engaged in new internal migration over this 4-year period. With international migration, even fewer households are likely to change status, reducing statistical power and requiring large samples. The second question is who are these households that change migration status, and in particular, are the impacts of migrating different for them than for those who do not change migration status? In equation 4, we had written the impact of migration, _β_ , without any subscript. But in practice, the impacts may be heterogeneous, and so the causal impact identified by fixed effects may differ from the average treatment effect. This point has been part of an important recent debate in the literature about the extent to which there is mis-allocation of labor through too little rural-to-urban migration. Incomes and productivity are much higher in urban areas than rural areas in many developing countries. However, using panel data from Kenya and Indonesia, Hamory et al. (2021) find the wage gains from moving to be relatively small. One potential explanation is that the individuals who would gain most from moving are constrained by lack of information, networks, or wealth, and so, since they are never observed to migrate, do not contribute to the estimate of the migration impact. The large gains in income seen by Baseler (2021) in a randomized experiment which provides information is consistent with this viewpoint.

The third, and most critical, question for the use of fixed effects is what caused some units to suddenly change their status? That is, our concern is that For example, in the Chen et al. (2009) study, we might be concerned that households experienced a shock that both affected their desire to migrate and the educational performance of their children. For example, a child may experience a negative health shock, which might reduce their performance in school, and entail large health expenditures in the household and less money to spend on education. A household member may then migrate to earn additional income to pay these expenses. Such an effect would bias the effect of migration downwards, since it is occurring due to shocks that also reduce educational outcomes. Conversely, there could be other omitted variables causing the change in migration that result in a positive bias. For example, the unobserved change could be that a relative outside the household gets an opportunity to migrate overseas. This relative could provide information or financial assistance to a household member to migrate. But that outside relative might also send remittances to the household, which could be spent on schooling and tutoring. If these remittances are unobserved, they would be an omitted variable leading the estimated effect of migration on child schooling to be biased in a positive direction.<sup>8</sup> The migration

> 8Even if remittances are observed in the data, simply controlling for remittances would be an imperfect solution, for a few reasons. First, remittances are typically not recorded in datasets in sufficient detail to allow separately controlling for remittances from non-household members and household members. One would want to control only for remittances from non-household members in this case. Second, if there is measurement error in remittances, they would only imperfectly control for this omitted variable, allowing

18