OUTPUT, OUTCOME, AND QUALITY ADJUSTMENT IN MEASURING HEALTH AND EDUCATION SERVICES

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1 bs_bs_banner row_ Revew of Income and Wealh Seres 58, Number 2, June 2012 DOI: /j x OUTPUT, OUTCOME, AND QUALITY ADJUSTMENT IN MEASURING HEALTH AND EDUCATION SERVICES by Paul Schreyer* OECD Sascs Drecorae, Pars Ths paper provdes an overvew of measurng prce and volume changes of he oupu of healh and educaon provders. In he naonal accouns, oupus should reflec he resuls of producon and hese canno normally be capured by oucome, he sae of healh or educaon of he populaon. However, we show ha oucome nformaon s requred when comes o qualy adjusmen of oupu measures. The paper clarfes ermnology, and dscusses oupu measuremen and qualy adjusmen mehods wh a focus on healh and educaon servces. JEL Codes: E01, I10, I20, O47 Keywords: healh and educaon servces, non-marke oupu, oupu and oucome, qualy adjusmen 1. Inroducon A major purpose of he naonal accouns s o measure prce and volume change of GDP and s major componens as well as producvy. For hs purpose, changes n volumes of oupu should be properly measured and reflec changes n qualy. However, n naonal accouns pracce, occurs ha npubased measures are used o rack oupu of ceran acves and no or nsuffcen qualy adjusmen s n place. A case n pon s servces such as educaon and healh ha are complex and for whch here are ofen no economcally sgnfcan prces. Ofen, mehodologes have reled on measurng he volumes or he prces of npus o oban a measure of he volume or prce of oupus. Ths means ha s mpossble o capure producvy change. Ignorng producvy changes means foregong mporan nformaon for analyss and polcy makers abou wo secors ha accoun for a leas 10 percen of GDP n many OECD counres. A recen revew of OECD counry pracces of healh and educaon oupu measuremen (Schreyer, 2010) reveals a heerogeneous pcure. In he feld of educaon, abou one hrd of all counres, manly European as well as Ausrala and New Zealand, have already mplemened oupu-based measures and ohers are plannng o do so. In ohers, work s a he research sage. A smlar pcure emerges for healh care alhough a larger number of counres have embraced oupu-based mehods. Tha sad, he caegorzaon of a mehod as npu- or oupu-based s no always clear cu and s even more dffcul o pass a judgmen on he appropraeness of qualy adjusmen mehods used. In sum, hus, a raher *Correspondence o: Paul Schreyer, OECD Sascs Drecorae, 2 rue André Pascal, Pars Cedex 16, France (Paul.Schreyer@oecd.org) The Auhor Revew of Income and Wealh 2012 Inernaonal Assocaon for Research n Income and Wealh Publshed by Blackwell Publshng, 9600 Garsngon Road, Oxford OX4 2DQ, UK and 350 Man S, Malden, MA, 02148, USA. 257

2 Revew of Income and Wealh, Seres 58, Number 2, June 2012 dsparae pcure emerges by way of mehods used, and consequenly nernaonal comparsons have o be conduced wh care. In many counres, healh and educaon servces are provded by governmen or oher non-marke producers. I s clear ha marke producon gves us drec observaons on he value of producon a curren prces whereas he value of non-marke producon s ypcally esmaed by summng up coss. Bu mos of he rcky ssues assocaed wh he measuremen of volume oupu apply o boh marke and non-marke producers. In parcular, he dffcules of keepng rack of qualy change and of enerng and exng producs are presen ndependenly of he nsuonal afflaon of he producng un. These problems are assocaed wh he ncreasngly complex naure of modern servces, for example n healh care, and no wh he queson of wheher hese servces are provded under marke condons or no. In consequence, many ssues of oupu measuremen are relevan for he acvy as a whole, and no only under condons of non-marke provson, alhough non-marke provson complcaes measuremen n several respecs. The dscusson abou he measuremen of healh and educaon servces s by no means new. In 1975, Peer Hll developed prncples and gudance for measurng healh, educaon, and collecve governmen servces (Hll, 1975). More recenly, he debae has resurfaced. Eurosa (2001) saed he desrably of applyng oupu-based measures o non-marke servces. In he Uned Kngdom, he opc was aken up by he wdely-dscussed Aknson Revew (Aknson, 2005). The measuremen of servces oupu and producvy has also been a longsandng opc of neres n he Uned Saes, wh a seres of publcaons ncludng Trple and Bosworh (2004) and Abraham and Macke (2006). Healh servces n parcular have been he subjec of research on cos-effecveness and producvy (Culer e al., 2006; Rosen and Culer, 2007), jus as educaon servces have been scrunzed for effcency and effecveness. When analyss proceeds from a healh care or educaonal polcy perspecve, measuremen ssues do no always surface, and where hey do s no always apparen how hey relae o measuremen prncples n he naonal accouns. One objecve of he presen paper s o provde hese lnks. 1 The prncple objecve of our effors here s o shed lgh on he measuremen of volume measures of oupu for complex and economcally mporan servce acves, and we shall frame our dscusson wh examples from healh and educaon, alhough hey may apply more broadly. Termnology s mporan n hs conex and Secon 2 sars by defnng oupu, oucome, npus, and acves. Secons 3 5 provde he economcs of measuremen n an ncreasngly complex seng. We move from he smple compeve case whou qualy 1 One parcular srand of producvy research s rooed n effcency analyss where hospals or educaonal esablshmens are compared usng Daa Envelopmen Analyss and Sochasc Froner Models as developed by Farrell (1957), Färe e al. (1985), and Agner e al. (1977). These mehods use eher lnear programmng or economerc echnques o assess he relave producvy of esablshmens, wh he added feaure of dsngushng beween effcency effecs (moves oward he effcency froner) and echncal change (moves of he effcency froner). Also, DEA models do no necessarly requre nformaon on prces; quany observaons of npus and oupus suffce. However, hese npus and oupus have o be well-defned o apply DEA and sochasc froner models, and consequenly hey do no provde help n measurng npus and oupus n he frs place The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

