Measuring adverse selection in managed health care

Ž. Journal of Health Economc 19 2000 829 854 www.elever.nlrlocatereconbae Meaurng advere electon n managed health care Rchard G. Frank a,), Jacob Glazer b, Thoma G. McGure c a HarÕard UnÕerty, HarÕard Medcal School, Department of Health Care Polcy, 180 Longwood AÕenue, Boton, MA 02115, USA b Tel AÕÕ UnÕerty, Tel AÕÕ, Irael c Boton UnÕerty, Boton, MA, USA Receved 1 September 1999; receved n reved form 1 May 2000; accepted 12 May 2000 Abtract Health plan pad by captaton have an ncentve to dtort the qualty of ervce they offer to attract proftable and to deter unproftable enrollee. We characterze plan ratonng a a Ahadow prceb on acce to varou area of care and how how the proft maxmzng hadow prce depend on the dperon n health cot, ndvdual forecat of ther health cot, the correlaton between ue n dfferent llne categore, and the rk adjutment ytem ued for payment. Thee factor are combned n an emprcally mplementable ndex that can be ued to dentfy the ervce that wll be mot dtorted by electon ncentve. q 2000 Elever Scence B.V. All rght reerved. JEL clafcaton: I10 Keyword: Managed health care; Captaton; Shadow prce ) Correpondng author. Tel.: q1-617-432-0178; fax: q1-617-432-1219. Ž. E-mal addre: frank@hcp.med.harvard.edu R.G. Frank. 0167-6296r00r$ - ee front matter q 2000 Elever Scence B.V. All rght reerved. Ž. PII: S0167-6296 00 00059-

830 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 1. Introducton Many countre are turnng to competton among managed care plan to make the tradeoff between cot and qualty n health care. In the U.S., major publc program and many prvate health nurance plan offer enrollee a choce of managed care plan pad by captaton. 1 Recent etmate are that 40% of the poor and dabled n Medcad and 14% of the elderly are enrolled n managed care plan pad by captaton Ž Medcare Payment Advory Common, 1998.. Medcad fgure are ncreang rapdly. In prvate health nurance, about three-quarter of the covered populaton already n ome form of managed care, though n many cae, employer contnue to bear ome or all of the health care cot rk Ž Jenen et al., 1997.. Health polcy n the Netherland, England, and other countre hare mlar eental feature. Irael, for example, recently reformed t health care ytem o that redent may chooe among everal managed care plan whch all mut offer a comprehenve baket of health care ervce et by regulaton. A common feature of uch reform for plan to receve a captaton payment from the government or prvate payer for each enrollee. 2 The captatonrmanaged care trategy rele on the dea that cot are controlled by the captaton payment and the AqualtyB of ervce enforced by the market. The bac ratonale for th health polcy the followng: the captaton payment plan receve gve them an ncentve to reduce cot Ž and qualty., whle the opportunty to attract enrollee gve plan an ncentve to ncreae qualty Žand cot.. Ideally, thee countervalng ncentve lead plan to make effcent choce about ervce qualty. Competton n the health nurance market ha well known drawback, the mot troublng one beng advere electon. A competton among managed care plan become the predomnant form of market nteracton n health care, advere electon take a new form whch much harder for polcy to addre than n conventonal health nurance. Wth old-fahoned fee-for-ervce nurance arrangement, a health plan mght provde good coverage for, ay, chld-care, to attract young healthy famle, and provde poor coverage for hoptal care for mental llne. If t appeared that refung to cover hoptal care for mental llne wa motvated by electon concern, publc polcy could force prvate nurer to offer the coverage through mandated beneft leglaton. A health nurance 1 For repreentatve dcuon n the U.S. context, ee Cutler Ž 1995., Newhoue Ž 1994., Enthoven and Snger Ž 1995.. See alo Netanyahu Common Ž 1990. for Irael, and van Vlet and van de Ven Ž 1992. for the Netherland. For a dcuon of tate-level reform n the Unted State, ee Holohan et al. Ž 1995.. Van de Ven and Ell Ž 2000. contan a recent and comprehenve revew. 2 For a recent urvey of how health plan are pad n the U.S. by all major payer group, ee Keenan Ž. et al. 2000.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 831 move away from conventonal fee-for-ervce plan, where enrollee have free choce of provder, and become Amanaged care,b the mechanm a health nurance plan ue to effectuate electon change from readly regulated conurance, deductble, lmt and excluon, to more dffcult-to-regulate nternal management procee whch raton care n a managed care plan. Reearcher focung on the economc of payment and managed care are well aware of the ue. Ell Ž 1998. label underprovon of care to avod bad rk a Akmpng.B Newhoue et al. Ž 1997. call t Atntng.B Cutler and Zeckhauer Ž 2000. call t Aplan manpulaton.b A Mller and Luft Ž 1997, p. 20. put t: Under the mple captaton payment that now ext, provder and plan face trong dncentve to excel n care for the cket and mot expenve patent. Plan that develop a trong reputaton for excellence n qualty of care for the cket wll attract new hgh-cot enrollee.... The flp de, of coure, that n repone to electon ncentve the plan mght provde too much of the ervce ued to treat the le erouly ll, n order to attract good rk. AToo muchb meant n an economc ene. A plan, motvated by electon, mght provde o much of certan ervce that the enrollee may not beneft n accord wth what t cot the plan to provde them ŽNewhoue et al., 1997, p. 28.. An mportant mplcaton of th obervaton captaton and managed care can be expected to generate too lttle care n ome area and too much n other. 3 Th lead, then, to the queton: How doe a regulator know whch ervce a managed care plan kmpng on or over-provdng to affect rk electon? Even f the regulator dd know, what could he or he do about t? Motvated by thee queton, publc regulatory bode and prvate payer have recently become ntereted n montorng the qualty of care n managed care plan. Montorng cont of dentfcaton of meaurable tandard Žconumer atfacton, health outcome, qualty of nput. agant whch a plan performance compared. There are many drawback to th approach from a polcy and an economc tandpont. At a recent conference, oberver noted that tandard have prolferated, and t dffcult to fnd tandard that are entve to ytem charactertc Ž Mtchell et al., 1997.. The tandard are at bet mperfect ndcator of value to enrollee. Rankng the mportance of dfferent tandard largely 3 Mller and Luft Ž 1997. revewed 37 tude meetng reearch tandard of qualty of care n managed care organzaton pad by captaton. In comparon to care outde of captatonrmanaged care, qualty wa found to be ometme hgher and ometme lower. However, the author called attenton to everal tude howng ytematcally lower qualty for Medcare enrollee wth chronc condton, reflectng a concern for chronc llnee expreed by other, uch a Schlenger and Mechanc Ž 1993..

