In Australia, compulsory third party insurance (CTP) covers

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1 COMPULSORY THIRD PARTY INSURANCE: METHODS OF MAKING EXPLICIT ALLOWANCE FOR INFLATION B. J. BRUTON and J. R. CUMPSTON Australia SUMMARY An inflatin index is essential when cnstructing claim payment mdels frm past payment data, and when prjecting these results t give estimates f the prvisins fr utstanding claims anti f necessary premiums. This paper examines the chice f inflatin indices fr cmpulsry third party insurance in tw Australian states. Tw different indices, ne based n average weekly earnings per emplyed male unit and the ther based n cnsumer prices, were tested. The index based n average weekly earnings was cnsidered t be superir in that past claim payment data, tgetlmr with this index, gave reasnably stable claim payment mdels. Sme experiments were made fr an actual ffice t illustrate tim effects f different inflatin rate assumptins. I. INTRODUCTION This paper briefly examines three prblems assciated with inflatin-- (a) When determining prvisins fr utstanding claims, and premium rates, hw can past claim payments be edjusted t remve the effects f inflatin? (b) What prprtin f claim payments, if any, is unaffected by inflatin after the accident? (c) What is the effect f different assumptins in establishing prvisins fr utstanding claims and premium rates? 2. GENERAL BACKGROUND In Australia, cmpulsry third party insurance (CTP) cvers persnal injury received in rad accidents, but nt damage t vehicles. The amunt payable is unlimited, but may be reduced if cntributry negligence by the injured persn ccurred. In Victria a large number f insurers shared the market until recently when statutry cntrl f premiums resulted in all but

2 COMPULSORY THIRD PARTY INSURANCE 6 5 tw insurers withdrawing frm the field. In Western Australia, the Mtr Vehicle Insurance Trust has had a statutry mnply fr abut twenty-five years, Data has been supplied by ne f the tw current Victrian insurers, and by the Mtr Vehicle Insurance Trust f W.A. These tw insurers arc f similar size, each making payments t abut 7,5 injured persns per annum. Wc recrd ur appreciatin in being able t publish figures frm these tw surces. 3" INSURED CASUALTIES Data was btained shwing the numbers f vehicles insured during each year (perid I July t fllwing 3 June), tgether with claim payments fr the crrespnding twelve mnths sub-divided by year f accident. It was cnsidered necessary t cnvert data n numbers f vehicles insured int data n insured casualties. In bth states the intrductin f legislatin making seat-belt use cmpulsry has led t a substantial decline in the numbers f persns injured r killed in rad accidents per registered vehicle. Fr this reasn it was cnsidered that the numbers f insured vehicles prvided a pr measure f the underlying expsure t risk. The increasing use f seat-belts may result in lwer claim payments per insured casualty, making insured casualties itself an unreliable measure. 4" ADJUSTMENT FOR INFLATION We cnsider it is mst desirable that explicit, allwance be made fr inflatin in determining premium rates and reserves fr utstanding claims. Accrdingly, past claim payments shuld be increased by subsequent inflatin rates t bring them t current values. The Australian Bureau f Statistics publishes a number f inflatin indices, f which the mst relevant are Average Weekly Earnings per Emplyed Male Unit (AWE), and Cnsumer Price Index (CPI). Payments made in respect f CTP insurance can be classified int a number f categries. Hspital,. medical, lss f incme and ther special damages amunt t apprximately 20% f ttal 5 "i ; ~ ~.

