The Pasts and Futures of Private Health Insurance in Australia

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1 The Pass and Fuures of Privae Healh Insurance in Ausralia Casey Quinn NCEPH Working Paper Number 47 W O R K I N G P A P E R S NATIONAL CENTRE FOR EPIDEMIOLOGY AND POPULATION HEALTH

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3 Naional Cenre for Epidemiology and Populaion Healh The Ausralian Naional Universiy The Pass and Fuures of Privae Healh Insurance in Ausralia Casey Quinn Naional Cenre for Epidemiology and Populaion Healh The Ausralian Naional Universiy NCEPH Working Paper Number 47 December 2002 By 1997 only abou 30% of he populaion in Ausralia was covered by privae healh insurance. Using wha has been labelled a carro and sick approach, he governmen implemened hree policies o alernaively enice and coerce Ausralians ino joining privae healh funds. These were he Privae Healh Insurance Incenives Scheme, he Privae Healh Insurance Incenives Ac 1998 and lifeime communiy raing. They were of wo basic ypes: financial incenives based upon subsidies and puniive axaion, and equiy incenives which miigaed premium raing resricions. A various imes prior o and since he implemenaion of hese policies, here has been much and varied predicion of boh heir impac on demand for privae healh insurance and he likely resul if hey had no been implemened. This paper follows up hese predicions o deermine which if any were borne ou, or were likely o be. I also adds o hese predicions is own esimaes of fuure membership of healh funds now ha lifeime communiy raing has been inroduced by using a non-deerminisic Auoregressive Inegraed Moving Average process. Among he resuls of he sudy is he conclusion ha, if he long-erm decline in membership winessed in he 1990s resumes, he governmen has mos likely bough iself a decade of respie before demand for privae healh insurance falls once again o levels seen in ADDRESS FOR CORRESPONDENCE: NATIONAL CENTRE FOR EPIDEMIOLOGY AND POPULATION HEALTH THE AUSTRALIAN NATIONAL UNIVERSITY CANBERRA AUSTRALIA ACT 0200 PHONE: FOR COPY OF PAPER FAX: This research was suppored by gran no / under he Naional Healh Research and Developmen Program of Healh Canada. Many hanks o Dr. Jim Buler, Prof. Don Lewis and Ms Aarhi Ayyar for heir invaluable conribuions.

4 The Pass and Fuures of Privae Healh Insurance Casey Quinn Phone: Fax: ISBN ISSN Naional Cenre for Epidemiology and Populaion Healh Published by he Naional Cenre for Epidemiology and Populaion Healh The Ausralian Naional Universiy CANBERRA AUSTRALIA ACT

5 CONTENTS 1. INTRODUCTION 1 2. THE INEVITABLE DECLINE OF PRIVATE HEALTH INSURANCE Privae Healh Insurance Incenives ( ) The Privae Healh Insurance Incenives Scheme The Privae Healh Insurance Incenives Ac The Lifeime Communiy Raing Scheme Policy Oucomes 7 3. FORECASTING METHODOLOGY Auoregressive, Inegraed Moving Average Processes Model Idenificaion and Esimaion Tes Predicaions Forecasing PRIVATE HEALTH INSURANCE WITH LIFETIME COMMUNITY RATING DISCUSSION AND CONCLUDING REMARKS 22 REFERENCES 27 APPENDIX I PREDICTIONS OF DECLINING HEALTH INSURANCE COVERAGE 29 APPENDIX II COMPLETE DERIVATION OF THE ARIMA (2,1,2) 32 3

