Regional disparities in mortality by heart attack: evidence from France

Transcription

1 Regional dispariies in moraliy by hear aack: evidence from France Lauren Gobillon y Carine Milcen z February 21, 2008 Absrac This paper sudies he deerminans of he regional dispariies in he moraliy of paiens reaed in a hospial for a hear aack in France. These deerminans can be some di erences in paien characerisics, reamens, hospial charaerisics, and local healhcare marke srucure. We assess heir imporance wih an exhausive adminisraive daase over he period using a srai ed duraion model. The raw dispariies in he propensiy o die wihin 15 days beween he exreme regions reaches 80%. I decreases o 47% afer conrolling for he paien characerisics and heir reamens. In fac, a variance analysis shows ha innovaive reamens play an imporan role. Remaining regional dispariies are signi canly relaed o he local healhcare marke srucure. The more paiens are locally concenraed in a few large hospials raher han many small ones, he lower he moraliy. Keywords: spaial healh dispariies, srai ed duraion model JEL code: I11, C41 We are graeful o Mareen Lindeboom, Thierry Magnac, Francesco Moscone and Jordan Rappopor for very useful discussions, as well as he paricipans of he 16 h EU Healh Economerics Workshop in Bergen and he 54h NARSC in Savannah. This projec was carried ou wih he nancial suppor of he French Direcion of Research, Sudies, Evaluaion and Saisics (DREES). We are responsible for all remaining errors. y INED, 133 boulevard Davou, Paris Cedex. Tel: 0033(1) lauren.gobillon@ined.fr. Webpage: hp://lauren.gobillon.free.fr. z PSE (CNRS-EHESS-ENPC-ENS), 48 boulevard Jourdan, Paris. milcen@pse.ens.fr. Webpage: hp:// 1

2 1 Inroducion Spaial dispariies in heah oucomes have become a major concern in France. A driver of hese dispariies is ofen hough o be he missallocaion of ressources caused by a lack of informaion on local needs. As a consequence, a reform in 1996 decenralized he funding of he healhcare sysem a he regional level. A global budge is now decided naionally before being dispached beween regions. Some public regional agencies allocae he regional budges beween local public and privae no-for-pro hospials afer some bargaining. Imporanly, i is no obvious wheher changing he regional budges is likely o have a sizable e ec on regional dispariies in oucomes. The e ec will be signi can if supply facors (like hospial capaciies or equipmens) are disribued unevenly over he erriory and hese facors a ec healh oucomes signi canly. By conas, changing regional budges will have a far smaller e ec if healh oucomes are mainly he resul of demand facors (like he age srucure and socioeconomic habis). Also, he way regional agencies should allocae heir regional budge beween hospials is debaable. I is no clear-cu wheher i is more e cien o have a few well-equipped hospials which concenrae all he paiens or many small hospials which cover well he whole regional erriory. In his paper, we quanify he spaial dispariies in he moraliy of paiens reaed in a hospial for an acue myocardial infarcion (hear aack). We hen assess he imporance of demand and supply facors in explaining hese dispariies. In he economic lieraure on healh oucomes, mos of he papers focus on he e ec of supply facors, using demand facors only as conrols. In ha perspecive, regional dispariies in oucomes may depend on he local managemen of paiens afer heir admission in hospials. This managemen is relaed boh o he quick admiance of paiens in an adequae hospial and he qualiy of care ha hey receive. A large lieraure focuses on he e ec of ownership on hospial performance. Many auhors compares for-pro and no-for-pro insiuions (McClellan and saiger, 2000; Hansman, 1996; Milcen, 2005). Some ohers sudy he change in ownership saus (Propper, Burgess and Green, 2004). 1 However, hese papers do no assess wheher here is some soring of hospials depending on heir ownership saus ha could lead o spaial dispariies in performances. Also, hey do no look much on he e ec of reamen qualiy provided by hospials on oucomes whereas here is an exensive lieraure in epidemiology on his issue for hear aack 1 Oher papers relaed o he opic include Newhouse, 1970; Culer and Horwiz, 1998; Silverman and Skinner, 2001; Sloan e al., 1999; Ho and Hamilon, 2000; Kessler and McClellan,

3 (see for insance Jollis e al., 1994). Some spaial disparies in he qualiy of reamens, possibly relaed o he local proporions of hospials in each ownership saus, may cause some spaial dispariies in oucomes. We will address his kind of issues in our sudy. In fac, he inernaional lieraure on spaial healh dispariies is sill scarce. There are some comparisons beween counries in he horizonal equiy in healh care uilizaion (see van Doorslaer e al., 1997, 1999, 2000). However, for sudies on a given counry, space is usually no he main opic and i is raher used as an exra-dimension o consruc some insrumens. For insance, Geweke, Gowrisankaran and Town (2003) explain he hospial choice wih he disance beween he place of residence and hospials. There are a few excepions like Mobley (2003) who sudies he e ec of he local healhcare srucure on prices, bu he emphasis is on healhcare acces raher han on healh oucome. Milcen (2005) evaluaes he e ec of space on he moraliy of paiens admied in a hospial for a hear aack bu only hrough he disance beween he place of residence and he hospial which is found o have a non-signi can e ec. In fac, i is quie possible ha he local healhcare marke srucure has an e ec on he local hospial performances. We may hink ha local ineracions and compeiion, as well as he local concenraion of paiens in a few hospials o bene from economies of scales, may a ec he local oucomes. These issues deserve more aenion. By conras, he lieraure on spaial dispariies in he elds of economic geography and urban economics has developed a lo in recen years. Some papers ry o assess o wha exen spaial dispariies in wages (Duranon and Monasiriois, 2004; Combes, Duranon and Gobillon, 2008) or unemploymen (Gobillon, Magnac and Selod, 2007) can be explained wih workers composiion e ecs, rm e ecs and rue locaion e ecs. We will borrow some ools from his lieraure as he seing is quie similar. For our sudy, we consruc a unique mached paiens-hospials daase from some exhausive French adminisraive records over he period. This original daase conains some informaion on he demographic characerisics of paiens, heir diagnoses and heir reamens. I also provides some deails on he hospials where he paiens are reaed like he locaion, he ownership saus and he capaciy. We show ha regional dispariies in moraliy are quie large. In paricular, he raw di erence in he propensiy o die wihin 15 days beween he exreme regions reaches 80%. We hen assess wheher hese spaial dispariies come from some local di erences in paien characerisics (demographic shifers and secondary diagnoses), reamens, hospial characerisics or healhcare marke srucure. We rs esimae a he paien level a 3

4 Cox duraion model srai ed by hospial (i.e. each hospial has a speci c baseline hazard) using he Srai ed Parial Likelihood Esimaor proposed by Ridder and Tunali (1999). This esimaor allows o recover he e ec of he paien-speci c variables (heir characerisics and reamens) while conrolling for hospial unobserved heerogeneiy. We hen reconsruc he survival funcions of hospials ne of individual e ecs and average hem a he regional level. We nd ha remaining regional dispariies are lower bu are sill signi can. The di erence in he propensiy o die wihin 15 days beween he exreme regions is now 47%. A variance analysis a he regional level shows ha regional di erences in innovaive reamens play an imporan role. We hen assess o wha exen he remaining regional dispariies can be explained wih some hospial and geographic characerisics. For ha purpose, we rs specify he hospial hazards as he produc of some hospial xed e ecs and a baseline hazard. We show how o recover he hospial xed e ecs using some momen condiions. We hen regress he hospial xed e ecs on some hospial and regional variables. Finally, we average he model a he regional level and conduc a variance analysis. We nd ha he local concenraion of hospial supply plays a signi can role. The more paiens are concenraed in a few large hospials raher han many small ones, he lower he moraliy. Afer hospial and geographic variables have been conrolled for, some unexplained regional dispariies sill remain. In a rs secion, we presen how he French healhcare sysem deals wih paiens admied in a hospial for an acue myocardial infarcion. A second secion describes our daase. We hen presen in a hird secion some descripive saisics on he regional dispariies in moraliy, demand facors and supply facors. The fourh secion deails he economeric mehodology used o idenify he causes of he regional dispariies in moraliy. The fh secion summarizes he resuls of he model. 2 Hear aack in he French conex 2.1 Healhcare organizaion In France, here are wo ypes of ownership: public and privae. For public hospials, all infrasrucures, equipmens and sa belong o he public secor. Invesmen in public hospials are nanced by public funding. The sa (including docors and nurses) consiss in salaried civil servans. For privae hospials, infrasrucures, equipmens and sa belong o he privae secor. The non-docor sa is salaried. Par of he docor sa is salaried and he oher par is 4

