On the Efficiency of Public and Private Health Care Systems: An Application to Alternative Health Policies in the United Kingdom

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1 On the Efficiency of ublic nd rivte Helth Cre Systes: An Appliction to Alterntive Helth olicies in the United Kingdo In W.H. rry Jnury 2001 Discussion per Resources for the Future 1616 Street, W Wshington, D.C Telephone: Fx: Internet: Resources for the Future. All rights reserved. o portion of this pper y be reproduced without perission of the uthors. Discussion ppers re reserch terils circulted by their uthors for purposes of infortion nd discussion. They hve not necessrily undergone forl peer review or editoril tretent.

2 On the Efficiency of ublic nd rivte Helth Cre Systes: An Appliction to Alterntive Helth olicies in the United Kingdo In W.H. rry Abstrct Helth policy will be jor issue in Britin s next generl election. The Lbour governent is coitted to substntil increse in fun for the tionl Helth Service (HS) nd hs eliinted tx relief for privte helth insurnce. The Conservtive Opposition prty fvors subsidizing privte helth insurnce, though it hs pledged to tch the governent s funding increses for the HS. This pper develops nd ipleents ethodology for estiting the welfre effects of incresing public nd privte helth cre in the United Kingdo, when these policies re finnced either by distortionry txes or by user fees for the HS. User fees re currently inil, nd the ntionl helth rket clers by creting witing costs. In the privte sector we ssue tht prices pproxitely reflect rginl supply costs, nd there re no witing lists. We find tht the welfre chnge fro incresing HS output could esily be negtive, prticulrly when extr spending is finnced by distortionry txes. In contrst, expnding privte helth cre is lwys efficiency-iproving in our siultions. In our centrl estites, incresing privte helth cre by pound s worth of output produces n efficiency gin of 55 pence, but incresing ntionl helth output produces net efficiency loss of 32 pence per pound! One reson for these results is tht incresing the output of rtioned helth cre hs biguous effects on the totl dedweight losses fro witing costs, but these costs unbiguously fll when the privte helth sector expn. Finncing policies by user fees voi the efficiency costs of rising distortionry txes, nd it lso produces efficiency gins by reducing witing lists. In fct, incresing ntionl helth cre output produces n overll efficiency gin in ost of our siultions, rther thn n efficiency loss, when the policy is finnced by higher user fees rther thn by distortionry txes. Still, the policy is generlly less efficient thn user fee finnced increse in privte helth cre. Key Wor: tionl Helth Service, privte helth cre, rtioning, subsidies, welfre effects JEL ubers: I18, I11, H42 ii

3 Contents 1. Introduction Model Assuptions Deriving Foruls for the Welfre Effect of Additionl Helth Spending... 9 A. olicies Finnced by Higher Txes... 9 B. olicies Finnced by Higher User Fees reter Vlues Epiricl Results A. Welfre Effects in the Helth Sector B. Tx-Finnced olicies C. olicies Finnced by User Fees Conclusion Appendix References iii

4 On the Efficiency of ublic nd rivte Helth Cre Systes: An Appliction to Alterntive Helth olicies in the United Kingdo In W.H. rry * 1. Introduction Recently, there hs been uch debte in the United Kingdo bout how to increse the level of helth cre spending to levels in coprble countries. Currently, the United Kingdo spen bout 6.8% of its gross doestic product (GD) on helth cre. Gerny spen 10.7% of its GD on helth, nd the United Sttes 13.9% (see Figure 1). 1 In prt, the reltively sll size of the U.K. helth sector is due to the tiny role plyed by the privte sector. rivte helth cre spending ccounts for just 1% of GD in the United Kingdo, in Itly it is 2.3%, in Frnce 2.5%, nd in the United Sttes 7.4% (Figure 1). Helth policy will be n issue in the next generl election in Britin. Tony Blir s Lbour governent is coitted to substntil increse in spending on the tionl Helth Service (HS), which provides helth cre for free t the point of consuption. Annul governent spending is set to increse fro 45 billion in to 59 billion in At the se tie the governent hs penlized the privte helth cre sector. In 1997 Chncellor of the Exchequer Gordon Brown scrpped tx relief for privte insurnce for pensioners, nd in 2000 he scrpped relief ginst ntionl insurnce contributions for eployers who provide privte edicl insurnce schees for eployees (cobined, these tx expenditures ounted to bout * Correspondence to: Dr. In W.H. rry, Resources for the Future, 1616 Street, Wshington, DC hone: (202) ; Eil: web: I grteful to Wlly Otes nd Mike Ton for helpful coents nd suggestions 1 This is despite the fct tht public spending on helth cre in the United Kingdo hs incresed by ore thn 3% per nnu in rel ters over the lst twenty yers (Eerson et l. 2000). 2 See For ore detils on the governent s helth policies, see the Helth olicy Docuent, vilble t 1