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7 1. Inroducion On February 7 h, 2000, he Senae Communiy Affairs Legislaion Commiee sa for consideraion of addiional esimaes. Among hese were new esimaes for he projeced cos of he Privae Healh Insurance Incenives Ac 1998, legislaion which was geared owards reversing an hisorically declining rend in privae healh insurance coverage, and easing he pressure on public hospials. I was esimaed a he ime ha his policy would cos $1.09 billion in he firs year 1. This subsequenly urned ou o be an underesimaion, wih new esimaes showing an increase o $1.67 billion. Re-esimaion of cos for he so-called ou years 2 also showed an increase, from an iniial $1.36 billion o $2.19 billion 3. Some of ha discussion follows. Mr Borhwick One of he poins was ha he coverage of privae healh insurance was on a very seady decline. So when Dr Wooding says you have o see wha oherwise would have happened, we were having a decline of abou wo per cen per annum. We have no go a decline of wo per cen per annum; we have go an increase of 214,000. The pressures on he public hospial sysem would have been inolerable if we had kep on having ha sor of decline, which seemed o be running over a span of years. CHAIR Tha is he poin. Wasn here demonsrable evidence? Mr Borhwick Exacly righ. There was demonsrable evidence. CHAIR When people dropped ou, he demand on he hospials increased. One can herefore only presume ha as people come back he demand on he hospials will decrease. Senaor Chris Evans We are rying o ge o how you measure ha. You can asser ha, Mr Borhwick - ha is wha he governmen does. Bu I am asking: How do we es ha? Mr Borhwick We had a long record of experience going back o he mid-eighies or so, which showed rend raes in he ake-up of privae healh insurance. There was a very seady, inexorable decline in he privae healh indusry. 1 Deparmen of Healh and Aged Care submission o he Senae Communiy Affairs Legislaion Commiee s inquiry ino he bills before heir inroducion ino Parliamen in The iniial esimaes were for four years he coss for he budge year a he ime and hree forward years, or ou years. 3 Senae Communiy Affairs Legislaion Commiee, Consideraion of Addiional Esimaes, February 7 h, 2000.

8 Senaor Chris Evans I suspec he jury is sill ou as o wheher ha has been haled - wheher his is a blip or wheher his has reversed ha long-erm rend. I suspec you would say o me, if you are consisen, We do no know ha ye. Senaor Herron I is he firs ime here has been a change in 16 o 20 years. A leas concede ha. Senaor Chris Evans I concede ha. All I am saying is wheher ha has haled he general decline in insurance is probably a quesion ha is no answerable. Mr Borhwick You have o look a he longer erm. Bu beween rebae changes, lifeime healh cover changes and changes in he srucure of he indusry, I hink we are headed in he righ direcion. 4 This excerp helps o elucidae he issues providing demarcaion lines for he wo sides of his argumen, namely hose ha were in favour of he 30% rebae as an appropriae ool for he governmen s policy and hose who were agains i. Specifically, hese issues were; he ulimae cos of he rebae o he governmen, wheher or no hose funds would in fac have been more effecive if given direcly o public hospials, he acual subsequen increase in healh fund membership and he duraion of any increase given a lack of proecion for consumers from he premium increases which were held o have conribued o he original decline. The governmen concurred wih he Majoriy Repor of he Senae Communiy Affairs Legislaion Commiee ino he Privae Healh Insurance Incenives Bill 1998 ha his bill would increase membership in healh funds significanly and wih some degree of longeviy. The Minoriy Repor of he commiee, along wih dissening repors from he Ausralian Democras and he Green pary, ook he view ha he expeced increases in membership of up o 50% were bes (ha is o say, he mos opimisic) esimaes boh in erms of he expeced increase and he esimaion iself. Furher, hey favoured he argumens submied o he commiee ha he decline in membership would only coninue, as an ad valorem subsidy failed o address he cos facors pushing up prices and promoing adverse selecion in he indusry. Quie apar from he argumens ha were made a he ime and are being made sill concerning he efficiency and equiy of he rebae, and leaving aside also he quesions over o wha exen any success in promoing healh insurance would ease he pressure on 4 Senae Communiy Affairs Legislaion Commiee, Consideraion of Addiional Esimaes, February 7 h, 2000, p

