Summary Measures of the Distribution of Household Financial Contributions to Health

Transcription

1 Chapter 40 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health Ke Xu, Jan Klavus, Ana Mylena Agular-Rvera, Guy Carrn, Radh Zeramdn, Chrstopher J.L. Murray Introducton Consderable attenton has recently been focused on the conceptual and emprcal ssues of measurng the farness of household fnancal contrbutons to the health system ( 4). WHO has argued that farness requres that health system payments are organzed n such a way that the burden of payments s equalzed across households. Equal burden s defned as an equal fracton of each household s capacty to pay (CTP). The rato of a household s health payments to ts capacty to pay s called the household fnancal contrbuton (HFC). If all households contrbute the same share of ther CTP, the HFC of each household wll equal the rato of a country s total health expendture (HE) to ts total capacty to pay (2). The dstrbuton of HFC across households vares across countres. Fgure 40. shows the HFC dstrbutons for Span and Azerbajan. The x-axs depcts the HFC and the y-axs measures proporton of households at varous levels of HFC. The HFC dstrbuton of Azerbajan s clearly more dspersed than that of Span. In Span, only a very small proporton of households have hgh health payments relatve to capacty to pay, whereas n Azerbajan the proporton of the populaton wth a relatvely hgh HFC s consderably greater. Vsually, a long rght-hand tal ndcates more unequal dstrbutons and potentally catastrophc payments for households. For many purposes, however, vsual comparsons are nsuffcent. To allow comparsons of the relatve farness of fnancal contrbutons across countres or over tme, the nformaton provded by the HFC dstrbuton needs to be captured n a summary measure. The purpose of ths chapter s to explore varous summary measures and to develop a justfcaton for the choce of a summary measure for the HFC dstrbuton. Secton two dscusses varous desrable propertes that the measure should possess. The subsequent secton contans an overvew of the survey data used n the analyss. Some common measures of ncome nequalty are presented n the fourth secton and a new measure, called the farness n fnancal contrbuton ndex (FFC), s proposed. Secton fve undertakes a comparatve analyss of the propertes of dfferent Fgure 40. Dstrbuton of household fnancal contrbutons (HFC), Span and Azerbajan Fracton Fracton.4 Span Household fnancal contrbuton.4 Azerbajan Household fnancal contrbuton

2 544 Health Systems Performance Assessment measures and hghlghts some mportant advantages of the FFC measure. Crtera for a Summary Measure of HFC There s a vast lterature on ndces to summarze ncome dstrbutons (5 8) and ther applcaton to the measurement of nequalty n the context of health care (9 3). Ideally, a summary measure of any dstrbuton should reflect the normatve vews of the socety by dsplayng varous propertes that are consstent wth those normatve expectatons. Ths could be acheved, for example, by choosng a measure that s more senstve to relatve than to absolute dfferences between households, or by emphaszng varous parts of the dstrbuton more heavly than others. Before turnng to an overvew of dfferent ndces, a number of crtera that a summary measure of HFC should possess are explored. These nclude a concern for catastrophc expendture, the preference for ndvdual-mean rather than nterpersonal dfferences, the property of constant nvarance, and the requrement that the ndex can be dsplayed n nterpretable unts. Concern for Catastrophc Expendture A good summary measure should reflect the normatve vew of the general publc and polcy-makers about the mportance of dfferent parts of the HFC dstrbuton. In partcular, there s a strong preference n most socetes for protectng ndvdual households from potentally catastrophc expendtures and for sharng the burden of health fnancng across households. For example, the possble mpact of varous health system fnancng mechansms on the well-beng of poor people has nfluenced the desgn of health systems and health nsurance mechansms n many dfferent settngs, and protectng people from catastrophc payments s now wdely accepted as an mportant objectve of health polcy (4 2). These concerns were tested on the general publc n a WHO survey about preferences for fnancng arrangements n the health system. The 007 respondents comprsed health professonals and people wth a specal nterest n health from over 00 countres, people wth knowledge of the health system and how t s fnanced. Respondents were asked the queston n Box 40.. More than 70% of respondents favoured the opton of ensurng that two households pad an equal proporton of ther dsposable ncome (capacty to pay), rather than one household rskng catastrophc expendture. Two varatons were asked subsequently: n the frst the choce was between one household contrbutng 200% of ts capacty to pay (by borrowng) versus two contrbutng 00%; n the second the choce