Abstract
The analysis of individual risks in insurance raises problems that occur in any statistical analysis of longitudinal data. Considering insurance data, the endogeneous variables are severity variables (for instance: number and cost of claims, duration of compensations, and so on). The exogeneous variables of the current period can be first be used as rating factors in an a priori rating model. The allowance for the history of the policyholder in a rating model is more intricate, and it can be performed from two different approaches. They are related to interpretations of serial correlation for individual data that can be summarized in the following way.
Thanks to Georges Dionne and to the referee for their comments. This paper benefited from a discussion with Daniel MacFadden. Financial support from the Fédération Française des Sociétés d’Assurance is acknowledged.
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References
Aitchison, J., and S.D. Silvey (1958), “Maximum Likelihood Estimation of Parameters Subject to Restraints”, The Annals of Mathematical Statistics 29, 813–828.
Bailey, A.L. (1950), “Credibility Procedures, Laplace’s Generalization of Bayes’s Rule and the Combination of Collateral Knowledge with Observed Data”, Proceedings of the Casualty Actuarial Society 37, 7–23.
Balestra, P., and M. Nerlove (1966), “Pooling Cross-Section and Time Series Data in the Estimation of a Dynamic Model: the Demand for Natural Gas”, Econometrica, 34, 585–612.
Bühlmann, H. (1967), “Experience Rating and Credibility”, ASTIN Bulletin 4, 199–207.
Cameron, A.C., and P.K. Trivedi (1990), “Regression-Based Tests for Overdispersion in the Poisson Model”, Journal of Econometrics 46, 347–364.
Chesher, A. (1984), “Testing for Neglected Heterogeneity”, Econometrica 52, 865–872.
Cox, D.R., and E.J. Snell (1971), “On Tests Statistics Calculated from Residuals”, Biometrika 58, 589–594.
Cox, D.R. (1983), “Some Remarks on Over-Dispersion”, Biometrika 70, 269–274.
Cummins, J. D., G. Dionne, J.B. Mac DONALD, and B.M. Pritchett (1990), “Application of the GB2 Distribution in Modelling Insurance Loss Processes”, Insurance: Mathematics and Economics 9, 257–272.
Davis, P., and P. Rabinowitz (1984), Methods of Numerical Integration. New York: Academic Press.
Dean, C., and J.F. Lawless (1989), “Tests for Detecting Overdispersion in Poisson Regression Models”, Journal of the American Statistical Association 84, 467–472.
Dionne, G., and C. Vanasse (1989), “A Generalization of Automobile Insurance Rating Models: the Negative Binomial Distribution with a Regression Component”, ASTIN Bulletin 19, 199–212.
Dionne, G., and C. Vanasse (1992), “Automobile Insurance Ratemaking in the Presence of Asymmetrical Information”, Journal of Applied Econometrics 7, 149–165.
Dionne, G., and N. Doherty (1992), “Adverse Selection in Insurance Markets: a Selective Survey”, in Contributions to Insurance Economics, Kluwer Academic Publishers (Editor: G. Dionne).
Dionne, G., and C. Vanasse (1997), “The Role of Memory and Saving in Long-Term Contracting with Moral Hazard: An Empirical Evidence in Automobile Insurance”, Mimeo, Risk Management Chair, HEC-Montreal.
Gerber, H., and D. Jones (1973), “Credibility Formulas with Geometric Weigths”, Proceedings of the Business and Economic Section, American Statistical Association, 229–230.
Gouriéroux, C., A. Monfort, and A. Trognon (1984a), “Pseudo Likelihood Methods: Theory”, Econometrica 52, 681–700.
Gouriéroux C., A. Monfort, and A. Trognon (1984b), “Pseudo likelihood methods: applications to Poisson models”, Econometrica 52, 701–720.
Gouriéroux, C., and A. Monfort (1991), “Simulation Based Inference in Models with Heterogeneity”, Annales d’Economie et de Statistique 20-21, 69–107.
Gouriéroux, C., A. Monfort, and E. Renault (1993), “Indirect Inference”, Journal of Applied Econometrics 8, 85–118.
Hansen, L.P. (1982), “Large Sample Properties of Generalized Method of Moments Estimators”, Econometrica 50, 1029–1054.
Hausman, La. (1978), “Specification tests in econometrics”, Econometrica 46, 1251–1271.
Hausman, J.A., B.H. Hall, and Z. Griliches (1984), “Econometric Models for Count Data with an Application to the Patents-R&D Relationship”, Econometrica 52, 909–938.
Jennrich, R.I. (1969), “Asymptotic Properties of Non-Linear Least Squares Estimators”, The Annals of Mathematical Statistics 40, 633–643.
Johnson, N.L., and S. Kotz (1969), Distribution in Statistics: Discrete Distributions. Boston: Houghton Mifflin Co.
Lancaster, T. (1990), The Econometric Analysis of Transition Data. Econometric Society Monographs, Cambridge University Press.
Lemaire, J.(1985), Automobile Insurance: Actuarial Models. Huebner International Series on Risk, Insurance and Economic Security.
Lemaire, J. (1995), Bonus-Malus Systems in Automobile Insurance. Huebner International Series on Risk, Insurance and Economic Security.
Lillard, L. (1993), “Simultaneous Equations for Hazards (Marriage Duration and Fertility Timing)”, Journal of Econometrics 56, 189–217.
Macfadden, D. (1989), “A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration”, Econometrica 57, 995–1026.
Mowbray, A.H. (1914), “How Extensive a Payroll Exposure Is Necessary To Give a Dependable Pure Premium”, Proceedings of the Casualty Actuarial Society 1, 24–30.
Pinquet, J., J.C. Robert, G. Pestre, and L. Montocchio, L. (1992), Tarification a Priori et a Posteriori des Risques en Assurance Automobile. Mémoire au Centre d’Études Actuarielles.
Pinquet, J. (1996), “Hétérogénéité Inexpliquée”, Document de travail THEMA 9611.
Pinquet, J. (1997a), “Allowance for Cost of Claims in Bonus-Malus Systems”, ASTIN Bulletin 27, 33–57.
Pinquet, J. (1997b), “Estimating and Testing for Time-Dependent Heterogeneity in a Poisson Model”, Document de travail THEMA 9705.
Pinquet, J. (1997c), “Testing for Heterogeneity Through Consistent Estimators”, Document de travail THEMA 9714.
Rao, C.R. (1948), “Large Sample Tests of Statistical Hypothesis Concerning Several Parameters with Applications to Problems of Estimation”, Proceedings of the Cambridge Philosophical Society 44, 50–57.
Silvey, S.D. (1959), “The Lagrangian Multiplier Test”, The Annals of Mathematical statistics 30, 389–407.
Sundt, B. (1981), “Credibility Estimators with Geometric Weights”, Insurance: Mathematics and Economics 7, 113–122.
White, H. (1982), “Maximum Likelihood Estimation of Misspecified Models”, Econometrica 50, 1–25.
Whitney, A.W. (1918), “The Theory of Experience Rating”, Proceedings of the Casualty Actuarial Society 4, 274–292.
Winter, R.A. (1992), “Moral Hazard and Insurance Contracts”, in Contributions to Insurance Economics, Kluwer Academic Publishers (Editor: G. Dionne).
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Pinquet, J. (1999). Allowance for Hidden Information by Heterogeneous Models and Applications to Insurance Rating. In: Dionne, G., Laberge-Nadeau, C. (eds) Automobile Insurance: Road Safety, New Drivers, Risks, Insurance Fraud and Regulation. Huebner International Series on Risk, Insurance, and Economic Security, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4058-8_3
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