9 he public healh secor 5, he argumen over he rend in healh fund membership is an ineresing one. During he inquiry ino his bill, boh submissions o and debae wihin he governmen gave rise o a variey of predicions, boh of he consequences if no rebae were graned and hose if he rebae were graned, boh immediaely and even years ino he scheme 6. This paper aemps o follow up hese predicions and see which, if any, find he mos suppor empirically. I will also add o hem is own esimaes of fuure levels of healh fund membership now ha lifeime communiy raing has been inroduced. I does so using a non-deerminisic Auoregressive, Inegraed Moving Average mehodology o model fund membership levels dynamically. More rigorous mehodologies are proposed and discussed in laer secions. 2. The Ineviable Decline of Privae Healh Insurance The hisory of privae healh insurance in Ausralia is a chequered one, due in par o boh he exisence and naure of publicly financed and/or provided healh care. Ausralia had a one poin in fac he disincion of being he only counry o have insiued compulsory universal healh insurance and hen removed i (Hall 1999), only o have insiued i once more wih he inroducion of Medicare in This ergiversaion in he public role in healh care has aken is oll on he demand for privae healh insurance, whose coverage raes naionally were a peaks of 80% in 1970 (Hall 1999). This fell during he period in which Medibank and Medibank II, he precursor o Medicare, were in operaion 7, and rose sharply again afer is disconinuaion in 1981 (see Figure 1). I fell abruply once more o 50% upon he inroducion of Medicare; an even disinguishable by he sharpes 5 Saving he public healh secor from increasing demands being placed upon i by hose leaving he privae secor was an imporan reason for he governmen pursuing subsidies for privae healh insurance. 6 See Appendix I for some of hese esimaes. 7 The decline in coverage of 18% poins in he year immediaely following he inroducion of Medibank has in fac been he greaes in he las hiry years. The increase in coverage in he year following is removal was around 12% poins (Indusry Commission 1997). 3

10 drop overall. Afer reaching raes as low as 30% in 1998, insurance coverage currenly sis marginally below 45% naionally, having again declined over he pas year 8. 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% Dec-76 Dec-78 Dec-80 Dec-82 Dec-84 Dec-86 Dec-88 Dec-90 Dec-92 Dec-94 Dec-96 Dec-98 Dec-00 Figure 1 Decline in Hospial Cover, This led o grave concern ha he sysemic srain in he public healh secor was being exacerbaed by an inheriance of paiens leaving he privae secor. In a submission o he inquiry ino he Privae Healh Insurance Incenives Bill he hen Miniser for Healh and Ageing, Dr. Michael Wooldridge, saed ha: he healh of he publicly funded healh secor depends upon a vial privae secor. Having some six million Ausralians wih privae healh insurance direcly pays for around one-hird of he coss of hospial care in Ausralia. If here were no privae secor, he exra coss borne by he axpayer would simply be unsusainable. 2.1 Privae Healh Insurance Incenives ( ) Using wha has been labelled a carro and sick approach, he governmen adminisered hree policies o alernaively enice and coerce Ausralians ino joining healh funds. These policies were of wo basic ypes; financial incenives, based upon subsidies and 8 Raes are based upon membership daa compiled by he Privae Healh Insurance Adminisraion Council, for he period ending March 31 s, Full coverage deails are available on heir websie, 4

