Medical Malpractice: The Optimal Negligence. Standard under Supply-side Cost Sharing

Transcription

1 Meical Malpractice: The Optimal Negligence Stanar uner Supply-sie Cost Sharing Anja Olbrich ;y Institute of Social Meicine an Health Economics, Otto-von-Guericke University Abstract This paper elaborates on the optimal negligence stanar in a worl where physicians choose amage prevention subject to erroneous court jugements an to the egree of supply-sie cost sharing. Liability uncertainty in malpractice lawsuits lea some physicians to provie excessive prevention an others to unerprovie, which results in a welfare loss compare to the poole rst-best equilibrium uner perfect information. The stanar that minimizes the welfare loss epen on the cost share: Uner traitional, close to full cost reimbursement it is lower than the rst-best stanar, while uner substantial supply-sie cost sharing it increases an may excee the rst best. JEL classi cation: I11, K13 Keywor: Meical malpractice, negligence rule, erroneous court jugments, efensive an negligent meicine Aress: Institute of Social Meicine an Health Economics (ISMHE), Otto-von- Guericke University, Leipziger Strasse 44, Mageburg, Germany. Tel.: Fax: anja.olbrich@meizin.uni-mageburg.e. y I thank Stefan Feler an Daniel Kuessner as well as the participants of the 5th European Conference on Health Economics in Lonon for helpful comments an iscussions. 1

2 1 Introuction Meical treatment, although utility enhancing in the rst place, exposes patients to the risk of an injury. The magnitue of risk epen partially on the physicians prevention activities, etermine by their choice of iagnostics an therapies. As prevention increases treatment costs, physicians will not necessarily reuce the risk to an appropriate level. However, aequate incentives for amage avoiance may be triggere by a liability rule. In this paper, I examine the impact of the negligence rule - the preominant liability principle for meical malpractice in the western worl. Uner this rule courts awar a compensation to injure patients only if physicians fail to comply with a particular negligence stanar. This provies physicians with an incentive to apply an appropriate level of amage prevention. I will focus my analysis on liability uncertainty arising from erroneous jugments of courts. Brennan et al. (1996) report from meical malpractice lawsuits that courts sometimes erroneously hol physicians liable who ahere to the relevant negligence stanar, an fail to etect careless behavior. This, in turn, a ects the incentives of the liability rule an physicians, fearing the threat of liability, may provie excessive amage prevention. Likewise, reckless physicians may unerprovie in the hope to escape liability. In fact, evience for both behavior patterns can be foun. Kessler an McClellan (2002b) show for the treatment of cariovascular iseases an Dubay et al. (1999) for obstetrics that excessive prevention exists. An estimate number of fatal injuries per year can be attribute to meical negligence in the USA (see Danzon, 2000). Using a formal moel of physicians behavior this paper o ers a joint explanation for both phenomena. It emonstrates how erroneous court jugments inuce eviations of amage prevention from a given negligence stanar, an thereby goes beyon approaches foun in the literature. For instance, a few papers have iscusse that excessive prevention is attribute to an excessive 2

3 level of compensation an other malpractice costs (see Kessler an McClellan, 2002a or Baicker an Chanra, 2004). Quinn (1998) links uninsurable reputation losses to excessive prevention in a formal analysis. The erive separate equilibrium in amage prevention implies a loss of the negligence rule s e ectiveness an with it a ecrease of welfare. This is because the society s expecte total costs of health care increase beyon the rst-best level achieve uner perfect information. In line with that, experts argue that excessive prevention signi cantly contributes to the ever rising costs of health care (Kessler an McClellan, 1997). The same allegation applies to insu cient prevention because it increases the probability of a amage occurrence (Kohn et al., 2000). Uner changing reimbursement conitions for health care the e ectiveness of liability incentives plays a particular role. Recently most western countries change their traitional, close to full cost reimbursement schemes to inclue a substantial supply-sie cost sharing in orer to stop the steay increase of treatment costs. By assigning physicians a consierable share of treatment cost, more e orts are exerte at cost containment (compare e.g. Ellis an McGuire, 1993). As supply-sie cost sharing increases expecte marginal treatment costs, physicians also reuce prevention activities an thereby increase the probability of a amage occurrence. For this reason a iscussion has arisen on whether the liability incentives nee to be change (see e.g. for the USA Kessler an McClellan, 2002b). German legal experts, focusing on the appropriate level of negligence stanar, generally isapprove changes. In particular they refuse lower stanar that incorporate a trae-o between costs an bene ts (see e.g. Ste en, 2000). Consequently most of the stanar evelope uner the generous reimbursement scheme in the past are also consiere to be optimal uner the new reimbursement conitions. In contrast I show that given a particular reimbursement scheme, imperfectly informe courts shoul trae-o costs an bene ts of amage prevention an apply an optimal negligence stanar that minimizes the society s 3