832 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 arbtrary. Qualty can be too hgh, a well a too low, and extng approache are all orented to a mnmum, not a maxmum tandard. 4 Gatherng nformaton on many tandard for many plan n a tmely fahon very expenve. Plan do not all have adequate admntratve capablty Ž Gold and Felt, 1995.. Enrollee move n and out of plan, makng meaure baed on performance at the peron level dffcult to mplement. Rewardng a ubet of qualty ndcator may dtort performance by health plan. In th paper we take a very dfferent approach to addre the queton of how to montor electon-related qualty dtorton n the market for health nurance wth managed care. We tart from the aumpton that plan maxmze proft. We how that to do o, each plan raton by, n effect, ettng a ervce-pecfc AhadowB prce for each ervce. We nterpret the hadow prce a characterzng the ncentõe a plan ha to dtort ervce away from the effcent level. The hadow prce capture how tghtly or looely a proft maxmzng plan hould raton ervce n a partcular category n t own elf-nteret. Once cot are normalzed, we can compare hadow prce acro ervce. Servce that the plan hould retran wll be characterzed by hgher hadow prce than ervce that the plan hould provde generouly. The hadow prce an operatonal concept, meaurable wth data from a health plan. We take the rato of the hadow prce for a partcular ervce to ome numerare ervce to create a Adtorton ndex.b The hadow prce a devce to capture the myrad of tratege a plan ue to raton care, other than by demand-de cot harng Ž lteral prce.. Shadow prce can reflect plan decon about capacty n varou ervce area, uch a the number of pecalt n a phycan network or the number of taff hred n a plan department. They could reflect the makeup of network or payment to provder, ncludng upply-de cot harng or the trngency of utlzaton revew. After developng the hadow prce meaure of electon dtorton and dcung the properte of ervce that wll be over and underprovded Ž Secton 2., we llutrate how thee hadow prce can be calculated wth data from a health plan Ž Secton 3.. Our purpoe at th tage not to draw concluon about whch ervce are dtorted. To do o one need data, jut now emergng, on the behavor of managed care plan. Our purpoe here to llutrate how to calculate the hadow prce wth health plan data, and to confront the ue nvolved n an emprcal applcaton. We go on to llutrate how our meaure can be ued to evaluate the effcency properte of varou tratege to deal wth advere electon, uch a rk adjutng payment to managed care plan. 4 Th paper dcue electon-related ncentve that could lead to qualty for varou ervce to be too hgh or too low. Another well-etablhed argument from health economc alo apple to the health nurance opton condered here. The federal tax ubdy provded through the tax-free employer contrbuton to employee health nurance may lead to too hgh qualty acro the board.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 833 An analogy mght be helpful at th pont. Another queton about the effcency of market more famlar: Whch frm output are mot dtorted by monopoly power? The drect approach to anwerng th would be to compare the extng prce of each frm to an etmate of what the prce would be n a compettve market. However, nce hypothezed compettve prce cannot be ealy oberved, more common an ndrect approach: etmate each frm elatcty of demand. Followng Lerner Ž 1934., we could ue demand elatcte to rank frm accordng to where output lkely to be dtorted mot. Demand elatcty doe not drectly meaure the dtorton; t mply a meaure of how bad the dtorton would be under the aumpton that the frm maxmze proft. In the market for managed care, the condton for proft maxmzaton nvolve more than an elatcty-drven markup, but the method we ue for expong dtorton exactly analogou to Lerner for flaggng monopoly. We do not meaure the dtorton drectly, but we do meaure the trength of the economc force creatng the dtorton. Our analy baed on a model of a proft-maxmzng managed care plan competng for enrollee. We aume that the plan cannot elect enrollee baed on ther future health care cot, ether becaue the plan doe not have th nformaton or becaue there an Aopen enrollmentb requrement. Conumer, however, have ome nformaton about ther future health care cot. The plan et the qualty of ervce n lght of t belef about conumer knowledge. We analyze the ncentve of the plan to dtort qualty n order to attract AgoodB enrollee thoe wth low expected future health care cot n relaton to the captated payment plan are pad. We fnd that ncentve to a plan to devote reource to ervce depend on the demand for that ervce among the plan current enrollee, how well potental enrollee can forecat ther demand for the ervce, whether the dtrbuton of thoe forecat unform or kewed n the populaton, the correlaton of thoe forecat wth forecat of other health care ue, and on the rk-adjutment ytem ued to pay for enrollee. We how how all thee factor ft together nto an ndex for each ervce the plan provde. Many paper have hown that conumer chooe health plan on the ba of ther antcpated pendng. Medcare program for payng HMO by captaton ha been tuded repeatedly n th regard. In a repreentatve analy, Hll and Brown Ž 1990. fnd that ndvdual choong to jon HMO for the frt tme were pendng 23% le than thoe who do not chooe to jon n the perod mmedately pror to jonng, and had a lower mortalty rate n the perod after jonng Žee alo Egger and Prhoda, 1982; Garfnkel et al., 1986; Brown et al., 1993.. The fndng of gnfcant advere electon n Medcare contnue to be borne out by more recent tude Ž Medcare Payment Advory Common, 1998.. Numerou other tude have alo found among other populaton that thoe choong to jon HMO are AhealtherB n ome way than thoe not jonng ŽCutler and Reber, 1998; Cutler and Zeckhauer, 2000; Gled et al., 2000; Robnon et al., 1993; Luft and Mller, 1988..

