mother suffers a loss of private consumption that is larger than that suffered from a migrant father.<sup>17</sup> The estimates may be biased by _selection into migration_ if households that choose to send one of the spouses away for migration systematically differ from nonmigrant households in terms of spouses’ preferences.<sup>18</sup> Indeed, figure 1 suggested that, if the returns to migration are not high enough, a mixed migration portfolio may not be optimal if either of the spouses was excessively selfish, that is, if either _α_ or _β_ were particularly high. In this sense, the estimated difference would be a _lower bound_ of the actual difference between men’s and women’s generosity toward children.<sup>19</sup> That women have stronger preferences for consumption on common goods than men has been highlighted by many studies: Thomas (1990), Lundberg et al. (1997), Duflo (2003), Qian (2008), and Ashraf (2009) all show that income accruing to women generates larger benefits for children than that accruing to men. Unfortunately, it is generally difficult to compare the magnitude of these estimates with those found in this paper because in most cases both the outcome and the explanatory variables are defined differently. Yet there are at least three papers that contain comparable estimates as they use as outcome variables the shifts in the shares of household expenditure. Aggregating their shares in a way that is comparable to the one used in this paper, Hoddinott and Haddad (1995) show that the shares of the household budget allocated to adult goods are between 3.2 and 6.6 percentage points lower in the case in which the woman earns the whole household budget with respect to the case in which it is the man. Similarly, Attanasio and Lechene (2002) find 17 An alternative mechanism underlying these results could be that women and men, when migrating, change their preferences over investment on children. Specifically, if women experienced very low returns to education when migrating, relative to what they observed before migrating, it may be that they decide to invest less on children’s education. This would explain the result that investments on children’s education are not affected by female versus male migration. To rule out this mechanism, I computed returns to education at each counterfactual destination and compared them to returns to education in the migrant’s home village. Results are reported in table S.4 in the supplemental appendix and show that there is no significant difference between returns to education observed in the home village and those observed by the migrant at destination. It is thus unlikely that the pattern of results observed can be explained by changes in preferences over investment on children’s human capital generated by the different migration experience of men and women.

18. Another source of selection bias may be due to differences between migrants who bring their children along and those who leave them behind. Table S.1 in the supplemental appendix shows that these are very similar, the only significant difference being the level of education, which is controlled for in all specifications.

19 Tables S.2 and S.3 in the supplemental appendix report the results of two different empirical specifications which are meant to account for _selection into migration_ . The first is panel fixed effect estimation in which I distinguish the effect of having one spouse away from that of having the mother instead of the father. The estimates show that households with migrant mothers still spend significantly more on adult goods. The difference (+6%) is smaller but not statistically different from that of table 11. Table S.3 in the supplemental appendix, instead, reports the estimates of a three-stage estimation (Wooldridge 2010) in which risk aversion is used in a first stage as instrument for selection into migration, and then, in a second stage, the usual instruments are used to correct for selection into female migration and the Inverse Mills Ratio from the first stage is included. Unfortunately, the inclusion of the IMR, weakens the instruments so that the final coefficients are very imprecisely estimated. The coefficient for adult goods yet is now considerably larger in magnitude.

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