Case studies using panel data models. (English) Zbl 1083.91538

Summary: We examine case studies from three different areas of insurance practice: health care, workers’ compensation, and group term life. These different case studies illustrate how the broad class of panel data models can be applied to different functional areas and to data that have different features. Panel data, also known as longitudinal data, models are regression-type models that have been developed extensively in the biological and economic sciences. The data features that we discuss include heteroscedasticity, random and fixed effect covariates, outliers, serial correlation, and limited dependent variable bias. We demonstrate the process of identifying these features using graphical and numerical diagnostic tools from standard statistical software. Our motivation for examining these cases comes from credibility rate making, a technique for pricing certain types of health care, property and casualty, workers’ compensation, and group life coverages. It has been a part of actuarial practice since Mowbray’s (1914) fundamental contribution. In earlier work, we showed how many types of credibility models could be expressed as special cases of panel data models. This paper exploits this link by using tools developed in connection with panel data models for credibility rate-making purposes. In particular, special routines written for credibility rate-making purposes are not required.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics


Full Text: DOI


[1] Baltagi B.H, Econometric Analysis of Panel Data (1995) · Zbl 0836.62105
[2] Baltagi B.H, Journal of Econometrics 77 pp 303– (1997) · Zbl 0900.62655
[3] Beenstock M, Journal of Risk and Insurance 55 pp 259– (1988)
[4] Browne M.J, Journal of Risk and Insurance 67 pp 73– (2000)
[5] Bühlmann H, ASTIN Bulletin 4 pp 199– (1967)
[6] Bühlmann h, Mitteilungen der Vereinigung Schweizerischer Versicherungs-Mathematiker 70 pp 111– (1970)
[7] Carroll A.M, Journal of Risk and Insurance 60 pp 185– (1993)
[8] Dannenburg D.R, Practical Actuarial Credibility Models (1996) · Zbl 0905.62101
[9] De Vylder F, ASTIN Bulletin 12 pp 115– (1981)
[10] Diggle P.J, Analysis of Longitudinal Data (1994)
[11] Frees E.W, Data Analysis Using Regression Models (1996)
[12] Frees E.W, Insurance: Mathematics and Economics 24 pp 229– (1999) · Zbl 0945.62112
[13] Goovaerts M.J, Credibility Theory (1987)
[14] Greene W.H, Econometric Analysis, 2. ed. (1993)
[15] Hachemeister C.A, Credibility: Theory and Applications pp 129– (1975)
[16] Hand D.J, Practical Longitudinal Data Analysis (1996)
[17] Harville D.A, Biometrika 61 pp 383– (1974) · Zbl 0281.62072
[18] Harville D.A, Journal of the American Statistical Association 72 pp 320– (1977)
[19] Hsiao C, Analysis of Panel Data (1986)
[20] Jewell W.S, Giornale dell’Instituto Italiano degli Attuari 38 pp 1– (1975)
[21] Kaas R, ASTIN Bulletin 27 pp 287– (1997)
[22] Klugman S, Bayesian Statistics in Actuarial Science (1992)
[23] Klugman S, Loss Models: From Data to Decisions (1998)
[24] Mowbray A.H, Proceedings of the Casualty Actuarial Society 1 pp 24– (1914)
[25] Patterson H.D, Biometrika 58 pp 545– (1971) · Zbl 0228.62046
[26] Rao C.R, Journal of the American Statistical Association 67 pp 112– (1970)
[27] Rizzo J.A, Journal of Risk and Insurance 56 pp 482– (1989)
[28] Robinson G.K, Statistical Science 6 pp 15– (1991) · Zbl 0955.62500
[29] Swamy P.A.V.B, Econometrica 38 pp 311– (1970) · Zbl 0195.48802
[30] Thies C.F, Journal of Risk and Insurance 55 pp 467– (1988)
[31] Weisberg S, Applied Linear Regression, 2. ed. (1985)
[32] Weiss M, Journal of Risk and Insurance 52 pp 199– (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.