4 expecte total costs with respect to amage prevention. Uner such optimal liability conitions, excessive an insu cient prevention cause i erent welfare e ects at the margin an, therefore, eviate from rst-best prevention, as e ne uner perfect information, in i erent irections. This rst-best level, then, allows me to aequately e ne efensive an negligent meicine. Given traitional, close to full cost reimbursement I prove that efensive meicine ominates the society s expecte total costs with respect to amage prevention, renering a stanar lower than the rst-best stanar optimal. The introuction of a substantial cost share changes the level of amage prevention an with it the valuation of efensive meicine compare to negligent meicine at the margin. This ten to increase the optimal stanar. The rest of the paper is organize as follows: Section 2 presents the moel an erives the physicians optimum in amage prevention an e orts uner uncertain liability. Section 3 etermines the optimal negligence stanar uner traitional reimbursement. The optimal ajustment of the stanar following the introuction of a substantial supply-sie cost sharing is erive in Section 4. Afterwar a comparison between the optimal stanar uner uncertain liability an the rst-best stanar is rawn. Conclusions an a iscussion of the results can be foun in Section 5. 2 The physicians behavior uner uncertain liability Proviers of meical treatment are assume to be risk-neutral. They ecie on the level of amage prevention y an e orts at cost containment e; of which the former is imperfectly observe by courts an the latter is unobservable. Treatment costs K(y; e) are uncertain so that the observe level of costs oes not reveal the exerte level of amage prevention an e orts. In orer to avoi ambiguous results I assume that the expecte treatment costs E[K(y; e)] C(y; e) are aitively separable in amage prevention an ef- 4

5 forts, i.e. C(y; e) = C(y) + C(e): Thus, the cross-erivative is zero (C ye = 0) an no interference between rst-orer conitions for optimal prevention an e orts occurs: Expecte costs are strictly convex in both arguments (C y > 0; C e < 0; C yy ; C ee > 0): The physicians e orts at cost containment cause a isutility that is measure in monetary terms H(e) an which is increasing at an increasing rate (H e > 0; H ee > 0). Reimbursement epen on the treatment costs. Expecte reimbursement takes the form of f + (1 )C(y; e) where f enotes a xe payment an is the supply-sie cost share. Then, = 1 represents a pure prospective payment, = 0 full cost reimbursement, an 0 < < 1 cost sharing. A possible amage L > 0 to the patients uring the treatment is measure in monetary terms. It occurs with probability P (y) that ecreases with the level of prevention at an increasing rate (P y < 0; P yy > 0). In line with the prevailing liability principle for meical malpractice, physicians take into account the potential payment of compensation. If courts were perfectly informe, the physicians expecte payment with prevention level y woul epen on the given negligence stanar s > 0: 8 >< 0 EL (s; y) = >: P (y)l if y s y < s 9 >= >; : (1) It implies that in case of an injury physicians only have to compensate the patients if they exert insu cient prevention as measure by the stanar (y < s) : 1 In contrast, ahering to the stanar (y s) always lea to an acquittal. The expecte payment of compensation changes when the physicians level of amage prevention is imperfectly observe by courts. Uner this conition courts base their jugments on a vague signal of amage prevention: This signal will eviate from the exerte prevention y with error term "; which is rawn uniformly from the interval [ x; x] : 2 The probability ensity function is g("): Thus, at a level of amage prevention not lower than the relevant negligence stanar y s the probability of erroneous liability takes the value 5

