models underlie both these measures and allow for Shapley decompositions of the factors contributing to the inequality measured by the dissimilarity index.

# _3.1 Descriptive Analyses_

The descriptive analyses of the state of ECD for each indicator are based on the mean value of an outcome for a population, specifically the average share or percentage experiencing that outcome. For instance, we calculate the percentage of children who are stunted in Morocco by taking the mean (average) of stunting across children. A similar method is used to assess the relationship between different indicators and background characteristics (circumstances). The average outcome for subgroups is calculated, for instance the percentage of girls stunted or the percentage of boys stunted. Sample weights are used throughout all the analyses to make statistics nationally representative.

# _3.2 Regression Analyses_

Underlying the calculation of the dissimilarity index and the calculation of the least advantaged/most advantaged simulations are regression analyses. Regression analyses are used to estimate how a particular circumstance—for instance, mother’s education—is related to an outcome while taking account of other characteristics such as household wealth. All the outcomes in this paper are binary—only values of 0 (no) or 1 (yes)—so we use a logit model to estimate the effects of circumstances on ECD outcomes. These regression analyses are not presented but underlie the least advantaged/most advantaged simulations and dissimilarity index calculations.

# _3.3 Dissimilarity Index_

Inequality in each ECD outcome is quantified with the dissimilarity index (D-index), which is commonly used to assess inequality in a binary outcome (de Barros, Ferreira, Vega, & Chanduvi, 2009; de Barros, Vega, & Saavedra, 2008). The D-index is derived by comparing group means for different combinations of circumstances to the population mean to quantify how outcomes differ by circumstances. The D-index for an ECD outcome can be calculated as, � (1) ��<sup>1</sup> �|�� ��̅| 2�̅ �� ���

where �̅ is the population mean for an outcome and �� is the mean for unique circumstance group _i_ .<sup>20</sup> The �� are population shares or sampling weights (de Barros, Ferreira, Vega, & Chanduvi, 2009). The D-index can be interpreted as the percentage of available opportunities (an outcome) that would have to have been allocated differently, that is redistributed from the children in groups that are better off to the children in groups that are worse off, for children to have had equal chances of an ECD outcome across groups (de Barros, Ferreira, Vega, & Chanduvi, 2009). When expressed as a percentage, the D-index ranges from 0 to 100, with 0 indicating a situation of equal chances across circumstances. We estimate the D-index based on the logit model discussed in the regression analyses section. The predicted probabilities of an outcome for each unique combination of circumstances are used as ��, the mean for unique circumstance group _i_ .<sup>21</sup>

> 20 It should be noted that for the D-index calculations (but not elsewhere) we reverse our coding of some variables so that we are assessing inequality in the optimal outcome (thus, not dying in the first year of life, rather than dying in the first year of life, and so on), to maintain comparability across both negative and positive outcomes.

> 21 We implement the D-index in STATA using the module hoi (Azevedo, Franco, Rubiano, & Hoyos, 2010).

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