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MODELLING AND ESTIMATING INDIVIDUAL AND FIRM EFFECTS WITH COUNT PANEL DATA

Published online by Cambridge University Press:  02 May 2018

Jean-François Angers ,
Denise Desjardins ,
Georges Dionne  and
François Guertin
Jean-François Angers
Affiliation:
Department of Mathematics and Statistics, University of Montreal, Montreal, Canada E-Mail: [email protected]
Denise Desjardins
Affiliation:
Canada Research Chair in Risk Management, HEC Montréal, Montreal, Canada E-Mail: [email protected]
Georges Dionne*
Affiliation:
Canada Research Chair in Risk Management, HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, room 4.454, Montreal, QC, H3T 2A7, Canada
François Guertin
Affiliation:
Calcul Québec, University of Montreal, Montreal, Canada E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We propose a new parametric model for the modelling and estimation of event distributions for individuals in different firms. The analysis uses panel data and takes into account individual and firm effects in a non-linear model. Non-observable factors are treated as random effects. In our application, the distribution of accidents is affected by observable and non-observable factors from vehicles, drivers and fleets of vehicles. Observable and unobservable factors are significant to explain road accidents, which mean that insurance pricing should take into account all these factors. A fixed effects model is also estimated to test the consistency of the random effects model.

Keywords

Individual effectfirm effectnon-linear modelpanel dataPoissonDirichletinsurance pricingR code
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1049 - 1078
Copyright
Copyright © Astin Bulletin 2018 

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References

Allison, P.D. and Waterman, R.P. (2002) Fixed-effects negative binomial regression models. Sociological Methodology, 32, 247–265.Google Scholar
Angers, J.-F., Desjardins, D., Dionne, G. and Guertin, F. (2006) Vehicle and fleet random effects in a model of insurance rating or fleets of vehicles. Astin Bulletin, 36, 25–77.Google Scholar
Baltagi, B.H. (1995) Econometric Analysis of Panel Data. Chichester: Wiley.Google Scholar
Boucher, J.P. and Denuit, M. (2006) Fixed versus random effects in Poisson regression models for claim counts: A case study with motor insurance. Astin Bulletin, 36, 285–301.Google Scholar
Boucher, J.-P., Denuit, M. and Guillen, M. (2008) Models of insurance claim counts with time dependence based on generalization of Poisson and negative binomial distributions. Casualty Actuary Society, 2, 135–162.Google Scholar
Boyer, M., Dionne, G. and Vanasse, C. (1992) Econometric models of accident distributions. In Contributions to Insurance Economics (ed. Dionne, G.), pp. 169–213. New York: Springer.Google Scholar
Cameron, A.C. and Trivedi, P.K. (1986) Econometric models based on count data: Comparisons and applications of some estimators and tests. Journal of Applied Econometrics, 1, 29–54.Google Scholar
Cameron, A.C. and Trivedi, P.K. (2013a) Regression Analysis of Count Data, Second Edition. Cambridge, UK: Cambridge University Press.Google Scholar
Cameron, A.C. and Trivedi, P.K. (2013b) Count Panel Data. Mimeo: University of California.Google Scholar
Chang, L. and Chen, W. (2005) Data mining of tree-based models to analyse freeway accident frequency. Journal of Safety Research, 36, 365–375.Google Scholar
Desjardins, D., Dionne, G. and Pinquet, J. (2001) Experience rating schemes for fleets of vehicles. Astin Bulletin, 31, 1, 81–106.Google Scholar
Dionne, G. and Vanasse, C. (1989) A generalization of automobile insurance rating models: The negative binomial distribution with a regression component. Astin Bulletin, 19, 199–212.Google Scholar
Dionne, G. and Vanasse, C. (1992) Automobile insurance ratemaking in the presence of asymmetrical information. Journal of Applied Econometrics, 7, 149–165.Google Scholar
Dionne, G., Gagné, R., Gagnon, F. and Vanasse, C. (1997) Debt, moral hazard and airline safety: An empirical evidence. Journal of Econometrics, 79, 379–402.Google Scholar
Dionne, G., Gagné, R. and Vanasse, C. (1998) Inferring technological parameters from incomplete panel data. Journal of Econometrics, 87, 303–327.Google Scholar
Fardilha, T., de Lourdes Centeno, M. and Esteves, R. (2016) Tariff systems for fleets of vehicles: A study on the portfolio of Fidelidade. European Actuarial Journal, 6, 331–349.Google Scholar
Fluet, C. (1999) Commercial vehicle insurance: Should fleet policies differ from single vehicle plans? In Automobile Insurance: Road Safety, New Drivers, Risks, Insurance Fraud and Regulation (eds. Dionne, G. and Laberge-Nadeau, C.), pp. 101–117. Kluwer Academic Press.Google Scholar
Frangos, N. and Vrontos, S.D. (2001) Design of optimal bonus-malus systems with a frequency and a security component on an individual basis in automobile insurance. Astin Bulletin, 31, 1–22.Google Scholar
Frees, E.W. and Valdez, E. (2011) Hierarchical insurance claims modeling. Journal of the American Statistical Association, 103, 1457–1469.Google Scholar
Gouriéroux, C., Monfort, A. and Trognon, A. (1984) Pseudo maximum likelihood methods: Applications to Poisson models. Econometrica, 52, 701–720.Google Scholar
Greene, W.H. (2004) The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects. Econometrics Journal, 7, 98–119.Google Scholar
Greene, W.H. (2007) Functional form and heterogeneity in models for count data. Foundations and Trends in Econometrics, 1 (2), 115–218.Google Scholar
Hausman, J.A. (1978) Specification tests in econometrics. Econometrica, 46, 1251–1271.Google Scholar
Hausman, J.A. and Wise, D.A. (1979) Attrition bias in experimental and panel data: The Gary income maintenance experiment. Econometrica, 47, 455–473.Google Scholar
Hausman, J.A., Hall, B.H. and Griliches, Z. (1984) Econometric models for count data with an application to the patents – R&D relationship. Econometrica, 52, 909–938.Google Scholar
Holmstrom, B. (1982) Moral hazard in teams. The Bell Journal of Economics, 13, 324–340.Google Scholar
Hsiao, C. (1986) Analysis of panel data. Econometric Society Monographs, no 11. Cambridge: Cambridge University Press.Google Scholar
Laffont, J.J. and Martimort, D. (2001) The Theory of Incentives: The Principal-Agent Model. Princeton: Princeton University Press.Google Scholar
Norberg, N. (1986) Hierarchical credibility: Analysis of a random effect linear model with nested classification. Scandinavian Actuarial Journal, 1986, 204–222.Google Scholar
Pinquet, J. (2013) Experience rating in non-life insurance. In Handbook of Insurance (ed. Dionne, G.), pp. 471–586. New York: Springer.Google Scholar
Purcaru, O. and Denuit, M. (2003) Dependence in dynamic claim frequency credibility models. Astin Bulletin, 33 (1), 23–40.Google Scholar
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