PUBLIC VS. PRIVATE HEALTH CARE SERVICES DEMAND IN ITALY. A COUNT DATA ANALYSIS ON SHAW DATA

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1 XIV CONFERENZA IL FUTURO DEI SISTEMI DI WELFARE NAZIONALI TRA INTEGRAZIONE EUROPEA E DECENTRAMENTO REGIONALE coordnamento, competzone, mobltà Pava, Unverstà, 4-5 ottobre 2002 PUBLIC VS. PRIVATE HEALTH CARE SERVICES DEMAND IN ITALY. A COUNT DATA ANALYSIS ON SHAW DATA DANIELE FABBRI and CHIARA MONFARDINI pubblcazone nternet realzzata con contrbuto della socetà talana d economa pubblca dpartmento d economa pubblca e terrtorale unverstà d Pava

2 PUBLIC VS. PRIVATE HEALTH CARE SERVICES DEMAND IN ITALY A COUNT DATA ANALYSIS ON SHAW DATA Danele Fabbr Chara Monfardn Dept. of Economcs - Unversty of Bologna Prelmnary Abstract: Understandng the underlyng process of the demand for health servces s a key to a better assessment of the forces that ncrease health care expendture. The Grossman model and the agency perspectve on patent-physcan relatonshp provde dfferent, despte complementary vews on ths process. In the Grossman tradton, as far as the demand for health care s essentally seen as the result of patents ntertemporal utlty maxmsaton, utlsaton s the product of ndvdual preferences. In the agency approach, physcans play an actve role n assessng the amount of servces that patents should consume. Therefore n the analyss of health servces consumpton the role played by dfferent types of provder can not be gnored. The mportance of such an ssue has been largely neglected n the lterature. In ths paper we make use of the new Survey on Health Agng and Wealth (SHAW) data to analyse health care servces utlsaton explctly acknowledgng the exstence of two dfferent classes of provders: publc and prvate. We consder vsts by a specalst physcan as the measure of ndvdual health servces utlsaton. In the tme span of the survey (year 2000), ndvduals can consume ths servce gong publc, prvate or both. In order to nvestgate on the determnants of these health servce utlsaton measures we estmate some alternatve count data regresson models, of whch we dscuss the relatve advantages and dsadvantages and the entaled dfferent nterpretaton of the results. JEL: C34, C35, C51, D12, I11 Ths verson: July 2002

3 1 INTRODUCTION Understandng the underlyng process of the demand for health servces s a key to a better assessment of the forces that ncrease health care expendture. The Grossman model and the agency perspectve on patent-physcan relatonshp provde dfferent, despte complementary vews on ths process. In the Grossman tradton, as far as the demand for health care s essentally seen as the result of patents ntertemporal utlty maxmsaton, utlsaton s prmarly patent determned, though condtoned by the health-care delvery system. In the agency approach, physcans play an actve role n assessng the amount of servces that patents should consume, up to the pont of dstortng demand accordng to ther own preferences. These two perspectves lead to two dfferent streams of econometrc modelng tradtons: one-step models n the Grossman tradton [see Duan et al. (1983) and Cameron et al. (1988)] and two-step models n the agency tradton [see Mannng et al. (1981) and Pohlmeer and Ulrch (1995)]. We revew ths econometrc lterature later n the paper. A common feature n these emprcal analyses s the assumpton of separablty of demand functons for dfferent servces. Bascally the demand for, say, general practtoners vsts s assumed to be ndependent from the demand for specalsts physcans. The only excepton s Gurmu and Elder (2000). We focus here on the problem of product dfferentaton. Exstng econometrc models perform aggregate demand analyss,.e. model the overall counts of physcan vsts or specalsts vsts consumed by ndvduals as explaned by covarates lke ncome, out-of-pocket payments, consurance rates, health condtons. In case patents, wthn an health-care delvery system, could receve the same servce by two dfferent classes of provders, say publc vs. prvate, major problems arse n performng aggregate demand estmaton (have to accommodate for jont demand modelng). In the Grossman tradton, gven the promnence attrbuted to patents' preferences, as far as the two classes of provders dffer systematcally n terms of unobservable characterstcs and prcng polces, estmatng an aggregate demand model may ntroduce major dstortons n emprcal nference. In partcular, publc provders tpcally mpose lower out-of-pocket payments but hgher watng tmes so that nference from aggregate models on behavoural coeffcents, lke prce and ncome elastctes, may be possbly based. In the agency perspectve, gven that the two classes of provders respond to dfferent ncentves structures, modelng utlzaton neglectng the systematc dfference among provders may produce nconsstent and unnterpretable results. In ths paper we make use of the new talan Survey on Health Agng and Wealth (SHAW), conducted n the year 2001, data to analyse health care servces utlsaton explctly acknowledgng the exstence of two dfferent classes of provders: publc and prvate. We consder vsts by a specalst physcan as the measure of ndvdual health servces utlsaton. In the year before the survey (year 2000), ndvduals can consume ths servce gong publc, prvate or both. Ths health servce utlsaton measure s modelled by some alternatve count data regresson models, of whch we dscuss the relatve advantages and dsadvantages and the entaled dfferent nterpretaton of the results. The paper s organzed as follows. In the next secton we qualtatvely revew the exstng econometrc lterature on health-care servces utlzaton. In secton 3 we present at length our emprcal strategy by dscussng the negatve bnomal model, the bvarate 1041

