NBER WORKING PAPER SERIES WILLINGNESS TO PAY FOR DRUG REHABILITATION: IMPLICATIONS FOR COST RECOVERY. David Bishai Jody Sindelar

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1 NBER WORKING PPER SERIES WILLINGNESS TO PY FOR DRUG REHBILITTION: IMPLICTIONS FOR COST RECOVERY David Bihai Jody Sindelar Working Paer htt:// NTIONL BUREU OF ECONOMIC RESERCH 1050 Maachuett venue Cambridge, M Setember 2006 Funding for thi reearch wa rovided by grant number R01- D09225 funded by the National Intitute on Drug bue. In addition, the author would like to thank tudy articiant and taff of the Baltimore Needle Exchange Project. The author gratefully acknowledge reearch uort for JS from the National Intitute on Drug bue to Yale Grant No. R01-D The view exreed herein are thoe of the author and do not necearily reflect the view of the National Bureau of Economic Reearch by David Bihai and Jody Sindelar. ll right reerved. Short ection of text, not to exceed two aragrah, may be quoted without exlicit ermiion rovided that full credit, including notice, i given to the ource.

2 Willingne to Pay for Drug Rehabilitation: Imlication for Cot Recovery David Bihai and Jody Sindelar NBER Working Paer No Setember 2006 JEL No. I1, I10 BSTRCT Objective: Thi tudy etimate the value that client lace on drug rehabilitation ervice at the time of intake and how thi value varie with the robability of ucce and availability of ocial ervice. Method: We interviewed 241 heroin uer who had been referred to, but had not yet entered, methadone maintenance treatment in Baltimore, Maryland. We aked each ubject to tate a reference among three hyothetical treatment rogram that varied acro 3 domain: weekly fee aid by the client out of ocket $5 to $100, reence/abence of cae management, and time ent heroin-free 3 to 24 month. Each ubject wa aked to comlete 18 orthogonal comarion. Subequently each ubject wa aked if they likely would enroll in their referred choice among the et of three. We comuted the exected willingne to ay WTP a the robability of enrollment time the fee conidered in each choice conidered from a multivariate logitic model that controlled for roduct attribute. We alo etimated the rice elaticity of demand. Reult: We found that 21% of client referred rogram that were logically dominated by other otion. The median exected fee ubject were willing to ay for a rogram that offered 3 month of heroin-free time wa $7.30 er week, riing to $17.11 er week for rogram that offered 24 month of heroin-free time. The availability of cae management increaed median WTP by $5.64 er week. The fee wa the mot imortant redictor of the elf-reorted robability of enrollment with a rice elaticity of SE Concluion: Client' median willingne to ay for drug rehabilitation fell hort of the average rogram cot of $82 er week, which reinforce the need for continued ubidization a drug treatment ha high oitive externalitie. Client will ay more for higher rate of treatment ucce and for the reence of cae management. Jody Sindelar Yale School of Public Health Yale Univerity School of Medicine 60 College Street, P.O. Box New Haven, CT and NBER jody.indelar@yale.edu

3 Introduction The economic burden of illicit drug ue wa etimated at $143 billion in 1998 $160 billion in 2003 Cartwright, W. S. and P. L. Solano 2003;Harwood, H. J., J. Fountain, and G Livermore Contributing to thi roblem are an etimated 119,000 heroin uer, 2.3 million cocaine uer, and 4.7 million merican who ued ain killer illicitly in 2003 Subtance bue and Mental Health Service initration Social cot are etimated to average $22,000 annually er illicit drug uer $160 billion/7.3 million uer Cartwright, W. S. and P. L. Solano n etimated 7.3 million illicit drug uer could be claified a needing ecialty treatment for their drug roblem Subtance bue and Mental Health Service initration Of thee, 1.5 million 20.8% were etimated to erceive a need for drug abue treatment. However, only 1.1 million 15% illicit drug uer actually received treatment for illicit drug Subtance bue and Mental Health Service initration Revenue from treatment came from a variety of ource, out of ocket 40.3%, rivate health inurance 32.1%, Medicaid 24.0%, ublic aitance 21.1%, Medicare 16.4%, or with the hel of family member 19% Subtance bue and Mental Health Service initration That only 21% of thoe with illicit drug roblem recognized a need for treatment and only 15% actually obtained treatment i the bai of a olicy dilemma. Treatment could hel to reduce the external cot that illicit drug uer imoe on ociety via crime, intereronal violence, read of dieae e.g. HIV/IDS and TB, and the ocially inured health harm which drug uer uffer. Many drug uer now enter treatment through coercion from the criminal jutice ytem. For examle, In California, Prooition 36 wa aed in 2000 to

