This paper analyzes inequality in Iran's health system from a financing perspective. Through grouped data of household budget published by Iran Statistic Center (ISC) and Beta Lorenz curve introduced in Kakwani (1980), it has been tried to extract Beta Lorenz curve and Kakwani progressivity index in each individual rural and urban district, and also to obtain other inequality measure in (1997-2007) Period.Then to study health inequality for the given period, we divided it into two sub-periods: (1997-2001) and (2002-2007) and finally to compare health inequality, using Bootstrap technique, we made a pseudo statistical population. Results show a degree of descending progressively in urban areas while in rural areas it has witnessed a slight improvement. However as the results show in both rural and urban areas, because of the negativity of Kakwani's index of the household expenditure which is financed by themselves is not progressive at all. Also the ratio of share richest quintile to poorest quintile for health care in urban and rural areas are 8.79 and 8.01 respectively

Moradi, Alireza

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveEquity of Health Care Financing: AnApplication to IranAlireza MoradiIslamic Azad University, Branch of Kermanshah6. May 2011Online at http://mpra.ub.uni-muenchen.de/33489/MPRA Paper No. 33489, posted 18. September 2011 18:49 UTCEquity of Health Care FinancingAn Application to IranAlireza Moradi ∗Department of EconomicsIslamic Azad University of Kermanshah BranchE-mail: alirezamoradi econ@iauksh.ac.ir6 May 2011AbstractThis paper analyzes inequality in Iran’s health system from a financing perspec-tive. Through grouped data of household budget published by Iran StatisticCenter (ISC) and Beta Lorenz curve introduced in Kakwani (1980), it has beentried to extract Beta Lorenz curve and Kakwani progressivity index in eachindividual rural and urban district, and also to obtain other inequality mea-sure in (1997-2007) Period.Then to study health inequality for the given period,we divided it into two sub-periods: (1997-2001) and (2002-2007) and finally tocompare health inequality, using Bootstrap technique, we made a pseudo sta-tistical population. Results show a degree of descending progressively in urbanareas while in rural areas it has witnessed a slight improvement. However as theresults show in both rural and urban areas, because of the negativity of Kak-wani’s index of the household expenditure which is financed by themselves isnot progressive at all. Also the ratio of share richest quintile to poorest quintilefor health care in urban and rural areas are 8.79 and 8.01 respectively.JEL codes: D31, D63, I18, P43.Key Words: Equity, Health care financing, Kakwani progressivity index,Iran.1 IntroductionThe Economist Nobel Prize winner, Amartya Sen, in his book ”Inequality Re-examined” argues that presently justice theory is imperceptible in some spaces,∗Assistant Professor, Faculty Member of Economics Department, Islamic Azad UniversityKermanshah Branch, Kermanshah, Iran.1unless we can realize the worth of equity. A person who believes in incomeequality, a supporter of democracy and a liberal, in their political philosophymay believe in some equalities, but non of them may have common grounds.The first person may emphasize the equality of income distribution, the secondone equal political rights and the last one equal freedom for all. Though thesesubjects are equally important and equality based on any of these variablescould be the basis of a theory on justice, yet equality is an absolute idea andthe prospect of a comprehensive social and economic equality is not so bright.However Health is a major concern for social justice. Health and getting to itare important to the economists due to the fact that health expenditures aresort of human capital and its improvement can bring about labor productivityand consequently economic growth. Even indices such as health expenditurevalue - either total or per capita expenditure - are indicators of the health carecondition in a country, however the way these expenditure are distributed isvery important because it has strong ties with social justice. This reason hasmade the health ministry officials of Iran to compile a strategic plan for equalitydistribution of health care.2 Methodological issues2.1 Measuring progressivity in financingThe progressivity of a health financing system refers to the extent to whichpayments for health care rise as a proportion of a household’s income when hisincome rises. There are different ways to obtain this progressivity, one approach,that we adopted in this paper, is to estimate progressivity index. Already, theliterature on tax progressivity has proposed a variety of such indices, but in thisstudy, we employ index health care financing, namely that of Kakwani Index(KI).