A Welfare Analysis of the Commonwealth Seniors Health Card. Abstract

Transcription

1 A Welfare Analyss of the Commonwealth Senors Health Card By Peter Smnsk, Unversty of Wollongong Abstract The Commonwealth Senors Health Card (CSHC) s a key element of a sute of benefts for Australa s self funded retrees. Its man component s a pharmaceutcal concesson, whch s analysed as a form of publc health nsurance. The utlty gan through rsk poolng s found to be neglgble under conservatve assumptons. The deadweght loss through moral hazard may be consderable. Fnally, the CSHC may be seen as an nequtable transfer, because CSHC holders are a partcularly wealthy populaton. Keywords: welfare, pharmaceutcals, health nsurance, Australa, retrement JEL classfcaton numbers: H42; H5; I38; H3.

2 I Introducton As structural ageng affects the populaton of almost all developed countres (OECD, 2007), the fscal sustanablty of publcly funded retrement ncome systems s beng questoned (Australan Government, 2007a; Blake and Mayhew, 2006; Holzmann et al., 2005; Whteford and Whtehouse, 2006). Australa s response has ncluded the provson of fnancal support for people who save for ther retrement. Ths ncludes preferental taxaton treatment for retrement savngs as well as drect benefts to self funded retrees. Paradoxcally, ths ncreasng support mples that these people are not entrely self funded. The effects of these polces warrant evaluaton, as do ther costs. The Commonwealth Senors Health Card (CSHC) s one of the man components of ths polcy sute. It provdes a prce concesson for pharmaceutcals, whch can be seen as a publc health nsurance polcy. It also provdes elgblty for other non cash benefts as well as cash benefts, condtonal on resdency requrements. The am of ths paper s to evaluate the welfare effects of the CSHC, focussng on the pharmaceutcal concesson. I estmate the welfare gan assocated wth rsk reducton and the welfare loss assocated wth moral hazard. 2 Equty s consdered by evaluatng the relatve ncome and wealth of recpents. Consderaton s also gven to the altrustc externaltes assocated wth health care and the applcablty of the chosen approach to publc health nsurance more broadly. The remander of the paper s organsed as follows. Secton II provdes a detaled descrpton of the CSHC. It consders changes to ts elgblty rules and the ncreasngly generous set of benefts to whch holders are enttled. It also provdes a profle of CSHC holders, whose dstngushng characterstc s wealth. Sectons III and IV estmate the welfare effects of rsk reducton and moral hazard, respectvely. Secton III fnds the welfare gan through rsk reducton to be neglgble under very conservatve assumptons and qute general specfcatons of the utlty functon. Even wthout The term self funded retree, now commonplace n Australan polcy dscourse, has no formal defnton. However, n typcal usage, t excludes anyone who receves any penson ncome. (See for example Commonwealth of Australa, 999; Department of the Parlamentary Lbrary, 200). Ths populaton s the subject of the analyss n ths paper. 2 The term moral hazard s wdely used n the lterature on nsurance. It often refers to the ncreased propensty to take rsks, resultng from the ncentves provded by nsurance. In the health economcs lterature, however, the term s commonly used n a dfferent sense. It often refers to the ncreased health care consumpton resultng from the reduced margnal prce of health care charactersed by health nsurance (see for example Folland et al., 2007: 66). Ths s the sense n whch the term s used here. 2

3 the pharmaceutcal concesson, consumers are already covered aganst hgh levels of pharmaceutcal expendture, so t s not surprsng that the addtonal reducton n rsk provded by the CSHC s neglgble. Secton IV estmates the welfare loss due to moral hazard. The deadweght loss s found to be substantal, even f a small prce elastcty of demand for pharmaceutcals s assumed. The senstvty of the estmates to the assumed parameters s consdered n detal. The assumptons underlyng the deadweght loss calculatons are of partcular mportance n analysng health care and health nsurance and these are dscussed n Secton V. Secton VI concludes. II The Commonwealth Senors Health Card The Commonwealth Senors Health Card (CSHC) was ntroduced n July 994. Its orgnal purpose was to provde pharmaceutcals at a concessonal prce to people of age penson age who met the penson ncome elgblty test, but who dd not meet other elgblty condtons. The majorty of such people dd not meet the assets test or resdency requrements. In Aprl 997 there were only 37,844 CSHC holders (Table ) (Standng Commttee on Famly and Communty Affars, 997). The concessonal prce for pharmaceutcals lsted on the Pharmaceutcal Benefts Scheme (PBS) was $2.60 per prescrpton at the tme. Other people elgble for the concesson nclude pensoners and low ncome earners. Consumers who were nelgble for the penson pad $6.00 per prescrpton. For both general and concessonal consumers, the prce s reduced after a consumer exceeds a gven annual out pocket expendture n a calendar year, as shall be dscussed subsequently. In January 999, there was a fundamental change n the role of the CSHC. The CSHC ncome elgblty threshold was no longer lnked to that of the age penson elgblty threshold. It was almost doubled to $40,000 per annum for sngles and $67,000 for couples. Offcally, the 999 CSHC polcy change was desgned to encourage people to save for ther own retrement. (Costello, 998: 5) The threshold was ncreased agan nomnally n July 2000 and more substantally n July 200, to $50,000 for sngles and $80,000 for couples (Australan Government, 2007b: Secton ). Immedately before the last of these threshold ncreases (June 200), there were 226,40 CSHC holders. (Department of Famly and Communty Servces, 2003a). Two years after the last ncrease (June 2003) there were 282,69 CSHC holders (Table ) (Department of Famly and Communty Servces, 2003b). The exact number of people who took up the card as a result of the ncome threshold reforms s unknown. 3 Recall that the 37,844 CSHC holders n 997 were all below the age penson 3 As wll be shown below, the ncome dstrbuton of CSHC holders s avalable at one pont n tme, usng the Household Expendture Survey (HES) of These data could be used to estmate the proporton of 3

