son preference in education.<sup>16</sup> A substantial body of evidence for the relevant cohorts in Indonesia shows higher returns to education for girls (e.g., Deolalikar (1993), and Behrman and Deolalikar (1995)), and thus rejects the labor market based explanation. This leaves gender norms as a plausible mechanism which we test using data from the matrilineal island West Sumatra, the home to the largest matrilineal tribe in the world (Minangkabau). If the crowding out observed at the national level is driven by gender bias against girls in the patrilineal islands, then we should not observe any crowding out of girls at the secondary level in the matrilineal island which is conrmed by the estimates.<sup>17</sup> Instead, the boys face signicant crowding out in matrilineal West Sumatra.

Fifth, our estimating equations use years of schooling and primary completion, based on the recent quadratic mobility models developed by Becker et al. (2015), and Becker et al. (2018). We also provide evidence on alternative models of mobility, based on years of schooling normalized by its standard deviation and schooling ranks.<sup>18</sup> We nd that the conclusions regarding the impact of Inpres schools on relative and absolute mobility of sons and daughters do not change substantially when we use the normalized model.<sup>19</sup> But the conclusions from the rank-rank mobility model are dierent, with no signicant eects of school construction even for sons. We discuss how to interpret such conicting evidence and provide guidance for advising policymakers.

The analysis and conclusions of this paper have wider implications. The evidence that the eects of government policies on relative mobility can be fundamentally dierent (with dierent signs) across educated and uneducated households is of more general interest. It underscores the importance of testing the default linear functional form of the mobility equation

> 16There is a growing recognition among economists that social norm is a rst order factor for understanding the persistent biases faced by women in many developing countries (Jayachandran (2015)).

> 17We underscore here that we are concerned with gender norms for the 1950s to 1960s birth cohorts. Even though evidence suggests no signicant gender bias in education in the recent decades in Indonesia (Afkar et al. (2020)), our ndings about gender bias in these older cohorts are consistent with other available evidence. For example, Maccini and Yang (2009) nd that girls' health and schooling outcomes in these cohorts were sensitive to early life rainfall shocks, but parents eectively insured the boys against such shocks, suggesting strong son preference.

> 18Following the inuential work on the rank-rank model for income mobility by Chetty eat al. (2014), many authors are increasingly adopting a rank-rank specication for intergenerational educational mobility (see, for example, Neidhofer et al. (2018), Hilger (2015), Asher et al. (2023)). This, however, ignores the fact that, unlike income, education is a discrete variable with limited support. For a discussion on the diculties in adopting the rank-rank model for education, see Ahsan et al. (2022).

> 19Relative mobility is measured by Pearson correlation in the normalized model.

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