Πk is as the Kakwani’s Index (KI) of health care payments on gross income(expenditure), which is defined by twice the area between the Lorenz curve forgross income (expenditure),  LEX(p), and the concentration curve for healthcare payments,  LHE(p), and the (p) indicates the population’s rank in the grossincome (expenditure) distribution.  LEX(p), shows relationship between the cu-mulative proportion of population of income and the cumulative percentage ofthe population, where the population is ranked according to its income (expen-diture), whilst  LEX(p), is formed by plotting the cumulative proportion of thepopulation (ranked by income) against the cumulative share of payments. Thuswe have :Πk = 2∫ 10( LEX(p)−  LHE(p)) dpΠk = (1− 2∫ 10 LHE(p) dp)− (1− 2∫ 10 LEX(p) dp))Πk = CI −Gini (1)2The degree of progressivity of the health care financing system can be as-sessed by calculating the difference between the concentration coefficient of pay-ments, CI, and the Gini coefficient of gross income, Gini. A positive KakwaniIndex (Πk > 0), indicates that the system is progressive, so that the Lorenzcurve of income lies above the concentration curve of payments, and vice versait is regressive when (Πk < 0); a zero value of (Πk) indicates proportionality ofthe payments, and therefore the Lorenz and concentration curves are coincident.A progressive system is one in which health care payments rise as a proportionof income as income rises, whilst a regressivity system is one in which paymentsfall as a proportion of income as income rises. A proportion system is onein which health care payments account for the same proportion of income foreveryone, irrespective of their income.Figure 1: The Kakwani Progressivity IndexThe kakwani index (KI) values range between -2 and +1 and is equal to thedifference between the Health care concentration index and Gini coefficient forincome (Expenditure). In this Paper, we estimate Gini coefficient for income(expenditure), and Concentration index for health care financing with Betalorenz curve. We do this by estimating Kakwani progressivity indices, which canbe used to quantify the progressivity or regressivity of health care financing usingthe available data. This approach, which has been used in health economics(Wagstaff and van Doorslaer 2000) is superior to the use of alternatives such asthe Fairness of Financial Contributions (FFC) index (Murray et al. 1989; WorldHealth Organization 2000) which as Wagstaff (2002) has established, cannotdistinguish between the progressivity or regressivity of health care financing.32.2 Beta Lorenz curveThe literature on the estimation of Lorenz curves provides a number of differentfunctional forms. One of the best performers among them is the Beta Lorenzcurve (Kakwani 1980). The Lorenz function for Beta Lorenz curve specificationis given in following. Equation of Lorenz curve L(p) is:L(p) = p− θpγ .(1− p)δ, (2)We can write equation (1) in Log form :Ln(p− L) = Ln(θ) + γ.Ln(p) + δ.Ln(1− p), (3)Then we have Equation (3) in stochastic form:Ln(p− L)︸ ︷︷ ︸Y= Ln(θ)︸ ︷︷ ︸λ+γ. Ln(p)︸ ︷︷ ︸X2+δ. Ln(1− p)︸ ︷︷ ︸X3+ε, (4)Equation (4) can be readily estimated using ordinary least squares (OLS) routine(the estimation of the Beta Lorenz curve parameters requires the inclusion ofthe intercept term) then we have : θ̂ = exp(λ̂), γ̂, δ̂ Kakwani (1980) indicatedthat Gini index equals with:Gini = 2.θ.B(1 + γ, 1 + δ), (5)we know that, B(1 + γ︸ ︷︷ ︸α, 1 + δ︸ ︷︷ ︸β) is Beta density function :B(x;α, β) =1B(α, β).∫ x0 Lα−1.(1− L)β−1 dp0 ≤ x ≤ 1 , α > 0 , β > 0.and we know the Beta density function related with Gamma density function:B(x;α, β) =Γ(α)Γ(β)Γ(α+ β)Then fitted lorenz curve L(p) equals with: L(p) =1B(α̂, β̂).