When a Random Sample Is Not Random: Bounds on the Effects of Migration on Household Members Left Behind

Abstract

A key problem in the literature on the economics of migration is how emigration of an individual affects households left behind. Answers to this question must confront a problem I refer to as invisible sample selection: when entire households migrate, no information about them remains in their source country. This problem occurs in addition to the question of selection of households into migration, i.e., which households send any migrants. This paper uses principal stratification to address both identification problems simultaneously for a setup with an instrumental variable for the migration of the principal migrant. I derive nonparametric bounds on the effect of migration on remaining household members under varying assumptions and discuss the assumptions implicitly made when the problem is ignored. Building on two widely cited studies, I show that transparent assumptions regarding the behavior of household members and selectivity of migrants allow identification of informative bounds but also that not adjusting for invisible selection may result in substantial bias.