5 rry 100 illion per nnu). In contrst, Willi Hgue s Conservtive Opposition prty fvors encourging the privte sector through tx subsidies. 3 However, the Conservtives hve lso pledged to tch Lbour s spending increses on the HS. The in rguent for the governent s providing free helth cre is tht it llows people to receive tretent bsed on clinicl need rther thn on bility to py. 4 In ddition, subsidies for helth cre either subsidies for privte insurnce or direct provision of public helth cre hve been defended on efficiency groun. In prticulr, helth subsidies y be second-best response to privte rket filures tht re due to dverse selection nd orl hzrd. High-risk people y crowd out low-risk people fro privte insurnce rkets by driving up verge preius. Moreover, when tretent costs re borne by the insurnce copny, people y go to the doctor ore often thn needed or dend higher-qulity cre thn needed, gin driving up preius. 5 But centrl otivtion for the recent boost in HS funding ws to increse output nd thereby reduce the verge wit tie for HS tretent. Since the onetry price to househol of using the HS is essentilly zero, nd the governent cnnot supply ll the tretent tht is dended t zero price, helth cre is rtioned by creting witing lists. In Februry 2000, 1.1 illion people in Englnd (2% of the popultion) were witing for hospitl ppointent for clinicl intervention, nd the verge witing tie for such ppointents ws ore thn four 3 It would reintroduce the tx reliefs bolished by Lbour nd would llow eployees (s well s eployers) soe deduction ginst pyroll txes for privte helth insurnce. In the United Sttes, eployer-provided helth insurnce is exept fro ll pyroll nd incoe txes, iplying substntil subsidy of bout 40%. 4 A centrl principle of the HS set out in the 1944 White per, A tionl Helth Service, ws the i tht everyone irrespective of ens, ge, sex, or occuption shll hve equl opportunity to benefit fro the best nd ost up to dte edicl nd llied services vilble. Besley et l. (1999) find evidence tht the HS does indeed ensure provision for the poor. In contrst, bout 43 illion nonelderly Aericns do not hve ny edicl insurnce (EBRI 1999). 5 For ore discussion of these issues, see, for exple, Arrow (1963), uly (1974), Zeckhuser (1970), nd Gynor et l. (2000). 2

6 rry onths (Eerson et l. 2000). This tie dely for receiving public helth cre is source of dedweight loss. 6 Incresed spending on the HS y therefore produce efficiency gins by reducing the verge wit tie for tretent. 7 It lso produces efficiency effects becuse the rginl benefit fro dditionl HS output y be below the rginl supply cost (see below). In ddition, efficiency losses rise becuse distortionry txes hve to be higher to finnce the dditionl public spending. 8 Tx subsidies for privte helth cre cn reduce HS witing ties if they induce soe people to leve the queue nd go privte. But they lso iply higher txes elsewhere in the econoy, nd the subsidy itself cretes price distortion in the privte helth cre rket, giving rise to efficiency effects. This pper nlyzes the welfre effects of policies to (rginlly) increse public nd privte helth cre output. These effects ste fro three sources: first, chnges in the totl witing costs in the rtioned helth cre sector; second, distortions between the rginl socil benefit nd the rginl socil cost in the public nd privte helth cre rkets, creted by policy intervention; nd third, generl equilibriu welfre effects tht rise fro interctions with the tx syste. We use n nlyticl odel tht provides siple foruls for ech of these coponents of the welfre chnge. These foruls re estited using wide rnges of plusible 6 This is siilr to the dedweight loss cused by trffic congestion. In this cse, ro re unpriced but re in liited supply t pek perio. The rket for pek-period driving clers by incresing the tie costs to otorists fro using the rod. ote tht in the cse of trffic congestion, people ctully lose tie queueing, but in the cse of HS witing lists, people suffer dely in receiving service rther thn physiclly stnding in queue. For good discussion distinguishing these different types of rtioning, see Liny nd Feigenbu (1984). Other notble contributions to the literture on rtioning by witing include icholls et l. (1971), Brzel (1974), nd Decon nd Sonsteile (1989). 7 In prctice, soe of the incresed public spending nnounced by Gordon Brown is likely to finnce py rises for HS workers, rther thn providing rel increse in output, nd in this respect we y overstte the efficiency gins fro higher HS spending. On the other hnd, higher wges y otivte workers to be ore productive. These issues re beyond the scope of our nlysis. 8 Alterntively, higher spending y be finnced out of the current governent budget surplus. But this iplies tht future txes will be higher thn they would otherwise hve been, in order to finnce the lrger crryover of ntionl debt. Hence it is stndrd to ssue tht the opportunity cost of incresed public spending is foregone tx cuts. 3