∫ x0 Lα̂−1.(1− L)β̂−1 dpOnce the Beta lorenz curve have been estimated, we can estimated share of kthdecile :SHk =1B(α̂,β̂).∫ kk−1  Lα̂−1.(1− L)β̂−1 dp1B(α̂,β̂).∫ 10 Lα̂−1.(1− L)β̂−1 dp, (6)4Note, in above equations : p, is cumulative proportion of population, L is cumu-lative proportion of expenditure if we obtain inequality in income, L = LEX(p)and L cumulative share of payments for health care if we obtain inequality inhealth care financing, L = LHE(p). For estimates Gini coefficient, Beta Lorenzcurve function and calculating share of deciles, we have used EViews program-ming facilities. It is worth noting that we have been using version (7.1). Ourcalculations are once for income and once for health expenses.13 DataWe use private expenditure data on health care financed by the households.These data are collected and published annually by the Iran Statistic Center(ISC) in rural and urban areas. In this paper, used data are during 1997-2007.Fortunately these data are high quality but unfortunately reliable data on publichealth expenditure do not exist. The data include measures of household incomeand detailed disaggregation of household expenditure data on a variety of goodsand services, including health care.4 Results for areas4.1 Results for urban areasIn this subsection we present the estimated Gini coefficients for income, healthexpenditure concentration indices and KIs household co-payments. The resultsare presented for urban areas of Iran, for the years 1997 to 2007. Table 1presents the Gini coefficient, concentration index of health care and Kakwani’sindex (KI). Considering the results of table 1, the mean of Kakwani’s indexin total period in urban areas has been negative and equals with (-0.022), Thisindicates that Health care financing in this area is descending. In addition, ratioof share richest quintile to poorest quintile for Health care is (8.79). Numberslisted in Column Kakwani’s index (KI) are obtained from subtract numberslisted in column (CI) from column (GINI). The following Figure (figure 3) showLorenz curves for Income and health care expenditure in urban areas in 2007.4.2 Results for Rural areasIn this subsection we present the estimated Gini coefficients for income, healthexpenditure concentration indices and KIs household co-payments. The resultsare presented for rural areas of Iran, for the years 1997 to 2007. Table 2 presentsthe Gini coefficient, concentration index of health care and Kakwani’s index(KI). Similar to the results in urban areas for rural areas, we’ve provided asimilar table. In table (2) you can see that the mean of Kakwani’s index in totalperiod in rural areas has been negative and equals with (-0.107), This indicates1Those interested in recreating results of this paper, can request EViews commands anddata from the author.5Table 1: Findings for urban areas: gini coefficient (Gini), concentration indexof health care (CI), Kakwani progressivity Index (Πk).Year Gini CI Πk Richest QuantilePoorest Quantile in Health Care1997 0.399886 0.360251 -0.039635 8.2254771998 0.394658 0.425048 0.030390 9.4437661999 0.399145 0.223239 -0.175906 6.1910922000 0.401198 0.437459 0.036261 9.6994242001 0.393432 0.450145 0.056713 11.1457752002 0.384205 0.275671 -0.108534 6.8930412003 0.401039 0.391689 -0.009350 8.7930632004 0.407243 0.446630 0.039387 9.8932972005 0.406566 0.272431 -0.134135 6.8471092006 0.411564 0.453520 0.041956 10.041772007 0.404977 0.424210 0.019233 9.542637Mean 0.400356 0.378208 -0.022147 8.7924023Figure 2: Gini coefficient, Kakwani index and concentration index [Urban]that Health care financing in this area is descending. In addition, ratio of sharerichest quintile to poorest quintile for Health care is (8.01). Numbers listedin column Kakwani’s index (KI) are obtained from subtract numbers listed incolumn (CI) from column (GINI). The following Figure (figure 5) show Lorenzcurves for Income and health care expenditure in rural areas in 2007.4.3 Bootstrap results for urban and rural areasIn this section, we provide evidence for changes in the Kakwani’s indices during1997-2007 period in urban and rural areas. For this purpose, as we already