was between a sngle household contrbutng 50% versus two contrbutng 25%. In both varatons all other households contrbuted 5% of ther capacty to pay. Agan, a substantal majorty of respondents thought t was more far to avod the rsk of catastrophc payments by ensurng equal proportonal contrbutons of capacty to pay, the majorty ncreasng as the payments became more catastrophc. These fndngs are consstent wth a strong preference for protectng households from catastrophc expendtures (22). We beleve, therefore, that these concerns should be captured by the summary ndex of HFC. Indvdual-Mean Dfference Many commonly used summary measures of nequalty can be classfed nto two man groups: those measurng nterndvdual dfferences and those measurng ndvdual-mean dfferences. An nterndvdual measure s concerned wth dfferences between every par of ndvduals or households n the sample. Ths type of measure would be preferable n settngs where people care more about the dfference between ther own contrbuton relatve to contrbutons of all other ndvduals n the populaton than the dfference between ther own contrbuton relatve to the average contrbuton n the populaton. The Gn coeffcent, wdely used to summarze the dstrbuton of ncome, belongs to ths group of measures. The preference for an ndvdual-mean measure n the context of HFC assessment arses from the normatve consderatons underlyng the equal burden prncple. The concern wth ndvdual-mean dfferences s consstent wth measurng the extent to whch the Box 40. Farness n Fnancal Contrbuton Survey Queston. In Populaton A all households contrbute 5% of ther dsposable ncome towards the health system, except for one household that must contrbute 00% of ts dsposable ncome. Dsposable ncome s ncome left after food expendtures are deducted. In populaton B all households contrbute 5% of ther dsposable ncome towards the health system, except for two households that each must contrbute 50% of ther dsposable ncome. Whch one of the two scenaros do you thnk s more far? The scenaro n Populaton A The scenaro n Populaton B The two scenaros are equally far I don t know

3 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 545 dstrbuton of HFC devates from the norm of equal burden. Constant Invarance Property The general formula for an ndvdual-mean dfference (IMD) measure of nequalty n the dstrbuton of varable y (n ths case the HFC) s: IMD( α, β) = n = y nµ µ β α [] where y s the household fnancal contrbuton (HFC) of household, μ s the mean fnancal contrbuton (.e. mean HFC), and n s the number of households n the sample. The choce of the parameter α s related to the sgnfcance attached to dfferences n fnancal contrbutons observed at the tals of the dstrbuton compared to those observed closer to the mean. For the dstrbuton of HFC, the hgher α becomes, the more mportance s attached to the tals of the dstrbuton, namely catastrophc spendng. The β coeffcent determnes the extent to whch the nequalty measure s relatve to the mean, or absolute. A value of β = reflects an nterest n a relatve measure. The measure s strctly relatve when β = α =. It s nvarant to proportonate changes n all observatons. Ths property s called scalar nvarance, or mean-ndependence, under whch the nequalty ndex remans unchanged f each ndvdual s HFC s multpled by the same postve scalar. In contrast, when β = 0 concern les exclusvely wth absolute devatons from the mean and the measure s nvarant to the addton of a postve constant to each ndvdual s observed HFC. Ths property s known as constant nvarance. A value of β between zero and one reflects a mx of concern between relatve and absolute dfferences. Constant nvarance s consstent wth the equal burden prncple. Consder a hypothetcal HFC dstrbuton A = {0., 0.2, 0.4, 0.5} wth a mean HFC of 0.3. Addng a constant of 0. to each contrbuton share yelds a dstrbuton of A = {0.2, 0.3, 0.5, 0.6}. Now the mean contrbuton share has ncreased to 0.4, relatve dfferences have decreased, but accordng to the constant nvarance property wth β = 0, the farness of these two dstrbutons s equal. Ths s mpled by the equal burden prncple, where farness s assessed wth respect to devatons from the deal state of all households payng equal shares of ther capacty to pay, whch would be the mean HFC. It can also be shown that the equal burden prncple s nconsstent wth the scalar nvarance property. Multplyng the HFC n dstrbuton A by a scalar of, say,.5 gves rse to a dstrbuton A 2 = {0.5, 0.3, 0.6, 0.75}. The mean of ths dstrbuton s Whle the relatve dfferences wth respect to the mean have remaned unchanged n the two dstrbutons, the dfferences between each observaton and the mean have ncreased. There s greater absolute dvergence from the deal of equal burden (mean HFC) n A 2. It s also true that multplyng the dstrbuton A by a scalar ncreases the hgher contrbuton shares relatvely more than the addton of a constant to each observaton. In the above example the relatve ncrease n A due to addng a constant of 0. s smaller the hgher