11 puniive axaion, and wha migh be called equiy incenives which miigaed premium raing resricions The Privae Healh Insurance Incenives Scheme The Privae Healh Insurance Incenives Scheme (PHIIS) was a policy ha ook effec as of July I was a argeed scheme combining boh of he aforemenioned carros and sicks. For hree income brackes he scheme provided subsidies of specified amouns for hose wihin he lowes bracke who subscribed o eligible insurance policies. Individuals in he highes bracke were axed puniively via he Medicare Levy Surcharge 9, while hose wihin he cenral bracke were subjec o neiher 10. Esimaes a he ime were ha his scheme would cos he governmen some $600 million annually, he equivalen of abou 11.5% of all Commonwealh expendiure on public hospials a he ime (Hall, De Abreu Lourenco and Viney 1999). The same esimaes prediced ha he measure would generae membership upake by people, eiher because of he subsidy 11 or in order o avoid penalisaion, each accouning for and people respecively The Privae Healh Insurance Incenives Ac 1998 The Privae Healh Insurance Incenives Ac 1998 was an amendmen o, or raher an expansion of he PHIIS, replacing i as of January 1 s I is now more commonly referred o as simply he 30% Rebae, as ha was is major accord. The Medicare Levy Surcharge for individuals and families was reained, bu significan aleraions were made o he subsidy ha, under he PHIIS, had been given o hose wih lower incomes who purchased privae healh insurance. The rebae srucure of pre-specified dollar amouns hp://www.phiac.gov.au/saisics/membershipcoverage/index.hm 9 This was a puniive ax of 1% on single incomes on or above $50,000 p.a. and family incomes on or above $100,000. This was waived on a pro raa basis for each day on which you had privae healh insurance. 10 Deails of he scheme can be found a hp://www.healh.gov.au/archive/1999/phiis/elib.hm, hough Buler (2002) provides an excellen analeca of boh he subsidies and he eligibiliy crieria. 11 The subsidy could be graned as an immediae premium reducion, a rebae from he Healh Insurance Commission which was implemening he policy, or a ax offse for ha year (Buler 2002). 5

12 was replaced wih an ad valorem subsidy of 30%, graned as eiher a ax offse or a premium reducion (wih he 30% apperaining o he premium purchased by each individual or family), and he eligibiliy crieria for policies was removed compleely. Mos significanly perhaps, so oo was he means esing of he rebae. This mean ha all individuals eligible for Medicare were eligible for he 30% rebae if hey joined a healh fund, and gave all hose wihin he PHIIS s highes income bracke he opporuniy o boh arac he 30% rebae and avoid he Medicare Levy Surcharge 12. In an effor o make insurance more aracive he Privae Healh Insurance Incenives Ac also conained he requiremen ha healh funds offer policies ha involved no gap, or known gap, coverage The Lifeime Communiy Raing Scheme Known also as Lifeime Healhcover, his ook effec afer a deadline exension from July 15 h 2000, and was buil upon he previous policies, in ha i did no remove or supersede any of he previous incenives, bu involved only a weaking of communiy raing o allow some degree of risk discriminaion on he par of healh funds. The deadline exension came because of he pressure being placed upon adminisraion wihin healh funds. Alhough he scheme had been announced in Sepember 1999, some nine monhs earlier, he bulk of he adverising and promoion ook place in he final monhs of he period, so ha demand would peak as he deadline drew near. Achieving his desired effec however mean ha wihin only weeks of he deadline i became clear ha he healh funds could no regiser all members, causing he deadline o be exended from is iniial dae of July 1 s 2000 by wo weeks. 12 This was in order o proec healh funds from inheriing an adverse risk selecion, such as was supposed o be he likely resul of only offering he rebae o low income earners. Offering a universal rebae would, conversely, proec boh he risk pool of healh funds and communiy raing generally. This issue can be seen more fully addressed in he Senae Communiy Affairs Commiee s Majoriy Repor on he Privae Healh Insurance Incenives Bill. 13 The gap here is he difference beween docor s fees and Medicare schedule fees, which had hihero mean ha while a public paien in a public hospial was fully covered, a privae paien in a public hospial could receive subsanial bills. Gap fees such as his dissuaded people from joining when, subjec o he availabiliy of a bed, hey could be fully covered as a public paien. They were widely held o be a main cause of individuals eiher no insuring or seeking reamen as a public paien, even when insured. 6

13 I was in order o ameliorae he effecs of moral hazard and adverse selecion ha he Commonwealh announced he Lifeime Communiy Raing Scheme. Healh funds were now allowed o charge a base premium for individuals under 30 years of age, while charging an addiional 2% for each year ha he individual was over 30 years of age a he ime hey joined he healh fund. The cap on his was a 70% increase, concomian wih hose enering when 65 years of age and over, who were herefore exemp from furher penaly. This policy had he advanage of being a concession o he privae healh insurance indusry and bearing no direc cos for he governmen. 2.2 Policy Oucomes The resuls of hese incenives can be seen in Figure 2 below. Noe where he implemenaion of each policy is marked, including he announcemen effec of lifeime communiy raing. Figure 2 Privae Healh Insurance Incenives [Source: Buler (2002)] Noe also ha his perains o policies for hospial cover. Clearly he PHIIS had lile effec, haling he decline in healh fund membership for only one quarer before i 7

