IDEAS home Printed from https://ideas.repec.org/a/bla/jrinsu/v76y2009i4p821-846.html
   My bibliography  Save this article

Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data

Author

Listed:
  • Jean‐Philippe Boucher
  • Michel Denuit
  • Montserrat Guillen

Abstract

The hunger for bonus is a well‐known phenomenon in insurance, meaning that the insured does not report all of his accidents to save bonus on his next year's premium. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is generated by censorship of this Poisson distribution. Then, we present new models for panel count data based on the zero‐inflated Poisson distribution. From the claims distributions, we propose an approximation of the accident distribution, which can provide insight into the behavior of insureds. A numerical illustration based on the reported claims of a Spanish insurance company is included to support this discussion.

Suggested Citation

  • Jean‐Philippe Boucher & Michel Denuit & Montserrat Guillen, 2009. "Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 821-846, December.
  • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:4:p:821-846
    DOI: 10.1111/j.1539-6975.2009.01321.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1539-6975.2009.01321.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1539-6975.2009.01321.x?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
    ---><---

    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. Dionne, G & Vanasse, C, 1992. "Automobile Insurance Ratemaking in the Presence of Asymmetrical Information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 149-165, April-Jun.
    3. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    4. Artis, Manuel & Ayuso, Mercedes & Guillen, Montserrat, 1999. "Modelling different types of automobile insurance fraud behaviour in the Spanish market," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 67-81, March.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Boucher, Jean-Philippe & Denuit, Michel, 2006. "Fixed versus Random Effects in Poisson Regression Models for Claim Counts: A Case Study with Motor Insurance," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 285-301, May.
    7. Mullahy, John, 1997. "Heterogeneity, Excess Zeros, and the Structure of Count Data Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 337-350, May-June.
    8. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    9. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    10. Philipson, Carl, 1960. "The Swedish Systems of Bonus," ASTIN Bulletin, Cambridge University Press, vol. 1(3), pages 134-141, April.
    11. Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.
    12. Walhin, Jean François & Paris, José, 2000. "The True Claim Amount and Frequency Distributions within a Bonus-Malus System," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 391-403, November.
    13. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    14. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    15. R. Golden, 2003. "Discrepancy Risk Model Selection Test theory for comparing possibly misspecified or nonnested models," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 229-249, June.
    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. Jean-Philippe Boucher & Steven Côté & Montserrat Guillen, 2017. "Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models," Risks, MDPI, vol. 5(4), pages 1-23, September.
    2. Minwoo Kim & Himchan Jeong & Dipak Dey, 2022. "Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach," Risks, MDPI, vol. 10(3), pages 1-11, March.
    3. Xuejun Jiang & Yunxian Li & Aijun Yang & Ruowei Zhou, 2020. "Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk," Empirical Economics, Springer, vol. 58(5), pages 2085-2103, May.
    4. Di Kuang & Bent Nielsen & Jens Perch Nielsen, 2011. "Forecasting in an Extended Chain‐Ladder‐Type Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 345-359, 06.

    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. Mihaela DAVID, 2014. "Modeling The Frequency Of Claims In Auto Insurance With Application To A French Case," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 13, pages 69-85, June.
    2. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    3. Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.
    4. Niklas Elert, 2014. "What determines entry? Evidence from Sweden," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 55-92, August.
    5. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    6. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
    7. Dahen, Hela & Dionne, Georges, 2010. "Scaling models for the severity and frequency of external operational loss data," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1484-1496, July.
    8. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    9. Denise Desjardins & Georges Dionne & Yang Lu, 2023. "Hierarchical random‐effects model for the insurance pricing of vehicles belonging to a fleet," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(2), pages 242-259, March.
    10. David Mihaela & Jemna Dănuţ-Vasile, 2015. "Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models," Scientific Annals of Economics and Business, Sciendo, vol. 62(2), pages 151-168, July.
    11. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    12. Christopher J. W. Zorn, 1998. "An Analytic and Empirical Examination of Zero-Inflated and Hurdle Poisson Specifications," Sociological Methods & Research, , vol. 26(3), pages 368-400, February.
    13. Gurmu, Shiferaw & Rilstone, Paul & Stern, Steven, 1998. "Semiparametric estimation of count regression models1," Journal of Econometrics, Elsevier, vol. 88(1), pages 123-150, November.
    14. Ulf‐ G. Gerdtham, 1997. "Equity in Health Care Utilization: Further Tests Based on Hurdle Models and Swedish Micro Data," Health Economics, John Wiley & Sons, Ltd., vol. 6(3), pages 303-319, May.
    15. Stefano Mainardi, 2003. "Testing convergence in life expectancies: count regression models on panel data," Prague Economic Papers, Prague University of Economics and Business, vol. 2003(4), pages 350-370.
    16. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2013. "Chi-squared tests for evaluation and comparison of asset pricing models," Journal of Econometrics, Elsevier, vol. 173(1), pages 108-125.
    17. Angers, Jean-François & Desjardins, Denise & Dionne, Georges, 2004. "Modèle Bayésien de tarification de l’assurance des flottes de véhicules," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 253-303, Juin-Sept.
    18. Georges Dionne & Olfa Ghali, 2005. "The (1992) Bonus‐Malus System in Tunisia: An Empirical Evaluation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(4), pages 609-633, December.
    19. Raymond Kan & Cesare Robotti & Jay Shanken, 2013. "Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology," Journal of Finance, American Finance Association, vol. 68(6), pages 2617-2649, December.
    20. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 40278, University Library of Munich, Germany.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jrinsu:v:76:y:2009:i:4:p:821-846. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/ariaaea.html .

    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.