4 negatve bnomal and the hurdle model we apply to our data. Secton 4 descrbes the data and specfcaton adopted. The major emprcal results are reported n secton 5. Secton 6 concludes the paper wth suggestons for future research. 2 MODELS FOR HEALTH SERVICE UTILIZATION The Grossman model and the physcan-patent agency model provde complementary explanatons for the demand for health care. We look at them n sequence. 2.1 THE GROSSMAN MODEL The Grossman model emphaszes the role played by patents' choce lookng at health and wealth as two nterrelated assets the values of whch are optmally controlled over tme by the ndvdual. In the case of health, the margnal utlty of holdng a margnal unt of stock has a consumpton and an nvestment component, whch together must always be equal to ts margnal user cost. Ths conssts of the nterets rate, health captal deprecaton and a possble change n the value of the health captal over tme. In ths context the demand for health care servces s a derved demand, n that servces are not consumed per se but serve to mantan or mprove upon a certan health status. The typcal form of the ndvdual demand functon for health care servces that emerges from the Grossman model s gven by: M ( t) = f [ H ( t), w( t), p ( t), age( t), E( t), X ( t)] m The demand for health care servces (for smplcty we call them medcal servces) at tme t, M(t), s endogenously codetermned 1 wth the latent varable "health status", H(t), and t s affected by the wage rate, w(t), a prce vector for medcal servces, p m (t), ndvdual age, age(t), the level of educaton, E(t), and a vector of envronmental effects, X(t). An hgher wage lowers the margnal ncentve to hold health as an asset for consumpton use, thus depressng the demand for medcal care. By way of contrast t ncreases the opportunty cost of sck tme, hence renforcng the ncentve to hold health as an asset. Assessng the mpact of wage on medcal servce demand s therefore an emprcal matter. The mpact of prces s negatve lke that of better educaton. Ths last one should lower the demand for nvestment n health because t contrbutes to lower health stock deprecaton. Demand for medcal care should ncrease wth ageng, because t s not optmal to let health stock declne n step wth deprecaton. 2.2 THE AGENCY APPROACH In the agency approach, physcans play an actve role n assessng the amount of servces that patents should consume as far as they typcally act a double role: performng checks on the status of patent's health stock and, condtonal on checks, supplyng treatments amed at restorng health stock to a desred level. Sgnfcant nformaton asymmetry may provde physcans the opportunty to nfluence demand through ther role as health evaluators. Ths nformatonal advantage s exploted provded that physcan's objectve functon dffers from patent's. In ths respect t s common to assume that physcans do not only follow Hppocratc oath (for example maxmzng ndvdual 1 The Grossman model s determnstc, so that desdered health stock always equal actual health stock, gven constrants. Therefore the demand for health servces, whch adjust exstng health stock net of deprecaton, s postvely lnked, one-to-one, wth endogenous health stock. 1042

5 health), but derve utlty also from ncome and lesure. Therefore, when ncome or lesure are talored to specfc procedures and/or servces, physcans wll dstort demand to perform more remuneratve, or less tme consumng, procedures/servces, f the margnal beneft of a specfc procedure outweghs the assocated margnal costs. In ths framework a large body of emprcal research s devoted to test the so called suppler nducend demand (SID) hypothess. The SID hypothess states that [McGure and Pauly (1991)] n the face of negatve ncome shocks, physcans may explot ther agency relatonshp wth patents by provdng excessve care. Income shocks examned n the lterature arse from three dfferent sources. A frst source s varaton n the physcan/populaton densty across areas: ncreased densty lowers the ncome of exstng stock of physcans, and t wll lead to ncreased utlsaton of medcal procedures n an nducement-type model. Income shocks may also emerge as the consequence of an exogenous change n demand due to epdemologcal shfts, evoluton of needs, varaton n tastes. However the most common source s varaton n fees pad to physcans, generally by government payers. The nducement model has tradtonally been tested by assessng how these three alternatve changes n the envronment facng physcans affect the utlsaton of medcal procedures 2. Despte each of these testng strateges face mportant problems they are qute convergent n suggestng that physcans, to some extent, do actually manage demand accordng to economc ncentves. 2.3 THE BASIC FRAMEWORK FOR MODELS OF VISITS' COUNTS The class of econometrc models of health servce demand we consder here s that concerned wth dscrete counts of medcal vsts. In ths case excess zeroes s the most relevant modelng ssue 3. From a purely statstcal vewpont bascally the problem conssts n buldng enough flexblty nto the econometrc model to account for the excess probablty mass concentrated n the zero counts. Tacklng the problem has major econometrc and economc mplcatons. For the sake of expostonal clarty we wll focus here on the economc ssues, ntroducng econometrc ssues but leavng detals on them to secton 4. In general terms the problem of bult-n-flexblty can be addressed n ether a sngle process perspectve (determnng both null and postve counts), or n a double process perspectve (one generatng the zeroes vs. the postves and one determnng the postves provded that a postve has been already generated). In the context of our problem ths amounts to say that n a sngle process approach all the vsts counts, zeroes ncluded, are drven by the same process. On the other hand, when a double process s envsaged contact process (to access to medcal treatment or not?) s dstngushed from utlzaton (gven that the frst answer s YES, how much to consume?). From an economc vewpont the double process perspectve has a natural appeal n the health economcs lterature as far as t dstngushes the two-part character of the decsonmakng process n health care demand [Stoddart and Barer (1981)]. Whle at the frst stage t s the patent who decdes whether or not she needs medcal attenton and 2 Representatve studes that use physcan densty changes to proxy for ncome shocks are Fuchs (1978) and Cromwell and Mtchell (1986). Gruber and Owngs (1996) use exogenous demand changes, whle Rce (1984) and Yp (1998) examne fee changes. 3 Smlar methodologcal problems arse whle consderng contnuous demand measures lke expendture [see Newhouse and The Insurance Experment Study Group (1993)]. 1043