4 allow of thoe convicted of 1t and 2nd time nonviolent, imle drug oeion to receive drug treatment intead of incarceration For illicit drug uer who recognize a need for treatment, ubidie for treatment can be jutified on the bai of the large ocial externalitie caued by drug illicit drug ue. Methadone maintenance treatment i etimated to cot $82 er week and many in methadone tay in treatment for month Roebuck, M. C., M. T. French, and. T. McLellan However, tudie have hown that treatment i cot effective Cartwright, W.S. 2000;Jofre- Bonet, M and JL Sindelar 2001;McColliter, K.E. and M.T. French Thu, it i in ociety interet to enure that thoe who deire treatment can obtain it and can receive effective, high quality care. Further, longer length of tay have been hown to roduce greater benefit Zarkin, G.., L.J. Dunla, J.W. Bray, and W.M. Wechberg Deite the comelling ublic interet, it i thought that there i inadequacy of ublic funding to rovide the good-quality, acceible care that would benefit not only the drug uer but ociety at large. One way to exand the ytem would be to ue rice dicrimination to rovide revenue to clinic by encouraging individual who are willing to ay to do o more often than currently occur. rational aroach to budgeting treatment ubidie would not require underwriting 100% of treatment for every client. One could ue a method of Ramey ricing to bae the ubidy for variou drug uer on their elaticity of demand Baumol, William J. and David F. Bradford Ramey ricing would et u a regime of rice dicrimination that maximize revenue to the drug rehabilitation ytem by charging more for thoe with higher demand and le for thoe with lower demand. To otimize a Ramey ricing ytem in drug treatment ervice, information on the rice elaticity and how it varie by rogram and

5 uer characteritic would be needed. However, information on rice elaticity for the demand for treatment for illicit drug ue i not currently available Cartwright, W. S. and P. L. Solano 2003, but ee Boriova, N. N. and. C. Gooan 2003 on travel time elaticity. The willingne of ordinary citizen to rovide ublic uort ha been tudied uing contingent valuation urvey method in mall-intercet amle from Brooklyn, NY and the Triad area of North Carolina where invetigator derived a mean willingne to ay of $37 er ayer toward exanion of drug treatment rogram couneling baed, not methadone to treat an additional atient er year Zarkin, G.., S. C. Cate, and M. V. Bala The objective of thi aer i to inform cot-haring trategie among uer, rovider and ayer of drug rehabilitation. In ection 1, we develo a welfare economic model of the otimal ubidy that a ocial lanner would ay to underwrite the drug rehabilitation of an illicit drug uer. Section 2 decribe the rimary data collected in Baltimore during a art of a conjoint analyi to etimate the demand for drug rehabilitation and lead to ection 3 where we decribe the method ued to analyze the data. In ection 4 we reent our reult. Finally in ection 5 we decribe limitation of the analyi and dicu imlication for olicy. 1. Model of the Otimal Subidy Suoe there i a oulation of addict and taxayer. There are N addict who ay no taxe and N T taxayer who ay a flat tax, τ. We aume N T >N and define the ratio of addict to taxayer a: θ N /N T. Each addict derive an identical income, y by inflicting roerty loe on the taxayer. Each taxayer ha income y T and y T >y. The average roerty lo er taxayer i y N /N T or θy. The addict have a demand for a medical

6 treatment, m, that i 100% ucceful in curing their addiction thereby converting them into taxayer. The treatment i available at rice, er eiode of treatment. There i no other way to cure addiction beide urchaing the treatment. We now conider a ocial lanner who want to maximize ocial welfare by devoting all of the tax toward a Pigouvian ubidy,, alied to the rice of the treatment. The ocial lanner budget contraint i N T τmn, which imlie that τθm. With the imlification that each member within the two uboulation i identical, an egalitarian ocial lanner weigh the utility of each member of the oulation equally, the ocial lanner roblem i to chooe in order to maximize W a follow: T T T [1] W N U m, c N U c i Normalizing the rice of c to be equal to 1, the reective budget contraint can be written a: [2] y c -m [3] y T c T τθy Inerting the budget contraint and the tax identity τθm into [1] we can recat the ocial welfare function a: T T T [4] W N [ U [ m ],[ y m ]] N [ U [ y θm θy ]] i Define the addict marginal rate of ubtitution between m and c a i ψ dc Define the ocial rate of ubtitution between addict conumtion and taxayer conumtion a

