School of Economics and Management

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1 School of Economics and Managemen TECHNICAL UNIVERSITY OF LISBON Deparmen of Economics Carlos Pesana Barros & Nicolas Peypoch Anónio Afonso and Sónia Fernandes A Comparaive Analysis of Produciviy Change in Ialian and Poruguese Airpors Assessing Hospial Efficiency: Non-parameric Evidence for Porugal WP 07/2008/DE/UECE WP 006/2007/DE WORKING PAPERS ISSN Nº

2 Assessing Hospial Efficiency: Non-parameric Evidence for Porugal * Anónio Afonso # and Sónia Fernandes $ February 2008 Absrac We compue DEA efficiency scores and Malmquis indexes for a panel daa se comprising 68 Poruguese public hospials belonging o he Naional Healh Sysem (NHS) in he period , when several unis sared being run in an enrepreneurial framework. Wih daa on hospial services and resource quaniies we consruc an oupu disance funcion, we assess by how much can oupu quaniies be proporionally expanded wihou changing inpu quaniies Our resuls show ha, on average, he NHS hospial secor revealed posiive bu small produciviy growh beween 2000 and The mean TFP indices vary beween 0.97 and.09, implying some differences in he Malmquis indices across specificaions. Furhermore, here are significan flucuaions among NHS hospials in erms of individual efficiency scores from one year o he oher. JEL classificaion: C4, C6, D24, H5, I2 Keywords: Public hospials, Daa Envelopmen Analysis, Malmquis indices, Porugal * The opinions expressed herein are hose of he auhors and do no necessarily reflec hose of he auhor s employers. # ISEG/TULisbon Technical Universiy of Lisbon, Deparmen of Economics; UECE Research Uni on Complexiy and Economics, R. Miguel Lupi 20, Lisbon, Porugal, aafonso@iseg.ul.p. UECE is suppored by FCT (Fundação para a Ciência e a Tecnologia, Porugal), financed by ERDF and Poruguese funds. $ Cour of Accouns, Av. da República, 65, Lisbon, Porugal, sonfer@sapo.p.

3 Conens Inroducion Overview of he Poruguese public hospial secor Produciviy measuremen Lieraure review Malmquis Produciviy Index Empirical analysis Daa Model specificaions Resuls and discussion Conclusion References

4 INTRODUCTION During he period Poruguese healh care expendiure has rapidly increased wih he share of public spending in oal healh spending also increasing from 60% in 992 o around 70% in On he oher hand, under a new legal framework, he enerprising model for he healh secor was he opion gradually preferred by he Governmen. For insance, in he end of 2002 he legal saus of 3 hospials (40 per cen) changed, from public insiuions of he Adminisraive Public Secor (SPA) ino hospial enerprises (SA) wih limied liabiliies. Wheher such changes can spur increases in performance and efficiency regarding he services provided o he public is hen a paramoun issue in a conex of limied public resources. Daa Envelopmen Analysis (DEA) has been widely used o calculae changes in Toal Facor Produciviy wihin he public hospials secor, where price daa is difficul o find and muli-oupu producion is relevan, since i does no require he imposiion of any behavioural assumpions such as revenue maximizaion or cos minimizaion (Lovell, 2000). DEA analysis has also been used recenly o assess he efficiency of he public secor in cross-counry analysis for overall public secor efficiency analysis (Afonso e al., 2005), and o asses local governmen spending efficiency (for insance for Porugal, Afonso and Fernandes, 2006). The aim of his paper is o esimae in a non-paramerical framework, measures of hospial echnical efficiency across 68 Poruguese hospials belonging o he Naional Healh Sysem (NHS) during he period For ha purpose we will use boh DEA analysis and compue Malmquis indexes. Addiionally, he paper also examines heerogeneiy and efficiency resuling from he recen privaisaion of some Poruguese hospials. The paper is organised as follows. Secion wo gives an overview of he Poruguese public hospial secor. Secion hree reviews he lieraure on he non-parameric measuremen of hospial efficiency and explains he analyical framework used in he paper. Secion four conducs our empirical efficiency analysis and discusses he resuls. Secion five concludes. 3

5 2 OVERVIEW OF THE PORTUGUESE PUBLIC HOSPITAL SECTOR Regarding he insiuional framework he Poruguese Naional Healh Care Sysem (NHS) was creaed in 979, following he approval of he Consiuion in 976. The healh service model hen pu in place was characerized by universal coverage, equiy concerns, and financed via ax revenues. In fac, he Consiuion guaraneed o all ciizens he righ o healh, o be provided by a universal Naional Healh Service, comprehensive and free of charge. New principles were inroduced in 990 for he organizaion and funcioning of he healh sysem and assigned an explici role o he privae for-profi and non-for-profi secors hrough conracing wih he NHS. 2 The objecives of he NHS in promoing efficiency, qualiy, accounabiliy and devoluion of power were also emphasised (see Oliveira and Pino, 2005; Benes e al., 2004). In wha concerns hospial care, radiionally i was a much cenralised secor dominaed by public provision, and according o several auhors i was characerized by inefficiency and performed poorly in erms of cos conainmen. 3 Recenly, and following healh reform rends in oher European counries, a new hospial managemen law was passed hrough Poruguese Parliamen in The purpose of his Law was o enable he changeover of some insiuions ino public enerprises as well as he se up of a series of enrepreneurial principles such as freedom of choice by he paien, budge conracing, and aciviy based paymen of professionals (Benes e al., 2004, pp. 6)). According o he definiion of Doceur and Oxley (2003), he Poruguese healh sysem was pu in place as a public-inegraed model. Nowadays, his model also exiss in he Nordic counries, Ausralia, Ialy and Greece. 2 Law nº 48/90 (see Base XXIV). The reforms inroduced in he 990s have been pushing he Poruguese healh sysem pu in place in he lae 970s owards a public-conrac model, characerized by an increased role and paricipaion of he privae secor (see Doceur and Oxley, 2003). 3 See, for example, Dixon and Mossialos (2000) and Oliveira and Pino (2005). Oliveira (2002) argues ha inefficiency arises among Poruguese public hospials for several reasons such as: () he paymen sysem o docors, radiionally based on collecive conracs, gives lile incenives for produciviy and resuls mainly in a lack of docors in he public sysem; (2) hospial adminisraions are no encouraged o keep wihin budges limis because radiionally hey are no penalised for overruns; (3) hospial adminisraions have lile auonomy in wha concerns managemen decisions abou invesmens and human resources. 4 Law nº 27/2002 ha inroduced amendmens o he 990 NHS Law. 4