834 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 Rk-adjutment of payment to managed care plan ntended to counteract ncentve to dtort ervce. The bac dea behnd rk adjutment the followng: If plan are pad more for enrollee lkely to be cotly, the plan wll not hun thee enrollee. Indvdual chooe plan baed on what they Ž the ndvdual. can predct. A rk adjutment ytem that pck up the predctable part of the varance n health cot thu able to addre danger of electon. 5 We wll how below, how rk adjutment work to affect plan ncentve to detect ervce qualty n order to affect the rk the plan draw n a populaton. 2. Proft maxmzaton n managed care We decrbe the behavor of a health plan Ž uch a an HMO. n a market for health nurance n whch potental enrollee chooe ther health plan. The health plan pad a premum Ž pobly rk-adjuted. for each ndvdual that jon. Indvdual dffer n ther needrdemand for health care, and chooe a plan to maxmze ther expected utlty. AHealth careb not a ngle commodty but a et of ervce maternty, mental health, emergency care, cardac care, and o on. A health plan chooe a ratonng or allocaton rule for each ervce. The plan choce of rule wll affect whch ndvdual fnd the plan attractve and wll therefore determne the plan revenue and cot. We aume that the plan mut accept every applcant, and we are ntereted n characterzng the plan ncentve to raton ervce. 2.1. Utlty and plan choce A health plan offer S ervce. Let m denote the amount the plan wll pend on provdng ervce to ndvdual, f he jon the plan, and let: m m 1, m,..., m 4. The value of the beneft ndvdual get from the plan, u Ž m., 2 S 5 How much of the health care cot varance ndvdual can antcpate not known. To get ome dea, emprcal reearcher have aumed that ndvdual know the nformaton contaned n certan potental explanatory varable, and then nvetgate how much of the varance explaned by thee covarate. In the mot well-known of thee tude, Newhoue Ž 1989. aume that ndvdual know the nformaton contaned n ther ndvdual tme nvarant contrbuton to the varance and the autoregreve component of ther mmedate pat pendng. Wth thee aumpton ndvdual can predct about a quarter of the varance. He regarded th a a reaonable AmnmumB of what ndvdual could predct. Currently avalable rk adjuter m a good deal of th predctable varance. Medcare current rk adjuter explan about 2% of total varance; propoed refnement mprove the explanatory power conderably, but only to about 9% ŽEll et al., 1996; Wener et al., 1996.. There reman conderable room for ytematc electon that would not be captured by a payment ytem baed on extng rk adjuter.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 835 compoed of two part, a valuaton of the ervce an ndvdual get from the plan, and a component of valuaton that ndependent of ervce. Thu, už m. ÕŽ m. qm Ž 1. where, Õ Ž m. Õ Ž m. The term Õ the ervce-related part of the valuaton and telf compoed of the um of the ndvdual valuaton of all ervce offered by the plan. The term Õ Ž Ø. the ndvdual valuaton of pendng on ervce, alo meaured n dollar, where Õ )0, Õ Y -0. For now, we proceed by aumng that the ndvdual know Õ Ž m. wth certanty. Later, we conder the cae when the ndvdual uncertan about h Õ Ž m.. The non-ervce component m, an ndvdual-pecfc factor Ž e.g. dtance or convenence. affectng ndvdual valuaton, known to peron. From the pont of vew of the plan, m unknown, but drawn from a dtrbuton F Ž m.. We aume that the premum the plan receve ha been predetermned and not part of the trategy the plan ue to nfluence electon. Premum dfference among plan Žf premum are pad by the enrollee. can be regarded a part of m. The plan wll be choen by ndvdual f u )u, where u the valuaton the ndvdual place on the next preferred plan. We analyze the behavor of a plan whch regard the behavor of all other plan a gven, o that u can be regarded a fxed. Gven m and u, ndvdual chooe the plan ff: m )u yõ Ž m.. For now, we aume that, for each, the plan ha exactly the ame nformaton a ndvdual about the ndvdual ervce-related valuaton of t ervce, Õ, and the utlty from the next preferred plan, u. For each ndvdual, the plan doe not know the true value of m but t know the dtrbuton from whch t drawn. Therefore, for a gven m and u, the probablty that ndvdual chooe the plan, from the pont of vew of the plan : 6 Ž. n Ž m. 1yF u yõ Ž m.. Ž 2. 2.2. Managed care Managed care raton the amount of health care a patent receve wth mnmal demand-de cot harng, and thu wthout mpong much fnancal rk on enrollee. 7 Two approache have been employed to model the ratonng proce. 6 An alternatve nterpretaton that ndex decrbe a group of people wth the ame Õ Ž m. functon and n Ž m. then the hare of th group that jon the plan. 7 Although health plan that are managed care may alo ue ome demand-de cot harng.

836 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 In an early model of managed care, Baumgardner Ž 1991. plan et a common quantty of care for peron wth the ame llne but who dffer n everty, an approach later employed by Pauly and Ramey Ž 1999.. Thee paper conder only a ngle llne and are concerned wth the properte of quantty ratonng compared to demand-de cot harng for purpoe of controllng moral hazard. Pauly and Ramey Ž 1999. how that ome quantty ettng alway part of the optmal combnaton of demand-de cot harng and ratonng. The plan of Glazer and McGure Ž 2000a. alo et quantty n a two-llne model focued on advere electon. They characterze equlbrum n the nurance market wth managed care to olve for the optmal rk adjutment polcy to counter electon ncentve. 8 An alternatve approach to modelng managed care, ued by Keeler et al. Ž 1998., to regard the plan a ettng a Ahadow prceb the patent mut AneedB or beneft from ervce above a certan threhold n order to qualfy for recept of ervce. In Keeler et al. Ž 1998., demand for one ervce, Ahealth care,b and the plan et jut one hadow prce. 9 Here, we adopt the hadow-prce approach to managed care but allow for many ervce n order to tudy electon ncentve. Let q be the ervce-pecfc hadow prce the plan et determnng acce to care for ervce. A patent wth a beneft functon for ervce of Õ Ž Ø. wll receve a quantty of ervce, m determned by: Õ Ž m. q. Ž 3. Let the amount of pendng determned by the equaton above be denoted by m Ž q.. Note that Ž 3. mply a demand functon, relatng the quantty of ervce to the Ž hadow. prce n a managed care plan. See Fg. 1. The ue of a hadow prce a a decrpton of ratonng n managed care permt a natural nterpretaton of the dvon of reponblty between the AmanagementB of a plan, preumably mot ntereted n proft, and the AclncanB n a plan who face the patent. Cot-concou management allocate a budget or a phycal capacty for a ervce. Clncan workng n the ervce area do the bet they can for patent gven the budget by ratonng care o that care goe to the patent that beneft mot. In th envronment, management n effect ettng a hadow prce for a ervce through t budget allocaton. It evdent n data that ndvdual wth the ame deae get dfferent quantte of ervce. The contant 8 Rk adjutment can be vewed a a tax-ubdary cheme ued to equalze ncentve to raton all ervce equally. Th dea developed n the general cae of many ervce n Glazer and McGure Ž 2000b.. 9 In Keeler et al. Ž 1998. plan are characterzed by a ngle prce, but do not chooe t level. Plan do not chooe premum or level of care and are thu nactve n term of electon.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 837 Fg. 1. Determnaton of pendng on ervce for ndvdual. hadow prce aumpton content wth managed care ratonng but wth more care beng receved by patent who AneedB t more. 10 2.3. Proft and proft maxmzaton Let qq, q,..., q 4 1 2 be a vector of hadow prce the plan chooe and m Ž q. m Ž q., m Ž q.,..., m Ž q.4 1 1 2 2 be the vector of pendng ndvdual get by jonng the plan. Defne n Ž q.'n Žm Ž q... Expected proft, p Ž q., to the plan wll depend on the ndvdual the plan expect to be member, the revenue the plan get for enrollng thee people, and the cot of each member. Thu, p Ž q. n Ž q. r y m Ž q., Ž 4. where r the Ž pobly rk-adjuted. revenue the plan receve for ndvdual. The plan wll chooe a vector of hadow prce to maxmze expected proft, Ž. 4. Defne p Ž q. to be the gan or lo on ndvdual : p Ž q. r y m Ž q.. Ž 5. Gven th, for one uch ervce Ždroppng the argument q and q from all functon., the condton for proft maxmzaton : dp dn p ynm 0. Ž 6. dq dq ž / Condton Ž. 6 ha two part. Conder the term ynm. If the hadow prce q raed, the plan wll pend le by m on ndvdual f he jon the plan. Th 10 In th way the hadow prce approach eem uperor to the quantty ettng approach n a context of a dtrbuton of demand for a ervce. The hadow prce method alo the AeffcentB way to raton a gven budget.