3 66 COMPULSORY THIRD PARTY INSURANCE payments. Legal and investigatin csts amunt t abut 2%, and general damages accunt fr the remaining 60%. Hspital and medical expenses, lss f incme payments and legal expenses can be expected t reflect changes in earnings patterns within the cmmunity. General damages are awarded by curts (r mutually settled befre actin) withut indicatin as t the basis f determinatin ; hwever, these amunts are set against the backgrund f general incme levels prevailing at pint f payment. Therefre, n a priri grunds it is cnsidered that AWE is likely t prve a mre relevant inflatin index than CPI. Hwever, a statistical methd f testing the apprpriateness f different indices wuld be useful. 5" CLAIM PAYMENTS PER INSURED CASUALTY Table I illustrates claim payments per insured casualty in respect f the Mtr Vehicle Insurance Trust f W.A., where past experience has been adjusted using AWE as the inflatin index Further tables are shwn in Appendix A fr Western Australian data using CPI t adjust past experience, and fr Victrian data using AWE and CPI. TABLE I Financial year f payment W.A. claim payments per insured casualty during each f the fllwing years (claim payments adjusted t 3]6/74 values using AWE index) year f accident 1966/ /68 x968/69 I969/7 197/7I 1971/72 x972/73 x973/74 $ $ $ $ $ $ $ $ t25 I 4 lot xz 3 I24" i24" x x4 33 I a x x I42 I56 x () IiI 93 I I56 98 I Ttal x,42i, x,878 1,716 1,7 9 1,68 x,52 1,7725 1,595 (* fr explan/ttin, see Appendix A).

4 year COMPULSORY THIRD PARTY INSURANCE 6 7 If the apprpriate inflatin index has been used, and the cnditins affecting payments have been stable, level amunts shuld appear in each rw f the abve table. Accrdingly, fr each rw a straight line was fitted n a least squares basis (ignring any values marked with asterisks). This is illustrated in the fllwing graph, where data frm the secnd, third, fifth and sixth rws f Table I, tgether with fitted lines, has been shwn 500 :~ayment per insured casualty 400 rw ,- rws ~- rw6 I I I I I I I I 66.'67 ~, /69 /70 /71 / Fig. i The slpe f each f the fitted lines was tested t see if it was significantly different frm zer. The fllwing table sets ut the slpes f each line tgether with an asterisk if the slpe was significantly different frm zer (at the 5% level). A tw-sided t-test was used, with (n- 2) degrees f freedm, where n was the number f bservatins. Fr bth states, the fitted lines btained using AWE ~ad a mixture f psitive and negative slpes. By cntrast, all but ne f the fitted lines' btained using CPI had psitive slpes. We cnsider this prvides sme indicatin that AWE is a mre suitable inflatin index than CPI in adjusting CTP experience.

5 68 COMPULSORY TIIIRD PARTY INSURANCE TABLE 2 Financial Slpes f trend lines fitted t claim payments per insured year f casualty (claim payments adjusted t 30/6/74 values) payment -- X,V.A. Victria?,,ear f AWE CPI AWE CPI accident index index index index O 1[ 12" --I --I I 2 15" xi 3 ~ I~* 5 7* 9* 29* 32* * 33* Althugh the significance levels between AWE and CPI were incnclusive, we cnsider that the lwer slpes generally prvide further cnfirmatin that AWE is a mre relevant index. 6. TESTS USING DIFFERENT PROPORTIONS UNAFFECTED BY INFLATION The preceding sectin assumes that all payments are affected by inflatin. Hwever, it is pssible that a prprtin f payments (fr example, hspital and medical expenses) is nt affected by inflatin after the accident. TA m.v. 3 Financial Slpes f trend lines fitted t claim payments per insured year f casualty (claim payments adjusted t 3/6/74 values using payment AWE index and assuming that prprtins (p) f payments -- are nt affected by inflatin after the accident) year f W.A. Victria accident p =. p---.2 p = 0. 4 p =. p = 0.2 p =. 4 0 II ]I I! --I --I ~I I II --I~ --it IO x 4 5 7* 8* 0* 29* 33* 37* I * 36* 41.