7 rry preter vlues for the United Kingdo. Our nlysis ssues tht pound of spending on the HS produces the se qulity of cre s pound of extr privte helth spending, side fro the wit costs. revious discussions of helth policies hve focused inly on equity issues nd the iplictions of rket filures in privte insurnce rkets (see, e.g., Brr 1998 nd Donlon 1998 in the U.K. context). Witing ties hve been nlyzed in the literture on rket rtioning (e.g., Liny nd Feigenbu 1984), but the focus hs been inly on the deterinnts of equilibriu witing ties. To our knowledge, ours is the first ttept to quntify the welfre effects of policy-induced chnges in wit ties. There is sll literture on the efficiency costs of finncing helth policies by distortionry txtion. For the United Sttes this efficiency cost hs been estited t 20 to 40 cents per dollr of spending (Browning nd Johnson 1980; Bllrd nd Goddeeris 1999). Our pper lso d to this literture by developing cost estites for the United Kingdo. More iportntly, it explores soe dditionl interctions between helth policies nd the tx systes tht hve not been previously recognized (see below), nd it copres tx finncing with finncing fro user fees. Our focus is on three in policy issues. First, do the efficiency effects fro reducing HS witing ties outweigh efficiency losses fro other sources, when spending on either public or privte helth cre is incresed? In other wor, cn dditionl helth cre spending, either privte or public, be justified on the groun of reducing witing lists, or re other justifictions, such s infortion syetries, required? Second, re the net efficiency gins or losses lrger per pound of dditionl spending on public or privte helth cre? Tht is, given tht the governent hs decided to expnd the overll helth cre sector, is it better on efficiency groun to expnd the public sector or the privte sector? Third, if dditionl revenues for these policies were finnced by user fees for the HS for exple, expnding prescription chrges, introducing fees for generl prctitioner visits rther thn by higher txes, how would this chnge the overll efficiency ipct of the policies? We find tht incresing ntionl helth cre output could ctully reduce socil welfre. The verge wit tie per opertion flls, but the totl nuber of opertions rises, iplying n biguous effect on the totl dedweight losses fro witing. Moreover, the efficiency costs of finncing dditionl ntionl helth cre output through distortionry txes further reduce the welfre perfornce of this policy. Only when the dend for ntionl helth cre is very inelstic such tht ore output hs reltively lrge ipct on reducing equilibriu witing ties does this policy produce n overll welfre gin in our siultions. 4

8 rry In contrst, incresing privte helth output lwys increses welfre in our nlysis. Becuse of the substitution between public nd privte helth cre, this policy unbiguously reduces the totl dedweight losses fro witing lists. 9 Also, its ipct on excerbting preexisting tx distortions is uch less significnt. Under lost ll preter scenrios, expnding privte helth cre is ore efficient thn expnding public helth cre, nd by potentilly lrge ount. For exple, under our centrl preter vlues, incresing privte helth by pound s worth of output produces net efficiency gin of 55 pence; incresing ntionl helth cre by pound s worth of output produces n efficiency loss of 32 pence. Finncing policies by user fees rther thn by txes significntly increses efficiency. This voi the efficiency losses cused by rising distortionry txes, nd it produces n efficiency benefit by reducing wit ties for rtioned helth cre. In fct, incresing ntionl helth cre output produces n overll efficiency gin in ost of our siultions, rther thn n efficiency loss, when the policy is finnced by higher user fees rther thn by distortionry txes. Still, the policy is generlly less efficient thn user fee finnced increse in privte helth cre. We ephsize nuber of cvets to the nlysis. First, becuse of preter uncertinty, it is not possible to ccurtely pin down the bsolute welfre effects of lterntive helth policies. onetheless, we re still ble to drw brod conclusions bout the reltive welfre effects of different policies nd deterine whether different policies re likely to increse or decrese econoic efficiency. Second, our nlysis ignores soe considertions tht would be iportnt in ore coprehensive policy evlution, including equity issues, politicl fesibility, nd infortionl probles in privte insurnce rkets. For exple, user fees pper ttrctive on efficiency groun, but they obviously hurt the poor disproportiontely nd therefore would be politiclly difficult to ipleent. 10 The rest of the pper is orgnized s follows. Section 2 describes the odel ssuptions. Section 3 derives foruls tht decopose the generl equilibriu welfre effects of dditionl 9 Other ppers tht hve studied the substitution between public nd privte provision of privte goo include Stiglitz (1974), Sonsteile (1982), Irelnd (1990), nd Besley nd Cote (1991). 10 Moreover, user fees could led to worse public helth for the poor, nd this could hve serious spillover effects if the incidence of infectious diseses increses. But these probles could be itigted in prt by ens-testing user fees. 5

