HERO OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working paper 2007: 5

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1 OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: THE CASE OF MEDICAL ERRORS Svrr Grpprud Institut of Halth Managmnt and Halth Economics, Univrsity of Oslo and Norwgian Univrsity of Lif Scincs, Aas, Norway UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working papr 2007: 5 HERO

2 OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: Th cas of mdical rrors Svrr Grpprud Institut of Halth Managmnt and Halth Economics, Univrsity of Oslo, P.O. Box 1089 Blindrn, 0317 Oslo, Norway and Norwgian Univrsity of Lif Scincs, PO 5003, N-1432, Aas, Norway. Halth Economics Rsarch Programm at th Univrsity of Oslo HERO 2007 JEL Cods: Kywords: D64, I18, K32, K42 Iatrognic injury, nforcmnt, administrativ sanctions Acknowldgmnts: I am indbtd to V. Christiansn and K. Brkk. Th usual disclaimr applis. This papr is part of th HERO program at th Univrsity of Oslo, and is fundd by th Norwgian Rsarch Council HERO and th authors Rproduction is prmittd whn th sourc is rfrrd to. Halth Economics Rsarch Programm at th Univrsity of Oslo Financial support from Th Rsarch Council of Norway is acknowldgd. ISSN (print vrsion.), ISSN (onlin), ISBN

3 Abstract Individuals oftn rspond with strong motions to bing pnalisd. Such rsponss suggst that informal pnaltis ar important and play a rol in crating dtrrnc. In this papr informal pnaltis ar analysd in th contxt of mdical rrors. Th introduction of informal pnaltis, if dpndnt upon formal ons, implis that: (i) th optimal nforcmnt rgim bcoms mor lnint, and in som cass th lack of formal punishmnt is prfrrd, (ii) th first-bst solution bcoms unattainabl, (iii) liability rats and formal pnalty lvl ar no longr prfct dtrrnc substituts. In addition, powrs of informal pnaltis provid a rational for administrativ sanctions (informal criticism, rprimands and warnings).

4 1. INTRODUCTION Th conomic litratur on dtrrnc and incntivs has primarily focusd on formal pnaltis with consumption implications. Formal pnaltis ar thos for which th pnalizing agnt is a rgulatory body (govrnmntal authority) that acts according to prdtrmind ruls. Consumption implications rfr to rductions in futur consumption possibilitis rsulting from matrial or physical dprivation,.g. fins or imprisonmnt. Bckr s (1968) influntial modl on criminal offncs is on xampl of such a prspctiv. Rgulatory bodis (authoritis), howvr, ar not th only pnalizing agnts; at last two othrs xist th offndrs thmslvs and othrs (.g. collagus and prs). For such typs of pnalizing agnts w can talk about informal pnaltis sinc thy triggr ngativ motions. Exampls ar flings of sham, mbarrassmnt and guilt, all a consqunc of violating moral (intrnalizd) and social norms. Th litratur on how norms shap bhaviour is xtnsiv in psychology and sociology. In conomics th intrst has bn lss; howvr, thr is now a growing litratur on altruism, pro-social bhaviours, rputation and intrinsic motivations, and thir implications on rwards and prformanc incntivs [s.g. Bnabou and Tirol (2003) and (2006) and th rfrncs thrin]. Our analysis adds to this litratur by focusing on th rol informal pnaltis has for crating dtrrnc. Th prsnc of informal pnalizing agnts raiss th qustion of to what dgr thy dissuad individuals from crtain socially unwantd acts, sinc thy do not rduc budgtary opportunitis. Qustions that will b addrssd ar: (i) can ngativ flings b utilizd in a maningful way? (ii) can such flings rplac or supplmnt lgal sanctions and incntivs? (iii) can th us of sanctions that do not affct budgt constraints in a dirct way, but only highlight wrongful actions, b xplaind by taking informal pnaltis into considration? Exampls of sanctions not having budgtary implications, in th following dnotd administrativ sanctions, ar warnings, rprimands, informal criticisms, confirmations of nglct of duty, and xclusion (loss of mmbrship). Som paprs in conomics discuss th rols slf-rspct and social rputation may hav in crating dtrrnc. Brnnan and Buchanan (1985) prciv lgal punishmnt not simply as a pric of an altrnativ cours of action, but also as a confirmation of wrongful action, and claim that th moral dimnsion in itslf modrats illgal bhaviour. Grasmick and Bursik (1990) prsnt a study of individuals intntion to violat th law givn th prcivd thrats (xpctd pnaltis) for thr diffrnt illgal activitis (tax vasion, drunk driving and ptty thft). Th dtrrnc ffct was found to b significant for lgal sanctions and sham. Sham was found to b mor ffctiv than lgal sanctions in th cas of tax vasion, whil qually ffctiv in th cas of drunk driving. Erard and Finstin (1994) find that guilt (violating intrnalisd valus) 3

5 and sham (violating social norms) ar important in xplaining actual rporting bhaviour in tax complianc. Gordon (1989) xtnds th work of Allingham and Sandmo (1972), by introducing non-pcuniary vasion costs (guilt, rduction of slf-imag and social stigma), to xplain that som taxpayrs nvr vad. Administrativ sanctions ar frquntly obsrvd in profssional associations,.g. architcts, dntists and lawyrs. 1 In Nordic countris, administrativ sanctions ar also commonly usd in th halth car sctor. Exampls of such institutions ar warnings, rprimands, informal criticism, confirmation of misconduct - th last bing a lttr from halth authoritis to an individual physician confirming that som dgr of wrong-doing occurrd in a givn tratmnt pisod. 2 Othr ractions from halth authoritis includ institutions such as clinical suprvision and trial-priods. Both imply som typ of tim-limitd monitoring in rspons to inadquat tratmnt. In Dnmark halth car workrs, primarily physicians, can b placd undr th clinical suprvision of collagus, whil Swdn uss a thr-yar trial priod during which thr is clos follow-up by halth authoritis. Ngativ prsonal xprincs ar common among halth car prsonnl whn it coms to mdical malpractic, rrors and nglignc. Eldvik (2000) finds that halth car workrs ract with surprisingly strong ngativ motions to administrativ sanctions. Flings of shock and dspair and motional conflicts such as angr, dprssion and vn suicids ar rportd. Th motional ractions that occur in rspons to matrial dprivation (fins, loss of authorisation, and suspnsion) ar found to b only slightly strongr. Othr studis find that significant ngativ ractions occur in rspons to procss (rviw and litigation) and outcom (confirmation of wrong-doing). Jain and Ogdn (1999) and Bakr (1999) obsrv that gnral practitionrs who rciv a patint complaint find th xprinc dvastating. Th patint complaint appars to b a punishmnt in itslf, rgardlss of th vntual dcision aftr rviw. Light (1979), Marjoribanks t al., (1996) and Huprt t al., (1996) study physicians xprincs with malpractic suits. All studis confirm th imprssion of strong ngativ flings among halth car workrs in rspons to such xprincs. Thr ar svral rasons why flings such as sham and guilt ar frquntly obsrvd in connction with advrs vnts. First, th act of causing harm to othrs involvs significant prsonal costs for thos involvd, vn in th absnc of any nglignc, particularly if injuris happn to idntifiabl individuals. Scond, th vry intnt of mdical activity is to hlp popl 1 Th disciplinary committ of th Norwgian Bar Association has th following thr administrativ sanctions at its disposal: (i) confirmation of misconduct, (ii) rprimands, and (iii) warnings. 2 1 out of 70 Norwgian practicing physicians rcivd a confirmation of mdical misconduct during 2005, whil 1 out of 330 rcivd a warning (Hlstilsynt, 2005). 4