6 therefore to access a physcan (contact analyss), n the second stage the health care provders toghether wth the patent determne the ntensty of the treatment (frequency analyss). Ths modelng approach has, gven certan condtons, a sound structural nterpretaton [see Santos Slva and Wndmejer (2001)] whch motvated ts braod adopton n the emprcal studes. Moreover t provdes a unfyng emprcal framework for the two abovementoned theores of health care demand. A Grossman-lke nterpretaton mght be called for explanng the contact decson, whle an agency perspectve could be nvoked for the nterpretaton of the frequency decson. Ths theoretcal partton underpns the choce and nterpretaton of typcal regressors' coeffcents ntroduced n each of the two-part components. Take for nstance the paper by Pohlmeer and Ulrch (1995). They estmate two dstnct two-part models for general practtoners vsts and for specalsts vsts on a sample of employed germans. They control for sex, ncome, age, educaton, chronc condtons, physcan densty n place of resdence, plus a set of other covarates. It s nterestng here to notce the results on physcan densty. The two-part model estmates show that physcan densty does not affect the contact choce whle t has a postve mpact on the frequency decson. The authors note that "whle physcan densty proxes an avalablty effect for the patent at the frst stage, t captures both demand and suppler response at the second stage. we are nclned to nterpret ths fndng as some evdence of suppler-nduced demand". Smlarly also other common covarates to the two parts are gven dfferent nterpretaton n the contanct and frequency analyss. A common feature of models for vst counts s the lack of control for medcal servces' prces. Pohlmeer and Ulrch (1995) s not an excepton. Ths s due to unavalablty of detaled data on sngle vsts outlays. As far as surveys are desgned to gather total number of vsts per tme perod no data are avalable on each vst payment 4. Therefore, monetary opportunty costs are typcally captured by prvate nsurance status varables [lke n Pohlmeer and Ulrch (1995) and Deb and Trved (1997)] or, more precsely, by ndvdual consurance rate [lke n Deb and Trved (2002)]. 5 The avalablty of prvate nsurance s found to postvely affect contact choce but not frequency choce [Pohlmeer and Ulrch (1995)]. Smlar effects are found for copayment rates: hgher copayment rates result n a lower probablty of contact whle frequency s unaffected [Deb and Trved (2002)]. These results are coherent wth a Grossman nterpretaton but less so wth an agency perspectve. Comng to the results concernng other typcal regressors n models for vsts' counts we see that some predctons of the Grossman model are frequently contradcted by emprcal evdence 6. In partcular good health status s found to be negatvely related to the number of vsts. Ths results s coherently consstent across all the papers we revewed despte dfferences n econometrc specfcaton. Educaton, typcally measured as years of schoolng, s usually found to ncrease vsts counts [see Deb and Trved (1997, 2002)]. Pohlmeer and Ulrch (1995) show that hgher educaton reduces contact decson for GPs vsts whle ncreases t for specalsts, n both cases unaffectng 4 Pohlmeer and Ulrch (1995) argue that the mpact of prces may be neglected gven that for many western health care systems the drect prce of medcal servces s close to zero. 5 Introducng nsurance status varables rases endogenety problems. See Cameron et al. (1988), Wndemejer and Santos Slva (1997), Vera Hernandez (1999). 6 Wagstaff concludes that "the majorty of the model's structural parameters are n fact of the 'wrong sgn'" [Wagstaff (1986), p. 216]. 1044

7 frequency. Santos Slva and Wndmejer fnd (2001) that educaton postvely affects contacts and negatvely affects frequency for specalsts vsts. Evdence concernng the mpact of ncome and age tends to be more coherent wth the theory. For the sake of completeness t has to be notced that, on a purely statstcal ground, there s no clear evdence that econometrc models based on the two process approach should be preferred to those relyng on a sngle process approach. Actually t has been shown [Deb and Trved (1997, 2002)] that suffcently flexble specfcaton, based on latent class analyss, let sngle process models better ft the emprcal dstrbuton of vsts' counts. We wll return on ths ssue later on. 2.4 THE AIMS OF OUR ANALYSIS In the followng we develop a count data analyss of specalst vsts n Italy. A remarkable feature of the market for medcal professonal consultancy n Italy s the presence of two broad dstngushable class of provders: publc, hghly regulated, specalsts, and prvate, less regulated, ones. We want to account for ths pecularty n our analyss, an ssue whch has been largely neglected n the lterature. Substtuton/complementarty relatonshps between these two classes of provders both arses from the demand and the supply sde suggestng that they cannot be separately examned. The fact prvate consultancy s typcally of hgher accuracy, mples lower watng tmes at the cost of hgher out-of-pocket payment comparng to publc ones rases the ssue of demand sde jont determnaton of both counts qute obvously. On the supply sde t s pretty relevant to realze that the role of physcan ncentves affect utlzaton. Indrect evdence of ths s provded by Table 1. In countres where general practtoners (GPs) are payed fee-for-servce, per-capta consultatons are slghtly more than n countres where they are payed accordng to captaton, but are almost double than n countres where GPs are salared. Ths provdes a strong, addtonal ratonale for our analyss of health servce utlzaton n whch we wll emphasze the role played by dfferent types of provder. 3 DATA AND INSTITUTIONAL SETTING Our data source s the new Survey on Health Agng and Wealth (SHAW) collected n The survey focusses on ndvduals aged 50 or more. The dataset ncludes a wde range of mcrolevel nformaton on socoeconomc characterstcs of ndvduals and households, ncludng specfc varables on workng and lvng condtons as well as varables on health condton and health care utlzaton. We restrct our attenton on householder, ether male or female. We preferred not to use observatons on householders' partners snce demand nterdependence through famly relatonshps could emerge [see Deb (2001)]. Gven the structure of the survey our choce affects the composton of our sample n that we have a larger ncdence of male householders comparng to the unverse of people aged 50 or more. The total sample conssts of 1050 ndvduals. We model, as a dependent varable, the number of vsts to a specalst physcan. These nclude optcans, dentsts and any other physcan specalsed n a certan feld. In performng our analyss of vst counts separately for publc and prvate specalsts we had to drop 35 observatons wth mssng values n counts for publc specalsts vsts and 40 n counts for publc specalsts vsts. Jont non mssng values are avalable for