3 Revew of Income and Wealh, Seres 58, Number 2, June 2012 change (Secon 3) o non-marke producon whou and wh qualy change (Secons 4 and 5). Our man concluson s ha despe he fac ha naonal accouns should focus on measurng oupus, n he presence of qualy change, mplc or explc nformaon abou oucomes s requred. Secon 5 also conans a proposal for he use of economerc echnques n he presence of non-marke producon. Secon 6 concludes. 2. Termnology Our pon of reference s an economc un ha ransforms volumes of npus no volumes of oupus. Inpus, he goods and servces o be ransformed, comprse labor servces, capal servces, and nermedae npus. Inpus are combned and ransformed by way of a producon echnology. Oupus are suably dfferenaed and are he number of consan-qualy acons or acves (n he case of servces), and he number of consan-qualy physcal uns (n he case of goods). Oucome s a sae 2 ha s valued by consumers a funconng car, he sae of healh, he level of knowledge ec. Oucomes are nfluenced by many facors, and one of hem may be he level of oupus. For example, he sae of healh (an oucome) s a funcon of medcal care (oupu of he healh ndusry), people s lfesyles, and he naural envronmen. Ofen, oucomes manfes hemselves wh a consderable lag o he provson of oupu as would be he case wh long-erm effecs on human healh. For all hese reasons, oucomes are dfferen from oupus. Ths dfference beween oupu and oucome has already been well descrbed by Hll (1975):... here s a danger ha he purpose for whch goods and servces are o be used may be confused wh he goods and servces hemselves....thus, n order o esablsh he naure of he oupu s necessary o examne carefully precsely wha good s acually exchanged beween producer and consumer or wha acvy s acually performed by he producer un for he benef of he user un (p. 13). Oucome would hen correspond o he purpose for whch goods and servces are o be used, and oupus o he goods and servces hemselves. In prncple, he producon boundary as defned n he naonal 2 Oucome has been used n dfferen ways n he relevan leraure on non-marke servces. Two usages are common: n he healh care leraure, oucome s ypcally defned as he resulng change n healh saus ha s drecly arbuable o he healh care receved. Trple (1998) ndcaes hs usage n he cos-effecveness leraure and quoes Gold e al. (1996), who defne a healh oucome as he end resul of a medcal nervenon, or he change n healh saus assocaed wh he nervenon over some evaluaon perod or over he paen s lfeme. Employed n hs sense, some auhors sugges ha he oupu of he healh care ndusry should be measured by oucome. Among naonal accounans, oucome s ypcally used o descrbe a sae ha consumers value, for example he healh saus whou necessarly relang he change n hs sae o he medcal nervenon. Eurosa (2001) gves as examples of oucome ndcaors he level of educaon of he populaon, lfe expecancy, or he level of crme. Aknson (2005) has he same usage of he word. Undersood n hs sense, oucome n self canno be a useful way o measure oupu or he effecveness of he healh or educaon sysem. In erms of naonal accouns semancs, he margnal conrbuon of he healh care ndusry o oucome s he equvalen o he noon of oucome as used n he healh care leraure. As long as a parcular defnon s used conssenly, he subsance of he argumen s of course unaffeced and he only queson s how useful a parcular defnon s for he purpose a hand. The presen paper follows n he lne of Eurosa (2001) and Aknson (2005), and employs he erm oucome n he sense of he naonal accouns leraure The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

4 Revew of Income and Wealh, Seres 58, Number 2, June 2012 accouns encompasses oupus, bu no oucome. A superfcal concluson would herefore be ha he naonal accouns sascan does no have o worry abou oucomes, only oupus. However, hngs are more complcaed. Whle oucomes are dfferen from oupus, hey are no ndependen. One of he conclusons of he presen paper wll n fac be ha s vrually mpossble n parcular for healh and educaon servces o defne qualy-adjused oupus whou nvokng oucomes one way or he oher. For he forhcomng dscusson, s useful o refne he defnon of oupus and oucomes n wo ways. Frs, oupus are broken down no wo componens: acves or processes and he qualy adjusmen appled o hem. Processes are observable and counable acons by whch servces are delvered, alhough her characerscs may change over me. For educaon, a ypcal process measure s he number of pupls or he number of pupl hours augh n a parcular grade. For healh, a ypcal process measure s he number of reamens of a parcular dsease such as hp replacemens. The purpose of qualy adjusmens appled o processes s o measure hem n consan-qualy uns ha are comparable over me or n space. Noe ha he ermnology above s dfferen bu conssen wh ermnology used n work relang o he healh or educaon sysem as a whole: for nsance, Rosen and Culer (2007) develop a sysem of naonal healh accouns ha brngs ogeher npus and oupus n he producon of healh. Medcal care s only one npu here; oher npus nclude he me people nves n healh (such as exercse and sleep), or research and developmen. The oupu of such a healh sysem s smply he sae of healh, oucome n our ermnology. I s apparen, however, ha he producon of he healh sysem as a whole s ousde he producon boundares of he sysem of naonal accouns. Thus, whle of sgnfcan analycal neres, does no help he naonal accounan n hs or her ques for beer capurng oupu and producvy nsde he esablshed producon boundares. 3. Compeve Markes, No Qualy Change n Producs Havng deal wh ermnology, we shall now urn o he heory of measuremen. Our reference case here s a suaon of compeve markes whou qualy change n producs. We separaely deal wh he consumer and producer sdes before brngng hem ogeher The Consumer Sde Our concepual dscusson sars wh a smple marke model of producers and consumers. For he momen, we ake ha producs are well-defned: oupu s expressed n observable, consan-qualy couns of processes. On he demand sde, consumers purchase he servces suppled by producers. Sandard economc heory arbues a uly funcon o consumers where uly (n unobserved uls ) depends on he quany of goods and servces consumed. Le households uly funcon be U = U(H ), where U sands for he level of uly n perod whch depends posvely on H, a sae of he world ha 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

5 Revew of Income and Wealh, Seres 58, Number 2, June 2012 consumers value. H corresponds o our noon of oucome. In general, H wll be vecor-valued because here are many dfferen saes valued by consumers for example, dfferen aspecs of he saus of healh, he level of knowledge, or he sae of he naural envronmen. Consumers aach uly o a good or o a servce because affecs oucome,.e., a parcular sae ha hey value. We could also say ha oucome s an nermedae sep beween consumpon and uly and hs s ndeed he way has been reaed n he leraure. In an applcaon o healh care, Bernd e al. (1998) dsngush beween medcal care ( oupu n our ermnology), he sae of healh ( oucome n our ermnology), and uly. They envsage a relaonshp whereby uly depends, among oher varables, on he sae of healh, and where he sae of healh s self dependen on healh care servces, on he envronmen, lfesyle ec. If we follow hs dea, oucomes depend, ner ala, on N dfferen servces consumed by households, and we shall label quanes of hese servces n perod as y = [ y, y, y, 1 2 3, yn ]. However, oucome H depends no only on servces y ha are purchased or obaned from producers bu also on a hos of oher facors, W. Examples nclude households behavor wh regard o smokng, alcohol consumpon, or physcal exercse. Or, n he case of educaon, W could sand for sudens effors or naural gfedness when H sands for educaonal aanmen and he sae of knowledge of he populaon. For he momen, we formulae our oucome funcon and nser no he uly funcon defned earler: (1) H = H( y, Ω ), and herefore U = U[ H( y, Ω )] = V[ y, Ω ]. Households demand servces o he pon where prces equal he margnal uly generaed by hese servces. In money erms, hs gves p = [ δu/ δy ]/ λ for = 1,...,N. Here, 1/l s he margnal uly of ncome ha s needed o conver uls no currency uns. I s no dffcul o see ha he margnal conrbuon of a good or a servce o uly s n fac a compose erm, namely he margnal conrbuon of he produc o oucome, δh/ δy, mulpled by he margnal conrbuon of oucome o uly, δu/ δy = [ δu/ δh][ δh/ δy ]. I follows ha he margnal conrbuon o oucome for a parcular produc, δh/ δy, relave o he margnal conrbuon of anoher produc j, equals he prce rao of he wo producs: (2) [ δh/ δy ]/[ δh/ δy ] = p / p. j j The measuremen mplcaon of hs relaon s ha here s a concepual lnk beween oucomes and sascal classfcaons for (consumer) goods and servces. Gven dfferen producs or produc ems (varans of a produc), he queson abou her groupng or classfcaon has o be answered wh respec o he purpose of he prce or volume ndex. The relaon above suggess ha from a consumer perspecve, he creron for groupng ndvdual ems s ha hey poenally offer he same conrbuon o oucomes,.e., hey sasfy he same or smlar consumer needs. Pu dfferenly, hey are subsues from a consumer 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

