penalty of all location circumstances (jointly) on the same HOIs, and in four cases this ratio is fourfold or larger. The only two exceptions to the joint dominance of demographic circumstances occur for sanitation and non-underweight. This is particularly important for sanitation, for which the ratio of the inequality penalty of location circumstances is 2.6 times the penalty associated with demographic circumstances. The fact that the _joint_ unequalizing effect of demographic circumstances is significantly larger than the average of the unequalizing effects of demographic circumstances considered _one by one_ suggests that there is some degree of (perverse) complementarity between unfavorable circumstances. That is to say, a household with two or three unfavorable circumstances would be subject to disproportionate penalties in its access to basic human development opportunities, well beyond the _linear_ proxies given by the IOC matrix.<sup>38</sup> _The Importance of Specific Circumstances across Sectors._ In order to understand whether certain circumstances are more unequalizing within some sector than in others, the same methodology used in the previous sub-section can be applied to analyze the IOC matrix _by sector_ . Table 8 reports, for 2000 and around 2009, the average inequality penalties for the HOIs _within each sector_ , and for each circumstance. Each row lists one of the four sectors and each column corresponds to one of the eight circumstances. In each row the cells corresponding to the three most unequalizing circumstances are highlighted, and additional cells are highlighted if they exceed the mean inequality penalty of the period.<sup>39</sup>

**Table 8. Analysis of the IOC Matrix: Inequality of Opportunity by Circumstance -IOC- within Sectors, Egypt, 2009 ***

|_Sector of opportunities \_<br>_circumstances_|_Gender_|_Number of_<br>_children_|_Presence of_<br>_elderly_|_Presence of_<br>_parents_|_Parents_<br>_Education_|_Income per_<br>_capita_|_Urban-rural_<br>_location_|_Regional_<br>_location_|_Mean_|
|---|---|---|---|---|---|---|---|---|---|
||||||_2009_|||||
|Education HOIs|**_1.5_**|**_3.2_**|**_1.6_**|**_1.5_**|**_5.5_**|**_2.7_**|**_1.7_**|**_2.0_**|**_2.5_**|
|Basic housingservices HOIs|0.9|**_2.1_**|0.9|0.9|**_2.1_**|**_2.7_**|**_4.6_**|**_2.7_**|2.1|
|Earlychildhood development HOIs|0.3|**_1.4 _**|0.2|0.0|0.8|**_2.9_**|0.3|**_1.5_**|0.9|
|Nutrition HOIs|0.7|**_1.6_**|0.1|0.1|0.9|**_1.4_**|0.6|**_1.5_**|0.9|
||||||_2000_|||||
|Education HOIs|0.5|**_1.6_**|0.1|0.0|**_2.2_**|0.5|0.7|0.5|0.8|
|Basic housingservices HOIs|0.0|**_2.6_**|0.3|0.0|**_2.6_**|**_2.5_**|**_3.3_**|**_2.3_**|1.7|
|Earlychildhood development HOIs|0.3|**_1.1_**|0.1|0.4|**_1.4_**|**_3.2_**|0.9|**_1.2_**|1.1|
|Nutrition HOIs|0.5|**_1.9_**|0.3|0.2|**_0.9_**|**_1.9_**|0.1|0.6|0.8|

_Note_ : * Each cell reports the mean of {IOCs} by sector for each circumstance. See Tables A.7 a, b, c and d in the Appendix. _Source_ : HIECS 2000 and 2009 surveys, EDHS 2000 and 2008, and authors’ calculations.

_Education_ . The first row in Table 8 shows the marginal effects of circumstances on education opportunities in 2009. The figures presented in the education row indicate that in this sector _all eight_ circumstances are significantly unequalizing, with _parents’ education_ being the most important (nearly twice the inequality penalty of other circumstances), followed by _number of children_ in the household and income per capita. These results suggest that, for education opportunities in 2009, all differences in circumstances matter for inequality of opportunities. It must be noted that this pattern differs from the situation in 2000, when only _two_ circumstances were significantly influential – parents’ education and number of children – and the inequality of

> 38 The Shapley decomposition presented below captures the correlation across circumstances and the results indicate that the number of most influential circumstances is smaller.

> 39 Reference values for the mean inequality penalty are 1.8 in 2009 and 1.2 in 2000.

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