8 observatons. Table 2 shows the tabulatons for the separate counts n our dependent varables. Zero counts are approxmately 60% of both dstrbutons; alternatvely, partecpaton rates are smlarly around 40%. 408 and 415 ndvduals are observed wth at least one vst to a publc and a prvate specalst respectvely. Prvate consultatons are more frequent on our sample due to larger ncdence of hgher counts vs. 3 on postve counts -. Contact decson process leads to smlar sample means partecpaton rates across provders' types, whle the second stage process dfferentates condtonal frequences of vsts across types. Ths provdes a frst evdence that the process underlyng the contact decson s dfferent from the second stage process. A frst ndcaton of overdsperson n the data s obtaned when the sample varance of the dependent count varable s found to be greater than ts sample mean. After ncluson of regressors, the Posson model sample condtonal varance wll decrease wth respect to the sample varance, whle the sample average of the condtonal mean wll be equal to the sample mean f a constant s ncluded among the regressors. Cameron and Trved pont out that f the sample varance s more than twce the sample mean ths s true n our data for both publc and prvate vsts - the data are lkely to exhbt overdsperson even after ncluson of regressors, as n cross-secton data regressons usually explan less than half of the varaton of the dependent varable. Table 3 contans a cross-tabulaton of the two knds of vsts whch reflects the vew that the two phenomena are jontly determned. It can be notced that the two count varables dsplay an excess of frequency of the par (0,0) about 36% of the total number of the observed pars of counts- n ther jont dstrbuton. We performed the Pearson Chsquare test on the correspondng contngency table, and found strong evdence of dependence between the two count varables. Explanatory varables are conventonal predsposng varables and varables capturng the access to medcal servces. Table 5 contans a descrpton of the varables used n ths pece of emprcal work. We tred to keep our specfcaton as parsmonous as possble, whle mmckng smlar specfcaton n the lterature. In ths respect our specfcaton s very close to Deb and Trved (1997) and qute smlar to Pohlmeer and Ulrch (1995) thus allowng us to make useful comparsons. It should be notced that publc specalsts are payed accordng to admnstered prces, whle prvate ones are free to set prces accordng to compettve pressures comng from close substtutes. Ths feature would suggest that controllng for out-of-pocket payments would be qute relevant n our case study. SHAW collects nformatons on total amount pad out-of-pocket for the cumulatve count of vsts, both specalst and generc, n each type of provder. However no-response rate was qute large (23% for publc and 17% for prvate vsts). Moreover averagng outlays across multple vsts could severely dstort results. We preferred, at ths stage, not to use payments nformaton n the modelng stage. 4 ECONOMETRIC MODELS FOR COUNT DATA 4.1 UNIVARIATE MODELS We model the demand for physcan servces by measurng t as counts of utlzaton,.e. number of vsts, resultng from an underlyng dscrete probablty functon. The smplest model for count data s based on the Posson dstrbuton, whch s characterzed by a sngle parameter µ. Havng avalable a sample of N ndependent observatons 1046

9 ( y, x ), where y denote the count varable of nterest and Posson regresson model s defned by the condtonal densty: x a set of covarates, the f P ( y µ e x; β) = µ y = 0,1,2,... (1) y! where: = exp( x ' β ), µ > 0. µ y The Posson dstrbuton mples the property of equdsperson: E ( y x ) = V ( y x ) = µ whch appears to be very restrctve n most emprcal applcatons, where the condtonal varance exceeds the condtonal mean. The standard parametrc model accountng for overdsperson s based on the Negatve Bnomal (NB) dstrbuton. Ths can be derved as a compound Posson process where the parameter of the Posson dstrbuton ncludes a gamma dstrbuted random varable reflectng ndvdual heterogenety: y Posson( µ ν ) wth ν ~ Gamma( α, λ) 7, wth α = λ, and the negatve bnomal ~ dstrbuton s obtaned by ntegratng over ν : f NB ( y x ; α, β) e = 0 ( µν ) ( µν ) y! Γ( y + α) α = y Γ( α ) Γ( + 1) µ + α y g( ν ) dν α y µ µ + α (2) where = exp( x ' β ) as above, and the condtonal mean and varance are gven by: µ E ( y x ) = µ 2 ( y x ) = µ + V φµ where φ = α 1 > 0 s an overdsperson parameter, makng the varance greater than the mean, as observed n many data sets. The parameters ( α, β ) can be estmated by the maxmzng numercally the log-lkelhood functon correspondng to the densty above (estmaton s automatcally mplemented n some statstcal packages, lke STATA). Ths s the most common mplementaton of the Negatve Bnomal Model, NB2 n the termnology of Cameron and Trved (1998). The addtonal parameter characterzng the NB dstrbuton makes t more flexble than the Posson, to whch t reduces when φ = 0. In most applcatons, NB regresson models are lkely to provde more effcent estmators than those based on Posson dstrbuton, as falure of the assumpton of equdsperson has smlar consequences to falure of the homoskedastcty assumpton n the lnear regresson model (Cameron and Trved, 1998). 7 The densty functon for the postve contnuous varable ν s gven by: α 1 α ν λ t a 1 g( ν ) = exp( λν ), where λ > 0, α > 0 and Γ( α ) = Γ( α) e t dt = ( a 1)!, a >

