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Long-tail longitudinal modeling of insurance company expenses

Author

Listed:
  • Shi, Peng
  • Frees, Edward W.

Abstract

The insurance industry is known to have high operating expenses in the financial services sector. Insurers, investors and regulators are interested in models to understand the behavior of expenses. However, the current practice ignores skewness, occasional negative values as well as their temporal dependence. Addressing these three features, this paper develops a longitudinal model of insurance company expenses that can be used for prediction, to identify unusual behavior, and to measure firm efficiency. Specifically, we use a three-parameter asymmetric Laplace density for the marginal distribution of insurers' expenses in each year. Copula functions are employed to accommodate their temporal dependence. As a function of explanatory variables, the location parameter allows us to analyze an insurer's expenses in light of the firm's characteristics. Our model can be interpreted as a longitudinal quantile regression. The analysis is performed using property-casualty insurance company data from the National Association of Insurance Commissioners of years 2001-2006. Due to the long-tailed nature of insurers' expenses, two alternative approaches are proposed to improve the performance of the longitudinal quantile regression model: rescaling and transformation. Predictive densities are derived that allow one to compare the predictions for individual insurers in a hold-out-sample. Both predictive models are shown to be reasonable with the rescaling method outperforming the transformation method. Compared with standard longitudinal models, our model is shown to be superior in identifying insurers' unusual behavior.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:303-314
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    References listed on IDEAS

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    1. Yin, Guosheng & Zeng, Donglin & Li, Hui, 2008. "Power-Transformed Linear Quantile Regression With Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1214-1224.
    2. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    3. Bali, Turan G., 2003. "The generalized extreme value distribution," Economics Letters, Elsevier, vol. 79(3), pages 423-427, June.
    4. 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.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    7. Turan G. Bali & Panayiotis Theodossiou, 2008. "Risk Measurement Performance of Alternative Distribution Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 411-437.
    8. 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.
    9. Toivanen, Otto, 1997. "Economies of scale and scope in the Finnish non-life insurance industry," Journal of Banking & Finance, Elsevier, vol. 21(6), pages 759-779, June.
    10. Fenn, Paul & Vencappa, Dev & Diacon, Stephen & Klumpes, Paul & O'Brien, Chris, 2008. "Market structure and the efficiency of European insurance companies: A stochastic frontier analysis," Journal of Banking & Finance, Elsevier, vol. 32(1), pages 86-100, January.
    11. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    12. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    13. Lindsey, J.K. & Lindsey, P.J., 2006. "Multivariate distributions with correlation matrices for nonlinear repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 720-732, February.
    14. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
    15. Roger Koenker & Zhijie Xiao, 2004. "Unit Root Quantile Autoregression Inference," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 775-787, January.
    16. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    17. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    18. Cummins, J. David & Weiss, Mary A., 1993. "Measuring cost efficiency in the property-liability insurance industry," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 463-481, April.
    19. F. Fecher & D. Kessler & S. Perelman & P. Pestieau, 1993. "Productive performance of the French insurance industry," Journal of Productivity Analysis, Springer, vol. 4(1), pages 77-93, June.
    20. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    21. Zimmer, David M. & Trivedi, Pravin K., 2006. "Using Trivariate Copulas to Model Sample Selection and Treatment Effects: Application to Family Health Care Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 63-76, January.
    22. Gardner, Lisa A. & Grace, Martin F., 1993. "X-Efficiency in the US life insurance industry," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 497-510, April.
    23. J. David Cummins & Mary A. Weiss, 1998. "Analyzing Firm Performance in the Insurance Industry Using Frontier Efficiency Methods," Center for Financial Institutions Working Papers 98-22, Wharton School Center for Financial Institutions, University of Pennsylvania.
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    Cited by:

    1. Shi, Peng & Valdez, Emiliano A., 2014. "Multivariate negative binomial models for insurance claim counts," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 18-29.
    2. Shi, Peng, 2012. "Multivariate longitudinal modeling of insurance company expenses," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 204-215.
    3. repec:eee:ecmode:v:67:y:2017:i:c:p:149-158 is not listed on IDEAS

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