6 There are several implicaions of he new hospial managemen law (see Lima and Whynes, 2003). Firs, collecive conracs were replaced by individual labour conracs, wih hospials being now free o hire personnel and use differen paymen sysems. 5 Second, i inroduced more flexibiliy in he NHS hospials managemen srucures and allowed he coexisence of public eniies wih privae eniies acing in a cooperaive way and sharing he same objecive of saisfying paien needs. Third, he radiional concep of he NHS hospial was replaced by he new concep of Nework of healh care providers, which according o aricle 2, nº of Law nº 27/2002, includes four ypes of hospials: 6 i. Public providers wih financial and adminisraive auonomy, under public managemen rules; 7 ii. Public providers wih adminisraive, financial and asse managemen auonomy, under privae managemen; iii. Providers under corporae law, wih equiy shares and he Sae as he exclusive shareholder; 8 iv. Sricly privae providers conraced by he Sae. Among he four possible ypes of hospials presened under he new legal framework, he enerprising model was he opion preferred by he Governmen. In he end of 2002 he legal saus of 3 hospials (40 per cen) changed, from public insiuions of he Adminisraive Public Secor (SPA) ino hospial enerprises (SA) wih limied liabiliies. In 2005, all hospial enerprises (SA) along wih 2 hospials ha radiionally belonged o SPA were ransformed ino corporae public eniies (EPE). 9 The purpose of his resrucuring sraegy was o increase hospial efficiency in erms of oupu producion and financing. A he end of 2006, he NHS comprised he oal number of public hospials (SPA and EPE) bu wih differen financing and accounabiliy rules. 5 As menioned by Oliveira and Pino (2005, pp. 23), his change ( ) is expeced o increase he mobiliy of human resources, improve performance incenives and reduce inefficiencies in hospials where he lack of docors has aced as a consrain on he use of resources. 6 See aricle, nº, Law nº 27/ See Decree-Law nº 88/ See Decree-Law nº 558/ See Decree-Law nº 233/

7 From a financing perspecive, over he las wo decades, Poruguese healh care expendiure has rapidly increased as a percenage of GDP. Figure repors he annual growh rae of public per capia expendiure on healh, in real erms, for he period The annual growh rae of public per capia expendiure averaged 9.2 percen beween 995 and 2000, and hen decreased hereafer. Addiionally, he share of public spending in oal healh spending also increased form 60% in 992 o around 70% in Figure Public expendiure on healh (Porugal) % of GDP real growh (%) % of public spending in oal healh spending (lhs) Real grow h of per capia spending on healh (rhs) Source: OECD. Alhough he period was characerized by increases in public hospials provision, namely in he number of oupaien consulaions, public healh expendiure however grew a a faser rae han producion (see Table ). Wha is more, for mos of he period, lengh of say decreased and occupancy raes did no significanly improve. According o Oliveira (2005:25), hese conradicory rends ( ) may be inerpreed as an indicaor for he lack of any efficiency gains. 6

8 Table Hospial uilisaion and supply indicaors, Porugal ( ) (Variaion in relaion o previous year is shown below) Oupaien consulaions (paiens observed, by desinaion) / ,7 497, , 578, ,3 753, ,03 0,07 0,05 0,04 0,09-0,02 0,05 0,03 0,0 0,07 0,07 0,04 0,06 0,06 Average lengh of say / 9,6 9,3 8,8 8,4 8,3 8,2 8 7,8 8 7,9 8,5 8,2 7,9 7,8 7,8-0,03-0,05-0,05-0,0-0,0-0,02-0,03 0,03-0,0 0,08-0,04-0,04-0,0 0,00 Occupancy rae (%) / 74,2 75,3 69,3 75,9 75,9 75,2 74,6 73,7 74,4 74,9 75,8 75,5 75,9 76,2 76,2 Toal expendiure on healh per capia, USD PPP / n.a 0,09 0,0 0,09 0,08 0,2 0,05 0,2 0,02 0,08 0,09 0,06 0,04 0,02 - Share of public expendiure on Toal expendiure on healh per capia (%) /3 65,5 62,8 59, ,4 6,7 64,7 64,8 65,4 67,6 69,4 70,6 70,5 69,7 n.a Annual growh rae of public per capia expendiure on healh, in real erms /4-8,2,7 4,7 0,9 4,7 5,9 7,8,3 4,7-0,5-0,3 n.a Per capia expendiure on hospial care, USD PPP / n.a Noes: n.a. - no available. / Insiue of Healh Financial Managemen and Informaics - IGIF ( ) and IGIF Conas Globais do SNS, 999, 2000; Direcção-Geral da Saúde, Cenros de Saúde e Hospiais - Recursos e Produção do SNS, ; OECD Healh Daa, 2003, 2nd ediion; OECD Healh Daa, /2 Daa for : OECD Healh Daa, 998; WHO Healh for All Daabase 999, IHS-HealhEcon calculaions 999. Daa for 990 and : WHO Healh for All Daabase, June 2003, IHS HealhEcon calculaions 2004; OECD Healh Daa, 2003, 2nd ediion; /3 Daa for : OECD Healh Daa, 998; WHO Healh for All daabase 999, IHS-HealhEcon calculaions 999. Daa for 990 and : WHO Healh for All Daabase, June 2003, IHS HealhEcon calculaions 2004; OECD Healh Daa, 2003, 2nd ediion; Daa for : OECD Healh Daa, 2003, 2nd ediion; OECD Healh Daa, /4 Daa for : OECD Healh Daa, /5 WHO Healh for All Daabase, June 2003, IHS-HealhEcon calculaions