7 dc dc T T uming that U c >0 and U c <0, would ordinarily enure that T T < dc dc and thu that <1 becaue of the higher income and lower marginal utility of taxayer conumtion. Thi would mean that reditribution of 1 unit of conumtion from a taxayer to an addict create a utility gain for the addict that outweigh the utility lo for the taxayer. It alo i oible that addiction could alo lower the marginal utility of conumtion becaue ubtance ue effectively atiate the leaure center in the brain. We imly tiulate that in general, T T and conider the two oibilitie of <1 and >1. dc dc The firt order condition that define the otimal ubidy * can be written a [5] * ψ See endix for derivation. Furthermore a hown in endix, d [6] 2 d So that the ubidy decline a the addict demand for treatment become more elatic. The otimal ubidy i 0 when 1 ψ

8 For the tyical cae where <1 and <1, the oint at which the otimal ubidy i zero occur at non-negative value of ψ when addict have a high willingne to ay for their own treatment. The otimal ubidy can become negative e.g. a urtax on treatment if addict have very high willingne to ay for treatment ψ>>0 or if it i ocially otimal to reditribute wealth from addict to taxayer becaue >>1. The otimal ubidy i negative 1 whenever ψ >. The foregoing conideration aly to the otimal ubidy auming that all addict are equal and have table reference. i well-known both from field exerience with addict and from economic theory Dockner, Engelbert and Gutav Feichtinger 1993, an individual addict demand for treatment waxe and wane over time. If each addict had cyclic reference o that their demand for treatment exhibited regular eak and trough, the otimal ubidy would need to be tailored to each addict a their willingne to comly with treatment waxed and waned. One could, in rincile, ae demand for treatment by reeatedly meauring an individual addict demand elaticity and then calibrate incentive and ubidie to kee ace with dynamic hift in demand. equation [6] indicate the otimal ubidy would have to kee ace with 1/ 2. more feaible aroach would be to find eaily meaured redictor of demand for drug rehabilitation ervice in order to follow the dynamic evolution of thee marker. 2. Study oulation Between January, 2002 and January, 2003, 247 heroin injection drug uer IDU who requeted and were granted an available methadone maintenance treatment lot by the

9 Needle Exchange Program NEP rogram taff were invited to articiate in a randomized, controlled trial of trength-baed cae management v. uual methadone maintenance. The articiation rate among thoe invited to articiate wa aroximately 99.2% 245 of 247. Within 7 day of the initial interview, only 34% of the articiant followed through and actually enrolled into the treatment lot to which they were aigned. Detail of thi randomized trial are available elewhere Strathdee, S.., Erin Rickett, S Huettner, Llewellyn J. Corneliu, D Bihai, Jennifer R. Haven, P. Beilenon, C Ra, J.J. Lloyd, and Carl. Latkin For IDU who agreed to enter the trial, a igned conent wa obtained and a baeline interview wa conducted rior to the treatment intake aointment. Thi tudy wa aroved by the John Hokin Bloomberg School of Public Health Committee on Human Reearch. To develo the urvey intrument, we held key informant interview with drug rehabilitation cae manager and their ainitrator. Thee revealed that rice, duration of effect and the availability of cae management would be the mot alient rogram feature to inquire about. We tudied five different rice $5, $25, $40, $60, and $100 er week; two different availabilitie of cae management available or not; and three different duration of treatment effect 3, 6, or 24 month of freedom from heroin. In order to cover a comlete and orthogonal et of thee roduct feature with minimal reondent burden we conulted Sawtooth oftware Louviere, Jordan J. 1988;Sawtooth Software Inc. 1999, and concluded that two arallel et of 18 equential choice among were neceary. Subject were randomized o that half of them aw each et. Each of the 18 choice imoed a new array of three hyothetical methadone maintenance rogram decrition liting the rice, duration of effect, and reence of cae management See Figure 1. ll ubject were told to exect

10 that they would have to ay for the hyothetical rogram themelve becaue inurance would not reimbure for the treatment. Card were-randomized o that each of the 5 rice wa faced in about 20% of encounter, each cae-management choice in roughly 50% and each effect duration in roughly 33% of roduct encounter. fter viewing the three otion, ubject were aked, From thee three card, which rogram would you PREFER? The ubequent quetion wa Would you actually enroll in thi rogram?. Each verion included one choice et in which one rogram clearly dominated the other two a choice having cae management, longer treatment effect, and lowet rice. Subject who referred dominated rogram were flagged. 3. Statitical nalyi The evaluation of each of thee 54 drug treatment rogram 18 et 3 rogram er et alway occurred in the context of exactly 2 cometitor rogram. The reondent indicated both which rogram they referred and, in a earate quetion, whether or not they would ay for the referred rogram. Thi analyi tudie the reone to the econd quetion whether they would ay. The deendent variable in our model i a binary variable indicating whether the reondent would ay out of ocket to enter treatment with the referred et of characteritic out of each et of the three alternative. The indeendent variable are the attribute rice, duration, and heroin-free time of the rogram conidered and the baeline eronal characteritic e.g. ocio-economic-demograhic a well a addiction everity indice. The generalized linear model which we tudied take the form [7] EYg -1 [β P P k β D Dur k β S S k β Xµ Quetion µ Subject ]

