Unisex Tariffs in Health Insurance

Transcription

1 The Geneva Papers, 2006, 31, ( ) r 2006 The International Association for the Study of Insurance Econoics /06 $ Unisex Tariffs in Health Insurance Oliver Riedel Business Adinistration, Risk Manageent and Insurance, University of Giessen, Giessen, Gerany. E-ail: oliver.t.riedel@wirtschaft.uni-giessen.de European legislation requires insurance copanies to calculate unisex tariffs after Deceber 21, Health insurance copanies can copensate the loss of gender-based priary preiu differentiation by using extended preiu refund systes (experience rating) to differentiate the preius between the risks ex post. In this paper, it is shown that about 2/3 of the current ratio between feales and ales expected financial burden can be reached through secondary preiu differentiation and the extended risk transfer (back) to the insured can be accepted. The Geneva Papers (2006) 31, doi: /palgrave.gpp Keywords: unisex tariffs; health insurance; experience rating; stochastic dynaic optiization; Monte-Carlo siulation; own contribution Introduction On Deceber 13, 2004, the Council of Europe adopted a directive to ipleent the principle of equal treatent between en and woen in the access to and supply of goods and services (Council Directive 2004/113/EC), which requires insurance copanies to base their calculations on unisex tariffs after Deceber 21, 2007, though eber states are still peritted to allow the use of the insured s gender as a risk paraeter if the risk assessent is based on relevant and accurate actuarial as well as statistic data excluding costs related to pregnancy and aternity. The Geran governent has already established unisex tariffs in various insurance classes. These require the private insurance industry to ipleent unisex tariffs in the copulsory nursing care insurance and fro 2006 on in state subsidy and tax break pensions ( Riester Pensions ). Therefore, obligatory unisex tariffs in Geran private (health) insurance see possible. In contrast to life insurance copanies, private health insurers can use not only priary (ex ante) but also secondary (experience-based) preiu differentiation. As unisex tariffs do not perit priary (gender) preiu differentiation, the focus is now on extended preiu refund systes as a way of copensating this. Priary and secondary preiu differentiation in health insurance Priary preiu differentiation is based on risk factors that can easily be observed in advance, such as gender and age in life insurance. Therefore, Geran private health insurance copanies calculate their preius in advance according to the actuarial equivalent principle and along the lines of life insurance, where the expected discounted paid preius equal the expected discounted payents by the insurer. For

2 P(N=1) P(N=1) P(N=1) P(N=1) P(C OP 3 ) The Geneva Papers on Risk and Insurance Issues and Practice 234 NCB 0 NCB 1 NCB 2 NCB 3 P(C>OP 1 ) P(C>OP 0 ) P(C OP 0 ) P(C>OP 2 ) P(C>OP 3 ) P(C OP 1 ) P(C OP 2 ) OP 0 OP 1 OP 2 OP 3 P(N=0) P(N=0) P(N=0) P(N=0) NCB 0 NCB 1 NCB 2 NCB 3 Figure 1. Out-of-pocket payent in preiu refund systes. these calculations, Geran private health insurers use three tariff factors: (1) state of health, (2) age at the beginning of the contract, and (3) gender of the insured. To include subjective risk factors in calculation (at least in retrospect), the insurer can use secondary preiu differentiation as a part of experience-based rating where the preiu depends on insurance payents in the past (clai s experience). 1 Usually, the insurer refunds a nuber of onthly preius if the insured did not receive payents fro the contract in the previous year with significant influence to the current year s de facto paid preiu. Optial out-of-pocket payent in private health insurance To deterine the extent of preiu refunds, the insurer generally considers the aount of years since the last insurance copensation. Usually, the insured receives one onthly preiu for every year in succession without indenification, though the axiu nuber of preiu refunds is liited to about three or four. 2 If the insurer pays for edical costs, the insured does not receive a preiu refund independent of her current no clai bonus class (Figure 1). If there has not been any edical treatent in the previous year (N¼0) and the insured has been in no clai bonus class (NBC) 1, the insured is now located in NBC 2 with the probability being P(N¼0), and ay, for exaple, receive a preiu refund of two onthly preius. If there was at least one edical treatent (N¼1), the insured has to decide whether she pays on her own to reach NBC 2 and get the preiu refund or whether she decides to shift the edical costs (C) to the insurer and receives no preiu refund in NBC 0. 1 See Karten (1993, pp ). 2 The preiu refund should be anticipated (not depending on the annual balance), because only such systes can be applied for the whole duration of the contract, see Farny (2000, pp ).

