Transcript Analyzing Health Equity Using Household Survey Data Lecture 12 Explaining Differences between Groups: Oaxaca Decomposition “Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy.

Analyzing Health Equity Using
Household Survey Data
Lecture 12
Explaining Differences between Groups:
Oaxaca Decomposition
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
What’s it all about?
• Having measured inequalities, natural next step is to seek
to account for them
• In this and the next lecture we examine methods of
decomposing inequality into its contributing factors
• Core idea is to explain the outcome variable by a set of
factors that vary systematically with SES
• E.g. poor have lower income but also less knowledge,
worse drinking water, lack insurance coverage, etc.
• Want to know extent to which inequalities in health status
are due to (a) inequalities in income, (b) inequalities in
knowledge, (c) inequalities in access to drinking water, etc.
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Interpretation of decomposition
results
• Decomposition methods are based on regression
analyses
• If regressions are purely descriptive, they reveal the
associations that characterise the health inequality
– Then inequality is explained in a statistical sense but
implications for policies to reduce inequality are limited
• If data allow identification of causal effects, then the
factors that generate the inequality are identified
– Then can draw conclusions about how policies would
impact on inequality
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Oaxaca(-Blinder) decomposition
• Oaxaca decomposes gap in mean of outcome vbl
between two groups
• Attraction of Oaxaca over decomposition in next
lecture is that it allows for the possibility that
inequalities caused in part by differences in effects of
determinants
• For example, health of the poor may be less
responsive to changes in insurance coverage, or to
changes in access to drinking water, etc.
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
  poor xi   ipoor if poor
yi   rich
rich