the contrbuton share. In contrast, n dstrbuton A 2 the HFC shares of all observatons ncrease by the same relatve amount. If the chosen nequalty measure attaches more weght to the hghest contrbuton shares, there s lkely to be an elevated potental for catastrophc payments, but the measure wll be totally nsenstve to these changes under scalar nvarance. The same apples, of course, to a measure that s constant nvarant, but the unobserved welfare mplcatons wll be smaller as the relatve effect becomes smaller at hgher contrbuton shares. In the context of ncome nequalty, scalar nvarance s usually consdered desrable (8). One reason for ths s ts robustness to lnear transformatons. For example, the welfare mplcatons of the measure reman the same whether a country s ncome dstrbuton s expressed n domestc or foregn currency unts (e.g. all observatons n domestc currency unts are multpled by a constant). Ths property s especally mportant for cross-country comparsons or comparsons over tme. In addton, even f ncome s measured n common currency unts, mean ncomes are lkely to dffer substantally between countres so reference to the mean level of ncome s mportant. In ths sense, the nvarance property (whether constant or scale) does not have a great mpact n the context of summarzng the HFC dstrbuton, whch s bounded by zero and unty. The varaton of mean HFC s relatvely small, the lowest value beng and the hghest value beng (see below for a descrpton of data). Interpretable Unts A somewhat related property concerns the scalng propertes of the measure. The strctest type of measure s determnable on a rato scale, where the rato

4 546 Health Systems Performance Assessment of two observatons remans the same regardless of the unts of measurement that are beng used. It s, therefore, possble to say that the second poorest household earns twce as much as the poorest household whether ncomes are measured n dollars or rupees. A looser type of measure s one that s expressed on an nterval scale, where ratos themselves have no meanng, but the ratos of dfferences do. For example, the dfference between the thrd and frst observaton n two dstrbutons mght be twce that of the dfference between the thrd and the second observatons. Measures wth rato or nterval scale propertes are called cardnal measures. In contrast, an ordnal measure s one that s concerned only wth the orderngs or rankngs of the observatons and the ratos of dfferences have no meanng. An ordnal measure s nvarant to any postve monotonc transformaton. For example, an ncome rankng of, 2, 3, 4 can be replaced by 00, 06, 20, 399 wthout any loss of consstency. In the context of an nequalty measure defned n the range 0 to, a measure wth nterval scale propertes mples that the dfference between 0.9 and 0.8 means the same thng as the dfference between 0.7 and 0.6. Ths property allows the measure to be nterpreted more easly, but to formally establsh the nterval-scale propertes of an ndex of the farness of the dstrbuton of the HFC would requre some type of preference measurement. For example, ths would enable t to be establshed f socety regarded a reducton of the ndex from 0.9 to 0.8 to be equally as valuable as a reducton from 0.5 to 0.4. Such an attempt to measure preferences has not been undertaken. In the absence of knowng the preferences underlyng such choces, an nequalty ndex that has a straghtforward nterpretaton and s expressble n natural unts s preferable to an ndex that nvolves some arbtrary transformaton of functonal form. Ths means that ndces such as the standard devaton or the coeffcent of varaton, both of whch are nterpretable n natural unts, would be more desrable measures than some of the entropy measures that have been proposed n the lterature, whch do not have readly nterpretable unts (7 8) (a more detaled descrpton of these measures wll be gven below). Crtera for a Summary Measure: Summary In summary, t would be desrable for an ndex of the farness of household fnancal contrbutons to gve more weght to households wth potentally catastrophc contrbutons; to be based on comparson of ndvdual-mean dfferences; to have the property of constant nvarance; and to be nterpretable n terms of some natural unt. Data Sources The emprcal analyss s based on household surveys conducted by varous statstcal agences n 59 countres, between 99 and The sample sze ranges from 03 households n Sweden to households n the Republc of Korea. They nclude Lvng Standards Measurement Studes (LSMS), Household Budget Surveys (HSB), Household Income and Expendture Surveys (HIES), and selected other surveys wth adequate nformaton on household ncome and expendture. There are several lmtatons of these data. Frstly, some of the surveys undertaken n the early 990s mght not reflect the mpact of more recent reforms n health system fnancng. Secondly, there s varaton n the recall perods used to ask questons related to health servce utlzaton and assocated expendture. Some surveys use a one month recall perod, some