11 where g -1 i an invere logitic link function and µ Quetion µ Subject are earate random effect aociated with each of the 18 quetion and each of the 245 ubject. Y i an indicator of whether the ubject would ay for the rogram and P k i a vector of the rogram own rice and the rice of the 2 cometing rogram aearing within each et of the 18 card et. Dur k and S K are reectively, vector of own and two cometing duration of freedom from heroin and own and two cometing indicator of availability of cae management. The vector X rereent individual reondent characteritic that might influence choice. We firt etimated thi model uing maximum likelihood method baed on the gllam rogram in Stata Rabe-Heketh, Sohia and nder Skrondal We ubequently ran imle logit model without any random effect ecification. The increaed efficiency of the comutationally intenive maximum likelihood aroach led to maller tandard error but coefficient etimate that were very cloe to the imle logit etimate. The ignificance of the coefficient wa the ame for the random effect and imle logit model. To eae interretation we exonentiated the logit coefficient to obtain etimate of odd ratio. We alo ued the mfx command in Stata 8.0 to convert the coefficient into marginal effect that could be interreted a own rice and cro rice elaticitie. Thee arc elaticitie have the conventional interretation: the ercentage increae in quantity demanded from a ercentage decreae in rice. The elaticity will only be valid around the mean of all of the covariate in the amle. It will reflect the reone to one rogram in an environment where there are 2 alternative each with the mean rice,

12 duration, and cae management availability of the roduct on the 18 et of rogram. It will alo reflect the mean income and erceived rik characteritic of the amle. 4. Reult For thi amle of heroin uer, the mean daily exenditure on heroin wa $64.63 SD $47.31, excluding two outlier who reorted ending over $1000 er day on heroin. Table 1 how the baic decritive data from the amle. The amle had a majority of non- Hianic frican merican and male. Self-reorted income had a mean of $1207, a median $855, and a maximum of $8000 er month. Only 8.5% of reondent were emloyed. Over 38% of reondent reorted deriving income from illegal ource; there may be underreorting. Reondent were aked to exre a reference for one of the three hyothetical treatment rogram in each of the 18 card et. Out of the 245 ubject, there were 5 refual to anwer reference quetion leading to the collection of reference tatement for et of three good. fter indicating which of the three wa referred, reondent were aked if they would ay the tiulated fee to enroll. The data decribe the outcome for 18 card et 3 rogram er card et 240 ubject 12,960 non-indeendent oortunitie to exre a willingne to urchae and or a reference. Figure 2 and 3 viually ummarize the reference data. Figure 2 how that the ubject intended to urchae the lowet riced $5.00 er week rogram 63% of the time when it wa couled with the romie of 24 month free of heroin. Thi willingne to urchae at $5.00 fell to 40% with only 6 month free of heroin and to 36% if only 3 month. Figure 2 rovide ome face validity; the roortion intending to enroll decreae ytematically with: 1 rice for a given time free heroin, and 2 time free from heroin at each

13 rice. That i, the loe are downward loing and increae by time heroin-free. Similarly, Figure 3 demontrate that the reence of cae management increae the robability of enrolling by about 10-20%, holding the fee contant. Figure 2 and 3 can be ued to calculate a ummary meaure of willingne to ay uing the area under each curve and the data on the redicted robabilitie of urchae. Thi can be done uing a logit model of equation [7] excluding the X variable to imute the robability of urchae ^ π i for the i-th reondent, for each of the 12,960 reondent-roduct air and data on the rice and other roduct attribute. The area under ^ each of the curve in Figure 2 and 3 are Σ i π i Pricei where Price i i the rice of the i- ^ th encountered roduct. One could interret π i Pricei a the tatitically exected revenue from the i-th eron-roduct encounter and offer ummary meaure of thi ditribution to convey willingne to ay of the amle. The kewne of the ditribution make the median a better ummary meaure than the mean Mitchell, R. and R. Caron If a drug rehabilitation rogram racticed erfect rice dicrimination in a range between $5 and $100, the median exected revenue er client correonding to area under the curve in Figure 2 would be $17.11, $8.42, and $7.39 for rogram that offered 24, 6, and 3 month of heroin-free time. For Figure 3, the correonding ummary meaure are $13.05 and $7.40 for rogram that do and do not offer cae management reectively. However, thee number could be underetimate of the true WTP a our 5 rice oint do not exhaut the full range of demand. can be een in Figure 2, there remain a many a 40% of ubject who ay they would urchae treatment at $100 er week. If thee ercentage