9 rry spending on public nd privte helth cre, under lterntive finncing options. Section 4 discusses plusible preter vlues for these foruls. Section 5 presents the epiricl results. Section 6 concludes. 2. Model Assuptions Consider sttic, representtive gent odel where the household utility function is: (2.1) U = U{ H ( H, H ), Y, l} k H H nd H re the consuption of ntionl helth cre output nd privte helth cre output respectively, Y is the consuption of ll other rket goo, nd l is leisure or nonrket tie. U(.) nd H(.) (subutility fro helth cre) re continuous, qusi-concve functions. k H represents the (totl) cost of witing for ntionl helth cre rther thn receiving instnt tretent, tht is, the cost of continued suffering nd reduced qulity of life while on the HS witing list. k = k ( k ) where k nd k re the verge wit cost nd the rginl wit cost, respectively, nd k ( k ) > 0. We ssue tht k > k, nd therefore k ( k ) < 1, becuse we need to represent the sitution in prctice where soe people re willing to py ore thn others to void witing for tretent. For exple, the vlue of k is reltively high for highincoe people nd those not opposed to using privte helth cre on ideologicl groun. Hence the rginl person using the HS hs higher opportunity cost of witing thn the infrrginl person. H is the current ount of helth cre provided by the governent, nd therefore in equilibriu H = H. H nd Y re produced by copetitive industries, nd H is provided publicly. We ssue tht the public sector iniizes production costs, s in the privte industry. 11 In ech industry we ssue perfectly elstic supply curves, which see plusible long-run ssuption. Lbor is the only input in production, nd lbor ernings re txed t rte t. We norlize units to iply tht supply prices, nd the gross wge, re unity. 11 If the incentive to iniize production costs is weker in the public sector thn in the privte sector, our nlysis will understte the efficiency costs of producing ore public helth cre. 6

10 rry Househol py the rket price for privte helth cre, lthough sll portion of these costs re tx deductible (see below). 12 We define 0 s < t s the effective rte of subsidy for privte helth cre. In our nlysis which bstrcts fro equity issues nd infortion syetries in insurnce rkets the privte benefits fro public nd privte helth spending re equl to the socil benefits. Therefore, the tx-subsidy siply cretes (sll) wedge of s between the rginl cost of supplying privte helth cre nd the rginl benefits to househol, iplying dedweight loss equl to the shded tringle in Figure 2(). There is sll user fee of c for public helth cre, which y represent prescription chrges. Househol would like to consue public helth cre up to the point where the rginl privte benefit equls c, tht is, H 1 in Figure 2(b). However, the governent provides only H in output becuse of budgetry constrints. Since the dend for public helth cre excee H when the price is c, helth cre ust be rtioned, nd this occurs through the expected wit tie for receiving tretent. 13 Thus, the full price of ntionl helth cre t the rgin is c + / λ, where λ is the rginl utility of incoe. The wit tie is exogenous to individul k househol but djusts t the rket level to equte dend nd supply. The totl dely cost, the shded trpezoid in Figure 2(b) equl to λ k H, is pure dedweight loss to the econoy: it represents the cost of hving to wit severl onths to get tretent Typiclly, in the privte sector people purchse insurnce to cover the costs of tretent in the event of illness or injury. The price of privte helth cre is, roughly speking, the verge preiu per household, where the totl preius pid by househol cover the expected costs of tretent born by privte suppliers. 13 For noneergency condition people re first referred to specilist by their generl prctitioner. The ptient is then put on witing list for HS hospitl tretent. The nuber of individuls on in-ptient witing lists hs incresed fro 400,000 to ore thn 1,200,000 in Englnd over the lst 40 yers, nd the verge wit tie ws bout four onths in 1999 (Eerson et l. 2000). For eergency conditions the wit ties re inil, nd hence there is little incentive to py for privte tretent. 14 Besley nd Cote (1991) develop odel of public nd privte helth cre in which the qulity of HS cre, which tkes ccount of wit ties, is fixed by the governent nd is inferior to tht in the privte sector, where there re no wit ties. The structure of our odel differs by llowing the wit tie to be endogenous rther thn exogenous. Other helth cre odels with endogenous witing ties include Liny nd Feigenbu (1984), Grvelle (1990), nd Goddrd et l. (1995). 7