9 3 PRODUCTIVITY MEASUREMENT In his secion we briefly review he lieraure on non-parameric measuremen of efficiency, noably regarding he hospial secor, and we also explain he analyical framework used in he paper. 3. Lieraure review Following Farrell (957), economic efficiency, also referred o as X-efficiency, has wo disinc componens: allocaive efficiency (AE) and echnical efficiency (TE). Boh componens are pu ogeher in he overall efficiency (OE) relaion as follows: OE = TE AE. () Technical efficiency (TE) refers o producing he maximum oupu from a se of given inpus (oupu-oriened) or, alernaively, he capaciy o minimise inpus o produce he same level of oupu (inpu-oriened). Thus, a decision-making uni (DMU), e.g. a public hospial, is echnically efficien when i operaes on is producion fronier. On he oher hand, allocaive efficiency (AE) reflecs he DMU abiliy o use he inpus in opimal proporions, in oher words, i refers o he use of an inpu mix ha maximizes revenue given oupu prices. A firm is overall efficien (OE) when i operaes on is cos or revenue fronier. Farrell s efficiency analysis (957) was proposed in a cross-secional conex. However, dynamic approximaions wih he objecive of quanifying efficiency changes over a period of ime are also possible. These are commonly done wihin he framework of produciviy measuremen. 0 In his conex, produciviy is defined as he raio of an index of oupu o an index of inpu use and produciviy change as he change of produciviy over ime. Index numbers are used o measure he changes in he levels of oupu produced and inpu used, beween a base period and he curren period. There are several index 0 See, for example, Coelli, Rao and Baese (998) and Balk (998). Hollingsworh, Dawson and Maniadakis (999, pp. 62). 8

10 number formulas. The mos popular indices are he Laspeyres and Paasche indices (he former uses he base-period daa on quaniies or prices as weighs, whereas he laer uses curren-period s as weighs), he Fisher index (a geomeric average of Laspeyres and Paasche indices) and he Törnqvis index (which is ofen presened in a log-change form and is he weighed average change in he log of he price or quaniy of a paricular good). 2 All hose indices menioned above rely on wo imporan assumpions abou he DMUs behaviour and echnology: (a) DMUs are economically efficien; (b) and echnologies exhibi global consan reurns o scale. To allow for inefficiencies one should replace producion funcions 3 by disance funcions (OECD, 200). Disance funcions are represenaions of muli-oupu and muli-inpu echnologies which assume neiher decision-making unis efficien behaviour nor consan reurns o scale. Furhermore, hey require only daa on inpu and oupu quaniies (Färe e al., 994) and can be compued in eiher he inpu or oupu orienaions. The Malmquis (953) produciviy index (MPI), firs proposed and laer inroduced in he produciviy measuremen lieraure by Caves, Chrisensen and Diewer (982), is defined in erms of disance funcions and i is based on Malmquis's proposal o consruc quaniy indices as raios of disance funcions in he conex of consumer heory. The MPI measures he oal facor produciviy (TFP) change beween wo daa poins in erms of raios of disance funcions. Färe e al. (994) exended furher he MPI o measure hospial produciviy. These auhors ook he Malmquis index defined in Caves, Chrisensen and Diewer (982), and illusraed how he componen disance 2 For he measuremen of he raes of change of oupus, inpus and produciviy, hese indices are usually linked ogeher o make annual comparisons of consecuive years over a given period. This means ha for every index for period +, period provides he base. There is a srong preference in he lieraure in favour of chained indices because hey involve only comparisons wih consecuive periods, measuring smaller changes. Therefore, and according o Coelli, Rao and Baese (998), some of he approximaions involved in he derivaion of heoreically meaningful produciviy indices are more likely o hold. 3 Producion funcions are represenaions of echnologies which assume ha firms operae echnically in a efficien way. 9

11 funcions could be esimaed using Daa Envelopmen Analysis (DEA), a nonparameric echnique. Moreover, hey were he firs o show how he resuling TFP indices could be decomposed ino an efficiency change par and a echnical change par (see Balk (998)). The advanage of he Malmquis index is ha, when panel daa are used, i allows he descripion of muli-oupu and muli-inpu producion echnologies requiring neiher a priori behavioural assumpions abou he producion echnology nor inpu or oupu price daa (Coelli, Rao and Baese, 998). Insead, i replaces hem wih informaion on he srucure of bes pracice service delivery echnology (Lovell, 2006, pp. 5). Furhermore, once he producion echnology is esimaed, his measuremen echnique is capable of decomposing TFP ino is wo componen pars: efficiency change and fronier change. The properies menioned above make he Malmquis index approach more appealing for measuring echnical efficiency and produciviy change in he public secor. 4 Indeed, price daa are no in general available in he public secor or, if hey exis, hey do no reflec he marginal coss. This is paricularly rue in he case of public hospials producing muliple oupus. There are wo main fronier esimaion mehods ha are based eiher direcly or indirecly upon a Malmquis index of he change in TFP: (i) sochasic fronier analysis (SFA) and (ii) daa envelopmen analysis (DEA). Alhough boh SFA and DEA are efficiency measuremen echniques capable of dealing wih panel daa, hey do differ remarkably beween each oher. On one hand, sochasic producion funcions measure deviaions from he ideal producion fronier wih an addiional error erm which denoes he inefficiency in he producion. Despie of aemping o disinguish he effec of noise from he effec of inefficiency, SFA disance funcions are parameric and deerminisic and as such hey may confound he effec of omied variables and measuremen errors, as well as possible misspecificaion of he funcional form (Jacobs, Smih and Sree, 2006). 5 4 See Jacobs, Smih and Sree (2006). 5 The parameric approach in efficiency measuremen was inroduced by Aigner, Lovell and Schmid (977) and Meeusen and van den Broeck (977). According o several auhors (Coelli, 2002; 0