14 remain high at rice of $150, $200, or even $250, there could be ubtantial rivate willingne to ay that i unmeaured in our model. Table 2 exlore whether or not model of willingne to ay are robut to the incluion or excluion of the 21% of ubject who were willing to urchae dominated roduct. Table 3 how that the effect of rice and roduct attribute on WTP are nearly identical whether or not all ubject are included. Cae management increae willingne to ay, whether or not irrational reonder are included, which confirm our aumtion that cae management i generally erceived a a normal good. In earate analye not hown a dummy variable indicating having referred dominated choice had no effect on the robability of declaring a willingne to ay. We ran additional analyi not hown to redict the robability of making a dominated choice. The odd of referring a dominated roduct were aociated with everal background variable, including eldom attending church lower odd, homelene higher odd and being married lower odd but not with chooling attainment. To maximize the ower of the amle, all of the ubject were retained for ubequent model and background variable were retained a covariate. In Table 3 we dilay the reult of 4 different multivariate model of the willingne to ay uing logitic regreion. Product attribute, eecially rice, are the mot owerful determinant of the deciion to urchae and eronal attribute including the reference for dominated otion have a very weak interaction with the effect of rice. The rincial ociodemograhic background variable aociated with WTP were co-reidence with female or with arent, which increaed WTP and frequent religiou ervice attendance which decreaed WTP. earate tudy of the data from thi trial confirmed that living with a exual artner increaed threefold the odd of actually entering treatment Lloyd, J. J., E. P.

15 Rickett, S.. Strathdee, L. J. Corneliu, D. Bihai, S. Huettner, J. R. Haven, and C. Latkin It may be that the highly religiou may ee their religiou articiation a a ubtitute for oioid agonit theray with methadone 1. The comonent of the addiction everity index had ooing effect. The ychiatric ubcale wa aociated with increaed willingne to ay while the medical and drug ue ubcale were aociated with decreaed willingne to ay. Baed on model 1 of Table 3, the rice elaticity of demand for drug treatment wa etimated at 0.39 baed on a comutation of marginal effect. Thi elaticity wa etimated at the amle mean of the roduct attribute imlying a cah rice of $48 er week of treatment, a mean tiulated treatment outcome of 10 month of freedom from heroin, and a 49% robability that there would be cae management ervice available. 5. Dicuion Our tudy revealed that drug addict have a relatively inelatic demand for methadone maintenance treatment with an arc elaticity of Thi i the firt etimate of rice elaticity in the literature. Thi etimate of elaticity i contingent on the etting of thi tudy and the et of hyothetical rogram arameter, a well a the characteritic of the amle oulation. Thu, the etimate of the rice elaticity i not a generalizable a we would like. However, a the firt etimate, we hoe that it ave the way for future reearch. Revealed reference data from rice exeriment in drug treatment clinic are difficult to obtain. Knowledge of the rice elaticity i imortant a there are many alication to olicy iue. 1 Marx may have had a different henomenon in mind when he declared that Religion i the oiate of the mae.

16 There i cant literature on the enitivity of demand to rogram characteritic. n imortant rior tudy Boriova, N. N. and. C. Gooan 2003 howed that addict have a willingne to ay for reduction in travel time to methadone maintenance, but did not addre the rice elaticity of treatment. Our reult have face validity in that increment in deirable rogram attribute uch a availability of cae management and the rogram tiulated time free from heroin deendence led to increment in demand. lo, we were able to rovide tronger validation through revealed reference. The 245 reondent in our trial were randomized after our urvey to treatment with cae management Strength Baed Cae Management SBCM or without cae management. ignment wa revealed right after the WTP urvey wa conducted and ubject who were aigned to SBCM immediately received an initial eion with a cae manager. We ubequently oberved whether the client actually followed through with the referral and later enrolled in the aigned treatment rogram by record linkage with the Baltimore Subtance bue Sytem. reorted in a earate aer 39.8% of client aigned SBCM enrolled in treatment, comared to 26.5% of thoe in the control arm Strathdee, S.., Erin Rickett, S Huettner, Llewellyn J. Corneliu, D Bihai, Jennifer R. Haven, P. Beilenon, J. J. Lloyd, C Ra, and Carl. Latkin Thi 12.8 ercentage oint difference in enrollment rate i imilar to the difference between the demand curve for cae management in the two curve hown in Figure 3. We found that roduct attribute, eecially rice, are the mot owerful determinant of the deciion to urchae. Thu, rogram characteritic may be the bet vehicle on which to bae rice dicrimination.