use three months, some use one year, and some use combnatons such as one month for outpatent servces and three months or a year for npatent servces. Thrdly, some survey data are of lower qualty than others. Efforts are contnually beng made to dentfy hgh qualty and most recent household surveys. An Overvew of Inequalty Measures General Class of Inequalty Measures As mentoned above, there are two general types of nequalty measures: one measurng nterndvdual dfferences and another measurng ndvdual-mean dfferences. The standard devaton, a commonly used statstcal dsperson measure, s of the IMD class where α = 2 and β = 0. The standard devaton for the HFC can be expressed as: σ = ( HFC µ ) n 2 [2] where HFC s the household fnancal contrbuton of household and µ s the mean HFC. Based on the concept of equal burden, an alternatve summary measure closely related to the standard devaton can be proposed. If t s agreed that health expendtures should be pooled and the burden should be shared

5 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 547 equally among households, t can be argued that the dstrbuton of HFC should not be compared to the mean HFC, but rather to a reference level that s equal to the rato of total health spendng to total capacty to pay. Let us assume that a health system rases a certan amount of health revenue (THE) THE = HFCCTP + HFC2CTP HFCnCTPn [3] where HE s the total health fnancal contrbuton of household and CTP s ts capacty to pay. Followng the defnton of farness statng that every household should contrbute the same share of ts capacty to pay, we have: HFC = HFC 2... = HFC n = κ [4] Makng use of equaton [4] n equaton [3] gves: so that HE = κ * CTP [5] HE κ = = HFC CTP o [6] HFC o s the health fnancng contrbuton all households would pay under the prncple of equal burden. The standard devaton of HFC, calculated usng the mean of the ndvdual observatons (labeled σ HF C ) and an augmented standard devaton usng the equal burden HFC (σ HFC o ) are shown n Table 40.. The fve countres wth the most dsperson of the HFC (standard devatons n excess of 0.50) are Ukrane, Argentna, Vetnam, Azerbajan, and Brazl. At the other extreme, the 0 countres wth the lowest levels of nequalty ( ) ncluded sx OECD countres as well as Morocco, Phlppnes, Romana, and Thaland. There are no substantal dfferences between the standard σ HF C and the augmented verson σ HFC o. The standard devaton gves some weght to the tal of the dstrbuton (.e. the parameter α = 2), so t s senstve to potentally catastrophc payments. It also satsfes the other desrable propertes; t s an ndvdual-mean dfference measure, t conforms to the constant nvarance property, and t s dsplayed n readly nterpretable unts because of the square root retransformaton. The FFC Index The FFC ndex was proposed recently by WHO to be the approprate measure to summarze the HFC dstrbuton (4). It s smlar n construct to the standard devaton. 2 However, nstead of settng α at 2, t s set at 3 to gve more weght to the rght-hand tal of the dstrbuton, households wth potentally catastrophc payments. In addton, the summed dspersons are subtracted from a reference level of. Consequently, the range of the ndex s from 0 to, the degree of farness ncreasng as the ndex approaches unty. The FFC ndex s defned as: FFC = n 3 = HFC µ 3 [7] n In order to transform the sum of the cubed dspersons from the mean back nto natural or orgnal unts, the cube root s taken. Table 40.2 reports the estmates of the FFC usng agan the two defntons of μ. Agan, there s very lttle dfference n the FFC between the two defntons of μ wth scores rangng from to Brazl, Vet Nam, Azerbajan, and Argentna are stll among the fve countres wth the least far dstrbutons of HFC, wth Jamaca now enterng the pcture. Ukrane mproves one rank. At the other end of the scale, Thaland and the Phlppnes drop out of the 0 countres wth the farest dstrbutons. The swtch n ranks becomes greater the farer the two measures are. Fgure 40.2 plots FFC usng the mean HFC (vertcal axs) aganst the FFC calculated usng the equal burden HFC (HFC o ). The rank order of countres s the same under the two approaches, although the absolute values can be slghtly hgher or slghtly lower evdenced by the fact that some ponts are just above the magnary 45-degree lne, and others just below. Because the FFC based on the equal burden HFC s consstent wth the defnton of farness of fnancal contrbutons used n ths chapter, t wll be used n all subsequent estmatons. Famly of Entropy Measures Thel s Inequalty Index Thel s ndex derves from the noton of entropy n nformaton theory. It s a measure that assesses the value of dfferent events wth respect to ther lkelhood of occurrence. Suppose there are n ndependent events and each occurs wth the probablty p, 0 p, and Σ p =. If the nformaton content of the more unlkely events s more valuable than that of events that are more lkely to occur, the functon h(p ), reflectng the nformaton content, must be decreasng n p.