6 Revew of Income and Wealh, Seres 58, Number 2, June 2012 perspecve. Conversely, f dfferen ems are no nerchangeable from a consumer perspecve, hey should be reaed as dfferen producs. In he presence of qualy change or new and dsappearng ems, he queson of groupng ems becomes mporan. Bu he pon o rean s ha he organzaon of prce or quany measuremen, n parcular how producs are classfed and srafed, canno proceed whou some reference o oucome, f one wans o brng n a consumer perspecve The Producer Sde We now urn o producers and ake ha her producon echnology can be represened by a cos funcon 3 ha shows he mnmum coss requred durng a gven perod o produce a quany of N producs y = [ y, y, y, 1 2 3, yn ], for a gven se of npu prces and for a gven echnology. In he case of healh servce producers, a parcular produc could conss of a consan-qualy reamen of a parcular dsease; n he case of educaon could be he consan-qualy hours of eachng provded for a parcular grade. To keep he exposon racable, wll be assumed ha here s a echnology se S for each produc ha lnks oupu y o a se of M npus, x = [ x1, x 2,, xm ]. Inpus are purchased a prces w = [ w 1, w2,, wm ] on facor markes where producers are prce akers. A cos funcon for produc can hen be wren as (3) C = C ( y, w) = mn{ w x:( y, w ) s conaned n S }; = 1,, N. A un or average cos funcon for oupu ype s defned as c ( y, w) C( y, w)/ y and measures he coss per un of oupu y durng perod. Wh consan reurns o scale whch we shall assume for convenence here, un coss are ndependen of he level of oupu, and average coss equal margnal coss. When producers mnmze coss, follows ha oal coss for a parcular produc are equal o mnmum coss: (4) C ( y, w ) c ( w ) y w = = x. We follow Dewer (2008) and defne he producer s or secor s oal cos funcon C as he sum of cos funcons for dfferen producs. Ths wll be helpful n he defnon of ndex numbers below: (5) N C ( y, w ) C ( y, w ) c ( w ) y w = = = x. N Under consan reurns o scale, and n a compeve marke, producers provde servces a he pon where prces equal margnal coss. More generally, under marke condons, excess profs are compeed away and prces wll equal average coss so ha: (6) p = c ( w ). 3 For more nformaon abou cos funcons see Shephard (1970) or Dewer (1974) The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

7 Revew of Income and Wealh, Seres 58, Number 2, June Combnng he Consumer and he Producer Sde When he consumer and he producer sde are combned, marke equlbrum s characerzed by (7) [ δu/ δh][ δh/ δy ]/ λ = p = c ( w ). Thus, margnal uly from consumpon and margnal coss of producon are equal n equlbrum. There s of course nohng new abou hs saemen. I s noneheless useful because we see ha n equlbrum, consumer valuaon and producer valuaon of a good or of a servce concde a he margn when here s a marke-clearng prce. The mplcaon s ha when weghs are needed o aggregae across producs, here s no need o nvoke eher a consumer or a producer perspecve he value of marke ransacons s all ha s needed and combnes he wo sdes of he marke. 4 Also, n he absence of qualy change and as long as here are no new or exng producs, would appear ha here s lle o worry abou he dsncon beween oupu and oucome marke prces jonly value he margnal conrbuon of consumpon o oucome and also reflec margnal producon coss. 4. Non-Marke Producon, No Qualy Change Havng esablshed he compeve case wh a well-defned se of producs ha does no change over me, we shall now drec aenon o he case of non-marke producon. When goods or servces are provded by non-marke producers, hey are provded a a prce ha does no cover coss and whch may even be zero. In hs case, he prce a whch producs are ransaced loses s sgnfcance as an ndcaor of margnal or average coss. Nor s he prce necessarly lnked o a uly-maxmzng quany of consumer demand, as was he case n he compeve envronmen. Therefore, our convenen lnk beween he producer and he consumer sde, esablshed n he frs secon, breaks down: (8) [ δu/ δy ]/ λ c ( w ). An mmedae consequence from hs suaon s ha he well-esablshed body of leraure on he heory of producer prce ndces, noably Fsher and Shell (1972), Archbald (1977), and Inernaonal Moneary Fund e al. (2004) no longer apples. The heory of he oupu prce ndex reles on revenue funcons for 4 Ths s a smplfcaon. In pracce, and n he presence of ranspor coss or axes, here s no unque marke prce and a dsncon has o be made beween dfferen valuaons. For example, from a consumer perspecve, a valuaon a purchasers prces s approprae, whch s nclusve of axes and ransporaon margns. From a producer perspecve, a valuaon a basc prces would be more approprae, whch excludes, for example, axes payable and subsdes recevable n conjuncon wh producon or sale. The saemen n he ex s also a smplfcaon n he sense ha oupu prce ndces for producers and npu prce ndces for consumers are ypcally compled a dfferen levels of aggregaon and on he bass of dfferen classfcaons. Ths may also lead o dfferences n weghs beween oupu prce ndces for producers and npu prce ndces for consumers. However, even when aggregaon happens dfferenly n he producer and n he consumer case, he prce a he lowes level of aggregaon a whch he ransacon akes place s a marke prce and reflecs he jon nfluences of producers and consumers The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

8 Revew of Income and Wealh, Seres 58, Number 2, June 2012 producers and spulaes revenue-maxmzng behavor, gven a se of marke prces for producers oupus. In a non-marke envronmen, 5 hs s no a useful assumpon, and consequenly, revenue funcons canno be used as a concepual bass for oupu prce ndces. However, measuremen can be based on un coss or quas prces. When ransacon prces are sgnfcanly below cos or zero, s cusomary n he naonal accouns o measure he money value of oupu as he sum of coss. One could also say ha oupu s valued a quas prces. They are hose (unobserved) prces ha emulae a compeve suaon where prces equal average coss per produc. Wh un coss a hand, hey can be reaed as f hey were prces: (9) p c ( w ). If we manan he (courageous) assumpon 6 ha non-marke producers are cos-mnmzng uns, hen mnmum coss equal acual coss or c ( w ) y = w x, and follows ha (10) py c( w ) y = w x. Expresson (10) saes he obvous, namely ha wh quas prces, he value oupu of produc equals he value of npus used n producon of produc. Ths s he way non-marke oupu s valued n he Sysem of Naonal Accouns. 7 Wha s mporan for he purpose a hand s he fac ha hs equaly of npus and oupus n value does no mply equaly of npus and oupus n volume or quany. If hs were he case, our effors o derve volume measures of oupu ha are separae from volume measures of npus would be pu n queson and wh any aemp o measure producvy change n non-marke producon. The man dfference beween cos-based prces of oupus and prces of npus s ha he former correspond o coss per un of oupu (such as he coss for one reamen of a hear aack or he coss for one year of schoolng), whereas he laer correspond o he coss per un of npu (such as wages per hour of a nurse or he salary of a eacher). 5 Noe ha despe he fac ha our dscusson has been couched n erms of non-marke producers, carres over o he more general case of regulaed ndusres. For example, Lawrence and Dewer (2006) measure he quany ndex of oupu for New Zealand elecrcy ules wh a cos-based ndex because here are no meanngful revenue shares or prces for he hree ypes of oupus denfed for ules: hroughpu of elecrcy, sysem lne capacy, and connecons. 6 The man advanage of hs assumpon s ha allows a concepually clean denfcaon of producvy change wh echncal change. Suppose ha cos changes are broken down no changes n he quany of oupu, changes n he prces of npus, and producvy change as n Dewer (2008). Then, one of he condons ha he measured producvy change s a reflecon of echncal change (or a shf of he cos funcon) s ha he assumpon of cos-mnmzng producers holds. If hs assumpon s relaxed, he measured producvy change can encompass several elemens, n parcular a movemen oward or away from he effcency froner and a movemen of he cos funcon self. As our presen concern s wh he measuremen of oupu and only ndrecly wh he measuremen of producvy, we have mananed he assumpon of cos-mnmzaon for reasons of smplcy. Gvng up hs assumpon would complcae he exposon and would requre more dscusson by way of applcable ndex number formulae. See also Balk (1998) for producvy measuremen when producers are no acng as cos mnmzers. 7 For a geness of he reamen of non-marke producon n he naonal accouns and he many ssues assocaed wh, see Vanol (2002) The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

