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Econometric approaches to measuring child inequalities in MENA International Experts Conference, UNICEF
Rabat, Morocco 22-23 May 2012 Nadia Belhaj Hassine
nbelhaj@idrc.org.eg
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Inequality & Equity Inequality of outcomes along economic dimensions Inequality of outcomes along non-economic
dimensionsInequality of opportunity: A parametric approachInequality of opportunity: A non-parametric approach
Presentation Outlines
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Inequality:
Focus is on how equal is the distribution of some economic and non economic dimensions of welfare (ex-post realization)
Equity (or Inequality of Opportunity):
Focus is on the ex-ante potential to achieve welfare outcome.Usual measures of inequality (Gini, Theil etc.) fail to capture deeper layers of inequality that may account for the sense of unfairness in Arab countries where the level of inequality is moderate. Understanding the sources of inequality is important for devising policies that address its underlying causes, especially the role of unequal opportunities.
Inequality & Equity
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Child inequalities can be measured along income,
wealth or expenditures of the household:Define & harmonize the well-being indicator: Inequality
measures are sensitive to the items included in the
expenditure aggregates: apples need to be compared to
apples.
Adjust for HH composition: equivalence of scaleAdjust for spatial and temporal price differences
Inequality of Outcomes Along Economic Dimensions
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Lorenz CurveGini IndexGeneral Entropy: GE(0), GE(1), GE(2)GE indices are decomposable into within group and between group measures of inequalityk groups in a population (identified by location, education, gender , etc.)
within between ϕ(k) is the proportion of the population in group kμk is the mean income of group kGE(k;θ) is the GE index of group k
is the GE index of the population if each member of group k was assigned income μk
Common tools to measuring inequality
GE() (k)k
k1
K
GE(k; )G E ( )
G E ()
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Inequality Determinants
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Standard decomposition techniques identify potential determinants of
inequality …and lay the foundation for deeper analysis.
An important limitation of summary measures of inequality and standard
decomposition techniques is that they provide little information
regarding what happens where in the distribution.
Inequality Determinants
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Use the Recentered Influence Function (RIF) regression by
Firpo, Fortin, Lemieux (2010) to decompose the welfare
gaps at different quantiles of the unconditional distribution
into the part explained by the difference in the distributions of
observed household characteristics (between regions,
urban-rural, over time etc.) and the part that is explained by
the difference in the distributions of returns to these
characteristics.
These components are then further decomposed to identify the
specific characteristics which contribute to widening the
welfare gap.
Unconditional Quantile Regression Decomposition
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The procedure is carried out in two stages:
1. Construct a counterfactual distribution of rural log well-being (the distribution that would have prevailed if rural HH have received the same returns to their characteristics as urban ones): F(y* X∣ U, βR)
y is log well being, X is the distribution of covariates, and β is the marginal effect of X on quantile qτ (returns) at the various quantiles.
• Use the kernel smoothing technique to estimate urban and rural log-welfare
distributions and compute welfare gap at each quantile
• Estimate the RIF unconditional quantile regressions for urban, rural and counterfactual welfare distributions:
• (Yk ; τ ) = X k k k= u,r
• (Yk ; τ ) is the RIF estimate for the τ th quantile,
Unconditional Quantile Regression Decomposition
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2. Decomposition:
τ (YU)− τ (YR) = X U U -X R U + X R U -X R R = (X U -X R U + X R (U -R)• The first term is the is the endowment effect: the contribution of the
HH characteristics to the welfare gap at the τ th quantile; the second is the return effect: the contribution of the difference in returns to the urban–rural gap
• the endowment effect and the return effect can be further decomposed into the contribution of individual explanatory variables to identify the specific characteristics, differentiated across Rural and Urban HH, which lead to the widening of welfare gap.
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Expenditures and summary measures of inequality ($PPP Cst 2004)
Food Expenditure Expend. Food & Non Durables Total Expenditure Mean Median Gini Theil Mean Median Gini Theil Mean Median Gini TheilEgypt
2000 49.42 42.03 0.26 0.12 93.93 71.87 0.33 0.23 104.69 80.22 0.34 0.242005 51.18 44.24 0.26 0.12 94.05 74.8 0.32 0.2 107.71 85.57 0.32 0.22009 40.72 35.7 0.26 0.12 85.43 69.28 0.31 0.19 101.23 80.93 0.31 0.2
Iraq 2007 47.06 39.92 0.31 0.17 101.1 80.08 0.36 0.23 148.82 114.58 0.37 0.26
Jordan 2006 62.53 51.89 0.33 0.21 156.42 123.71 0.34 0.21 196.39 151.4 0.36 0.242008 66.91 56.27 0.31 0.17 158.19 126.75 0.33 0.19 195.87 153.04 0.34 0.21
Libya 2003 52.08 43.32 0.32 0.19 99.95 84.49 0.31 0.18 136.5 114.43 0.31 0.17
Mauritania 2000 44.12 34.33 0.39 0.28 53.59 40.35 0.41 0.31 55.26 41.38 0.41 0.322004 94.77 59.79 0.48 0.46 118.72 80.32 0.45 0.4 121.48 81.32 0.45 0.41
Palestine 1996 43.71 37.88 0.29 0.15 107.3 87.22 0.35 0.22 134.3 106.2 0.35 0.232009 43.18 35.88 0.32 0.19 121.5 94.83 0.36 0.24 151.5 114.1 0.38 0.26
Syria 1997 51.79 43.99 0.29 0.15 83.27 68.42 0.32 0.19 83.67 68.72 0.32 0.192004 80.55 65.27 0.33 0.19 144.6 108.5 0.38 0.27 165.5 126.6 0.36 0.25
Tunisia 2005 72.72 60.56 0.33 0.21 162.6 120.1 0.41 0.3 210.5 153.4 0.41 0.33
Yemen 1998 49.69 41.71 0.33 0.18 90.1 74.51 0.33 0.2 102.3 77.5 0.38 0.282006 33.02 27.47 0.33 0.2 66.57 50.55 0.38 0.32 78.27 55.27 0.42 0.43
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Standard Decomposition by HH attributes Education Gender Age Emp.stat. Fam. type Marital Region Urban/RuralEgypt
2000 27.00% 0.10% 0.80% 1.30% 18.30% 0.80% 26.50% 20.50%2004/5 24.30% 0.60% 2.00% 1.80% 19.40% 1.90% 22.00% 18.00%2008/9 23.20% 0.40% 1.90% 2.10% 19.80% 0.90% 19.90% 17.70%
Iraq 2007 4.40% 0.10% 0.20% 1.90% 16.20% 0.70% 19.40% 8.50%
Jordan 2002 17.40% 0.60% 3.80% 2.50% 23.60% 2.00% 9.70% 2.50%2008 15.40% 1.00% 6.90% 6.20% 24.60% 2.10% 11.90% 3.40%
Libya 2003 2.10% 1.00% 4.10% 0.10% 29.70% 2.10% 0.90% 0.30%
Mauritania 2004 4.10% 0.10% 1.20% 1.00% 9.70% 0.20% 0.40% 0.60%
Palestine 1996 8.10% 0.20% 0.60% 2.70% 19.80% 1.30% 7.30% 11.80%2009 5.80% 0.70% 4.30% 3.60% 18.90% 1.70% 4.50% 0.60%
Syria 1997 3.10% 0.40% 1.50% 1.30% 14.90% 0.90% 0.70% 0.80%2004 4.70% 3.40% 4.40% 6.00% 26.40% 6.90% 4.40% 6.00%
Tunisia 2005 22.20% 0.10% 0.70% 2.20% 8.80% 11.50%
Yemen 1998 9.40% 0.00% 1.10% 1.50% 11.70% 0.30% 12.60% 11.60%2006 7.30% 0.30% 0.40% 0.40% 8.50% 0.90% 7.00% 10.60%
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Education, family type and regional location of the HH are the most important determinants of overall inequality.
Slight decline over time of the importance of Head educational attainment as a determinant of inequality
Signs of income convergence between urban and rural areas and across regions in Egypt and Yemen.
The evaluation of between groups inequality against the maximum benchmark proposed by Elbers et al. 2007 confirm the consistency of these results.
Between-Groups Decomposition
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-.20
.2.4
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Diff
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.1 .2 .3 .4 .5 .6 .7 .8 .9Quantiles
Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Area for Egypt 2000
0.2
.4.6
Diff
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.1 .2 .3 .4 .5 .6 .7 .8 .9Quantiles
Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Area for Egypt 2009
Unconditional Quantile Regression Decomposition
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• Dominance of endowments effects: welfare gap is caused primarily by the fact that urban households have superior characteristics
• Endowment effects and returns effects are both larger at higher quantiles, resulting in a larger urban–rural gap at higher quantiles.
• The Gap decreased over time except for the lowest quantile. The returns effects increased over time while the endowments effects decreased.
Unconditional Quantile Regression Decomposition
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0.2
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Region for Egypt 2000
.1.2
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Region for Egypt 2009
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Area for Syria 2004
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Area for Syria 1997
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Region for Iraq 2007
0.1
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Confidence interval / endowment effect Confidence interval /returns effect Endowment effect Returns effect
Returns effects and endowment effects by Area for Iraq 2007
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Differences in characteristics such as hhsize, source of income and % of child under 14 matter the most important for lowest quantiles, while differences in educational attainment and experience matter much more for those who are well off.
The gap due to differences in educational attainment is decreasing over time while the gap due the returns to education is widening:
Urban markets are now paying more for educational and experience attributes than rural markets would.
Unconditional Quantile Regression Decomposition
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Regional differences in HH characteristics matter more than differences in returns to those characteristics at the bottom of the distribution
At the higher quantiles the welfare gap is caused primarily by the differences in returns, to those characteristics even though Metropolitan HH have superior characteristics.
Convergence of welfare levels between Metropolitan and the other regions despite an increase in the magnitude of the returns effects (returns to education particularly)
Unconditional Quantile Regression Decomposition
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Non-Economic Welfare• Inequality measures can be applied to non-economic
outcomes– Health: Anthropometric measures of child nutrition:
• Weight-for-Height (W/H)• Height-for-Age (H/A)• Weight-for-Age (W/A)
– Education:• Years of schooling• Test scores
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Standardizing the Measures
• Comparison is with distribution in ref. pop. for individuals of same sex and age (in months) or height
• Three ways of comparing to ref. population:– z-score (std. deviation score): difference between value of
indicator and median of reference population divided by std. deviation of reference pop.
– Percent of Median: ratio of value of indicator and median value for ref. pop.
– Percentile rank: rank position of individual on reference distribution expressed as percent of group the individual equals or exceeds
• All three standardized measured are calculated in DHS
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Standardized Indicators
• z-score is preferred:– Allows for calculation of means and std. dev. Of
populations and sub-population, which cannot be done using percentiles
– Changes at the extremes will not be necessarily reflected in changes in percentiles
– Percent of median does not correct for the variability in the reference population
• Criteria for malnourishment when using z-scores– z-score of -2 or lower (two standard deviations below
the reference median) is typical cutoff
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Health Inequality Measures
• Mean health indicator by quintile of an economic welfare measure– Grouped measure of health disparity
• Concentration Curves– Captures how the distribution of the health
variable relates to the distribution of a variable measuring living standards, which ranks individuals from poorest to richest
• Concentration Indices
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Inequality of Education
• Two main measures of education inequality– Standard deviation of schooling measures the
absolute deviation– Education Gini measures relative inequality
• The measure can be used to examine inequality in attainment (years of schooling), financing or enrollment.
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Education Gini• Just like the calculation of any Gini, education Gini can be
calculated as follows if individual data on educational attainment is available
But if only grouped data is available, then
Where pi , pj are the prop. of pop. with level of schooling i, j.yi, yj are the years of schooling for levels i and j
Gini 12n2
y i y jj1
n
i1
n
Gini 12
pi p j y i y jj 1
M
i1
M
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Parametric Approaches to Measuring Inequality of Opportunity
(Roemer 1998)
Outcome (income, education, status…)
Outside the individual control
Inequality due to circumstances: Inequality of opportunity
Effort
Individual responsible choices
Inequality due to effort
Circumstances(race, gender, parents background, region of birth..)
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Simulate the reduction in overall inequality that would be attained if circumstance were equalized. The difference between the observed and the counterfactual inequality is interpreted as a measure of inequality of opportunity.
Bourguignon, Ferreira and Menedez (2007)
Methodology
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The empirical model
The earnings function can be specified in the following log-linear form :
iiii vECy )ln(
iii Cy )ln(
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• The counterfactual distribution is obtained by replacing yi with its estimated value, from the reduce form: ii Cy ˆˆexp~
The empirical model
where I(F) is the inequality measures (Gini, Theil, ..) defined on the outcome distribution.
yFI
yFIyFII
~~
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Total Partial Effects
Total IOP Opp. share Gender Moth.Edu. Fath.Edu. Bir Reg.
2006
Rural 0.404*** 0.030*** 0.075*** 0.006 0.004 0.003 0.031***
(0.061) (0.004) (0.014) (0.035) (0.004) (0.007) (0.003)
Urban 0.423*** 0.086*** 0.203*** 0.060*** 0.050*** 0.063*** 0.046***
(0.028) (0.008) (0.020) (0.010) (0.010) (0.008) (0.009)
Men 0.412*** 0.067*** 0.162*** 0.027** 0.053*** 0.032***
(0.031) (0.007) (0.016) (0.009) (0.012) (0.008)
Women 0.445*** 0.097*** 0.219*** 0.009 0.006 0.005
(0.069) (0.010) (0.039) (0.009) (0.009) (0.010)
Age 29 0.345*** 0.043*** 0.126*** 0.006 0.031 0.018 0.007
(0.042) (0.012) (0.026) (0.018) (0.028) (0.015) (0.013)
Age 44 0.453*** 0.049* 0.108* 0.053* 0.049** 0.065*** 0.052***
(0.047) (0.020) (0.049) (0.021) (0.018) (0.013) (0.010)
Age 45+ 0.381*** 0.032** 0.083** 0.011 0.010 0.020 0.015
(0.047) (0.010) (0.028) (0.008) (0.011) (0.017) (0.012)
Total 0.423*** 0.064*** 0.151*** 0.010 0.018* 0.034*** 0.024**
(0.030) (0.012) (0.029) (0.012) (0.008) (0.008) (0.008)
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.1.1
5.2
.25
.3M
ean
loga
rithm
ic d
evia
tion
1988 1998 2006
parametric CI/parametric
Inequality of opportunity share
3232
Table1. IOP Math Score 2007
Math Score 2007
GE(2) GINI
Total Within Between IOP_res Total Within Between IOP_res
Algeria 0.00926*** 0.00861*** 0.000655*** 0.0699*** 0.0769*** 0.0741*** 0.0202*** 0.0358***
Bahrain 0.0189*** 0.0145*** 0.00446*** 0.235*** 0.111*** 0.0963*** 0.0528*** 0.129***
Palestine 0.0320*** 0.0240*** 0.00835*** 0.253*** 0.144*** 0.124*** 0.0717*** 0.139***
Iran 0.0212*** 0.0142*** 0.00638*** 0.333*** 0.116*** 0.0948*** 0.0645*** 0.185***
Jordan 0.0260*** 0.0194*** 0.00871*** 0.254*** 0.130*** 0.112*** 0.0732*** 0.141***
Kuwait 0.0197*** 0.0152*** 0.00479*** 0.230*** 0.112*** 0.0986*** 0.0545*** 0.123***
Lebanon 0.0111*** 0.00700*** 0.00453*** 0.370*** 0.0850*** 0.0667*** 0.0545*** 0.215***
Morocco 0.0184*** 0.0146*** 0.00425*** 0.205*** 0.109*** 0.0970*** 0.0498*** 0.112***
Oman 0.0277*** 0.0202*** 0.00791*** 0.272*** 0.134*** 0.114*** 0.0706*** 0.150***
Qatar 0.0388*** 0.0263*** 0.0125*** 0.323*** 0.156*** 0.128*** 0.0890*** 0.178***
Saudi Arabia 0.0216*** 0.0156*** 0.00588*** 0.280*** 0.118*** 0.0995*** 0.0612*** 0.155***
Syria 0.0175*** 0.0134*** 0.00444*** 0.236*** 0.106*** 0.0921*** 0.0534*** 0.131***
Tunisia 0.0105*** 0.00775*** 0.00275*** 0.262*** 0.0821*** 0.0704*** 0.0417*** 0.143***
Turkey 0.0306*** 0.0187*** 0.0112*** 0.388*** 0.140*** 0.109*** 0.0839*** 0.219***
Egypt 0.0267*** 0.0178*** 0.00880*** 0.333*** 0.132*** 0.107*** 0.0750*** 0.188***
Dubai 0.0216*** 0.0132*** 0.00929*** 0.387*** 0.118*** 0.0917*** 0.0772*** 0.222***
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0.2
.4.6
Gen
eral
Ent
ropy
GE(
2)
Algeria Morocco Kuwait Bahrain Syria Palestine Jordan Tunisia Oman S.Arabia Qatar Iran Egypt Lebanon Dubai Turkey
Total Girl
Boy CI/Total
CI/Girl CI/Boy
Math Scores (parametric)Share of Inequality of Opportunity TIMSS 2007
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Total Inequality
Egyp...
Egyp
...
Egyp...
Egyp...
Egyp...
Egyp...
Egyp
...0.000
0.001
0.002
0.003
0.004He
ight
Ineq
ualit
y
0
0.001
0.002
0.00300000000000001
0.00400000000000001
Heig
ht In
equa
lity