5 self-employed. The public secor is under a global budge sysem. Par of he privae secor is under he same global budge sysem. Privae hospials which bene from his budge are called no-for-pro hospials (NFP). Every year, he governmen deermines he global budge and chooses how o divide i beween regions (see Graph A1 for a map of he French regions). The regional budge is dispached beween NFP and public hospials hrough bilaeral bargaining beween he regional regulaor and he direcors of hospials. Since he Juppé reform in 1996, he bargaining power of regional regulaors has increased signi canly and regional local auhoriies have gained more in uence on he regional hospial organizaion. NFP and public hospials should gran access o hospial care o every paiens. They canno make any pro. Hospials in he privae secor (excluding NFP) are paid by fee-for-services and can selec paiens. The selecion is usually done o maximize pro aking ino accoun he socio-economic caracerisics of paiens (like solvabiliy) and heir healh. These hospials have no consrain on pro s and are called forpro hospials (FP). All hese di erences sugges ha hospials have di eren incenives o provide healh care o paiens depending on heir saus (public or privae) and mode of reimbursmen (fee-for-service or global budge). This is paricularly rue for innovaive procedures ha are cosly. Indeed, forpro hospials are nanced via a fee-for-service sysem. Supplies such as sens are reimbursed ex-pos in addiion o he fee-for-service paymen. Docors have an incenive o perform innovaive procedures as hey receive addiional fees for performing hem. By conras, i is more di cul for public and no-for-pro hospials o purchase expensive devices as he public budge does no accoun for cosly innovaive procedures (caheerizaion, angioplasy or sen). However, hese hospials sill perform some innovaive acs (Dormon and Milcen, 2006). In fac, docors may have some indirec incenives o perform innovaive procedures such as improving heir repuaion or learning by doing. Individuals do no have he same access o healh care depending on he hospial saus and he mode of reimbursmen. Paiens are no charged in public hospials excep for a small ou-ofpocke bu hey incur charges in privae hospials. By conras, for-pro hospials x he price of caering and procedures, and paiens are reimbursed on he basis of public hospial charges only. The di erence beween he price and reimbursmen can be huge. The siuaion is inermediae in no-for-pro hopials as hey only x he price of caering. 5

6 2.2 Treamens of hear aack In his paper, we focus on one single disease. Indeed, evidence shows ha he e ec of characerisics (sex, age,...) on moraliy is disease-speci c (Wray e al., 1997). We seleced he Acue Myocardial Infarcion (hear aack) for four reasons. Firs, i belongs o he ischemic-disease group ha has been he primary cause of moraliy in France, before geing second recenly afer cancer. Second, moraliy from AMI has been widely sudied in he lieraure o assess he qualiy of hospial care in he US and he UK. This lieraure can by used for comparison (see Goworisakaran and Town, 2002, for he US, and Propper, Burgess and Green, 2004, for he UK). Third, AMI is a well-de ned pahology wih only a few re-admission due o is clinical de niion. Fourh, moraliy from AMI is an even frequen enough o yield some reliable saisical resuls. We focus only on he says of paiens who arrived a he hospial afer a hear-aack crisis. This sample includes people who were old by heir docor o go o he hospial because of a hear problem and hose who were ransferred from an emergency uni o a cardiac care uni. We leave aside says in emergency unis when paiens died or where sen back home. Indeed, he healh of paiens in emergency unis is usually no sabilized and hese paiens canno be cured wih he usual reamens which are risky and can cause brual deah. Before paiens arrive a he hospial or when hey jus ge in, hey may receive hrombolyic drugs. In he hospial, paiens can bene from various reamens and procedures. These include cardiac caheers (denoed as CATH hereafer), percuaneous ransluminal coronary angioplasy (PTCA), sen and bypass surgery. A caheer is a exible and hin pipe which is insalled in a vein o faciliae injecions and drips. I may also be used o clean areries o improve he blood ow. A bypass surgery reroue, or bypass, is a vein or arery colleced on he paien s body and se up o derive blood from coronary areries o avoid clogged secions. I allows o improve he blood ow and he oxygenaion of he hear. The angioplasy and he sen are some alernaives o he bypass o improve he blood ow in clogged areries. They are used when areries are oo clogged. An angioplasy consiss in in aing a balloon in a blockage o creae a channel. This procedure is cosly as i induces for one say an increase in coss which ranges from 30% o 60% (Dormon and Milcen, 2002). The sen is a spring-shaped proshesis which is used as a complemen o angioplasy. I is pu inside he balloon o keep he arery dilaed. The use of one or several sens wih an angioplasy signi canly improves he resuls. We are going o sudy he e ec of reamens over he period. Angioplasies and sens were some innovaive reamens around 1998 and have generalized such ha hey are used a wide scale in In 6

7 paricular, he use of angioplasy wih sen has increased from 15% in 1998 o 31% in In his aricle, he erm sen will refer o an angioplasy ogeher wih one or more sens, he erm angioplasy will refer o an angioplasy wihou sen, and he erm caheerism will refer o a caheerism wihou angioplasy and sen. 2.3 Spaial feaures We now propose a spaial overview of hear aack. Firs noe ha paiens who experience an AMI and wan o be reaed in a NFP or a public hospial usually have o go o a hospial wihin heir region of residence. However, some paiens are someimes ransferred o a neighbouring hospial in anoher region. Also, a paien who ges sick in anoher region may be cured here. Over he period, he proporion of AMI paiens reaed wihin heir region of residence is very high a 92:9%. This proporion is slighly lower for for-pro hospials (91:4%) han for public hospials (93:1%) and NFP (95:8%). Togeher wih he regional organizaion of healhcare, hese saicics suppor he fac ha regions can be viewed as local healhcare markes for hear aack. Depending on heir residenial locaion, paiens do no face he same supply of healhcare as he local composiion of hospials by saus and mode of reimbursmen varies widely across space. In 1999, he proporion of beds in public hospials is large in Franche-Comé (in he eas) where i reaches 80% and in he wes. By conras, i is only 46% in he PACA region (in he souhern French Riviera). The proporion of NFP is he highes in some easern regions a he German border (Alsace and Lorraine) for hisorical reasons. Conversely, he proporion of beds in for-pro hospials is larger in he French Riviera where he populaion is older and richer. The local ownership composiion of bed capaciies is closely relaed o he local ownership composiion of hospials where AMI paiens are reaed. Graph 1 shows ha around Paris and in souhern regions, he proporion of paiens reaed in a for-pro hospial is higher. These regions ofen provide more innovaive reamens han he ohers, like sens as shown in Graph 2. In fac, he rank correlaion beween he proporions of sens and AMI paiens in for-pro hospials is :61. When considering NFP hospials insead of for-pro hospials, he correlaion is sill quie high a :44. [Inser Graphs 1 and 2] 7

8 We also conruced he probabiliy o die wihin 15 days (see Graph 3). 2 This probabiliy is quie low in he Paris region, he eas and souh-eas. I is larger in he wes and souh-wes. There is no obvious relaionship beween he probabiliy o die and he proporions of sens or for-pro hospials (rank correlaions: :09 and :14 respecively). However, souh easern regions which have a large proporion of for-pro hospials performing innovaive reamens also concenrae older people who are more likely o die. Hence, i is necessary o perform an economeric analysis o disenangle he e ec of age and more generally from individual aribues (demographic characerisics and secondary diagnosis) from ha of hospial composiion and reamens. [Inser Graph 3] 3 The daase 3.1 Daa sources on paiens, hospials and areas For our sudy, he primary daase is he PMSI (Programme de Médicalisaion des Sysèmes d Informaion). This daase provides he records of all paiens discharged from any French acue-care hospial over he period. I is compulsory for hospials o provide hese records on a yearly basis. 3 Three nice feaures of his daase are ha i provides some informaion a he paien level, i keeps rack of hospials across ime, and i is exhausive boh for he public and privae secors. 4 A limi of he daa is ha paiens canno be followed across ime if hey come back again laer in he same hospial or if hey change hospial. The daase conains some basic informaion on demographic characerisics of paiens (age and sex), as well as some very deailed informaion on diagnoses and reamens. In our analysis, we can hus ake ino accoun all secondary coronary diagnoses as well as all echnics used o cure paiens. The daase also provides us wih he ype of enry (wheher he paiens come from heir residence, anoher care service in he same hospial or anoher hospial) as well as he ype of exi (deah, home reurn, ransfer o anoher hospial or ransfer o anoher care service). 2 See below for more deails on how his probabiliy was compued. 3 An excepion is local hospials for which i is no compulsory. This does no a ec our sudy since hese hospials do no ake care of AMI paiens. 4 I should be menioned however ha only 90% of he privae secor was covered in 1998 and 95% in