9 Revew of Income and Wealh, Seres 58, Number 2, June 2012 Dewer (2008) shows formally how a cos-based volume ndex of oupu can be defned. He proposes a famly of cos-based oupu quany ndces and focuses on he Laspeyres (Q L), on he Paasche (Q P), and on he Fsher (Q F) case. In lne wh he economc approach oward ndex numbers, Dewer defnes he Laspeyres verson of a cos-based oupu quany ndex as he (hypohecal) oal cos C 0 (y 1, w 0 ) of producng he oupu vecor y 1 of perod 1 under he condons of perod 0 echnology and npu prces, dvded by he acual coss of perod 0, C 0 (y 0, w 0 ). Smlarly, he defnes a Paasche ype ndex as he acual coss of perod 1, C 1 (y 1, w 1 ), dvded by he hypohecal coss C 1 (y 0, w 1 ) ha would have been ncurred, had he producs of perod 0 been produced n perod 1, under he echnologcal consrans of perod 1 and gven perod 1 npu prces: (11) N 0 1 N 0 0 L N N P 12 / F = [ QLQP]. Q = C ( y, w )/ C ( y, w ) = c y c y Q = C ( y, w )/ C ( y 0, w 1 ) = cy 1 1 cy 1 0 Q For a number of praccal reasons, we prefer workng wh a prce raher han a quany ndex àladewer for non-marke producers and hen deflae oal coss by a prce ndex. To hs end, we consruc an ndrec ndex of quas prces by dvdng oal coss by he volume ndex of oupu: (12) N 1 0 N 0 0 L P N 1 1 N 0 1 P = [ C ( y, w )/ C ( y, w )]/ QL = cy c y 12 / F = [ PLPP]. P = [ C ( y, w )/ C ( y, w )]/ Q = c y c y P P A useful nerpreaon of hs quas-prce ndex can be obaned by rewrng he Laspeyres or Paasche verson n expresson (12). For example, afer nserng he heorecal expresson for Q P no he frs lne of (12), P L can be presened as he produc of wo erms: (13) PL = [ C ( y, w )/ C ( y, w )]/ QP = [ C ( y, w )/ C ( y, w )]/[ C ( y, w 1 )/ C 1 ( y 0, w 1 )] = [ C ( y, w )/ C ( y, w )] = [ C ( y, w )/ C ( y, w )][ C ( y, w )/ C ( y, w )]. The frs erm n he las lne of (13) s an economc ndex of npu prces: coss are compared beween wo suaons, wh echnology and he level of oupu held fxed, bu npu prces allowed o vary. The second erm n he same lne s an nvered producvy ndex: for a gven reference oupu and npu prces, changes n mnmum coss beween he perods are compared. Smlar ransformaons could be appled o P P and hen combned wh P L o yeld a decomposon of P F, bu here s no need o presen hem here. The man pon can easly be explaned wh he decomposon of P L only: n a marke suaon, a producvy ndex equals an npu prce ndex dvded by an (oupu) prce ndex: f oupu prces rse less rapdly han npu prces, hs mples producvy mprovemens. In he 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

10 Revew of Income and Wealh, Seres 58, Number 2, June 2012 presen non-marke case, he quas-prce ndex for oupus plays a smlar role as he oupu prce ndex n a marke suaon. If quas prces (un coss) rse less rapdly han npu prces, here has been producvy change. The measuremen of producvy as a shf n he cos funcon s a wellesablshed mehodology. Whenever here are suaons of mperfec compeon, or non-consan reurns o scale n producon, here are a leas wo ways of measurng producvy change as a shf of he producon possbly curve or a shf of he cos funcon. 8 The wo approaches do no generally yeld he same resul and here s no srong a pror reason o prefer one over he oher. We conclude ha he cos-based producvy measure s a fully vald measure of echncal change for non-marke producers. Bu (13) also shows ha despe he fac ha much of he dscusson abou non-marke producers has been by way of coss, we are lendng an oupu perspecve o our calculaons: un coss or quas prces are producvy-adjused npu prces and he producvy adjusmen marks he movemen from an npu perspecve oward an oupu perspecve n measurng non-marke acvy. Ths s no always well undersood, because coss are rghly seen as npu-relaed varables. Bu he above makes clear ha consderng coss per un of oupu dfferenaes an oupu perspecve from consderng coss per un of npu,.e., he npu perspecve. The oupu perspecve remans a proxy only nsofar as brngs n no drec consumer valuaon un coss are no a produc of he nerplay beween producers and consumers as n he marke case. Un coss are only reflecve of he supply sde. However, some elemens of consumer valuaon ener he pcure when comes o qualy adjusmen, and hs s he opc of he followng secon. Recen work by he OECD (Koechln e al., 2010) follows hs avenue. Quas prces for hospal servces were colleced across a sample of OECD counres. Wh cos weghs aached o each ype of servce, hese prce comparsons consue purchasng power pares for hospal servces ha can be used as a spaal deflaor of naonal nomnal expendure on hospal servces. Such oupu-based esmaes help o answer he queson of wheher dfferences n healh expendure beween counres reflec dfferences n he volume of healh care provson, or dfferences n he quas prce or un cos of reamens. 5. Non-Marke Producon and Qualy Change 5.1. Oucome, Srafcaon, and Implc Qualy Adjusmen There s an exensve leraure on how o deal wh qualy change n exsng producs, wh he ex of old producs and wh he enry of new producs f one wans o comple prce or quany ndces. Qualy change couns among he mos challengng measuremen faced by prce sascans. Early references nclude Sone (1956) and Grlches (1971), and more recen ones Inernaonal Moneary Fund e al. (2004) and Trple (2006). The reader s referred o hese volumes for 8 Balk (1998) provdes a full reamen of he varous producvy measures. In hs ermnology, our measure of echncal change would be labeled a dual npu based echncal change ndex (p. 58). Dewer and Nakamura (2007) also dscuss dual, cos based measures of producvy change The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

