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Estimation and Testing for Functional Form in Pure Premium Regression Models

Published online by Cambridge University Press:  29 August 2014

Scott E. Harrington
Scott E. Harrington*
Affiliation:
University of Pennsylvania
*
Insurance Department, Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA
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Abstract

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Estimation of pure premiums for alternative rate classes using regression methods requires the choice of a functional form for the statistical model. Common choices include linear and log-linear models. This paper considers maximum likelihood estimation and testing for functional form using the power transformation suggested by Box and Cox. The linear and log-linear models are special cases of this transformation. Application of the procedure is illustrated using auto insurance claims data from the state of Massachusetts and from the United Kingdom. The predictive accuracy of the method compares favorably to that for the linear and log-linear models for both data sets.

Keywords

Pure premium regression modelsfunctional formmaximum likelihood estimationpower transformation
Type
Astin Competition 1985: Prize-Winning Papers and Other Selected Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue S1 , April 1986 , pp. S31 - S43
Copyright
Copyright © International Actuarial Association 1986

References

Ajne, B. (1974) A Note on the Multiplicative Ratemaking Model. ASTIN Bulletin 8, 144–153.CrossRefGoogle Scholar
Albrecht, P. (1983) Parametric Multiple Regression Risk Models: Theory and Statistical Analysis. Insurance: Mathematics and Economics 2, 49–66.Google Scholar
Almer, B. (1957) Risk Analysis in Theory and Practical Statistics. 15th International Congress of Actuaries 2, 314–353.Google Scholar
Amemiya, T. (1973) Regression Analysis When the Variance of the Dependent Variable is Proportional to the Square of its Expectation. Journal of the American Statistical Association 68, 928–934.CrossRefGoogle Scholar
Bailey, R. (1963) Insurance Rates with Minimum Bias. Proceedings of the Casualty Actuarial Society 50, 4–11.Google Scholar
Bailey, R. and Simon, L. (1960) Two Studies in Automobile Insurance Ratemaking. Proceedings of the Casualty Actuarial Society 47, 1–19.Google Scholar
Box, G. and Cox, D. (1964) An Analysis of Transformations. Journal of the Royal Statistical Society B 26, 211–243.Google Scholar
Chamberlain, C. (1980) Relativity Pricing through Analysis of Variance. Pricing Property and Casualty Insurance Contracts, 1980 CAS Discussion Paper Program, San Juan, Puerto Rico.Google Scholar
Chang, L. and Fairley, W. (1978) An Estimation Model for Multivariate Insurance Rate Classification. Automobile Insurance Risk Classification: Equity & Accuracy. Boston, Mass.: Massachusetts Division of Insurance.Google Scholar
Chang, L. and Fairley, W. (1979) Pricing Automobile Insurance Under Multivariate Classification of Risks: Additive versus Multiplicative. Journal of Risk and Insurance 46, 75–98.CrossRefGoogle Scholar
Coutts, S. (1984) Motor Insurance Rating, An Actuarial Approach. Journal of the Institute of Actuaries 111, 87–148.CrossRefGoogle Scholar
Eeghen, J., Greup, E. and Nijssen, J. (1983) Ratemaking. Surveys of Actuarial Studies No. 2. Nationale-Nederlanden N.V. Research Department, Rotterdam, the Netherlands.Google Scholar
Fairley, W., Tomberlin, T. and Weisberg, H. (1981) Pricing Automobile Insurance Under a Cross-Classification of Risks: Evidence from New Jersey. Journal of Risk and Insurance 48, 505–514.CrossRefGoogle Scholar
Freifelder, L. (1984) Estimation of Classification Factor Relativities: A Modeling Approach. Paper presented at the 1984 Risk Theory Seminar, Los Angeles, California.Google Scholar
Holmes, R. (1970) Discriminatory Bias in Rates Charged by the Canadian Auto Insurance Industry. Journal of the American Statistical Association 65, 108–122.CrossRefGoogle Scholar
Johnson, P. and Hey, G. (1971) Statistical Studies in Motor Insurance. Journal of the Institute of Actuaries 97, 201–232.Google Scholar
Jung, J. (1968) On Automobile Insurance Ratemaking. ASTIN Bulletin 5, 41–48.CrossRefGoogle Scholar
Lahiri, K. and Egy, D. (1981) Joint Estimation and Testing for Functional Form and Heteroskedasticity. Journal of Econometrics 15, 299–307.CrossRefGoogle Scholar
Lund, R. (1975) Tables for an Approximate Test for Outliers in Linear Models. Technometrics 17, 473–476.CrossRefGoogle Scholar
Nelson, H. and Granger, C. (1979) Experience with Using the Box-Cox Transformation when Forecasting Economic Time Series. Journal of Econometrics 10, 57–69.CrossRefGoogle Scholar
Oberhofer, W. and Kmenta, J. (1974) A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models. Econometrica 42, 579–590.CrossRefGoogle Scholar
Samson, D. and Thomas, H. (1984) Claims Modeling in Auto Insurance. Department of Business Administration, University of Illinois, Urbana, Illinois.Google Scholar
Sant, D. (1980) Estimating Expected Losses in Auto Insurance. Journal of Risk and Insurance 47, 133–151.CrossRefGoogle Scholar
Seal, H. (1968) The Use of Multiple Regression in Risk Classification Based on Proportionate Losses. 18th International Congress of Actuaries 2, 659–664.Google Scholar
Weisberg, H. and Tomberlin, T. (1982) A Statistical Perspective on Actuarial Methods for Estimating Pure Premiums from Cross-Classified Data. Journal of Risk and Insurance 49, 539–563.CrossRefGoogle Scholar
Weisberg, H., Tomberlin, T. and Chatterjee, S. (1984) Predicting Insurance Losses Under Cross-Classification: A Comparison of Alternative Approaches. Journal of Business and Economic Statistics 2, 170–178.Google Scholar
Wilcken, C. (1971) Comment on ‘Discriminatory Bias in Rates Charged by the Canadian Automobile Insurance Industry’. Journal of the American Statistical Association 66, 289–291.Google Scholar