9 We only keep paiens whose pahology was coded as an acue myocardial infarcion in he enh inernaional code of disease (ICD-10-CM), i.e. he paiens for which he code was I21 or I22. Before 35, hear aacks are ofen relaed o a hear disfuncion. As a consequence, we resrain our aenion o he paiens more han 35 following hus he OMS de niion. Afer deleing observaions wih missing values for he variables used in our sudy (which are only a very few), we end up wih 421; 185 says (in 1; 130 hospials) over he period. We mach our daase wih he hospial records from he SAE survey (Saisiques Annuelles des Eablissemens de sané) ha was conduced every year over he period. The SAE survey conains some informaion on he municipaliy where each hospial is locaed, he number of beds (in surgery and in oal) and he number of days ha beds are occupied (in surgery and in oal). The maching rae is very good and reaches 97% of he says (which corresponds o 408; 592 says in 1; 084 hospials). The municipaliy code in he SAE survey also allowed us o mach our daase wih some variables a he municipaliy level coming from oher sources. These variables will be used in our esimaions as proxies o conrol for he municipaliy averages of individual unobserved socio-economic characerisics. Indeed, he lieraure has shown ha here can be some large socio-economic dispariies in healh oucomes (see for insance Lindeboom and van Doorslear, 2004; Eilé and Milcen, 2006). Our municipaliy variables include he municipal unemploymen rae compued from he 1999 populaion census, he median household income from he 2000 Income Tax daase and he exisence of a poor area in he municipaliy (poor areas being de ned by a 1997 law). These indicaors should (a leas parially) capure some spaial di erences in lifesyle ha can have an impac on he healh of paiens and heir propensiy o die from AMI. Also, hanks o he municipaliy code, we could idenify he urban area in which hospials are locaed. 5 We compued he local numbers of beds as a measure of he ineracions beween hospials wihin a given urban area. This variable also capures congesion e ecs and we will be able o esimae only he e ec of ineracions ne of congesion. We also compued a regional Her ndahl index a he urban area level using he number of paiens in hospials wihin each urban area. The Her ndahl index measures for a given urban area o wha exen paiens are equi-disribued beween hospials or 5 An urban area is de ned as an urban cener (wih more han 5,000 jobs) and he municipaliies in is cachmen area. There are 359 urban areas in mainland France and hey do no cover he whole erriory (as some municipaliies are excluded and remain rural). 9

10 concenraed wihin a few hospials. 6 When consrucing urban area variables, we were confroned wih a few hospials in municipaliies which do no belong o any areas or o several of hem. We hus inroduced some dummies for hese wo cases as conrols. As we will use hospial variables which should be ime-invarian in our analysis (see Secion 4 and 5), all hospial and geographic variables are averaged across years. There are 406; 197 says (in 1; 080 hospials) for which we have all he informaion on hospial and geographic variables. We do no have any informaion on wha happpened o ransferred paiens before heir ransfer. In paricular, we do no know how hey were reaed and how long hey have already sayed in a hospial. As a consequence, we resric our aenion o paiens who come from heir place of residence. We end up wih 341; 861 says (in 1; 105 hospials) for which all he informaion is available on paien variables (and 331; 246 says in 1; 060 hospials for which all he informaion is available on hospial and geographic variables). 3.2 Preliminary saisics For each hospial, we hen compued a gross survival funcion for exi o deah using he Kaplan- Meier esimaor. This esimaor reas oher exis (home reurn and ransfers) as censored. As we are mosly ineresed in hospial dispariies across regions, we compued he average survival funcion by region. 7 Observaions were weighed by he number of paiens sill a risk in he hospials. 8 We seleced he region wih he highes survival funcion (Alsace), he region wih he 6 The Her ndahl index for an urban area u is H u = X j2u pj p u 2 where j indices he hospials, pj is he number of paiens in hospial j, and p u = X j2up j is he oal number of paiens wihin he urban area u. H u increases from 1 N u o 1 as he concenraion of paiens increases, where N u is he number of hospials in he urban area u. Wen H u = 1 N u, he paiens are equi-disribued beween he N u hospials. When H u = 1, hey are all reaed wihin one hospial. 7 We could have direcly compued a survival funcion for each region. However, we believe ha he relevan uni a which he reamen of paiens akes place is he hospial. Also, our approach a he hospial level parallels he resuls obained for he model presened in Secion 5. 8 When he lengh of say increases, he number of paiens in a given hospial decreases. Above a given lengh of say afer which here is no paien a risk anymore, i is no possible o esimae he survival funcion. We hen arbirary considered ha he hospial survival funcions remained consan afer his lengh of say. When we compue he average survival funcions by region, his assumpion does no have much e ec for shor/medium lengh of says. Indeed, only small hospials do no have any paiens a risk anymore for hese lenghs of says. As a consequence, we compued our descripive saisics only for says below feen days o minimize he e ec 10

11 lowes survival funcion (Languedoc-Roussillon), and he Ile-de-France region ha corresponds mosly o he Greaer Paris Area and is he mos densely populaed. Graph 4 represens he survival funcions of hese hree regions as well as heir con dence inervals (Graph A2 in appendix represens he survival funcions for all he regions and Table A1 ranks he regions according o heir probabiliy o die wihin 15 days). I shows ha he average survival funcions of any wo regions are signi canly di eren. [Inser Graph 4] Table 1 repors some dispariy indices beween regions in he probabiliy o die wihin 1, 5, 10 and 15 days (de ned as one minus he Kaplan-Meier). These indices are he max/min raio, he Gini index and he coe cien of variaion. The Gini indices and he coe ciens of variaion are compued in wo sages. Firs, we compue he average of a given individual variable (for insance, a deah dummy) by region. Then, we compue he regional dispariy indices for he resuling variable (in our example, he share of deahs in he region), weighing he observaions by he number of paiens in he region. The max/min raio shows ha regional dispariies are signi can. Indeed, he di erence in he probabiliy o die wihin 15 days beween he Maximum (Languedoc-Roussillon) and he Minimum (Alsace) is 80%. However, more global indices like he Gini index (0:07) and he coe cien of variaion (:218) remain quie small and sugges ha dispariies are no sysemaic. Ineresingly, dispariies are a bi larger for he probabiliy of deah wihin 1 day (Max/Min raio of 94%). This may be due o di eren behaviours across regions in ransfers and home reurns a early days of AMI. The regional dispariies may be explained wih some spaial dispariies in demand facors (demographic shifers and secondary diagnosis) or in supply facors (reamens, characerisics of hospials and local healhcare marke srucure). The purpose of he paper is o disenangle hese wo ypes of e ecs. Poenial candidaes are buil from paien and hospial variables aggregaed a he regional level. We now presen some regional dispariy indices for hese candidaes. We mosly commen he resuls obained for he Gini indices as hey are global measures of dispariies and hey are no sensiive o he level of magniude as he max/min raio (alernaively, we could also commen he resuls obained wih he coe ciens of variaion which are similar). In he sequel, we will say o ease he presenaion ha dispariies are small when he index is inferior o :1, hey are moderae for an index from :1 o :2, hey are large for an index from :2 o :3, and hey are very large for an index above :3. of our assumpion. 11

12 We rs consider variables relaed o paiens which were averaged a he regional level. We nd ha here are signi can dispariies across regions for some demographic variables: more speci cally he Gini index is moderae for females aged (:12) and males who are more han 85 (:11). For diagnoses, dispariies are ofen moderae or large, he Gini index reaching :23 for surgical French DRGs (.23), :15 for he severiy index and :13 for a hisory of vascular diseases and for sroke. Noe ha he Gini index is mos ofen moderae for diagnoses relaed o speci c behaviours before he hear aack such as obesiy (:17), excessive smoking (:16), and alcohol problems (:14). I is smaller for diabees (:08). For reamens, dispariies are ofen large or very large. The Gini index reaches goes up o :53 for dilaaions oher han PTCA and :37 for he cabbage or coronary bypass surgery. These wo high dispariy indices are no surprising as he relaed reamens are (very) seldomly applied. More usual reamens like angioplasy and sen sill have a large Gini index which akes he value :28 and :21, respecively. Dispariies are far smaller for he caheer which is a more widespread reamen (:10). Overall, he Gini indices show ha poenial explanaions of dispariies in he propensiy o die can be relaed o he hree ypes of variables: demographic characerisics, diagnoses and reamens. Our economeric analysis will deermine which ype of explanaion has he larges explanaory power. [Inser T able 1] We hen compued regional dispariy indices for he hospial and geographic variables used in our regressions. Whereas hospial variables measure capaciies and saus (public, for-pro and NFP), geographic variables are mean o capure scale economies and local ineracions. For a given variable, we consruced is regional average, weighing he observaions by he number of paiens in he hospials. The resuling regional average is hen used o compue dispariy indices a he regional level. Resuls are repored in Table 2. As previously, we only commen Gini indices. We begin wih hospial variables. There are large dispariies across regions in he average size of hospials measured by he oal number of paiens (:23) or he number of AMI paiens (0:27). Dispariies are even larger for he number of beds (:49) and he number of beds in surgery (:47). There dispariies poin ou a some soring of hospials according o heir size. Finally, dispariies are smaller bu sill large for he hospial saus and more speci cally for being a for-pro hospials (:24). We now commen he resuls for geographic variables. We observe some very large dispariies in he number of beds in in he urban area (Gini index :66). Disparies are also signi can for 12