said,6Figure 3: Lorenz curves for income and health expenditure 2007 [Urban]Table 2: Findings for rural areas: gini coefficient (Gini), concentration index ofhealth care (CI),Kakwani progressivity Index (Πk).Year Gini CI Πk Richest QuantilePoorest Quantile in Health Care1997 0.422666 -0.1180 -0.21455 6.0041131998 0.444711 -0.0991 -0.01104 10.962861999 0.430977 0.0189 0.03162 11.309132000 0.427509 0.0189 -0.19778 6.2733982001 0.411402 0.0189 -0.19991 6.0454752002 0.411408 0.0189 0.06201 10.484732003 0.390743 0.0189 -0.16231 6.2568282004 0.410273 0.0189 0.00708 10.541112005 0.411684 0.0189 -0.18088 6.2871532006 0.422348 0.0189 -0.17175 6.5465592007 0.437263 0.0189 -0.14313 7.412589Mean 0.420089 0.312761 -0.10733 8.011267we divided the sample into two sub-period 1997-2001 and 2002-2007 and finally7Figure 4: Gini coefficient, Kakwani index and concentration index [Rural]Figure 5: Lorenz curves for income and health expenditure 2007 [Rural]compared Health inequality using Bootstrap technique. The following graphsfor each of urban and rural areas indicated that sample size for each sub-periodincreases to 10000 observations. for urban and rural areas, in graphs 6 and 7,we obtained Mean’s Kakwani indices for two sub-samples above, respectively.For calculating Bootstrap simulation, we have used MATLAB programming8facilities, it is worth noting that we have been using version (7.8).Figure 6: Distribution of kakwani’s index for progressivity health care financingsystem in urban areas, (Bootstrap simulation with 10000 iterations)Figure 7: Distribution of kakwani’s index for progressivity health care financingsystem in rural area, (Bootstrap simulation with 10000 iterations)The results in Table 3 show in both rural and urban areas because of nega-tivity of Kakwani’s index of the household expenditures which are financed bythemselves are not progressive at all. But changes in Kakwani’s indices showthat in urban areas degrees of progressivity is more negative, while in rural areasthe situation has improved.9Table 3: bootstrap simulation for Kakwani progressivity Index (KI).RegionsSub-Sample Urban Rural(1997-2001) -0.0181 -0.1180(2002-2007) -0.0249 -0.0991Change in Kakwani Index (∆Πk) -0.0068 0.01895 ResultsKakwani’s index which is based on the un-proportionality of financing approach(for health expenditures) shows a degree of descending progressivity in urbanareas while in rural areas it has witnessed a slight improvement. However as theresults show in both rural and urban area because of negativity of Kakwani’sindex of the household expenditures which are financed by themselves is notprogressive at all. Also the ratio of share richest quintile to poorest quintile forhealth care in urban and rural areas are 8.79 and 8.01 respectively (see tables 1and 2).AcknowledgmentsI would like to express our deepest gratitude to professor Kambiz H Kiani fortheir suggestions. I would also like to thanks Ali Ahmadi for Careful reading ofthe paper.References[1] Anand, S, F, Peter and A, Sen (Ed.)(2004), ”Public health, Ethics, andEquity”, Published in the United States, Oxford University Press Inc., NewYork.[2] Effron, B, and R, Tibshirani, (1993), ”An Introduction to the Bootstrap”,Chapman and Hall Inc, London.[3] Gerdtham, U, G, Sundberg, G,(1998), ’Redistributive effects of Swedishhealth care finance’. , International Journal of Health Planning and Man-agement 13: 289-306, 9 (1957), 417–434.[4] Kakwani, Nanak C, (1977), ’Applications of Lorenz Curves in EconomicAnalysis’. , Econometrica, Vol. 45, No. 3, pp. 719-727, April. 9 (1957), 417–434.[5] Lairson, D,R, Hindson, P, Hauquitz, A, (1995), ’Equity of health care inAustralia’ , ISocial Science and Medicine 41- 475-482. 9 (1957), 417-434.10[6] Management and Planning Organization of Iran (2004), ”Iran Fourth Socio-Economic Development Act’ , Government of Iran: Tehran.[7] Murray, C.J.L., Knaul, F., Musgrove, P., Xu, K., Kawabata, K, (2000)”Defining and Measuring Fairness in Financial Contribution to the HealthSystem’ , Global Programme on Evidence for Health Policy Discussion PaperSeries: No. 24. World Health Organization: Geneva.[8] O’Donnell, O., van Doorslaer, E., Wagstaff, A. And Lindelow, M. (2007),’Analyzing Health Equity Using Household Survey Data - A Guide to Tech-niques and Their Implementation’ , The World Bank: Geneva.