6 548 Health Systems Performance Assessment Table 40. Standard devaton of HFC and augmented standard devaton based on equal burden HFC (HFC o ) Country σ HFCo σ HF C Country σ HFCo σ HF C Argentna Lthuana Azerbajan Maurtus Bangladesh Mexco Belgum Morocco Brazl Namba Bulgara Ncaragua Camboda Norway Canada Panama Colomba Paraguay Costa Rca Peru Croata Phlppnes Czech Republc Portugal Denmark Republc of Korea Djbout Romana Egypt Senegal Estona Slovaka Fnland Slovena France South Afrca Germany Span Ghana Sr Lanka Greece Sweden Guyana Swtzerland Hungary Thaland Iceland Unted Kngdom Indonesa Ukrane Israel USA Jamaca Vet Nam Kyrgyzstan Yemen Latva Zamba Lebanon Fgure 40.2 The FFC ndex based on equal burden HFC (HFC o ) and HFC mean (HF C) FFC (HFC) FFC (HFC o ) It s assumed that two events and j are statstcally ndependent and meet the condton ( ) = + h p p h( p ) h( p ) [8] j j One functon satsfyng the decreasng nformaton content property of p s: h( p) = ln( ) p [9] The expected nformaton content, or entropy, of a stuaton H(p) s the weghted sum of the ndvdual events h(.), the weghts beng the respectve probabltes: H( p) = ph( p) = p ln( ) p [0] The expresson s a measure of the degree to whch the probabltes of the varous events are equal. It s obvous from equaton [0] that the closer the p are

7 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 549 Table 40.2 The FFC ndex based on equal burden HFC (HFC o ) and HFC mean (HF C) FFC Country HFC o HF C Country HFCo HF C Argentna Lthuana Azerbajan Maurtus Bangladesh Mexco Belgum Morocco Brazl Namba Bulgara Ncaragua Camboda Norway Canada Panama Colomba Paraguay Costa Rca Peru Croata Phlppnes Czech Republc Portugal Denmark Republc of Korea Djbout Romana Egypt Senegal Estona Slovaka Fnland Slovena France South Afrca Germany Span Ghana Sr Lanka Greece Sweden Guyana Swtzerland Hungary Thaland Iceland Unted Kngdom Indonesa Ukrane Israel USA Jamaca Vet Nam Kyrgyzstan Yemen Latva Zamba Lebanon FFC to /n, the smaller the dfferences n probabltes, and the greater the entropy. A maxmum s obtaned when the probablty of all events s equal; n that case equaton [0] becomes ln(n), as p = /n. Thel s ndex (T) measures the dfference between the maxmum and the expected nformaton content of a stuaton, namely: Equaton [] can be wrtten as: T = ln( n) H( p) [] T = p ln( n ) ln( p ) [2] When Thel s entropy ndex s appled to ncome nequalty measurement, p can be nterpreted as: p = y y [3] where y s the ncome of household and Σ y s total ncome. Equaton [2] can be rewrtten as: y y T = n ln( ) [4] µ µ where µ s the mean ncome. Thel s ndex can have any non-negatve value. It equals zero when there s no nequalty and ncreases wth more nequalty. The Mean Logarthmc Devaton Another ndex belongng to the entropy famly of nequalty measures s the mean logarthmc devaton (MLD). It s defned as: MLD = n ln µ [5] y

8 550 Health Systems Performance Assessment where y s the ncome of household and µ s the mean ncome across all households. MLD equals zero n the case of perfect equalty and hgher values ndcate more nequalty. Lke the Thel ndex, the MLD has no upper lmt. Entropy Measures Appled to the HFC As the defnton of farness used here requres more weght to be placed on those households that are burdened wth potentally catastrophc health payments, we defne y = HFC. In dong so, t can be verfed that n the case of Thel s entropy measure, the nformaton content h(.) wll be larger, the larger the value of HFC or the fnancal burden of households. Equaton [4] can be rewrtten as: HFC T = n HFC o HFC ln( ) [6] HFC The same adjustment can be appled to the MLD HFC o MLD = n ln [7] HFC Inequalty results for the 59 countres usng Thel s measure and the MLD are presented n Table There s very lttle varaton n the level of the ndces across countres, although the results are not wholly consstent wth the orderng gven earler by the standard devaton or the FFC. For example, some of the countres classfed then as relatvely unfar are now ncluded among countres wth a relatvely hgh degree of farness (e.g. Egypt, Paraguay), and vce versa (e.g. Sweden, Thaland). Both the Thel and MLD measures belong to the ndvdual-mean famly of nequalty measures n the sense that they are comparng ndvdual contrbutons to the mean (as a rato). They also attach specfc concern to potentally catastrophc health payments, as larger weght s attached to households wth very hgh contrbuton shares. However, they do not satsfy the constant nvarance property. In addton, the unts of the ndces do not have a straghtforward nterpretaton because of ther