838 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 term alway potve, reflectng the avng the plan can acheve by ratonng more trngently. The other term, Ž dn rdq. p, may be potve or negatve for any ndvdual. The term d nrd q alway negatve, reflectng the fact that everyone wll fnd the plan omewhat le attractve a q raed. The p wll be potve or negatve, dependng on whether the rk-adjuted revenue above or below the cot the ndvdual wll ncur gven the ratonng n the plan. The dea behnd competton among managed care plan that the frt term mut after ummaton be negatve the plan by ratonng too tghtly wll loe proftable cutomer to balance the plan ncentve to reduce ervce to the extng enrollee. To ee what Ž. 6 mple for varou ervce, we make ome ubttuton. The change n the probablty of jonng can be wrtten a the product of two dervatve: dn dn dõ. Ž 7. dq dõ dq From Ž. 2, d n rdõ mply F, and from Ž. 1 and Ž. 3, dõrd q qm. Aumng that the elatcty of demand for ervce the ame for all ndvdual for every q, and denotng th elatcty by e, we get: em m, Ž 8. q for every. Note that the aumpton that for every hadow prce q the elatcty of demand for ervce the ame for all ndvdual doe not mply, of coure, that all ndvdual have the ame demand curve for that ervce. It only mple that demand curve of dfferent ndvdual, for a certan ervce, are Ahorzontal multplcatonb of ome AbacB demand functon for the ervce. Indvdual wll dffer n ther relatve demand. One nterpretaton of th aumpton, a n Glazer and McGure Ž 2000a., that gven omeone ck, a common functon decrbe valuaton of a ervce, but people dffer n the probablty that they become ll. Subttutng for m from Ž. 8, we can rewrte Ž. 6 a: nem F em p y 0. Ž 9. q Multplyng through by Ž q re. and ummng the term eparately, or q F m p y nm 0, nm q. F m p Ž 10.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 839 From Ž 10. we can make ome obervaton about q n proft maxmzaton. The numerator of Ž 10. reflect the ncentve the plan ha to ave money on t expected enrollee. The greater the numerator, the larger wll be q. The denomnator decrbe the expected gan a plan acrfce by long enrollee. The denomnator contan a product mp weghted by the change n enrollment probablty, F. Some enrollee wll be proftable, wth p )0 gven the rk adjutment formula n ue, and ome wll be unproftable, wth p - 0. The aocaton between thee gan and loe and pendng wll determne the value of the denomnator. For any ervce provded n proft maxmzaton, the denomnator of Ž 10. mut be potve, mplyng that n proft maxmzaton, provon of all ervce on average attract proftable enrollee. Th obervaton echoe a concluon from the health care payment lterature where under propectve payment ytem, the enrollment repone, or more generally, demand repone, nduce a provder to upply a noncontractble nput Ž correpondng here to q.. See Rogeron Ž 1994., Ma Ž 1995., or Ma and McGure Ž 1997.. Creatng proft on the margn n th way to nduce frm AeffortB ncontent wth zero proftablty unle margnal cot are le than average cot or the payer ue a two-part tarff of ome knd to rembure the provder. In a frt-bet allocaton, a payer or regulator would nduce the plan to et q 1, leadng to an equalty between the margnal beneft of pendng on a ervce and t margnal cot. Eq. Ž 10. how how a payer could do th for th one ervce by manpulatng the payment r. For a gven level of payment r,f q were too hgh, for example, the payer could mply ncreae r by ome factor, payng more for every potental enrollee. That would rae the denomnator of Ž 10. and nduce more pendng. In the one ervce cae, rk adjutment not neceary, mply payng more for all enrollee wll do. It only f a plan manpulate qualty n more than one dmenon of qualty that rk adjutment of premum pad to the plan ha a role n counterng electon ncentve. 11 2.4. Uncertanty So far we have aumed that each ndvdual know wth certanty h valuaton of each of the ervce Õ Ž m., and, hence, gven ome q, the dollar amount of the dfferent ervce that wll be provded to hm upon jonng the plan. In order to make our model more realtc and to prepare for emprcal applcaton, we hall now allow for each ndvdual to be uncertan about h future demand for the dfferent ervce. Let u uppoe that each ndvdual ha a et of pror 11 Rk adjutment mght alo need to deal wth ndvdual-pecfc dcrmnaton, uch a, n the extreme, outrght denal of enrollee. Glazer and McGure Ž 2000b. conder the queton of how bet to degn rk adjutment when qualty dcrmnaton and ndvdual electon are both concern.