[9] Sen, A. (1992), ’Inequality Reexamined’ , Cambridge, MA: Harvard Univer-sity Press, and Oxford: Clarendon Press.[10] Spence, M. M, Louis, (2009), ’Health and growth’ , The World Bank, Wash-ington, DC.[11] Statistical Center of Iran (1997-2007), ’Household Expenditure and IncomeSurveys’ , Tehran: Statistical Center of Iran.[12] Statistical Center of Iran. (2005), ’Records Complex-Household Expendi-ture and Income Survey in Urban and Rural Areas’ , The Management andPlanning Organization of Iran: Tehran.[13] Wagstaff, A. (2002), ’Measuring equity in health care financing: reactionsand alternatives to the world health organization’s fairness of financial con-tribution index’ , Health Economics 11: 103-115.[14] Wagstaff, A. (2002), ’Measuring equity in health care financing: reactionsand alternatives to the world health organization’s fairness of financial con-tribution index’ , Health Economics 11: 103-115.[15] Wagstaff, A., van Doorslaer, E. (2000), ’Equity in health care finance anddelivery’ , In A. Culyer, J. P. Newhouse (eds) Handbook of Health Eco-nomics 1B: 1803-1861. Elsevier Science, Amsterdam.[16] Wagstaff, A., van Doorslaer, E. (1992), ”Equity in the finance of health care:some international comparisons’, Journal of Health Economics 11, 361-387.[17] Wagstaff, A., van Doorslaer, E., Paci, P. (1989), ’Equity in the finance anddelivery of health care: some tentative cross-country comparisons’ , OxfordReview of Economics and Policy 5: 89-112.11

English

Equity of Health Care Financing: An Application to Iran

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Equity of Health Care Financing: An
Application to Iran
Alireza Moradi
Islamic Azad University, Branch of Kermanshah
6. May 2011
Online at http://mpra.ub.uni-muenchen.de/33489/
MPRA Paper No. 33489, posted 18. September 2011 18:49 UTC
Equity of Health Care Financing
An Application to Iran
Alireza Moradi ∗
Department of Economics
Islamic Azad University of Kermanshah Branch
E-mail: alirezamoradi econ@iauksh.ac.ir
6 May 2011
Abstract
This paper analyzes inequality in Iran’s health system from a financing perspec-
tive. Through grouped data of household budget published by Iran Statistic
Center (ISC) and Beta Lorenz curve introduced in Kakwani (1980), it has been
tried to extract Beta Lorenz curve and Kakwani progressivity index in each
individual rural and urban district, and also to obtain other inequality mea-
sure in (1997-2007) Period.Then to study health inequality for the given period,
we divided it into two sub-periods: (1997-2001) and (2002-2007) and finally to
compare health inequality, using Bootstrap technique, we made a pseudo sta-
tistical population. Results show a degree of descending progressively in urban
areas while in rural areas it has witnessed a slight improvement. However as the
results show in both rural and urban areas, because of the negativity of Kak-
wani’s index of the household expenditure which is financed by themselves is
not progressive at all. Also the ratio of share richest quintile to poorest quintile
for health care in urban and rural areas are 8.79 and 8.01 respectively.
JEL codes: D31, D63, I18, P43.
Key Words: Equity, Health care financing, Kakwani progressivity index,
Iran.
1 Introduction
The Economist Nobel Prize winner, Amartya Sen, in his book ”Inequality Re-
examined” argues that presently justice theory is imperceptible in some spaces,
∗Assistant Professor, Faculty Member of Economics Department, Islamic Azad University
Kermanshah Branch, Kermanshah, Iran.
1
unless we can realize the worth of equity. A person who believes in income
equality, a supporter of democracy and a liberal, in their political philosophy
may believe in some equalities, but non of them may have common grounds.
The first person may emphasize the equality of income distribution, the second
one equal political rights and the last one equal freedom for all. Though these
subjects are equally important and equality based on any of these variables
could be the basis of a theory on justice, yet equality is an absolute idea and
the prospect of a comprehensive social and economic equality is not so bright.
