Nonparametric Bounds on the Effect of Deductibles in Health Care Insurance on Doctor Visits - Swiss Evidence

Transcription

1 DISCUSSION PAPER SERIES IZA DP No Nonparameric Bounds on he Effec of Deducibles in Healh Care Insurance on Docor Visis - Swiss Evidence Michael Gerfin Marin Schellhorn May 2005 Forschungsinsiu zur Zukunf der Arbei Insiue for he Sudy of Labor

2 Nonparameric Bounds on he Effec of Deducibles in Healh Care Insurance on Docor Visis Swiss Evidence Michael Gerfin Universiy of Bern and IZA Bonn Marin Schellhorn GSF, Insiue of Healh Economics and Healh Care Managemen, Munich, Universiy of Bern and IZA Bonn Discussion Paper No May 2005 IZA P.O. Box Bonn Germany Phone: Fax: Any opinions expressed here are hose of he auhor(s) and no hose of he insiue. Research disseminaed by IZA may include views on policy, bu he insiue iself akes no insiuional policy posiions. The Insiue for he Sudy of Labor (IZA) in Bonn is a local and virual inernaional research cener and a place of communicaion beween science, poliics and business. IZA is an independen nonprofi company suppored by Deusche Pos World Ne. The cener is associaed wih he Universiy of Bonn and offers a simulaing research environmen hrough is research neworks, research suppor, and visiors and docoral programs. IZA engages in (i) original and inernaionally compeiive research in all fields of labor economics, (ii) developmen of policy conceps, and (iii) disseminaion of research resuls and conceps o he ineresed public. IZA Discussion Papers ofen represen preliminary work and are circulaed o encourage discussion. Ciaion of such a paper should accoun for is provisional characer. A revised version may be available direcly from he auhor.

3 IZA Discussion Paper No May 2005 ABSTRACT Nonparameric Bounds on he Effec of Deducibles in Healh Care Insurance on Docor Visis Swiss Evidence We evaluae he effec of he size of deducibles in he basic healh insurance in Swizerland on he probabiliy of a docor visi. We employ nonparameric bounding echniques o minimise saisical assumpions. In order o ighen he bounds we consider hree furher assumpions: mean independence of an insrumen, monoone reamen response, and monoone reamen selecion. Under he firs wo assumpions we are able o bound he reamen effec of high deducibles compared o low deducibles below zero. Adding he hird assumpion allows o ighen he bounds furher. We conclude ha here is a negaive reamen effec. JEL Classificaion: C14, I19 Keywords: reamen effecs, bounds, healh insurance Corresponding auhor: Michael Gerfin Deparmen of Economics Universiä Bern Gesellschafssr. 49 CH 3012 Bern Swizerland michael.gerfin@vwi.unibe.ch Michael Gerfin hanks he Swiss Science Foundaion for financial suppor (Gran ). We hank he Federal Office of Saisics for permission o use he daa (Swiss Healh Survey) and Rober E. Leu for making he second wave of he daa possible.

4 1. Inroducion Healh care expendiure increased considerably in Swizerland in he pas years. Beween 1998 and 2002 he increase amouned o 22%. As a consequence he average premium for he compulsory basic healh insurance increased by even 24% in he same period. Currenly, he average premium amouns o abou 10% of he median of equivalen household income. For many families paying he healh care insurance premium has become a major financial burden. No surprisingly, his developmen has pu healh care coss on op of he healh and social policy agenda. One insrumen hough o reduce he growh in healh care expendiure is increased cos sharing because boh insurance heory predics and empirical evidence confirms ha here is a negaive correlaion beween he degree of cos sharing and expendiure. The Swiss healh insurance law from 1996 provides he possibiliy of cos sharing in basic healh insurance. The insured can choose beween 5 possible deducible levels ranging from a minimum of 230 CHF per year o a maximum of 1500 CHF. Choosing higher deducibles is combined wih premium reducions. 1 However, as is well known he negaive correlaion beween he degree of cos sharing and he demand for healh care can be due o wo reasons: seleciviy or moral hazard. If only healhy people who do no go o he docor anyway choose high deducibles he observed negaive correlaion is mainly due o seleciviy. In his case he size of he deducible has no impac on healh care demand and healh care coss. If on he oher hand people become more cos-aware and change heir healh care demand behaviour here is a causal effec of he deducibles, hus reducing he moral hazard problem. Hence, in order o assess he cos-reducing poenial of variable deducibles i is necessary o isolae he moral hazard (or reamen) effec. The empirical evidence on he exisence of moral hazard effecs is mixed. Probably he mos famous sudy is he RAND experimen (Manning e al., 1987). In his experimen people in several US saes were randomly assigned o differen insurance plans. These plans differed in he degree of cos sharing beween paiens and insurance company. The main resul is ha higher cos sharing reduces healh care demand (measured by he number of docor visis). Chiappori e al. (1998) analyse a naural experimen in France where healh insurance companies varied in 1 Since January 2005 he maximum deducible is 2500 CHF. 2

5 heir reacion o a change in healh insurance regulaions. They do no find a significan effec of increased cos sharing on healh care demand measured by he number of visis o general praciioners. On he oher hand hey esimae a significan effec on he number of home visis. Winkelmann (2004) analyses he effec of inroducing a fee for drug prescripions in Germany in he year Using panel daa he esimaes a significan reducion of he expeced number of docor visis due o his reform. The empirical evidence for Swizerland is mixed as well. Gardiol e al (2003) and Werblow and Felder (2003) esimae a significan negaive effec of he size of he deducible on healh care coss. On he oher hand, Schellhorn (2001, 2004) does no find any significan effecs of he deducible on he number of docor visis. The firs wo papers are based on daa from a large insurance company, each covering only one canon 2, whereas Schellhorn uses daa from he Swiss Healh Survey, which covers all of Swizerland. One cenral problem of he exising empirical evidence for Swizerland is he underlying economerics. The insurance company daa used by Werblow and Felder (2003) are very informaive regarding healh care coss. However, here is a lack of variables ha may help o solve he selecion problem. No surprisingly, he paper is no very clear abou exclusion resricions. The esimaion mehod is a parameric selecion model. Given hese problems i is no clear wheher he esimaed parameers are unbiased esimaes of he causal effec of deducibles on healh care coss. Gardiol e al. (2003) use daa from he same insurance company, bu for a differen canon. Their idenificaion sraegy is based on he assumpion ha here should be no moral hazard effec wih respec o hospial expendiure (based on empirical evidence ha he price elasiciy of hospial care is close o zero). Under his assumpion he esimaed effec of he deducible on hospial coss is only due o selecion. Given his esimae of he selecion effec i is possible o decompose he esimaed coefficiens for oupaien care ino he moral hazard and he selecion effec. The esimaion mehod is he parameric wo-par model. Hence idenificaion depends crucially boh on he assumpion regarding hospial expendiure and he correc specificaion of he saisical model. The papers by Schellhorn employ zero inflaed coun daa regression models wih endogenous regressors. In his case he 2 The daa in Werblow and Felder are for he canon of Zurich, he daa used by Gardiol e al. are for he canon of Vaud. 3

6 exclusion resricions are clearly explained. However, esimaing he model requires srong disribuional assumpions ha may be violaed by he daa a hand. For hese reasons in his paper we esimae he effec of deducibles on he probabiliy of going o he docor wih as lile saisical assumpions as possible. We employ he mehod of nonparameric bounds on he reamen effec inroduced by Manski (1990) and furher developed among ohers by Manski (1997), Manski and Pepper (2000) and Shaik and Vylacil (2005). Imposing several weak assumpions allows o bound he reamen effec away from zero. Our resuls indicae a negaive effec of higher deducibles on he probabiliy of going o a docor. This paper is organised as follows: secion 2 gives a brief overview of he Swiss healh insurance sysem. The daa used in he empirical analysis are described in secion 3. Secion 4 presens he esimaion sraegy and secion 5 discusses he esimaion resuls. Secion 6 concludes. 2. The Swiss Healh Insurance Sysem Since he reform of he healh insurance law in 1996 a basic healh insurance is mandaory in Swizerland. This basic healh insurance is provided by compeing privae insurers and covers a widely defined se of medical services. The healh insurance premium is heavily regulaed. Premiums for aduls can vary beween hree regions in each canon bu are no allowed o be relaed o risk-facors like age and sex or income. Every individual is insured wih a separae conrac. In 2002, he insured faced a choice beween a minimal deducible of 230 CHF and higher deducibles of 400, 600, 1200 or 1500 CHF are opional. In order o make higher deducibles aracive hey are combined wih premium reducions. These reducions are regulaed o be a mos (8%, 15%, 30% and 40%) of he premium wih he minimal deducible. Therefore, he poenial savings from choosing a higher deducible vary subsanially beween canons and regions. We will use his fac o generae an insrumenal variable in our esimaion sraegy. The insured have free choice beween he insurance companies wih open enrollmen and can change heir insurer and heir deducible a he beginning of each calendar year. In 2002, he average monhly insurance premium for he conrac wih he minimal deducible was 245 CHF and varied beween 159 CHF in he canon of Appenzell and 364 CHF in he canon of Geneva. 4

7 There is a large variance of premia wihin canons as well. For example, he average premium in he canon of Zurich was 249 CHF in 2002; he lowes premium was 170 CHF and he larges premium was 390 CHF for virually he same insurance. The main reason for his huge spread of he premia is ha insurance companies face differen risk and cos srucures. To reduce he amoun of risk selecion induced by his ype of premium regulaion all insurance companies have o paricipae in a risk-adjusmen pool. Depending on he risk srucure of heir enrollees insurers pay or receive conribuions from his pool. There is a co-paymen rae of 10% when coss exceed he chosen deducible. There is a ceiling for co-paymens of 600 SFr. per year irrespecive of he chosen deducible. Healh insurance premiums and ou-of-pocke paymens can ea up a subsanial par of household income especially in larger families. To ease he financial hardship associaed wih per capia premiums, governmen provides means esed subsidies o low income residens. In 2001 roughly one hird of he insured were subsidized o some exen, and abou 15% of all enrollee premium paymens were paid for by he governmen. Subsidies are paid if premiums exceed a cerain percenage of household income usually 8%-10%. The maximum amoun paid is ypically he mean of he premiums of all insurance companies in he canon. Compulsory basic insurance covers oupaien care, including a wide variey of providers, hospial care (100% coverage on he general ward of a public or publicly subsidized hospial in he enrollees canon, excep for a co-paymen of CHF 10 per day), prescripion drugs lised, prevenive vaccinaions, prescribed reamens in healh resors and alernaive medicine. In addiion, here are conribuions o cerain prevenive ess, home care, glasses and medical devices as well as ransporaion and salvage expenses. In emergency cases up o wice he rae of he canonal ariffs are paid for reamens abroad. Denal care, by conras, is only covered in case of acciden or severe denal problems. Compulsory insurance in he fee-for-service secor offers direc access and free choice of physician for oupaien care (general praciioners and specialiss). Excep for emergency cases hospialisaion requires referral by a physician. There is no choice of physician in he hospial. However, paiens may freely choose among all hospials which are included on he canonal eligibiliy lis. Supplemenary insurance covers addiional reamens and check-ups, all drugs, exended home 5

8 care, provides generally higher benefis and up o 100% universal coverage world wide. Mos imporan i provides access o he privae ward of all public and privae hospials in a one or wobedroom and free choice of physician in he hospial (medical or assisan medical direcor), depending on insurance package. 3. Daa The daa come from he Swiss Healh Survey (SHS) 2002 conduced by he Federal Bureau of Saisics. This cross secion conains a large number of socioeconomic characerisics and informaion on healh saus and healh care uilisaion in he pas 12 monhs. In his paper we use he subsample of hose whose inerview ook place in he firs quarer of These persons were inerviewed a second ime 6 monhs afer he firs inerview. 3 This second inerview gives informaion on healh care demand since he firs inerview and deailed informaion on healh care insurance. Persons were asked o provide he name of heir insurance company which allowed o compue he precise healh insurance premium each person has o pay. Hence his subsample provides all he relevan informaion: deducible choice a he beginning of 2002 and healh care demand in he firs 6 monhs of In addiion, here are several imporan variables o conrol for selecion: age, gender, subjecive healh saus, previous demand behaviour and risk facors like weigh or smoking. This subsample of he SHS 2002 conains 3623 observaions. Afer deleing individuals younger han 19 (hese face differen regulaions concerning deducibles) and individuals in alernaive forms of insurance such as HMO and individuals wih missing informaion on crucial variables he daa conains 2860 observaions. Table 1 provides descripive saisics of some cenral variables separaed by reamen saus. In he remainder of his paper we consider hree possible reamen saes denoed by D, where 0 if deducible = 230 D = 1 if deducible {400,600} 2 if deducible {1200,1500} This appears o be a naural combinaion of he 5 possible deducible levels. A lile less han half 3 This addiional inerview was financed by he Naional Research Program 45, Fuure of he Social Sae. 6

9 of he individuals have chosen he lowes deducible. Roughly one hird oped for he medium deducible, and he remaining 18% decided o ake he larges deducible. No surprisingly, his group is on average younger and feels more healhy. Also no surprisingly men are more likely o op for he larges deducible. There are also noicable differences wih respec o educaion, income, previous healh care demand, and he premium if he person had chosen he lowes deducible. This premium is compued using he informaion on he insurance company and he region of residence. The higher his hypoheical premium he higher is he saving poenial for choosing higher deducibles. As discussed in secion 2 here is a large variaion in his impued premium. The oucome variable used in his paper is he indicaor variable aking he value one if he person did see a docor (eiher general praciioner or specialis) in he pas 6 monhs. In he lowes deducible group 64% had a leas one docor visi, whereas only 40% in he highes deducible group wen o he docor. This finding corresponds o he well known negaive correlaion beween he degree of cos sharing and healh care uilisaion. The same is rue if we consider number of docor visis. People in he lowes deducible group had on average 2.8 docor visis compared o 1.3 visis of people in he highes deducible group. However, comparing he average number of docor visis condiional on having seen a docor reveals a much less pronounced difference across groups. This finding corresponds o he well known fac ha he main choice people have is wheher o see a docor or no. Given hey decided on a firs consulaion furher docor visis are o a large exen ou of heir conrol. For his reason we focus on he probabiliy of going o a docor as oucome variable. 7