6 rcovr from bad halth, not to worsn it, a fact that may rinforc such costs. Finally, rrors (injuris) may not occur intntionally, as in othr harmful activitis (crims, nvironmntal pollution and tax vasion), but accidntally. As a consqunc, many physicians act in good faith. In th following, I prsnt an analytical modl of rror prvntion and considr th nglignc liability rul. Providrs partly intrnalis thir patints wll-bing (altruism). Tratmnt dcisions and prcautionary car ar collapsd into on dcision (ffort). Various informational imprfctions ar also introducd. Providr ffort is unobsrvd by patints and imprfctly (x-post) vrifid by th rgulator. Patints inability to obsrv halth car quality xplains th xistnc of malpractic law and othr institutions daling with quality nhancmnt in halth car. Th modl follows th convntional approach in accidnt modls by assuming an injury probability function dcrasing in ffort. Blundrs, slips and misundrstandings may happn rgardlss of th amount of rsourcs invstd in prvnting thm. Physicians may rr as a rsult of inadquat knowldg or training, and must invst in skills to rduc th probability of making mistaks (Arln and MacLod, 2005). In addition, court rrors may happn sinc nglignc ruls ar implmntd undr imprfct information. 3 It is gnrally too costly for a rgulator to undrtak a complt x-ant spcification of du car standards (lgal standards), thus w ar confrontd with an incomplt contract problm. This analysis is rlatd to arlir work on tort liability (s.g. Brown, 1973; Shavll, 1980 and Danzon, 1985). In addition th modl draws upon th works of Bckr (1968) and Polinski and Shavll (1979). Important findings in this litratur ar; fins ar prfrrd ovr imprisonmnt, optimal dtrrnc is achivd by stting uniformly maximal pnaltis for all crims, whil th probability of conviction is st at th minimum ncssary to nforc complianc with law. This last finding has bn modifid in subsqunt works by including risk prfrncs (Polinski and Shavll, 1979), risk baring costs among non-offndrs (Kaplow, 1989), th possibility of invsting in avoiding activitis (Fridmann, 1981; Malik, 1990), lgal xpnditurs by dfndants and proscutors (Rubinfld and Sappington, 1987) and fairnss and lgitimacy considrations. Sction 2 prsnts a bnchmark modl without informal pnaltis (th convntional modl). Th rol of informal pnaltis is analysd in Sction 3. Sction 4 concluds and summariss th implications for policy prscription and assssmnt. 3 A rviw undr th nglignc rul nds to lgally stablish injury, causality and substandard car rlativ to a standard that may b vaguly dfind x-ant. Th imprfct ability to distinguish btwn truly carful and nglignt injuris introducs th possibility of court rrors. 5

7 2. A CONVENTIONAL MODEL OF ERROR PREVENTION A mdical rror (advrs vnt), as dfind in th mdical litratur, rfrs to an injury causd by mdical mismanagmnt rathr than by th undrlying disas or th condition of th patint (Dpartmnt of Halth, 2000). Th sam litratur oftn distinguishs btwn rrors that ar prvntabl and unprvntabl rlativ to th currnt stat of mdical knowldg. Nglignt rrors rprsnt a subst of prvntabl rrors that satisfy crtain lgal critria. Th modl assums providr liability (th nglignc rul), considrs formal pnaltis (fins) and includs thr possibl stats: th non-occurrnc of mdical rrors, th occurrnc of mdical rrors and th occurrnc of liabl mdical rrors. Th halth status of th patint, h, is assumd indpndnt of prvntiv ffort,, and qual to h givn th non-occurrnc of an rror or h for th occurrnc of an rror whr h > h > 0. Furthrmor, thr is a probability P () that th mdical rror occurs, whr P (0) = 1, lim P ( ) 0, P() < 0and P () > 0. Th occurrnc of mdical rrors is typically not public information. Culln t al., (1995) and Barach and Small (2000) find that th shar that rmains undiscovrd is btwn 50 and 90%. Harvard Mdical Practic Study (1990) finds that only 6-7% of patints suffring an injury du to nglignc ar blivd to rciv compnsation. Errors that bcom known to th rgulator do so primarily bcaus of patint complaints. In th following th paramtr q [ 0,1] dnots, givn th occurrnc of a mdical rror, th shar of rrors for which th providr is hld liabl. 4 Thus q is th conditional probability of bing dtctd and hld liabl (liability rat). Th liability rat may dpnd on such factors as patints awarnss of iatrognic injuris, th dfinition of du car and invstmnts in th rviw and auditing procsss. Th pnalty imposd by th rgulator, t 0, is a montary fin (matrial dprivation). Patint-physician intractions ar charactrisd by th influnc of physicians on halth car us (physician agncy). Formal modlling approachs of this rlationship includ som typ of humanitarian objctivs in providr utility functions rathr than pur profit-maximization. Implicit tratmnts of agncy introduc (thical) constraints or boundaris on tratmnt intnsitis (Ma and McGuir, 1997; Ivrsn and Lurås, 2000), or assum that providr disutility is imposd if acting against th bst intrst of th patint (Dranov, 1988; McGuir and Pauly, 1991). Mor xplicit tratmnts includ patints utility or halth bnfits as part of providr utility functions 4 Consrvativ stimats from th litratur find that 1% of hospital admissions rsult in nglignt rrors, s.g. Brnnan t al., (1991); Wilson t al., (1995); Thomas t al.,(1999). 6