6 of R s y x g(")" = G(s y): In case of y < s the probability of an erroneous acquittal amounts to 1 G(s y). The null hypothesis assumes physicians to comply with the negligence stanar, so that G(s y) = p I (s; y) enominates the probability of an erroneous court jugment of type 1 an 1 G(s y) = p II (s; y) the probability of an erroneous court jugment of type 2, respectively: Unlike Polinsky an Shavell (1989), who assume error probabilities as given, the negligence stanar an prevention activities in this moel etermine the error probability. The probability of a type 1 error increases with the negligence stanar, ecreases with the level of amage prevention, an vice versa for the probability of a type 2 error, i.e. p I s; p II y > 0 an p I y; p II s < 0: The expecte payment of compensation, therefore, amounts to: 8 >< gel (s; y) = >: 1 p I (s; y)p (y)l p II (s; y) P (y)l if y s y < s 9 >= >; : (2) The physicians expecte pro ts consist of the expecte reimbursement minus the expecte costs of treatment an the expecte payment of compensation: E (y; e) = f + (1 )C(y; e) C(y; e) H(e) g EL (s; y) : (3) Because the negligence rule forms a iscontinuity in expecte pro ts at the negligence stanar, two necessary conitions for optimal prevention activities arise: C y p I (s; y i ) P y (y i )L p I yp (y i )L = 0 if y s, (4) C y 1 p II (s; y i ) P y (y i )L + p II y P (y i )L = 0 if y < s: (5) Both conitions may be ful lle at the same time so that a separate equilibrium arises. In this case physicians increase amage prevention un- 6

7 til expecte marginal treatment costs C y equal expecte marginal bene ts. Expecte marginal bene ts consist of a reuce expecte compensation an epen on the relative value of exerte prevention compare to the stanar. Proposition 1 If physicians bear a positive cost share > 0 an can not increase their expecte pro t by changing the level of amage prevention, a separate equilibrium with insu cient an excessive prevention y I < s < y E arises. Figure 1 gives an illustration of this proposition. The physicians expecte treatment costs with respect to amage prevention C(y) are epicte by the continuous, strictly increasing function. The expecte payment of compensation EL g (s; y) is represente by the strictly ecreasing function, having a kink at y = s; which is ue to the transition from type 1 to type 2 errors at the stanar: The probability of erroneously holing a iligent physician liable at the stanar approximates the probability of holing a careless physician liable close to the stanar: p I (s; s)p (s) 1 p II (s; y) P (y). An optimum above the stanar characterizes a iligent physician who is proviing excessive prevention (i = E): It is epicte in gure 1 at the minimum of the thick line. Accoring to conition (4) the probability of an erroneous court jugment of type 1 etermines the physician s expecte bene ts of extene prevention. Full cost reimbursement = 0 is a su cient conition for excessive prevention to be present. An optimum below the stanar, as shown in gure 1 at the minimum of the thin line, belongs to a careless physician who is proviing insu cient prevention (i = I). Conition (5) inicates that the probability of an erroneous court jugment of type 2 reuces the incentive for proviing aitional amage prevention. A positive supply-sie cost share > 0, leaing to increasing expecte marginal treatment costs, turns out to be a necessary conition for insu cient prevention to be optimal. 3 A su cient conition for a separate equilibrium is that both types of physicians have no incentive to change the level of amage prevention. Uner 7

8 a uniform xe payment f an a positive cost share this is ful lle if larger expecte treatment costs of excessive prevention exactly balance the larger expecte payment of compensation ue to insu cient prevention: [C(yE ) C(y I )] = EL g (s; yi ) EL g (s; y E ) > 0. 4 This case is represente in gure 1. Figure 1 about here The physicians reactions on a marginal variation of the negligence stanar s an the cost share can be erive, applying a comparative static analysis of the rst-orer conitions (4) an (5). As emonstrate in the Appenix y the level of amage prevention increases with the stanar i > 0 : Since a higher stanar increases (ecreases) the probability of a type 1 (type 2) error, the marginal liability pressure increases, which in turn inuces physicians to exert more amage prevention. In contrast, amage prevention ecreases with the physicians cost share y i marginal treatment costs. < 0; channelle by an increase of expecte The optimal e orts at cost containment e follow from the conition: H e (e ) = C e (e ) : (6) E orts, thus, only epen on the reimbursement scheme. At the optimum the marginal isutility of e orts equals the marginal bene t in form of reuce expecte treatment costs: Conition (6) implies that uner full cost reimbursement ( = 0) physicians have no incentive to save resources (i.e. e = 0). As in (6) the marginal bene t of reuce expecte treatment costs increases with the physicians cost share, e orts increase too e > 0. 8