11 rry We ssue tht the benefit to househol fro dditionl tretent (gross of the oney nd tie cost) is the se for both the public nd the privte sector (for given qulity of hospitl stff nd equipent). In equilibriu: (2.2) c + k / λ = 1 s Tht is, the full price per unit of public helth cre ust equl the oney price of privte helth cre. 15 ote tht this iplies tht the wedge between the rginl supply cost nd the rginl benefit to consuers is s, the se s in the privte helth rket (see Figure 2). Also note tht since k lwys djusts to intin condition (2.2), increses in the user fee re exctly offset by fll in k, when H nd s re constnt. The governent budget constrint is: (2.3) G + ( 1 c) H + sh = tl where G is n exogenous spending requireent nd L is lbor supply. For siplicity, we tret G s lup-su trnsfer to househol. Eqution (2.3) equtes expenditure on the trnsfer pyent, ntionl helth cre (net of user fee revenues), nd the tx expenditure for privte helth cre, with revenues fro the lbor tx. The household budget constrint is: (2.4) ch + ( 1 s) H + Y = (1 t) L + G The left side of (2.4) is onetry spending on consuption goo, where the onetry price of ntionl nd privte helth cre is c nd 1-s respectively. The right side is net of tx lbor incoe plus the governent trnsfer. Househol lso fce the tie constrint L = L + l where L is the tie endowent. Using dulity, the household optiiztion proble cn be expressed: (2.5) e( U, s, c + k, t) = Min ch + (1 s) H + Y (1 t L ) { U{ H ( H + H ), Y, L l} k ( k H U } 1 λ ) 15 If, for exple, c + k > 1 s privte sector until k flls enough to restore equilibriu. / λ, then people t the rgin would quit witing for the HS nd ove to the 8

12 rry where e(.) is the expenditure function nd U is the xiized vlue of utility. The solution to this proble yiel the copensted dend nd lbor supply functions: (2.6) H = H ( s, c + k, t) ; H = H ( s, c + k, t) ; Y = Y ( s, c + k, t) ; L = L( s, c + k, t) where we hve norlized the rginl utility of incoe to unity (this is resonble when we re deling with increentl policy chnges). Differentiting the expenditure function in (2.5), nd noting tht in equilibriu e (2.7) = H s e k ; = H k H = H, we cn obtin: e ; = H c e ; = L t 3. Deriving Foruls for the Welfre Effect of Additionl Helth Spending We now derive foruls for the efficiency effect of policies to increse public nd privte helth cre output by the se increentl ount, finnced both by higher txes nd by higher user fees. 16 A. olicies Finnced by Higher Txes (i) Incresing the privte helth subsidy. Consider n increentl increse in the privte helth subsidy finnced by rising the lbor tx. The welfre gin fro this policy is defined by: de / (3.1) dwt = / The nuertor in (3.1) is the lup-su trnsfer tht would hve to be tken wy fro the household to keep utility constnt following n increentl increse in s (tking into ccount induced chnges in t nd k ). The denointor is the increse in privte helth consuption 16 An lterntive pproch would be to copre the efficiency of incresing governent spending on the HS with tht of incresing the subsidy outly for privte helth cre, ech by pound. In this cse the increse in output would be different in the public nd privte helth rkets. In fct, the chnge in output would lso differ ccording to whether polices re finnced by higher txes or higher user fees. This would ke the cost coprisons cross policies ore difficult to interpret. 9

13 rry fro n increentl increse in s. Hence helth output. 17 Soe nipultion gives (see Appendix A): (3.2) = dk dw + t s H k + dw t is the welfre gin per unit of dditionl privte Eqution (3.2) decoposes the welfre effect into three coponents. The first ter, s, is the welfre loss fro the increse in the shded tringle in Figure 2() due to the privte helth output effect. For the low levels of subsidy ssued below, however, this effect is epiriclly sll. The second ter is the efficiency benefit fro reducing dely costs (the trpezoid in Figure 2(b)) in the ntionl helth cre rket. It equls the reduction in verge dely cost (the ter in brckets) ties the quntity of public helth cre. The dely cost flls becuse the increse in privte helth consuption shifts in the dend curve for public helth cre. The third ter is the welfre gin or loss in the lbor rket. This equls the chnge in lbor supply ties the lbor tx, where the lbor tx equls the difference between the vlue rginl product of lbor (equl to the gross wge) nd the rginl opportunity cost of leisure tie (the net wge). We cn decopose the welfre effect in the lbor rket into the following two expressions (see Appendix): dl L (3.3) t = H s M + + t( 1+ M ) s where (3.4) M L t = t L L + t t t ε L = 1 t t 1 ε 1 t L dl t nd ε = ( L / (1 t))(1 t) L is the (copensted) lbor supply elsticity. L / 17 Under this definition of the welfre chnge, quntity chnges depend on copensted price effects (i.e., pure substitution effects). This pproch hs been defended by Browning et l. (1997) nd Fne nd Jones (1997). 10

