children may suffer a more severe emotional loss (Cortes 2015); finally, because men and women have different preferences over investments on children (Thomas 1990; Duflo 2003; Qian 2008), so that the change in the structure of the household induced by migration of one of the spouses is likely to have different effects depending on who migrates and who stays.<sup>4</sup> The present paper moves in the latter direction and complements the existing literature by investigating the allocation of resources within the household in order to understand whether spousal migration generates diversions of the household budget that affect children.

Answering this question requires understanding what are the determinants of female migration. The few existing papers that investigated this aspect seem to suggest that female migration would be a means to provide the family left behind with a more stable and reliable source of income than what would be in case of male migration, this would happen because the jobs chosen by migrant women are typically less risky than those chosen by men (Lauby and Stark 1988) and because women are intrinsically more attached to the family left behind and thus tend to send more remittances (de la Briére et al. 2002). Building on this literature, I propose a sequential model in which first the two spouses cooperatively decide who should migrate so as to maximize the expected returns from migration while minimizing the associated risk, second, the migrant spouse chooses how much to send back home through remittances, and finally the spouse left behind chooses how to allocate the available household budget across different commodities. The resulting subgame perfect Nash equilibrium will be one in which diversions of the budget off of children-related expenditures are offset by a strategic change in the amount of remittances that the migrant sends back, so that the share of budget devoted to childrenrelated expenditures is the same no matter whether it is the mother or the father that migrates, even if the two have different preferences over investments on children.

The empirical analysis, based on Indonesian data, shows indeed that, when the mother migrates and the husband is left behind with the children, the share of income spent for exclusively adult goods increases but that devoted to children-related expenditures does not change significantly. The results are obtained through a two-stage least squares estimation procedure that exploits a set of instrumental variables derived from the theoretical setup, that is, the expected value and volatility of previous migrants’ earnings. Note that these results do not necessarily imply that children are no worse off when left behind with the father instead of the mother because other mechanisms, different from that of the allocation of the budget may play a crucial role; to shed light on this, I further estimate the effects of maternal versus paternal migration on children’s health and education indicators and find no difference in health measures but a significant decrease in the amount of time spent at school for children left with their fathers mirrored by an increase in the amount of time devoted to housework. This type of disruptive effect is likely to explain the result found by Cortes (2015) that children of migrant mothers are more likely to lag behind at school than children of migrant fathers.

> 4 A similar reasoning has been applied to the case in which one of the spouses passes away by Gertler et al. (2004).

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