3 Oliver Riedel Unisex Tariffs in Health Insurance 235 When the optial out-of-pocket payent (OP) is calculated, further edical treatents during the following years have to be taken into consideration and stochastic dynaic optiization 3 should be used. If risk neutral behaviour is assued, the optial OP iniizes the expected discounted health cost for the entire life, which consists of insurance preius, OP and preiu refunds and is higher than the next year s preiu refund (aspect of investent in future preiu refunds). 4 The expected financial burden till death at each age only depends on the OP at this age, assuing the optial insured s decisions during the following years till death, and can be calculated for each age, and NBC i according to (Markov process): EðCi ðop i ÞÞ ¼yearly preiu preiu refund 2 þð1 q Þ 6PðN ¼ 0Þ EðCiþ1 þ1 4 fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2 þ PðN ¼ 1Þ 6 4 following costs without edical treatent ZOP i xf ðxþdx 0 fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} expected out-of-pocket payent þ PðC OP i Þ EðC þ1 iþ1 Þ fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} expected cost reduction by out-of-pocket payent ðnbc iþ1þ þ PðC 4OP i Þ EðC0 þ1 Þ fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} no effect by out-of-pocket payent ðnbc 0Þ 33 5 ð1þ where OP i is the out-of-pocket payent for NBC i and age ; C the rando variable of health costs at age ; f the density function of health costs at age ; E(C i (OP i )) the expected financial burden till death as a function of OP i, NBC i and þ age ; E(C 1 i þ 1 ) the expected financial burden fro age þ 1 till death assuing optial out-of-pocket payent fro age þ 1 till death; 6 q is the probability of death at age. 3 The procedure of stochastic dynaic optiization is extensively presented in Neuann and Morlock (2002, pp ). 4 See Riedel (2005, pp. 7 9). 5 If the insured is in the highest NBC i she will stay in this class without payents by the insurer and cannot reach NBC i þ 1. 6 E(C 101 i )¼0 will be used as the starting point of optiization.

4 The Geneva Papers on Risk and Insurance Issues and Practice ales EUR NBC 2&3 NBC 1 NBC age feales EUR NBC 2&3 NBC 1 NBC age Figure 2. Optial out-of-pocket payent. This equation is iniized by OP i ¼ EðC þ1 0 Þ EðC þ1 iþ1 Þ: ð2þ The resulting optial OP (beginning of the contract at age 30) is shown in Figure 2 using the preiu refund syste presented in Figure 1. It is calculated using the statistics (published by Geran insurance supervisors) ortality rate, probability of cancellation and estiated expected edical costs. 7 To obtain ore detailed inforation about the distribution of edical costs and the probability of edical treatent, a Geran health insurance copany s portfolio of 72,667 policyholders has been analysed. Explicitly, only the net risk preiu is considered. The 10 per cent loading to prevent the insured fro high preius at retireent age is only iplicitly considered because a rise in health costs would only affect the preius for people under the age of 65. It can be shown that different refund systes result in different aounts of financial burden for the insured. 8 Therefore, priary and secondary differentiations have to be analysed siultaneously. 7 See VerBAV (Deceber 2002), VerBaFin (June 2003) and VerBaFin (Noveber 2003). 8 See Riedel (2005, pp ).