6 COMPULSORY TItlR1) PARTY INSURANCE 6 9 The fllwing table examines the slpe f fitted lines using AWE as an inflatin index but assuming 20% and 4% f payments are nt affected by inflatin. As in the preceding table, the asterisks indicate the statistical significance f the difference frm zer f the slpes f the fitted lines. The abve results d nt prvide any clear supprt fr any particular chice f p. Mst f the available data, hwever, came frm a perid f lw stable inflatin rates. Data frm a perid f unstable inflatin rates is necessary befre any clear indicatin as t the true value f p can be btained. 7. WEIGtITING FACTOR In rder t reduce tlle effect f year by year fluctuatins, it seems desirable that several years' past experience shuld be cmbined when making estimates fr future experience. Hwever, it is likely that varius changes have ccurred in past years which culd permanently affect future experience, e.g. the grwing use f seat-belts has reduced the severity f rad accidents. Therefre, we cnsider that data frm recent years is likely t be mre reliable than ld data. This suggests that estimates shuld be made using weighted averages f data frm several years, placing mre weight n the mst recent data. A methd by which this can be achieved is described in Appendix 13. This methd invlves the use f a weighting factr in the range t i. Claim payments made "n" years ag are weighted by the factr raised t the pwer (n ~ I). A zer weighting factr nly cnsiders the mst recent year's data, and a weighting factr f I gives a simple mean f the estimates derived frm all the available payment data. 8. EFFECT OF VARYING ASSUMPTIONS T illustrate the effect f yarying assumptins n premium rates and prgisins fr utstanding claims, the fllwing estimates were made fr the Mtr Vehicle Insurance Trust f \,V.A.

7 70 COMPULSORY TIIIRD PARTY INSURANCE TABLE. 4 Premiums Estimates f necessary earned prenliums during I974/75 Weight- High future inflatin Lw future inflatin ing factr AWl:. AWE CPI AWE AWE CPI index, index, iudex, index, imlex, index, p =. p = 0. 4 p = 0.0 p =. p = 0.4 p =. $M $M SM SM $M SM I3.2 [ i. 0.2 ~ r6.o ,4 I I x , Range f estimates 3 % 2 % i i % 4 % 2 / 1 % TABLE 5 Outstanding claims Estimates f prvisins necessary fr utstanding claims at 3/6]74 Weight- High future inflatin Lw future inflatin ing factr AXVE AWE CPI AWE AWE CPI index, index, index, index, index, index, p----. p = 0. 4 p =. p =. p= 0.4 p =. $M $M SM $M SM SM I I. I 37. I 33. t i t.6 3I Range f estimates 3 % 2 % 12 % 3 % 1% 12 % Inflatin was taken int accunt n the fllwing bases: High.future inflatin: AWE increases by 28%, 24%, 2%, 16% and 13% fr years t 1978/79 and lo% p.a. thereafter. Lve future inflatin: AWE increases by 7% fr each future year.

8 C()MPULSORY TIIIRI) PARTY INSURANCE 71 In all cases CPI increases have been taken as 4% p.a. less than thse fr AWE. Tlle abve estimates were made assuming: investment earnings f 9 / p.a. in future claims administratin expenses f I /O f the average prvisin fr utstanding claims during the year average premium delay f ne mnth initial expenses f 1% f premiums prfit and slvency margins f 12.5% f premiums. The abve estimates shw that when high future inflatin is expected, the use f a lw index (such as CPI) can, as wuld be expected, lead t underestimatin f necessary future premiums and prvisins fr utstanding claims. In such cnditins, the use f a mre apprpriate index (such as AWE) but t high a value f p, can als lead t underestimatin. Where a lw index is used, the degree f underestimatin increases as the weighting factr increases. This ccurs because increasing weight is being placed n payments made many years ag, which have nt prperly been cnverted t current values. If lw future inflatin is expected, the use f a lw index can als lead t underestimatin. The use f a mre suitable index, but t high a value f p, may hwever cause very little errr. This is because a high value f p leads t higher claim payments per insured casualty derived frm past data, cmpensating partly r whlly fr the underestimatin f the future effects f inflatin. We cnsider that sme indicatin f the relevance f the inflatin index can be btained frm the range f results btained with different weighting methds. The abve tables shw that the estimates btained using CPI as an index have a much greater spread than thse btained using AWE. If there is reasn t believe that the underlying payment prcess has been stable fr a number f years, then a wide range f estimates resulting frm different weighting methds suggests that an inapprpriate inflatin index has been used. This is nly a rugh criterin, hwever, and it wuld appear unwise t cnclude frm the abve ranges that the use f AWE with p = 0.4 is better than the use ~f AWE with p =.. The abve tables clearly shw tile effect f high inflatin n this class~ f insurance.!i ~