11 Revew of Income and Wealh, Seres 58, Number 2, June 2012 a more complee reamen of qualy adjusmen mehods. The ask n hs secon s wofold: o dscuss how he measuremen of qualy change relaes o oupus and oucomes; and o propose a mehod for qualy adjusmen for he non-marke case. To sar, we ce Trple (2006, p. 15) and recall some key prncples and mehods ha are followed n measurng qualy change. Agences ha esmae prce ndexes employ, near unversally, one fundamenal mehodologcal prncple. The agency chooses a sample of sellers... and of producs. I collecs a prce n he nal perod for each of he producs seleced. Then, a some second perod, collecs he prce for exacly he same produc, from he same seller, ha was seleced n he nal perod. The prce ndex s compued by machng he prce for he second perod wh he nal prce, observaon by observaon or model by model as s ofen somewha naccuraely called. One echnque o deal wh qualy change n producs s hus o group hem such ha only producs of he same specfcaon are compared over me or n space. Such groupng or machng ensures ha only prces or quanes of producs of he same or very smlar qualy are compared. The dea s ha producs of dfferen qualy are reaed as dfferen producs. Examples for such groupng n educaon are esablshmens ha provde dfferen servces, such as boardng schools as opposed o day-me schools or hospals wh dfferen levels of nonmedcal servces. The (quas) prce of a parcular medcal reamen would hen be followed nsde he group of esablshmens of a parcular ype. Ths s a way of conrollng for qualy characerscs and o rack a prce for a consan qualy servce. Noe, however, ha groupng also reles on an mporan assumpon: o show a prce or quany movemen ha s represenave of a produc group, he prce or quany movemens of hose producs ha are mached have o be a good ndcaor of he prce or quany movemens of hose producs ha are no mached n parcular producs ha are newly enerng he marke. Prce or quany changes ha arse ousde he sample of mached producs are gnored. The non-marke case on whch our aenon s focused here shows also he mporance of choosng he rgh level of aggregaon where machng akes place. And s agan consderaons of oucome ha govern hs choce. Take he followng case. Two medcal procedures are consdered, of dfferen un coss, bu equally neresng from he consumer s vewpon boh procedures rea he same medcal problem equally well. In oher words, he conrbuon of each reamen o oucome, from a consumer perspecve, s he same. Treang each procedure as a separae produc,.e., seng he elemenary level for he consrucon of he prce or volume ndex below each procedure, can lead o counernuve resuls: more of he cheaper bu equally helpful reamen ranslaes no a declne n he volume of oupu when, as would ofen be he case, he new procedure only gradually replaces he old procedure. Ths s bes llusraed by way of an example (Schreyer, 2010). Suppose here are wo reamens for a dsease, radonal surgery and laser reamen, and assume ha laser reamen s nroduced n perod 1 (see Table 1). In addon, as may well be he case, he un cos 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

12 Revew of Income and Wealh, Seres 58, Number 2, June 2012 TABLE 1 Volume Indces and Qualy Change; ANumercal Example Tradonal Surgery Laser Surgery Perod 0 Perod 1 Perod 2 Perod 0 Perod 1 Perod 2 Un cos Number of nervenons Toal cos of laser reamen s lower han he un cos of radonal surgery. The oal number of nervenons n each perod remans he same. Now consder a (smplfed) mached-model approach oward calculang a volume change from perod 0 o perod 1. In he smples case, he volume ndex s gven by he quany changes n he wo reamens, each weghed by he cos share occupes n perod 0. As laser surgery does no ye exs n perod 0, receves a zero wegh so he volume ndex of reamens s smply he change n he number of radonal surgery nervenons, or (40/50-1) =-20%. Beween perods 1 and 2, he correspondng volume ndex equals [s T(5/40) + s L(45/ 10)] - 1 =-7.1%, where s T = 82% and s L = 18% are he perod 1 cos shares of he radonal and laser reamens, respecvely. Ths approach reas he wo reamens as dfferen producs, and he sharp drop n he oal volume ndex n perod 1 reflecs he new goods problem ha arses when new producs ener he sample ha canno be compared wh quanes n he base perod. The mplc assumpon n hs model s ha consumer valuaon of he wo producs s capured by he relave un coss, so f laser surgery s cheaper han radonal surgery, he mehod mplcly qualy-adjuss downward he quany of laser surgery when combned wh radonal surgery. In a perfec marke, he prce of he radonal reamen would see an nsananeous downward adjusmen, brngng consumer valuaon of he wo processes n lne. A dfferen resul arses when s consdered ha he wo reamens are perfec subsues,.e., ha hey are n fac he same produc. In hs case, no cos weghng s appled beween he wo reamens and he number of reamens s smply added up. As here are 50 nervenons n every perod, he resul s a volume ndex ha shows zero growh and a declnng prce ndex, reflecng he drop n average un coss of reamen. The prevous mehod s jusfed f consumers are ndfferen o he wo reamens. If hs s no he case, and hey prefer laser over radonal surgery because he former s less nrusve or requres fewer days of recovery, an explc qualy-adjusmen s needed. Such an adjusmen can be appled o he quany measures, eher by scalng up he quany of laser reamens or by scalng down he quany of radonal reamens. Whchever way hs s done, he mplcaon s always ha one reamen s expressed n equvalens of he oher, and he rao should n some way reflec consumer preferences. Alernavely, prces or un coss could be rescaled before consrucng a prce ndex. Suppose he adjusmen facor s 1.1 each laser reamen s he equvalen of 1.1 radonal reamens. Then, expressed n radonal surgery-equvalens, he number of reamens s 50 n perod 0, = 51 n perod 1 and = 54.5 n perod 2. The resulng 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

13 Revew of Income and Wealh, Seres 58, Number 2, June 2012 volume ndex s +2% n perod 1 and +6.9% n perod 2. Obvously, he dffculy les n deermnng he adjusmen facor whch should: () reflec consumer preferences; and () be undmensonal. We conclude ha even n a suaon where machng beween producs s perfec, and no explc qualy adjusmen may be needed, some reasonng abou oucome s n place, f only o group subsuable producs ogeher n one sraum. No judgmen abou subsuably can be made whou nvokng, a leas mplcly, some judgmen abou oucomes. Bu machng s rarely perfec. Machng of he quas prces or volumes of non-marke servces such as healh and educaon servces s unlkely o conrol compleely for parcular characerscs assocaed wh he provson of hese servces. Or a represenave servce may change s characerscs, akn o a produc ha prce collecors are no more able o fnd n a parcular oule and ha has o be replaced wh a new produc. These are he nsances where explc qualy adjusmen comes no play, of whch more laer Oucome and Explc Qualy Adjusmen If machng s nsuffcen o conrol for key characerscs of servce provson, oher, explc, echnques have o be nvoked o accoun for qualy change. In general, he qualy of a produc can be expressed by he quany of s characerscs. Qualy change can hen be capured by he change n characerscs. Smlarly, prce changes n producs can be arbued o pure prce changes and o hose prce changes ha reflec changes n produc characerscs. Ths s he approach followed by hedonc prce ndces 9 ha are now well esablshed among sascal agences. Qualy adjusmens requre he denfcaon of a se of characerscs such as he speed, engne sze, or equpmen for a car, or he processor speed for a compuer. Culer and Bernd (2001) use paen characerscs, nformaon on dfferen ypes of depresson, varables on medcaon and he lke o esmae a hedonc prce model for he reamen of depresson; he dea beng o solae hose prce changes ha are due o changes n characerscs from hose prce changes ha consue nflaon. An mporan resul of he hedonc model s ha allows he denfcaon of characerscs and provdes a marke valuaon of each one. 10 Marke valuaon, n urn, s a convenen way of aggregang across characerscs because everyhng s expressed n a sngle moneary un. A a frs glance, hedonc regressons would appear o be badly sued for a non-marke envronmen, gven ha hedonc mehods are all abou exracng marke nformaon from examnng he lnk beween marke prces and produc characerscs. A a second glance, however, he basc prncples of hedonc regressons would appear o be adapable for a non-marke envronmen, albe wh a dfferen nerpreaon. 9 See Trple (2006) for a comprehensve dscusson and a full se of references. 10 Rosen (1974) demonsraed ha n general, hose characerscs of a produc wll show up n he funcon ha are valued by consumers and ha have cos mplcaons for producers The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