10 Table 1: Descripive saisics Variable Deducible:230 Deducible:400/600 Deducible:1200/1500 Female Age Educaion: high Educaion: average Educaion: low Smoke: yes Smoke: never Smoke: no any more Subjecive healh: excellen Subjecive healh: good Subjecive healh: no good Income Premium (a lowes deducible) Docor visi in 2001: 1 = yes Docor visi in 2002: 1 = yes Number of docor visis Number of docor visiss (excluding zeros) Number of observaions 1,362 (47.6%) 975 (34.1%) 523 (18.3%) Source: Swiss Healh Survey 2002, own calculaions Table A.1 in he Appendix displays ordered probi esimaes of he deerminans of deducible choice. These esimaes clearly indicae ha deducible choice is srongly influenced by income, previous healh care demand (measured by he number of docor visis, a dummy for hospial say and a dummy for exhausion of deducible in he previous year), he hypoheical premium in case of he lowes deducible and regional differences. The esimaion sraegy described below requires an insrumenal variable. Possible insrumens given he ordered probi resuls could be he regional indicaors reflecing premium differences across canons (as used in Schellhorn, 2001, 2004) or he impued premium. The oher significan variables in Table A.1 do no appear o be valid insrumens because i is likely ha hey influence he oucome as well. We use he impued premium as an insrumen in our analysis. The reasoning is ha he premium does no affec he coss of going o a docor. Recall ha he premium for basic insurance is independen of risk facors such as age or previous illnesses. Hence we believe ha he impued premium saisfies he weak assumpions required for an insrumen as oulined below. In fac, hese assumpions are weaker han hose necessary for 8

11 2SLS. 4. Esimaion sraegy For each person i we observe ( Yi, Di, X i), where Y i is he oucome variable, D i is he indicaor of reamen, Di {0,1, 2} as defined above, and X i is a vecor of covariaes. To simplify noaion he subscrip i will be dropped in he following. The observed oucome Y is given by (1) Y = 1[ D = ] Y, = 0,1,2 where Y is he poenial oucome if D = and 1[ ] is he indicaor funcion equal o one if he expression in brackes is rue. The average reamen effec (ATE) is defined as (2) s, ATE E[ Y X ] E[ Ys X ] E[ Y Ys X ], s = =, where ATE,s measures he effec of reamen relaive o reamen s. In order o make he noaion more compac we leave he condiioning on X implici in he following. As is well known ATE is no idenified by he daa. This can be easily shown by wriing (3) EY [ ] = EY [ D= PD ] [ = ] + EY [ D PD ] [ ] The daa idenify E[ Y D = ], P[ D = ] and P[ D ] bu no EY [ D ]. The large and growing lieraure on esimaing reamen effecs is primarily concerned wih solving his idenificaion problem. There is a large variey of idenificaion sraegies: condiional independence assumpions, parameric selecion models and esimaors using insrumenal variables. These assumpions can be very srong boh in erms of funcional form and disribuional assumpions. Necessary exclusion resricions for insrumenal variables and selecion models are ofen difficul o jusify. In his paper we analyse he effec of deducible choice wih as few assumpions as possible. We 9

12 employ he mehod of nonparameric bounds on reamen effecs inroduced by Manski (1990). Furher developmens have been made by Manski (1997), Manski and Pepper (2000), Heckman and Vylacil (2001) and Vylacil and Shaik (2004), among ohers. Applicaions are sill relaively rare; examples include Pepper (2000), Ginher (2000), Gonzalez (2004) and Bhaacharya e al. (2005). The main idea of esimaing bounds can be illusraed as follows. Replace he unobserved EY [ D ] in EY [ ] = EY [ D= PD ] [ = ] + EY [ D PD ] [ ] by is bounds where l Y is he smalles value Y can ake and l Y and u Y, u Y is he larges value Y can ake. The lower l l bound for EY [ ] is hen B = EY [ D= PD ] [ = ] + YPD [ ] and he corresponding upper u u bound for EY [ ] is B = EY [ D= PD ] [ = ] + Y PD [ ] l u If EY [ ] is a probabiliy we have: Y = 0; Y = 1. Hence he bounds for EY [ ] are (6) E[ Y D= PD ] [ = ] EY [ ] EY [ D= PD ] [ = ] + PD [ ] or compacly l (6 ) B EY [ ] B u l u wih B 1 as lower bound and B 1 as upper bound of EY [ ]. Now all erms in (6) are idenified. If EY [ ] is bounded hen ATE is bounded as well. Assume ha > s. The lower bound of ATE is he difference beween he lower bound of EY [ ] and he upper bound of EY [ s ], and he upper bound is he difference beween he upper bound of EY [ ] and he lower bound of EY [ s ] (7), ( B l u ) s ( u l Bs ATE B Bs) These are he wors-case bounds of Manski (1990). In pracice hese bounds are oo wide o be useful (and hey always conain zero). The esimaes in he presen conex are displayed in Appendix Table A.1. Therefore, Manski (1990, 1997) considers addiional informaion ha can be applied. He analyses he case where an insrumen Z is available ha saisfies 10