x


if nonpoor
i
i

equation for
non-poor
y
ynon-poor
equation for
poor
ypoor
xpoor
xnon-poor
x
Gap between mean outcomes:
y non- poor - y poor   non- poor x non- poor -  poor x poor
equation for
non-poor
y
ynon-poor
equation for
poor
ypoor
xpoor
xnon-poor
x
But how far due to diffs in ’s
rather than diffs in x’s?
equation for
non-poor
y
ynon-poor
equation for
poor
ypoor
xpoor
xnon-poor
x
Oaxaxa decomposition #1
y non- poor - y poor  Dx poor  D x non- poor
equation for
non-poor
y
ynon-poor
Dxnon-poor equation for
poor
Dx poor
ypoor
xpoor
xnon-poor
x
Oaxaca decomposition #2
y non- poor - y poor  Dx non- poor  D x poor
equation for
non-poor
y
ynon-poor
Dxnon-poor
Dxnon-poor equation for
poor
Dx poor
Dxpoor
ypoor
xpoor
xnon-poor
x
A general decomposition
y non- poor - y poor  Dx poor  D x poor  DxD
 E  C  CE
E – gap in ‘endowments’ (“explained”)
C – gap in ‘coefficients’ (“unexplained”)
CE – interaction of differences in endowments &
coefficients
Oaxaca decomposition #1:
y non- poor - y poor  Dx poor  D x non- poor  E   CE  C 
Oaxaca decomposition #2:
y non- poor - y poor  Dx non- poor  D x poor   E  CE   C
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Other decompositions
y non- poor - y poor  Dx  D non- poor   I - D   poor   D  x non- poor  I - D   x poor D 
I is the identity matrix, D is a matrix of weights
D=0  Oaxaca decomposition #1
D=1  Oaxaca decomposition #2
diag(D)=0.5  diffs. in x’s weighted by mean of coeff. vectors
(Cotton, 1988)
diag(D)=Nnp/N  diffs. In x’s weighted by sample fraction
(Reimers, 1983)
non-poor
And a further decomposition (Neumark, 1988):
y non- poor - y poor  Dx P   x non- poor   non- poor -  P   x poor   P -  poor 
where  P is the coefficient vector estimated from pooling the two groups
Decomposition of poor–nonpoor
differences in child malnutrition in
Vietnam
poor==0
poor==1
Fraction
.081201
0
-5.81
2.99
Total
.081201
Mean HAZ z-score kids<10 yrs:
Poor = -1.86
Non-poor = -1.44
Diff = 0.42
U.S. reference group = 0.00
0
-5.81
height for age
Histograms by poor
Height-for-age z-scores
2.99
The regression equation
• y is the HAZ malnutrition score
• Same regression model as Wagstaff et al.(2003)
• x includes
–
–
–
–
–
–
–
log of the child’s age in months (lnage)
sex = 1 if male
safewtr = 1 if drinking water is safe
oksan = 1 if satisfactory sanitation,
years of schooling of the child’s mother (schmom)
log of HH per capita consumption (lnpcexp)
poor = 1 if child’s HH is poor (if pcexp<Dong
1,790,000 )
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Differences in means between
non-poor and poor
Variables
Non-poor
Poor
Lnage
4.021
3.952
Sex
0.513
0.491
Safwtr
0.421
0.221
Oksan
0.313
0.069
schmom
7.696
5.739
lnpcexp
7.99
7.162
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Are there signficant differences in
the coefficients?
haz
xi: reg haz i.poor*lnage i.poor*sex i.poor*safwtr i.poor*oksan i.poor*schmom i.poor*lnpcexp [aw=wt]
testparm poor _I*
_Ipoor_1
lnage
_IpooXlnag~1
_Ipoor_1
sex
_IpooXsex_1
_Ipoor_1
safwtr
_IpooXsafw~1
_Ipoor_1
oksan
_IpooXoksa~1
_Ipoor_1
schmom
_IpooXschm~1
_Ipoor_1
lnpcexp
_IpooXlnpc~1
_cons
Coef.
Std. Err.
t
P>t
[95% Conf.
Interval]
0.8700504
-0.3210769
-0.0713262
(dropped)
-0.0878692
-0.0779383
(dropped)
0.1648151
-0.0205021
(dropped)
0.1949967
-0.2293099
(dropped)
-0.0030194
0.0180123
(dropped)
0.5441721
-0.0769853
-4.560642
0.8744995
0.027344
0.0433432
0.99
-11.74
-1.65
0.32
0
0.1
-0.8443397
-0.3746828
-0.1562972
2.584441
-0.2674711
0.0136448
0.0405808
0.0641627
-2.17
-1.21
0.03
0.225
-0.1674248
-0.2037244
-0.0083136
0.0478479
0.0448485
0.0768307
3.67
-0.27
0
0.79
0.0768931
-0.171123
0.2527371
0.1301187
0.0505462
0.1160704
3.86
-1.98
0
0.048
0.0959047
-0.4568571
0.2940886
-0.0017626
0.0056652
0.0093292
-0.53
1.93
0.594
0.054
-0.0141256
-0.000277
0.0080868
0.0363015
0.0500458
0.1188602
0.4121991
10.87
-0.65
-11.06
0
0.517
0
0.446061
-0.3100017
-5.368727
0.6422831
0.1560311
-3.752557
F( 7, 5154) = 2.03
Prob > F = 0.0472
On an individual basis, differences in effects are only signif. (10%)
For sanitation and mother’s education
Decomposition of poor-nonpoor
malnutrition gap into main effects
decompose haz lnage sex safwtr oksan schmom lnpcexp
[pw=wt], by(poor) detail estimates
Mean prediction high (H):
-1.442
Mean prediction low (L):
-1.861
Raw differential (R) {H-L}:
0.419
- due to endowments (E):
0.406
- due to coefficients (C):
-0.082
- due to interaction (CE):
0.095
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Main decomposition results with
different weighting schemes
D:
0
1
0.5
0.562
*
Unexplained (U){C+(1-D)CE}:
0.014
-0.082
-0.034
-0.038
-0.032
Explained (V) {E+D*CE}:
0.406
0.501
0.454
0.458
0.451
3.2
-19.5
-8.1
-9.1
-7.5
96.8
119.5
108.1
109.1
107.5
% unexplained {U/R}:
% explained (V/R):
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Which covariates explain most of the
gap?
explained: D =
Variables
E(D=0)
C
CE
1
0.5
0.543
*
lnage
-0.027
0.282
0.005
-0.022
-0.024
-0.024
-0.024
Sex
-0.004
0.038
0.002
-0.002
-0.003
-0.003
-0.003
safwtr
0.029
0.005
0.004
0.033
0.031
0.031
0.033
oksan
-0.008
0.016
0.056
0.048
0.02
0.022
0.036
schmom
0.029
-0.103
-0.035
-0.006
0.012
0.01
0.009
lnpcexp
0.387
0.551
0.064
0.45
0.419
0.421
0.4
_cons
0
-0.87
0
0
0
0
0
Total
0.406
-0.082
0.095
0.501
0.454
0.458
0.451
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Contributions of Differences in Means and in
Coefficients to Poor–Nonpoor Difference in
Mean HAZ
1.50
contribution to gap in HAZ
1.00
lnpcexp
0.50
constant
schmom
0.00
oksan
safwtr
sex
-0.50
lnage
Total
-1.00
-1.50
x's
b's
Cotton
x's
b's
Reimers
x's
b's
Neumark
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Decomposition of differences in
complete distributions
• The standard Oaxaca-type decomposition explains
differences in means
• But differences in other parameters are of interest
e.g. % kids malnourished
• Machado & Mata (2005) show how to decompose
differences in full distributions using quantile
regression
• This has the further advantage of allowing the
effects of covariates to vary across the distribution
e.g. income can have a larger effect at higher than
lower levels of nutrition
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Explaining change in the full distribution
of HAZ in Vietnam b/w 1993 & 1998
.4
Figure 2: Simulated and counterfactual distributions of height-for-age z-scores
children < 10 years, Vietnam 1993 & 1998
1993
1998
.2
0
.1
density
.3
1993 coeffs. & 1998 covariates
-5
-4
-3
-2
-1
0
height-for-age z-score
1
2
3
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity