IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v38y2011i10p2271-2287.html
   My bibliography  Save this article

A copula regression model for estimating firm efficiency in the insurance industry

Author

Listed:
  • Peng Shi
  • Wei Zhang

Abstract

This article considers the estimation of insurers' cost-efficiency in a longitudinal context. The current practice ignores the tails of the cost distribution, where the most and least efficient insurers belong to. To address this issue, we propose a copula regression model to estimate insurers' cost frontier. Both time-invariant and time-varying efficiency are adapted to this framework and various temporal patterns are considered. In our method, flexible distributions are allowed for the marginals, and the subject heterogeneity is accommodated through an association matrix. Specifically, when fitting to the insurance data, we perform a GB2 regression on insurers total cost and employ a t-copula to capture their intertemporal dependencies. In doing so, we provide a nonlinear formulation of the stochastic panel frontier and the parameters are easily estimated by likelihood-based method. Based on a translog cost function, the X-efficiency is estimated for US property-casualty insurers. An economic analysis provides evidences of economies of scale and the consistency between the cost-efficiency and other performance measures.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2271-2287
    DOI: 10.1080/02664763.2010.545376
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664763.2010.545376
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2010.545376?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    2. PARK, Byeong & SIMAR, Léopold, 1992. "Efficient semiparametric estimation in stochastic frontier model," LIDAM Discussion Papers CORE 1992013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Frees, Edward W. & Shi, Peng & Valdez, Emiliano A., 2009. "Actuarial Applications of a Hierarchical Insurance Claims Model," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 165-197, May.
    4. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    5. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    6. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    7. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    8. McDonald, James B. & Butler, Richard J., 1990. "Regression models for positive random variables," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 227-251.
    9. Shi, Peng & Frees, Edward W., 2010. "Long-tail longitudinal modeling of insurance company expenses," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 303-314, December.
    10. 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.
    11. 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.
    12. Park, B. U. & Sickles, R. C. & Simar, L., 1998. "Stochastic panel frontiers: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 84(2), pages 273-301, June.
    13. 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.
    14. 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.
    15. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    16. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    17. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    18. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    19. McDonald, James B & Butler, Richard J, 1987. "Some Generalized Mixture Distributions with an Application to Unemployment Duration," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 232-240, May.
    20. Kumbhakar, Subal C & Hjalmarsson, Lennart, 1995. "Labour-Use Efficiency in Swedish Social Insurance Offices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(1), pages 33-47, Jan.-Marc.
    21. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    22. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    23. 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.
    24. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christine Amsler & Peter Schmidt & Wen-Jen Tsay, 2019. "Evaluating the CDF of the distribution of the stochastic frontier composed error," Journal of Productivity Analysis, Springer, vol. 52(1), pages 29-35, December.
    2. Graziella Bonanno & Domenico De Giovanni & Filippo Domma, 2017. "The ‘wrong skewness’ problem: a re-specification of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 47(1), pages 49-64, February.
    3. Schmidt, Rouven & Kneib, Thomas, 2023. "Multivariate distributional stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Huang, Tai-Hsin & Lin, Chung-I & Chen, Kuan-Chen, 2017. "Evaluating efficiencies of Chinese commercial banks in the context of stochastic multistage technologies," Pacific-Basin Finance Journal, Elsevier, vol. 41(C), pages 93-110.
    5. Huang, Tai-Hsin & Chen, Kuan-Chen & Lin, Chung-I, 2018. "An extension from network DEA to copula-based network SFA: Evidence from the U.S. commercial banks in 2009," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 51-62.
    6. Huang, Tai-Hsin & Hu, Chu-Nan & Chang, Bao-Guang, 2018. "Competition, efficiency, and innovation in Taiwan’s banking industry — An application of copula methods," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 362-375.
    7. Wondmagegn Tirkaso & Atakelty Hailu, 2022. "Does neighborhood matter? Spatial proximity and farmers’ technical efficiency," Agricultural Economics, International Association of Agricultural Economists, vol. 53(3), pages 374-386, May.
    8. Tai-Hsin Huang & Nan-Hung Liu & Subal C. Kumbhakar, 2018. "Joint estimation of the Lerner index and cost efficiency using copula methods," Empirical Economics, Springer, vol. 54(2), pages 799-822, March.
    9. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sickles, Robin C., 2005. "Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings," Journal of Econometrics, Elsevier, vol. 126(2), pages 305-334, June.
    2. Ali M. Oumer & Amin Mugera & Michael Burton & Atakelty Hailu, 2022. "Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia," Journal of Productivity Analysis, Springer, vol. 57(2), pages 213-241, April.
    3. Roberto Colombi & Subal Kumbhakar & Gianmaria Martini & Giorgio Vittadini, 2014. "Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency," Journal of Productivity Analysis, Springer, vol. 42(2), pages 123-136, October.
    4. 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.
    5. Farsi, Mehdi & Filippini, Massimo, 2009. "An analysis of cost efficiency in Swiss multi-utilities," Energy Economics, Elsevier, vol. 31(2), pages 306-315, March.
    6. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    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. 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.
    9. Martini, Gianmaria & Scotti, Davide & Viola, Domenico & Vittadini, Giorgio, 2020. "Persistent and temporary inefficiency in airport cost function: An application to Italy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 999-1019.
    10. Belotti, Federico & Ilardi, Giuseppe, 2018. "Consistent inference in fixed-effects stochastic frontier models," Journal of Econometrics, Elsevier, vol. 202(2), pages 161-177.
    11. Roberto Colombi & Gianmaria Martini & Giorgio Vittadini, 2017. "Determinants of transient and persistent hospital efficiency: The case of Italy," Health Economics, John Wiley & Sons, Ltd., vol. 26(S2), pages 5-22, September.
    12. Badunenko, Oleg & D’Inverno, Giovanna & De Witte, Kristof, 2023. "On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects," European Journal of Operational Research, Elsevier, vol. 310(1), pages 432-447.
    13. Young Hoon Lee & David Berri, 2008. "A Re‐Examination Of Production Functions And Efficiency Estimates For The National Basketball Association," Scottish Journal of Political Economy, Scottish Economic Society, vol. 55(1), pages 51-66, February.
    14. Quang Nguyen & Sean Pascoe & Louisa Coglan & Son Nghiem, 2021. "The sensitivity of efficiency scores to input and other choices in stochastic frontier analysis: an empirical investigation," Journal of Productivity Analysis, Springer, vol. 55(1), pages 31-40, February.
    15. Anbes Tenaye, 2020. "Technical Efficiency of Smallholder Agriculture in Developing Countries: The Case of Ethiopia," Economies, MDPI, vol. 8(2), pages 1-27, April.
    16. William C. Horrace & Peter Schmidt, 2002. "Confidence Statements for Efficiency Estimates from Stochastic Frontier Models," Econometrics 0206006, University Library of Munich, Germany.
    17. Peter Dawson & Stephen Dobson & Bill Gerrard, 2000. "Estimating Coaching Efficiency in Professional Team Sports: Evidence from English Association Football," Scottish Journal of Political Economy, Scottish Economic Society, vol. 47(4), pages 399-421, September.
    18. Badunenko, Oleg & Kumbhakar, Subal C., 2016. "When, where and how to estimate persistent and transient efficiency in stochastic frontier panel data models," European Journal of Operational Research, Elsevier, vol. 255(1), pages 272-287.
    19. I. Fraser & W. Horrace, 2003. "Technical Efficiency of Australian Wool Production: Point and Confidence Interval Estimates," Journal of Productivity Analysis, Springer, vol. 20(2), pages 169-190, September.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2271-2287. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.