8 (s.g. Farly, 1986; Ellis and McGuir, 1986, 1990; Danzon, 1994 and Chalkly and Malcomson; 1998). Hr, w follow Ellis and McGuir (1990) by choosing a providr bnfit function, z, that is th sum of th utility of nt walth, U(A), and patint halth status. Nt walth, A, is th diffrnc btwn Y, th initial lvl of providr walth, and th fin, t, hnc th maximal fin that can b imposd is t=y. 5 Th trms βh and βh ar agncy utilitis, for th occurrnc and non-occurrnc of an rror, rspctivly; hr β (0,1] dnots th dgr of providr agncy. 6 A strictly positiv β nsurs a positiv lvl of prvntiv ffort in th absnc of any rgulatory intrvntion. Th concpt of patrnalistic altruism is oftn usd to dscrib prfrncs for which spcific lmnts of othrs utilitis (.g. halth or halth bnfits) ar includd (Archibald and Donaldson, 1976). Thus, for β < 1 our modl can b said to assum partial patrnalistic altruism. Th providr disutility function of prvntiv ffort, k(), is strictly convx. Th paymnt contract is a pur capitation contract (fixd pr patint and is part of Y). 7 W can now analys th optimal bhaviour of a givn providr. Th providr s xpctd pay-off, z, from trating th patint is: z () = (1 P ()) UY ( ) + βh + P ()(1 quy ) ( ) + quy ( t) + βh k (), (1a) which by simplification bcoms: z () = UY ( ) PqUY () [ ( ) UY ( t) ] + β H () k (), (1b) whr H () (1 P()) h+ P() h. (1c) H() is th xpctd halth status of th patint, and, from formr assumptions, is strictly concav in ; H > 0 and H < 0. Th following xprssion, for any nforcmnt rgim {q,t}, dtrmins optimal prvntiv ffort, : [ ] β H ( ) P( quy ) ( ) UY ( t) = k( ) (2) Optimal prvntiv ffort quats marginal nt bnfits (sum of th marginal agncy utility and th marginal rduction in th xpctd pnalty) with th marginal disutility of ffort. U(Y)-U(Y-t), 5 Th complt providr bnfit function is as follows; Z( A, f, h) = U( A) + f + βhwhr f is th halth stock of providrs. Hr w ignor f sinc th halth of providrs is assumd constant. 6 Ellis and McGuir dfin β as th constant rat of substitution btwn walth (nt incom) and bnfits from tratmnt, whr β =1 is dnotd as prfct agncy. This trm may b confusing sinc providrs, contingnt upon paymnt schduls, will trad-off patint s bnfits with own nt incom (partial agncy). Providrs rprsnt th full intrst of patints only whn own financial motivations ar absnt. Incomlisur modls and pur profit maximizing providrs ar opposit xtrms (absnt agncy). 7 Pur altruistic prfrncs add nothing nw as long co-paymnts ar indpndnt of providr ffort. 7

9 calld th incom pnalty, is th utility loss if th providr is pnalisd by t. Th scond ordr condition (s.o.c.) is availabl in App. A.1. Eq. (2) implicitly dfins ffort as function of both policy paramtrs: = E( q, t ), and thir impacts ar found by diffrntiating (2) with rspct to, t and q, which yilds (s App. A.2-3); 8 d zt = Et = > 0 (3a) dt z d zq = Eq = > 0 (3b) dq z Eqs. (3a,b) confirm th standard conclusions that prvntiv ffort improvs with highr fins and liability rats (improvd dtrrnc). A providr invsts last prvntiv ffort (tsts, prcautionary car, numbr of visits, scond opinions) whn unrgulatd ( q= t = 0 ). To rank and compar various solutions w nd to dfin a critria function. Th social wlfar function, S, is dfind as th unwightd sum of providr utility and patint utility minus social costs (liability costs and rhabilitation costs). Th providr utility function, z, is dfind abov, whil th patint bnfit function, B, is as follows: B( wh, ) = U( w) + hwhr w is th initial walth lvl of th patint. It follows from our spcification that th patint, unlik th providr, is non-altruistic. Th liability cost function is m(q) whr m > 0 and m 0, and is mant to rflct audit costs, rviw costs and conflict rsolution costs,.g. lgal costs. Although th liability rat (q) is a function of patint complaints, it is partly undr rgulator influnc and can, for xampl, b affctd by: (i) changing th ruls, (ii) informational campaigns, and (iii) various othr invstmnts. Exampls includ changing du car standards and burdns of proof, making whistl-blowing mandatory, invsting to rduc th frquncy of court rrors, undrtaking mor thorough invstigations in rspons to patint complaints, and ncouraging slf-rporting by, for xampl, lowring th administrativ costs of rporting. Rhabilitation costs, C, rfr to costs byond patint utility losss that follow from advrs vnts. Exampls ar invstmnts in rhabilitation, mdical xpnss, nw tsts and longr hospital stays. Vincnt t al., (2001) find that advrs vnts xtnd hospital stays by an avrag of ight days. 9 Two choics in our spcification of wlfar function nd to b clarifid. Th first issu concrns our inclusion of altruistic prfrncs, which mans that halth bnfits now ntr twic q qq 8 Argumnts ar omittd whnvr doing so crats no confusion. 9 Such costs ar important but oftn ignord in modls on mdical malpractic. Kohn t al., (1999) find that in 1997 annual costs in th Unitd Stats associatd with prvntabl mdical rrors amountd to $17-29 billions. Mor than 50% of ths costs wr halth car costs. Such costs ar sldom born by th individual providrs but by hospitals and/or third-party payrs (insurrs). 8

10 in social wlfar: first, bcaus of patints own valuation (patint utilitis), and scond, bcaus of providrs valuation (agncy utilitis). Th litratur on physician agncy frquntly uss a diffrnt approach. Ellis and McGuir (1990) ignor patints bnfits in th physicians objctiv function whn dfining social wlfar in ordr to avoid doubl-counting of patint bnfits. Th sam approach is chosn by Chalkly and Malcomson (1998) on th grounds that bnvolnc rprsnts a dsir to do what is in th social intrst and, as such, should hav no rol in dtrmining what th social intrst is. 10 Knntt (1980) rfrs to a particular typ of altruism, gnuin altruism, whr th concrn for othrs is rflctd in thir bhavior without driving any utility from th sam bhavior. According to this typ of altruism, humanitarian prfrncs in objctiv functions dscrib bhavior but should not b rgardd as having ffcts on utility lvls and thrby social wlfar. 11 A somwhat diffrnt rational for gnuin altruism follows if humanitarian objctivs ar prcivd as following from structural modls of physician agncy. Now altruistic prfrncs bcom rducd form formulations of physician patint intractions i.., portrayd as Nash bargaining gams, coalition gams or gams of rpatd intractions (s Chon and Ma, 2004). W choos to includ altruistic prfrncs in th wlfar function as a mattr of compltnss; xcluding altruistic prfrncs from th social wlfar function (th gnuin wlfar function) is a spcial cas of our mor gnral formulation, and will also b discussd blow. Th scond issu concrns whthr fins ar socially nutral transfrs or not. Throughout th papr I will, in ordr to kp th analysis as simpl as possibl, impos rstrictions so that fins can b tratd as socially nutral transfrs. On simpl way of doing it is to assum linar utility functions in walth (s App. A.5-A.10 for furthr dtails). Th social wlfar function, S, givn th abov assumptions, can now b xprssd as: S () = UY ( ) + Uw ( ) pc () + (1 + β ) H () k () mq () (4) Th doubl-counting of patints halth bnfits (altruism) is capturd by(1 + β ) H ( ). Th gnuin wlfar function is assumd by stting β = 0 which yilds lowr social wlfar for similar ffort lvls. Th first bst lvl, ê (full information solution), is drivd by maximizing (4) with rgard to, which yilds (th s.o.c. is prsntd in App. A.4): (1 + β ) H ( ˆ) p ( ˆ) C = k ( ˆ) (5) Th social first-ordr condition (s 5) dviats from th privat first-ordr condition (s 2) in two rspcts. First, halth improvmnts ar valud mor highly in (5). Not that this conclusion 10 Howvr, what is in th social intrst nd not b in th patint s intrst. 11 Such an assumption is somwhat controvrsial bcaus it rlaxs a fundamntal assumption in conomics - that individuals maximiz thir own utility. 9