13 EY [ X, Z] = EY [ X], i.e. Z saisfies mean independence. In his case he bounds change o l (8) B = { EY D= Z= zpd= Z= z} IV, sup [, ] [, ] z and u (9) B { EY D Z z P D Z z P D Z z } 4, = inf [ =, = ] [ =, = ] + [, = ] IV z Ineresingly, Heckman and Vylacil (2001) show for he case of binary reamens ha imposing a hreshold crossing model srucure on he reamen choice leads o formally idenical bounds. Using he hypoheical premium if everybody chooses he lowes deducible as insrumen sill yields bounds ha are much oo wide o be helpful. Table A.1 in he Appendix displays he esimaes. Manski (1997) inroduced he noion of monoone reamen response (MTR). MTR means ha if > s han Y Ys or Y Ys: In our case MTR implies Y Ys, i.e. wih increasing deducibles he probabiliy of going o he docor is no increasing. In oher words assuming MTR implies ha we know he sign of he reamen effec. This is a srong assumpion bu i appears reasonable in our case; he quesion is wheher he reamen effec is zero or negaive, which is compaible wih he MTR assumpion. 5 Under MTR he bounds are modified as follows (ignoring he presence of insrumen Z for he momen). The firs hing o noe is ha MTR implies ha EY [ ] EY [ ]. Then s (10) B l, = EY [ D PD ] ( ) MTR and (11) B u, = E[ Y D ] P( D ) + P[ D > ] MTR 4 5 If Z is discree he supremum is he maximum and he infemum is he minimum over he possible values of Z. There are of course applicaions where i is impossible o make he MTR assumpion. For example, he sign of he effec of several acive labour marke programmes is no obvious a priori. Anoher example is he effec of caherizaion of emergency paiens, which is analysed by Bhaacharya e al. (2005). 11

14 Comparing (10) and (11) wih (6) shows ha under MTR no only observaions wih D = are informaive for esimaing he bounds of EY [ ] bu all observaions are informaive. Because MTR implies ha EY [ ] EY [ ] for > s all observaions wih reamen equal o or larger han s can be used o compue he lower bound of EY [ ]. Combining MTR wih he IV Z is sraighforward. We have o compue (10) and (11) condiional on Z and ake he supremum and infemum, respecively, wih respec o Z. Ineresingly, here is a igh link o he bounds inroduced by Shaikh and Vylacil (2005) who assume ha boh reamen choice and oucome are binary and generaed by a nonparameric hreshold crossing model. These assumpions are sronger han hose imposed by Manski bu i is no necessary o know he sign of he reamen effec a priori. I can be shown ha he Shaikh and Vylacil bounds are idenical o he MTR + IV bounds if he assumed sign of he reamen effec corresponds o he sign idenified by he Shaikh and Vylacil assumpions. Manski and Pepper (2000) inroduce he assumpion of monoone reamen selecion (MTS). Formally, MTS can be expressed as EY [ D= ) EY [ D= s], s<. 6 In words MTS implies ha persons who chose higher deducibles have weakly lower mean response funcions. In our case his means ha people who choose he highes deducible have a lower probabiliy of seeing a docor han hose who choose a low deducible would have if hey had chosen he highes deducible. In oher words people who choose lower deducibles have observed and unobserved characerisics ha make hem more likely o see a docor even if hey had he highes deducible. If we are willing o make his assumpion he bounds for EY [ ] can be wrien as (again ignoring he insrumen Z for he momen) (12) B l, = EY [ D= PD ] [ ] MTS and 6 Or EY [ D= ) EY [ D= s], s<, depending wheher we assume ha he reamen effec is negaive or posiive. 12

15 (13) B u, = EY [ D= PD ] [ ] + PD [ < ] 7 MTS These bounds follow sraighforwardly from he MTS assumpion. The lower bound for EY [ ] is EY [ D= ] imes he probabiliy PD [ ] because by assumpion for each D< i mus be rue ha EY [ ] is a mos as large as EY [ D= ]. Hence compared o he wors case bounds he lower bound is increased by EY [ D= PD ] [ < ]. The upper bound can be expained by similar argumens. I is easy o show ha he binary reamen case MTS implies ha he reamen effec canno be larger in absolue erms han he oal absolue difference in he oucome variable. Hence MTS implies ha reamen selecion is raional. I is possible o combine he MTS assumpion wih he mean independence assumpion for he insrumen Z and wih he MTR assumpion. Combining MTR and MTS yields he following bounds for EY [ ] (he derivaion is sraighforward, see Manski and Pepper, 2000) (14) B l, = EY [ D= upd ] [ = u] + EY [ D= PD ] [ ] MTR+ MTS u > and (15) B u, = EY [ D= upd ] [ = u] + EY [ D= ] PD [ ] MTR+ MTS u < The firs par in (14) and (15) comes from he MTR assumpion and he second par from he MTS assumpion. Again incorporaing he insrumen Z is sraighforward. In his case he lower bound is he maximum of (14) condiional on Z over all values of Z and he upper bound is he minimum of (15) condiional on Z over all values of Z. An ineresing feaure of he bounds in (14) and (15) is ha hey do no longer depend on he bounds l u Y and Y. There is again a igh link o he bounds considered by Bhaacharya e al. (2005). They combine he Shaikh and Vylacil bounds (which are closely relaed o he MTR+IV assumpion by Manski) wih an assumpion of posiive quadran dependence. Posiive quadran dependence corresponds o MTS in he sense ha people wih unobserved characerisics ha make hem 7 See Manski and Pepper (2000) for he derivaion. 13

16 more likely o choose he reamen also have unobserved characerisics ha make hem more likely o have a posiive oucome, i.e. ha hey have a weakly higher mean response funcion. 8 In oher words, his assumpion implies ha here is selecion on unobservables ha are correlaed wih he unobservables in he oucome equaion. Summarizing, we make hree addiional assumpions (and combinaions hereof) in order o ighen he no-assumpion bounds on he reamen effec of deducibles. Of hese assumpions he mean independence assumpion for he insrumen Z is weak and he MTR and he MTS assumpions appear o be reasonable in he presen conex. 6. Resuls This secion presens he main resuls of he described bounding analysis. A full se of resuls is presened in he Appendix. No surprisingly i urns ou ha mos of he bounding sraegies yield bounds ha are oo wide o be informaive. This is especially rue for he wors case bounds, he IV bounds bu also for he MTR and he MTS bounds. Table 2 displays he esimaed bounds under he MTR+IV and under he MTR+MTS+IV assumpions. If one is willing o accep he MTR+IV assumpions he resuls indicae a negaive reamen effec comparing he highes deducible wih he lowes deducible (ATE 0,2 ). However, he bounds are sill relaively wide (beween -.68 and -.07). The bounds for he oher wo ramen effecs (ATE 0,1 and ATE 1,2 ) include zero. Table 2: Esimaed Bounds of ATE under MTR +IV and MTR +MTS +IV, Z=Premium MTR + IV MTR + MTS + IV ATE 0,1 ATE 1,2 ATE 0,2 ATE 0,1 ATE 1,2 ATE 0,2 B l B u B l B u B l B u B l B u B l B u B l B u Source: Swiss Healh Survey 2002, own calculaions Adding he MTS assumpion ighens he bounds considerably. Now boh ATE 1,2 and ATE 0,2 are bounded away from zero. Under hese assumpions ATE 0,2 is bounded beween -.11 and Recall ha he Shaikh and Vylacil bounds are only applicable o binary reamens and oucomes. 14

17 Given ha he oal difference beween he oucomes of reamen 0 and reamen 2 is -.24 ( ; see Table 1) we conclude from his resul ha he reamen effec (he moral hazard effec) is abou one hird of he oal difference. So far we have ignored he fac ha he bounds are esimaed. The upper par of Table 3 repeas he esimaed bounds under he MTR+MTS+IV assumpion and displays boosrapped confidence inervals for hese esimaes. The firs hing o noe is ha he upper bound for ATE 1,2 is no significanly differen from zero. However, in he case of ATE 0,2 he esimaed confidence bands do no include zero. Table 3: Esimaed Bounds of ATE and Confidence Inervals under MTR +MTS +IV, Z=Premium and Esimaed Treamen Effecs based on Propensiy Score Maching MTR + MTS + IV ATE 0,1 ATE 1,2 ATE 0,2 B l B u B l B u B l B u [ ] 1 [ ] [ ] [ ] [ ] [ ] Condiional Independence Propensiy Score Maching ATE 0,1 ATE 1,2 ATE 0, Source: Swiss Healh Survey 2002, own calculaions 1 The figures in brackes are 95% confidence bands for he esimaed bounds based on 1000 boosrap replicaions Propensiy scores are compued according o he ordered probi resuls displayed in Table A.1. Maching is done as neares neighbor maching;, sandard errors are compued according o he bias-adjused mehod proposed by Abadie und Imbens (2004). Ialic prin indicaes significance on he 10% level, bold prin indicaes significance on he 5% level. The lower par of Table 3 presens esimaes of he reamen effec based on he popular propensiy score maching echnique. Propensiy score maching is based on he condiional independence assumpion, i.e. condiional on all observable facors X influencing boh reamen choice and oucomes reamen and poenial oucomes are independen. Hence condiional independence is ofen called selecion on observables. Insead of condiioning on X Rosenbaum and Rubin (1983) have shown ha i is sufficien o condiion on he propensiy score, i.e. he probabiliy of choosing reamen given X. Formally, he propensiy score in he presen conex is PD ( = X) obained from he ordered probi esimaes (see Appendix Table A.1). The 15

18 maching esimaes displayed in Table 3 are compued using neares neighbour maching, i.e. o each person in reamen group we mach ha observaion from reamen group s which is closes in erms of he propensiy score. The maching esimae of ATE 1,2 is 0.09 and is saisically significanly differen from zero. 9 The corresponding esimae of ATE 0,2 is 0.13 and also saisically significanly differen from zero. Ineresingly, in boh cases hese esimaes are very close o he bounds esimaed under IV+MTR+MTS and lie wihin he confidence bands of hese bounds. This finding suggess ha he condiional independence assumpion underlying he maching esimaes appears o be valid in he presen conex. The main reason for his is ha we are able o conrol for pas realisaions of he oucome variable which should ake accoun of unobserved characerisics influencing he probabiliy of seeing a docor. 7. Conclusions There is an ongoing debae in healh economics wheher cos sharing in healh insurance changes he behaviour of paiens. The well documened negaive correlaion beween he degree of cos sharing and healh care coss can be aribued o changes in behaviour (reducion of moral hazard) or selecion (more healhy people selec higher cos sharing). Previous empirical evidence for Swizerland, which was obained based on srong idenificaion assumpions, is mixed. In his paper we esimae he effec of deducibles wih as few saisical assumpions as possible. We employ he nonparameric bounding echniques inroduced by Manski (1990) and furher developed by Manski (1997), Manski and Pepper (2000) and Shaikh and Vylacil (2005), among ohers. Treamen is ordered in our applicaion. We consider hree possible reamen saes: low deducible, medium deducible and high deducible. The oucome variable is he probabiliy of going o he docor. Our empirical analysis shows ha we need some assumpions o ighen he bounds; he noassumpion bounds are oo wide o be useful. We consider hree furher assumpions: a mean independence assumpion for an insrumen, he assumpion ha reamen response is monoone (i.e. we assume he sign of he reamen effec o be known), and he assumpion ha reamen selecion is monoone (i.e. he mean response funcion differs across reamen choices). Under 16

19 he firs wo assumpions we esimae bounds for he reamen effec of he high deducible compared o he low deducible ha are below zero. Hence given hese wo assumpions we conclude ha here is a negaive reamen effec (i.e. here is a change in behaviour). This finding is in conras o previous empirical analyses based on he same daa. Adding he hird assumpion allows o ighen he bounds furher o an inerval of 0.04 (he esimaed bounds are 0.11 and 0.07). The research presened in his paper can be exended in several direcions. So far, we did no conrol for covariaes. I is possible ha he esimaed bounds differ for differen subgroups. Mehodologically, we plan o apply o bounding echniques proposed by Shaikh and Vylacil (2005) and Bhaacharya e al. (2005). To do so, we need o concenrae on binary reamens (as opposed o hree reamens in he presen applicaion). Given ha here appears o be mainly an effec of he high deducible compared o he low deducible he reducion o a binary reamen appears o be meaningful. Finally, we can aemp o expand he Shaikh and Vylacil analysis o ordered reamens. 9 Sandard errors are compued according o he bias-adjused mehod proposed by Abadie und Imbens (2004) 17

20 References Abadie, A. and G. Imbens (2004), Large Sample Properies of Maching Esimaors for Average Treamen Effecs, Economerica, forhcoming. Bhaacharya, J., A. Shaikh, and E. Vylacil (2005), Treamen Effec Bounds: An applicaion o Swan-Ganz Caherizaion, working paper, Deparmen of Economics, Universiy of Sanford. Bundesam für Sozialversicherung BSV (Hrsg., 2002): Saisik über die Krankenversicherung 2001, Bern. Chiappori, P.-A., F. Durand, and P.-Y. Geoffard (1998), Moral hazard and he demand for physician services : Firs lessons from a french naural experimen, European Economic Review, 42, Gardiol, L., P. Geoffard and C, Grandchamp (2003): Separaing Selecion and Incenive Effecs: An Economeric sudy of Swiss insurance claims daa, Working Paper , DELTA, Paris. Ginher, D.K. (2000), Alernaive Esimaes of he Effec of Schooling on earnings, Review of Economics and Saisics, 82, Gonzalez, L. (2004), "Nonparameric Bounds on he Reurns o Language Skills", Journal of Applied Economerics, forhcoming. Heckman, J. and E. Vylacil (2001), Insrumenal variables, selecion models, and igh bounds on he average reamen effec, in: Lechner, M. and F. Pfeiffer (eds), Economeric Evaluaion of Acive Labor Marke Policies in Europe, Physica Verlag, Heidelberg and New York. Manning, W.G., J.P. Newhouse, N. Duan, E.B. Keeler, A. Leibowiz, and M.S. Marquis (1987), Healh Insurance and he Demand for Medical Care: Evidence from a Randomized Experimen, American Economic Review, 77, Manski, C.F. (1990), Nonparameric Bounds on reamen effecs, American Economic Review, Papers and Proceedings, 80: Manski, C.F. (1994), The selecion problem, in: Manski, C.F. and D. McFadden (eds), Advances in Economerics: Sixh World Congress, Cambidge Universiy Press, Cambridge Manski, C.F: (1997), Monoone Treamen Response, Economerica, 65, Manski, C.F. and J. Pepper (2000), Monoone insrumenal variables: wih an applicaion o he reurns o schooling, Economerica 68, Pepper, J. (2000), The Inergeneraional Transmission of welfare receip: A Nonparameric Bounds Analysis, Review of Economics and Saisics, 82, Rosenbaum, P.R. and Rubin, D.B. (1983): The Cenral Role of he Propensiy Score in Observaional Sudies for Causal Effecs, Biomerika 70: 1, Rosenbaum, P.R. and Rubin, D.B. (1985): Consrucing a Conrol Group Using Mulivariae Mached Sampling Mehods ha Incorporae he Propensiy Score, The American Saisician 39: Schellhorn, M. (2001): The Effec of Variable Healh Insurance Deducibles on he Demand for Physician Visis, Healh Economics 10: Schellhorn, M. (2004), Wählbare Selbsbehale in der Krankenversicherung in der Schweiz: Nachfrageseuerung oder Selekion?, Diskussionsschrifen des Volkswirschaflichen Insius der Universiä Bern 04/02. Shaikh, A. and E. Vylacil (2005): Threshold Crossing Models and Bounds on Treamen Effecs: A nonparameric analysis, working paper, Deparmen of Economics, Universiy of Sanford. Werblow, A. and S. Felder (2003): Der Einfluss von freiwilligen Selbsbehalen in der Gesezlichen Krankenversicherung. Evidenz aus der Schweiz, Schmollers Jahrbuch 123: Winkelmann, R. (2004), "Healh Care Reform and he Number of Docor Visis - An Economeric Analysis", Journal of Applied Economerics, 19, Zweifel, P. und W. G. Manning (2000), Moral Hazard and Consumer Incenives in Healh Care, in: A.J. Culyer and J.P Newhouse (eds.), Handbook of Healh Economics 1A:

21 APPENDIX Table A.1: Ordered Probi Esimaes of Deducible Choice Variable coefficien -value male x age male x age male x age male x age female x age female age female x age female x age female x age secundary educaion eriary educaion unemployed log household income Swiss Single Married Widow nonsmoker heavy smoker underweigh overweigh region lemanique region espace mielland region norh-wes region eas region cenral region souh (icino) subjecive healh excelllen subjecive healh good subjecive healh average Premium wih lowes deducible Hospial visi las year number of docor visis las year chronic disease pregnan subjecive healh worse han in previous year used up deducible in previous year Disance o neares physician cuoff cuoff Number of observaions 2860 Log Likelihood Source: Swiss Healh Survey 2002, own calculaions. Bold prin indicaes significance on he 5% level. 19

22 Table A.2: Esimaed bounds for ATE under differen assumpions ATE 0,1 ATE 1,2 ATE 0,2 B l B u B l B u B l B u Wors case IV MTR MTS MTR + MTS MTR + IV MTS + IV MTR+MTS+IV Source: Swiss Healh Survey 2002, own calculaions 20