12 On he oher hand, DEA is a non-parameric 6 local index, which means ha i needs fewer assumpions abou he form of he producion echnology han SFA, allowing produciviy change and is componens o be producer-specific (Jacobs, Smih and Sree, 2006). By conras, i canno disinguish beween saisical noise and inefficiency. However, DEA became widely used o calculae changes in TFP wihin he public hospials secor, where price daa is difficul o find and muli-oupu producion is relevan, because i needs fewer assumpions abou he form of he producion echnology han SFA, hus no requiring he imposiion of any behavioural assumpions such as revenue maximizaion or cos minimizaion. DEA analysis has also been used recenly o assess he efficiency of he public secor in cross-counry analysis in such areas as educaion, healh (Afonso and S. Aubyn, 2005, 2006), for overall public secor efficiency analysis (Afonso e al., 2005), and o asses local governmen spending efficiency (Afonso and Fernandes, 2006). Among dynamic approximaions wih he objecive of quanifying he evoluion of produciviy over a period of ime, he mos widely used in DEA environmen is he Malmquis produciviy index. 7 In Table 2 we review some non-parameric applicaions measuring hospial efficiency wih panel daa. Hollingsworh, Dawson and Maniadakis, 999; 62), he main reference in his field is Nishimizu and Page (982), because i was only aferwards ha produciviy changes sared o be aribued o an efficiency componen besides he echnological one. Nishimizu and Page (982) applied he linear programming mehods proposed by Aigner and Chu (968) o social secor panel daa of Yugoslavia o consruc parameric producion froniers and measured produciviy growh as he sum of wo componens: efficiency change and echnical change. 6 Nonparameric fronier mehods measure he efficiency of a DMU by he disance beween he DMU s observed level of inpus and oupus and he bes pracice producion fronier. This disance measure was inroduced by Shepard (970) and firs made operaional by Farrell (957). Charnes, Cooper and Rhodes (978) formulaed i ino a linear programming model (DEA). For a survey of DEA mehodologies, see for example, Seiford and Thrall (990). 7 See Grosskopf (993), Färe, Grosskopf and Roos (997), Coelli, Rao and Baese (998), Hollingsworh, Dawson and Maniadakis (999) and Hollingsworh (2003).

13 Table 2 Non-Parameric Hospial Efficiency wih Panel Daa Reference Daa sample Mehod Färe, Grosskopf, Lindgren and Roos (994) Burgess and Wilson (995) Small and middlesized noneaching hospials in Sweden ( ) U.S. hospials ( ) Variables (a) Inpu Oupu DEA Real labour inpu; real non-labour Inpaien discharges; long-erm paien inpu. (b) bed days (represenaive cos drivers of long-erm chronic care); docors visis (proxy of ambulaory care). (c) DEA Acue care inpaien days; case-mix weighed acue care inpaien discharges; long-erm care inpaien days; number of oupaien visis; ambulaory surgical procedures; inpaien surgical procedures. Direc oupus: number of acue-care hospial beds, weighed by a scope-ofservices index; number of long-erm hospial beds; regisered nurses measured in FTE; licensed pracical nurses measured in FTE; oher clinical labour measured in FTE; non-clinical labour measured in FTE; long-erm care labour measured in FTE. (d) Linna (998) Acue care hospials in Finland ( ) DEA; SFA Cos variable: ne operaing coss; Fixed facor variable: oal number (TN) of beds; Price variables: average hourly wage rae of labour; annual price index for local governmen healh care expendiure. Oupus: Toal number (TN) of emergency visis; oal sum of schedule and follow-up visis; DRGweighed number of oal admissions; TN of bed-days exceeding he cu-off poin defined in he oulier analysis; Number of residens receiving year of raining; TN of on-he-job raining weeks of nurses; TN of impacweighed scienific publicaions; Exogenous variables: eaching dummy indicaing he eaching saus of he hospial; readmission rae for he admissions; year of he observaion. Maniadakis, Hollingsworh and Thanassoulis (999) Hospials in Scoland (99-996) DEA Docors; nurses; oher personnel; beds; 00 cubic meers of building; admissions for sroke; admissions for fracured neck of femur; admissions for myocardial infracion. Inermediae oupus: acciden and emergency aendances; adjused oupaien aendances; adjused day cases; adjused inpaien discharges. (e) Oupu (final): Sandardised survivals afer admission for sroke; sandardised survivals afer admission for fracured neck of femur; sandardised survivals afer admission for myocardial infracion. (f) McCallion, Glass, Jackson, Kerr and McKillop (2000) Norhern Ireland hospials in UK ( ) DEA Nursing saff; adminisraive saff; ancillary saff; specialiss; bed complemen. Toal number of inpaiens (using discharges raher han lengh of say) and oupaiens regisered in he following four oupu caegories: general surgery; general medical; maerniy; acciden and emergency. Sommersguer- Reichmann (2000) Hospials in Ausria ( ) DEA Full-ime-equivalen of labour; oal number of beds; oal expenses for exernal medical services. Number of paiens reaed in he oupaien care uni; oal number of credi poins according o he crucial secor muliplied wih a seering facor. Maniadakis, and Thanassoulis (2000) Acue hospials in Scoland (99-996) DEA Docors (WTE); nurses (WTE); oher personnel (WTE); beds (annual saffed); cubic meers (per 00); price variables. Acciden and emergency aendances; adjused oupaiens; adjused day cases; adjused inpaiens. Zere (2000); Zere, McInyre and Addison (200) Non-academic Wesern Cape (Souh Africa) hospials ( ) DEA Hospials Level I and II: oal recurren expendiure (including salaries of personnel, expendiure on drugs and oher supplies); bed-size. Hospials Level III: recurren expendiure. Inpaien days; oupaien visis. 2

