IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v44y2009i2p214-228.html
   My bibliography  Save this article

Multivariate probit models for conditional claim-types

Author

Listed:
  • Young, Gary
  • Valdez, Emiliano A.
  • Kohn, Robert

Abstract

This paper considers statistical modeling of the types of claim in a portfolio of insurance policies. For some classes of insurance contracts, in a particular period, it is possible to have a record of whether or not there is a claim on the policy, the types of claims made on the policy, and the amount of claims arising from each of the types. A typical example is automobile insurance where in the event of a claim, we are able to observe the amounts that arise from say injury to oneself, damage to one's own property, damage to a third party's property, and injury to a third party. Modeling the frequency and the severity components of the claims can be handled using traditional actuarial procedures. However, modeling the claim-type component is less known and in this paper, we recommend analyzing the distribution of these claim-types using multivariate probit models, which can be viewed as latent variable threshold models for the analysis of multivariate binary data. A recent article by Valdez and Frees [Valdez, E.A., Frees, E.W., Longitudinal modeling of Singapore motor insurance. University of New South Wales and the University of Wisconsin-Madison. Working Paper. Dated 28 December 2005, available from: http://wwwdocs.fce.unsw.edu.au/actuarial/research/papers/2006/Valdez-Frees-2005.pdf] considered this decomposition to extend the traditional model by including the conditional claim-type component, and proposed the multinomial logit model to empirically estimate this component. However, it is well known in the literature that this type of model assumes independence across the different outcomes. We investigate the appropriateness of fitting a multivariate probit model to the conditional claim-type component in which the outcomes may in fact be correlated, with possible inclusion of important covariates. Our estimation results show that when the outcomes are correlated, the multinomial logit model produces substantially different predictions relative to the true predictions; and second, through a simulation analysis, we find that even in ideal conditions under which the outcomes are independent, multinomial logit is still a poor approximation to the true underlying outcome probabilities relative to the multivariate probit model. The results of this paper serve to highlight the trade-off between tractability and flexibility when choosing the appropriate model.

Suggested Citation

  • Young, Gary & Valdez, Emiliano A. & Kohn, Robert, 2009. "Multivariate probit models for conditional claim-types," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 214-228, April.
  • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:214-228
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(08)00142-X
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Small, Kenneth A & Hsiao, Cheng, 1985. "Multinomial Logit Specification Tests," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-627, October.
    2. repec:ags:stataj:117568 is not listed on IDEAS
    3. Lorenzo Cappellari & Stephen P. Jenkins, 2006. "Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation," Stata Journal, StataCorp LP, vol. 6(2), pages 156-189, June.
    4. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    5. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 28(02), pages 205-220, November.
    6. Balia, Silvia & Jones, Andrew M., 2008. "Mortality, lifestyle and socio-economic status," Journal of Health Economics, Elsevier, vol. 27(1), pages 1-26, January.
    7. Weeks, Melvyn, 1997. " The Multinomial Probit Model Revisited: A Discussion of Parameter Estimability, Identification and Specification Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 11(3), pages 297-320, September.
    8. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    9. Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July.
    10. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
    11. repec:ags:stataj:116115 is not listed on IDEAS
    12. Cappellari, Lorenzo & Jenkins, Stephen P., 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 0(Number 3), pages 1-17.
    13. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    14. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
    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. repec:eee:jotrge:v:66:y:2018:i:c:p:291-299 is not listed on IDEAS
    2. repec:ags:ijameu:262367 is not listed on IDEAS
    3. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    4. repec:ris:apltrx:0332 is not listed on IDEAS
    5. repec:kap:transp:v:45:y:2018:i:2:d:10.1007_s11116-017-9824-9 is not listed on IDEAS
    6. Ulimwengu, John & Sanyal, Prabuddha, 2011. "Joint estimation of farmers' stated willingness to pay for agricultural services:," IFPRI discussion papers 1070, International Food Policy Research Institute (IFPRI).
    7. Oparinde, Adewale & Hodge, Ian, 2011. "Building livelihood resilience: a case study of factors affecting farm households’ adoption of coping and adaptive strategies in rural Nigeria," MPRA Paper 39162, 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:eee:insuma:v:44:y:2009:i:2:p:214-228. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.