14 rry The first expression on the right in (3.3) is the welfre cost of finncing the dditionl subsidy pyent through distortionry lbor txtion, or the revenue-finncing effect. 18 This is the product of two ters. The ter in prentheses, which equls d ( sh ) /, is the increse in subsidy outlys required to increse H by one unit. M denotes the rginl excess burden (MEB) of lbor txtion, tht is, the welfre loss fro rising one extr pound of revenue by incresing the lbor tx. 19 The second ter in (3.3) is the efficiency gin fro the positive ipct on lbor supply s the subsidy lowers the oney price of goo nd hence increses the rel wge. This hs been tered the tx-interction effect in other policy contexts (e.g., Goulder 1995). The increse in lbor supply produces welfre gin of ( 1+ M ) t per unit, when we tke into ccount the gp (t) between the gross nd net wge, nd the efficiency vlue of the increse in lbor tx revenues per unit increse in lbor supply ( Mt ). Iposing wek seprbility between goo nd leisure in the utility function, we cn obtin (see Appendix): (3.5) dw t = s + 1 s k M s η s (1 s) + Mζ η ( η ) 1 where 1 s c + k H I (3.6) η = < 0 ; η = < 0 ; ζ = > 0 d(1 s) H dk H I H η nd η re the own price elsticities of dend for privte nd public helth cre respectively, nd ζ is the expenditure elsticity for privte helth cre (I denotes disposble incoe). The lst three ters on the right in (3.5) correspond to the chnge in wit costs, the revenue-finncing effect, nd the tx-interction effect. As discussed below, privte helth cre is probbly luxury good ( ζ > 1) nd is therefore reltively strong substitute for leisure (see, e.g., Deton 1981). Suppose tht s = 0; then in this cse there would be net welfre gin fro 18 This terinology is fro rry (1998). 19 ote tht the nuertor of the first expression for M in (3.4) is the welfre loss fro n increentl increse in t nd the denointor is the increse in revenue fro n increentl increse in t. Hence M is the welfre loss per pound of extr revenue. See Browning (1987) for thorough discussion of the rginl excess burden of txtion. 11

15 rry the revenue-finncing effect nd the tx-interction effect in (3.5). In other wor, up to point, subsidizing privte helth cre could be justified on the groun of tx-efficiency. 20 (ii) Incresing public helth cre. Consider unit increse in public helth output, finnced by incresing the lbor tx. The welfre chnge fro this policy is: de (3.7) dwt = Soe nipultions yield (see Appendix): (3.8) dw { ( c + k )} t + H dk k k s = 1 + t dl There re four sources of welfre chnge fro incresing public helth output by one unit. First is welfre loss of 1 ( c + k ) = s, the gp between the rginl supply cost nd the rginl benefit to househol (i.e., the ddition to the shded tringle in Figure 2(b)). Second is the welfre effect fro the chnge in dely costs (the ter in prentheses). Agin, there is n efficiency benefit equl to the fll in verge dely costs ( k dk / ) ties the quntity of public helth cre. And the fll in dely costs will be lrger thn before, since the price effect is direct rther thn indirect (copre the relevnt ters in (3.2) nd (3.8) nd note tht / < 1). But since public helth output is rginlly higher, dely costs lso increse by k. Hence, on blnce, the dedweight losses fro wit costs could ctully increse. Third, there is welfre loss in the privte helth rket ( slight reduction in the shded tringle in Figure 2()), since dend flls in response to the lower price of public helth. Agin, since s is sll for the United Kingdo, the first nd third ters in (3.8) re epiriclly uniportnt (see below). 20 Conversely, if ζ < 1, privte helth would be reltively wek leisure substitute, nd the subsidy cuses net efficiency loss fro interctions with preexisting txes. These results re consistent with the theory of optil coodity txes, which iplies tht reltively strong (wek) leisure substitutes should be subsidized (txed) reltive to other goo. Our nlysis siplifies by ignoring possible feedbck effects of iproved helth on lbor productivity. This turns out to be coplicted theoreticl issue, nd the overll ipcts on lbor supply re biguous (Willis 1998). Moreover, the reltive epiricl gnitude of these feedbck effects y not be tht lrge becuse disproportionte ount of helth spending is on the elderly, nonworking popultion. 12

16 rry The fourth source of welfre chnge is in the lbor rket, nd this cn lso be expressed (see Appendix): dl (3.9) t M 1 c + s = Copring (3.9) nd (3.3), we see two crucil differences. First, the revenue-finncing effect is lrger. In this cse, the revenue-finncing effect is the MEB ultiplied by the revenue cost of the extr unit of ntionl helth output, 1 c, net of the induced chnge in subsidy outlys in the privte helth rket. But since c nd s re sll, the revenue-finncing effect is close to M (see below). In contrst, the revenue-finncing effect is well below M for the privte helth subsidy, since the dend for privte helth cre is elstic (plug s sll nd η >> 1 in the revenue-finncing effect in (3.5)). The second difference is tht there is no offsetting txinterction effect in (3.9). Incresing (free) ntionl helth cre does not ffect the onetry price of consuption goo nd therefore does not ffect the rel household wge, nd hence it does not chnge the return-to-work effort. In short, incresing public helth cre increses efficiency only if it reduces the totl dedweight losses fro witing ties, nd if it does so by ore thn enough to offset the efficiency cost of the revenue-finncing effect. In contrst, subsidizing privte helth cre lwys increses efficiency in our siultions. This is becuse it unbiguously reduces the dedweight losses fro witing, nd the efficiency effects fro interctions with the tx syste re uch sller, if not positive. Using (2.2), (3.6), (3.8), nd (3.9), we cn obtin: 1 s (3.10) dw t s + k (1 s c) s M 1 c + s η = These four ters correspond to the public helth output effect, the chnge in wit costs, the privte helth output effect, nd the revenue-finncing effect. B. olicies Finnced by Higher User Fees (i) Incresing the privte helth subsidy. The welfre gin fro this policy, when finnced by higher user fees rther thn by higher txes, is (see Appendix): k dc dl (3.11) dw c = s + H k + + t H 13