9 3 The optimal stanar uner traitional reimbursement With a given bene t of treatment for patients, the society s goal is to minimize the consumption of resources by meical malpractice an by insu cient e orts at cost containment. Given a particular reimbursement scheme courts shoul therefore apply an optimal negligence stanar s (); which minimizes the expecte total costs with respect to amage prevention an e orts at cost containment ET C: Since reimbursement is a transfer from patients to physicians an the physicians ecisions epen on the negligence stanar, on the cost share as well as on the attainability of a non-negative expecte pro t, the expecte total costs amount to: ET C [yi (; s) ; e ()] = X $ i [C (; s) + H () + P (; s) L] ; (7) i=e;i where $ i is the share of type i physicians. Traitional reimbursement schemes such as fee-for-services or even cost reimbursement imply a positive but very low supply-sie cost share =! 0. This comes close to full cost reimbursement an the physicians ecisions at any negligence stanar s are as expecte: As expecte marginal costs of amage prevention an expecte marginal bene ts of e orts ecrease to almost zero, physicians provie excessive prevention y E > s an exert very low e orts at cost containment e () = e! 0. On the other han insu cient prevention plays only a minor role. Since ecreasing the liability threat by more amage prevention is very cheap, the eviation from a stanar is very low: s yi =. The minimization of the society s expecte total costs (7) uner traitional reimbursement, then, yiel the optimal negligence stanar s (): It is etermine by the rst-orer conition: 5 9

10 $ E [C y (; s ) + P y (; s )L] y E + $ I [C y (; s ) + P y (; s )L] y I = 0: (8) This expression shows that the stanar s impact on amage prevention an, as a consequence, on the society s expecte total costs etermine the optimal stanar. Moreover, a worl with perfect information about the physicians amage prevention turns out to be a special case: Uner this conition all physicians comply with every single stanar so that both terms in (8) collapse into one. The expecte total costs are minimize by the rst-best level of amage prevention y F B, where expecte full marginal costs an expecte marginal bene ts balance C y y F B = P y y F B L (see e.g. Cooter an Ulen, 2000 for the Han-Rule). Courts shoul therefore set the stanar at the rst-best level of amage prevention inepenent of the reimbursement scheme s = y F B. 6 In contrast erroneous jugments of courts inuce a separate equilibrium in amage prevention, which increases the expecte total costs with respect to amage prevention beyon the rst-best level. The society attempting to choose an optimal stanar, thus, faces a trae-o as escribe by (8): Increasing the stanar will increase the amount of excessive prevention. If amage prevention excee the rst-best level ye (; s ) > y F B ; expecte total costs will increase. Consequentially I call prevention in this interval efensive meicine. At the same time insu cient prevention ecreases which below the rstbest level yi (; s ) < y F B ecreases expecte total costs. On this account amage prevention in this interval is enominate negligent meicine: At the optimum the two opposite e ects of efensive an negligent meicine balance. Proposition 2 Uner traitional reimbursement = imperfectly informe courts shoul apply an optimal stanar that is lower than the rst-best stanar s () < y F B : Uner traitional reimbursement expecte marginal costs of amage pre- 10

11 vention are so low that the probability of erroneous liability inuces a share of physicians to largely exten amage prevention. So if the rst-best stanar s = y F B were applie, efensive meicine woul cause substantial marginal costs to the society. At the same time the eviation of negligent meicine from the rst-best stanar woul be very small an expecte marginal bene ts of ecrease negligent meicine woul take a very low value C y y I (; y F B ) + P y y I (; y F B ) L! 0: Consiering this asymmetry of expecte marginal costs an expecte marginal bene ts, efensive meicine turns out to be the major problem uner traitional reimbursement. As a result ecreasing the stanar below the rst-best mainly prouces expecte bene ts on account of reuce efensive meicine. At the optimum a stanar lower than the rst-best stanar s () < y F B ensures that the society s expecte total costs with respect to amage prevention are minimize. 4 The optimal stanar uner cost sharing 4.1 The optimal stanar Western countries have introuce reimbursement schemes with a substantial supply-sie cost sharing > in orer to increase the physicians e orts at cost containment. As supply-sie cost sharing increases expecte marginal treatment costs, physicians also reuce amage prevention activities an thereby increase the probability of a amage to the patients. Uner uncertain liability it can be shown that the society s expecte total costs with respect to amage prevention an e orts at cost containment ecrease with an implementation of a substantial cost share. From (7), the expecte total cost function erive with respect to the physicians cost share is: 11