However Health is a major concern for social justice. Health and getting to it
are important to the economists due to the fact that health expenditures are
sort of human capital and its improvement can bring about labor productivity
and consequently economic growth. Even indices such as health expenditure
value - either total or per capita expenditure - are indicators of the health care
condition in a country, however the way these expenditure are distributed is
very important because it has strong ties with social justice. This reason has
made the health ministry officials of Iran to compile a strategic plan for equality
distribution of health care.
2 Methodological issues
2.1 Measuring progressivity in financing
The progressivity of a health financing system refers to the extent to which
payments for health care rise as a proportion of a household’s income when his
income rises. There are different ways to obtain this progressivity, one approach,
that we adopted in this paper, is to estimate progressivity index. Already, the
literature on tax progressivity has proposed a variety of such indices, but in this
study, we employ index health care financing, namely that of Kakwani Index
(KI).Πk is as the Kakwani’s Index (KI) of health care payments on gross income
(expenditure), which is defined by twice the area between the Lorenz curve for
gross income (expenditure),  LEX(p), and the concentration curve for health
care payments,  LHE(p), and the (p) indicates the population’s rank in the gross
income (expenditure) distribution.  LEX(p), shows relationship between the cu-
mulative proportion of population of income and the cumulative percentage of
the population, where the population is ranked according to its income (expen-
diture), whilst  LEX(p), is formed by plotting the cumulative proportion of the
population (ranked by income) against the cumulative share of payments. Thus
we have :
Πk = 2
∫ 1
0
( LEX(p)−  LHE(p)) dp
Πk = (1− 2
∫ 1
0
 LHE(p) dp)− (1− 2
∫ 1
0
 LEX(p) dp))
Πk = CI −Gini (1)
2
The degree of progressivity of the health care financing system can be as-
sessed by calculating the difference between the concentration coefficient of pay-
ments, CI, and the Gini coefficient of gross income, Gini. A positive Kakwani
Index (Πk > 0), indicates that the system is progressive, so that the Lorenz
curve of income lies above the concentration curve of payments, and vice versa
it is regressive when (Πk < 0); a zero value of (Πk) indicates proportionality of
the payments, and therefore the Lorenz and concentration curves are coincident.
A progressive system is one in which health care payments rise as a proportion
of income as income rises, whilst a regressivity system is one in which payments
fall as a proportion of income as income rises. A proportion system is one
in which health care payments account for the same proportion of income for
everyone, irrespective of their income.
Figure 1: The Kakwani Progressivity Index
The kakwani index (KI) values range between -2 and +1 and is equal to the
difference between the Health care concentration index and Gini coefficient for
income (Expenditure). In this Paper, we estimate Gini coefficient for income
(expenditure), and Concentration index for health care financing with Beta
lorenz curve. We do this by estimating Kakwani progressivity indices, which can
be used to quantify the progressivity or regressivity of health care financing using
the available data. This approach, which has been used in health economics
(Wagstaff and van Doorslaer 2000) is superior to the use of alternatives such as
the Fairness of Financial Contributions (FFC) index (Murray et al. 1989; World
Health Organization 2000) which as Wagstaff (2002) has established, cannot
distinguish between the progressivity or regressivity of health care financing.
3
2.2 Beta Lorenz curve
The literature on the estimation of Lorenz curves provides a number of different
functional forms. One of the best performers among them is the Beta Lorenz
curve (Kakwani 1980). The Lorenz function for Beta Lorenz curve specification
is given in following. Equation of Lorenz curve L(p) is:
L(p) = p− θpγ .(1− p)δ, (2)
We can write equation (1) in Log form :
Ln(p− L) = Ln(θ) + γ.Ln(p) + δ.Ln(1− p), (3)
Then we have Equation (3) in stochastic form:
Ln(p− L)︸ ︷︷ ︸
Y
= Ln(θ)︸ ︷︷ ︸
λ
+γ. Ln(p)︸ ︷︷ ︸
X2
+δ. Ln(1− p)︸ ︷︷ ︸
X3
+ε, (4)
Equation (4) can be readily estimated using ordinary least squares (OLS) routine
(the estimation of the Beta Lorenz curve parameters requires the inclusion of
the intercept term) then we have : θ̂ = exp(λ̂), γ̂, δ̂ Kakwani (1980) indicated
that Gini index equals with:
Gini = 2.θ.B(1 + γ, 1 + δ), (5)
we know that, B(1 + γ︸ ︷︷ ︸
α
, 1 + δ︸ ︷︷ ︸
β
) is Beta density function :
B(x;α, β) =
1
B(α, β)
.
∫ x
0
 Lα−1.(1− L)β−1 dp
0 ≤ x ≤ 1 , α > 0 , β > 0.
and we know the Beta density function related with Gamma density function:
B(x;α, β) =
Γ(α)Γ(β)
Γ(α+ β)
Then fitted lorenz curve L(p) equals with:
 L(p) =
1
B(α̂, β̂)
.
∫ x
0
 Lα̂−1.(1− L)β̂−1 dp
Once the Beta lorenz curve have been estimated, we can estimated share of kth
decile :
SHk =
1
B(α̂,β̂)
.
∫ k
k−1  L
α̂−1.(1− L)β̂−1 dp
1
B(α̂,β̂)
.
∫ 1
0
 Lα̂−1.(1− L)β̂−1 dp
, (6)
4
Note, in above equations : p, is cumulative proportion of population, L is cumu-
lative proportion of expenditure if we obtain inequality in income, L = LEX(p)
and L cumulative share of payments for health care if we obtain inequality in
health care financing, L = LHE(p). For estimates Gini coefficient, Beta Lorenz
curve function and calculating share of deciles, we have used EViews program-
ming facilities. It is worth noting that we have been using version (7.1). Our
calculations are once for income and once for health expenses.1
3 Data
We use private expenditure data on health care financed by the households.
These data are collected and published annually by the Iran Statistic Center
(ISC) in rural and urban areas. In this paper, used data are during 1997-2007.
Fortunately these data are high quality but unfortunately reliable data on public
health expenditure do not exist. The data include measures of household income
and detailed disaggregation of household expenditure data on a variety of goods
and services, including health care.
4 Results for areas
4.1 Results for urban areas
In this subsection we present the estimated Gini coefficients for income, health
expenditure concentration indices and KIs household co-payments. The results
are presented for urban areas of Iran, for the years 1997 to 2007. Table 1
presents the Gini coefficient, concentration index of health care and Kakwani’s
index (KI). Considering the results of table 1, the mean of Kakwani’s index
in total period in urban areas has been negative and equals with (-0.022), This
indicates that Health care financing in this area is descending. In addition, ratio
of share richest quintile to poorest quintile for Health care is (8.79). Numbers
listed in Column Kakwani’s index (KI) are obtained from subtract numbers
listed in column (CI) from column (GINI). The following Figure (figure 3) show
Lorenz curves for Income and health care expenditure in urban areas in 2007.
4.2 Results for Rural areas
In this subsection we present the estimated Gini coefficients for income, health
expenditure concentration indices and KIs household co-payments. The results
are presented for rural areas of Iran, for the years 1997 to 2007. Table 2 presents
the Gini coefficient, concentration index of health care and Kakwani’s index
(KI). Similar to the results in urban areas for rural areas, we’ve provided a
similar table. In table (2) you can see that the mean of Kakwani’s index in total
period in rural areas has been negative and equals with (-0.107), This indicates
1Those interested in recreating results of this paper, can request EViews commands and
data from the author.
5
Table 1: Findings for urban areas: gini coefficient (Gini), concentration index
of health care (CI), Kakwani progressivity Index (Πk).