17 rry Copring (3.2) nd (3.11), we see tht wit costs re reduced by n dditionl effect. Given the dend for ntionl helth cre, nd becuse output is fixed, the increse in user fees is fully offset by fll in the (rginl) wit cost. Soe nipultion gives (see Appendix): (3.12) dw c s + 1 s 1 s 1 s M k + k s + ζ η η η 1+ M Copring (3.5) nd (3.12), we find no revenue-finncing effect. Insted, the third ter in (3.12) is the efficiency gin fro the ipct of higher user fees on reducing witing costs. This ter equls the rginl subsidy pyent ties k k ). Therefore, finncing this policy ( by user fees rther thn by txes not only voi the costly revenue-finncing effect, but it lso produces direct efficiency gin by reducing the excess dend for rtioned helth cre nd hence the dedweight losses fro witing. (ii) Incresing public helth cre. Finlly, the welfre chnge fro incresing public helth output finnced by user fees is (see Appendix): 1 s (3.13) dwc s + k (1 s c) + k 1 c + s s η Agin, copring with (3.10), we see tht the welfre perfornce of this policy iproves becuse there is no revenue-finncing effect, nd becuse higher user fees reduce witing costs. Tble 1 surizes the coponents of the welfre chnges under ll the policies discussed in this section. 4. reter Vlues This section describes the rnges of preter vlues we use to estite the welfre chnge foruls. These vlues re surized in Tble 1. Our objective in the subsequent siultions is not to ttept relly ccurte estites of the welfre chnges, but rther to illustrte the sign of the welfre chnges, nd the reltive rnking of policies, over wide rnges of plusible preter scenrios. Tx subsidy for privte helth cre. rivte helth insurnce in the United Kingdo is no longer eligible for ny relief fro pyroll or incoe txtion. urchsed inputs into privte helth cre production re subject to the vlue-dded tx of 17.5%, but the finl output is not. In 14

18 rry other wor, there is sll tx subsidy for edicl services, reltive to other finl goo, becuse the vlue dded t the finl stge of production of edicl services is not covered by the vlue-dded tx. We dopt benchrk vlue of s = 0.05, but s noted below the results re only odertely sensitive to lterntive vlues. Helth dend nd expenditure elsticities. Besley et l. (1999) estite tht the expenditure elsticity of dend for privte helth cre is round 2.2% in the United Kingdo, which is brodly consistent with results fro ropper (1993). We consider rnge of 1.0 to 3.0 for ζ with strting vlue of 2.0. We would expect the dend for HS cre to be inelstic with respect to its full price, becuse substitution possibilities re liited by the sll size of the privte sector, nd ny househol re ideologiclly opposed to using the privte sector (ropper 1993). Liny nd Feigenbu (1984) estited n elsticity of 0.55 to 0.70, but Mrtin nd Sith (1999) report elsticities bout hlf this gnitude. We dopt rnge of 0.3 to 0.7 for η, with strting vlue of 0.5. We re not wre of ny studies tht directly estite the own price dend elsticity for privte helth cre in the United Kingdo, but other evidence suggests this elsticity ight be firly high. Besley et l. (1999) estited tht 1% increse in witing costs for the HS ight increse privte insurnce by 12%. For the United Sttes, estites of the own price elsticity for privte edicl insurnce rnge between bout 0.5 nd 1.5 (e.g., uly 1986; helps 1992). We would expect the U.K. elsticity to be lot lrger becuse the quntity of privte helth cre is uch sller in the United Kingdo (Figure 1). 21 We illustrte cses where η vries between 2 nd 10. ote tht η only ppers in the revenue-finncing nd tx-interction effect ters in the bove welfre chnge foruls, nd is therefore less iportnt thn η. In prctice, in response to n increse in s, the dend for privte helth insurnce will increse becuse () people substitute privte helth cre for public helth cre, (b) people increse their overll dend for helth cre reltive to other (nonhelth) goo, nd (c) people who re lredy in the privte sector increse the ount of their insurnce. If (b) nd (c) were 21 The effective price is lso uch lower in the United Sttes becuse of the exeption of privte helth insurnce fro personl nd pyroll txes. ote tht dend elsticities re lrger the higher the price nd the sller the quntity. 15