4 ncome elgblty threshold. If ths number was to stay constant over tme, then perhaps 87% of CSHC holders n 2003 had become elgble due to the ncrease n the threshold. 4 Ths s a very rough approxmaton, but t suggests that most CSHC holders may have become elgble due to the reforms. Pror to September 200, the PBS concesson was the only beneft of the CSHC. Snce then, there has been a number of addtonal cash benefts ntroduced whch are lnked to CSHC elgblty. From September 200, CSHC holders who meet resdency requrement are also elgble for the Telephone Allowance. Ths s a cash beneft ntally worth $72 per year (pad quarterly) for people who have a telephone connected n ther name or ther partner's name. Ths has ncreased ncrementally to $85.60 by December Age pensoners are also elgble for the Telephone Allowance. From December 2004, CSHC holders who meet resdency requrements are enttled to the Senors Concesson Allowance, a cash beneft ntally worth $200 per year (pad n two nstalments). Ths has ncreased ncrementally to $24 by December Age pensoners are not elgble for ths beneft. However, age pensoners are elgble for the Utltes Allowance and varous concessons from State and Terrtory governments for servces such as property and water rates, energy blls, publc transport and motor vehcle regstraton, many of whch are not avalable to CSHC holders. Indeed the Senors Concesson Allowance was ntroduced because of such concessons. In turn, the Senors Concesson Allowance has provded elgblty for two one off payments. In June 2007, a payment of $500 was made to Senors Concesson Allowees as well as to age pensoners. In June 2006, a one off payment of $02.80 was made to Senors Concesson Allowees. The same payment was made to age pensoners. Notably, however, age pensoners who were members of a couple (not separated due to llness) only receved half of ths amount each, whlst coupled Senors Concesson Allowees each receved the full amount. Non concesson card holders were not elgble for these payments. It s also notable that a smlar payment (worth $300) was made n 200 to age pensoners, but not to CSHC holders. recpents whose ncome falls between the old and new thresholds. However, ths may be msleadng because of the applcaton of CSHC ncome elgblty rules. Applcants meet the CSHC ncome elgblty test f ther ncome n the prevous fnancal year was below the threshold. However, applcants can also meet the ncome test on the bass of an estmate of ncome n the current fnancal year, f they can demonstrate a change n crcumstances snce the end of the prevous fnancal year. 4 Ths estmate becomes 86% f t s assumed that ths number ncreased n proporton wth the age penson age populaton (takng nto account the ncrease n the age elgblty threshold for women from 60.5 to 62 years between 997 and 2003). 4

5 CSHC holders mght also be more lkely to be bulk blled 5 for GP servces than non concessonal patents. In February 2004, the Commonwealth Government ntroduced fnancal ncentves for GPs to bulk bll concesson card holders and chldren aged under 6. However, there does not seem to be any avalable data that quantfes the extent to whch CSHC holders are actually bulk blled. From March 2004, CSHC holders are enttled to concessonal coverage under the extended Medcare Safety Net. Under ths scheme, 80% of non hosptal out of pocket medcal expenses are rembursed by the government after such expendture exceeds a gven threshold. In 2007, ths threshold s $59.50 per year for concesson card holders, and $039 for non concesson card holders. Thus the addtonal concessonal coverage s worth a maxmum of 80% ($039 $59.50) = $45.60 per year per recpent. Data on the dstrbuton of annual out of pocket medcal expenses of CSHC holders are not avalable, and so the average value of ths concesson to CSHC holders s unknown. However, the average annual out of pocket expendture by CSHC holders s estmated to be $257 n , and the proporton exceedng $59.50 s no more than %. 6 Furthermore, both concesson card holders and general patents are also elgble for the (orgnal) Medcare Safety Net. Under ths scheme, 00% of the Medcare Schedule Fee s rembursed for patents whose gap fees exceed an annual threshold. The gap s the dfference between the Medcare Schedule Fee and the amount rembursed by Medcare. The gap s equal to 5% of the Schedule Fee, although practtoners are free to charge n excess of the Schedule Fee. In 2007, the threshold for ths scheme s $ Wthout access to relevant data, the nteracton between the orgnal and extended Medcare Safety Nets s dffcult to gauge. Nevertheless, t s clear that the average value of ths scheme to CSHC holders (n excess of ts value to non concessonal patents) s lkely to be small. An upper bound s calculated as the maxmum beneft multpled by the maxmum proporton of benefcares = $45.60 % = $ The actual value may be consderably smaller than ths. 5 Bulk bllng s a bllng system whch ncludes no charge for the patent. 6 Author s calculatons from the ABS Household Expendture Survey Expanded Confdentalsed Unt Record Fle. Expendture n ths data set s recorded on a household bass. Household expendture s assumed to be equally dstrbuted between household members. Respondents are asked to recall expendture on medcal servces over the prevous three months. The dstrbuton of annual expendture cannot be derved from these data. The varance of expendture s lkely to be greater for a short recall perod than a long recall perod. However, an upper bound of the proporton of people exceedng the threshold can be derved by assumng that the three month recall perod s representatve of the full year for each household. Under ths assumpton,.0% of CSHC holders exceeded the $59.50 threshold. Thus a maxmum of.0% of CSHC receve any beneft from the Medcare Safety Net. Smlarly, no more than 8% exceed the $039 threshold, hence benefttng from the maxmum value of the concesson. 5