17 Policy Imlication. The key olicy iue i how to increae the number of heroin uer who obtain treatment. Our finding ugget a erha greater role for rivate ayment. With Ramey ricing and rice dicrimination for rivate ayer, the total revenue for treatment clinic could be exanded. Currently, there i amle rice dicrimination not only by individual aying out of ocket, but alo by ublic ayer and rivate inurer. However, taking a Ramey ricing aroach might hel to otimize the ytem and to rovide greater benefit through treatment. The ainitrative challenge of actually imoing a ytem of Ramey rice that charged each client in erfect roortion to their willingne to ay would be formidable. Intead of individual level rice dicrimination, market egmentation might be more likely. The market could be egmented erha by clinic or by rogram within a clinic, with ome clinic or rogram offering higher ervice quality or ecific ervice which would attract thoe more willing to ay. Our tudy how that cae management or concierge tye ervice increae willingne to ay. Iue of equity might urface with uch rice dicrimination, but thi concern would by artially offet by the otential to increae fund for treatment. The cyclical nature of demand would be difficult to addre, however, a addict dro in and out of treatment reeatedly during the coure of their dieae. It would be far better to ue a dynamic ubidy ytem to kee individual in treatment, but it would be quite difficult to deign an effective, dynamic ubidy ytem. lthough our etimate ugget a role for rivate ayment, our etimate of exected revenue from heroin addict fall ignificantly hort of being able to finance the full cot of drug rehabilitation. ccording to our etimate, a drug rehabilitation ytem that could maintain a dicriminatory ricing regimen would obtain a median exected revenue er addict of $7.40 to $17.11 er week with a clientele imilar to our amle. Thi would not

18 cover the cot of outatient methadone maintenance rogram which average $82 er week, with the leat cot rogram at $42 er week Roebuck, M. C., M. T. French, and. T. McLellan Thi ugget that ubidie ranging from $65 to $75 er atient er week would be neceary in order to make u the difference. Note that couneling baed drug treatment cot coniderably le and the length of tay i much horter, but there are no data on WTP. One could argue for ubidie equal to the full cot of treatment becaue of the large negative externalitie of drug ue joint with the fact that drug uer eem reitant to entering treatment on their own many come to treatment under the dure of the criminal jutice. Indeed, a rior tudy found that the availability of free drug treatment wa the mot imortant redictor of actual treatment entry Booth, R. E., C. Kwiatkowki, M. Y. Iguchi, F. Pinto, and D. John However, co-ayment generate income and the revenue could be ued to increae the uly of treatment lot and conduct outreach. Demand for treatment might be increaed by uing the revenue for ocial marketing e.g. ublic ervice announcement if ome of the revenue accrued to government ayer. To the extent that rovider rea ome of the revenue of higher co-ayment, they could finance marketing camaign for their clinic which might illover benefit to increaing the overall demand a well a attract client to their ecific clinic. nother alternative to increaing demand would be to ay drug addict to eek treatment. The otimal co-ayment for elected addict could be negative in order to attract addict who reently have no deire for treatment. Contingency management technique are currently being deigned to ay thoe in treatment to attend couneling eion and to make ayment contingent on verified abtinence from drug. Some of the ytem are

19 deigned with ecalating ayment ytem which increae the rice of ue of drug over time and with booter ayment. Thee ytem have been found to be effective and could erha erve a the bai of a dynamic negative ubidy Petry, N.M., J. Pierce, M.L. Stitzer, J. Blaine, J.M. Roll, and. Cohen Thi tudy how that drug addict demand deend on rice, ervice amenitie and erceived treatment outcome. Etimate of addict rice elaticity for drug treatment have many olicy alication, one of which i the develoment of an otimal ubidy ytem. Segmentation of the market for drug rehabilitation i currently racticed in many urban area and enable rogram to charge differential uer fee baed on accomanying amenitie like ervice hour and location. The aroriate deloyment of cot-haring mechanim can increae the revenue for rogram and otentially free u ublic fund to further exand treatment availability and conduct outreach. Informed and thoughtful develoment of cotharing mechanim for drug treatment can exand ervice caacity and reduce the negative externalitie aociated with drug ue.

