et al.  Semiparametric estimation of fixed-effects panel data varying coefficient models , 2009 .

[16]  A New Diagnostic Test for Cross-Section Uncorrelatedness in Nonparametric Panel Data Models , 2010 .

[17]  Jianqing Fan,et al.  Nonlinear Time Series : Nonparametric and Parametric Methods , 2005 .

[18]  D. Freedman.  On Tail Probabilities for Martingales , 1975 .

[19]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[20]  Zongwu Cai,et al.  Trending time-varying coefficient time series models with serially correlated errors , 2007 .

[21]  P. Robinson,et al.  Nonparametric Estimation of Time-Varying Parameters , 1989 .

[22]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

[23]  P. Phillips.  The Mysteries of Trend , 2010 .

[24]  Jiti Gao,et al.  A New Diagnostic Test for Cross-Section Independence in Nonparametric Panel Data Model , 2009 .

[25]  Q. Shao,et al.  Weak convergence for weighted empirical processes of dependent sequences , 1996 .

[26]  P. Robinson,et al.  Nonparametric trending regression with cross-sectional dependence , 2011 .

[27]  Peter Hackl,et al.  Statistical analysis and forecasting of economic structural change , 1989 .

[28]  John Odenckantz,et al.  Nonparametric Statistics for Stochastic Processes: Estimation and Prediction , 2000, Technometrics.

[29]  Jianqing Fan,et al.  Profile likelihood inferences on semiparametric varying-coefficient partially linear models , 2005 .

[30]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[31]  John Duffy,et al.  A Cross-Country Empirical Investigation of the Aggregate Production Function Specification , 2000 .