14 Revew of Income and Wealh, Seres 58, Number 2, June 2012 To demonsrae hs dea, we shall augmen he smple producer model above by produc characerscs. Thus, for every produc y ( =1, 2,, N ) here s a vecor of n() characerscs z [ z1, z 2,, zn() ] ha qualfes hs produc. Characerscs play a double role. Frs, hey help dealng wh heerogeney. Truly homogenous producs are rare f hey exs a all, and every ype of produc conans a more or less mporan elemen of heerogeney. For example, f healh produc y 1 s reamen of a hear aack, hs wll encompass srokes of dfferen severy, and paens of dfferen age sufferng from a sroke. If old paens requre more nense reamen han young paens, or f more severe srokes necessae more nense care han less severe srokes, here are n fac dfferen servces nvolved. To some degree, hs can be accommodaed by srafcaon and machng (see above), bu only up o a pon. Addonal heerogeney s bes capured by denfyng, hrough knowledge of he produc, hose characerscs ha make one servce dsnc from anoher. The varable z 11 could hus be age of paen, he varable z 12 degree of severy of sroke, and so on. Second, characerscs help dealng wh qualy dfferences. In he case of healh servces, for example, observaons on he same ype of reamen may come from dfferen nsuons, for whch here exs addonal explc nformaon on characerscs ha are consdered arbues of qualy from a consumer perspecve, for example he n-hospal wang me afer a hp fracure. 11 Wang me s an example of a drec measure of a qualy characersc. Oher characerscs may only be capured ndrecly. For example, he reamen of a parcular dsease may or may no nclude he use of a scanner. If here are reasons o beleve ha he use of ceran ypes of modern equpmen ncreases he qualy of dagnoss, hs s a relevan varable o be pcked up. Ye anoher ype of characersc may have o do wh secondary producs or amenes provded by he un ha produces servces. For example, he same medcal servce can be provded n hospals wh dfferen ypes of accommodaon servces: mulple versus sngle-paen rooms, qualy of meals, equpmen of rooms wh phones and TV ses, ec. The oal average coss per reamen n wo dfferen esablshmens canno be compared unless one conrols for hese characerscs. A smlar case can be made for educaon esablshmens wh regard o he provson of meals n school or he lesure acves on offer. An mporan characersc for he healh and educaon area s he number and qualy of personnel per paen or per suden. Class sze, for example, has long been quoed as an mporan qualy characersc of schools. Wang me, f no measured drecly, can probably be racked well by he number of nurses or docors per paen, and s an obvous qualy characersc for medcal servces. However, we have o be careful n nroducng npu measures les here be a danger of fallng back no measurng he volume of oupus by he volume of npus. And hs s exacly wha we had se ou o ge away from n he frs place! Whch characerscs are admssble? And how should hey be nroduced? In a marke suaon, he relevan characerscs are hose ha are valued by consumers and whch also have a cos assocaed wh her provson. In he frs 11 Ths s an example from he OECD Healh Care Qualy Indcaors (see Armeso e al., 2007) The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

15 Revew of Income and Wealh, Seres 58, Number 2, June 2012 place, hs means hey are valued by consumers bu also mples ha here s a cos assocaed wh he provson of characerscs, oherwse hey would have no mpac on prces. By analogy hen, n he non-marke case, he choce of characerscs should be such ha hey are prmarly relevan for consumers,.e., hey are uly-enhancng. Characerscs ha are only or predomnanly relevan for producers, such as wheher caerng s carred ou n-house or wheher s ousourced, should no be canddaes for characerscs. There s no sngle, unversal rule here and he choce of characerscs, as n all hedonc regresson sudes, s a maer of knowledge of he produc. The choce of characerscs brngs us back o he noon of oucome. Idenfcaon of relevan characerscs canno proceed whou recourse o oucome only oucome consderaons from a consumer perspecve wll help geng on wh he choce of qualy characerscs o be ncluded n he hedonc regresson n a non-marke conex. I s worh nong ha hs s no an ssue specfc o non-marke servces, alhough may be more accenuaed n hs conex. Emprcal dffcules wh he choce of characerscs are also an mporan ssue for marke-provded producs, such as compuers n Trple (2006, p. 167): In he end, economc heory does no specfy he characerscs. Choosng he characerscs requres markeng or engneerng or oher nformaon abou he produc and wha buyers wan o do wh. The dfference o he non-marke case s ha n a marke conex, he hedonc regresson provdes a marke valuaon of he characersc n queson,.e., a valuaon ha arses as he nersecon beween consumers and producers. In he non-marke conex, he valuaon s confned o he cos sde. I could be seen as he margnal valuaon of he characersc by he non-marke nsuon or by he governmen hrough s choce of allocang resources o dfferen characerscs. Havng dscussed he naure of characerscs z, we shall now lnk hem o he cos funcon ha consues he measuremen framework. Recall ha for every produc, here was a un cos funcon c ( w ). y remans he rgh measure for he volume oupu bu we now have o allow for he fac ha y may be no drecly observable. We shall call he observable, bu no qualy-adjused measure of oupu, ζ. For example, ζ could be he oal number of sroke reamens n dfferen hospals, rrespecve of he age of paens or of he severy of cases reaed. To model qualy change one can say ha he qualy-adjused, bu unobserved oupu y equals a measure of unadjused bu observable oupu ζ, mulpled by a qualy-adjusmen funcon g, whch n urn depends on he characerscs z ha aach o each produc. Characerscs should be defned n such a way ha a bgger quany of characerscs s assocaed wh hgher qualy. (14) y = ζ g ( z ). Toal coss for a non-marke produc should reman nvaran o how hey are spl up no a un cos and a quany componen. Ths requres ha (15) c ( w ) y = uζ, 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