6 Table 2 summarses the non PBS benefts receved by each CSHC card holder n The total s $ for 2007 plus the unmeasured values of addtonal bulk bllng and the concessonal threshold n the Medcare Safety Net. Older people wthout concesson cards are not elgble for any of these benefts. Age pensoners are elgble for all of these benefts except for the Senors Concesson Allowance. The Household Expendture Survey s perhaps the only natonally representatve data set avalable whch explctly dentfes CSHC holders. Table 3 shows summary statstcs for CSHC holders, wth comparsons to non CSHC holders of age penson age and to younger people (ncludng chldren). Approxmately 0% of older people were CSHC holders. On average, CSHC holders were one year younger than non CSHC holders of age penson age and a slghtly larger percentage (2%) was male. Ther average equvalsed current dsposable ncome was consderably hgher ($02 per week) than that of non CSHC holders of age penson age, but consderably lower ($78) than that of younger people. CSHC holders are located throughout the ncome dstrbuton, although relatvely few are n the top quntle. In comparson, non CHSC holders of age penson age are concentrated n the bottom half of the dstrbuton. Whlst CSHC holders appear to fare poorly relatve to younger people on these ncome measures, t s noted that cash ncome s not a good metrc for comparsons of lvng standards between older people and younger people. Ths s due to the excluson of mputed rental ncome from owner occuped housng, whch greatly benefts older people relatve to younger people (see Saunders and Smnsk, 2005; Yates, 99). Ths s reflected n the last row of Table 3, whch shows that 88% of CSHC holders lve n an owner occuped dwellng wthout a mortgage, compared wth 77% of non CSHC holders of age penson age and just 23% of younger people. The dstngushng characterstc of CSHC holders s wealth. Ther net wealth per capta was $623,898, almost twce that of other older people and almost four tmes that of younger people. CSHC holders are hghly concentrated at the top of the wealth dstrbuton. The majorty (59%) of CSHC holders are n the top decle of the wealth dstrbuton, whle only 6.5% are n the bottom 60% of the dstrbuton. III The Welfare Gan of Rsk Poolng Health nsurance provdes protecton aganst the fnancal consequences of adverse health shocks. It also protects aganst welfare loss due to poor health to the extent that lower prces for health care translate nto hgher health care consumpton. In ths secton, I abstract from the effects of such 6

7 behavoural responses to prce, snce they are analysed n detal n the next secton. Let I denote ncome. Let x and y denote pharmaceutcal and non pharmaceutcal consumpton respectvely. Let p denote the prce of pharmaceutcals, whle the prce of y s normalsed to. Income s equal to total consumpton, so that I = px + y. Consder a health state dependent utlty functon of the followng form: U = U ( y) + U ( h) 2 () Where h s health. In ths model, health effects utlty ndependently of (non pharmaceutcal) consumpton. The model does not allow for the possblty that the margnal utlty of consumpton vares wth health status. It s shown n Appendx that a more general specfcaton, whch allows the margnal utlty of consumpton to decrease wth sckness, would result n an even smaller utlty gan due to rsk poolng. However, the more restrctve specfcaton s used n the body of the text as t s analytcally tractable. Let h, n turn, be a functon of pharmaceutcal consumpton (x) and the exogenous pre treatment health status (θ), over whch there s uncertanty. Pharmaceutcal consumpton s a functon of θ, and I. It does not contrbute drectly to utlty. Assume that U s the constant relatve rsk averson (CRRA) functon. The functonal form of U 2 remans unspecfed: ρ ρ y ( I px) U = + U2( h) = + U2( ) ρ ρ h (2) where ρ s the Arrow Pratt relatve rsk averson parameter. The CRRA utlty functon assumes that rsk averson s negatvely proportonal to wealth (or consumpton) (Pratt, 964). Many avalable estmates of ρ are n respect to utlty as a functon of wealth and so are not relevant here (see Hartley et al., 2006 for a revew of such estmates; and Meyer and Meyer, 2005 for a formal dscusson of the relatonshp between CRRA utlty functons of wealth and consumpton). Estmates of ρ n respect to utlty as a functon of consumpton nclude 4. n a study based on hypothetcal gambles over permanent changes to ncome (Barsky et al., 997). That study also found very lttle varaton n ths estmate by ncome quntle, supportng the assumpton of CRRA for consumpton. There have been several other studes whch explot savngs responses to nterest rates to measure the ntertemporal elastcty of consumpton, whch n turn s the nverse of ρ. These estmates for ρ nclude 2.5 (Engen, 993; cted by Engen and Gruber, 200) and between 2 and 5 (Sknner, 985). The consstency of these estmates justfy the long lne of smulaton lterature descrbed by 7

8 Fnkelsten and McKnght (2005) whch takes ρ to be 3. In the present study, I follow Fnkelsten and McKnght (2005; 2008) by assumng that ρ s equal to 3, and testng senstvty to values of and 5. It s acknowledged that all of the estmates for ρ revewed above are wth respect to the USA. To the author s knowledge, correspondng estmates do not exst for Australa. To mplement ths approach, t s necessary to estmate the extent of uncertanty over pre treatment health status or at least over the resultng pharmaceutcal consumpton. Whlst x s a random varable, t may not be completely random. In partcular, health status s lkely to be serally correlated. Several approaches have been used n related studes to address ths ssue. In the RAND Health Insurance Experment, partcpants were asked to predct future health care consumpton. Mannng and Marqus (996) compared these responses to actual consumpton, thus measurng the extent to whch t was predcted. Fnkelsten and McKnght (2008) modelled the dstrbuton of health care consumpton before and after the ntroducton of the Medcare scheme n the Unted States. The data to mplement such approaches for the CSHC are not avalable. In fact, the annual dstrbuton of pharmaceutcal expendture s not readly avalable for even one pont n tme for the populaton of nterest. 7 However, ths s not a major lmtaton. The approach taken here s to make conservatve assumptons over the dstrbuton of out of pocket pharmaceutcal expendture and the extent of uncertanty over future consumpton. Despte these assumptons, the utlty value of the CSHC due to rsk poolng s found to be neglgble. Pharmaceutcal consumpton s assumed to be completely random, regardless of pror health status or other observable characterstcs. Ths approach wll overestmate the uncertanty over pharmaceutcal consumpton (and hence the utlty value of rsk poolng). Followng Smnsk (2008a), the annual number of PBS pharmaceutcal prescrptons consumed s assumed to follow an overdspersed count data process, wth a mean of 33.. The extent of overdsperson s unknown, but s parametersed through a Negatve Bnomal process (see Cameron and Trved, 998: equaton (3.26) for the densty functon). Fgure shows three such dstrbutons. The frst s the Posson dstrbuton, whch s a specal case of the Negatve Bnomal wth the overdsperson parameter (α) equal to zero. Ths s also almost dentcal to a Normal dstrbuton. The other dstrbutons are Negatve Bnomal wth α set to 0.3, and 7 HES ncludes self reported household expendture on prescrpton medcaton n a two week perod. The dstrbuton of ths amount s unlkely to be a useful proxy for the shape of the annual dstrbuton for at least two reasons. The varance of expendture n two week recall perod s lkely to be much greater than that of annual expendture. Secondly, not all prescrpton medcatons are lsted on the PBS. Patents would pay the full cost of any such medcatons, thereby ncreasng the varance further. 8