12 ET C (; s) = X i=e;i $ i fc y (; s) + P y (; s) Lg y i + (1 ) C e () e : (9) Evaluate at the point of traitional reimbursement with = the rst term in the sum (i = E) takes a negative value an the secon term (i = I) is positive, which can be interprete as the society s expecte bene ts of ecrease efensive meicine an expecte costs of aggravate negligent meicine ue to a higher cost share. A su cient conition for a ecrease of expecte total costs, therefore, is that the etrimental e ect of a higher cost share on amage prevention (measure in relative marginal terms) is not larger than the relative expecte bene- ts of ecrease efensive meicine: y I (;s) y E (;s) $ EC y[y E (;s)]+py[y E (;s)]l $ I C y[y I (;s)]+py[y I (;s)]l : This is in particular ful lle at the rst-best stanar s = y F B ; where the relative expecte bene ts of ecrease efensive meicine are very large (compare Section 3). From conition (8) follows that at the optimal stanar uner traitional reimbursement s = s () the etrimental e ect of a higher cost share on amage prevention must not be larger than the stimulating e ect of a higher stanar: y I (;s ) y E (;s ) y I (;s ) y E (;s ) (compare the Appenix): The sign of the thir term is negative because increase e orts unambiguously curb expecte treatment costs C e < 0: In conclusion (9) can become negative ET C(;s) j = < 0, inicating that the society bene ts from an introuction of a substantial cost share. A substantial supply-sie cost share changes the level of negligent an efensive meicine, which may have an e ect on the optimal negligence stanar s. In orer to clarify this correlation conition (8) is totally i erentiate with respect to the negligence stanar an the cost share; yieling: P = i=e;i $ i(c yy+p yyl) y i y i +$ E(C y+p yl) 2 y E +$ I(C y+p yl) 2 y I ET C ss : (10) With s as the unique optimum, the enominator is negative. The rst term 12

13 in the nominator is negative too: Because expecte treatment costs an the amage probability are convex in amage prevention, the society s expecte total marginal bene ts of a higher stanar increase with a higher cost share. Since a supply-sie cost share can be assume not to increase the stanar s positive in uence on amage prevention 2 y i nominator is non-positive. 0; the secon term in the Only the thir term can become positive: As emonstrate above, the society bene ts from a higher stanar that reuces negligent meicine. However, if cost sharing ecreases the positive in uence of the stanar 2 y I society s bene ts of a higher stanar ecreases. < 0; the Proposition 3 The introuction of a substantial supply-sie cost share shoul be accompanie by an increase of the optimal negligence stanar cost sharing weakly a ects the stanar s in uence on negligent meicine. > 0 if This proposition is riven by three istinct forces: An increase of the supply-sie cost share lea physicians to ecrease prevention activities. This in turn ecreases expecte marginal costs of efensive meicine an increases the society s expecte bene ts of less negligent meicine ( rst term in the nominator). Furthermore, the society s expecte total costs of efensive meicine as such are not increase by supply-sie cost sharing (secon term). Due to the thir term in the nominator the proposition nee not always hol. As shown in the Appenix, by inserting the necessary conition for an optimal stanar (8) into the nominator of (10) an a minor transformation, a su cient conition for Proposition 3 evolves. It emphasizes the importance of elasticities y i = ; 2y i y i 0: As long as a higher cost share oes not have more impact on the stanar s e ectiveness in ecreasing negligent meicine than in increasing efensive meicine, the optimal negligence stanar increases with supply-sie cost sharing: If y I ; ; then y E ; > 0: (11) 13