11 also mattrs for th gnuin wlfar function ( β =0 in 5) as long as physicians ar imprfctly altruistic ( β < 1 in 2). Scond, rhabilitation costs ar now takn into account. Hnc, th providr ignors social bnfits and social costs (xtrnalitis) which bcom th vry rason that incntivs ar ndd to induc providrs to dlivr th quantity and quality of car that would hav bn chosn by informd patints. In th following th problm of optimal nforcmnt is analyzd. Th rgulator is unabl to obsrv providr ffort, and a contract contingnt upon halth outcoms is dsignd. Patint complaints signal possibl suboptimal car and th rgulator, by th us of mdical rviws, is to assss whthr nglignt acts wr involvd or not (imprfct x-post vrification). Th optimal nforcmnt rgim is drivd by insrting E(, tq) into S, and maximising with rspct to t and q. By following this procdur, using (2), w find (s App. A.11 for th s.o.c.): ( ) St ( q, t) = Et H PC+ Pq U( Y) U( Y t ) (6a) ( ) S ( q, t) = E H P C+ P q U( Y) U( Y t) m q q q (6b) A first conclusion is that q = t = 0 (a non-punitiv rgim) cannot b part of an optimal * * nforcmnt rgim sinc both drivativs, givn formr conclusions, ar positiv for valus of q and t sufficintly clos to zro. Th optimal nforcmnt rgim, givn an intrior solution, is drivd by incrasing th ratio of q to t, for * q > 0 whil kping th xpctd incom pnalty, ( ( ) ( )), constant. This procdur raiss social costs, sinc liability costs bcom quy UY t highr whil th dtrrnc prssur rmains unchangd, thus th optimal fin is th maximal on; t * = Y sinc for any t Y it will b optimal to rais t and lowr q. Th optimal nforcmnt * *, rgim ( q t =Y) satisfis th following conditions: H q U Y U < C (7) P * [ ( ) (0)] * [ ( ) (0)] H m q q U Y U = C + (8) P P E For a maximal fin, q * q is st to balanc th xpctd incom pnalty with th sum of marginal bnfits and costs (xtrnalitis) and a trm rflcting marginal audit costs. Th optimal liability rat * ( q ) incrass with rhabilitation costs and marginal xpctd halth bnfits, but dcrass with marginal liability costs. It is also obsrvd that an uppr cornr solution cannot b ruld out sinc S (1, Y ) may b positiv. Th optimal nforcmnt rgim dscribd in (7) and (8) yilds a q 10

12 scond-bst solution. Th rason lis with th fact that in ordr to induc th first-bst ffort lvl, givn informational imprfctions, liability costs ar incurrd, and undr-dtrrnc * follows ( < ˆ ) (for proof s App. A.12-14). Rsult 1: Givn social xtrnalitis and th absnc of informal pnaltis, rgulatory intrvntion * * is always optimal; ( q > 0; t > 0). In th prsnc of liability costs, th optimal fin is th maximal on; t * = Y. Various spcial cass can b considrd. Considr first th situation whr th liability rat can b changd at no costs. Now, th right sid of both xprssions coincid and optimal nforcmnt is dscribd by a mnu of t and q combinations that all simultanously fulfill (7) and (8). Th two policy instrumnts ar prfct substituts in crating dtrrnc and th optimal ffort lvl is now qual to th first-bst lvl ( ê = * ; prfct dtrrnc). Givn a gnuin wlfar function and kping th assumption of no liability costs, implis that (7) can b xprssd as follows; H q U( Y) U( Y t*) = C (1 β ) (9) P * [ ] It is obsrvd from (9) that th optimal xpctd incom pnalty dcrass with dgr of agncy ( β ). Furthrmor, a punitiv rgim, givn prfct agncy ( β = 1), is still in social dmand bcaus of rhabilitation costs. If, for som rason, th liability rat is fixd at a low lvl, it could b that (7) cannot b fulfilld and w hav a third-bst solution. Th abov findings confirm standard conclusions about optimal nforcmnt in th prsnc of social xtrnalitis. Optimal dtrrnc, givn costly monitoring or auditing, is achivd by maximal fins and yilds a scond-bst solution and undr-dtrrnc. Howvr, our findings dviat from statmnts in th litratur that halth providrs, if acting as prfct agnts, should not b xposd to any malpractic prssur sinc th appropriat quality and ffort will b providd (s.g. Ksslr and McClllan 2002a). In our modl, som prssur is ndd, vn for a gnuin wlfar function, sinc rror tratmnt costs ar not intrnalisd by th providr Th following thr conditions must b mt for providr liability to b unncssary: (i) prfct agncy; (ii) fully intrnalisd (or absnt) rror tratmnt costs, and (iii) a gnuin wlfar function. 11

13 3. A MODEL OF ERROR PREVENTION WITH INFORMAL PENALTIES. In th convntional modl, individuals rfrain from doing somthing out of far of matrial dprivation (th incom pnalty). This framwork is now xtndd by including informal pnaltis,.g. motional and anxity costs, imposd by th slf or by collagus and prs. 13 Ths pnaltis ar viwd as utility pnaltis in th sns that utility, dfind ovr initial walth, is lowrd in som stats for unchangd consumption possibilitis. Th litratur rfrrd to in th introduction suggsts that at last two groups of informal pnaltis ar rlvant for halth car workrs. First, rviws or litigation procsss ar strssful xprincs for thos involvd,.g. bing suspctd or confrontd by angry patints (th procss). Scond, whn th rgulator (judicial systm) confirms som typ of wrongdoing by holding somon rsponsibl, such advrs flings can b rinforcd (th outcom). Th modl prsntd blow will allow for both typs of informal pnaltis. Furthrmor, to simplify th analysis, liability costs ar now st qual to zro, but th providr will still b portrayd as bing altruistic (patrnalistic). A natural qustion is whthr obsrvd ngativ motions (informal pnaltis) among halth car workrs in fact follow from providr altruism and not bcaus of rasons of slf-rspct and social rputation. Providr altruism is, howvr, too simpl an xplanation for svral rasons: (i) strong motional ractions also occur whn patint injuris ar ngligibl, (ii) motional ractions diffr for similar injuris, (iii) th dgr to which such incidnts bcom common knowldg plays a rol, (iv) givn th occurrnc of patint injury, bing undr rviw or not mattrs, and (v) th implmntation of formal pnaltis and thir magnitud impacts th typ and significanc of ractions. In th following, th informal pnaltis associatd with ach stat ar dscribd. Th first stat, th non-occurrnc of mdical rrors, is similar to th sam stat in th convntional modl. For th nxt two stats, howvr, informal pnaltis ar introducd. Th scond stat, with a conditional probability qual to 1-q, rfrs to an advrs vnt for which th providr is not hld liabl. This stat yilds a utility qual to V(Y) < U(Y), which implis that providrs who xprinc advrs vnts but ar not hld liabl, ar wors off rlativ to not xprincing an advrs vnt. This assumption capturs th fact that providrs charactriz thmslvs as th scondary victims, bing hurt by th occurrnc of mdical rrors. This stat ncompasss all typs of advrs vnts xcpt thos for which nglignc is confirmd, i.., injuris causd by normal risks, undtctd rrors including thos likly to b judgd as nglignt ons if thy 13 Th litratur somtims apply th concpt of significant othrs rathr than collagus/prs (s.g. Grasmick and Bursik, 1990). 12