Year Gini CI Πk Richest QuantilePoorest Quantile in Health Care
1997 0.399886 0.360251 -0.039635 8.225477
1998 0.394658 0.425048 0.030390 9.443766
1999 0.399145 0.223239 -0.175906 6.191092
2000 0.401198 0.437459 0.036261 9.699424
2001 0.393432 0.450145 0.056713 11.145775
2002 0.384205 0.275671 -0.108534 6.893041
2003 0.401039 0.391689 -0.009350 8.793063
2004 0.407243 0.446630 0.039387 9.893297
2005 0.406566 0.272431 -0.134135 6.847109
2006 0.411564 0.453520 0.041956 10.04177
2007 0.404977 0.424210 0.019233 9.542637
Mean 0.400356 0.378208 -0.022147 8.7924023
Figure 2: Gini coefficient, Kakwani index and concentration index [Urban]
that Health care financing in this area is descending. In addition, ratio of share
richest quintile to poorest quintile for Health care is (8.01). Numbers listed
in column Kakwani’s index (KI) are obtained from subtract numbers listed in
column (CI) from column (GINI). The following Figure (figure 5) show Lorenz
curves for Income and health care expenditure in rural areas in 2007.
4.3 Bootstrap results for urban and rural areas
In this section, we provide evidence for changes in the Kakwani’s indices during
1997-2007 period in urban and rural areas. For this purpose, as we already said,
6
Figure 3: Lorenz curves for income and health expenditure 2007 [Urban]
Table 2: Findings for rural areas: gini coefficient (Gini), concentration index of
health care (CI),Kakwani progressivity Index (Πk).
Year Gini CI Πk Richest QuantilePoorest Quantile in Health Care
1997 0.422666 -0.1180 -0.21455 6.004113
1998 0.444711 -0.0991 -0.01104 10.96286
1999 0.430977 0.0189 0.03162 11.30913
2000 0.427509 0.0189 -0.19778 6.273398
2001 0.411402 0.0189 -0.19991 6.045475
2002 0.411408 0.0189 0.06201 10.48473
2003 0.390743 0.0189 -0.16231 6.256828
2004 0.410273 0.0189 0.00708 10.54111
2005 0.411684 0.0189 -0.18088 6.287153
2006 0.422348 0.0189 -0.17175 6.546559
2007 0.437263 0.0189 -0.14313 7.412589
Mean 0.420089 0.312761 -0.10733 8.011267
we divided the sample into two sub-period 1997-2001 and 2002-2007 and finally
7
Figure 4: Gini coefficient, Kakwani index and concentration index [Rural]
Figure 5: Lorenz curves for income and health expenditure 2007 [Rural]
compared Health inequality using Bootstrap technique. The following graphs
for each of urban and rural areas indicated that sample size for each sub-period
increases to 10000 observations. for urban and rural areas, in graphs 6 and 7,
we obtained Mean’s Kakwani indices for two sub-samples above, respectively.
For calculating Bootstrap simulation, we have used MATLAB programming
8
facilities, it is worth noting that we have been using version (7.8).
Figure 6: Distribution of kakwani’s index for progressivity health care financing
system in urban areas, (Bootstrap simulation with 10000 iterations)
Figure 7: Distribution of kakwani’s index for progressivity health care financing
system in rural area, (Bootstrap simulation with 10000 iterations)
The results in Table 3 show in both rural and urban areas because of nega-
tivity of Kakwani’s index of the household expenditures which are financed by
themselves are not progressive at all. But changes in Kakwani’s indices show
that in urban areas degrees of progressivity is more negative, while in rural areas
the situation has improved.
9
Table 3: bootstrap simulation for Kakwani progressivity Index (KI).
Regions
Sub-Sample Urban Rural
(1997-2001) -0.0181 -0.1180
(2002-2007) -0.0249 -0.0991
Change in Kakwani Index (∆Πk) -0.0068 0.0189
5 Results
Kakwani’s index which is based on the un-proportionality of financing approach
(for health expenditures) shows a degree of descending progressivity in urban
areas while in rural areas it has witnessed a slight improvement. However as the
results show in both rural and urban area because of negativity of Kakwani’s
index of the household expenditures which are financed by themselves is not
progressive at all. Also the ratio of share richest quintile to poorest quintile for
health care in urban and rural areas are 8.79 and 8.01 respectively (see tables 1
and 2).
Acknowledgments
I would like to express our deepest gratitude to professor Kambiz H Kiani for
their suggestions. I would also like to thanks Ali Ahmadi for Careful reading of
the paper.
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11


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