9 respectvely. When α =, the varance of the Negatve Bnomal s 34 tmes larger than that of the Posson. Assume the dstrbuton of the number of prescrptons purchased s the same under general and concessonal prce schedules (the welfare effect of responses to prce are the subject of the next secton). Each of the probablty dstrbutons of prescrpton counts n Fgure corresponds wth a dstrbuton of pharmaceutcal expendture under general and concessonal prce schedules, respectvely. For a gven person, the probablty dstrbuton of non pharmaceutcal consumpton s a functon only of PBS concesson status. An llustraton of these dstrbutons under both sets of prces s shown n Fgure 2 for a sngle person. In ths example, the negatve bnomal dstrbuton s assumed to have α equal to 0.3. The dscontnuty n the dstrbuton under general prces occurs at the pont where the safety net s nvoked. In the dstrbuton under concesson prces, expendture s capped at a maxmum of $ per year, after whch all subsequent prescrptons are free to the consumer. In the model beng developed here, the effect of the CSHC s to replace the general prce probablty dstrbuton of non pharmaceutcal consumpton wth the correspondng concesson prce dstrbuton. For couples, safety net elgblty s based on combned pharmaceutcal consumpton. The probablty dstrbutons of ther non pharmaceutcal consumpton thus dffer from those n Fgure 2 and they are not shown. The results that follow dfferentate between sngle and coupled CSHC holders. It s assumed that each member of a couple ndependently faces the same probablty dstrbuton of prescrpton counts and that ncome s shared wthn the household. The man fndngs are unchanged under alternate assumptons (for example perfectly correlated pharmaceutcal consumpton and/or no ncome poolng by couples). The expected utlty (wth a CSHC card) s: c E( U ) = U ( y) f ( y) dy+ U ( h) g( θ ) dθ 2 (3) where y s non pharmaceutcal consumpton, f s the probablty densty functon depcted n the frst panel of Fgure 2 (or the correspondng densty under dfferent assumptons about dsperson), g s an unspecfed probablty densty of pre treatment health states (θ). The expected utlty wthout a concesson card s gven by: g E( U ) = U ( y) f ( y) dy+ U ( h) g( θ ) dθ 2 2 (4) 9

10 where f 2 s the probablty densty functon depcted n the second panel of Fgure 2 (or the correspondng dstrbuton under dfferent assumptons about dsperson). The second ntegral s dentcal to that of E(U c ) snce no response to prce n pharmaceutcal consumpton has been assumed n ths secton. A ratonal consumer s ndfferent between possessng a CSHC or recevng a cash payment M when the utlty of each stuaton s equal: U( y+ M) f2( ydy ) + U2( hg ) ( θ ) d θ = U( y) f( y) dy + U2( hg ) ( θ ) dθ (5) Whch mples that: U( y+ M) f( ydy ) = U( y) f( ydy ) 2 (6) Wth ρ = 3, ths becomes: ( ) y M y f ( y) ( ) = 2 2 f2 ydy dy (7) Wth ρ = 3 and α = 0.3, M s evaluated to be $ for sngles. The actuarally far nsurance premum s the dfference n expected pharmaceutcal expendture (under concessonal and general g c prces) = Exp ( ) Exp ( ) = $ Thus the contrbuton to utlty assocated wth rsk reducton s worth $3.66 per year, or 0.6% of the actuarally far premum. For couples, M s estmated to be $ (or $ per person). Ths s lower for couples because they are more lkely than sngles to reach the safety net threshold under general prces. The contrbuton to utlty through rsk reducton s also smaller for couples at just 0.% of the actuarally far premum. Ths s manly because couples effectvely self nsure aganst rsk, by poolng ther combned ncome. 8 Table 4 shows the results under varous assumed values for α and ρ. Even under assumptons of hgh dsperson of the PBS consumpton dstrbuton (α = ), hgh rsk averson (ρ = 5) and completely random future health status, the value of the CHSC to rsk reducton s equal to only 2.4% of the actuarally far premum value of the card for sngles, and.3% for couples. The actual value s lkely to be less than % and s hence neglgble. 8 If t s assumed that couples do not pool ncome, the value of the concesson through rsk reducton ncreases to 0.5% of the actuarally far premum. If t s assumed that pharmaceutcal consumpton s perfectly correlated wthn couples, the value s 0.2% of the actuarally far premum, regardless f ncome s assumed to be pooled. 0