10 An alternatve way of dealng wth the excess zeros dsplayed by most count varables s represented by the hurdle model. Ths modfcaton of the basc model was frstly ntroduced by Mullahy (1986), and thereafter receved a great deal of attenton n the emprcal analyss of the usage of medcal servces. The hurdle model can be nterpreted as a two part model, n whch a bnary model for the decson of use, determnng the probablty of crossng a zero threshold, s combned wth a truncated count data model on postve counts, explanng the extent of use condtonally to some use. To llustrate the hurdle model, defne a dummy varable descrbng the non use of a doctor n a gven perod:.e. d = 1 f y = 0. The probablty functon s then gven by: f H [ ] (1 d (1 f (0 x ; ϑ )) f ( y x, y > 0; ) ( y x ; ϑ (3) where: d 1, ϑ2 ) = f1(0 x; ϑ1 ) 1 1 trunc ϑ2 ) f 1( 0 x; ϑ1 ) = pr( y = 0 x; ϑ1 ) f trunc ( y x, y > f 0; ϑ2 ) = 1 2 ( y x; ϑ2 ) f (0 x ; ϑ ) 2 2 The model specfes a bnary probablty determnng whether the count has a zero realzaton. If the realzaton s postve, the hurdle s crossed and the condtonal dstrbuton s descrbed by a truncated count model. The two processes can be drven by the same explanatory varables, but the nterpretaton of parameters wll be dfferent dependng on the consdered stage. The log-lkelhood functons correspondng to (3) factors n two components, whch can be separately maxmzed on the whole sample and on the postve observatons respectvely: ln L( ϑ 1, ϑ2 ) = d ln f1 ( ϑ1 ) + (1 d )ln(1 f1 ( ϑ1 )) + ln f 2 ( ϑ2 ) ln(1 f2 (0)) Estmaton of the parameters requres some choce for the two densty functons. In our applcaton we use a probt model for the bnary outcome, and a truncated negatve bnomal densty for the ntensty of use part of the model. 4.2 THE MULTIVARIATE APPROACH The applcaton of multvarate non-lnear non-gaussan models as those arsng when the am of the analyss s the jont explanaton of a gven number of count varables s stll relatvely rare. Ths s true despte the knd of event counts typcally examned n the health economcs lterature s often represented by dfferent measures of health care utlzaton lke number of doctor consultaton, ether general practtoner or specalst, nondoctor health professonal vsts, prescrpton drug use etc. These measures are lkely to be jontly dependent and ther nterrelaton can be descrbed n an analogous way to the seemngly unrelated regresson model. The Posson bvarate model s the most popular model n ths context. As llustrated by Cameron and Trved (1998), ths model can be obtaned by the so-called trvarate reducton technque (Kocherlakota and Kocherlakota, 1993), consstng n the convoluton of ndependent random counts wth a common component n the sum. The man features of ths model are the followng. The margnal dstrbutons are both Posson, and the margnal model, f correctly specfed, gve d =

11 consstent but neffcent estmates wth respect to jont estmaton. The correlaton coeffcent mpled by the jont dstrbuton s ndvdual specfc and fully descrbes the dependence structure of the varables, but t s not very flexble, as t s bound to be nonnegatve. Fnally, the model mposes the restrcton of equdsperson on each count varables. Smlarly to the unvarate framework, the bvarate Negatve Model represents an useful tool to handle overdspersed count data. Marshall and Olkn (1990) generate a bvarate negatve bnomal mxture begnnng wth two margnal Posson dstrbutons whose parameters contan a common gamma-dstrbuted heterogenety term. Ths approach s also followed by Gurmu and Elder (2000), who generalze the bvarate negatve bnomal dstrbuton by postulatng a frst-degree polynomal expanson of the unobserved heterogenety term, based agan on a gamma densty. Ths amounts to the ntroducton of a further parameter n the jont dstrbuton, and makes the bvarate negatve bnomal a testable model nested n the generalzed one. We present hereafter the bvarate negatve bnomal model whose estmaton results are descrbed n the next secton. Usng the same notaton as n the unvarate case, let the two jont count varables be Posson dstrbuted as follows: y Posson( µ ν ), y Posson( µ ν ), wth 1 ~ 1 2 ~ 2 µ exp( ' j = x jβ j ), j=1,2, and ν s a common unobserved heterogenety term wth gamma densty g( ν ). Smlarly to the unvarate case, the jont densty s derved by ntegratng over the heterogenety term: f BIVNB where ( y 1, y 2 x ; α, β, β 1 2 ) = 0 = 2 j= 1 2 j= 1 µ. = µ 1 + µ 2, y. = y1 + y2. e µ Γ( y ( µ ν ) j y j j y j ( µ jν ) g ( ν ) dν y j! j Γ( y. + α ) α + 1) Γ( α ) y.. ( α + y. ) (1 ) The margnal dstrbutons of ths model are stll negatve bnomal, and the correlaton between the two count varables (condtonal to the covarates) s ndvdual specfc, beng a functon of the µ, and constraned to be non-negatve: j µ 1µ Corr ( y 1, y 2 x ) = ( µ 1 + µ 1 α )( µ 2 + µ 2 α ) (5) α + µ α (4) 5 RESULTS 5.1 THE NEGATIVE BINOMIAL ESTIMATES We start our emprcal analyss by estmatng two unvarate NB models on the number of specalst publc and prvate consultatons respectvely. Ths approach gnores the jont nature of the two health care demand determnaton processes, and takes nto account the excess-zeros pattern by specfyng a more general statstcal dstrbuton than the Posson. The Maxmum Lkelhood estmaton results 8 reported n Table 7 reveal that 8 The estmaton has been obtaned usng STATA