14 bcam public, and advrs vnts that triggr patint complaints but for which nglignc is not confirmd. Th shift in utility rflcts strssful xprincs du to: (i) patint complaints and litigation procsss and th flings of bing suspctd or bing th objct of othrs ngativ motions (patints, patint family, and collagus), (ii) various typs of irrational slf-rproach and x-post rgrts about x-ant tratmnt stratgis, and, (iii) flings of guilt from kping rrors scrt and th far of bing dtctd. Th pnalty, UY ( ) VY ( ), is dnotd th rror pnalty. Th third stat, with a conditional probability qual to q, concrns advrs vnts for which providrs ar hld rsponsibl for nglignc, and yilds a utility qual to WY ( tt, ) < VY ( ) t. Th xprincd loss of utility, VY ( ) WY ( tt, ), hr dnotd th nglignc sanction, contains on formal and two informal pnaltis. Th first argumnt in WY ( tt, ) is th convntional ffct whr fins rduc consumption possibilitis and thus utility (th incom pnalty). Th scond argumnt, howvr, is nw and rflcts a sparat ngativ ffct of t on utility; W (, ) < 0 2 Y t t (th crowding pnalty). Th crowding pnalty capturs th ffct that th significanc of informal pnaltis may incras with th siz of th fin. Taking th drivativ of WY ( tt, ) with rgard to th fin yilds: 14 W t (Y t,t) = W 1(Y t,t) + W 2(Y t,t) < 0 (10) Th third pnalty follows sinc providr utility undrgos a ngativ shift vn if no fin is imposd. This is sn whn insrting for t=0 in WY ( tt, ) which yilds WY (,0) < VY ( ). Now, th loss of utility is VY ( ) WY (,0) (th rsponsibility pnalty). 15 Th stat-dpndnt utility function outlind abov assums four diffrnt pnaltis. First w hav th rror pnalty which is an informal on. Thn w hav thr additional ons, all bing part of th nglignc sanction, of which on is formal (th incom pnalty) and two informal. Th two informal pnaltis (th rsponsibility pnalty and th crowding pnalty) captur th ida that holding providrs rsponsibl for rrors triggrs ngativ motions. Th significanc of informal pnaltis is contingnt upon th law itslf sinc thr is a stigma attachd to bing hld liabl. Evidnc, rfrrd to in th introduction, on halth car workrs rsponss to administrativ sanctions,.g. rprimands and informal criticism, sms to support this assumption. Although administrativ sanctions hav no dirct impact on consumption possibilitis, thy ar nonthlss dscribd as causing strssful xprincs - most probably 14 Th numbrd subscripts (drivativs) point to th rlvant argumnt in W(Y-t,t). 15 Th modl-stup dos not xplicitly considr court rrors although th modl assumptions allow for courts inaccuracy. Typ I rrors, th conviction of a truly carful providr, ar xpctd to caus significant informal pnaltis, but ar not xplicitly tratd in this modl. 13

15 bcaus thy confirm providr wrong-doings (blam). Bing publicly chargd maks providrs fl insultd, disgracd and humiliatd. Th rsponsibility pnalty rprsnts ngativ ractions in th absnc of fins. In addition, th siz of th formal pnalty (th fin) can b said to convy an obsrvabl signal about th dgr of wrong-doing. Th highr th fin, th mor thir comptnc and prformanc abilitis hav bn qustiond and th highr utility loss (th crowding pnalty). Th stat-dpndnt utility function is still linar in walth and th marginal utility of walth is assumd th sam across all stats. In ordr to dscrib optimal agnt bhavior w follow th procdur of sction 2. Expctd providr bnfits, r(), is now obtaind by rplacing th utility function in th convntional modl with th stat-dpndnt utility function, thus w gt; r () = UY ( ) PX () + β H () k () (11) whr H(E) is still dfind by (1c), and X U( Y) V( Y) q[ V( Y) W( Y t, t) ] = + (12) Th following xprssion dtrmins optimal providr ffort, (s App. B.1 for s.o.c.): β H ( ) P ( ) X = k ( ) (13) As bfor (13) implicitly dfins an optimal ffort function: = ( q, t ). (14) Both policy variabls ar positiv argumnts in th ffort function (s App. B.2-5). Now, comparing (13), with th sam condition of th convntional modl (s 2), on important diffrnc is obsrvd by looking at X (s 12). X is th rror pnalty plus q multiplid by th nglignc sanction. Not that th paralll xprssion in th convntional modl is q multiplid by th incom pnalty (s 2). Th following xprssions for X ar drivd for ach of th informal pnaltis considrd individually: EP X = UY ( ) VY ( ) + qvy [ ( ) VY ( t)] CP X = quy [ (,0) UY ( tt, )] RP X = qu [ ( Y) W( Y t)] EP Thus X is th xprssion for X whn th only informal pnalty considrd is th rror pnalty, i.., th crowding and rsponsibility pnaltis ar absnt and so on. 16 Consquntly, ach of th 16 i Th notation for X drivs from th following procdurs: (i) an absnt crowding pnalty implis that W(Y-t,t) is xprssd as W(Y-t), (ii) an absnt rsponsibility pnalty implis that th W-function is rplacd by th V-function, and (iii) an absnt rror pnalty implis that th V-function is rplacd by th U- function. If all thr informal pnaltis ar st qual to zro thn X coincids with th xpctd Incom pnalty. This notation will b usd throughout th papr whn spcial cass ar considrd. 14