20 Reference Baumol, William J. and David F. Bradford "Otimal Dearture from Marginal Cot Pricing." merican Economic Review, 60:3, Booth, R. E., C. Kwiatkowki, M. Y. Iguchi, F. Pinto, and D. John "Facilitating treatment entry among out-of-treatment injection drug uer." Public Health Re, 113 Sul 1, Boriova, N. N. and. C. Gooan "Meauring the value of time for methadone maintenance client: willingne to ay, willingne to accet, and the wage rate." Health Econ, 12:4, Cartwright, W. S. and P. L. Solano "The economic of ublic health: financing drug abue treatment ervice." Health Policy, 66:3, Cartwright, W.S "Cot-benefit analyi of drug treatment ervice: Review of the literature." Journal of Mental Health Policy Economic, 3, Dockner, Engelbert and Gutav Feichtinger "Cyclical Conumtion Pattern and Rational ddiction." merican Economic Review, 83:1, Harwood, H. J., J. Fountain, and G Livermore The Economic Cot of lcohol and Drug bue in the United State, Betheda, MD: NIH. Jofre-Bonet, M and JL Sindelar "Drug Treatment a a Crime Fighting Tool." Journal of Mental Health Policy and Economic, 4:4,

21 Lloyd, J. J., E. P. Rickett, S.. Strathdee, L. J. Corneliu, D. Bihai, S. Huettner, J. R. Haven, and C. Latkin "Social contextual factor aociated with entry into oiate agonit treatment among injection drug uer." m J Drug lcohol bue, 31:4, Louviere, Jordan J nalyzing Deciion-Making: Metric Conjoint nalyi. London: Sage Publication. McColliter, K.E. and M.T. French "The relative contribution of outcome domain in the total economic benefit of addiction intervention: review of firt finding " ddiction, 98:12, Mitchell, R. and R. Caron Uing Survey to Value Public Good: The Contingent Valuation Method. Wahington, DC: Reource for the Future. Petry, N.M., J. Pierce, M.L. Stitzer, J. Blaine, J.M. Roll, and. Cohen "Prize-baed incentive imrove outcome of timulant abuer in outatient ychoocial treatment rogram: national drug abue treatment clinical trial network tudy." rchive of General Pychiatry, 62, Rabe-Heketh, Sohia and nder Skrondal "Reliable etimation of generalized linear mixed model uing adative quadrature." The Stata Journal, 2:1, Roebuck, M. C., M. T. French, and. T. McLellan "DTStat: reult from 85 tudie uing the Drug bue Treatment Cot nalyi Program." J Subt bue Treat, 25:1,

22 Sawtooth Software Inc The CBC Sytem Uer' Manual. Evanton, IL: Sawtooth Technologie. Strathdee, S.., Erin Rickett, S Huettner, Llewellyn J. Corneliu, D Bihai, Jennifer R. Haven, P. Beilenon, J. J. Lloyd, C Ra, and Carl. Latkin "Cae Management Imrove Entry into Drug Treatment among Injection Drug Uer Referred from a Needle Exchange Program." John Hokin Univerity: Baltimore. Strathdee, S.., Erin Rickett, S Huettner, Llewellyn J. Corneliu, D Bihai, Jennifer R. Haven, P. Beilenon, C Ra, J.J. Lloyd, and Carl. Latkin "Cae Management to Imrove Entry into Drug Treatment mong Injection Drug Uer Referred from a Needle Exchange Program." In Pre. Subtance bue and Mental Health Service initration Overview of Finding from the 2003 National Survey on Drug Ue and Health. Rockville, MD: Office of lied Studie. Zarkin, G.., S. C. Cate, and M. V. Bala "Etimating the willingne to ay for drug abue treatment: a ilot tudy." J Subt bue Treat, 18:2, Zarkin, G.., L.J. Dunla, J.W. Bray, and W.M. Wechberg "The Effect of Treatment Comletion and Length of Stay on Emloyment and Crime in Outatient Drug-free Treatment." Journal of Subtance bue Treatment, 23:4,

23 Table Table 1. Samle Decritive Number Non Miing Mean or Frequency SD ge at interview in year Male % Married 244 8% Non-hianic black % Non-hianic white % Hianic 244 1% Mile from their zi code to treatment referral ite % non-elf HH member female % Live in other' houe/at % ny uort from illegal % Individual Income er month Live with arent 245 6% Family Social Statu SI Subcale Pychiatric Severity SI Subcale Legal Severity SI Subcale lcohol Severity SI Subcale Drug Severity SI Subcale Emloyment Severity SI Subcale Medical Severity SI Subcale