13 he Her ndhal index compued a he urban area level (:20). Finally, regional dispariies in municipaliy variables used as proxies for unobserved demand facors are a bes moderae, he Gini index reaching :17 for he presence of a poor area in he municipaliy. [Inser T able 2] Overall, demand and supply facors boh consiue poenial candidae o explain he regional dispariies in moraliy. We now presen our empirical mehodology o disenangle heir e ecs. 4 Economeric mehod We rs give a brief descripion of he economeric model before urning o a more formal presenaion of our approach. Even if we are ineresed in sudying di erences in moraliy across regions, we build our model around hospial unis. Indeed, hospials have some speci c behaviour and e ciency which should be properly accouned for o avoid misspeci caion biases. Hence, we use a Cox duraion model a he paien level srai ed by hospial. This model conains some paien-speci c explanaory variables (demographic shifers, diagnoses and reamens), as well as a speci c survival funcion for each hospial which is lef unspeci ed. Ridder and Tunali (1999) explain how o esimae his model using he srai ed parial likelihood esimaor (SPLE) and esablish he heoreical properies of he esimaors. Lindeboom and Kerkhofs (2000) apply heir mehodology o quanify he e ec of school on job sickness of eachers and Gobillon, Magnac and Selod (2007) use i o analyze he e ec of locaion on nding a job in he Paris region. This mehodology is more general han he ones usually used in he healh lieraure on moraliy which ake ino accoun he hospial unobserved heerogeneiy a bes wih hospial xed e ecs (Milcen, 2005). I can be applied even when he sample size and he number of hospials are large as in our case, whereas i is no even compuaionally possible o esimae direcly some hospial xed e ecs. Afer esimaing he hospial survival funcions, we average hem a he regional level o sudy he regional dispariies in moraliy ne of he e ec of paien-speci c variables. We hen link he remaining regional dispariies o some local di erences in hospial and geographic characerisics. For ha purpose, we make he addiional assumpion ha he hospial hazards wrie muliplicaively as he produc of a hospial xed e ec and a baseline hazard. We show how o esimae he hospial xed e ecs using empirical momen condiions. We hen explain hese xed e ecs wih hospial and geographic variables and nally average he model a he regional 13

14 level o perform a regional variance analysis. 9 We now presen our approach more formally. For each paien, we observe he lengh of say in he hospial and he ype of exi (deah, home reurn or ransfer). In he sequel, we only sudy exi o deah. All oher exis are reaed as censored. We specify he hasard funcion of a paien i in a hospial j (i) as: ( jx i ; j (i)) = j(i) () exp (X i ) (1) where j () is he insananeous hazard funcion for hospial j, X i are he paien-speci c explanaory variables and are heir e ec on deah. Insofar, he hospial hazards are lef compleely unspeci ed and allow for a very general sudy of regional dispariies in deah using regional averages. Also, his semi-parameric approach avoids biases on he esimaor of coe ciens which could arise from a misspeci caion of he hospial hazards. The model is esimaed by srai ed parial maximum likelihood. The conribuion o likelihood of a paien i who dies afer a duraion i is his probabiliy o die condiionally on someone a risk in his hospial dying afer his duraion. I wries: exp (X i ) P i = X (2) exp (X i ) i2 j(i) ( i ) where j ( i ) is he se of paiens a risk a day i in hospial j, i.e. he se of paiens ha are sill in hospial j afer saying here for i days. The parial likelihood o be maximized hen wries: L = P i. Denoe, b he esimaed coe ciens of paien-speci c explanaory variables. I i is possible o compue he inegraed hazard funcion j () of any hospial j using he Breslow (1974) s esimaor. I wries: b j () = Z 0 I (N j (s) > 0) X dn j (s) (3) exp X i b i2 j (s) where I () is he indicaor funcion, N j (s) = card j (s), and dn j (s) is he number of paiens exiing from hospial j beween he days s and s + 1. From he Breslow s esimaor, we compue a survival funcion for each hospial j as exp( j b ()) (an esimaor of is sandard error is recovered 9 A emping alernaive approach is o esimae all he coe ciens in one sage only inroducing all he paien, hospial and geographic variables in a simple Cox model. However, such an approach does no ake ino accoun he hospial unobserved heerogeneiy. Consequenly, sandard errors of he coe ciens may be highly biased (see Moulon, 1990). Our approach properly accouns for his issue. 14

15 using he dela mehod). The hospial survival funcions will be averaged a he regional level o sudy regional dispariies in moraliy afer any number of days. We hen sudy he deerminans of hospial dispariies by specifying he hospial hazard raes in a muliplicaive way: j () = j () (4) where j is a hospial xed e ec and () is a baseline hazard common o all hospials. We show in appendix how o esimae he parameers using empirical momens derived from (4). 10 ha we need an idenifying resricion since j and () can be ideni ed separaely only up o a P 1 muliplicaive consan. We impose for convenience ha: N N () = 1 where N is he number of paiens sill a risk a he beginning of day and N = P appendix), we ge: () = j = 1 X N j N N 2 j () j; 1 X N N j j ()! 1! 1 1 N Noe N. Afer some calculaions (see! X N j j () j! 1 X N N j j j () where N j is he number of paiens a risk a ime in hospial j, N j = P N j, and he sum on, P, goes from = 1 o = T (here, we x T = 30 for convenience). I is possible o obain some esimaors of () and j replacing j () by he esimaor b j () = b j () b j ( 1) in he righhand side of equaions (5) and (6). These esimaors are denoed b () and b j. We show in appendix 10 In doing so, we depar from he log-linear esimaion mehod proposed by Gobillon, Magnac and Selod (2007). Our approach is more adequae when exis are scarce as in our case. Indeed, Gobillon, Magnac and Z k Selod spli he imeline ino K inervals denoed [ k 1 ; k ]. Inroduce k = () d= ( k k 1 ) and y jk = k 1 [ j ( k ) j ( k 1 )] = ( k k 1 ). Inegraing (4) over each inerval and aking h he log, hey ge: ln y jk = ln j + ln k. y jk is no observed bu can be replaced wih a consisen esimaor: by jk = bj ( k ) j b ( k 1 )i = ( k k 1 ). The equaion o esimae is hen: ln by jk = ln j + ln k + jk where jk = ln by jk (5) (6) ln y jk is he sampling error. This equaion can be esimaed wih sandard linear panel mehods. The auhors use weighed leas square where he weighs are he number of individuals a risk a he beginning of he inerval. A limi of his mehod is ha ln y jk can be replaced by is esimaor ln by jk only if by jk 6= 0. When i is no he case, observaions should be dropped from he sample. When implemening his approach o our case, his could be an issue as exis are scarce and a signi can number of observaions should be dropped when he ime spen in he hospials ges large. In pracice however, he resuls obained wih he wo approaches are quie similar. 15

16 how o compue he covariance marices of b 0 = b (1) ; :::; b (T ) and b = (b 1 ; :::; b J ) 0. We hen ry o explain he hospial xed e ecs wih some hospial and geographic variables denoed Z j. We specify: j = exp Z j + j where are he coe ciens of hospial and geographic variables, and j includes some unobserved hospial and geographic e ecs. For a given hospial j, aking he log and replacing he hospial xed e ec wih is esimaor, we ge: where j = ln b j ln b j = Z j + j + j (7) ln j is he sampling error on he hospial xed e ec. Equaion (7) can be esimaed using weighed leas squares where he weigh is he number of paiens in he hospials. Gobillon, Magnac and Selod (2007) explain how o compue he sandard errors and propose a R-square formula which accouns for he sampling error. We use heir formulas in our empirical applicaion. Noe ha for a given hospial, equaion (7) is well de ned only when here is a leas one paien dying in he hospial over he period (oherwise he quaniy b j from which we ake he log would be zero). This condiion may no be veri ed for hospials ha have only a few paiens. In fac, hese hospials have a negligible weigh and hey are dropped from our sample. We nally average equaion (7) a he regional level and conduc a variance analysis for he resuling equaion. 5 Resuls Table 3 repors he esimaion resuls of he rs-sage equaion (1). The demographic characerisics have he usual e ec on he propensiy o die. Females are more likely o die han males. This is consisen wih care being more proecive for males han for females possibly because of biological di erences like he smaller arge vessel size and he increased vessel oruosiy of females (Milcen e al., 2007). However, he gender di erence is signi can only a younger ages (beween 35 and 55 year old). Also, he propensiy o die increases wih age. The severiy index is found o have a posiive e ec on he propensiy o die. Inuiively, one also expecs secondary diagnoses o have a posiive e ec as hey deeriorae healh. This is rue empirically for renal failure, sroke, hear failure, conducion disease, alcohol. Oher secondary diagnosis have a more surprising negaive e ec: diabees, obesiy, excessive smoking, vascular disease, peripheral arerial disease, previous coronary arery disease, hyperension. These resuls may be explained by prevenive healh care. Indeed, hese secondary diagnoses may poin ou a 16