14 Accoring to this conition, Proposition 3 hol in particular uner traitional reimbursement with 2 y I = 0. y i =! 0 an uner a zero cross-erivative ; 4.2 Comparison with the rst-best stanar The introuction of a substantial supply-sie cost share may require an increase of the optimal negligence stanar. In this case the optimal stanar approximates the rst-best stanar an may even excee it. The evaluation of (8) at the rst-best stanar ET C j s=y F B gives a conition inicating the value of the optimal stanar s () compare to rst-best stanar. If the stimulating e ect of a higher stanar on amage prevention (measure in relative marginal terms) exactly equals the relative costs of increase efensive meicine, the optimal stanar takes the rst-best value s () = y F B : y I(;y F B ) y E (;yf B ) = $ E C y y E (; y F B ) + P y y E (; y F B ) L $ I C y [yi (; yf B )] + P y [yi (; yf B )] L : (12) The optimal negligence stanar oes not take the rst-best level, if the left han sie of (12) is always lower than the right han sie. This is, for example, the case with a very large share of efensive physicians $ E $ I! 1 or if efensive physicians react very sensitively to an increase of the stanar y I( ;yf B ) beyon the rst-best level! 0: In both cases the expecte marginal y E (;yf B ) costs of a stanar equal to or higher than the rst-best stanar are too high ue to efensive meicine an the society s expecte total costs with respect to amage prevention are minimize by a lower stanar s () < y F B. 5 Conclusions an Discussion This paper aresses provier incentives for preventing amages to patients in course of a meical treatment. Uner the negligence rule - the preominant liability principle for meical malpractice - physicians have to pay a compensation to injure patients only if the court observes that they faile to comply 14

15 with the promulgate negligence stanar. In orer to avoi this payment physicians exert the level of amage prevention given by the stanar. A problem arises when information about the physicians level of amage prevention is imperfect. If courts base their jugments on a vague signal of amage prevention, the incentives of the negligence rule change. Since physicians account for uncertain liability in their pro t optimization, a welfareecreasing separate equilibrium in amage prevention arises. If physicians eviate from rst-best amage prevention, as e ne uner perfect information, in i erent irections efensive an negligent meicine occur. By assuming that the negligence stanar an exerte prevention etermine the probability of an erroneous court jugment, I erive a stanar that balances marginal welfare e ects of negligent an efensive meicine, minimizing the society s expecte total costs with respect to amage prevention. Furthermore the reimbursement scheme is shown to in uence the optimal stanar. Uner traitional, close to full cost reimbursement a stanar lower than the rst-best stanar is optimal. With an introuction of a substantial supply-sie cost share, the optimal stanar may increase. Interestingly there s no guarantee that the optimal stanar ever achieves the rst-best negligence stanar. If the share of efensive physicians is very large or efensive physicians react very sensitively to an increasing stanar, the optimal stanar shoul always be lower than the rst-best stanar. This is in line with Danzon (2000) noting that the rst-best level of amage prevention is certainly not the appropriate negligence stanar. She argues that, given the costs of obtaining information an controlling moral hazar in health care markets, a eviating stanar is more likely to maximize welfare. With the nings of this paper the question of whether liability incentives shoul be mae compatible with the new reimbursement schemes for meical health care services can be answere - at least with respect to the negligence stanar. This topic is of some importance especially in countries where a substantial supply-sie cost sharing in health care has been introuce. Since the cost share etermines the optimal negligence stanar, a realignment of 15

16 the stanar is actually inicate. Danzon (1997) points out that stanar, as they evelop uner traitional reimbursement, fail to incorporate a trae-o between marginal bene ts an costs of prevention activities. In the context of the moel presente here traitional stanar excee the rst-best level by far an preserving them, as suggeste by legal experts, certainly causes a welfare loss. Feess an Ossig (2004) also examine the relationship between liability an reimbursement incentives. In contrast to the present paper they aopt the insurer s point of view an etermine the optimal supply-sie cost share at a given egree of liability risk. Furthermore, Feess an Ossig base the analysis on some kin of a strict liability rule an assume prevention costs as unobservable. The latter is implemente by H(y; e) > 0; H y > 0 an a positive cross-erivative H ye > 0: This connects a higher liability risk with a higher supply-sie cost share, backing an complementing my result: If cost sharing not only irectly but also inirectly (via a positive cross-erivative) ecreases negligent an efensive meicine, the society s expecte total marginal bene ts of a higher stanar aitionally increase. Apart from that, the perspective of the analysis chosen by Feess an Ossig can be challenge. At present, reimbursement schemes with a substantial supply-sie cost share have alreay been introuce an the question is, rather, whether liability incentives nee to be ajuste. For example, there is an ongoing iscussion among German legal experts whether negligence stanar nee to be aapte to new reimbursement conitions establishe by the statutory health insurance (Kern, 2002). Empirical research in the USA concerns the optimal liability policy in an era of manage care (see Section 1). Therefore, the moel evelope in the paper at han ts better the problems of toay. In consieration of the interepenence of provier incentives, an innovative approach woul be to simultaneously optimize cost share an negligence stanar. Keeping the erivation tractable an the results practicable is emaning an I leave this for future research. Furthermore Demougin an Fluet (2005) emonstrate that the stanar of proof etermines the liabil- 16