rather complex structure and the logarthmc transformaton. Atknson s Index Atknson s ndex s derved by makng addtonal assumptons about the functonal form of the underlyng socal welfare functon, welfare weghts, and the relatonshp between transfers and changes n nequalty. o Suppose the utlty functon for each household s the same and takes the form: ( e) U( y a b y ) = + e for e not equal to, and [8] U( y) = ln( y) [9] when e =. The parameter e n the formula, normally bounded by the lmts of 0 and, determnes the level of nequalty averson. The larger the value of e, the greater socety s concern about nequalty. It s assumed that e s non-negatve whch mples a concave utlty functon. It follows that the hgher the value of e, the more concave the utlty functon when e equals zero, t becomes a straght lne. Under a socal welfare functon that s an addtve functon of ndvdual utltes, socal welfare wll be maxmzed when everyone s ncome s equal to the mean ncome. Atknson s measure ndcates the degree of nequalty by takng devatons from ths maxmum. The measure can be derved as follows. Frst, t s necessary to determne the equalzed level of ncome, y e, that, f gven to each ndvdual n the populaton, would lead to the same level of socal welfare (W*) whch s obtaned from the observed ncome dstrbuton * W = a + b ( e) y U( ye) U( ye) e = n = [20] whch after nserton to equaton [8] gves: y e e e = y n [2] The second step s to compare the equally dstrbuted ncome (y e ) and the mean ncome (µ). Atknson s ndex (A) can now be wrtten as: e e ye y A = = n [22] µ µ Atknson s ndex les between zero (complete equalty) and one (maxmum nequalty). A dstngushng feature of ths ndex s ts ablty to capture movements n dfferent segments of the dstrbuton by changes n the value of the parameter e. In order for Atknson s ndex to reflect the characterstc that people s utlty s nversely related to the burden of health payments, set y = HFC n the formula, namely:

9 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 55 Table 40.3 Thel s ndex and the mean logarthmc devaton (MLD) Country Thel MLD Country Thel MLD Argentna Lthuana Azerbajan Maurtus Bangladesh Mexco Belgum Morocco Brazl Namba Bulgara Ncaragua Camboda Norway Canada Panama Colomba Paraguay Costa Rca Peru Croata Phlppnes Czech Republc Portugal Denmark Republc of Korea Djbout Romana Egypt Senegal Estona Slovaka Fnland Slovena France South Afrca Germany Span Ghana Sr Lanka Greece Sweden Guyana Swtzerland Hungary Thaland Iceland Unted Kngdom Indonesa Ukrane Israel USA Jamaca Vet Nam Kyrgyzstan Yemen Latva Zamba Lebanon HFC A = n HFCo e e [23] Not surprsngly, the greater the value of e, the more nequalty n health system contrbutons s observed n all countres (Table 40.4). However, the relatve dfferences between countres vary as e ncreases. For example, when e ncreases from 0.30 to 0.35, Atknson s ndex ncreases by n Azerbajan and only by n Bangladesh. Smlarly, the ncrease s n Ukrane compared to an ncrease of n the Unted Kngdom. In countres where the ncrease s greater there s more unfarness n the HFC at the tal of the dstrbuton. Atknson s ndex satsfes the crtera of ndvdualmean dfference and a concern about potentally catastrophc health payments. An ncreased concern would be expressed by hgher values of the coeffcent e. Atknson s ndex s also expressed n nterpretable unts. However, t does not satsfy the constant nvarance property. Comparson of Dfferent Measures Ths comparson focuses on the rank order dfferences between the varous possble summary measures of the dstrbuton of HFC. Countres are ordered from those wth the hghest equalty () to the lowest equalty ones (59) n Table The rankng of FFC dffers substantally from the rankng gven by some of the other nequalty measures n several cases. For example, the Czech Republc s ranked 9th usng the FFC measure, but 24 th usng the standard devaton, and between 9 th and 2 st usng other ndces. Belgum s ranked at 0 by the FFC, 23 by the standard devaton, and between 7 and 9 by the other ndces. The rankngs gven by the standard devaton, Atknson, Thel,