17 paiens who have been moniored more carefully before and afer having a hear aack (Milcen, 2005). All reamens have he expeced negaive e ec on he propensiy o die: CABG, caheerism, PTCA, oher dilaaion and sen. The sen, which is he mos innovaive procedure, has he sronges negaive e ec. Afer conrolling for hese reamens, he DRG index capuring he heaviness of surgical procedures has a posiive e e on he propensiy o die. This can re ec he increased chances o die because of more cumbersome and risky surgery. [Inser T able 3] From he esimaed coe ciens, b we consruced an inegraed hazard for each hospial using he Breslow s esimaor and averaged he corresponding hospial survival funcions by region (weighing by he number of paiens a risk in he hospials). 11 Regions a exremes are he same as when sudying he raw daa: Alsace (a he German border) usually exhibis he highes survival funcion and Languedoc-Roussillon (in he Souh-Eas) he lowes. Graph 5 represens he survival funcions (as well as heir con dence inervals) for hese wo exremes and for Ilede-France (he Paris region). 12 The di erence beween he exreme regions are smaller bu sill signi can. [Inser Graph 5] We quanify he regional dispariies wih he same indices as in he descripive secion 3.2 for he probabiliy o die wihin 1, 5, 10 and 15 days (de ned as one minus he survival funcion of he model). Resuls repored in Table 4 show ha he di erence in he probabiliy o die wihin 15 days beween he exreme regions has decreased from 80% o 47% (his corresponds o a 41% 11 This kind of aggregaion is quie common in he labour lieraure. For insance, Abowd, Kramarz and Margolis (1999) esimae a wage equaion ha includes some rm xed e ecs. They hen compue some indusry xed e ecs as he averages of he esimaed rm xed e ecs for rms belonging o each indusry (weighing he observaions by he number of workers in he rms). 12 Graph A3 in appendix represens he survival funcions for all he regions and Table A2 ranks he regions according o survival afer 15 days. Curves obained wih he model are no sricly comparable wih hose obained from raw daa wih he Kaplan-Meier esimaor as insananeous hospial hazards were normalized wih an ad-hoc rule. To ge close o comparabiliy, we muliplied insananeous hospial hazards by a consan which was chosen such ha in absence of hospial heerogeneiy (i.e. j () = () for all ), he expeced inegraed hazard a day 1 is equal o he expeced inegraed hazard obained from he raw daa (de ned as minus he logarihm of he Kaplan-Meier esimaor). This normalizaion allows o obain an average survival funcion of he same magniude as he one obained from raw daa wih he Kaplan-Meier esimaor. 17

18 decrease). More sysemaic dispariy indices like he coe cien of variaion and he Gini index also decrease, bu o a lesser exen (by 19% and 17%, respecively). In a variance-analysis spiri, we de ned a pseudo-r 2 as one minus he raio beween he variance in he probabiliy o die wihin a given number of days compued from he model and he variance compued from raw daa. A 1 and 5 days, he pseudo-r 2 is nearly 60%. Hence, explanaory variables would explain more han half of he regional dispariies in early deah. However, i is lower a 10 days (48%), and decreases even more o reach 40% a 15 days. This suggess ha par of he early regional dispariies may be due o di eren imings of deah evens across regions. Also, here may be some speci c regional behaviours for ransfers and home reurns which would a ec he local composiion of paiens and hence would have an impac on he di erence beween he hospial survival funcions obained from he model and from he Kaplan-Meier esimaors. Ineresingly, he ranking of regions obained for deah wihin 15 days is no ha di eren from he one obained from he raw daa (unweighed rank correlaion: :70). This means ha conrolling for individual variables does no change much he ranking of regions. [Inser T able 4] We hen supposed ha each insananeous hospial hazard wries muliplicaively as he produc of a hospial xed e ec and a baseline hazard. The parameers of he muliplicaive model are esimaed using empirical momens as explained in he previous secion. Graph 6 displays he baseline hazard and he con dence inerval a each day. Remember ha he weighed average of he insananeous baseline hazards is normalized o zero. We obain ha he baseline hazard decreases sharply in he rs wo days and hen more smoohly unil he eighh day. I remains consan aferward. The sharp decrease jus afer enry in he hospial can be explained by violen deahs ha are quie common in early days of hear aack. [Inser Graph 6] We hen regress he hospial xed e ecs on a se of hospial and geographic variables. Resuls are repored in Table 5 (esimaed regional dummies corresponding o he speci caion of column 3 are repored in Appendix A3). When we only inroduce hospial variables (column 1), he adjused-r 2 is quie low a 0: I is larger a 0:23 when only geographic variables ener he speci caion 13 This adjused-r 2 accouns for he sampling error and is formula is given in Gobillon, Magnac and Selod (2007). 18

19 (column 2). Ineresingly, when inroducing boh groups of variables (column 3), he R 2 a 0:28 is below he sum of R 2 of he wo separae regessions (0:36), which suggess ha variables are quie correlaed. Also, i is higher han he R 2 of each separae regression, which suggess ha each of he wo groups has some explanaory power of is own. We now commen he sign of he esimaed coe ciens for he full speci caion (column 3). We nd ha he propensiy o die is nearly he same in for-pro hospials and public hospials. This resul may look surprising bu i comes from he fac ha we conrol for innovaive reamens (mainly angioplasy and sen). If we drop he variables relaed o innovaive reamens from he rs-sage speci caion, he propensiy o die in public hospials becomes higher han in for-pro hospials (see Table A3 in appendix). Hence, he higher e ciency of for-pro hospials would come from a wider use of innovaive reamens. We also nd ha he propensiy o die in a NFP hospial is lower han in public or for-pro hospials. The proporion of paiens in he hospial reaed for an AMI has a negaive and signi can e ec. I is possible ha hospials concenraing AMI paiens are specialized in hear-relaed pahologies and hus have a higher e ciency. The number of beds as well as heir occupaion rae have no e ec on moraliy. The propensiy o die is lower in hospials wih a higher proporion of beds in surgery (wheher conrolling for innovaive reamens or no). In fac, hospials wih a high proporion of beds in surgery could be specialized in serious diseases and have a higher qualiy sa. The propensiy o die also decreases wih he occupaion rae of beds in surgery (signi canly a 10% only). I is possible ha hospials wih a high occupaion rae are also hose which are he more e cien and he more likely o arac paiens. Among municipal variables, he presence of a poor area has a posiive e ec (signi can a 10%) on he propensiy o die, whereas he median income and he unemploymen rae have no signi can e ec. The posiive e ec of he presence of a poor area can be explained wih a deerioed healh of local people (he general healh saus being no capured wih diagnoses variables). The number of beds in he urban area has a posiive signi can e ec which urns ou o be negaive bu no signi can when innovaive reamens are no conrolled for. An inerpreaion can be ha larger markes propose more innovaive reamens bu also yield more congesion. These wo e ecs would compensae bu afer conrolling for he innovaive reamens, only he congesion e ecs would remain. The Her ndahl index for he number of paiens across hospials compued a he urban area level has a signi can negaive e ec. This resul suggess ha he fewer he hospials in which paiens are concenraed, he lower he propensiy o die. 19

20 Finally, regional dummies always have a negaive e ec compared o he reference (Languedoc- Roussillon) and heir e ec is mos ofen signi can. Di erences may be explained by unobserved regional facors such as he regional di erences in he propensiy o ransfer paiens when hey are likely o die. Indeed, recall ha we work only on paiens who come from heir place of residence and no from a ransfer. Noe ha sandard errors are quie large and wo regions should be far enough in he disribuion of regional e ecs for he di eren beween heir e ecs o be signi can. The ranking of regional e ecs is nearly uncorrelaed wih he probabiliy o die wihin 15 days obained from raw daa (unweighed rank correlaion: :02) and wih ha obained from he model (unweighed rank correlaion: :11). [Inser T able 5] We now perform a variance analysis a he regional level. Taking he logarihm of equaion (1) under he muliplicaive assumpion (4), and compuing he average for any region r gives: 1 X ln ( jx i ; j (i)) = X r + ln r + () N r ijj(i)2r where N r is he number of paiens in region r, X r is he regional average of individual explanaory variables and ln r is he regional average of hospial xed e ecs weighed by he number of paiens in he hospials. I is possible o qualiaively assess he relaive explanaory power of righ-hand side erms compuing heir variance and heir correlaion wih he lef-hand side erm (see Abowd, Kramarz and Margolis, 1999). In fac, he larger he variance and he correlaion, he higher he explanaory power. In pracice, as and ln r are no observed, we use heir esimaors b and d ln r (he laer being de ned as he weighed average of [ln j ) o compue he righ-hande side erms. An esimaor of he lef-hand side erm is obained from he sum of righ-hand side erms. Using he same approach, we also assess he explanaory power of X r s b for some sub-groups X r s of explanaory variables. Imporanly, noe ha his procedure measures he explanaory power ex ane before any lering process of paiens hrough ranfers or home reurns. We can furher assess he explanaory power of hospial and geographic variables. Taking he log of he expression of hospial xed e ecs and averaging a he regional level, we ge: ln r = Z r + r where Z r and r are he regional averages of explanaory variables and random erms, respecively. We can assess he explanaory power of Z r and Z r s, for some sub-groups Z r s of explanaory variables, in he same way as for individual variables (replacing by is esimaor). 20