5 Oliver Riedel Unisex Tariffs in Health Insurance 237 Risk aversion is odelled by liited OP, for exaple, next year s obtainable preiu refund or the annual preiu, because stochastic dynaic optiization cannot be used analogically for risk-averse utility functions. 9 Experience rating and unisex tariffs in health insurance According to Rothschild and Stiglitz, 10 the effects of adverse selection can be neglected if different insurance policies with different extents of coverage are offered. Under these conditions, there is a self-selection and both types of risks can be calculated risk adequate. Because the eployer pays 50 per cent of the preiu but a 0 per cent share of the deductible, deductibles are neither popular nor applicable in Geran private health insurance. Technically unisex tariffs are only a variation of priary preiu differentiation. Because the total financial burden of the insured depends on priary and secondary preiu differentiation, a change of refund systes (to one with ore no clais bonus classes and/or higher preiu refunds in each class) could copensate the effects of adverse selection on unisex tariffs. 11 The financial burden using unisex tariffs consists of unisex coponents (yearly preiu) and gender-based coponents (probability of edical treatent, distribution of edical costs) and is therefore located between the financial burden of gender-based tariffs and unisex tariffs without a preiu refund syste. To illustrate the effects of the two coponents of the financial burden, a basic odel is used without a preiu refund syste (or deductibles as discussed above) and dynaic effects. 12 There is only one clais aount; therefore, the insured has a wealth of W 1 without and W 2 with edical treatent. With priary preiu differentiation each insured buys full insurance (contract B f or B ) and pays a gender-based preiu, resulting in a utility of U g (U f g ) for ale (feale). The full-coverage contract C is calculated as a unisex tariff; it is sybolized by the dotted line. In this situation, the feales will be better off (U f u >U f g ) and the ales will be worse off (U u >U g ) copared to gender-based tariffs perhaps en will even be better off if they do not buy any insurance contract, depending on the utility function (as in Figure 3). Considering now (extended) preiu refund systes, there will be OP, which can be interpreted and illustrated as soe kind of a deductible that is gender-based, calculated even with a unisex preiu. Therefore, such a contract is located below the 451-line and on a contract line (dotted in Figure 4) between the unisex tariff C and the gender-based preiu B (B f ). If the insured can choose between different refund systes, he (she) will select a contract D (D f ), whose utility spd U u ( spd U u f ) is lower (higher) than the utility of the 9 See Baberg and Coenenberg (2004, pp ). 10 Rothschild and Stiglitz (1976). 11 Morlock and Zipelann (1999) analysed analogue effects on the Geran car insurance arket. 12 The sae arguentation holds for a coparison between ore and less extended preiu refund systes.

6 The Geneva Papers on Risk and Insurance Issues and Practice 238 W 2 U g f U u f C B B f A U g U u W 1 Figure 3. Contracts without a preiu refund syste. W 2 C B D A U g spd U u U u W 1 Figure 4. and secondary preiu differentiation ale insured. gender-based contract but higher (lower) than that of the unisex contract without a preiu refund syste. If the insured cannot choose which refund syste is used (as in the Geran Private Health Insurance), an optial contract will any ties not be available. In soe cases the insured would even prefer no preiu refund syste rather than an extended one (see Figure 5, contract E vs. contract C), but regarding liited OP (for exaple to the next year s obtainable preiu refund, where the insured cannot lose if he pays on his own) this proble sees not to be very iportant. After this basic odel has been presented, the effects of unisex tariffs are analysed using the stochastic dynaic optiization presented in the section entitled Optial out-of-pocket payent in private health insurance. The odel shows that the expected financial burden of feales (current calculation) is approxiately 63 per cent higher than that of ales depending on the age (30 years) and the NBC at the beginning of the contract, the rise of health costs, interest rate and OP liit (1 per cent, 3 per cent p.a. and 1.25 ties next year s discounted preiu refund). In Table 1, it is shown that extended preiu refund systes could diinish (to soe extent) the effects of unisex tariffs even for the risk-averse insured and also

7 Oliver Riedel Unisex Tariffs in Health Insurance 239 W 2 U u B C U g spd U u E A W 1 Figure 5. Male insured could prefer no preiu refund syste. Table 1 Ratio between feales and ales expected financial burden Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8] differentiate between high and low risks of each gender. 13 (Results of other types of OP liits are presented in the appendix.) The risk transfer back to the insured increases in relation to the increase in secondary preiu differentiation. To rate this effect, a Monte-Carlo siulation has been executed presented are the 5 per cent, 25 per cent, 50 per cent, 75 per cent and 95 per cent percentiles (Figure 6). This rise in uncertainty can be accepted by the risk-averse insured because the OP is strongly liited. Furtherore, with unisex tariffs and syste C, after soe years of being insured: the 75 per cent percentile of ales financial burden is less than the 5 per cent percentile without change of the refund syste; and the 50 per cent percentile of feales financial burden is less than the 25 per cent percentile of current calculation (Figure 7). 13 For risk-neutral behaviour, see Riedel and Muench (2005, pp ).

8 The Geneva Papers on Risk and Insurance Issues and Practice 240 Max. Current Calculation (Age 85) - Syste A EUR % 50% 5% Min. ale 75% 25% feale Unisex-Tariffs (Age 85) - Syste C EUR ale feale Figure 6. Financial burden. Feales (Age 35) EUR Current Calculation and Syste A Males (Age 35) Unisex and Syste C EUR Unisex and Syste A Unisex and Syste C Figure 7. Financial burden.