19 rry zero, then / = 1, but if () were zero, / = 0. However, () is likely to be sizble reltive to both (b) nd (c), 22 nd we consider rnge of 0.4 to 0.8 for /. 23 Reltion between rginl nd verge witing costs. There is not relly ny evidence tht cn be used to pin down k k ). But it ust be less thn unity; it would equl one only if ( everyone hd the se willingness to py to void witing for tretent, which is clerly not the cse. In ddition, it ust be positive, since the verge person suffers positive cost fro hving to wit longer for tretent. We illustrte wide rnge of possibilities fro k k ) = 0.25 to ( 0.75 with centrl vlue of 0.5. The low vlue represents reltively wide dispersion in the opportunity costs of witing ong people using rtioned cre, nd the high vlue represents reltively nrrow dispersion in the opportunity costs of witing. User fees. We ssue tht user fees ount to 2% of the supply price of ntionl helth cre. This figure is obtined by ultiplying the resource cost of prescriptions ( 4.7 billion) by the frction of prescriptions tht househol (s opposed to the governent) py for (0.15), nd dividing by ntionl helth spending ( 37 billion). 24 Lbor supply elsticity. In our highly ggregted odel, the lbor supply elsticity represents the cobined responsiveness of the prticiption rte nd verge hours worked per eployee, to chnges in net wges, verged cross ll ebers (le nd fele) of the lbor force. A plethor of studies hve been done for the United Sttes (e.g., Killingsworth 1983), nd ggregting estites for le nd fele elsticities, plusible centrl vlue for the 22 The degree of substitution between public nd privte helth goo is uch lrger thn tht between helth s whole nd other (nonhelth) goo. In ddition, the rnge of privte polices offered is reltively nrrow in the United Kingdo, liiting the bility of people with existing policies to increse spending on insurnce (ropper 1993). 23 Conversely, if ntionl helth cre output were increentlly incresed, the induced increse in dend would coe inly fro people who exclusively use the HS rther thn fro people oving fro the privte sector to the HS. Since, ccording to Figure 1, the privte sector is 17.5% the size of the public sector, we tke / to be Our results re not sensitive to lterntive vlues, becuse this ter is ultiplied by s, very sll nuber, in the welfre chnge foruls. 24 See nd (Tble C19). These figures re for

20 rry (econoywide) copensted elsticity is bout About two-thir of the responsiveness is due to the prticiption decision nd one-third to the hours-worked decision. The few studies tht hve been done for the United Kingdo yield brodly siilr vlues for le nd fele elsticities (e.g., Blundell 1997). Given the vrince of estites cross studies, we consider rnge of vlues fro 0.2 nd 0.5. Lbor tx rte. We consider rnge of 0.36 to 0.42 for the U.K. lbor tx rte, with strting vlue of These figures re fro rry (2000) nd represent the cobined burden on gross lbor incoe of incoe txes, pyroll txes, nd txes on goo (excluding externlity txes, such s gsoline txes). 26 Using (3.4), these figures iply centrl vlue of 0.29 for the rginl excess burden of txtion, with low nd high vlues of 0.13 nd Epiricl Results This section provides epiricl estites of the welfre effects of the helth policies. We strt by focusing only on welfre effects in the helth sector. Subsections B nd C estite the welfre effects fro finncing the policies by txes nd by user fees. A. Welfre Effects in the Helth Sector (i) ublic helth subsidy. Figure 3 illustrtes the rginl welfre effect of incresed spending on public helth cre, ccording to the forul in eqution (3.10), but ignoring the revenuefinncing ter. The verticl xis indictes the rginl welfre gin or loss in poun per pound of incresed output, nd on the horizontl xis we vry k ( k ) cross its rnge fro 0.25 to The dshed curves indicte the welfre effect fro the chnge in wit ties only; the solid curves lso include the output effects in the public nd privte helth rkets. The upper, iddle, nd lower sets of curves correspond to cses in which the dend elsticity for ntionl helth cre is 0.3, 0.5 nd 0.7, respectively. There re severl noteworthy points. 25 This is bsed on recent survey of opinion ong lbor econoists reported in Fuchs et l. (1998), Tble 2. It ssues weights of.6 nd.4 for the le nd fele elsticities, respectively. 26 This is n verge rte of tx nd is relevnt for the lbor force prticiption decision, the jor deterinnt of the lbor supply elsticity. In principle we should use weighted verge of the verge nd (higher) rginl tx rte, s the ltter is relevnt for the hours-worked decision. This would increse the centrl vlue to bout 42% (rry 2000). But on the other hnd, this figure y overstte the true tx burden little, since portion of the pyroll tx y effectively be offset by higher expected retireent incoe (Feltein nd Swick 1992). 17

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