21 We nd ha individual variables have a far larger power han hospial e ecs in explaining regional dispariies in moraliy (see Table 6a). Indeed, heir variance is ve o six imes larger. Ineresingly, among he individual variables, i is he innovaive reamens which have he larges explanaory power. This means ha regional dispariies in innovaive reamens are a key facor in explaining regional dispariies in moraliy. This has some imporan consequences for he regional funding of innovaive equipmens. Of course, he age-and-sex regional composiion also plays a role. Ineresingly, he hospial and geographic e ecs have a larger variance han he composiion e ecs, which suggess ha heir role in explaining regional dispariies is signi can. Noe ha he sum of variances for groups of individual variables is far smaller han heir sum. This comes from fairly large correlaions beween groups. In paricular, regions where paiens are aged and mosly females are also hose in which more innovaive reamens are performed (correlaion beween he demographic e ecs and he e ec of innovaive reamens: :57). When rying o explain regional dispariies in hospial xed e ecs, we nd ha hospial variables do no have much explanaory power (Table 6b). In paricular, he local composiion of ownership saus does no play much. By conras, geographic variables have a large explanaory power. The local size of he marke (measured by he local number of beds) and he local concenraion of paiens play a signi can role. 14 This is no he case of municipaliy variables. Finally, residual local e ecs capured by regional dummies have a large variance. This means ha some regional unobserved facors have a large e ec on regional dispariies in AMI deah. [Inser T able 6a and 6b] (8) 6 Conclusion In his paper, we sudied he regional dispariies in moraliy for paiens admied in hospials for a hear aack. This was done using a unique mached paiens-hospials daase over he period consruced from exhausive adminisraive records. For paiens, his daase conains some informaion on demographic characerics (sex and age), diagnoses and reamens. For hospials, i gives some deails on he locaion, he saus, he mode of reimbursmen and he 14 Noe ha he local size of he marke and he local concenraion of paiens have an e ec ha is posiively correlaed wih hospial xed e ecs. However, heir correlaion wih he overall inegraed hazard (las column in Table 6b) is negaive. This is because hese e ecs are more han compensaed by regional xed e ecs and he e ecs of innovaive reamens. 21

22 capaciy. We showed ha regional dispariies are fairly large. The di erence in he propensiy o die beween he exreme regions reaches 80%. We analyzed he causes of hese dispariies using a Cox duraion model srai ed by hospials. This model allows for a speci c hospial baseline hazard and conrols for individual observed heerogeneiy. Hence, i capures di erences in hospial behaviours when reaing he paiens. The survival funcions of hospials were averaged a he regional level o assess wheher here are sill some regional dispariies afer individual variables have been conrolled for. Regional dispariies decrease bu remain signi can: he di erence in he propensiy o die beween he exreme regions is sill 47%. Ineresingly, he exen o which paiens are reaed wih innovaive procedures a he regional level plays a major role in he decrease of he dispariies. We hen assessed o wha exen he remaining regional dispariies could be explained wih he local composiion of hospials and geographic e ecs. This was done regressing hospial hazards on hospial and geographic variables, and averaging he model a he regional level. We found ha once reamens have been conrolled for, hospial variables do no play much. By conras, geographic variables, and in paricular he local concenraion of paiens, play a signi can role. The more paiens are concenraed in a few large hospials raher han many small ones, he lower he moraliy. Afer hospial and geographic variables have been conrolled for, some signi can regional dispariies sill remain. The scope of our analysis is limied because paiens were no racked in he daa when hey were ransferred o anoher hospial. For paiens who were ransferred, we had o consider ha he lengh of say was censored. An ineresing exension of our work would be o sudy he sraegic behaviour of hospials when ransferring paiens. Indeed, some hospials may ry o minimize heir moraliy rae by ransferring he paiens who are he mos likely o die even when hey are well equipped and can conduc some innovaive reamens. Ohers, like local hospials, may ry o increase he propensiy o survive of some paiens by sending hen o more e cien esablishmens. I should be possible o conduc such an analysis in he fuure when daa racking paiens (which exis) will be made available for research. 22

23 7 Appendix: second-sage esimaion In his appendix, we explain how o consruc some esimaors of he baseline hazard and hospial xed e ecs. We rs average equaion (4) across ime, weighing he observaions by he number of paiens a risk a each dae. We obain: 1 X 1 X N j () = j N () N N where N is he number of paiens a risk a he beginning of period, N = P N wih P he sum from 1 o T days (wih T = 30 in he applicaion). A naural idenifying resricion is ha P 1 he average of insananeous hazards equals one: N N () = 1. We obain: j = 1 X N j () (9) N I is possible o consruc an esimaor of hospial xed e ecs from his formula, bu weighs (namely: N ) are no hospial-speci c and hus do no re ec hospial speci ciies. Hence, we propose anoher esimaor of hospial xed e ecs in he sequel which we believe beer capure hospial speci ciies. We also average equaion (4) across hospials, weighing by he number of paiens a risk (summed across all daes) in each hospial. We ge: P 1 N 2 j; 1 N 1 N X N j j () = 1 N j! X N j j () where N j = P N j wih N j he number of paiens a risk in hospial j a he beginning of dae (such ha N = P N j ). Replacing j wih is expression (9), we obain: () = j! 1! P N j N j () N j j (). An esimaor of he hazard rae a dae in hospial j j can be consruced from he Breslow s esimaor such ha b j () = b j () b j ( 1). A naural esimaor of he baseline hazard is hen: b 1 X () = N j N N 2 b j () j; j! 1 1 N! X N j b j () We hen consruc an esimaor of a given hospial xed e ec j averaging equaion (4) across ime for his hospial and weighing by he number of paiens a risk a he beginning of each j 23

24 day in his hospial. We obain: An esimaor of he hospial xed e ec is hen: b j = 1 X 1 X N N j j j () = j N N j j ()! 1 1 X N N j j b ()! 1 X N N j j b j () (10) We also compued he asympoic variances of b = b (1) ; :::; b (T ) 0 and b = (b1 ; :::; b J ) 0, denoed V e V, wih he dela mehod. Indeed, he covariance marix of b J = b1 (1) ; :::; b J (T ) 0 can be esimaed from Ridder e Tunali (1999). Is esimaor is denoed V b J. We can hen compue he esimaors: V = b b b 0 b and V = 0 b 0 b. The b b are given J b b k b k () = = NN k P N j N b j () 1 f=g j; N k P 1 N j; b fk=jg () b j NN k N X " # 2 N j b () (11) P N j j N b j () j; P N b b k () P (12) N j; b () In pracice, o simplify he compuaions, we negleced he second erm on he righ-hand side of (12). This is only a sligh approximaion ha does no have much impac on he esimaed variance of b j. I amouns o neglec in (10) he variaions of 1 erms b j () compared o he variaions of 1 is supposed o be non-random in (10). N j P N j P N j b () wih respec o he N j b j () which is far larger. Pu di erenly, b () References [1] Abowd M., Kramarz F. and D. N. Margolis (1999), High wage workers and high wage rms, Economerica, 67(2), pp [2] Combes PPh., Duranon G. and L. Gobillon (2008), Spaial Wage Dispariies: Soring Maers, Journal of Urban Economics, 63, pp

25 [3] Culer D.M. and J.R. Horwiz (1998), Convering Hospials from No-for-Pro o For-Pro Saes: Why and Wha E ecs?, NBER Working Paper no [4] Dormon B. and C. Milcen (2002), Quelle régulaion pour les hôpiaux publics français?, Revue d Economie Poliique, 17(2). [5] Dormon B. and C. Milcen (2006), Innovaion di usion under budge consrain. Microeconomeric evidence on hear aack in France, The Annals of Economics and Saisics. [6] Duranon G. and V. Monasiriois (2004), Mind he Gaps: The Evoluion of Regional Inequaliies in he U.K , 42(2), pp [7] Eilé F. and C. Milcen (2006) Income-relaed reporing heerogeneiy in self-assessed healh: evidence from France, Healh Economics, 15(9), pp [8] Geweke J., Gowrisankaran G. and R. Town (2003), Bayesian Inference For Hospial Qualiy in a Selecion Model, Economerica, 71, pp [9] Gobillon L., Magnac T. and H. Selod (2007), The e ec of locaion on nding a job in he Greaer Paris Area, CEPR Working Paper no [10] Gowrisankaran G. and R. Town (2002), Compeiion, Payers, and Hospial Qualiy, NBER Working Paper no [11] Hansman H.B. (1996), The ownership of Enerprise, Cambridge, Havard Universiy Press. [12] Ho V. and B. Hamilon (2000), Hospial mergers and acquisiions: Does marke consolidaion harm paiens?, Journal of Healh Economics, 19(5), pp [13] Idler E.L. and Y. Benyamini (1997), Self-raed healh and moraliy: a review of wenyseven communiy sudies, Journal of Healh and Social Behavior, 38, pp [14] Jollis J., Peerson E., DeLong E., Mark D., Collins S., Muhlbaier L. and D. Prior (1994), The Relaion beween he Volume of Coronary Angioplasy Procedures a Hospials Treaing Medicare Bene ciaries and Shor-Term Moraliy, The New England Journal of Medicine, 24(331), pp [15] Kessler D. and M. McClellan (2002), The e ecs of hospial ownership on medical produciviy, RAND Journal of Economics, 33(3), pp