16 thr abov xprssions rflcts on of th informal pnaltis and th incom pnalty. Th social wlfar function, R, still dfind as th sum of physician and patint bnfits minus social costs, bcoms: 17 R() U( Y) U( w) P() C (1 β) H() k() P() [ U( Y) V( Y) ] q[ V( Y) ( Y,) t ] { } = Φ (15) whr: Φ ( Y,) t = W( Y t,) t +Δ U( w,) t = W( Y t,) t + U( w+ t) U( w) (16) Th last trm in (15) now maks social wlfar to diffr in on important from social wlfar of sction 2 (s 4). This trm is th rror pnalty plus th liability rat multiplid by VY ( ) Φ ( Yt, ). Φ( Yt, ) is th social utility of walth whn a providr is find bing th sum of providr utility in th sam stat and th incras in patint utility that follows from th rdistributd fin ( Δ U( w, t) ; transfr utility gain). VY ( ) Φ( Yt, ) contains two informal pnaltis - th rsponsibility pnalty and th crowding pnalty. This is bcaus th formal pnalty (th incom pnalty) and th transfr utility gain cancl ach othr out whn fins ar social nutral transfrs. Furthrmor, it follows from (16) that Φ( Yt, ) is strictly highr than WY ( tt, ) for a strictly positiv t and qual to WY ( tt, ) for t =0 sinc Δ U( w,0) = 0. Th chang in Φ( Yt, ) from a highr t, using formr assumptions, is Φ ( Yt,) = W ( Y tt,) + W ( Y tt,) + U( w+ t) = W( Y tt,) < 0 (17) t 1 2 t 2 It follows from (17) that Φ( Yt, ) is affctd by a chang in t only if thr is a crowding ffct. Th first-bst lvl, ê, (full information solution) is drivd by maximizing (15) with rspct to, which yilds (th s.o.c. is prsntd in App. B.6): [ ] (1 + β ) H ( ˆ) P ( ˆ) C P ( ˆ) U( Y) V( Y) = k ( ˆ) (18) Th third trm in (18), th marginal chang in xpctd rror pnalty, rflcts an additional social bnfit from invsting in prvntiv masurs compard to th convntional modl. Thus, th first-bst lvl, dfind by (18), is strictly highr than th sam lvl dfind by (5). Th optimal nforcmnt rgim is drivd by insrting (14) into (15), and maximising this xprssion with rspct to q and t whil using (13) (th s.o.c. is availabl in App. B.7), which yilds: Rt ( qt, ) = t H PC + Pq Δ U( wt, ) + Pq ( ) Φt( Yt, ) (19a) 17 As in th prcding sction, a gnuin wlfar function implis that 0 β =. Th spcification of th wlfar function will dpnd on th prspctiv chosn. On altrnativ approach is to portray th social plannr as th trating clinician. If so, it is dbatabl whthr both agncy prfrncs and th rror pnalty should b includd. 15

17 [ ] Rq( q, t) = q H PC+ P qδu( w, t) P( ) V( Y) Φ( Y, t) (19b) Th last trm in both quations (th prfrnc trms), ar nw compard to th convntional modl (s 6). Both prfrnc trms show up bcaus of th informal pnaltis (th rsponsibility pnalty and th crowding pnalty), and both ar strictly ngativ which implis that th us of liability rats and fins incur marginal costs for socity (policy costs). Optimal nforcmnt will now b discussd in thr stags. First, thr possibl cornr solutions ar considrd. Scond, th intrior solution is analysd. Third, th intrior solution is discussd for ach of th thr informal pnaltis at a tim. A first conclusion is that a nonpunitiv rgim, as an optimal policy, no longr can b ruld out as was th cas in sction 2. This is sn by valuating (19b) for q = 0. This again implis that t = 0, sinc a positiv t for q = 0 dos not affct physician bhaviour (s 13), consquntly th first-ordr condition (19a) dos not xist. Now, (19b) bcoms: [ ] [ ] R (0,0) = H PC P( ) V( Y) Φ ( Y,0), q q which is strictly ngativ if: [ ] < [ Φ ] lim H PC lim P( ) V( Y) ( Y,0) q q 0 q 0 Th lft hand sid masurs th marginal social bnfit from a highr liability rat (q) whil th right hand sid is th marginal social cost from th sam chang. Th xprssion in squar brackts on th right hand sid quals VY ( ) WY (,0) for t=0 which is th rsponsibility pnalty. 18 * Hnc, q = 0 (no rgulation) bcoms incrasingly likly th lowr ar rhabilitation costs, th lowr is th marginal halth bnfit, and th highr is th rsponsibility pnalty. A nonpunitiv rgim can b optimal for an additional rason. On way to illustrat this is by ignoring th rsponsibility pnalty - which implis that th abov xprssion for R q (0,0) is strictly positiv. In addition, (19a) now bcoms: 19 [ ] R ( q,0) = H PC + P( ) qv ( Y,0). t t t If R ( q,0) < 0 q> 0 thn q * = 0. This occurs if th crowding pnalty, V ( Y,0), is sufficintly t ngativ. W hav shown that a non-punitiv rgim, for liability costs qual to zro, can b an optimal rgulatory policy. This may happn if policy triggrs significant social costs in trms of t 18 From (16) w gt that Φ ( Y,0) = W( Y,0) sinc Δ U( w,0) = 0is zro. 19 Givn an absnt rsponsibility pnalty, th V-function rplacs th W-function in (17) which givs Φ ( Y,0) = V ( Y,0). t t 16

18 strong ngativ motions and if such motions induc significant bhavioural rsponss. Furthrmor, th rsponsibility pnalty, th crowding pnalty, or both can in principl mak a non-punitiv policy th prfrrd on. Th rror pnalty, on th othr hand, can not sustain th sam conclusion. Th rason is that th rror pnalty is xognous (policy-indpndnt). For th rsponsibility pnalty and th crowding pnalty this is not th cas. Both pnaltis ar ndognous in th sns that policy (q and t) affct thir significanc. W hav shown that if th rsponsibility pnalty is sufficintly high, rgulatory intrvntion, howvr insignificant, may induc dtrrnc bnfits that ar outwighd by social costs (ffort costs and th crowding of providr utility). Ovr-dtrrnc may also occur if th marginal crowding pnalty, valuatd at t=0, is high. It is also obsrvd that th scond (uppr) cornr solution ( q * = 1, t * = Y ) can not b ruld out sinc both Rt (1, Y ) and Rq (1, Y ) can b strictly positiv. Howvr, such an outcom is lss likly th highr th crowding pnalty and th rsponsibility pnalty, and th lowr ar rror tratmnt costs and marginal halth bnfits. Rsult 2: Givn social xtrnalitis and th prsnc of ndognous informal pnaltis, * * rgulatory intrvntion nd not b optimal ( q = t = 0). Such a rgim bcoms mor likly, (i) th highr th rsponsibility pnalty, VY ( ) WY (,0), and, (ii) th highr th marginal crowding pnalty, W2 ( Y t, t), valuatd at t=0. An intrsting obsrvation from (13) is that providrs ar affctd by q whn t=0. This maks possibl a third cornr solution whr t * = 0 and q * > 0, which rflcts th cas whr rsponsibility is assignd but no matrial dprivation is involvd. By valuating (19a,b) for such a policy choic, th conditions for optimality bcom as follows: 20 R ( q,0) = H P C + P( ) qw ( Y,0) < 0 t t 2 (20a) [ ] Rq( q,0) = q H PC P( ) V( Y) W( Y,0) 0 (20b) Th abov conditions ar simultanously fulfilld if: (i) th rsponsibility pnalty is zro or rlativly insignificant (s 20b), and (ii) if imposing a fin lads to a strong ngativ shift in providr utility that th marginal crowding pnalty valuatd at t=0 is significant (s 20a). Th 20 From (17) w gt that Φ t ( q,0) = W2 ( Y,0), whil from (16) Φ ( Y,0) = W( Y,0) sinc Δ U( w,0) = 0is zro. 17

