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

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  • Han, Chirok
  • Orea, Luis
  • Schmidt, Peter

Abstract

This paper is an extension of Ahn, Lee and Schmidt (2001) to allow a parametric function for time-varying coefficients on the individual effects. It is shown that the main results of Ahn, Lee and Schmidt (2001) hold for our model too. Least squares is consistent, given white noise errors, but less efficient than a GMM estimator. An application of the GMM estimators to the measurement of cost efficiency of Spanish banks is also included. The empirical study shows the consequences of increasing the number of assumptions made regarding the error term. The GMM estimates, especially for private banks, cast doubt on the normality assumption supporting the traditional MLE frontier models.

Suggested Citation

  • Han, Chirok & Orea, Luis & Schmidt, Peter, 2002. "Estimation of a Panel Data Model with Parametric Temporal Variation in Individual Effects," Efficiency Series Papers 2002/05, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    • Handle: RePEc:oeg:wpaper:2002/05
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    File URL: https://www.unioviedo.es/oeg/ESP/esp_2002_05.pdf
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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.
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    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.
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    5. 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.
    6. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    7. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Jinyuan Chang & Zhentao Shi & Jia Zhang, 2021. "Culling the herd of moments with penalized empirical likelihood," Papers 2108.03382, arXiv.org, revised May 2022.
    9. 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.
    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. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    12. Satchachai, Panutat & Schmidt, Peter, 2008. "GMM with more moment conditions than observations," Economics Letters, Elsevier, vol. 99(2), pages 252-255, May.
    13. 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.
    14. 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.
    15. Willam Greene, 2005. "Fixed and Random Effects in Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 23(1), pages 7-32, January.
    16. 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.
    17. 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.
    18. Millimet, Daniel L. & Bellemare, Marc, 2023. "Fixed Effects and Causal Inference," IZA Discussion Papers 16202, Institute of Labor Economics (IZA).
    19. 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).
    20. 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.
    21. 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).
    22. 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.
    23. 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.

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    More about this item

    Keywords

    panel data; individual effects; temporal variation; GMM; cost efficiency; banks;
    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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