12 the Posson dstrbuton s ndeed rejected by the data, as the nestng parameter φ s found to be sgnfcantly dfferent from zero. Ths confrms the stylzed facts on overdsperson of the data emerged by the descrptve analyss. The man fndngs concernng the role of the nserted explanatory varables are the followng. Famly ncome appears to be an mportant determnant of the number of prvate consultatons, wth hgher ncome famles tendng to ncrease ther utlzaton of prvate health care. Also, the level of schoolng has not a sgnfcant mpact on prvate servces demand. On the contrary, the demand of publc specalst vsts s not affected by the famly ncome varable, whle t postvely reacts to an ncrease n the years of schoolng. The educaton effect result agrees wth the conventonal reason that educaton makes ndvduals more nformed consumers of medcal care servces, and sgnals that more educated people are orented towards a more frequent use of the servces offered nsde the publc sector. The possesson of a prvate health nsurance ncreases the consultaton of prvate specalst. Ths s a common result n the appled lterature whch s coherent wth fours stores. The frst one relates to prce elastctes (beng double nsured allows to access prvate health care at lower out-of-pocket payments). Accordng to the second explanaton, ths could also be the effect of an adverse selecton process makng the frequent health servces users to look for supplementary coverage and cost rembursment. 9 A thrd key of nterpretaton s represented by moral hazard where ncentves by the patent and the physcans for over-treatement algne aganst the nsurer. The last possble explanaton has to do wth suppler nduced demand n a wde sense Pohlmeer and Ulrch fnd no evdence of such behavour as the prvate nsurance dummy s only sgnfcant n the frs stage.e. contact decson- of ther hurdle model. Turnng to the demographc varables, we fnd that ndvdual s age play no role n both equatons. The effect of ths varable s usually found to be negatve untl some age (whch vares from 33 to 52 n dfferent studes), and ncreasng thereafter. We observe coherent coeffcent sgns, but these parameters are not enough precsely estmated. Women appear to seek more medcal care than men, as usually evdenced n emprcal studes. In our context, ths s true both for prvate and publc specalst consultatons. The health status measures dsplay the usual emprcal lnk wth the degree of utlzaton of medcal care. Ths ncreases when chronc condtons or physcal lmtatons are present, the level of self-perceved health s poor and n presence of eyesght troubles (for prvate vsts), and decreases wth excellent self-assessed health (publc vsts). Indvduals who never smoked seek less both publc and prvate medcal consultatons. Customary consumers of super-alchoolc drnks use more publc specalst servces and less prvate doctor vsts. Regonal-specfc unobservable factors make the demand for publc doctor consultaton n central and southern Italy lower than n northern Italy. The effect of the sze of the communty of resdence, amed at proxyng the opportunty costs of vstng a physcan, turns out not to be sgnfcant. Fnally, the varables whch proxy the accessblty to the two knd of medcal servces show the expected sgn, wth the rato of physcans per bed n prvate provders exhbtng a negatve effect on the number of vsts 9 Followng ths nterpretaton, a problem of endogenety of the prvate nsurance varable can be envsaged. 1050

13 demanded from publc physcans and the amount of per-capta publc expendture ncreasng the number of publc specalst consultatons. 5.2 THE BIVARIATE NEGATIVE BINOMIAL ESTIMATES Table 8 dsplays the Maxmum Lkelhood Estmaton 10 results we get when the number of publc and prvate vsts s allowed to be generated by a jont process represented by the bvarate negatve dstrbuton. Ths modellng framework acknowledges both features emerged from the descrptve analyss: overdsperson and dependency of the two health utlzaton varables. Takng nto account ther jont determnaton wll provde more effcent estmaton of the parameters. Some relevant dfferences wth respect to the unvarate estmaton results are observed n the magntude and sgnfcance of the estmated coeffcents (notce, n partcular, that the prvate nsurance ndcator looses ts explanatory power n the prvate equaton), whle the drecton of the analysed effects keeps generally the same. The most nterestng result s represented by the condtonal correlaton value, whch s obtaned as the after-estmaton sample average of the correlaton coeffcent n (5). Ths average measure of correlaton s qute hgh (although t should be accompaned by a precson of estmaton measure). Gurmu and Elder (2000) fnd a value of 0.3 n ther applcaton to counts of doctor and non-doctor consultatons, that they clam to be strongly dependent also accordng to some ndependency tests proposed by Cameron and Trved (1998). Two comments on ths observed correlaton measure are due. Frst, the cross tabulaton n Table 3 shows that the two count varables exhbt a pattern that we can call jont overdsperson, meanng that they not only exhbt an excess of zero values n ther margnal dstrbutons, but also an excess of frequency of the par (0,0) about 36% of the total number of the observed pars of counts- n ther jont bvarate densty functon. If we adopt the two-part nterpretaton of the unvarate hurdle model and generalze t to a bvarate settng, ths group represents the non-users of medcal servces, decdng not to contact any knd of physcans. The composton of ths group s lkely to dstort the correlaton coeffcent. If, for example, ths group s manly generated by the populaton of the healthy people, ths wll nduce a hgher correlaton coeffcent for the two counts. A second pont concerns the possblty of a partcular nterpretaton of the estmated correlaton, n case the condtonal (to the observable regressors) correlaton can be nterpreted as the correlaton between the unobservable part of the non lnear regresson model. In our example ths s manly represented by out-of-pocket payments for the prvate doctor vsts. These wll enter both equaton of the model, wth negatve sgn n the prvate equaton. Fndng a postve correlaton after estmaton could then be nterpreted as evdence that prvate servces prces affect negatvely also the demand for publc ones, showng that the two goods as complements. Ths nterpretaton seems not approprate n our present study, n the lght of what appears a major lmtaton of the NB bvarate model: the correlaton s constraned to be non-negatve. Nevertheless, the above consderatons push our future analyss n the drecton of a bvarate hurdle model 11, n whch the frst part s amed at explanng the zero-parwse observatons (no-contact wth any medcal servces provders), whle the second s condtonal to some contact (ether wth publc or prvate provder). Generalzng the 10 We made use of the GAUSS routnes kndly made avalable by Gurmu and Elder (2000). 11 To our knowledge, the only applcaton of bvarate hurdle models s gven by Hellstrom on number of lesure trps and total number of overnght stays on Swedsh toursm data. 1051