16 Revew of Income and Wealh, Seres 58, Number 2, June 2012 where u c y /ζ has been defned as he unadjused un cos for produc. In combnaon wh (14) one obans (16) u = c ( w ) y / ζ = c ( w ) g ( z ), or, akng logs, lnu = lnc ( w ) + ln g ( z ). The las expresson resembles a hedonc funcon. 12 Qualy-unadjused measures of un coss of non-marke oupu are broken down no a erm ha reflecs he rue, qualy-adjused un coss and a erm ha capures he effecs of characerscs. When se up as a hedonc regresson, he relaonshp (16) consues an emprcal avenue oward correcng for dfferences n qualy or more generally, for dfferences n characerscs beween dfferen observaons whn he same ype of produc. There s a vas leraure on hedonc regressons and prce measuremen, 13 and we shall no expand on here beyond provdng a skech for an mplemenaon mehod. In a non-marke conex, one can hnk abou {u k } as a se of observaons on unadjused un coss for a parcular produc, for example coss per caarac reamen n perods = 0, 1 from a cross-secon of hospals, where each observaon s ndexed by k = 1,2,...,K. A hedonc regresson ha uses he dummy varable mehod hen akes he followng form: (17) n () lnu = β + αd + β ln z + ε. k 0 m m mk k Here, he hedonc equaon n he las lne of (16) has been ransformed no an mplemenable form by seng he qualy-adjused un coss lnc o equal he regresson parameers b 0 + ad, where D s a dummy varable ha equals 1 n perod = 1and ha equals zero n perod = 0. The qualy adjusmen erm ln g n () ( z ) has been specfed as m βm ln zmk and a sascal error erm ε k has been added. Wh suable economerc mehods, parameer esmaes of he varous coeffcens are obaned. Of parcular neres here s he parameer a ha comes wh he me dummy 14 varable. In anlog form, represens he qualy-adjused ndex 15 of un coss for produc : (18) 1 0 lnc ln c = ( β + α) β = α A hedonc funcon s a relaon beween prces of varees or models of heerogenous goods or servces and he quanes of characerscs conaned n hem (Trple, 2006, p. 229). 13 Cour (1939) s frequenly creded o have been one of he frs researchers o use a hedonc funcon for purposes of prce measuremen. 14 To smplfy noaon, we made no dsncon beween heorecal parameer values b 0, a ec. and esmaed parameer values as hey are obaned from he regresson. 15 Trple and McDonald (1977) showed ha he specfcaon of he hedonc regresson mples a ceran ndex number formula n he aggregaon of he ndvdual observaons. For he double-log 1 1 specfcaon used here, one ges exp( ) [ ( ) / K ( 1 ) 0 1 α =Π / Π( ) / K u u ( 0 ) ]/ QA. QA s a qualy adjusmen k k k k n βn k znk K k znk K erm of he followng form QA = exp{ [ ln / ln / ]}. Ths s a erm ha capures dfferences n characerscs beween he wo perods, where each dfference ges weghed wh he correspondng regresson coeffcen. In he absence of changes n characerscs beween he wo perods, and no change n he number of observaons, QA equals uny The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

17 Revew of Income and Wealh, Seres 58, Number 2, June 2012 Hedonc coeffcens are hus a ool for esmang he qualy-adjused rae of change n un coss. In a marke conex, hedonc coeffcens reflec he valuaon of characerscs by he neracon of consumers and producers as shown by Rosen (1974). When compeon s mperfec, nerpreng coeffcens becomes more dffcul, because n addon o consumer preferences and producer coss, he degree of marke power affecs he sze and possbly he sgn of coeffcens, as dscussed by Pakes (2003). In a non-marke seng, here s no drec marke neracon beween consumers and producers. Resources are allocaed by producers, more or less n response o demand, bu he valuaon of characerscs s a cos valuaon. Thus, coeffcens n he hedonc equaon above provde an ndcaon abou he echnology of supply of characerscs and s cos srucure. Supply n a non-marke conex does no drecly nerac wh demand. In such a suaon, regresson coeffcens are ndcave of coss or producer valuaon. However, despe he fac ha he valuaon of characerscs s a cos valuaon, he choce of characerscs should largely reflec a consumer perspecve as was explaned earler. The above skech of a hedonc mehod has no been esed and convenenly gnores he many emprcal problems ha s mplemenaon would lkely have o face. Daa requremens are probably enormous and a core queson, he choce of characerscs, makes hs approach a challengng ask. Noneheless, exploraory sudes would be helpful o assess feasbly and usefulness Oupu as he Margnal Conrbuon o Oucome One consequence of (8) was he napplcably of he heory of oupu prce ndces. We solved hs by reverng o un coss or quas prces. In so dong, we mplcly sgned up o anoher decson on how o deal wh he nequaly of margnal uly and margnal coss: quas prces or cos-based oupu volumes àla Dewer (2008) mply ha weghs are cos shares of goods and servces, and no expendure shares ha reflec consumer uly. When came o qualy change, we suck wh a cos-based approach bu appled explc qualy adjusmen o un coss, and mplcly, o volume measures of oupu. Oucomes played an ndrec role only n he sense ha hey helped srafyng acvy couns and choosng he se of characerscs for qualy adjusmen. An alernave way of consrucng volume and prce ndces of oupu consss of drecly nvokng he consumer perspecve and consrucng measures of oupu ha are based on a produc s margnal conrbuon o oucome. Aknson (2005) pus hs forward as one of he mehods of measurng he oupu of non-marke producers. In our noaon, hs would mean rackng movemens of oupu hrough observaon of movemens of oucomes caused by he change n oupu,.e., δh/ δy. One obvous advanage of hs procedure s ha a leas n concep provdes a soluon o he problem of qualy adjusmen. If all ha consumers care abou s oucome, and we are able o race oucome and measure s change, hen here s no need o explcly qualy-adjus measures of producon. Under an oucome-based approach, he volume of oupu s aken as he margnal conrbuon of he produc o oucome as perceved by he consumer. Consder frs a non-marke producer, whose value of producon has been se o 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

18 Revew of Income and Wealh, Seres 58, Number 2, June 2012 equal coss. Wh hs consran, oal coss would equal he oal value of each produc s conrbuon o oucome: (19) Toal value of producon = uζ = [( δu/ δh )/ λ ][( δh / δy ) y ]. As before, we allow for qualy change n he provson of goods or servces. 1 0 Thus, a drec comparson of unadjused un coss over me, u/ u, would gve rse 1 0 o a based prce ndex, and a comparson of unadjused quanes, ζ/ ζ, would gve rse o a based volume ndex because he qualy of he observed uns ζ changes over me. A he same me, all ha can be drecly observed are he unadjused un coss along wh he unadjused quanes. An oucome-based approach oward measurng prces and volumes deals wh qualy change n he followng way: he money value of he conrbuon o uly ha a change n oucome generaes, s aken as he rue prce pw ( δu/ δh )/ λ. On he volume sde, he margnal conrbuon of he good or servce o oucome would consue he rue quany yw, ( δh / δ y ) y. By way of example from healh servces, p W would correspond o he ne gans n welfare from an addonal lfe-year and y W, would correspond o he number of lfe-years ganed from a medcal servce of ype. Noe ha when he usual assumpon of declnng margnal uly apples, he rue prce of healh servces p W declnes wh an mproved sae of healh, as d 2 U/dH 2 < 0, everyhng else beng equal. Alhough no drecly observable from ransacons on he marke, hese rue prces and quanes can n prncple be esmaed. In he area of educaon, he semnal work by Jorgenson and Fraumen (1989) s an example where he margnal conrbuon o oucome n he form of addons o human capal due o educaon s aken as he oupu measure of he educaon secor. In he area of healh care, here s an ncreasng number of sudes ha have used measures of oucome o value healh care oupu. 16 For example, Culer e al. (1998) pursue hs research avenue and derve a prce ndex for hear aack reamen. Concepually, her cos-of-lvng ndex s comparable o he change n p W. I s measured as (one mnus) he ne benef from a change n hear aack reamen. If he benefs from medcal pracce changes are greaer han he coss, consumers are beer off and he cos of lvng declnes. Emprcally, hen, he 1 0 auhors measure pw/ pw 1 va esmang he ne benefs from mprovemen n 1 0 healh due o he reamen of hear aacks. Gven an esmae for pw/ pw and gven he consran (11), we can work ou he mpled qualy adjusmen facor o he observed quanes: (20) y / y = [ ζ / ζ ][( u / u )/( p / p )]. W, W, W W y Ths shows ha he ndex of qualy-adjused volumes of medcal servces 1 0 / y corresponds o he ndex of unadjused quanes ζ / ζ mes a qualy 1 0 W, W, 16 See also he volume eded by Culer and Bernd (2001) for oher examples of new medcal care prce ndces The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