840 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 belef about h poble health care demand, and that the plan hare thee belef. Let T denote the et of poble health tate of each ndvdual and let t denote an element of T. Let z Õ Ž m., Õ Ž m.,..., Õ Ž m.4 t t1 t1 t 2 t 2 t t denote the vector of S valuaton functon for the S ervce, f the health tate realzed to be t. We aume that for each t and, Õ Ž. t atfe the properte dcued earler. Each ndvdual uncertan about h health tate t, but ha ome pror Ž. 12 dtrbuton belef f over the et of poble tate. Let x t be ome random varable, the value of whch depend on the tate t, and let f be a dtrbuton functon defned over T. Let E wx x f t denote the expected value of x t wth repect to the dtrbuton f. The modfed model ha three move: frt, the plan chooe t level of hadow prce qž q, q,..., q. 1 2, econd, the ndvdual chooe whether or not to jon the plan Ž n a manner tuded below., and fnally the ndvdual health tate realzed and ervce are provded. For a gven hadow prce q and a valuaton functon Õ t, the plan expend- ture on th ndvdual on ervce wll be m Ž q., gven by: Ž. Õ m Ž q. q. t t Ž. Let z Ž q. Õ m Ž q. t t t The ndvdual expected utlty : m q E wz Ž q.x f t. Let ut denote the ndvdual utlty f h health tate t and he chooe the next bet plan. Thu, E wu x f t the ndvdual expected utlty f he chooe the alternatve plan. We aume no aymmetry of nformaton between the plan and the ndvdual regardng the ndvdual health tate. Thu, the plan know the ndvdual pror belef, f, about h future health tate. 13 The plan, however, doe not know the true value of m, although t hold belef FŽ m. about t cumulatve dtrbuton. t 12 To ue conventonal termnology, ndvdual pror belef, f, can be thought of a the ndvdual Atype.B A wll be dcued n Secton 3, one can make dfferent aumpton about how an ndvdual pror belef are formed. Under ome of thee aumpton Že.g., belef are on the ba of AageB and AexB only., everal ndvdual may have the ame pror belef, and hence be of the ame Atype.B Thereafter, we wll contnue ung the termnology Andvdual B, but one can thnk of th a Andvdual of type.b 13 Although t mplfe the expoton, the aumpton that the plan know each ndvdual pror belef much too trong for what we need. It eay to how that all of our reult wll go through under a much weaker aumpton: that the plan only know the dtrbuton of pror belef over the populaton, or, n other word, that the plan only know the dtrbuton of AtypeB n the populaton. Th a tandard aumpton n the aymmetrc nformaton lterature.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 841 A plan mpong hadow prce q gauge the ndvdual lkelhood of jonng the plan a: Ž. fž. f t tž. Ž. n q 1yF E u yõ q. 2 yeldng an expected proft on the ndvdual of: ž / p q n q rye m q. 5 fž. fž. f tž. Ž. The plan chooe each q to maxmze expected proft. To fnd proft-maxmzng value of q, we dfferentate the above wth repect to q : dp Ž q. ž / f F E Õ m rye m yn E m f t t f t f f t 6 dq Ung the fact that Õ q for all t, and aumng that m Ž em rq. t t t for all t, we get that the rght-hand de of Eq. Ž6. become: nmˆ f e F mˆ ry mˆ y, where me ˆ wm ˆx. ž ž / q / f We can now how how the plan chooe t proft maxmzng hadow prce n th cae. Aume a populaton of N ndvdual. Each ndvdual ha ome pror belef f over the et of poble health tate. Retorng the ubcrpt to Eq. Ž6., ummng Eq. Ž6. over all and ettng t equal to zero, the proft maxmzng q wll be: nmˆ w x Ž. Ž. q 10 F mˆ r y mˆ ž / 1,..., where mˆ E wm x f t ndvdual predcted expendture on ervce, where the predcton wth repect to the ndvdual pror belef about h future expendture on ervce. Defne ˆ p r y m ˆ. 1,..., To nvetgate whch hadow prce are et hgh relatve to other hadow prce, Ž we ue Eq. 10. to contruct a rato of q to q where ome other ervce. We mplfy by abtractng from ndvdual dfference n enrollment repone by aumng that F F. Th amount to ayng that an ncreae n the value of plan ncreae the lkelhood of jonng for all ndvdual equally. Eq. Ž10. can now be ued to wrte the rato of two hadow prce, q and q. Note that the F term cancel out of th expreon: mˆ pˆ nm ˆ q. Ž 10 Y. q mˆ ˆ p nmˆ

842 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 There no partcular reaon to expect Ž10 Y. to be equal for all ervce par unle the rk adjutment ytem o good a to equalze the relatve ncentve to upply each ervce. 2.5. The effect of ndõdual nformaton Informaton play an mportant role n creatng dtorton of advere electon. We are now ready to tudy how ndvdual nformaton Ž belef. about ther future health care need affect the plan proft maxmzng hadow prce. Let mˆ r mˆ r N N ) ) Ž mˆ ym. 2 2 ˆ Ž ryr. r ˆ N N mˆ ymˆ mˆ ymˆ Ž r yr. mˆ ymˆ ˆ r, ˆ rr Nˆˆ Nˆ ˆM 1,..., Ž.Ž. Ž. mˆ r 14 and aume that n n, and F 1 for all. Eq. Ž10. can then be wrtten a nmˆ q Ž 11. 2 rmˆ qrˆ ˆ y ˆ q ˆ r ˆ ˆ qmˆ Mˆ Ž. ž / r r, 1,..., / The effect of an ndvdual nformaton on the choce of q enter through ˆ. Suppoe, ntally, that all ndvdual are dentcal n ther belef about ther health care need of all ervce for the comng perod. In uch a cae, ˆ 0 for all and q Ž nrrymˆ. for all. Thu, n th cae all hadow prce are the ame and no dtorton occur. Th reult ndependent of the rk adjutment ytem and of correlaton of predcted pendng for dfferent llnee. Suppoe, now, that ndvdual have ome nformaton that make them dffer from each other wth repect to ther belef about ther need of ome ervce. In uch a cae, ˆ )0. Suppoe that there no rk adjutment, o r r. We can ee that the more heterogeneou are ndvdual wth repect to ther m ˆ, the larger wll be ˆ and the hgher wll be the hadow prce q. Th the tandard advere 14 Th true wth a unform dtrbuton.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 843 electon reult. The better the nformaton that ndvdual have about ther future need, the bgger wll be the dtorton created by the plan n order to attract the proftable ndvdual. The effect of correlaton among pendng on dfferent ervce on the hadow prce can alo be oberved n Ž 11.. If need are not at all correlated, then r ˆ, 0 and the only effect on the hadow prce come from ndvdual nformaton ˆ. If, however, need are correlated, ˆ r )0 and the larger r, ˆ, the hgher wll be the hadow prce of ervce and. A alo evdent from Ž 11., rk adjutment can counter the dtortve force dcued above. The larger the correlaton between predcted pendng on ervce and rk adjutment payment, ˆr, r, the hgher wll be the denomnator of Ž 11., and the lower the hadow prce. 3. Meaurng hadow prce: an emprcal llutraton In th ecton we llutrate how to ue our meaure. A we noted n the ntroducton, the data we wll ue are from an AunmanagedB plan, o the fndng are merely an example of how to mplement our framework. In other word, our purpoe here to llutrate how to ue preently avalable data to calculate a dtorton ndex. The element that feed nto ncentve to dtort, uch a predctablty of varou ervce, and correlaton among ue n varou categore of ervce, are lkely to be largely common to managed and unmanaged pattern of care. Our ue of Medcad data mean that the populaton not repreentatve, but our fndng are at leat uggetve. Recall from Ž 11. that the proft maxmzng hadow prce depend on the ndvdual expectaton regardng ther future health need. Therefore, the emprcal buldng block for meaurng hadow prce are the expected pendng of ndvdual by ervce cla and the correlaton of expected pendng acro ervce under dfferng nformaton aumpton. Our man trategy here amed at obtanng etmate of future pendng, condtonal on the nformaton aumpton, whch mnmze the forecat error. The performance of a number of etmaton tratege for health care pendng data ha been aeed over the pat 15 year. Duan et al. Ž 1983, 1984. and Mannng et al. Ž 1981. contend that two-part model mnmze mean forecat error under dtrbutonal aumpton commonly exhbted by health pendng data. Two-part model cont of one equaton, typcally a logt, for the yerno decon about ue, and a econd equaton, typcally etmated by OLS, decrbng the extent of ue, gven ome ue. We ue a two-part model for etmaton under dfferng nformaton aumpton. An Anformatonal aumptonb mean, operatonally, whch covarate to nclude n the model. The pece of Eq. Ž 11. are computed from the predcted value generated from thee etmated model.