14 Table 2 (con.) Reference Daa sample Mehod Chirikos and Sear (2000) Linna (2000) Florida (USA) acue care hospials ( ) Finnish hospials ( ) DEA; SFA DEA Inpu Cos or annual expenses are broken down by six caegories: () wage and salary paymens o personnel engaged in paien care aciviies; (2) wage and salary paymens o personnel engaged in all non-paien care cenres; (3) oher expenses in paien care cos cenres; (4) capial coss - adjused depreciaion charges - for plan asses; (5) adjused depreciaion charges for fixed and movable equipmen; (6) oher non-paien (adminisraive) coss aribuable o capial use. (g) Personnel: number of docors in full ime equivalens; number of oher saff in full ime equivalens; Cos variables: oal cos of maerial and equipmen; Beds: oal number. Variables Oupu Inermediae producs: oal admissions scaled by mean DRG weighs; inpaien days ne of he day of admission divided by hree caegories - Medicare; Medicaid; Blue Cross, oher privae payers, and selfpay paiens; wo composie indexes of oupaien service aciviy - one reflecs he provision of special ess and procedures and i is cas in admission-equivalen erms, and he oher measures he level of aciviy in ambulaory cenres generaing oupaien revenue in emergency room-equivalen erms. Oupaien reamen: oal number of emergency visis; oal sum of scheduled and follow-up visis; Inpaien reamen: DRG-weighed number of oal admissions; DRGweighed number of oal episodes; oal number of bed-days exceeding he cu-off poin defined in he oulier analysis; Teaching variables: number of residens receiving one year of raining a he hospial; oal number of on-he-job raining weeks of nurses; Research variable: oal number of impac-weighed scienific publicaions. Solà and Prior (200) Spanish (Caalan) hospials ( ) DEA Healh saff: full-ime medical and nursing personnel; Oher saff: oher non-healh care saff, also full-ime; Beds: number of beds assigned o coninuous care of paiens admied; Maerials: oal value of curren purchases in Spanish peseas. Oupus Acue: in-paien days spen in medical care, surgery, obserics, gynaecology and paediarics; Longsay: in-paien days spen in long-say care and psychiary; Inensive: inpaien days spen in inensive care; Visis: medical care on an oupaien basis, for he diagnosis, reaing and monioring of illness. (h) Undesirable oupus (i) Prevalence of nosocomial infecions: number of clinically acive infecions divided by he number of paiens sudied. Noes: (a) DEA - Daa Envelopmen Analysis; SFA - Sochasic Fronier Analysis. (b) Real labour inpu was esimaed in wo seps: firs, average labour expendiure per hour is esimaed for four ypes of labour in he hospial secor; hen, a labour expendiure index is esimaed for each hospial, which is used o deflae annual oal labour expendiure. The consumer price index was used o deflae non-labour hospial expendiures. (c) See Breyer (987). (d) FTE - Full Time Equivalens. (e) Three inermediae oupus were adjused for case-mix. (f) This inpu-oupu se ries o capure he qualiy of services produced. (g) These six caegories are used direcly in he DEA model; he sum of he six iems is used o consruc he dependen variable in he SFA model. Annual cos is scaled by a cross-secional, sae hospial price index ha adjuss for nominal differences in inpu prices across local hospial markes. (h) The auhors undersand in-paien days as he combinaion of nigh say and he ime corresponding o he serving of a main meal (lunch or supper). (i) The auhors undersand undesirable oupus as lack of qualiy. 3

15 3.2 Malmquis Produciviy Index In his sub-secion we briefly explain he Malmquis produciviy index (MPI), which we will use ahead in he empirical analysis. We begin by specifying he producion echnology using he oupu se as follows: P(x) = {y: x can produce y}, (2) where P(x) represens he se of all oupus vecor, y, which can be produced using he inpu vecor, x. Assuming ha echnology saisfies several axioms, 8 he disance funcion (oupu oriened) is defined by d ( x, y) = min{ δ : ( y / δ ) P( )}. (3) 0 x If y is an elemen of P(x), he scalar δ will assume a value equal or inferior o one if y is on or above he producion possibiliies fronier, respecively. The values given by (3) are hen used o calculae he MPI. Following Färe e al. (994), he oupu-oriened Malmquis TFP 9 change beween period and period + is given by: + d (, ) (, ) o y+ x+ d o y+ x+ m o ( y, x, y+, x+ ) =, + (4) d o ( y, x ) d o ( y, x ) / 2 where d y, x ) represens he disance from he period + observaion and he o ( + + period echnology. A value of o period + whereas a value of m o > indicaes growh in produciviy from period m o < indicaes a decline. This approach differs from he formulaion of he Malmquis produciviy index proposed by Caves, Chrisensen and Diewer (982) because equaion (4) is he 8 See Coelli, Rao and Baese (998). 9 In an oupu disance funcion, he objecive is o maximize he proporional expansion of he oupu vecor for a given inpu vecor. 4

16 geomeric mean of he shif in echnology beween he wo periods, and +. The firs uses reference echnology corresponding o period, whereas he second does he same for period +. This procedure is used o avoid he necessiy o arbirarily choose one or oher period as he reference base. Färe e al. (994) furher decomposed he Malmquis index ino wo componens: one measuring efficiency change and anoher measuring fronier change as follows: + d (, ) (, ) (, ) o y+ x+ d o y+ x+ d o y x m o ( y, x, y+, x+ ) =, + + (5) d o ( y, x ) d o ( y+, x+ ) d o ( y, x ) / 2 or equivalenly M = E T. The raio ouside he square brackes in he righ-hand side of (5), denoed as E, indicaes he levels of efficiency relaive o he boundaries for years and + and wheher or no a movemen owards or away from he bes-pracice fronier has occurred beween hese wo periods, and +. The expression inside he square brackes in he righ-hand side of (5), denoed by T, reflecs echnical change measured by he geomeric mean of he movemens experienced by he bes-pracice echnology beween period and +. The inerpreaion of he resuls is similar for boh coefficiens: a value greaer han one indicaes improvemen from period o period +, whereas a value of less han one indicaes a decline. Figure 2 illusraes he definiion and measuremen of he oupu-oriened Malmquis index for he simple case where a DMU (e.g. a public hospial) uses only a single ype of inpu, x, o produce a single ype of oupu, y. In he example depiced in Figure 2, he DMU is producing a a level of produciviy less han wha is feasible under each period s producion fronier. The MPI indicaes under consan reurns o scale echnology he poenial rise in produciviy as he fronier shifs from period o +. For example, he DMU a ime could produce oupu y p for inpu x ; wih he same inpu x i could produce oupu y q a period +. 5