19 rol of th crowding pnalty for raching such a conclusion bcoms clar whn ignoring th sam pnalty. If so, Φ ( Y,0) = 0, which implis that (20a) bcoms: t Rt ( q,0) = t H PC < 0, which, according to formr assumptions nvr can b tru. An optimal nforcmnt policy of th typ{ q * > 0, * t = 0 }, is possibl if th incurrd policy costs from assigning rsponsibility (th rsponsibility pnalty) ar lss than th social dtrrnc gains that follow from th sam policy, on th sam tim as th incurrd policy costs from imposing a small but positiv fin ar highr than social dtrrnc bnfit. This rsult is intrsting bcaus it xplains a frquntly obsrvd phnomnon in halth car rgulation th prsnc of formal pnaltis that do not involv matrial dprivations (administrativ sanctions). Such sanctions can now b undrstood as fficint institutions. 21,22 Rsult 3: Givn social xtrnalitis and th prsnc of ndognous informal pnaltis, th optimal rgulatory intrvntion may b on for which rsponsibility is assignd but no fin * * imposd ( q > 0; t = 0). Such an nforcmnt rgim bcoms mor likly th lowr th rsponsibility pnalty, VY ( ) WY (,0), and th highr th marginal crowding pnalty, W2 ( Y t, t), valuatd at t=0. Now, th intrior solution will b invstigatd. W know from th prvious discussion that this solution is likly if both th rsponsibility pnalty and th crowding pnalty ar modst or wak. By rwriting (19a,b) with (16) and (17), th optimality conditions (19a,b) can b prsntd in th following way: * * * * * H P() qw2 ( Y t, t) q Δ U( w, t ) = C (21a) P P t * * * * * H P()[ V( Y) W( Y t, t ) ΔU( w, t )] q Δ U( w, t ) = C + (21b) P P q 21 Administrativ sanctions (.g. rprimands and informal criticism) can b undrstood as pnaltis dsignd to crat dtrrnc by utilizing informal pnaltis. An additional justification has bn thir rol as guidanc to individual providrs (fdback on how to improv futur clinical prformanc). Howvr, th prsnc of ngativ motions in rspons to such sanctions confirms that providrs do not prciv thm solly as pdagogical instrumnts. Both fins and administrativ sanctions can b prcivd as formal pnaltis (institutions) in th sns that thy both ar initiatd by a rgulatory authority, howvr, hr th distinction btwn formal and informal pnaltis rfrs to th pnalizing agnt. 22 An additional conclusion from th abov discussion is that a highr C (rhabilitation costs), ctris paribus, maks th two cornr solutions (no rgulation and administrativ sanctions) lss likly. 18

20 Th lft hand sid of (21a,b) is th xpctd incom pnalty sinc bing qual to th xpctd transfr utility gain. Th optimal nforcmnt rgim dscribd in (21a,b) yilds undr-dtrrnc ( * < ˆ; s App. B.8-11). Th first-bst prvntiv ffort lvl () ˆ bcoms too costly to attain du to th prsnc of informal pnaltis, thus w hav idntifid a scond-bst solution. Th rol of informal pnaltis is similar to th rol of liability costs in th convntional modl. If liability costs wr includd, th scond-bst would bcom a third-bst. In th following, thr spcial cass ar considrd to shd mor light on th mchanisms at play. In addition, such an approach will b hlpful in dtrmining th rlativ importanc of th two policy instrumnts (q and t) in crating optimal dtrrnc. First, w considr th rror pnalty, ignoring th rsponsibility pnalty and th crowding pnalty. W know that W ( Y t, t) 2 in (21a) is zro whn th crowding pnalty is absnt (s 17). Furthrmor, VY ( ) WY ( tt, ) ΔUwt (, ) in (21b) is also zro whn both th crowding pnalty and th rsponsibility pnalty ar absnt. 23 Sinc both prfrnc trms in (21) ar zro, thr ar no policy costs associatd with q and t. Th optimal intrior solution is now charactrizd by: H Δ (, ) = (22) * * q U w t C P Th condition in (22) has similaritis with th sam condition for th convntional modl whn liability costs ar ignord (s 9). Howvr, th prsnc of an rror pnalty changs th optimal xpctd incom pnalty from q * [ U( Y) U( Y t * )], in th convntional modl, to * * Δ (, ) = [ ( ) ( )] in (22). Th liability rat and th fin ar now prfct dtrrnc q U W t q V Y V Y t substituts sinc nithr imposs policy costs. For th sam rason, th first-bst ffort lvl is attainabl. If liability costs wr introducd into th modl, th conclusion of sction 2 would mattr a maximal pnalty combind with a liability rat st at th minimum ncssary to nforc optimal complianc. Not that th first-bst ffort lvl that now mattrs may dviat from th first-bst ffort in th convntional modl. Th prsnc of an rror pnalty, although bing xognous, introducs an additional privat (and social) cost as compard to th convntional modl. Th risk of xprincing such a utility loss in association with advrs vnts will now mak it mor important both for providrs (and socity) to avoid such an outcom. 23 An absnt crowding pnalty implis that W(Y-t,t) is rplacd by W(Y-t). An absnt rsponsibility pnalty implis that th W-function can b rplacd by th V-function. Thus, VY ( ) WY ( tt, ) Δ Uwt (, ) quals VY ( ) VY ( t) Δ Uwt (, ). By insrting for th transfr utility gain, Δ U( w, t) = V( Y) V( Y t), th xprssion bcoms zro. 19