844 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 3.1. Data The data are health clam and enrollment fle from the Mchgan Medcad program for the year 1991 1993. We choe a ubet of the data for applcaton of our model. It therefore mportant to hghlght that the data we ue cont largely of pendng by poor women Ž 90%.; thu, calculated hadow prce may dffer from thoe for other populaton. The ample cont of ndvdual adult who were elgble for Medcad n 1991 through the Ad to Famle wth Dependent Chldren Ž AFDC. program, and who were contnuouly enrolled n th or another Medcad program through the end of 1993. We excluded ndvdual who joned an HMO durng the tudy tme-perod. The reultng ample conted of 16,131 ndvdual, wth a mean age of 32 year. 3.2. Defnng erõce There are a varety of approache one could take to dentfyng Aervce,B rangng from very pecfc treatment, uch a angoplaty, to group of treatment whch would be aocated wth an llne, uch a care for hypertenon. In th paper we defne a AervceB a all the treatment receved n connecton wth certan dagnotc clafcaton. We dentfy nne clae of ervce: Ž. 1 brth related, Ž. 2 cancer care, Ž. 3 gatrontetnal problem, Ž. 4 heart care, Ž. 5 hypertenon, Ž. 6 njurerpoonng, Ž. 7 mental healthrubtance abue, Ž. 8 muculokeletal problem, and Ž. 9 an Aall other category.b Each of the ervce defned by a groupng of ICD-9-CM dagnotc code. 15 We choe group of condton accordng to everal crtera. At leat 7.5% of the populaton wa treated for each condton n a year. We ncluded condton that were a mx of chronc Ž cancer, hypertenon, mental health care. and acute condton Žgatro- ntetnal, njure, and brth-related.. Treatment for ome condton are lkely to be expenve, ome much le o. Some treatment for ncluded condton are arguably qute predctable, uch a brth-related pendng, whle other mght be condered more random, uch a njure and poonng. We clafy all health care clam accordng to the prmary dagno attached to the clam. 3.3. Pattern of pendng Table 1 decrbe pattern of utlzaton and pendng for the ample n 1993. The xth and eventh column of Table 1 ndcate ome of the key element of the formula for hadow prce Ž 11.. The xth column report the ntertemporal correlaton between pendng on each of our nne ervce categore and the um of pendng on all other ervce. None of correlaton exceed 0.20, wth the 15 Our groupng of ervce by ICD-9 code avalable from the author.

Table 1 Ue and cot n Mchgan medcad AFDC 1993 Servce Probablty Expected pendng Expected Percent of Correlaton wth Correlaton wth own of any ue gven ue Ž US$. cot Ž US$. total cot all other cot cot lat year Brth-related 0.167 3904 653 19.2 0.007 0.122 Cancer care 0.109 1159 126 3.7 0.155 0.127 Gatrontetnal 0.204 1186 242 7.1 0.167 0.166 Heart care 0.070 1542 108 3.2 0.089 0.079 Hypertenon 0.093 249 23 0.7 0.114 0.317 Injurerpoonng 0.344 701 241 7.1 0.189 0.033 Mental healthrubtance abue 0.143 1671 239 7.0 0.032 0.385 Muculokeletal 0.306 683 209 6.1 0.115 0.215 Otherrmng 0.926 1692 1567 45.9 0.313 0.288 R.G. Frank et al.rjournal of Health Economc 19 ( 2000 ) 829 854 845