24 Table 2. Etimate of WTP: Comaring reult including and excluding ubject who irrationally referred dominated choice Individual who irrationally elected Deendent Variable: WTP dominated choice Included are: Excluded Price of the rogram under conideration *** 8.22** vailability of cae management in the rogram under conideration *** 8.34** Time free of heroin in the rogram under conideration *** 10.99** Price of the firt alternative *** 4.85** Price of the econd alternative ** vailability of cae management in the the firt alternative *** 2.18* vailability of cae management in the the econd alternative *** -0.9 Time free of heroin in the the firt alternative ** Time free of heroin in the the econd alternative *** 5.53** Obervation Robut z-tatitic in arenthee * ignificant at 10%; ** ignificant at 5%; *** ignificant at 1%

25 Table 3 Logitic Model of WTP for Drug Rehabilitation Model 1 Model 2 Model 3 Model 4 Model 5 Price of the rogram under conideration *** 8.43*** 7.97*** 8.50*** 8.17*** vailability of cae management in the rogram under conideration *** 5.90*** 7.41*** 6.01*** 5.69*** Time free of heroin in the rogram under conideration *** 11.27*** 12.81*** 11.23*** 10.54*** Price of the firt alternative *** 4.22*** 5.08*** 4.08*** 4.00*** Price of the econd alternative vailability of cae management in the the firt alternative vailability of cae management in the the econd alternative Time free of heroin in the the firt alternative Time free of heroin in the the econd 2.8 *** 2.52** *** 2.56** *** 3.05*** 3.19*** 3.08*** 3.14*** *** 3.20*** 2.95*** 3.22*** 3.13*** *** 5.19*** 4.09*** 5.20*** 4.69*** *** 7.43*** 6.70*** 7.64*** 7.13*** alternative ge at interview in year Male Married Non-hianic black Non-hianic white Hianic Mile from their zi code to treatment referral ite % non-elf HH member female ** 2.66*** 2.43** ttend vc <1/month ttend vc 2-3/month ttend vc weekly ttend vc >1/wk ** 2.26** 2.05** Live in other' houe/at ny uort from illegal Individual Income er month Live with arent * 1.76* 2.02** Pychiatric Severity SI Subcale ** Drug Severity SI Subcale ** Medical Severity SI Subcale Contant *** 8.71*** 4.75*** 3.93*** 2.67*** Obervation Robut z-tatitic in arenthee * ignificant at 10%; ** ignificant at 5%; *** ignificant at 1%

26 Figure 1 Set 8 One of the 18 Set of Card for Each Subject Program Program B Program C Price $ er Week $25 Price $ er Week $40 Price $ er Week $60 vailability of Social Service No vailability of Social Service No vailability of Social Service Ye Time Sent Heroin Free 3 month Time Sent Heroin Free 6 month Time Sent Heroin Free 6 month Verion 1

27 Figure 2 Willingne to Pay By Duration of Treatment Effect Proortion Willing to Pay $0 $20 $40 $60 $80 $100 $120 Fee in Dollar Heroin Free for 3 Month Heroin Free for 6 Month Heroin Free for 24 Month

28 Figure 3 Willingne to Pay By vailability of Cae Management Proortion Willing to Pay $0 $20 $40 $60 $80 $100 $120 Fee in Dollar Cae Management vailable Cae Management Not vailable

29 endix The firt order condition for Equation 1 i: 1 1 5] [ noting that ] [ o but ] [ 2] [ 0 1] [ T T T T T T T T T dy dy m d d m dy d m dy d m N N d m dy N d m dy N d m N d m dy N d m dy N d N d m dy N d m dy d N θ θ θ θ θ θ Define dy dy T

30 ] [ 1 ] 1 [ 11] [ udv/v vdu - lying quotient rule du/v ] [ 1 1 9] [ 1 1 8] [ 7] [ 1 1 6] [ d d d d du u dv v MRS MRS MRS MRS MRS

31 endix B Derivation of condition for zero ubidy: B B B If B ψ ψ ψ ψ 1 4] [ 1 3] [ 1 2] [ 1` ] [ > < > > >

32 cknowledgement: Funding for thi reearch wa rovided by grant number R01- D09225 funded by the National Intitute on Drug bue. In addition, the author would like to thank tudy articiant and taff of the Baltimore Needle Exchange Project. The author gratefully acknowledge reearch uort for JS from the National Intitute on Drug bue to Yale Grant No. R01-D14471.