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Stochastic frontier models with multiple time-varying individual effects


  • Seung Ahn
  • Young Lee


  • Peter Schmidt


This paper proposes a flexible time-varying stochastic frontier model. Similarly to Lee and Schmidt [1993, In: Fried H, Lovell CAK, Schmidt S (eds) The measurement of productive efficiency: techniques and applications. Oxford University Press, Oxford], we assume that individual firms’ technical inefficiencies vary over time. However, the model, which we call the “multiple time-varying individual effects” model, is more general in that it allows multiple factors determining firm-specific time-varying technical inefficiencies. This allows the temporal pattern of inefficiency to vary over firms. The number of such factors can be consistently estimated. The model is applied to data on Indonesian rice farms, and the changes in the efficiency rankings of farms over time demonstrate the model’s flexibility. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:27:y:2007:i:1:p:1-12
    DOI: 10.1007/s11123-006-0020-8

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    References listed on IDEAS

    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. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. Sangho Kim & Young Hoon Lee, 2006. "The productivity debate of East Asia revisited: a stochastic frontier approach," Applied Economics, Taylor & Francis Journals, vol. 38(14), pages 1697-1706.
    4. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    5. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
    6. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    7. Viliam Druska & William C. Horrace, 2004. "Generalized Moments Estimation for Spatial Panel Data: Indonesian Rice Farming," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 185-198.
    8. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
    9. 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.
    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.
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    Cited by:

    1. Ahn, Seung C. & Perez, M. Fabricio, 2010. "GMM estimation of the number of latent factors: With application to international stock markets," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 783-802, September.
    2. Young Hoon Lee, 2013. "Estimation of temporal variations in fan loyalty: application of multi-factor models," Chapters,in: The Econometrics of Sport, chapter 8, pages 135-153 Edward Elgar Publishing.
    3. Sickles, Robin C. & Hao, Jiaqi & Shang, Chenjun, 2015. "Panel Data and Productivity Measurement," Working Papers 15-018, Rice University, Department of Economics.
    4. Antonio Alvarez & Carlos Arias, 2014. "A selection of relevant issues in applied stochastic frontier analysis," Economics and Business Letters, Oviedo University Press, vol. 3(1), pages 3-11.
    5. Camilla Mastromarco & Laura Serlenga & Yongcheol Shin, 2012. "Is Globalization Driving Efficiency? A Threshold Stochastic Frontier Panel Data Modeling Approach," Review of International Economics, Wiley Blackwell, vol. 20(3), pages 563-579, August.
    6. Sakano, Ryoichi & Obeng, Kofi, 2011. "Examining the Inefficiency of Transit Systems Using Latent Class Stochastic Frontier Models," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 50(2).
    7. Perez, Marcos & Ahn, Seung Chan, 2007. "GMM Estimation of the Number of Latent Factors," MPRA Paper 4862, University Library of Munich, Germany.
    8. Pavlos Almanidis & Giannis Karagiannis & Robin Sickles, 2015. "Semi-nonparametric spline modifications to the Cornwell–Schmidt–Sickles estimator: an analysis of US banking productivity," Empirical Economics, Springer, vol. 48(1), pages 169-191, February.
    9. Roman Matkovskyy, 2016. "Arbitrary temporal heterogeneity in time of European countries panel model," Economics Bulletin, AccessEcon, vol. 36(1), pages 576-587.
    10. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    11. repec:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0515-5 is not listed on IDEAS
    12. Mastromarco Camilla & Laura Serlenga & Yongcheol Shin, 2013. "Globalisation and technological convergence in the EU," Journal of Productivity Analysis, Springer, vol. 40(1), pages 15-29, August.
    13. Grigorios Emvalomatis, 2012. "Adjustment and unobserved heterogeneity in dynamic stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 37(1), pages 7-16, February.
    14. Chen, Yueh H. & Lin, Winston T., 2009. "Analyzing the relationships between information technology, inputs substitution and national characteristics based on CES stochastic frontier production models," International Journal of Production Economics, Elsevier, vol. 120(2), pages 552-569, August.
    15. repec:liu:liucej:v:13:y:2016:i:2:p:135-167 is not listed on IDEAS
    16. Dang, Viet Anh & Kim, Minjoo & Shin, Yongcheol, 2015. "In search of robust methods for dynamic panel data models in empirical corporate finance," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 84-98.
    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. Young Hoon Lee, 2009. "Frontier Models and their Application to the Sports Industry," Working Papers 0903, Research Institute for Market Economy, Sogang University, revised 2009.
    19. Bernd Frick & Young Lee, 2011. "Temporal variations in technical efficiency: evidence from German soccer," Journal of Productivity Analysis, Springer, vol. 35(1), pages 15-24, February.

    More about this item


    Time-varying technical efficiency; Stochastic frontiers; Panel data; C51; D24;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity


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