14 bvarate truncated dstrbuton to a Posson-lognormal (or NB-lognormal), model as proposed by Wnkelmann (2001) n the unvarate case, would allow a flexble correlaton pattern between the two count varables. Ths would relax both the non-negatvty constrant of the condtonal correlaton coeffcent and one of the basc constranng feature of the conventonal hurdle model,.e. the ndependence between the hurdle step and the truncated dstrbuton. 5.3 THE HURDLE MODEL ESTIMATES In the present analyss we lmt our attenton to the unvarate hurdle approach, as the development of the bvarate model requres a deeper methodologcal nvestgaton. The sngle equaton modellng exercse neglects the jont mechansm determnng the demand of the consdered servces, but can nevertheless shed some lght on the opportunty of separately modellng the two subsequent stages correspondng to contact and frequency decsons. The Maxmum Lkelhood estmaton results of the two parts of the model (probt at the frst stage, truncated negatve bnomal at the second one) are contaned n Tables 9 and A frst look at both tables reveals that the frst stage model exhbts a better ft than the second stage one. As Pohlmeer and Ulrch pont out, household data are better suted to quantfy the determnants of the contact decson, whle the frequency of use also depends on supply sde factors on whch observable nformaton s lmted. Also, the number of observatons s consderably reduced n the second part of the model. Despte ths, there s a number of relevant comments concernng dfferences between the parameters across the two stages and, more nterestngly, wth the unvarate NB model, whch does not dstngush between the two parts. The varables ncluded as regressors exert on the modelled probablty of noncontactng a publc/prvate specalst a smlar effect to what was found n the sngle equaton NB model. To hgher famly ncome corresponds hgher probablty of contactng a prvate specalst. The ncome varable s now sgnfcant also n determnng a less probable contact wth a publc specalst. Consstently wth our prevous fndngs, more educated ndvdual tend to have hgher probablty of contactng a publc physcan. It has to be notced that ths set of varables turns out not to be relevant n the second stage model. Pohlmeer and Ulrch fnd the same result on both the counts of general practtoner and specalst vsts. Ths means that once the knd of provder s chosen, ncome and educaton do not affect the frequency behavour. The female dummy, health status varables, the regonal dummes and the number of physcans per bed n prvate hosptals have the same sgn effect n both parts of the model, and ths s stll consstent wth the nterpretaton we put forward for the unvarate NB model. But the hurdle model allows to dsentangle ther coeffcents on the contact decson and the number of vsts respectvely. These parameters are mostly sgnfcant at both stages and have dfferent magntudes. Publc per-capta expendture only affects postvely the decson to contact of a publc specalst, but not the number of referrals. The second measure of accessblty, represented by the number of doctors per bed n publc hosptals s now sgnfcant n the second part of the model and negatvely related to the number of vsts provded by prvate specalsts..fnally, an nterestng remark has to do wth the role of the possesson of a prvate health nsurance. Ths has no mportance 12 In order to mplement estmaton wth the truncated negatve bnomal dstrbuton we resorted to the STATA ado fle provded by Hlbe (1999) on the Stata Techncal Bulletn. 1052

15 n the contact of ether knd of specalsts, but s postvely affectng the frequency of both prvate and publc specalst vsts. Ths last evdence s plausably due to an adverse selecton effect, wth the frequent users beng doubly nsured. 6 CONCLUSIONS In the present paper we develop a count data analyss of specalst vsts n Italy. A remarkable feature of the market for medcal professonal consultancy n Italy s the presence of two broad dstngushable class of provders: publc, hghly regulated, specalsts, and prvate, less regulated, ones. We want to account for ths pecularty n our analyss, an ssue whch has been largely neglected n the lterature. Exstng econometrc models perform aggregate demand analyss,.e. model the overall counts of physcan vsts or specalsts vsts consumed by ndvduals as explaned by covarates lke ncome, out-of-pocket payments, consurance rates, health condtons. In case patents, wthn an health-care delvery system, could receve the same servce by two dfferent classes of provders, say publc vs. prvate, major problems arse n performng aggregate demand estmaton. In ths paper we make use of the new talan Survey on Health Agng and Wealth (SHAW), conducted n the year 2001, data to analyse health care servces utlsaton explctly acknowledgng the exstence of two dfferent classes of provders: publc and prvate. We consder vsts by a specalst physcan as the measure of ndvdual health servces utlsaton. In the year before the survey (year 2000), ndvduals can consume ths servce gong publc, prvate or both. Ths health servce utlsaton measure s modelled by some alternatve count data regresson models. From the unvarate Negatve Bnomal model estmates we derved emprcal evdence coherent wth common fndngs n ths stream of lterature. Moreover we receved a strong confrmaton of the mportance of modellng the two counts as drven by dfferent, despte non necessarly, ndenpendent processes. Ths concluson s further supported by the results from the bvarate Negatve Bnomal estmate. The hurdle model ndcates the mportance of a further dmenson, arsng by separate consderaton of the contact and frequency decson processes. Therefore our frst exploratve analyss, despte not conclusve, ponts out the major features of a devsable model for our pecular case study. Accordngly our future research should move towards a bvarate hurdle model, n whch the frst part s amed at explanng the zero-parwse observatons, whle the second s condtonal to some contact. A requrement of ths model s a flexble condtonal correlaton, between the two count varables, allowng for possbly negatve values. An alternatve approach 13 s a bvarate count model wth Latent Classes. In a sngle equaton framwork Deb and Trved (2002) suggests that two-part models are domnated by Latent Class Models (LCM). The varaton n demand for health care s explaned 13 The major lmtaton n the lterature based on hurdle model s due to the possbly msconceved assumpton that zeroes reflect the choce of not contactng a physcan. Actually both zeroes and postves mght be the product of two related process: emergence of need and servce utlzaton. Indvduals may decde not to contact a physcan ether because they don't need t or because they prefer not to do t even f they need. Smlarly we may observe low levels of utlzaton ether because of a low level of need or because of a low preference for treatment. 1053

16 relatvely more by ndvdual ntrnsc characterstcs than by physcan or supply factors. Despte the Prncpal-Agent framework seems relevant n ths context, however, from a statstcal pont of vew, LCM models provde better performance than classcal TPM as far as "t s better to permts mxng wth respect to both zeros and postves" (dfferent processes descrbng for example healtyh/nfrequent users and lls/frequent users can generate both zeros and postves counts) 14. A careful comparson between bvarate hurdle model and a bvarate count model wth latent classes should be developed on both statstcal and economc nterpretaton grounds. 14 Ths s coherent wth analogous results n hosptal proflng lterature [see Slber, Rosenbaum and Ross (1995)] where t s shown that ndvdual predctors explan more than 80% of the varaton n ndvdual medcal outcome. 1054