11 IV Moral Hazard and Deadweght Loss In ths secton, I consder the deadweght loss (DWL) assocated wth the PBS component of the CSHC. DWL s the dfference between the socal cost of the CSHC and the mnmum cash amount that ratonal recpents would be wllng to receve nstead of the CSHC. The key assumptons underlyng these calculatons are dscussed n detal n the followng secton and should be consdered when nterpretng these results. The key parameter whch nfluences the results s the prce elastcty of demand for pharmaceutcals. Explotng the CSHC polcy change as a natural experment, Smnsk (2008a) estmated the prce elastcty to be 0. for ths populaton. Ths value s adopted here, wth senstvty tested to other values. For ths exercse, t s assumed that there s no uncertanty, snce uncertanty was addressed n the prevous secton. In ths model, consumers know ther own health status wth certanty for the mmedate accountng perod (a calendar year). For ths health status and a gven prce, there s a unque quantty of pharmaceutcals consumed, whch maxmses the utlty of a gven consumer. Ths consumer s utlty functon depends on pharmaceutcal consumpton and non pharmaceutcal consumpton. In summary, the approach taken s to derve the Hcksan compensatng varaton (HCV) for such a consumer under a number of dfferent scenaros (Hausman, 98; Hcks, 943). The dfference between the cost to government and the HCV s the DWL component of government expendture. Consder a demand functon for pharmaceutcals for person. Let the quantty demanded and prce of pharmaceutcals be denoted x and p, respectvely. Let y be the quantty demanded of the composte of all other goods. The prce of y s normalsed to and s fxed. Income s denoted I. Assume that the demand functon exhbts constant prce and ncome elastctes. Under these assumptons, the Marshallan demand functon for pharmaceutcals can be wrtten as: x = c p α I δ (8) where α and δ are the own prce and ncome elastctes of demand for pharmaceutcals, c s ndvdual specfc and vares wth health status and preferences for pharmaceutcal versus non pharmaceutcal consumpton, but these are assumed fxed for the accountng perod and are known wth certanty. Consder the followng ndrect utlty functon:

12 I p c I p V δ α δ α + + = + ), ( (9) Ths utlty functon corresponds to the demand functon gven n (8). For a gven utlty u, the correspondng expendture functon s derved by solvng (9) for I, whch s now denoted e (p,u ): = p c u u p e δ α α δ ) ( ), ( (0) Ths s the mnmum expendture requred to acheve utlty u, gven the prce p. Consder the consequences of the abolton of the CSHC, whch would change p from p 0 to p. The compensaton n ncome whch would result n no change n utlty gven the prce change s the Hcksan compensatng varaton: HCV = = p c u p c u u p e u p e δ α δ α α δ α δ 0 0 ) ( ) ( ), ( ), ( () Fgure 3 shows the nomnal prce schedules for general and concessonal consumers. For CHSC holders n 2007, the frst 56 PBS medcatons cost $4.90 each. Addtonal prescrptons are free. For non concesson card holders, the frst 43 prescrptons cost an estmated average of $24.56 each. 9 Addtonal prescrptons cost $4.90 each. The zero prce after 56 prescrptons for concesson card holders s a complcaton for the analyss. Demand s undefned for a zero prce n the constant elastcty demand functon. However, t s noted that the full cost of obtanng a prescrpton s not truly zero. There are non monetary (tme) costs assocated wth obtanng the medcatons, as well as (tme and possble monetary) costs assocated wth seeng a GP to obtan a prescrpton. Ths unmeasured cost mght be small for several reasons. GP care s free for most Australans, especally older people (for around 85% of people aged 65 and over) (Abbott, 2005). For most medcatons, GPs can prescrbe several courses (up to sx) at one tme. They can also prescrbe as many dfferent types of medcaton at one tme as deemed approprate. Furthermore, many people wll have needed to see ther GP n any case, for reasons other than to obtan the prescrpton. Nevertheless, t s dffcult to estmate the net value of 9 The notonal general co payment amount was $30.70 n However, some lsted drugs have a lower prce. The rato of average out of pocket prce to the lsted co payment prce for CSHC holders was estmated by Smnsk (2008a) and s appled here. 2

13 these costs. For the purpose of the llustraton, ths unmeasured cost s assumed to be $ per prescrpton. Ths s appled throughout the analyss, regardless of the cash prce. Senstvty of the results s shown for alternatve assumptons of $0.50 and $5. Consder a CSHC holder wth α = 0., δ =2, I = $40,000 and consumpton of 30 unts of pharmaceutcals (x 0 =30). Substtutng these values nto (8), c s equal to 2.2 * 0 8. Evaluatng (9) at these values results n a utlty value of 2.5 * 0 5. If the concesson was removed (f p s ncreased to p ), what would be the compensaton requred to mantan utlty at the same level? Substtutng nto (), the compensatng varaton s evaluated to be $547. Ths consumer would be ndfferent between a health concesson card and a cash beneft of $547. Now consder the cost to government of the CSHC subsdy. At p=$25.56, x = 25.9 (from (8)), whch s the component of consumpton not nduced by the CSHC. For each of these 25.9 prescrptons, the cost to government s equal to the dfference between the concessonal and general PBS prces, whch s $24.56 $4.90 = $9.66. An addtonal = 4.09 prescrptons were nduced by the prce change (moral hazard). In the absence of the CSHC, these would not have been consumed at all. For these 4.09 prescrptons, the unt cost to government s greater than for each of the orgnal It s equal to the full government contrbuton of these drugs. For concesson card holders ths s estmated to be $32. 0 In total, the cost to government of the CSHC for ths consumer s equal to 25.9 * ($24.56 $4.90) * 32 = $640. The DWL s the dfference between HCV and government cost = $94, or 5% of ts cost. The above example s a specal case n a more general stuaton, charactersed by a nonlnear prce schedule (Fgure 3). The quantty demanded n the example above s to the left of the dscontnutes n both prce schedules (x 0 <43). Ths quantty and the assocated margnal prce s labelled a n Fgure 3. Quantty demanded and the margnal prce n the counterfactual (concessonal PBS prces) s labelled A. A wll also always be to the left of the dscontnutes, snce the margnal prce n the general schedule s less than or equal to the concesson prce at all ponts n the prce schedule. Let Scenaro refer to the stuaton where x 0 <43. In Scenaro 2, x 0 s between the prce dscontnutes n the two prce schedules (43 < x 0 < 56 prescrptons n the year, labelled b ). To calculate the correspondng HCV, t s necessary to calculate utlty under the counterfactual, whch s the general prce schedule. To do so, one must confront the ssues posed by the nonlnear prce schedule. The optmal consumpton level n the 0 Ths s equal to the total government contrbuton to PBS expendture for concesson card holders dvded by the number of prescrptons. Correspondng data are not avalable for the subset of CSHC cardholders. 3