26 [16] Lindeboom M. and M. Kerkhofs (2000), Mulisae Models for Clusered Duraion Daa - an Applicaion o Workplace E ecs on Individual Sickness Abseneeism, The Review of Economics and Saisics, 82(4), pp [17] Lindeboom, M. and E. van Doorslaer (2004), Cu-poin Shif and Index Shif in Self-repored Healh, Journal of Healh Economics, 23, pp [18] McClellan M. and D.O. Saiger (2000), Comparing Hospial Qualiy a For-Pro and Nofor-Pro Hospials, in The Changing Hospial Indusry: Comparing No-for-Pro and For- Pro Insiuions, D.M. Culer ed., Universiy of Chicago Press. [19] Milcen C. (2005), Hospial Ownership, Reimbursemen Sysems and Moraliy raes, Healh Economics, 14, pp [20] Milcen C., Dormon B., Durand-Zaleski I. and P.G. Seg (2007), Gender Di erences in Hospial Moraliy and Use of Percuaneous Coronary Inervenion in Acue Myocardial Infarcion, Circulaion, 115(7), pp [21] Mobley L.R. (2003), Esimaing hospial marke pricing: an equilibrium approach using spaial economerics, Regional Sciencs and Urban economics, 49, pp [22] Moulon (1990), An Illusraion of a Pifall in Esimaing he E ecs of Aggregae Variables on Micro Unis, The Review of Economics and Saisics, 72(2), pp [23] Newhouse J. (1970), Toward a Theory of Nonpro Insiuions, American Economic Review, 60(1), pp [24] Pauly M.V. and M. Redish (1973), The No-for-Pro Hospial as a Physicians cooperaive, American Economic Review, 63, pp [25] Propper C., Burgess S. and K. Green (2004), Does compeiion beween hospials improve he qualiy of care? Hospial deah rae and he NHS inernal marke, Journal of Public Economics, 88(7-8), pp [26] Ridder G. and I. Tunali (1999), Srai ed parial likelihood esimaion, Journal of Economerics, 92(2), pp

27 [27] Silverman E.M.and J.S. Skinner (2001), Are For-Pro Hospials Really di eren? Medicare Upcoding and Marke Srucure, NBER Working Paper no [28] Sloan F., Picone, G., Taylor D. and S. Chou (2001), Hospial Ownership and Cos and Qualiy of Care: Is There a Dime s Worh of Di erence?, Journal of Healh Economics, 20(1), pp [29] Van Doorslaer E., Wagsa A., Bleichrod H., Calonge S., Gerdham U.G., Ger n M., Geurs J., Gross L., Häkkinen U., Leu R., O Donnell O., Propper C., Pu er F., Rodriguez M., Sundberg G. and O. Winkelhake (1997), Socioeconomic inequaliies in healh: some inernaional comparisons, Journal of Healh Economics, 16(1), pp [30] Van Doorslaer E., Wagsa A., van der Burg H., Chrisiansen T., Cioni G., Di Biase R., Gerdham U., Ger n M., Gross L., Häkkinen U., John J., Johnson P., Klavus J., Lachaud C., Laurisen J., Leu R., Nolan B., Perán E., Pereira J., Propper C., Pu er F., Rochaix L., Rodriguez M., Schellhorn M., Sundberg G. and O. Winkelhake (1999), The redisribuive e ec of healh care nancing in 12 OECD counries, Journal of Healh Economics, 18, pp [31] Van Doorslaer E., Wagsa A., van der Burg H., Chrisiansen T., De Graeve D., Duchesne I., Gerdham U.G., Ger n M., Geurs J., Gross L., Häkkinen U., John J., Klavus J., Leu R.E., Nolan B., O Donnell O., Propper C., Pu er F., Schellhorn M., Sundberg G., Winkelhake O. (2000), Equiy in he delivery of healh care in Europe and he US, Journal of Healh Economics 19(5), pp

28 Table 1: dispariy indices for he regional averages of individual variables Mean Min Max Max/Min Sd. Dev. Coeff. of variaion Number of AMI paiens Deah Female, year old Female, year old Female, year old Female, year old Female, more han 85 year old Male, year old Male, year old Male, year old Male, year old Male, more han 85 year old Excessive smoking Alcohol problems Obesiy Diabees mellius Hyperension (MH) Renal failure Conducion disease (TC) Peripheral arerial disease (AR) Vascular disease (VC) Hisory of coronary arery disease (COEUR) Sroke (CER) Hear failure (IC) Severiy index (IGS) Cabbage or Coronary Bypass surgery (CABG) Cardiac caheerizaion Percuaneous ransluminal coronary Angioplasy Oher dilaaion han PTCA \ Percuaneous revascularizaion using coronary sens (PCI sening) Surgical French DRGs (GHMC) Source: compued from he PMSI daase ( ). Observed used o consruc he dispariy indices are weighed by he number of AMI paiens. Gini

29 Table 2: dispariy indices for he regional averages of hospial and geographic variables Mean Min Max Max/Min Sd. Dev. Coeff. of variaion Gini Proba. of deah wihin 1 day (KM) Proba. of deah wihin 5 days (KM) Proba. of deah wihin 10 days (KM) Proba. of deah wihin 15 days (KM) Number of paiens Number of AMI paiens Proporion of AMI paiens Public No-for-profi \ For-profi Unemploymen rae Poor area in he municipaliy Municipaliy median income Proporion of beds in surgery Number of beds in surgery Proporion of surgery occupied beds Number of beds Proporion of occupied beds Number of beds in he urban area Herfindahl index for hospials in he urban area Source: compued from he PMSI, he SAE, and he municipaliy daases ( ). Observed used o consruc he dispariy indices are weighed by he number of AMI paiens.

30 Table 3: esimaed coefficiens for he individual variables Variable Female, year old Female, year old Female, year old Female, more han 85 year old Male, year old Male, year old Male, year old Male, year old Male, more han 85 year old Excessive smoking Alcohol problems Obesiy Diabees mellius Hyperension (MH) Renal failure Conducion disease (TC) Peripheral arerial disease (AR) Vascular disease (VC) Hisory of coronary arery disease (COEUR) Sroke (CER) Hear failure (IC) Severiy index (IGS) Cabbage or Coronary Bypass surgery (CABG) Cardiac caheerizaion Percuaneous Transluminal Coronary Angioplasy Oher dilaaion han PTCA Percuaneous revascularizaion using coronary sens (PCI sening) Surgical French DRGs (GHMC) Esimae *** (0.1113) *** (0.0965) *** (0.0943) *** (0.0941) *** (0.1015) ** (0.0986) *** (0.0948) *** (0.0941) *** (0.0948) *** (0.0410) *** (0.0654) *** (0.0413) *** (0.0180) *** (0.0155) *** (0.0183) *** (0.0126) (0.0242) *** (0.0282) *** (0.0290) *** (0.0237) *** (0.0134) *** (0.0148) *** (0.0853) *** (0.0299) *** (0.0385) *** (0.2181) *** (0.0261) *** (0.0358) Source: compued from he PMSI daase ( ). Noe: ***: significan a 1%; **: significan a 5%; *: significan a 10%. Number of observaions: 341, 861; mean log-likelihood:

31 Table 4: dispariy indices for he regional probabiliy o die obained from he model Mean Min Max Max/Min Sd. Dev. Coeff. of variaion Gini Probabiliy of deah wihin 1 day Probabiliy of deah wihin 5 days Probabiliy of deah wihin 10 days Probabiliy of deah wihin 15 days Source: compued from he PMSI daase ( ). Noe: for a given region, he survival funcion is consruced as he regional average of he model survival funcions compued for every hospials locaed wihin he region. Table 5: regression of hospial fixed effecs on hospial and geographic variables Variable Regression (1) Regression (2) Regression (3) Consan *** (0.216) *** (1.445) *** (1.517) For-profi hospial 0.286*** (0.041) (0.056) No-for-profi hospial (0.071) ** (0.075) Proporion of AMI paiens in he hospial *** (0.175) ** (0.234) Number of beds (in log) 0.107*** (0.016) (0.024) Occupaion rae of beds (0.223) (0.224) Proporion of beds in surgery (0.090) *** (0.091) Occupaion rae of beds in surgery (0.161) * (0.157) Median municipaliy income (0.148) (0.155) Presence of a poor area in he municipaliy 0.079** (0.031) 0.065** (0.031) Municipaliy unemploymen rae (0.565) (0.583) Number of beds in he urban area 0.064*** (0.022) 0.061** (0.027) Herfindahl index for he healhcare srucure *** (0.089) *** (0.094) Regional dummies Non Oui Oui Number of hospials Corresponding number of paiens 332, , ,827 Adjused-R² Source: compued from he PMSI, he SAE, and he municipaliy daases ( ). Noe: ***: significan a 1%; **: significan a 5%; *: significan a 10%. We inroduced a dummy for he municipaliy no o be in an urban area (dummy for rural area), and a dummy for he municipaliy o be relaed o several urban areas (dummy for muli-polarized municipaliy).