846 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 excepton of the AotherB category. Correlaton wth pendng n the prevou year for each category a meaure of the pertence of pendng, reported n the eventh column. Pertent pendng probably more predctable. Several of the llnee thought to be more chronc n character, hypertenon, mental healthrubtance abue and muculokeletal condton, dplay relatvely hgh correlaton n ervce-pecfc pendng over tme. Mental-health pendng ha the hghet year-to-year correlaton. 3.4. Etmaton of component of the rato of hadow prce 3.4.1. Rk-adjuted premum We frt calculate the premum aumng that a ngle payment made for all enrollee. Th premum baed on the mple average level of pendng acro all enrollee and correpond to a cae wth no rk adjutment. We next contruct two et of true Ark-adjutedB premum, one baed on the Ambulatory Dagno Group Ž ADG. clafcaton ytem Ž Wener et al., 1996. and one baed on the DCG clafcaton ytem Ž Ell et al., 1996.. 16 In each cae we adjuted the rk-adjuted premum upward to make the margnal proft per enrollee potve on average, a t mut be f plan are to be nduced to compete for enrollee by ervce qualty for all ervce. 17 The ncreae n premum wa 50%. 3.4.2. Expected pendng The varable mˆ the expected level of pendng by each ndvdual for each category of ervce. Etmatng expected pendng requre aumpton about the nformaton avalable to ndvdual. The lterature reflect a wde range of concepton of what conumer mght know about ther health rk. Newhoue Ž 1989. ugget that ndvdual know ome of the nformaton contaned n meaurable apect of health tatu plu the tme nvarant-peron pecfc component of the unoberved factor contrbutng to varaton n health care pendng. Welch Ž 1985. make a mlar aumpton, referrng to a ApermanentB component of health pendng that ndvdual-pecfc. Welch peculate that ndvdual mght know more than th and be able to forecat ue of ome acute ervce uch a brth and ome other llnee. Some emprcal work on plan choce confrm the preence of conderable ndvdual knowledge. Ell Ž 1985. and Perneger et al. Ž 1995. how that an ndvdual htorcal pattern of pendng affect health plan choce. Other reearch pont to the fact that ndvdual appear to elect plan on 16 We ued publcly avalable algorthm to mplement thee rk adjutment ytem. The ADG algorthm the 1997 veron of the oftware provded by Jonathan Wener at John Hopkn Unverty. The HCC algorthm the 1997 veron of the oftware provded by Randy Ell of Boton Unverty. 17 One alternatve would be to ntroduce ome fxed cot aumpton. If ACMC and AC cloe to average premum, there wll be ome ervce the plan wll not wh to provde at all! To be wllng to provde ome of a ervce, a plan mut make ome expected proft on t. Another alternatve would be to aume a plan requred to offer at leat ome mnmum of every type of ervce.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 847 the ba of nformaton not contaned n rk adjutment ytem ŽCutler, 1994; Ettner et al., 1998.. We conder the mplcaton of everal nformatonal aumpton. Recall that f ndvdual can predct nothng, there no electon problem, o no mulaton need to be done for th cae. We tart wth the aumpton that ndvdual can predct baed on age and ex. That, we aume all ndvdual predct they wll pend the average for a peron of ther age and ex for each ervce category. Alternatvely, we aume ndvdual can alo ue the nformaton contaned n pror ue. A wll be een hortly, f ndvdual know all the nformaton contaned n pror ue, extng rk adjuter cannot cope wth the electon-nduced neffcence, and ome ervce would have very hgh or very low q n proft maxmzaton. In the mulaton, we therefore equp ndvdual wth ome of the nformaton n pror ue, 40%, to llutrate the mpact of more nformaton. In order to contruct thee etmate under dfferent nformaton condton, we etmate a ere of two-part model. Each two-part model ue rght-hand de varable at ther 1991 value to explan ervce-pecfc pendng n 1992. Varable ncluded n the model correpond to nformaton ndvdual are aumed to be able to ue to predct pendng. We etmate two et of regreon, one wth age and ex a rght-hand varable and one wth age, ex, and pror pendng. The etmated coeffcent from each par of ervce pecfc regreon are then appled to 1992 value of the rght hand de varable to generate etmate of expected pendng for each ndvdual n 1993. Followng Duan et al. Ž 1983. and Mannng et al. Ž 1981., each two-part model pecfed a: logt Ž PrŽ Spendng on ervce )0.. b 1 q 1 Ž 12. ( Ž Spendng on ervce Npendng)0. b q Ž 13. 2 2 where ndexe the ndvdual enrollee, a vector of ndvdual charactertc Ž ether age, ex, or age, ex, and pror ue., b a vector of coeffcent to be etmated and a random error term. Eq. Ž 12. a logt regreon. Eq. Ž 13. a lnear regreon that etmate the mpact of the on the quare root of the level of pendng on each ervce for ndvdual wth potve pendng on that ervce. We choe the quare root tranformaton to deal wth kewne n the dtrbuton of pendng rather than the more common logarthmc tranformaton becaue the mearng etmator for the quare root model le entve to heterokedatcty than the log tranformaton. 18 The dffculte n retranformng the two-part model have been treated n detal by Mannng Ž 1998. and Mullahy 18 We teted for heterokedatcty logarthmc of the pecfcaton ung the Breuch Pagan tet and rejected homokedatcty. Moreover, the heterokedatcty wa not a mple functon of any rght hand varable uch a prevou pendng. The heterokedatcty wa attenuated, but tll preent, under the quare root pecfcaton ung the Breuch Pagan tet.

848 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 Ž. 19 1998. Snce th applcaton call for predctng 1993 pendng ung 1992 data and coeffcent from the two-part model of 1992 pendng on 1991 rght de varable, a Amearng factorb taken from the error term of the 1991 1992 regreon. Becaue we ue a quare root tranformaton, the mearng factor addtve a oppoed to the multplcatve form n the cae of the logarthmc tranformaton. The reultng emprcal analy cont of a et of 18 regreon for each of the two nformatonal aumpton we make. 3.4.3. Plan enrollment We aume that competng managed care plan are n a ymmetrc equlbrum, and the plan therefore enroll a repreentatve ample of the populaton. To etmate plan pendng on each ervce, the nm n the numerator of Ž 10., we wll mply ue the average pendng n the ample. 3.5. A welfare ndex The welfare lo aocated wth a et of q can be approxmated by: L 0.5Ž Dq.Ž Dm. Ž 14. where Dq the abolute value of the dcrepancy between the q for ervce and the econd bet q, and D m the change n pendng nduced by the dcrepancy n q. For purpoe of th analy we defne D q a the dfference between q and the weghted average q for all ervce type contaned n Table 3. Thu, for each ervce, we take the expendture-weghted average q for each nformatonrrk adjutment combnaton, and compute D q baed on that. Snce D q n percentage term, D m mply D q multpled by demand elatcty, whch we aume for mplcty 0.25 for all ervce, except for mental health Ž. whch we et at 0.5, baed on Newhoue et al. 1997. 3.6. Reult We ummarze the predcton of the 18 two-part model n Table 2 by reportng the correlaton between actual and predcted ervce pecfc pendng level. Th correlaton negatvely and monotoncally related to the abolute predcton error of the pendng model. A expected, correlaton between actual and predcted pendng are generally qute low for all ervce when only age and ex related nformaton known by conumer. The brth-related correlaton 19 Thoe paper how the entvty of expected pendng etmate to dtrbutonal properte uch a heterokedatcty. The ue of a tranformaton to account for kewne n the pendng data necetate ue of the AmearngB etmator to retranform the predcted value of pendng to the expected level of pendng content wth the orgnal dtrbuton of pendng Ž Duan et al., 1983..

