We provide evidence that most Mexican children exposed to the international migration of their fathers experience further variations in their living arrangements, or the dissolution of the marital union of their parents. Children left behind typically join the household of their maternal grandparents. These changes have relevant implications for the analysis of the effects of migration and remittances: they interfere with the identification of instances of paternal migration in standard cross-sectional or longitudinal surveys, and they can give rise to heterogeneity in the effects of interest making some key household-level variables endogenous with respect to the treatment.