21 Now, considr th rsponsibility pnalty only (th rror pnalty and th crowding pnalty ar absnt), and th following optimality conditions: 24 H Δ (, ) < (23a) * * q U w t C P * * H P ()[ UY ( ) WY ( )] q Δ U( w, t ) = C + (23b) P P q From (23a) it obsrvd that an absnt crowding pnalty implis that changs in t occur at no policy costs whil from (23b) it follows that a chang in q incurs such costs. Consquntly, incrasing th ratio btwn q and t, for q ( ) * > 0, whil kping th xpctd incom pnalty, * Δ (, ) = ( ) ( ), constant, will rsult in highr policy costs. Hnc, th optimal q U w t q W Y W Y t fin must b th maximal on, t * = Y, whil q * is adjustd to mak (23b) binding. This nforcmnt rgim is similar to th on drivd for th convntional modl with liability costs. Consquntly, liability costs and th rsponsibility pnalty hav similar implications for optimal nforcmnt. 25 Th prsnc of th rsponsibility pnalty maks q and t imprfct dtrrnc substituts and t th prfrrd policy instrumnt. 26 Now, considr th crowding pnalty only (th rror pnalty and th rsponsibility pnalty ar absnt), and th following optimality conditions: 27 * * * * * H P() qu2 ( Y t, t ) q Δ U( w, t ) = C (24a) P P t H P()[ U( Y,0) U( Y t, t ) ΔU( w, t )] Δ = + (24b) ' * * * * * * q U( w, t ) C P ' ' ' P q Dspit th absnc of th rsponsibility pnalty, both prfrnc trms ar ngativ. This mans that th prsnc of th crowding pnalty inducs policy costs for both policy instrumnts. Thir rlativ attractivnss now dpnds on thir rlativ policy costs,.g. a mor significant 24 An absnt crowding pnalty implis that WY ( tt, ) is rplacd by WY ( t), now W 2 ( Y t, t) is zro (s 21a). An absnt rror pnalty implis that th V-function is rplacd by th U-function. Now, VY ( ) WY ( tt, ) ΔUwt (, ) in (21b) quals UY ( ) WY ( t) Δ Uwt (, ). By insrting for Δ U( w, t) = W( Y) W( Y t) w gt UY ( ) WY ( )(s 23b). 25 Howvr, (23) diffrs from (7) sinc a significant rsponsibility pnalty can rul out an intrior solution (non-punitiv rgim). Th optimal nforcmnt rgim yilds a scond-bst. Considring liability costs would induc a third-bst. 26 Anothr possibility is that (23a) binds whil (23b) is an inquality, howvr, this possibility can b ruld out sinc it suggsts an optimal policy for which q=0 and t>0. 27 An absnt rror pnalty and an absnt rsponsibility pnalty implis that both th V-function and th W- function ar rplacd by th U-function. Consquntly, W ( Y t, t) in (21a) can b writtn as U ( Y t, t) (s a) whil VY ( ) WY ( tt, ) ΔUwt (, ) in (21ba) quals UY (,0) UY ( tt, ) Δ Uwt (, ) (s 24b). 20

22 (marginal) crowding ffct will chang th rlativ attractivnss btwn q and t. Optimal nforcmnt can now, dpndnt on th prfrnc trms, b charactrisd by various combinations of th lvls of th two policy instrumnts. Rsult 4: Givn social xtrnalitis and th prsnc of ndognous informal pnaltis, th * * optimal rgulatory intrvntion may b on with a positiv fin; ( q > 0; t > 0). Such an nforcmnt rgim bcoms mor likly th lowr th rsponsibility pnalty, VY ( ) WY (,0), and th lowr th marginal crowding pnalty, W ( Y t, t) 2, valuatd at t=0. Th optimal positiv lvls of q and t will dpnd on th rlativ significanc of th rsponsibility pnalty to th (marginal) crowding pnalty. 4. CONCLUSIONS Strong ngativ sntimnts in rspons to th imposition of pnaltis ar common. Consquntly, such motions (informal pnaltis) crat dtrrnc incntivs and should b addrssd whn analysing optimal nforcmnt. In this study such an approach is undrtakn. First, a convntional framwork is applid to study optimal rror prvntion. Hr, standard conclusions ar confirmd: (i) som dtrrnc is ndd sinc th privat problm dos not coincid with th social on, (ii) fins and liability rats ar prfct dtrrnc substituts (optimal mnu) if monitoring is costlss, and (iii) first-bst dtrrnc is achivd by maximal pnaltis if monitoring is costly. Ths conclusions do not chang with th two spcifications of th social wlfar function or th dgr of providr agncy. Th abov findings ar modifid whn thr informal pnaltis ar introducd. Th first on, th rror pnalty which is indpndnt of policy (xognous), has minor ffcts on optimal dtrrnc. Th nxt two, th rsponsibility pnalty and th crowding pnalty, which ar ndognous in policy, chang policy prscriptions in various ways and rcommnd lss punitiv nforcmnt rgims. Now pnaltis blow thir maximum lvl ar found to b wlfarimproving and no rgulation can b an optimal policy. Th first-bst solution bcoms unattainabl, with or without liability costs, forcing us to sarch for scond and third-bst policis. Sinc incntiv provision (dlgation) coms at a cost, optimal nforcmnt yilds undr-dtrrnc, and fins and liability rats ar imprfct dtrrnc substituts. Furthrmor, an optimal nforcmnt rgim charactrisd by a positiv liability rat and a fin qual to zro, is possibl, hnc administrativ sanctions, institutions that assign rsponsibility but do not involv any matrial dprivations, can b undrstood as rational ons. A ncssary condition for such a 21

23 conclusion is that informal pnaltis ar highly snsitiv to formal pnaltis, i.., a small positiv fin yilds a significant shift in providr utility. Our conclusions may hav rlvanc for othr aras whr informal pnaltis ar important, i.., traffic safty and workplac accidnts. Th dtrrnt valu of mdical malpractic liability has bn qustiond bcaus tortfasors ar typically protctd by liability insuranc, and bcaus othr incntivs such as xprinc rating, mandating lvls of insuranc covrag and informd halth car purchasrs, ar wak or absnt. Howvr, such prsumptions ignor th rol informal pnaltis, which ar uninsurabl, may hav in arrsting moral hazard. Furthrmor, parts of th xplanation for a numbr of rcnt proposals for tort rform such as strict liability, ntrpris liability and no-fault systms, may li with th significanc of informal pnaltis (assign lss blam). 28 Informal pnaltis may also xplain a puzzl apparing in th litratur: Halth car workrs xprss a significant far of xprincing mdical rrors and much vidnc confirms th practic of dfnsiv mdicin (s.g. Summrton, 1995; Symon, 2000; Ksslr and McClllan, 1996, 2002a,b; and Dubay t al., 1999) at th sam tim as formal providr liability in halth car appars to b rathr limitd. 29 Valus of profssionalism and mdical thics ar promotd to protct patints and dlivr high-quality car, and informal pnaltis, at last to som xtnt, bcom th othr sid of th coin. In this prspctiv, valus stablishd to prvnt imprfct agncy bcom th vry rason that xtrnal rgulation (dtrrnc) in pursuit of th sam objctivs, bcoms costly. Policydpndnt informal pnaltis mak rgulation lss ffctiv, and th rgulator can b said to b bttr off in a convntional modl for which corrct social incntivs can b dsignd at lowr costs. Th significanc of informal pnaltis can b affctd by policy in othr ways. Thy may bcom lss important ovr tim by campaigning against mdical culturs of naming, blaming and shaming, and mor important if th us of sanctions is announcd publicly,.g. to mploys, collagus and mdical associations. An important dimnsion of informal pnaltis, as with prfrncs in gnral, i.., risk avrsion, disutility of ffort and altruism, is thir idiosyncratic charactr. Thir significanc varis across providrs, institutions (local culturs) and, prhaps, countris (national culturs). Thir impact may also vary across mdical spcialtis du to slf-slction ffcts among providrs. This analysis rcommnds pnaltis that vary across providrs according to individuals 28 An injurd prsons right to rcovr damags in no-fault systms dos not ncssarily dpnd on fault alon, but also on som objctiv critria. 29 Loss of authorisation and imprisonmnt occur vry sldom and mainly for criminal acts such as drug abus and sxual offncs, rlativly rar occurrncs in normal clinical practic. 22