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 849 Table 2 Correlaton between actual and predcted pendng wth dfferent nformaton aumpton Servce Model a Age ex Age ex pror pendng Brth-related 0.210 0.216 Cancer care 0.035 0.104 Gatrontetnal 0.031 0.184 Heart care 0.075 0.104 Hypertenon 0.055 0.227 Injurerpoonng 0.002 0.014 Mental healthrubtance abue 0.019 0.306 Muculokeletal 0.073 0.178 Otherrmng 0.052 0.099 a All correlaton are gnfcant at p-0.01. between actual and predcted pendng, however, relatvely large at 0.21 Ž probably a reult unque to a Medcad ample.. Wth pror ue ncluded, the correlaton between predcted and actual pendng mprove markedly for mot ervce. The hadow prce mpled by ndvdual predcton and a rk adjutment polcy are contaned n Table 3. Two nformaton aumpton are combned wth three rk-adjutment polce to produce x et of proft-maxmzng hadow prce. The q for the AotherB category normalzed to 1.00 n all cae, o each Table 3 Shadow prce for three nformaton aumpton and three rk adjutment ytem Servce Informaton aumpton Age, ex Age, ex 40% of pror ue Rk adjuter Rk adjuter None ADG HCC None ADG HCC Brth-related 1.15 1.25 1.23 0.19 0.35 0.43 Cancer care 0.99 0.98 0.98 0.17 0.28 0.34 Gatrontetnal 0.99 0.99 0.99 0.18 0.29 0.36 Heart care 1.00 0.90 0.89 0.19 0.27 0.33 Hypertenon 1.01 0.87 0.87 0.27 0.26 0.28 Injurerpoonng 1.00 1.02 1.02 0.31 0.45 0.52 Mental healthrubtance abue 0.99 0.98 0.98 3.73 0.67 0.76 Muculokeletal 0.97 0.94 0.95 0.18 0.27 0.33 Otherrmng 1.00 1.00 1.00 1.00 1.00 1.00 Weghted average of q 1.03 1.04 1.04 0.82 0.67 0.70 Welfare lo Ž %. 0.6 1.1 1.0 9.7 3.9 3.6 Note: All hadow prce are relatve to OtherrMng Category. Welfare lo n term of percent of total expendture.

850 ( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 entry n the table need to be read a the hadow prce relatve to th numerare. Begn wth the frt three column of reult, computed for the aumpton that ndvdual can forecat health cot baed only on ther own age and ex. The very frt column how the conequence of no rk adjutment wth th nformatonal aumpton. Indvdual cannot forecat very well at all, o the ncentve plan have to dtort are mall, even wth no rk adjutment. All etmated q are cloe to 1.00 wth the excepton of brth-related expendture. Rk adjutment ung ADG and HCC magnfe the dtorton n the cae of brth-related ervce, heart care and care for hypertenon. The explanaton that people who antcpate ung thee ervce are pad for relatvely generouly n thee two rk adjutment formulae. The welfare lo meaure at the bottom of the table corroborate the q reult. When there no rk adjutment and people forecat on age and ex, there not much dtorton, a ndcated by the welfare lo a a percentage of pendng. Rk adjutment exacerbate the welfare lo, though the magntude not hgh. The econd panel of three column preent calculated q, aumng ndvdual can predct pendng baed on 40% of the nformaton contaned n pror pendng. Note that wth no rk adjutment, mental health and ubtance abue ervce are qute dtorted a evdenced by the q of 3.73. Rk adjutment attenuate the dtorton, movng all q toward unty. Mental health and ubtance abue ervce contnue to have the larget ervce-pecfc q. The two rk-adjutment ytem tuded, ADG and HCC, have very mlar effect on ncentve. For ome ervce, notably brth-related expendture, rk adjutment mprove matter, movng the proft-maxmzng q cloer to the overall average, but a favorable effect of rk adjutment not unform. The ncentve to overprovde care for hypertenon are exacerbated by rk adjutment. Mental health and ubtance abue change from a ervce that tend to be underprovded to one much cloer to the average wth ether rk adjutment ytem. Wthout rk adjutment, the welfare lo due to electon n the cae when ndvdual know 40% of the nformaton n pror ue ha ren to almot 10% of pendng. 20 Rk adjutment appear to be qute effectve, reducng the meaured dtorton to about 50% of t orgnal magntude. 21 A mlar analy could be conducted to examne how hadow prce change f we were to Acarve-outB any of the ervce from the overall nurance contract. The obvou canddate for a carve-out, baed on Table 3, mental health and ubtance abue. 20 Th lkely to be a conervatve meaure becaue of the way we contruct elatcty. 21 A next tep n th analy would be to fnd the Aoptmal rk adjutment.b Gven a et of varable avalable for rk adjutng, Eq. Ž 14. could be mnmzed wth repect to the weght on the rk adjuter. It turn out t poble to fully AolveB the optmal rk adjutment problem for the ervce f there are enough degree of freedom n the varable avalable for rk adjutment ŽGlazer and McGure, 2000b.. Th oluton, or the mnmzaton of Eq. Ž 14., requre nformaton on what plan beleve ndvdual can predct.

( ) R.G. Frank et al.rjournal of Health Economc 19 2000 829 854 851 A Table 3 how, the calculaton for hadow prce are entve to how much nformaton ndvdual have n makng ther predcton. When we examned a cenaro wth ndvdual knowng a much a 50% of pror ue, proft-maxmzng the q went Aoff the chart,b gnalng that ncentve to over and underprovde are very trong. 4. Concluon Health plan pad by captaton have an ncentve to dtort the qualty of ervce they offer to attract proftable and deter unproftable enrollee. Characterzng plan ratonng a mpong a Ahadow prceb on acce to care, we how that the proft maxmzng hadow prce for each ervce depend on the dperon n health cot, how well ndvdual forecat ther health cot, the correlaton among ue n llne categore, and the rk adjutment ytem ued for payment. We further how how thee factor can be combned to form an emprcally mplementable ndex that can be ued to dentfy the ervce that wll be mot dtorted n competton among managed care plan. A mple welfare meaure developed that meaure the dtorton caued by electon ncentve. We apply our dea to a Medcad data et to llutrate how to calculate dtorton ncentve, and we conduct polcy analye of rk adjutment. From the practcal tandpont of health polcy, our paper how how the ncentve to dtort ervce depend n a relatvely traghtforward way on mean and correlaton among predcted value of health care ervce n a populaton. Several nteretng fndng emerge from the mall data et we analyze. The mot trkng the mportance of ndvdual knowledge and ther ablty to forecat ther health expene. Th factor ha been apprecated n abtract term n earler wrtng, but the dramatc effect that nformaton ha on ncentve ha not been emprcally demontrated. Accordng to our prelmnary analy, f people know what they are ometme commonly aumed to know Žage, ex and pror pendng., electon ncentve would be very evere. Study of what ndvdual forecat a key area of emprcal reearch. In our model f ndvdual know Atoo much,b ome ervce are not provded at all. We therefore analyze hypothetcal cae n whch ndvdual are not allowed to know Atoo much.b Wthn th lmtaton, we llutrate how rk adjutment can be aeed. Two propoed rk adjutment ytem have gnfcant and mlar effect n term of cuttng the magntude of dtorton ncentve. Acknowledgement Reearch upport from the Health Care Fnancng Admntraton Cooperatve Agreement a18-c-9034r1, grant a K05-MH01263 from the Natonal Inttute of

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