17 Figure 2 Oupu-oriened Malmquis Produciviy Index (MPI) Using Consan Reurns o Scale The decomposiion of he Malmquis index according o equaion (5) is given by he disance funcions in equaions (6) and (7): E y + r = (6) y / y / y p y = y + / y / y / 2 + q p T. (7) / y r y y / y q According o equaions (6) and (7), efficiency change (E) is he raio of he oupuoriened measure of Farrell echnical efficiency in period + o ha in period and echnical change (T) is he geomeric mean of he shif in echnology beween period + and. 6

18 7 If we calculae he Malmquis index in a DEA environmen assuming consan reurns o scale echnology (CRS), hen four linear programming problems should be solved for each hospial o compue he four disance funcions which appear in equaion (4) in each pair of adjacen ime periods. The four oupu-oriened DEA linear programs are given in equaions (8) o (): { } max ), (,,, + Φ Φ = λ λ λ λ φ i i X x Y y s x y d ; (8) where Φ is he echnical efficiency, Y is he oupu marix, ( ) N λ is a vecor of consans, and X is he inpu marix, { } max ), (,,, + Φ Φ = λ λ λ λ φ i i X x Y y s x y d ; (9) { } max ), (,,, + Φ Φ = λ λ λ λ φ i i X x Y y s x y d ; (0) { } max ), (,,, + Φ Φ = λ λ λ λ φ X x Y y s x y d i i. () Equaions (8) and (9) represen he case where a daa poin observed in a period is

19 compared o he fronier of ha period. Similarly, in equaions (0) and (), daa poins are compared o he fronier of he previous period. Equaions (8) o (0) should be solved once for each DMU. To consruc a chain index, i is necessary o solve for N*(3T-2) linear programs, where N is he number of DMUs and T is he number of ime periods (Coelli, Rao and Baese, 998). For example, in he case of 68 hospials across five years, our maximum daa se, i is necessary o solve 884 linear programs, i.e. [68*(3*5-2)]. 4 EMPIRICAL ANALYSIS 4. Daa In our analysis we envisage individual or merged NHS hospial as organizaions ha annually ransform healh services (y) from he consumpion of several facors of producion or inpus (x). Daa on hospial producion were sourced mainly from he Poruguese Healh General Direcorae s annual saisics, Cenros de Saúde e Hospiais - Recursos e Produção do SNS. These annual saisics measure consisenly since 2000 he same aspecs of hospial aciviy, which allows overcoming some of he problems ha may occur when dealing wih longiudinal daa. 20 Our daa se consiss of 68 annual observaions regarding hospial producion during he period The number of our observaions does no change over he period, in order o consruc a balanced panel. 2 In Porugal, hospials are classified wihin hree caegories: cenral, disric and disric level one. This classificaion indicaes he number of specialiies which a given hospial is equipped o rea, reflecing he ype of services i may offer. For example, disric hospials level one (DH) only provide inernal medicine, surgery and a few basic specialiies whereas disric hospials (DH) provide a considerable range of specialized 20 As poined by Jacobs, Smih and Sree (2006), longiudinal daa on hospial producion can be affeced by changes over ime in daa collecion mehods, echnology, and by hospials merger aciviy. 2 We excluded from our daa se Psychiaric Hospials, Regional Ceners of Alcohology (Cenros Regionais de Alcoologia), Recovering Psychiaric Ceners (Cenros Psiquiáricos de Recuperação), and Oncology Insiues (IPO). Indeed, he aforemenioned NHS eniies are defined by he Poruguese Healh General Direcorae as specialized healh insiuions. 8

20 services. 22 By conras, cenral hospials (CH) provide specialized services wih advanced echnology and highly qualified human resources. In his conex, hospials wih he fewes number of specialiies rea simpler cases, and if we compare hem wih DH and CH hey are less equipped wih advanced medical echnology such as he compuerised axial omography scanners (CAT). In Table 3 he 68 hospials are disribued among he abovemenioned hree caegories wihin each region. Accordingly, 46 per cen of he hospials observed are disric hospials (DH), of which 4 per cen are in he Cenro region. On he oher hand, 29 per cen of he hospials are cenral hospials (CH), 23 of which 55 per cen belong o he LVT region. Disric hospials level one (DH) represen 25 per cen of our sample, of which almos 60 per cen belong o Cenro region. I should be noed ha here are no CH or DH in eiher Alenejo or in Algarve regions. Table 3 Disribuion of observaions by hospial caegory and by region (2005) Region Type of Hospial/Merger Toal CH DH (a) DH Alenejo Algarve - - Cenro LVT (b) Nore Toal Noes: (a) The hospial Amadora-Sinra was included in his caegory. (b) Lisboa e Vale do Tejo. In 2005, only 57 per cen of he hospials observed belonged o he general governmen secor (SPA). 24 The remaining 4 per cen had been ransformed, in 2002, ino hospial companies (SA). 25 As menioned by Quinela, Carvalho and Tranquada (2006:5), changes in hospial oupu may occur due o ( ) merging, spliing, creaion and disappearance of unis. In conras, ( ) he [hospial] oupu rend should no be affeced by changes in he 22 See OECD (2004, pp. 57). 23 Of which 3 are eaching hospials: S. João (in Poro), Sana Maria (in Lisbon) and Universidade de Coimbra (in Coimbra). 24 The hospial Amadora-Sinra was included in disinc caegory named ohers. 25 In 2005, all hospials SA were ransformed ino enrepreneurial public eniies (EPE) along wih 2 more SPA hospials (see aricle of Decree-Law nº 233/2005). Tables I and II in he Appendix lis all SPA and SA/EPE hospials in funcion by

21 legal saus especially when he uni coninues o be engaged in he same aciviy he same way. Having his in mind, we only consider in he analysis hose mergers 26 ha were creaed before or during As for he idenificaion of he hospials legal saus, he disincion beween SA (henceforh, EPE) and SPA hospials ha came ino force only in 2003, was applied o our sample from 2000 onwards. In wha concerns he inpu variables, we use he number of acive docors (DOCTORS), nurses (NURSES) and oher saff (OTHERSTAFF) o measure labour inpu, and he number of available beds for inpaien reamen (BEDS) o proxy capial inpu. Moreover, a range of oupus are considered in our analysis (see Table 4). 27 These variables consis of volume measures ha according o he lieraure reflec he quaniy of hospial service provision (inermediae oupu) and no hospial oucomes (improved healh saus). 26 Hospials merger aciviy refers o he congregaion of wo or more hospials of differen naure bu wih resource cenralizaion. 27 Since no informaion is available on he relaive imporance of cerain oupus, we do no apply weigh resricions in he analysis. 20