17 ity incentives uner imperfect information. Due to technical similarities with the negligence stanar in the present moel, the epenence of the optimal stanar of proof on the supply-sie cost share coul be shown. 17

18 Notes 1 As in the stanar literature I assume that courts can not etermine the potential amages uner compliance with the negligence stanar. Uner this realistic assumption physicians are always hel liable for the total amage L. 2 Elin (1994) moels imperfect information about prevention in the same way. A normal istribution of errors woul not change the results if aitional assumptions about secon-orer erivatives of the cumulative istribution function are impose. 3 See the Appenix for the secon-orer conitions. 4 The Appenix shows that splitte xe payments f i or a particular preference for iligence among a share of physicians also lea to the separate equilibrium. 5 See the Appenix for the complete approach an also for the secon-orer conition. 6 As shown by Olbrich (2004) y F B is also the optimal negligence stanar when courts are perfectly informe an physicians i er w.r.t. intrinsic motivation. 18

19 Appenix Appenix Section 2 Excessive amage prevention y E > s is a globally optimal ecision, since E yy (ye ) = C yy (ye ) 2pI yp y (ye ) L pi (s; ye ) P yy (ye ) L is negative. Insu cient amage prevention y I < s constitutes a global optimum, since E yy (y I ) = C yy (yi )+2pII y P y (yi ) L 1 p II (s; yi ) P yy (yi ) L is negative. A separate equilibrium arises if physicians expect equal pro ts inepenent of their behavior E (ye ; e ) = E (yi ; e ) : With f i = C(yi ; e ) + H (e ) + EL g (s; yi ) expecte pro ts are zero an the xe payment can but nee not i er between physicians (see Section 2). If expecte treatment costs plus payment of compensation uner a uniform payment f are lower with insu cient prevention, a separate equilibrium also arises with a share $ E of physicians who su er a su ciently large isutility D when acting recklessly: h i D > [C(yE ) C(y I )] + gel (s; y E ) EL g (s; y I ) : Optimal amage prevention an e orts respon to a variation of the negligence stanar an the cost share. In orer to etermine the reactions a comparative static analysis of the physicians necessary conitions (4), (5) an (6) is applie. It reveals for the stanar: ye = pi sp y(ye) > 0; y I = pii s P y(yi) > 0; E yy(ye)=l E yy(yi)=l an for the cost share: y i = Cy(y i ) E yy(y i ) < 0, e = Ce(e ) H ee(e ) > 0: 19

20 Appenix Section 3 The complete optimization program of (8) is: min s ET C [yi (; s) ; e] = P n i=e;i $ i f i + (1 )C [yi (; s) ; e] + P [yi (; s)] L EL g o [s; yi (; s)] w.r.t. E [y i (; s) ; e] 0 with i = E; I: The secon-orer conition of the optimal negligence stanar is obtaine from (8). Deriving it w.r.t. the negligence stanar, s is a global solution if: $ i Pi=E;I [C yy (s ) + P yy (s ) L] y i 2 + [Cy (s ) + P y (s ) L] 2 y i () 2 > 0: Assuming that the positive in uence of the stanar on amage prevention non-increasing 2 yi 0 (i = E; I); overcautious physicians shoul react rather () 2 insensitively at the margin so that 2 ye () is low or zero. 2 Appenix Section 4 The society s expecte total costs with respect to amage prevention an e orts at cost containment can be shown to ecrease with an implementation of a substantial cost share at the optimal stanar uner traitional reimbursement s (). Evaluating (9) at [; s ()] an inserting conition (8) yiel a su cient conition for this result: $ E [C y (; s ) + P y (; s )L] y E (;s ) y E (;s ) y I (;s ) yi (;s ) 0: Since the expecte total costs increase with more efensive meicine, the rst term in brackets is negative an the secon term positive, this is true for y I (;s ) y E (;s ) y I (;s ) y E (;s ) : A su cient conition for Proposition 3 to hol erives by inserting (8) into the nominator of (10). The nominator, then, takes P i=e;i $ i (C yy + P yy L) y i yi + $ E (C y + P y L) 2 y E y E y I 2 y I which is always negative with a non-positive term in brackets. Transforming it yiel ; 2 y I y I 2 y E y E or y I ; y E ; : 20

