The model presented above is estimated by a probit regression when considering literacy, primary school completion, and secondary school completion as ����, and by a linear regression analogous to difference-in-differences when using years of education as the dependent variable. In the latter case, �� measures the difference in average years of education between nonindigenous men and nonindigenous women, while in the former case the marginal effect of �� indicates the difference in the likelihood that a nonindigenous woman will be literate or have completed primary or secondary education relative to a nonindigenous man. In addition, in the probit models, the signs of a coefficient and of its respective marginal effect are the same, so that, when using any of the four dependent variables, �� �0 indicates that non-indigenous women have a lower expected education outcome than non-indigenous men, all other things equal. The differentiated impacts of ethnic groups, similarly, are captured by ��, �� and �� (or the associated marginal effects), which measure the role of being Aymara, Quechua or other indigenous group on educational outcomes, respectively.

The cumulative impacts of gender and ethnicity on educational outcomes are captured by the interaction terms, with �� (or the associated marginal effect) showing the _additional_ effect of being both female and Aymara on education outcomes (�� ∗�� �1 ⇔�� �1 ∧ �� �1). That is, in the linear model, the difference in years of education (controlling for age, age-squared, and place of birth) between Aymara women and nonindigenous men is �� ��� ���, while the gap between Quechua women and nonindigenous men is �� ��� ���. For women that belong to other indigenous groups, it is �� ��� ���. So, if �� is statistically significant and has the same sign as �� ���, then the cost (benefit) of being an Aymara woman is greater than the cost (benefit) of just being a woman, plus the cost (benefit) of being Aymara. In other words, there is a unique experience at the intersection of the two identities. The same holds for �� with respect to Quechua women and for �� with respect to other indigenous women.

Each of the four models discussed above are estimated separately for different age cohorts, allowing for the fact that penalties for gender, ethnicity, and their intersectionality may change over generations. In addition, separate analyses by cohort allow the province coefficients to vary over age groups, accounting for differences in the pace of change by location. Given the structure of the census data, the errors �� are clustered at the household level.

# **4. Results**

The regression results are presented in four figures, as they are easier to visualize, showing not only the relative magnitude of each coefficient, but also trends over different age cohorts across different subgroups. The full regression results, including a summary table showing the comparable sizes of cumulative educational disadvantages of females from different ethnic groups and age cohorts (relative to nonindigenous men), are presented in Appendix B. Across models, almost all of the estimated coefficients are statistically significant at the 99 percent confidence level. It is important to recall that the coefficient estimates and associated marginal effects are based on the full census data, and as such, they are not prone to questions of external validity.

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