14 counterfactual (x ) mght also le between the dscontnutes (denoted B ). However, the consumer may derve hgher utlty from a lower level of pharmaceutcal consumpton, x < 43, gven the hgher prce of each of the frst 43 prescrptons. Nonlnear prce schedules pose consderable dffcultes for the analyss of health care demand (Keeler et al., 977). However, under the assumptons outlned above, the consumer knows ther health status for the accountng perod wth certanty. Ths consumer can thus choose an optmal level of consumpton for the entre year at the begnnng of the perod. If they choose a pont to the left of the dscontnuty (x <43), the assocated utlty and HCV can be calculated usng the same technques as Scenaro, wth prce equal to $ If the optmum consumpton level s to the rght of the dscontnuty (x >43) they wll face an effectve prce of $5.90 per prescrpton. Ths effectve prce s relevant to every prescrpton consdered for purchase durng the year, snce the consumer knows wth certanty that an addtonal prescrpton purchase wll result n an addtonal expendture of only $5.90 for the year. The actual expendture on pharmaceutcals, however, s greater than ths, snce the cost of pharmaceutcals s $25.46 $5.90 hgher for the frst 43 prescrptons. The effect of ths on consumpton and utlty s a pure ncome effect, equal to a reducton n ncome equal to ($25.46 $5.90) * 43 prescrptons = $845. Therefore, f the consumer chooses a consumpton level greater than 43 prescrptons n the counterfactual, the HCV s exactly equal to $845. To summarse, pharmaceutcal consumpton n the counterfactual wll be to the left of the prce dscontnuty (x <43 prescrptons) f the assocated utlty s greater than consumpton above the dscontnuty. In other words, f V(25.46, 40000) > V(5.9, ). The cost to government and DWL are calculated usng the same methods as Scenaro. To llustrate, take a consumer wth the same parameters as n the frst example, wth the excepton that he consumes 50 unts of pharmaceutcals (x 0 =50). From (8), c s equal to 3.7 * 0 8. In the counterfactual, utlty s hgher f the consumer purchases more than 43 prescrptons, as V(5.9, ) = 2.57 * 0 5 > V(25.46, 40000) = 2.58 * 0 5. The optmal x = HCV s evaluated to be $845. The cost to government of the CSHC for ths consumer s equal to 43 * ($24.56 $4.90) + 2. * 32 = $93. The DWL s $67, or just 7% of ts cost to government. Ths s a much smaller DWL than n Scenaro. Ths s because the effectve prce for concesson cardholders s the same as that of non card holders. The DWL s drven solely through an ncome effect. However, f x 0 s slghtly lower (48 unts), a much larger DWL s calculated. In ths case, the optmum consumpton n the counterfactual s to the left of the prce dscontnuty (x<43). It s n fact 4

15 4.5 prescrptons. The assocated DWL s $43, or 4% of the cost to government. It s drven by both ncome and prce effects. In Scenaro 3, x 0 >56 (denoted c n Fgure 3). Consder a consumer wth the same parameters as n the frst two scenaros, wth the excepton that he consumes 80 unts of pharmaceutcals (x 0 =80). Snce x 0 >56, the nomnal margnal prce s assumed to be $ per prescrpton as dscussed above. To account for the ncome effect assocated wth payng $5.90 for each of the frst 56 prescrptons, ncome s effectvely reduced by ($5.90 $)*56 = $ From (8), c s equal to 5. * 0 8. In the counterfactual, utlty s maxmsed wth x = 65. prescrptons. HCV s evaluated to be $908. The cost to government of the CSHC for ths consumer s equal to $367. The DWL s $459, or 34% of ts cost to government. If the assumed addtonal prce of pharmaceutcals s ncreased to $5, the DWL falls to 20% of the government cost. If t s assumed to be 50c, the DWL ncreases to 39%. Regardless of the choce of ths parameter, the DWL s hghest n Scenaro 3. The left panel of Table 5 summarses the results for the three llustratve consumpton levels and the assumed prce loadng per prescrpton (α and δ are fxed at 0. and 2, respectvely). The value of the card to the recpent clearly depends on the consumpton level, wth hgh consumers beneftng more than low consumers. DWL also vares consderably at the dfferent levels of consumpton, beng hghest for hgh consumers and lowest for those who consume 50 prescrptons. The estmated HCV s not partcularly senstve to the assumed prce loadng due to unobserved costs. However, the estmated DWL s senstve to the prce loadng, partcularly at the top of the dstrbuton (where pharmaceutcals are nomnally free). The mddle and rght panels of Table 5 shows the average HCV and DWL across the assumed dstrbutons of consumpton for sngles and couples, respectvely. As before, the assumed value of the overdsperson parameter s 0.3, and consumpton s assumed to be uncorrelated between members of couples. The preferred estmate for the average HCV of the PBS component of the CSHC s $547 for sngles and $842 for couples ($42 per coupled person). As n the prevous exercse, above, ths estmate for coupled people s lower than for sngles because couples are more lkely to reach the safety net threshold under general prces than sngles. The estmates are not partcularly senstve to the assumed overdsperson, nor to the assumed prce loadng. The DWL percentages n the mddle and rght panels are the percentage of total government expendture that s DWL (rather than the average of DWL percentages across the dstrbuton). In the preferred estmate for sngles, the DWL s equal 7.7% of government expendture, but ths s senstve to the assumed overdsperson and prce loadng. The estmated DWL percentage s hgher for couples than for 5