9 72 COMPULSORY TItlRI) PARTY INSURANCE Table I : Table 6 : Table 7 : Table 8 : Financial ),,ear f payment APPENDIX A Claim payments per insured casualty See sectin 5 f text. Western Australia data using CPI t adjust past experience. Victrian data using AWE t adjust past experience. Victrian data using CPI t adjust past experience. "I'A I~L1~ 6 W.A. claim l)ayments per insured casualty during each f the fllwing years (claina payulents adjusted t 3/6/74 values using CPI index) year f accident 1966/67 I967] / /7 197/ / / /74 $ $ $ $ $ $ $ $ q lo2 I12* 118" x ii q loo Ttal 977 1,356 1,299 t,371 1,447 1,352 1,554 1,516 Financial year f payment TABLE 7 Victrian claim pa.yments per insured casualty during each f the fllwing years (claim payments adjusted t 3/6/74 values using A WE index) year f 1965/ I966/ 1967] 1968/ 1969/ 197] 1971/ 1972/ 1973/ accident $ $ $ $ $ $ $ $ $ * ~53" 50* t () I l i

10 COMI'ULSORY TIIIRI) I'ARTY INSURANCE 73 TABLE 8 Financial year f payment year f accident Victrian claim payments per insured casualty during each f the fllwing years (claim payments adjusted t 30/6[74 values using CPI index) x9651 I966/ / 1969/ 197/ I97I/ x972/ 1973/ $ $ $ $ $ $ $ $ $ I 16 I * 49* 48* 193 x96 ~ r4 56x t I I Values marked with an asterisk are suspect, as they depend cnsiderably n the accuracy f adjustments made in rder t remve the effects f n-fault payment schemes. A//the Victrian values are apprximate, as they have been derived frm recrds sub-divided by year f reprting, nt year f accident. APPENDIX ]3 Estimatin meth, ds Let re(k) be the claim payments (in current values) per unit f risk, paid ill the (k w I)th year after the 3rear f accident, which is t be estimated c(j) be the cnversin factr used t cnvert claim payments during the j'th mst recent payment year t current values (assuming that loo% f all payments are directly linked t the inflatin index) e(j) be the expsure t risk in the j'th mst recent accident year p be the prprtin f claim payments nt affected by inflatin after the accident P(j, k) be the claim payments made in the j'th mst recent payment year as a result f accidents in the (k ~ I)th year prir t the payment year

11 ~4 COMPULSORY TilIRD PARTY INSURANCE n be the number f payment years fr which data is available M(j, k) be the estimate f re(k) derived frm P(j, k) w be the weighting" factr used when cmbining values f M(j, k) in rder t make an estimate f re(h) g(i) be the increase in the inflatin index frecast during the i'th future year and F(i, j) be the claim payments in tlle i'th future year resulting frm the j'th mst recent accident year. The estimatin methds used in this paper were: l'(j, k) [ c(j) c(j) ] M(j,/,) - e(j + h-- ~) (~ _ P) + f' c(j) + k -- ~),.(k) = '" F(i, j) = ~(j) ~J-'M(j, k) N wj -~,,~(i + j) [ c(j) P + (i --p)c(j) ri (i k-i