14 reurned o is previous rend. The 30% rebae had greaer success, albei slowly. All old an increase in membership of 7% can be observed, alhough his is a conenious figure due o he overlapping naure of he announcemen of lifeime communiy raing prior o is implemenaion. The greaes increases in membership in fac come in his period of overlap, making i difficul o deermine o which policy he increase is aribuable. Easily he mos successful policy was he lifeime communiy raing scheme, which lead o membership reurning o raes of around 45% naionally, no seen since he 1980s. Defence of he wo former iniiaives and paricularly he 30% rebae has come primarily in order o defend he now $2.8 billion cos being carried. Such defence is based around he following argumens; 1. Tha he level of coverage subsequen o he implemenaion of each iniiaive mus be gauged relaive o wha migh have been he case had he incenive no been graned. For example, he PHIIS should be measured no agains coverage immediaely before July 1997, bu raher agains some laer hypoheical period in which he PHIIS did no exis. 2. Tha we can only observe saes wih neiher a rebae nor lifeime communiy raing, he rebae and no lifeime communiy raing, or boh. Wha is unobservable is a sae wih lifeime communiy raing and no 30% rebae. The argumen hen is ha he success of he final policy is aribuable in par a leas, o he prior exisence of he subsidy. As par of a wors-case scenario presened o he Senae inquiry, he Ausralian Healh Insurance Associaion (AHIA) made he claim ha while privae healh insurance membership losses have been declining (sic) a a relaively consan figure, i is more han likely he sysem will suddenly go ino free-fall. The main hrus of heir esimaion was ha membership raes would decline o zero by 2016 (see Appendix) unless he dropou rae were o compound, or go ino free-fall, in which case i would fall o zero wihin only five years from he ime he free-fall began. This free-fall was also held o be unpredicable, while hey considered even he firs esimaes conservaive. No accoun was made eiher of he model used o arrive a his forecas, or is derivaion. Using a long 8

15 run exponenial rend he Indusry Commission (1997) was able o forecas a far sofer decline, so sof in fac ha insurance coverage fell only o 11% naionwide by he year 2030 (see Appendix). Given ha his forecas used only daa from June 1994 o June 1996, i is assumed ha a more accurae predicion lies somewhere beween hese wo. Frech, Hopkins and MacDonald (2002) in fac used a deerminisic rend for he period o arrive a resuls quie similar o hose presened in he curren sudy. 3. Forecasing Mehodology Looking a privae healh insurance coverage since 1976 (see Figure 1) here is cerainly an illusion hough a convincing one of lineariy in he declining rend. Even beween 1981 and 1984 when Ausralia was emporarily wihou compulsory universal healh care he decline looks o be on a pah barely differen o ha observed eiher side of i. Upon closer inspecion hough i can be seen ha he rends vary across loose periods in ime, wihin which hey are fairly sable. The demarcaion for hese periods can be seen in he policy iniiaives of he governmen as well as oher evens menioned earlier, namely; The 2.5% levy on axable income inroduced in The removal of Medibank, increased subsidies o healh funds, and awarding of a 32% income ax rebae for basic hospial cover in A docor s dispue affecing public hospials, which began in Wihdrawal of subsidies o privae hospials, and healh funds being made o conribue o medical coss and he reinsurance pool 14 in The recession in he early 1990s. This segregaion was used in order o es he hypohesis ha he period was simply a srucural shif, and could be adjused o fi he remainder of he series, an approach consisen wih analyses by Gilchris (1976) and Meyler, Kenny and Quinn 14 The reinsurance pool is a form of mandaory insurance for healh funds, ino or from which hey conribue or wihdraw funds depending upon how he risk profile of heir members changes. The governmen had been subsidising conribuions o he pool. 9