16 sngles, at 26.% n the preferred model. For couples, the DWL estmate s much less senstve to the assumed overdsperson, but remans senstve to the prce loadng. Table 6 shows the senstvty of results to the prce elastcty of demand for pharmaceutcals (δ s fxed at 2 and the prce loadng s $). The value of the card to the recpent does not vary greatly wth prce elastcty. The estmated cost to government of the card vares far more wth ths parameter. Thus the share of government expendture that s DWL also vares consderably. Table 7 shows the senstvty of results to the ncome elastcty of demand for pharmaceutcals (α s fxed at 0. and the prce loadng s $). Nether the HCV nor the DWL s senstve to ncome elastcty. The results are also nsenstve to the assumed ncome of the consumer. For example, the HCV vares by just $2 between I = $30,000 and I = $50,000 for sngles. The correspondng varaton n DWL s 0.4%. The above analyss has assumed a constant elastcty demand functon. Ths appears to be the only specfcaton flexble enough to mpose the same prce elastcty for both of the dscrete prce changes that characterse the nonlnear prce schedules under consderaton. As an example, consder a log lnear demand functon, commonly used n studes of health care utlsaton: ln = + β + β2 x a p I (2) Consder the dscrete prce change from $5.90 per prescrpton to $25.56 per prescrpton. For the (arc) prce elastcty to equal 0. n ths demand functon, β must equal However, to mpose the same prce elastcty for a change from $ to $5.90, β must be much larger ( ). Thus t s mpossble to mplement the above approach wth a log lnear demand functon that s consstent across all consumpton levels. To summarse, the average HCV of the PBS concesson for CSHC holders s estmated to be $547 for sngles and $842 for couples. Ths estmate s not greatly senstve to varatons n any of the assumed parameters. The deadweght loss of the concesson s estmated to equal 7.7% of the cost to government for sngles and 26.6% for couples. The DWL estmate s senstve to the assumed prce If, however, each prce change s consdered n solaton wth dfferent log lnear demand functons, correspondng estmates can be generated. Ths produces smlar estmates of HCV (3 4% hgher than the preferred approach at all consumpton levels) and slghtly smaller estmates of DWL (2 25% smaller). Nevertheless, the valdty of such an approach s questonable. 6

17 elastcty of demand, the assumed prce loadng and, for sngles, the assumed overdsperson n the dstrbuton of consumpton. Regardless of the assumed parameters, the DWL percentage s greater for couples than for sngles, whch reflects ther hgher lkelhood of surpassng the concesson safety net threshold. The concesson provdes no nsurance value through rsk poolng. However, there s lkely to be consderable varaton between ndvduals around the average value of the concesson. Ths varaton s prmarly due to dfferences n PBS consumpton levels, whch reflect preferences over pharmaceutcal versus non pharmaceutcal consumpton. These, n turn, wll be partally a functon of health status. V Interpretng Deadweght Loss The deadweght loss estmated n the prevous secton results drectly from consumers responsveness to pharmaceutcal prces. Whether the hgher consumpton assocated wth lower prces can be nterpreted to reduce welfare rests on several assumptons, whch can be problematc n the analyss of health care n general (see Rce, 998 for a detaled crtcal ntroducton to these ssues). Perhaps some of these assumptons are more lkely to hold for the CSHC populaton than for other populatons groups who are more responsve to prce. Nevertheless, t s unlkely that all of these assumptons hold for all CSHC holders, and the effect of ths on welfare s dffcult to quantfy. Thus the estmated welfare loss assocated wth moral hazard must be consdered n lght of the unmeasured consequences of possble volatons of the assumptons that are lsted below. The frst set of assumptons concerns revealed preferences. Tradtonal demand theory assumes that consumers wll respond to a prce change n a way whch maxmses ther ndvdual wellbeng. Ths requres that consumers be perfectly nformed of the health consequences of changng the quantty of ther pharmaceutcal consumpton. They must also be able to wegh up the effect of any such health consequences aganst the utlty from consumpton of other commodtes. Fnally, behavour s assumed to be motvated by personal wellbeng, rather than a broader concern over the consequences of ones actons on others (see especally Sen, 973 for a dscusson of ths last pont). Even f consumers are well nformed, ratonal and self nterested, a reducton n pharmaceutcal consumpton may translate to hgher consumpton of other forms of health care whch are also subsdsed by government. Ths may result n more expensve treatment, such as emergency hosptal treatment, for nstance (see Newhouse, 2006 for a revew of evdence to ths effect; and especally Tamblyn et al., 200 n relaton to pharmaceutcal subsdes for older people). 7

18 Fnally, the deadweght loss calculatons do not account for the altrustc externaltes that characterse health care markets (Hall, 200; Thurow, 974). Altrustc externaltes are assocated wth what Tobn (970) calls specfc egaltaransm. People are generally less wllng to tolerate nequalty of access to health care than to other commodtes. Thus the health (and health care) of a gven person may enter the utlty functons of others. However, ths may be a mnor ssue n the case of the CSHC. CHSC holders have been found to be qute unresponsve to a pharmaceutcal prce change. The card may have lttle f any effect on ther health. Thus externaltes assocated wth ther health status are lkely to be small. Smlarly, the utlty gan from the altrusm of subsdsng the consumpton of ths wealthy populaton may be smaller than that ganed through supportng poorer groups. VI Concluson Ths paper has analysed the welfare mplcatons of the Commonwealth Senors Health Card, focussng on the pharmaceutcal concesson whch the card provdes. Its man feature s a par of models whch estmate the welfare gan of rsk poolng and the welfare loss of moral hazard, respectvely. I fnd that the welfare gan through rsk reducton s neglgble, whle the welfare loss through moral hazard may be substantal. The deadweght loss of the concesson s estmated to equal 8% of the cost to government ncurred on sngles and 26% for couples. Ths s despte a relatvely small estmated prce elastcty of demand for pharmaceutcals for ths populaton ( 0.). Whlst the deadweght loss estmates are senstve to the assumed parameters, most estmates exceed 0% for sngles and 5% for couples. These results must be consdered n the context of the assumptons dscussed n secton V, whch demonstrates the dffcultes nvolved n analysng the welfare mplcatons of health care programs. Some of these assumptons wll unquestonably be volated to some extent and t has not been possble to quantfy the mplcatons of these volatons. However, the extent of these volatons may be less severe gven the wealth of the CSHC populaton and ther apparently small prce elastcty of demand. These assumptons deserve even more consderaton n analyses of health care programs that cover populatons that are poorer or more responsve to prce. If t s accepted that the deadweght loss of the CSHC pharmaceutcal concesson represents welfare loss, a cash transfer may be a more effcent use of resources. On the other hand, the concesson has greater value for people wth hgher PBS consumpton. To the extent that hgher PBS consumpton reflects poorer health, the concesson s perhaps more equtable than the equvalent cash transfer. 8

19 However, CSHC holders are a partcularly wealthy populaton and so the CSHC may be regarded as an nequtable transfer. If so, socal welfare may be mproved by redrectng resources towards programs that are more effcent and/or more equtable than the CSHC. Fnally, t s noted that the CSHC may elct behavoural responses n the realms of savng and labour supply, whch are addtonal consderatons for analyses of ts welfare mplcatons. Indeed, the CSHC s ntended to encourage people to save for retrement. Whether the card has had such an effect has not been establshed, although Smnsk (2008b) suggests that whlst the CSHC creates ncentves for some people to save for retrement, t may have the opposte effect on others. VII Appendx Secton III estmates the welfare gan of the CSHC due to rsk poolng. It uses a health statedependent utlty functon whch does not allow the margnal utlty of consumpton to vary wth health status. There s some evdence that the margnal utlty of consumpton decreases wth sckness (ncreases wth health) (e.g. Fnkelsten et al., 2008; Vscus and Evans, 990). Ths s not a lmtaton to the analyss f pharmaceutcal consumpton completely restores full health, but ths s unrealstc. Ths appendx outlnes the mplcatons of relaxng ths assumpton. Specfcally, I show that the value of rsk avodance s even smaller f the margnal utlty of consumpton decreases wth sckness. Equaton (6) n the body of the text states that a consumer s ndfferent between a cash transfer of M and a pharmaceutcal concesson. Here, the analyss s smplfed by assumng only two health states, good and bad, whch have probabltes of g and b, respectvely. The bad health state elcts consumpton of x pharmaceutcals at a prce of p. The good health state requres no pharmaceutcal consumpton. The nonlnear prce concesson of the CSHC s replaced by a pure subsdy that s equal to ( r)*00% of general out of pocket expendture (r s the rate of co nsurance). Fnally, the margnal utlty of consumpton n the bad health state s equal to γ tmes the margnal utlty of consumpton n the good state. Thus margnal utlty of consumpton s lower n poor health when γ <. Wth these modfcatons, an equaton that s equvalent to (6) s: gu ( I + M ) + bγu ( I px + M ) = gu ( I) + bγu ( I rpx) (A) Let the utlty of non pharmaceutcal consumpton be a CRRA functon, where ρ can take any value. 9

20 ρ ρ ρ ρ ( I + M) ( I px+ M) I ( I rpx) g + bγ = g + bγ ρ ρ ρ ρ (A2) It wll be shown that dm/dγ > 0 n general. Ths mples that a lower margnal utlty of consumpton n poor health results n a lower cash equvalent value of the subsdy. Further, the expected government expendture on the subsdy s equal to b( r)x regardless of γ. It follows that the welfare gan of the subsdy due to rsk reducton s also lower under the assumpton of lower margnal utlty of consumpton n poor health. To fnd dm/dγ, equaton (A2) s mplctly dfferentated: ρ ρ ρ dm ( I px + M ) ρ dm ( I rpx) gi ( + M) + b γ ( I px M) b dγ + + = ρ dγ ρ (A3) Make dm/dγ the subject: dm b I rpx I px+ M = ρ dγ g( I + M) + bγ( I px+ M) ρ ρ ( ρ) ( ) ( ) ρ (A4) Note that g, I, M, b, γ are all greater than or equal to zero. Also, I > px as long as pharmaceutcal consumpton does not exceed ncome. Therefore the denomnator of (A4) s postve, and dm/dγ has the same sgn as: ( ρ) ( I rpx) ρ ( I px+ M) ρ (A5) When ρ >, ( ) ρ < 0 and when ρ <, ( ) ρ > 0. The second term of (A5) s negatve when: ( I rpx) ρ ( I px M) < + ρ (A6) When ρ >, (A6) mples: I rpx > I px + M whch smplfes to: M < px( r). Smlarly, the second term of (A5) s postve when ρ < and M < px( r). Therefore, from (A5), dm/dγ > 0 f M < px( r) regardless of the value of ρ. To see f ths nequalty holds, consder the expected utlty n the left hand sde of (A). If the transfer (M) s equal to px( r), expected utlty s: gu ( I + px[ r]) + bγu ( I rpx) (A7) But ths s greater than the rght hand sde of (A), snce px > 0 and r <. Therefore, for the equalty n (A) to hold, the transfer (M) must be smaller, so that M < px( r) must hold n general. Therefore, dm/dγ > 0. 20