19 Revew of Income and Wealh, Seres 58, Number 2, June adjusmen facor ( u/ u )/( pw/ pw) ha s jus he rao beween he ndex of unadjused un coss and he cos of lvng ndex. 17 I s useful o compare hs resul wh he hedonc adjusmen descrbed n he prevous secon. Expressons (16) and (18) aken ogeher yeld a formally smlar qualy adjusmen where he regresson coeffcen a replaces he cos of lvng 1 0 ndex p / p : W W (21) y / y = [ ζ / ζ ][( u / u )/exp( α)].,, Despe he formal smlary, here s of course no reason why he wo adjusmens should be emprcally equvalen. The qualy adjusmen facor n (20) s based on a non-paramerc calculaon ha reles on a one-dmensonal measure oucome ha s supposed o subsume all qualy aspecs of producon. The qualy adjusmen n (21), on he oher hand, s based on a paramerc calculaon ha uses mul-dmensonal qualy characerscs, o whch cos weghs are appled. The lnk o oucome remans ndrec n ha only he choce of characerscs reflecs consderaons of oucome, bu no drec measure of oucome eners he se of characerscs. There are many praccal consderaons before any of hese approaches can be mplemened, and oupu measures ha rely on he margnal conrbuon o oucome such as n (20) are a long way from beng regular feaures n sascal programs. Noe he followng emprcal ssues. I s no obvous how o denfy he margnal mpac of oupu o oucome. As was menoned earler n hs paper, oucomes (for example, he sae of healh) are affeced by many facors, no only by he good or servce under consderaon. Thus, he effec of healh care on he sae of healh should no be affeced by any oher facors ha nfluence consumer oucome, such as he lfesyle of paens. I s emprcally dffcul o conrol for hese oher nfluences on oucome. For example, Culer e al. (2006), n a major sudy on he value of medcal spendng n he Uned Saes, have o rely on common sense argumens and some general resuls from medcal research o esmae he par of mproved lfe expecancy ha s arbuable o medcal care. 18 A more suble ssue s he followng: a measure of he conrbuon o oucomes should reflec he normal, or expeced effec of he acvy whose oupu s o be measured. Normal, average, or expeced effecs should be consdered raher han ex-pos, ndvdual effecs. Ths dsncon arses n he conex of servce provson where he consumer s ypcally acvely nvolved n he provson 17 Trple (1998), referrng o he cos-of-lvng adjusmen by Culer e al. (1998) pons ou ha here s grea relucance o pu a moneary value on lves saved or exended and ye such a valuaon s necessary o measure he prce change pw / p 1 W. He suggess he drec use of cos-effecveness sudes n healh care by usng an adjusmen facor ha s based on Qualy-Adjused Lfe Years (QALY). Chrsan (2007) apples an adjusmen of hs knd o a volume ndex of hospal servces and fnds a sgnfcan posve effec on he measured rae of oupu. 18 Analyses aggregaed from reamens clearly shown o be medcally effecve sugges ha a leas half he lfe-expecancy gans snce 1950 are due o medcal advances. Abou 90 percen of he gans n lfe expecancy are arbuable o mprovemens n he raes of deah n nfancy and he raes of deah from cardovascular dsease. Prevalng esmaes sugges ha a leas half he reducon n hese raes are due o medcal care. We herefore assumed n our base case ha 50 percen of he oal gans n lfe expecancy were due o medcal care (Culer e al., 2006, p. 921) The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh

20 Revew of Income and Wealh, Seres 58, Number 2, June 2012 of he produc. I would seem ha a measure of servce producon should no be nfluenced by he ndvdual capacy of he consumer o make use of hese servces. For example, he same eachng acvy performed on wo dfferen sudens should be measured as he same quany of eachng servces oward each suden, even f urns ou ha one of hem benefs less from eachng han he oher. Or he same medcal reamen, appled o wo dfferen persons wh he same dsease (and smlar paen characerscs), should be measured as equal quanes of medcal servces. Unless, ha s, he wo persons come from dfferen groups of paens, where groups s undersood as ses of paens wh characerscs ha requre a pror dfferen servces, for example young and old persons for parcular reamens. I s easy o see ha makng hs dfference n pracce wll be dffcul and somemes mpossble. Ths lms he applcably of oupu mehods ha rely on he drec conrbuon o oucomes. 6. Conclusons Ths paper looked a he noons of oupu and oucome n he conex of servce acves wh marke and non-marke producers. We sared by defnng he varous noons, n parcular npus, processes/acves, oupus, and oucomes. The followng man conclusons were derved. Even n he smples marke model whou any qualy change n producs, oupu measuremen may requre some, ofen mplc, reference o oucome when producs are grouped and classfed. Thus, oupu and oucome are dfferen, bu hey are no ndependen of each oher. Wh non-marke producers, he equaly of margnal uly and un cos raos breaks down. The money value of oupu s deermned as he sum of coss of npus, bu s possble o consruc meanngful ndces of cos-based volumes and quas prces along wh ndces of volumes and prces of npus. Akn o he smple marke case, cos-based ndces are no vod of mplc nformaon abou uly and oucome ypcally, hs eners va he produc classfcaon on he bass of whch aggregaon akes place. In he presence of qualy change, all exsng mehods requre mplc or explc nformaon or reasonng abou oucome. The smples and mos wdelyused way of conrollng for qualy change machng or srafcaon requres mplc saemens abou he smlary of producs n her capacy o generae oucome when producs are grouped ogeher. A second mehod uses explc nformaon on produc characerscs o adjus un coss for dfferences n characerscs. The choce of characerscs canno proceed whou consderng oucome. Problems of qualy adjusmen arse wheher servces are provded by marke or non-marke producers. The fac ha here s an observable marke ransacon n one perod and anoher marke ransacon n he nex does no mply ha hey are comparable oherwse, prce sascans would be n he convenen suaon of only havng o deal wh qualy adjusmen for non-marke producon. Ths s of course no he case. Alhough he dsncon beween marke and non-marke producers s useful and has consequences for measurng he curren 2012 The Auhor Revew of Income and Wealh Inernaonal Assocaon for Research n Income and Wealh