Upper and lower constraints for sensitivity of experience rating are discussed by Lemaire(1988). A single widely advocated criterion predictive accuracy is shown here to provide both upper and lower constraints. This is illustrated by a simulation of impact of four bonus-malus systems on rating of a driver with long term consistent parameters. All four are found to be under-responsive to such a driver's individual experience. Lemaire's (1988) invited article in this Journal elucidated functioning of several countries' bonus-malus rating systems for automobile insurance. This comment reviews some aspects of those systems from perspective of American actuarial tradition. A bonus-malus system (BMS) is a particular form of experience rating. Experience rating has been used in most lines of insurance in US, beginning with workers' compensation in years before World War I. It is generally used as a supplement to classification rating, in recognition that there are differences among risks, identifiable by individual risk that are not accounted for by classification rates. sensitivity of a rating plan has both upper and lower constraints. Lemaire introduces concept of efficiency, which measures incremental change in premium induced by an incremental change in an insured's true loss frequency. ratio of these changes should be 100 percent for perfect efficiency. sensitivity of plans reviewed never reaches this level, due to constraints of market resistance to high surcharges and a social reluctance towards having plan financially encourage non-reporting of accidents. Similar constraints have operated in Western Hemisphere. For instance, Snader (1980) points out that sensitivity of a 1940 US workers' compensation experience rating plan was determined in part by specifying that smallest rated risk could be debited no more than 25 percent for a single accident. Gary G. Venter is President of Workers' Compensation Reinsurance Bureau, New York, New York. This content downloaded from 157.55.39.17 on Wed, 06 Jul 2016 06:15:00 UTC All use subject to http://about.jstor.org/terms A Comparative Analysis of Most European And Japanese Bonus-malus Systems 543 main criterion cited for optimal plan sensitivity, however, has been how well plan estimates individual insured results. For instance, Meyers (1985) says The purpose of experience rating is to estimate expected loss ratio, Venter (1987) says the degree to which an insured should be charged for past loss experience is degree to which that experience is predictive of future loss experience, or Freifelder (1985) says The accurate prediction of an insured's true loss potential is goal of ratemaking process. This note will explore BMS plan sensitivity from viewpoint of predictive accuracy. Predictive accuracy provides both an upper and lower constraint on sensitivity of a plan to risk experience. If plan is not sensitive enough, high risk insureds will be undercharged and good risks overcharged. If plan is too sensitive, opposite will occur, as random fluctuations in experience will be accorded too much weight. This happens currently with experience rating of large commercial risks, which are sometimes given full credibility. Lemaire's concept of efficiency is related to predictive accuracy, in that a 100 percent efficient plan in actuarial balance should be highly accurate. Nonetheless, as will be seen below, plans with comparable measures of efficiency do not necessarily predict equally well. A direct measure of predictive accuracy could be developed by using a risk's relative charge from BMS as an estimate of its relative frequency. By simulation, estimated frequency could be compared to true frequency, and average of squared errors, for example, could provide a measure of predictive accuracy of plan. An analytic result using expected squared error approach to evaluating experience rating can be found in Freifelder (1985) where, rather than using BMS type rules, experience rating is based on Bayes estimation in gamma-Poisson model, introduced by Greenwood and Yule (1920) and by Keffer (1929). Applying this approach to bonus-malus systems, a simulation was performed for four countries' BMS's at five assumed claim frequencies (X). Each risk kept its assumed frequency over time. For each risk, 20 years of simulated experience were put through BMS rules to determine a rating level, and hence an implied estimated frequency level. At each claim frequency 10,000 such risks were simulated, and for each risk estimated frequency was compared to assumed frequency that generated experience. resulting mean squared errors for each assumed frequency are shown in Table 1.