10 552 Health Systems Performance Assessment Table 40.4 Inequalty n HFC mpled by Atknson s ndex Country e = 0.2 e = 0.25 e = 0.30 e = 0.35 Country e = 0.2 e = 0.25 e = 0.30 e = 0.35 Argentna Lthuana Azerbajan Maurtus Bangladesh Mexco Belgum Morocco Brazl Namba Bulgara Ncaragua Camboda Norway Canada Panama Colomba Paraguay Costa Rca Peru Croata Phlppnes Czech Republc Portugal Denmark Republc of Korea Djbout Romana Egypt Senegal Estona Slovaka Fnland Slovena France South Afrca Germany Span Ghana Sr Lanka Greece Sweden Guyana Swtzerland Hungary Thaland Iceland Unted Kngdom Indonesa Ukrane Israel USA Jamaca Vet Nam Kyrgyzstan Yemen Latva Zamba Lebanon and MLD measures are closer to each other than the ranks gven by the FFC. It also seems that the dfferences n rankngs are more pronounced the hgher the degree of farness. These dfferences stem from the dverse theoretcal approaches and the degree of nequalty averson ncluded n each measure. To llustrate, Fgure 40.3 presents the dstrbutons of HFC n Vet Nam and Zamba. The x-axs measures the HFC, and the y- axs shows the densty functon or the proporton of households observed to have any gven HFC. Vsual observaton ndcates that Vet Nam has a thcker tal to the dstrbuton than Zamba. Correspondngly Zamba has a hgher concentraton of low HFC shares at the left-hand sde of the dstrbuton. Because the FFC ndex s hghly senstve to the rghthand tal of the dstrbuton, Vet Nam ranks lower than Zamba accordng to t. Except for the standard devaton, ths s not the case for the other nequalty measures, whch rank the two countres equally (Table 40.5). Despte the varaton n ranks, the rank correlaton coeffcents of the dfferent ndces are hgh (Table 40.6). The correlaton between each ndex and the FFC s systematcally lower than that between the other ndces because of the greater weght gven to the tal of the dstrbuton by the cubc functon used n the FFC. In addton to the rank correlaton coeffcents, regular Pearson s correlaton coeffcents were calculated. They confrmed the very hgh correlaton between the dfferent measures. Concludng Remarks A good summary measure for the dstrbuton of HFC should meet the followng crtera. It should:

11 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 553 Table 40.5 Rank order usng dfferent nequalty measures Country FFC σ HFC0 0.2 Atknson s ndex Thel MLD Country FFC σ HFC0 0.2 Atknson s ndex Thel MLD Slovaka Croata Unted Kngdom Sr Lanka Denmark Ghana Sweden Bulgara Canada Costa Rca Morocco Maurtus Germany USA Hungary Indonesa Czech Republc Greece Belgum Mexco Romana Djbout Fnland Yemen Span Republc of Korea Israel Portugal South Afrca Lebanon Senegal Egypt Icelend Ncaragua Slovena Latva France Zamba Thaland Paraguay Norway Peru Guyana Colomba Phlppnes Camboda Namba Panama Lthuana Ukrane Swtzerland Jamaca Kyrgyzstan Argentna Estona Vet Nam Bangladesh Azerbajan Croata Brazl gve greater weght to the tal of the dstrbuton, partcularly households wth potentally catastrophc health payments; be based on comparsons of ndvdual-mean dfferences rather than nterndvdual dfferences; have the constant-nvarance property; and be nterpretable n natural unts on the nterval scale. Table 40.7 summarzes the propertes of the varous nequalty measures consdered. The plus and mnus sgns ndcate whether the crtera are fulflled or not. If both a + and are shown, t means that the crteron s not fully satsfed. The FFC and standard devaton met all four crtera although the standard devaton does not attach as much weght to households wth potentally catastrophc health payments as the FFC. Thel s measure and the MLD do not satsfy the constant nvarance property, and are less concerned wth potentally catastrophc health contrbutons than the FFC. In add- Fgure 40.3 HFC dstrbutons, Vet Nam and Zamba Zamba Vet Nam 0 HFC

12 554 Health Systems Performance Assessment Table 40.6 The rank correlaton coeffcent of dfferent nequalty measures FFC FFC Standard devaton 0.90 Standard devaton Atknson (.20) Atknson (.20) Atknson (.25) Atknson (.25) Atknson (.30) Atknson (.30) Atknson (.35) Thel Atknson (.35) Thel MLD MLD Table 40.7 Comparson of dfferent summary measures Measure Concern about catastrophc expendture Indvdualmean dfference ton, they are not expressed n easly nterpretable unts. Atknson s ndex has consderable flexblty n weghng the dfferent parts of the dstrbuton dfferently: a hgher e makes ths ndex more senstve to the changes at the tal of the HFC dstrbuton. It s also expressed n nterpretable unts, but t volates the constant nvarance property. No sngle ndcator can explan all features of the unfarness of household fnancal contrbutons to the health system. The FFC measure proposed n ths chapter satsfes the crtera establshed for a summary ndex of the dstrbuton of household fnancal contrbutons. As such, t provdes a tool for polcy-makers to assess how household contrbutons to health devate from the concept of equal burden, when the burden of payments s assessed aganst households capacty to pay. It also ncorporates concern for the burden resultng from potentally catastrophc health payments. As such t s a useful tool for polcy analyss. Acknowledgements Constant nvarance Interpretable unts FFC σhfc o +/ Thel +/ + MLD +/ + Atknson The authors would lke to thank Davd B. Evans and Wllam D. Savedoff for ther comments on the manuscrpt. We are also grateful to Nathale Etomba and Anna Moore for data and reference searches. Notes Data for Span are from the Encuesta Contnua de Hogares 996 wth a sample sze of The Azerbajan data are the Survey of Lvng Condtons 995 wth 2 05 households. 