16 (1998). We can see wihin each period differences in he average quarerly decline in healh fund membership. Average decline in percenage poins exhibis almos idenical coefficiens of variaion hough, excep for he period. Chow ess for srucural change performed in boh SAS and Shazam suppor his proposiion. The resuls in boh cases find a srucural change in he series only in Observaions from lae-1984 onwards were used for he idenificaion and esimaion of an Auoregressive, Inegraed Moving Average (ARIMA) model for forecasing alernae and fuure series 15. This ensured a subsanial and relaively sable series could be capured ha was of a fairly reliable size, and also ensured ha he final model would no be buil around oo local a mean. Thus, while sill hardly a global parameerisaion, i should give more accurae esimaion in oher periods. By using he longer ime period he model would hopefully be able o smooh ou over changes or shocks such as in and , and enable forecass o allow for hem in he fuure. Ineresingly, he resuls of he model used here were quie similar o hose of Frech, Hopkins and MacDonald (2002) who used a narrower ime series. 3.1 Auoregressive, Inegraed Moving Average Processes Auoregressive Moving Average (ARMA) models are wha are known as mixed models, in ha hey are a parameric combinaion of boh he Auoregressive process; y φ + a Firs-Order Auoregressive Process (AR(1)) = y 1 or 15 Daa used in he esimaion of insurance coverage and is forecasing, and indeed all daa used ha is sourced o he Privae Healh Insurance Adminisraion Council, is provided by PHIAC on heir websie, hp://www.phiac.gov.au/saisics/membershipcoverage/index.hm Tables are available for membership and benefis of hospial and ancillary policies, by age cohor and gender. Noe ha in he laer quarers of he series his sudy used daa labelled Preliminary, which by his ime may have been Revised and could be slighly differen. For he purposes of his sudy only basic hospial cover was used. Coverage under ancillary policies can be seen, and in fac is fairly similar o hospial over ime. All graphs and analysis based upon such daa however are he work and responsibiliy of he auhor. 10

17 ( 1 φ B ) y = a where y is some ime series y in he h period. a is some error erm for he series in he h period ( yˆ ). B is a so-called backshif operaor φ is he auoregressive parameer, y and of he Moving Average process; y = a θa Firs-Order Moving Average Process (MA(1)) or y = ( 1 θb) a where θ is he moving average parameer 16. An example of a firs order ARMA model hen is ( 1 φb ) y = (1 θb) ARMA(1,1) Process a An ARMA model also requires ha (i) he ime series mus be saionary, and (ii) he ime series mus be inverible, respecively. The ARIMA model is used for non-saionary series ha are inegraed, meaning hey can be made saionary by differencing, and i is his differenced series ha is hen fi wih an ARMA model. An example of an ARIMA (1,1,1) wih one period of auoregression, one period of differencing and one period of moving average, respecively is given by ( 1 φb )( y y 1) = (1 θb) a ARIMA (1,1,1) Process 16 See Mills (1996) for a more deailed presenaion of Auoregressive and Moving Average models. 11

18 or ( 1 φb ) y = (1 θb) a The saionariy condiion is ha φ < 1while he inverabiliy condiion is ha θ < 1. This also gives rise o anoher commonly used model specificaion in forecasing ime series, he deerminisic rend. This is when boh φ and θ equal 1 and a ime parameer exiss, so he value of he series a any poin will depend upon is saring values and curren poin in ime. Forecasing can hen be done using even a simple linear rend. Frech, Hopkins and MacDonald (2002) in fac use a deerminisic model fairly effecively agains privae healh insurance coverage. In his sudy a non-deerminisic ARIMA was specified, in order o boh allow capuring some long erm impac of curren or pas evens, and o minimise error from mis-specifying he series. Given ha he series was made quie saionary by firs differencing, and saisfied ess for uni roos, his choice appeared jusified Model Idenificaion and Esimaion Using SAS, he bes indicaions from he Auocorrelaions, Parial and Inverse Auocorrelaions were ha one of eiher an ARIMA (2,1,1), (2,1,2), (2,1,3) or (3,1,3) would be mos appropriae. The resuls of comparison are below. Table 1 Comparaive Variance and Informaion Crieria Parameers Variance AIC SBC (2,1,1) (2,1,2) (2,1,3) (3,1,3) I can be seen from he able above ha he selecion crieria minimum variance, minimum informaion crieria all favour he specificaion of an ARIMA (2,1,2). 17 While Frech, Hopkins and MacDonald (2002) use a deerminisic model, heir choice was no less jusified, as i was simply based upon differen assumpions concerning he daa generaion process. 12

19 Auocorrelaion checks of he residuals for whie noise also indicaed ha his was no an over-parameerisaion. Esimaion of his specificaion using he ARIMA procedure in SAS gave he following; Table 2 Condiional Leas Squares Esimaion Resuls Parameer Coefficien Esimae Sd Error Value p Value Lag Mean < MA1, < MA1, < AR1, AR1, < This, in erms of funcional form, appears as se ou below in is final derivaion (see Appendix II for a complee derivaion): y ˆ µ = y yy y 3 + a a a 2 where he mean µ is some local average decline (for his model i is of course an average for he period 1984:3-1997:2). 3.3 Tes Predicions Single-sep ahead forecass were made in various sub-secions of he series before he model was used for any long-erm forecasing 18. One of hese was almos he enire period, using single-sep-ahead forecass unil December 1989, and hence forecasing solely upon on he srengh of he model. This enabled he esimaes o be checked period by period, as well o see how capably he model allows for he brief shock in The resuls of he forecass for he laer quarers in he period can be seen below (see Table 3, Figure 3). 13

20 Table 3 Observed v. Prediced Insurance Coverage, Observed Forecas Quarer Coverage Coverage Forecas Error Sd Error Mar % 43.85% Jun % 43.06% Sep % 43.13% Dec % 42.82% Mar % 42.15% Jun % 41.93% Sep % 41.70% Dec % 41.18% Mar % 40.82% Jun % 40.57% Sep % 40.15% Dec % 39.75% Mar % 39.45% Jun % 39.09% Sep % 38.69% Dec % 38.36% The sandard error of he esimae looks quie promising, as does he error variance, only The closeness of his fi can also be seen in he graph. As expeced here is some error around he ime he recession and premium increases coincided. 18 Due o he breviy of he series, comparison ook place over some of he same ime periods ha were used in model idenificaion and esimaion, bu his doesn appear o have conribued o any noiceable bias. 14

21 55% 50% 45% 40% 35% 30% Observed Coverage Forecas Coverage 25% 20% Jun-84 Jun-85 Jun-86 Jun-87 Jun-88 Jun-89 Jun-90 Jun-91 Jun-92 Jun-93 Figure 3 - Observed v. Prediced Insurance Coverage, The model was also fied o pre-medicare daa, namely from 1976 onwards, and i was found o have performed remarkably well. This is surprising given he changes o healh care ha had aken place, bu he predicions held wih quie small degrees of error even unil mid For purposes of parsimony only every December quarer has been presened here. 15

22 Table 4 Observed v. Prediced Insurance Coverage Quarer Observed Coverage Forecas Coverage Forecas Error Sd Error Dec % 66.00% Dec % 67.82% Dec % 63.70% Dec % 59.93% Dec % 56.18% Dec % 54.11% Dec % 53.44% Dec % 51.95% Dec % 50.36% Dec % 48.91% Dec % 47.50% Dec % 46.07% Dec % 44.63% Dec % 43.19% Dec % 41.75% Dec % 40.32% Dec % 38.88% Dec % 37.44% Dec % 36.01% Dec % 34.57% Dec % 33.13% Dec % 31.50% This series of forecass had an error variance of also, hough i did have more variaion earlier in he series because of he period in which Ausralia was wihou universal healh insurance. The full series can be seen graphically, below 16

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