9 Oliver Riedel Unisex Tariffs in Health Insurance 241 Especially in long-ter insurance, the contract iplies a coverage of changes in the health status of the insured during the contract. 14 Therefore, it can be socially desirable if chronic diseases are excluded fro the refund syste. Fro the insurer s point of view, the sae applies for preventive edical check-ups. Conclusion The ipleentation of unisex tariffs in health insurance is technically only a variation of priary preiu differentiation. Because the expected financial burden of the insured is also deterined by secondary preiu differentiation, private health insurance has (in contrast to e.g. life insurance) the opportunity to copensate lower priary differentiation by extended secondary differentiation. Extended preiu refund systes lead, even in unisex tariffs, to widely differentiated expected financial burdens of different types of risks between and aong sexes. References Baberg, G. and Coenenberg, A.G. (2004) Betriebswirtschaftliche Entscheidungslehre, 12th edn., Mu nchen: Verlag Vahlen. Farny, D. (2000) Versicherungsbetriebslehre, 3rd edn., Karlsruhe: Verlag Versicherungswirtschaft. Karten, W. (1993) Das Einzelrisiko und seine Kalkulation Versicherungswirtschaftliches Studienwerk, Studientext 12, Versicherungsbetriebslehre, Wiesbaden: Th. Gabler. Meyer, U. (1997) Langfristige Versicherungsverhältnisse in der Privaten Krankenversicherung, in L. Männer (ed) Langfristige Versicherungsverha ltnisse O konoie, Technik, Institutionen, Karlsruhe: Verlag Versicherungswirtschaft. Morlock, M. and Zipelann, M. (1999) Bonus-alus systes influence of priary preiu differentiation on bonus-alus systes, K-Foru 1/99: Neuann, K. and Morlock, M. (2002) Operations Research, 2nd edn., Mu nchen, Wien: Hanser Fachbuch. Riedel, O. (2005) Wie wirkt eine Änderung der Beitragsrückerstattung auf die Belastung der Versicherten in der PKV, Geran Riskand Insurance Review, 1 21, online: riedelpaper.pdf. Riedel, O. and Muench, C. (2005) Zur Bedeutung der sekundären Präiendifferenzierung bei Unisex-Tarifen in der Krankenversicherung, Zeitschrift fu r die gesate Versicherungswissenschaft 3: Rothschild, M. and Stiglitz, J. (1976) Equilibriu in copetitive insurance arkets: an essay on the econoics of iperfect inforation, Quarterly Journal of Econoics 90(4): Appendix A Tables 2 7 show the details of the ratio between feales and ales expected financial burden, subject to various conditions. 14 See Meyer (1997, pp ).

10 The Geneva Papers on Risk and Insurance Issues and Practice 242 Table 2 Ratio between feales and ales expected financial burden, unliited OP Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8] Table 3 Ratio between feales and ales expected financial burden, OP liited to 1-tie the next year s discounted preiu refund Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8] Table 4 Ratio between feales and ales expected financial burden, OP liited to 1.5-ties the next year s discounted preiu refund Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8]

11 Oliver Riedel Unisex Tariffs in Health Insurance 243 Table 5 Ratio between feales and ales expected financial burden, OP liited to 2-ties the next year s discounted preiu refund Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8] Table 6 Ratio between feales and ales expected financial burden, OP liited to 1-tie the current preiu Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8] Table 7 Ratio between feales and ales expected financial burden, OP liited to 2-ties the current preiu Syste A [0 (1) 3 0, 1, 2, 3] Syste A [0 (1) 3] Syste B [0 (1) 11] Syste C [0 (2) 10] Syste D [0 (3) 9] Syste E [0 (4) 8]

12 The Geneva Papers on Risk and Insurance Issues and Practice 244 About the Author Oliver Riedel studied fro 1990 to 1995 econoatheatics (business atheatics) at the University of Haburg, with ain focus on insurance atheatics and insurance business. Fro 1996 to 2004 he worked as a teaching and research assistant at the chair of risk anageent and insurance at the University of Giessen. During this tie he wrote his thesis about the econoic effects of environental liability rules, which was accepted in 2003 by the Departent of Econoics and Business Adinistration. Since 2004 he is assistant professor (Wissenschaftlicher Assistant) in Giessen. His research interests are risk anageent, environental econoics, health and public casualty insurance.