2 The FFC ndex defned here s dfferent from the one used n The World Health Report 2000 where t was defned as: FFC WHR = 4 n = 3 HFC HFC 0. 25n Compared to ths verson of the FFC ndex, the new FFC has the addtonal property of beng defned n readly nterpretable unts because of the cubc root retransformaton. References () Murray CJL et al. Assessng the dstrbuton of household fnancal contrbutons to the health system: concepts and emprcal applcaton. In: Murray CJL, Evans DB, eds. Health systems performance assessment: debates, methods and emprcsm. Geneva, World Health Organzaton, (2) Xu K et al. Household health system contrbutons and capacty to pay: defntonal, emprcal, and techncal challenges. In: Murray CJL, Evans DB, eds. Health systems performance assessment: debates, methods and emprcsm. Geneva, World Health Organzaton, (3) Xu K et al. The mpact of vertcal and horzontal nequalty on the farness n fnancal contrbuton ndex. In: Murray CJL, Evans DB, eds. Health systems performance

13 Summary Measures of the Dstrbuton of Household Fnancal Contrbutons to Health 555 assessment: debates, methods and emprcsm. Geneva, World Health Organzaton, (4) Xu K et al. Understandng household catastrophc health expendtures: a mult-country analyss. In: Murray CJL, Evans DB, eds. Health systems performance assessment: debates, methods and emprcsm. Geneva, World Health Organzaton, (5) Aronson JR, Johnson P, Lambert P. Redstrbutve effect and unequal ncome tax treatment n the U.K. The Economc Journal, 994, 04: (6) Kakwan N. Measurement of tax progressvty: an nternatonal comparson. The Economc Journal, 977, 87:7 80. (7) Kolm SC. The ratonal foundatons of ncome nequalty measurement. In: Slber J, ed. Handbook on ncome nequalty measurement. London, Kluwer Academc Publshers, 999:9 00. (8) Jenkns S. The measurement of ncome nequalty. In: Osberg L, ed. Economc nequalty and poverty nternatonal perspectves. London, Sharpe ME, 99: (9) Wagstaff A et al. Equty n the fnance of health care: some further nternatonal comparsons. Journal of Health Economcs, 999, 8: (0) Wagstaff A, van Doorslaer E. Payng for health care: quantfyng farness, catastrophe, and mpovershment, wth applcatons to Vet Nam, World Bank Workng Paper No Washngton, DC, World Bank, 200. () Kakwan N, Wagstaff A, van Doorslaer E. Socoeconomc nequaltes n health: measurement, computaton, and statstcal nference. Journal of Econometrcs, 997, 77(): (2) van Doorslaer E et al. Equty n the delvery of health care: some nternatonal comparsons. Journal of Health Economcs, 992, : (3) Wagstaff A, van Doorslaer E. Equty n the fnance and delvery of health care: concepts and defntons. In: van Doorslaer E, Wagstaff A, Rutten F, eds. Equty n the fnance and delvery of health care: an nternatonal perspectve. Oxford, Oxford Medcal Publcatons, 993: 2 9. (4) World Health Organzaton. The World Health Report Health Systems: Improvng Performance. Geneva, World Health Organzaton, (5) World Health Organzaton. The World Health Report 200. Mental Health: New Understandng, New Hope. Geneva, World Health Organzaton, 200. (6) World Health Organzaton. The World Health Report Reducng Rsks, Promotng Healthy Lfe. Geneva, World Health Organzaton, (7) Kawabata K, Xu K, Carrn G. Preventng mpovershment through protecton aganst catastrophc health expendture. Bulletn of the World Health Organzaton, 2002, 80:62. (8) Flmer D, Hammer J, Prchett L. Weak lnks n the chan II: a prescrpton for health polcy n poor countres. World Bank Research Observer, 2002, 7: (9) Musgrove P. Publc spendng on health care: how are dfferent crtera related? Health Polcy, 2000, 53: (20) Evans RG et al. Controllng health expendtures the Canadan realty. The New England Journal of Medcne, 989, 320: (2) Russel S, Glson L. User fee polces to promote health servce access for poor: a wolf n sheep s clothng? Internatonal Journal of Health Servces, 997, 27: (22) Murray CJL et al. Defnng and measurng farness n fnancal contrbuton to the health system. EIP Dscusson Paper No. 24. Geneva, World Health Organzaton, URL: dscusson_papers/dscusson_papers.cfm#