22 Table 4 Variables used in he empirical analysis (a) Variable Descripion Observaions Inermediae oupus INPAT-ICM ICM-weighed number of paiens who leave hospial afer inpaien admission. Number of paiens who leave hospial afer inpaien admission in ha period, weighed by he respecive index of case-mix (ICM). The ICM is defined as he raio beween he oal number of equivalen paiens weighed by he relaive share of he corresponding Diagnosis Relaed Group (GDH) and he oal number of equivalen paiens. 28 INPAT-DAYS Hospialisaion days Toal days used by all inpaiens, measured for a given ime period, and excluding he exi day. OUTPAT Number of oupaien visis EMERG Number of emergency episodes SURGERY Number of surgeries CAT produced Caegorical variable indicaing he possession of CAT equipmen: 2 if i exiss; oherwise Only NHS hospials ha had CAT in 2000 were considered. This variable ries o capure an increasingly imporan branch of hospial aciviy: diagnosis. Inpus DOCTORS Number of acive docors Healh professionals ha in he final day of he reference period worked in a given hospial. NURSES Number of acive nurses Healh professionals ha in he final day of he reference period worked in a given hospial. OTHERSTAFF BEDS Number of acive workers oher han docors and nurses Number of available beds (a) Source: Direcorae-General of Healh (DGS). Healh professionals ha in he final day of he reference period worked in a given hospial. Number of available beds for inpaien reamen. Alhough here are claims in he lieraure ha he final hospial oupu or oucome is improved healh saus of he populaion, which in urn is affeced by various facors oher han healh care, such as moher s healh, housing, educaion or food (see Färe e al., 997), here is noneheless a general agreemen ha measuring improvemens in healh saus is very difficul mainly due o he muli-dimensional naure of healh iself, he exreme subjeciviy of measuring realiies such as paien s improved healh saus and qualiy of life and he lack of proper informaion. Thus, i is common o approach hospials oupus by volume measures ha do no inend o reflec he qualiy of he service rendered bu are assumed o somehow posiively 28 Daa on he case-mix index was provided by Adminisração Cenral do Sisema de Saúde (ACSS) upon our reques. ACSS is a public insiue responsible for he managemen of he financing sysem of he NHS. 2

23 influence he healh saus of he populaion (Breyer, 987). 29 In his conex, we measure he number of hospialised reaed paiens weighed by he respecive index of case-mix (INPAT-ICM), 30 he oal number of inpaien days (INPAT-DAYS), of oupaien visis (OUTPAT), of emergency episodes (EMERG-TOT) and of surgeries produced (SURGERY). We also consider a caegorical variable indicaing if a given hospial has or has no CAT equipmen since 2000 (CAT). Table 5 summarises he descripive saisics of our daa se, where we observe he significan posiive relaive change of boh he number of oupaien visis and of surgeries beween 2000 and By conras, here was a sligh decrease in he average number of available beds and in hospialisaion days for he same period. 29 See also Grosskopf and Valdmanis (987). 30 To ake ino accoun he hospial case-mix, we weighed he number of reaed paiens by he corresponding index of case-mix (ICM) ha is annually esimaed by Insiuo de Gesão Informáica e Financeira da Saúde (IGIF) variable INPAT-ICM. 22

24 Inpus Oupus Table 5 Descripive saisics of inpu and oupu variables Indicaors Beds Mean Min Max Docors Mean Min Max Nurses Mean Min Max Oher Healh Saff Mean Min Max Inpaien Days Mean Min Max Oupaien Visis Mean Min Max Emergencies Mean Min Max Emergencies: reamen in he same hospial Mean Min Max Emergencies: ransfer o anoher hospial Mean Min Max Inpaiens weighed by ICM Mean Min Max Surgeries Mean Min Max

25 4.2 Model specificaions We use daa on hospial services and resource quaniies o consruc an oupu disance funcion, hus addressing he quesion: by how much can he (inermediae) oupu quaniies increase proporionally wihou changing inpu quaniies? This approach is consisen wih he assumpion ha hospial managers behave as resource-consrained service maximisers (see Lovell, 2002). Valdmanis (992), based on Nunamaker (985), recommends ha researchers should specify wihin a DEA analysis differen models from he daase o evaluae wheher he ranking and efficiency of an individual DMU is variable-specific (or model-specific) or wheher he resuls are robus o changes in daase specificaions. 3 Consequenly, firs we defined a basic model and hen we inroduce changes ha ook he form of alernaive inpu/oupu definiions and/or he definiion and selecion of differen populaions wihin our daase. In Table 6 we characerise he alernaive models used in our analysis. In our basic model (Model I) we only consider inpu and oupu variables for which we have informaion for all he 68 hospials for he period (4 inpu and 5 oupu variables), hus guaraneeing a balanced panel. In order o es he effec of decreasing he number of inpu and oupu variables, we specify Model II (2 inpu and 3 oupu variables). As noed before, he classificaion of he hospials may o some degree ake accoun of hospial s case-mix and facors likely o affec he service rendered such as saffing qualificaions and medical echnology used. To also ake ino accoun hese differences in our analysis, we specified Models III and IV where we seleced wihin our daase only disric hospials and disric level one hospials. However, we added o he analysis wo more oupu variables because here is more informaion for his subgroup in erms of oupus compared o he basic model (Model I). The cross-secion sample 3 Anoher opion is o compare he resuls of a DEA sudy wih resuls from oher efficiency evaluaion mehods (e.g. SFA) applied o he same daase. 24