21 References Baicker, Katherine, an Amitabh Chanra. (2004). "The e ect of malpractice liability on the elivery of health care." NBER Working Paper Series. Brennan, Troyen A., Colin M. Sox, an Helen R. Burstin. (1996). Relation between negligent averse events an the outcomes of meical-malpractice litigation. The New Englan Journal of Meicine 335, Cooter, Robert, an Thomas Ulen. (2000). Law an Economics. Reaing, Mass.: Aison-Wesley. Danzon, Patricia M. (1997). "Tort liabilty: A mine el for manage care." The Journal of Legal Stuies 26, Danzon, Patricia M. (2000). "Liability for meical malpractice." In Culyer, Anthony J., an Joseph P. (e.), Hanbook of Health Economics, Vol. 1B. Amsteram: Elsevier Science. Demougin, Dominique, an Claue Fluet. (2005). "Deterrence versus juicial error: A comparative view of stanar of proof." Journal of Institutional an Theoretical Economics 161, Dubay, Lisa, Robert Kaestner, an Timothy Waimann. (1999). "The impact of malpractice fears on cesarean section rates." Journal of Health Economics 18, Elin, Aaron S. (1994). "E cient stanar of ue care: Shoul courts n more parties negligent uner comparative negligence?" International Review of Law an Economics 14, Ellis, Ranall P., an Thomas G. McGuire. (1993). "Supply-sie an emanie cost sharing in health care." Journal of Economic Perspectives 7, Feess, Eberhar, an Sonja Ossig. (2004). "Reimbursement schemes for hospitals, malpractice liability, an intrinsic motivation." Working Paper Aachen University. 21

22 Kern, Bern-Rüiger. (2002). "Haftungsrechtliche Aspekte bei er Abweichung von meizinischen Qualitätsstanar un qualitätssichernen Vorgaben in er gesetzlichen Krankenversicherung." Gesunheitsrecht 1, 5-9. Kessler, Daniel, an Mark McClellan. (1997). "The e ects of malpractice pressure an liability reforms on physicians perceptions of meical care." Law an Contemporary Problems 60, Kessler, Daniel, an Mark McClellan. (2002a). "How liability law a ects meical prouctivity." Journal of Health Economics 21, Kessler, Daniel, an Mark McClellan. (2002b). "Malpractice law an health care reform: optimal liability policy in an era of manage care." Journal of Public Economics 84, Kohn, Lina T., Janet Corrigan, an Molla S. Donalon (e.). (2000). To err is human. Washington, DC: National Acaemy Press. Olbrich, Anja. (2004). "Heterogeneous physicians, imperfect courts, an the negligence stanar." Unpublishe Working Paper. Polinsky, A. Mitchell, an Steven Shavell. (1989). "Legal error, litigation, an the incentive to obey the law." Journal of Law, Economics & Organization 5, Quinn, Robert. (1998). "Meical malpractice insurance: The reputation e ect an efensive meicine." Journal of Risk an Insurance 65, Ste en, Erich. (2000). "Die Arzthaftung im Spannungsfel zu en Anspruchsbegrenzungen es Sozialrechts für en Kassenpatienten." In Hans Erich Branner, Horst Hagen, an Rolf Stürner (e.), Festschrift für Karlmann Geiß: Zum 65. Geburtstag. Köln: Carl Heymanns Verlag. 22

23 II [ 1- p (s,0)] P(0)L II τc(y)+ 1- p (s, y) P(y)L I τc(y)+ p (s, y)p(y)l τc(y) * * f-τc(e )- H(e ) II 1- p (s, y) P(y)L I p (s,s)p(s)l I p (s, y)p(y)l EL(s, y) * yi s * y E Prevention y Figure 1. Expecte costs at separate equilibrium * * ( y,y ) with a uniform payment f. I E