circumstances, which defines the groups between which the equality of opportunities is examined, is necessarily limited by the information that is available from surveys. To consider just a few examples, as indicated above, access to opportunities for a child may be influenced to some extent by the child’s ethnic group or tribe at birth. However, because ethnic and tribal affiliation is not included in the household surveys (for sensitivity reasons), this characteristic cannot be incorporated as a circumstance in the analysis. Information on the region where the child is located, wherever available, has been used as an extremely rough proxy to compensate for the absence of information on ethnicity. Another example: even when a timely record of vaccinations is critical for the health of children, this information is not provided by respondents in the household surveys. Given that the list of circumstances cannot be completely comprehensive, the HOI that is computed using just the available circumstances would serve as a theoretical “upper bound” (Paes de Barros et al. 2008).<sup>18</sup> This means that adding the important circumstances currently missing would very likely _add_ to the penalty for inequality and drive the HOI downward. In simple terms, the “true” HOI, if one could obtain that, would not show a picture that is better than what the HOI, based on limited information, suggests.

Only children under the age of 18 years are considered for all the opportunities studied. As discussed earlier in this paper, focusing on the children and young individuals obviates the need to make the distinction between access and utilization related to effort, attitudes, or preferences of the child or the child’s parents. Assuming that children do not take any part in decisions associated with his or her health care or education is not free of caveats, however. Personal maturity and family dynamics may make this generalization troublesome, more so as an individual approaches the age of majority. Furthermore, education in many countries is mandatory only until the age of 14, increasing the probability of teenagers engaging in labor activities, and, therefore, having perhaps more say in household decision making. These considerations are typically assumed away for simplicity. Similarly, household preferences (not only children’s) may play a significant role in decision making, but they are typically simplified in the HOI analysis. For example, a child may have access to a school at a reasonably close location, but may not attend school because the parents do not value education or because the school is of a low quality. In such instances, that child will be treated as having no access to school. If this is a basic service, society must ensure that the child uses the service, which might entail not only having a school nearby, but also maintaining schools at a satisfactory level of quality or requiring obligatory attendance. In such cases, the HOI measure will overestimate the extent of inequality of opportunities, counting such households as failing to access the public service when, in fact, they do not want to use the existing services.

> 18 While this theoretical property may not always hold when the HOI is estimated from a logistic regression as it is done in most cases, it would be rare to find cases where adding a circumstance would actually increase HOI.

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