17 7 REFERENCES Cameron, A.C., P.K. Trved, 1998, "Regresson Analyss of Count Data", Cambrdge Unversty Press, Cambrdge. Cameron, A.C., P.K. Trved, F. Mlne and J. Pggott, 1988, "A Mcroeconometrc Model of the Demand for Health Care and Health Insurance n Australa", Revew of Economc Studes; 55(1), pp Deb, P. and A.M. Holmes, 1998, "Substtuton of Physcans and Other Provders n Outpatent Mental Health Care", Health Economcs; 7(4), pp Deb, P. and P. Trved, 1997, "Demand for medcal care by the elderly: a fnte mxture approach", Journal of Appled Econometrcs, 12, pp Dustmann, C. and F. Wndmejer, 1999, "Wages and the Demand for Health-A Lfe Cycle Analyss", Insttute for Fscal Studes Workng Paper: W99/20. Grossman, M., 1982, "The demand for health after a decade", Journal of Health Economcs, 1(1), pp Gurmu, S. and J. Elder, 2000, "Generalzed Bvarate Count Data Regresson Models", Economcs Letters; 68(1), pp Gurmu, S., 1997, "Sem-Parametrc Estmaton of Hurdle Regresson Models wth an Applcaton to Medcal Utlzaton", Journal of Appled Econometrcs, 12, pp Hellstrom, J., 2001(?), "An Endogenously Stratfed Bvarate Count Data Model for Household Toursm Demand", mmeo Dept. of Economcs, Umea Unversty. Hlbe, J (1999), "Zero-truncated Posson and negatve bnomal regresson", Stata Techncal Bulletn 1/99, pp.37-40; Reprnts Vol 8, pp Karatzas, G., 1992, "On the Effect of Income and Relatve Prce on the Demand for Health Care-- The EEC Evdence: Comment", Appled Economcs; 24(11), pp Kocherlakota, S. and K. Kocherlakota, 1993, Bvarate Dscrete Dstrbutons, New York, Marcel Dekker. Lopez N.A., 1998, "Unobserved Heterogenety and Censorng n the Demand for Health Care", Health Economcs; 7(5), pp Mannng et al., 1981, "A Two-Part Model of the Demand for Medcal Care: Prelmnary Study from the Health Insurance Study", n Sheffler R.M. and L.F. Rosster, eds., Health, Economcs, and Health Economcs, Amsterdam, North-Holland, pp Marshall, A.W. and I. Olkn, 1990, "Multvarate Dstrbutons Generated from Mxtures of Convoluton and Product Famles" n H.W. Block, A.R. Sampson and T.H. Davds eds., Topcs n Statstcal Dependence, IMS Lecture Notes-Monograph Seres, volume 16, Mullahy, J., 1986, "Specfcaton and testng of some modfed count data models", Journal of Econometrcs, 33 (3), pp Mullahy, J., 1998, "Much Ado About Two: Reconsderng Retransformaton and the Two-Part Model n Health Econometrcs", Journal of Health Economcs, 17(3), pp Muurnen, J. M., 1982, "Demand for health - A generalsed Grossman model", Journal of Health Economcs, 1(1), pp Newhouse and The Insurance Experment Study Group, 1993, Free for All? Lessons from the RAND Health Insurance Expendture, Cambrdge, Harvard Unversty Press. 1055

18 Pohlmeer, W. and V. Ulrch, 1995, "An Econometrc Model of the Two-Part Decsonmakng Process n the Demand for Health Care", Journal of Human Resources; 30(2), pp Propper, C., 2000, "The Demand for Prvate Health Care n the UK", Journal of Health Economcs; 19(6), pp Santos Slva, J.M.C. and F. Wndmejer, 2001, "Two-Part Multple Spell Models for Health Care Demand", Journal of Econometrcs; 104(1), pp Schellhorn, M., 2001, "The Effect of Varable Health Insurance Deductbles on the Demand for Physcan Vsts", Health Economcs; 10(5), pp Schellhorn, M., et al.., 2000, "Health Servces Utlzaton of Elderly Swss: Evdence from Panel Data, Health Economcs"; 9(6), pp Slber, J.H., P.R. Rosenbaum and R.N. Ross, 1995, Comparng the Contrbutons of Groups of Predctors: Whch Outcomes Vary wth Hosptal rather than Patents Characterstcs?, Journal of the Amercan Statstcal Assocaton, 90(429), pp Stoddart, G.L. and M.L. Barer, 1981, "Analyses of the Demand and Utlzaton Through Epsodes of Medcal Care", n van der Gaag, J. and M. Perelman, eds., Health, Economcs and Health Economcs, Amsterdam, North-Holland. Vera Hernandez, A.M., 1999, "Duplcate Coverage and Demand for Health Care. The Case of Catalona", Health Economcs; 8(7), pp Wagstaff, A., 1986, "The Demand for Health - Some New Emprcal Evdence", Journal of Health Economcs, 5(3), pp Wndmejer, F. and J.M.C. Santos Slva, 1997, "Endogenety n Count Data Models: An Applcaton to Demand for Health Care", Journal of Appled Econometrcs; 12(3), pp Wnkelmann, R. (2001), "Health Care Reform and the Number of Doctor Vsts An Econometrc Analyss", CEPR Dscusson Paper Seres, No Zwefel, P. and F. Breyer, 1997, Health Economcs, Oxford, Oxford Unversty Press. 1056

19 Table 1: Per-capta general practtoners' consultatons across some European countres Belgum 7.9 France Subgroup mean Fee-for-servce Germany Italy 6.7 Netherlands 5.7 Captaton Unted Kngdom Salary Fnland 4.0 Iceland 4.9 Norway 3.8 Portugal 3.2 Sweden Source: Our elaboraton on OECD Health Data '99, OECD, Pars,

20 Table 2: Tabulatons of specalsts vsts n our sample PUBLIC PRIVATE Count Freq. Percent Cum. Freq. Percent Cum Total Postves Mean Varance St. dev. Mean Varance St. dev. Full Sample Postve counts Partecpaton rate