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Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

Author

Listed:
  • Jia Chen
  • Jiti Gao

    ()

  • Degui Li

    ()

Abstract

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 nonparametric time trend function. As both the time series length T and the cross-sectional size N tend to infinity simultaneously, the resulting estimator of the parameter vector is asymptotically normal with a rate of convergence of Op(NT)^{-1/2}. Meanwhile, the asymptotic distribution for the estimator of the nonparametric trend function is also established with a rate of convergence of Op(NTh)^{-1/2}. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method is applied to analyze a CPI data set as well as an input-output data set.

Suggested Citation

  • Jia Chen & Jiti Gao & Degui Li, 2011. "Semiparametric Trending Panel Data Models with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/11, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2011-15
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    References listed on IDEAS

    as
    1. Jia Chen & Jiti Gao & Degui Li, 2009. "A New Diagnostic Test for Cross-Section Independence in Nonparametric Panel Data Model," School of Economics Working Papers 2009-16, University of Adelaide, School of Economics.
    2. Jiti Gao & Kim Hawthorne, 2006. "Semiparametric estimation and testing of the trend of temperature series," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 332-355, July.
    3. Degui Li & Jia Chen & Jiti Gao, 2011. "Non‐parametric time‐varying coefficient panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 387-408, October.
    4. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    5. Duffy, John & Papageorgiou, Chris, 2000. "A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
    6. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, January.
    7. Atak, Alev & Linton, Oliver & Xiao, Zhijie, 2011. "A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom," Journal of Econometrics, Elsevier, vol. 164(1), pages 92-115, September.
    8. Peter C. B. Phillips, 2010. "The Mysteries of Trend," Cowles Foundation Discussion Papers 1771, Cowles Foundation for Research in Economics, Yale University.
    9. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    10. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
    11. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    12. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    13. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "A New Diagnostic Test For Cross-Section Uncorrelatedness In Nonparametric Panel Data Models," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1144-1163, October.
    14. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    15. Jinhong You & Xian Zhou & Yong Zhou, 2011. "Series Estimation in Partially Linear In‐Slide Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 89-107, March.
    16. Robinson, Peter M., 2012. "Nonparametric trending regression with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 4-14.
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    Citations

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    Cited by:

    1. Tingting Cheng & Jiti Gao & Xibin Zhang, 2015. "Bayesian Bandwidth Estimation In Nonparametric Time-Varying Coefficient Models," Monash Econometrics and Business Statistics Working Papers 3/15, Monash University, Department of Econometrics and Business Statistics.
    2. Guohua Feng & Jiti Gao & Xiaohui Zhang, 2016. "Estimation of Technical Change and Price Elasticities: A Categorical Time-varying Coefficient Approach," Monash Econometrics and Business Statistics Working Papers 2/16, Monash University, Department of Econometrics and Business Statistics.
    3. Jia Chen & Jiti Gao, 2014. "Semiparametric Model Selection in Panel Data Models with Deterministic Trends and Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/14, Monash University, Department of Econometrics and Business Statistics.
    4. Jiti Gao & Kai Xia, 2017. "Heterogeneous panel data models with cross-sectional dependence," Monash Econometrics and Business Statistics Working Papers 16/17, Monash University, Department of Econometrics and Business Statistics.
    5. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    6. Jiti Gao & Oliver Linton & Bin Peng, 2017. "Inference on a Semiparametric Model with Global Power Law and Local Nonparametric Trends," Monash Econometrics and Business Statistics Working Papers 10/17, Monash University, Department of Econometrics and Business Statistics.
    7. repec:eee:econom:v:202:y:2018:i:2:p:286-305 is not listed on IDEAS
    8. repec:eee:eneeco:v:67:y:2017:i:c:p:255-267 is not listed on IDEAS
    9. KiHoon Jimmy Hong & Bin Peng & Xiaohui Zhang, 2014. "Capturing the Impact of Latent Industry-Wide Shocks with Dynamic Panel Model," Research Paper Series 347, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Chaohua Dong & Jiti Gao & Bin Peng, 2015. "Partially Linear Panel Data Models with Cross-Sectional Dependence and Nonstationarity," Monash Econometrics and Business Statistics Working Papers 7/15, Monash University, Department of Econometrics and Business Statistics.
    11. Boneva, Lena & Linton, Oliver & Vogt, Michael, 2015. "A semiparametric model for heterogeneous panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 327-345.
    12. Lee, Yoon-Jin, 2014. "Testing a linear dynamic panel data model against nonlinear alternatives," Journal of Econometrics, Elsevier, vol. 178(P1), pages 146-166.
    13. Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    14. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    15. Jia Chen & Degui Li & Jiti Gao, 2013. "Non- and Semi-Parametric Panel Data Models: A Selective Review," Monash Econometrics and Business Statistics Working Papers 18/13, Monash University, Department of Econometrics and Business Statistics.
    16. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Varying-coefficient panel data models with partially observed factor structure," Monash Econometrics and Business Statistics Working Papers 1/18, Monash University, Department of Econometrics and Business Statistics.
    17. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    18. repec:eee:econom:v:202:y:2018:i:2:p:245-267 is not listed on IDEAS
    19. Jiti Gao & Bin Peng & Zhao Ren & Xiaohui Zhang, 2015. "Variable Selection for a Categorical Varying-Coefficient Model with Identifications for Determinants of Body Mass Index," Monash Econometrics and Business Statistics Working Papers 21/15, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Cross-sectional dependence; nonlinear time trend; panel data; profile likelihood; semiparametric regression.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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