This paper reexamines the literature on the impact of migration on household members left behind at origin. The empirical problem previous studies address is the self-selection of households into migration, i.e. the endogenous decision as to whether or not send a migrant. Yet, the subsequent selection of which family members migrate and which stay behind generates additional identification problems that have remained largely ignored. To tackle this second form of selectivity within the households, I model the behavior of families using latent stratification and potential outcome (Imbens and Angrist, 1994; Rubin, 1974). I show that the point-identification of the causal impact of migration requires strong behavioral assumptions rarely satisfied even with ideal experimental data. As a practical solution, I derive non parametric bounds under different sets of weaker assumptions. Using Mexican panel data, I show that standard estimates ignoring the intra-household selection into migration may suffer from substantial bias.
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