26 belonging o his group consiss of 48 hospials, 3 of which are disric hospials, and 7 are disric hospials level one. The insabiliy of he environmenal conex and of he regulaory regime of he NHS hospials spurred by he 2002 reform moivaed he specificaion of Models V and VII, where we individualize wo sub-groups, SPA hospials and SA/EPE hospials, respecively. In Model V and VII we use he same inpu and oupu variables specified for Model I. Model VI and VIII only differ from he previous models in wha concerns he oupu measures used. In order o es he homogeneiy of our observaions, we define wo sub-groups of hospials based on he following crieria: hose wih CAT equipmen since 2000 (34 hospials), and hose wihou CAT equipmen since 2000 (34 hospials), hus dividing our iniial sample ino wo equal pars. 25

27 Table 6 Model Specificaions Models I II III IV Indicaors Inpus # Oupus # BEDS; DOCTORS; 4 INPAT-DAYS; OUTPAT; EMERG-TOT; 5 NURSES; INPAT-ICM; SURGERY. OTHERSTAFF BEDS; 2 OUTPAT; EMERG-TOT; INPAT-ICM. 3 HEALTHSTAFF BEDS; DOCTORS; NURSES; OTHERSTAFF. BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; INPAT-ICM; SURGERY. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; EMERG-NONTRANSF; EMERG- TRANSF; INPAT-ICM; SURGERY. 5 7 Nº of DMUs Descripion These models include all observaions. These models only consider disric (DH) and disric levelone (DH) hospials. V VI BEDS; DOCTORS; NURSES; OTHERSTAFF. BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; INPAT-ICM; SURGERY. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; EMERG-NONTRANSF; EMERG- TRANSF; INPAT-ICM; SURGERY These models only consider SPA hospials. VII VIII BEDS; DOCTORS; NURSES; OTHERSTAFF. BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; INPAT-ICM; SURGERY. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; EMERG-NONTRANSF; EMERG- TRANSF; INPAT-ICM; SURGERY These models only consider SA/EPE hospials. IX X BEDS; DOCTORS; NURSES; OTHERSTAFF BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; INPAT-ICM; SURGERY. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; EMERG-NONTRANSF; EMERG- TRANSF; INPAT-ICM; SURGERY These models only consider hospials wih CAT equipmen in XI BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; EMERG-TOT; INPAT-ICM; SURGERY. 5 These models only consider hospials wihou CAT equipmen in 2000, regardless of having bough i aferwards. XII BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT; INPAT-ICM; SURGERY XIII BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT EMERG-TOT; INPAT-ICM; SURGERY. 5 These models only consider hospials wih emergency service informaion XIV BEDS; DOCTORS; NURSES; OTHERSTAFF. 4 INPAT-DAYS; OUTPAT EMERG-TOT; EMERG-NONTRANSF; EMERG- TRANSF; INPAT-ICM; SURGERY

28 Finally, we es wo models (Models XIII and XIV) where only he NHS hospials wih emergency service informaion were considered Resuls and discussion We now urn o evaluae he produciviy growh in he service provision of hospials by subjecing he daa o a Malmquis index analysis. 33 Addiionally, in order o es if here is any poenial for efficiency and produciviy improvemens by he Poruguese NHS hospials and, if so, o quanify he corresponding magniudes, he daa was furher subjeced o a yearly DEA analysis. Here, i is assumed ha hospial managers aemp o maximise he services ha hey provide and ha such services can be approximaed by he indicaors discussed in he preceding secion. The DEA formulaion ha we use in his sudy corresponds o he Charnes, Cooper and Rhodes (978) formulaion. 34 Table 8 shows he evoluion (annual means) of he Malmquis TFP index and of is echnological (T) and efficiency (E) componens beween 2000 and 2005 for Model I. Table 8 Mean Produciviy Indices for Model I ( ) Efficiency Technical TFP / Change (E) Change (T) 00/ / / / / Mean / TFP - Toal Facor Produciviy. Preliminary esimaes for our basic model (Model I) show ha, on average, he NHS hospial secor revealed posiive bu small produciviy growh (TFP) levels beween 2000 and 2004, whereas in 2005 here was a sligh decrease in TFP. I is also possible o 32 Hospials wihou emergency service informaion are he following ones: H. Sana Mara, H. Pulido Valene, H. Sana Cruz, H. Oropédico de Ouão, H. Joaquim Urbano and Insiuo Ofalmológico Gama Pino. 33 Measures of DEA disance funcions and of Malmquis TFP index and is componens (EC and TC) were esimaed using he DEAP programme. The esimaed DEA model imposes consan reurns o scale, an opion in line wih he lieraure reviewed in Table For a deailed descripion of he DEA linear programming problem imposing consan reurns o scale, see Grifell-Tajé and Lovell (995) and Coelli, Rao and Baese (998). 27

29 conclude from Table 8 ha he efficiency change componen of TFP plays, on average, a major role in produciviy growh han he echnical change componen. Furhermore, he TPF summary esimaes for individual hospials (annual means) indicae ha more han half of he NHS hospials observed (42 ou of 68) show eiher posiive or no relaive change in TFP beween 2000 and 2005, whereas he remaining hospials (26) show TFP decline (see Table A4 in he Appendix). Table 8 summarises changes in oal facor produciviy (TFP) for our basic model (Model I) and for he several alernaive specificaions using he variables lised in Table 6. Addiionally, we repor in Tables A5a-A5c in he Appendix he variaion of TFP indices and is componens over ime for all models (see Table 8). Table 8 Malmquis TFP summary resuls, hospials means ( ) Models I II III IV V VI VII VIII IX X XI XII XIII XIV Mean Min Max Sdev % of oal < % of oal DMU Noe ha models III, V, VII, IX, XI and XIII differ from our basic model in erms of he unis (hospials) analysed, esing for homogeneiy, whereas models IV, VI, VIII, X and XIV go a sep furher, esing also for differen oupu specificaions (he number of oupu indicaors uilized across all hese models is now 7 raher han 5). Sill according o Table 8, TFP indices vary on average beween (Model XII) and.07 (Models VI). Moreover, and across all models, here are more NHS hospials ha show eiher posiive or no change in produciviy across he eleven esed models, whereas beween 7 and 27 reveal produciviy decline. 28