Measuring inequalities in health

Adam WagstaffAbdo Yazbeck

Today’s menu

Concentration curves and indices (AW) Combining levels and inequalities into a

single achievement index (AY) Benefit incidence analysis (AY) Inequalities in financial burden of health

care payments (AW)

Concentration curves and indices

Adam Wagstaff

Which country is less equal?

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India Mali

U5M

R p

er

1000 liv

e b

irth

s

Poorest"quintile"2nd poorest"quintileMiddle "quintile"

2nd richest"quintile"Richest"quintile"

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25%

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75%

100%

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Cum. % births, ranked by "wealth"

Cum

. %

of

und

er-fi

ve d

eath

s L(s) India

L(s) Mali

CI = 2 x area between 450 line and concentration curve

CI < 0 when variableis higher amongst poor

U5MR concentration curves

Setting data up for CC chart

Equality L(s) India L(s) Mali0% 0% 0%

23% 23% 30%45% 45% 59%66% 66% 79%85% 85% 93%

100% 100% 100%0% 0%

21% 25%42% 49%63% 69%83% 89%

100% 100%

Computing CI: grouped data

Wealth No. of rel % cumul % U5MR No. of rel % cumul % Conc.group births births births per 1000 deaths deaths deaths Index

0% 0%Poorest 29939 23% 23% 154.7 4632 30% 30% - 0.00082nd 28776 22% 45% 152.9 4400 29% 59% - 0.0267Middle 26528 20% 66% 119.5 3170 21% 79% - 0.05924th 24689 19% 85% 86.9 2145 14% 93% - 0.0827Richest 19739 15% 100% 54.3 1072 7% 100% 0.0000Total/average 129671 118.8 15419 - 0.1694

)(...)()( 1123321221 TTTT LpLpLpLpLpLpC

Computing CI: micro-data

Can use where variable of interest (y) defined and measured at individual level—not case with U5MR

Use “convenient covariance” result Compute: mean of y—call it Generate individual’s fractional rank in SES

distribution—call it R Then compute CI = 2 cov(y,R) / If data are weighted,

– generate a weighted fractional frank, and – compute a weighted covariance

Computing std errors for CIs

Grouped data case:– Are variances of group means known? If

they are, can get a more precise estimate– Use formulae in TN #7—compute in Excel;

spreadsheet available from Bank team Micro-data case

– Estimate in regression below using Newey-West estimator in Stata: equals CI; std error is robust std error of CI

iii

R uRy

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Health care payments

Adam Wagstaff

Different concerns over health care payments Health care payments affect HHs’ ability

to purchase other things that matter to their well being—food, shelter, etc.

But what’s an equitable distribution?– One where payments don’t absorb more

than x% of income—i.e. aren’t catastrophic– One where payments don’t push HHs into

poverty or further into poverty if already there?

– Or one where payments are proportional to ability to pay?

Rural China—payments relative to income

Out-of-pocket payments Rural Hebei and Liaoning, 1995-97

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Households ranked by income (N=790)

Annual pre

- and p

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-OO

P

consu

mpti

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Yuan)

Out-of-pocket payments Rural Hebei and Liaoning, 1995-97

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Households ranked by income (N=790)

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consu

mpti

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Yuan)

85% of prepayment income

Rural China—payments relative to 15% threshold

Rural China—payments relative to poverty line

Out-of-pocket payments Rural Hebei and Liaoning, 1995-97

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Households ranked by income (N=790)

Annual pre

- and p

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consu

mpti

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Yuan)

Poverty line

How much catastrophe?

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cumul % pop

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Ps

as

% s

pendin

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All spending

Food spending

Vietnam case study

18% of Vietnamese population in 1993 had out-of-pocket expenditures in excess of 25% of non-food consumption

How much catastrophe?

1. Incidence of catastrophic costs can be measured as proportion (headcount) exceeding threshold level zcat : Hcat

2. Intensity of catastrophic costs can be measured as the average excess (or gap) : Gcat

3. If , in addition, we want to take into account that the incidence of catastrophic costs matters more for the poor, we can use the rank-weighted intensity, defined as

where CO is the concentration index of the “overshoot” spending.Clearly, if excesses concentrated amongst the poor, CO

will be negative and

1-Ocat cat OW G C

Ocat catW G

Catastrophe in Vietnam

threshold level z

Out-of-pocket health expenditure 5% 10% 15% 25%

as % of total expenditure per cap

Headcount (H) 38.19% 18.40% 9.26% -

Mean gap (G) 2.85% 1.51% 0.84% -

Mean positive gap (MPG) 7.47% 8.21% 9.06% -

as % of non-food expenditure per cap

Headcount (H) 67.17% 46.52% 33.25% 17.88%

Mean gap (G) 9.95% 7.14% 5.17% 2.70%

Mean positive gap (MPG) 14.81% 15.36% 15.55% 15.11%

How much poverty impact?

Cum % sample

Poverty line

Pre-payment income

Income

A = pre-payment poverty gap

Pre-payment headcount

How much poverty impact?

Cum % sample

Poverty line

Pre-payment income

Income

Post-payment income

A = pre-payment poverty gap

Pre-payment headcount

Post-payment headcount

C

Bdeepening poverty of pre-payment poor

addition to poverty gap from the new poor

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1 500 999 1498 1997 2496 2995 3494 3993 4492 4991 5490 5989

Households ranked by expend w/out hc payments

HH

exp

endi

ture

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tiple

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PL

Pov line = VND 1.8m/year Expend w/out hc payments

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1 500 999 1498 1997 2496 2995 3494 3993 4492 4991 5490 5989

Households ranked by expend w/out hc payments

HH

exp

endi

ture

as

mul

tiple

of

PL

Pov line = VND 1.8m/year Expend w/out hc paymentsHC payments

Out-of-pocket payments for health care pushed 2.6m Vietnamese into poverty in 1998.

Increased headcount by 23% and poverty gap by 25%

Impoverishment in Vietnam

How progressive?

Regressive: OOPs larger (as a % of income) at lower income levels; less inequality in OOPs than in pre-payment income; Cf. progressive

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0% 25% 50% 75% 100%cumul % sample, ranked by income

cum

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com

e an

d O

OPs

Equality

Lorenz curve, pre-payment income

OOPs concentration curve

Lorenz curve shows income inequality; concentration curve shows OOPs inequality

Gini is twice area between Lorenz curve & 450 line; concentration index is twice area between CC and 450 line

Kakwani index is twice area between CC and Lorenz curve, or ; positive when progressive

How regressive are OOPs?

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Chin

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Peru

Bulg

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akw

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ity index

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Sources: Wagstaff, van Doorslaer, et al. (1998), authors’ calculationsSources: Wagstaff, van Doorslaer, et al. (1998), authors’ calculations