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Estimation of a Panel Data Model with Parametric Temporal Variation in Individual Effects

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  • Peter Schmidt
  • Chirok Han
  • Luis Orea

Abstract

This paper considers models with time-varying individual effects (also known as factor models). The paper extends Ahn, Lee and Schmidt, Journal of Econometrics, 2001 and Bai, Econometrica, 2003 to allow a parametric function of time for the time factor. It provides a fixed-effects treatment of random effects models suggested by Kumbhakar and by Battese and Coelli for the frontier production function problem. The paper presents a number of GMM estimators based on assumptions of different strengths. Least squares has unusual properties: consistency depends on white noise errors, and given white noise errors it is less efficient than a GMM estimator. The model is applied to the measurement of the cost efficiency of Spanish banks

Suggested Citation

  • Peter Schmidt & Chirok Han & Luis Orea, 2004. "Estimation of a Panel Data Model with Parametric Temporal Variation in Individual Effects," Econometric Society 2004 Far Eastern Meetings 519, Econometric Society.
    • Handle: RePEc:ecm:feam04:519
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    References listed on IDEAS

    as
    1. Han, Chirok & Orea, Luis & Schmidt, Peter, 2005. "Estimation of a panel data model with parametric temporal variation in individual effects," Journal of Econometrics, Elsevier, vol. 126(2), pages 241-267, June.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian efficiency analysis through individual effects: Hospital cost frontiers," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 77-105.
    4. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    5. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    6. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    7. Cuesta, Rafael A. & Orea, Luis, 2002. "Mergers and technical efficiency in Spanish savings banks: A stochastic distance function approach," Journal of Banking & Finance, Elsevier, vol. 26(12), pages 2231-2247.
    8. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    9. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, vol. 101(2), pages 219-255, April.
    10. Cornwell, Christopher & Schmidt, Peter & Sickles, Robin C., 1990. "Production frontiers with cross-sectional and time-series variation in efficiency levels," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 185-200.
    11. Sealey, Calvin W, Jr & Lindley, James T, 1977. "Inputs, Outputs, and a Theory of Production and Cost at Depository Financial Institutions," Journal of Finance, American Finance Association, vol. 32(4), pages 1251-1266, September.
    12. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    13. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
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    Citations

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    Cited by:

    1. William Horrace & Seth Richards-Shubik & Ian Wright, 2015. "Expected efficiency ranks from parametric stochastic frontier models," Empirical Economics, Springer, vol. 48(2), pages 829-848, March.
    2. Hsu, Chih-Chiang & Lin, Chang-Ching & Yin, Shou-Yung, 2012. "Estimation of a panel stochastic frontier model with unobserved common shocks," MPRA Paper 37313, University Library of Munich, Germany.
    3. Millimet, Daniel L. & Bellemare, Marc, 2023. "Fixed Effects and Causal Inference," IZA Discussion Papers 16202, Institute of Labor Economics (IZA).
    4. Jinyuan Chang & Zhentao Shi & Jia Zhang, 2021. "Culling the herd of moments with penalized empirical likelihood," Papers 2108.03382, arXiv.org, revised May 2022.
    5. Peng Shi & Wei Zhang, 2011. "A copula regression model for estimating firm efficiency in the insurance industry," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2271-2287.
    6. Peng Shi & Wei Zhang, 2011. "Time-varying X-efficiency: evidence from US property casualty insurers," Applied Economics Letters, Taylor & Francis Journals, vol. 18(3), pages 217-221.
    7. Kneip, Alois & Sickles, Robin C. & Song, Wonho, 2012. "A New Panel Data Treatment For Heterogeneity In Time Trends," Econometric Theory, Cambridge University Press, vol. 28(3), pages 590-628, June.
    8. Zha, Jianping & Tan, Ting & Fan, Rong & Xu, Han & Ma, Siqi, 2020. "How to reduce energy intensity to achieve sustainable development of China's transport sector? A cross-regional comparison analysis," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    9. Sarafidis, Vasilis & Yamagata, Takashi & Robertson, Donald, 2009. "A test of cross section dependence for a linear dynamic panel model with regressors," Journal of Econometrics, Elsevier, vol. 148(2), pages 149-161, February.
    10. Lee, Young Hoon, 2006. "A stochastic production frontier model with group-specific temporal variation in technical efficiency," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1616-1630, November.
    11. Orea, Luis, 2007. "Estimating Firm-Specific Market Power: A Composed Error Term Approach," Efficiency Series Papers 2007/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    12. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
    13. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    14. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    15. Han, Chirok & Orea, Luis & Schmidt, Peter, 2005. "Estimation of a panel data model with parametric temporal variation in individual effects," Journal of Econometrics, Elsevier, vol. 126(2), pages 241-267, June.
    16. Young H. Lee, 2014. "Stochastic Frontier Models Using GAUSS," Working Papers 1403, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    17. Lee, Young Hoon, 2010. "Group-specific stochastic production frontier models with parametric specifications," European Journal of Operational Research, Elsevier, vol. 200(2), pages 508-517, January.
    18. Willam Greene, 2005. "Fixed and Random Effects in Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 23(1), pages 7-32, January.
    19. Federico Belotti & Silvio Daidone & Giuseppe Ilardi & Vincenzo Atella, 2013. "Stochastic frontier analysis using Stata," Stata Journal, StataCorp LP, vol. 13(4), pages 718-758, December.
    20. William C. Horrace & Kurt E. Schnier, 2010. "Fixed-Effect Estimation of Highly Mobile Production Technologies," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(5), pages 1432-1445.
    21. Satchachai, Panutat & Schmidt, Peter, 2008. "GMM with more moment conditions than observations," Economics Letters, Elsevier, vol. 99(2), pages 252-255, May.
    22. Seung Ahn & Young Lee & Peter Schmidt, 2007. "Stochastic frontier models with multiple time-varying individual effects," Journal of Productivity Analysis, Springer, vol. 27(1), pages 1-12, February.
    23. Mehdi Farsi & Aurelio Fetz & Massimo Filippini, 2007. "Benchmarking and Regulation in the Electricity Distribution Sector," CEPE Working paper series 07-54, CEPE Center for Energy Policy and Economics, ETH Zurich.

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    More about this item

    Keywords

    GMM; fixed effects; factor model; time-varying individual effects;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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