32 Table 6a: variance analysis a he regional level (firs sage) Group of variables from which we consider he effec Variance Correlaion wih he inegraed hazard Inegraed hazard Individual variables (averaged a he regional level) Innovaive reamens Non-innovaive reamens Diagnoses Demographic variables (age x sex) Log-hospial fixed effecs (averaged a he regional level) Source: compued from he PMSI, he SAE, and he municipaliy daases ( ). Table 6b: variance analysis a he regional level (hird sage) Group of variables from which we consider he effec Variance Corr. wih log-hosp. fixed effecs Correlaion wih he inegraed hazard Log-hospial fixed effecs (averaged a he regional level) Hospial and geographic variables (averaged a he regional level) Hospial variables Saus and mode of reimbursemen Proporion of AMI paiens Beds (capaciy and occupaion rae) Geographic Variables Municipaliy variables Income-relaed variables Dummies for he municipaliy o be rural or muli-polarized Number of beds in he urban area Herfindahl index for healhcare srucure Regional dummies Source: compued from he PMSI, he SAE, and he municipaliy daases ( ).

33 Graph 1: Regional proporions of paiens reaed by for-profi hospials Graph 2: Regional proporions of paiens reaed wih sens

34 Graph 3: Regional probabiliies o die wihin fifeen days (in %) Noe: for a given region, he probabiliy o die is consruced as one minus he regional average of Kaplan-Meier esimaors compued for every hospials locaed wihin he region. Graph 4: Sample of regional survival funcions (Kaplan-Meier) Source: compued from he PMSI daase ( ). Noe: for a given region, he survival funcion is consruced as he regional average of Kaplan-Meier esimaors compued for every hospials locaed wihin he region.

35 Graph 5: Sample of regional survival funcions (model) Source: compued from he PMSI daase ( ). Noe: for a given region, he survival funcion is consruced as he regional average of he model survival funcions compued for every hospials locaed wihin he region. Graph 6: Baseline insananeous hazard for exi o deah 2,5 2 Insananeous hazard 1,5 1 Coefficien Lower bound Upper bound 0, Time (in days) Source: compued from he PMSI daase ( ).

36 Appendix Table A1: regional probabiliy o die wihin 15 days (Kaplan-Meier) Region code Name Probabiliy o die 91 Languedoc-Roussillon 15.31% 22 Picardie 15.28% 25 Basse-Normandie 14.48% 53 Breagne 14.45% 73 Midi-Pyrénées 13.97% 52 Pays de la Loire 13.67% 72 Aquiaine 13.64% 24 Cenre 13.51% 83 Auvergne 13.46% 21 Champagne-Ardenne 12.96% 93 Provence Alpes Côe d Azur 12.93% 54 Poiou Charenes 12.87% 31 Nord-Pas-de-Calais 12.73% 26 Bourgogne 12.71% 23 Haue-Normandie 12.60% 43 Franche-Comé 12.13% 82 Rhône-Alpes 12.03% 74 Limousin 11.88% 41 Lorraine 11.67% 11 Ile-de-France 9.93% 42 Alsace 8.51% Source: compued from he PMSI daase ( ). Noe: for a given region, he probabiliy o die is equal o one minus he survival funcion. An esimaor of his survival funcion is consruced as he regional average of Kaplan-Meier esimaors compued for every hospials locaed wihin he region. Table A2: regional probabiliy o die wihin 15 days (model) Numéro de région Nom Probabiliy o die 91 Languedoc-Roussillon 14.40% (1) 72 Aquiaine 13.95% (7) 93 Provence Alpes Côe d Azur 11.06% (11) 83 Auvergne 12.85% (9) 22 Picardie 12.00% (2) 31 Nord-Pas-de-Calais 11.92% (13) 24 Cenre 11.68% (8) 73 Midi-Pyrénées 11.68% (5) 53 Breagne 11.25% (4) 25 Basse-Normandie 11.13% (3) 82 Rhône-Alpes 11.11% (17) 11 Ile-de-France 11.06% (20) 41 Lorraine 11.03% (19) 43 Franche-Comé 10.81% (16) 52 Pays de la Loire 10.60% (6) 21 Champagne-Ardenne 10.59% (10) 23 Haue-Normandie 10.47% (15) 74 Limousin 9.92% (18) 54 Poiou Charenes 9.87% (12) 26 Bourgogne 9.85% (14) 42 Alsace 9.84% (21) Source: compued from he PMSI daase ( ). Noe: for a given region, for a given region, he probabiliy o die is equal o one minus he survival funcion. An esimaor of his survival funcion is consruced as he regional average of he model survival funcions compued for every hospials locaed wihin he region. In he las column, he ranking of he regions obained from raw daa is repored in parenhesis.

37 Table A3: regression of hospial fixed effecs on aggregaed variables, innovaive reamens are no conrolled for Variable Regression (1) Regression (2) Regression (3) Consan *** (0.200) *** (1.400) *** (1.439) For-profi hospial *** (0.038) *** (0.053) No-for-profi hospial *** (0.066) *** (0.071) Proporion of AMI paiens in he hospial *** (0.162) ** (0.222) Number of beds (in log) (0.015) (0.023) Occupaion rae of beds (0.207) (0.212) Proporion of beds in surgery *** (0.084) *** (0.086) Occupaion rae of beds in surgery (0.150) (0.150) Median municipaliy income (0.143) (0.147) Presence of a poor area in he municipaliy (0.030) (0.030) Municipaliy unemploymen rae (0.547) (0.551) Number of beds in he urban area ** (0.021) ** (0.026) Herfindahl index for he healhcare srucure (0.086) *** (0.088) Regional dummies Non Oui Oui Number of hospials Corresponding number of paiens 332, , ,827 Adjused-R² Source: compued from he PMSI, he SAE, and he municipaliy daases ( ). Noe: ***: significan a 1%; **: significan a 5%; *: significan a 10%. We inroduced a dummy for he municipaliy no o be in an urban area (dummy for rural area), and a dummy for he municipaliy o be relaed o several urban areas (dummy for muli-polarized municipaliy).

38 Table A4: regional dummies obained from he hospial fixed-effec regression Region code Name Coefficien 91 Languedoc-Roussillon < Reference > (1) Basse-Normandie * (0.090) Lorraine ** (0.088) Picardie ** (0.086) Breagne ** (0.080) Aquiaine ** (0.075) Champagne-Ardenne ** (0.090) Provence Alpes Côe d Azur *** (0.071) Bourgogne ** (0.088) Cenre *** (0.083) Limousin ** (0.102) Auvergne *** (0.089) Franche-Comé ** (0.101) Poiou Charenes *** (0.087) Pays de la Loire *** (0.079) Rhône-Alpes *** (0.074) Midi-Pyrénées *** (0.077) Nord-Pas-de-Calais *** (0.070) Alsace *** (0.098) Haue-Normandie *** (0.087) Ile-de-France *** (0.108) Source: compued from he PMSI, he SAE, and he municipaliy daases ( ). Noe: in he las column, he ranking of he regions obained from raw daa is repored in parenhesis. (3) (19) (2) (4) (7) (10) (11) (4) (8) (18) (9) (16) (12) (6) (17) (5) (13) (21) (15) (20)

39 Graph A1: Map of he French Regions Regions. 11: Ile-de-France; 21: Champagne-Ardenne; 22: Picardie; 23: Haue-Normandie; 24: Cenre; 25: Basse-Normandie; 26: Bourgogne; 31: Nord Pas-de-Calais; 41: Lorraine; 42: Alsace; 43: Franche-Comé; 52: Pays de la Loire; 53: Breagne; 54: Poiou- Charenes; 72: Aquiaine; 73: Midi-Pyrénées; 74: Limousin; 82: Rhônes-Alpes; 83: Auvergne; 91: Languedoc-Roussillon; 93: Provence - Alpes Côes d Azur. Graph A2: Regional survival funcions (Kaplan-Meier) Source: compued from he PMSI daase ( ). Noe: for a given region, he survival funcion is consruced as he regional average of Kaplan-Meier esimaors compued for every hospials locaed wihin he region.