When a random sample is not random: Bounds on the effect of migration on household members left behind

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. Since estimation is typically based on source country data, invisible sample selection yields biased estimates if all-move households differ from households that send only a subset of their members abroad. I address this identification problem and derive nonparametric bounds within a principal stratification framework. Instrumental variables estimates are biased, even if all-move households do not differ in their potential outcomes. For this case, I derive a corrected instrumental variables estimator. I illustrate the approach using individual and household data from widely cited, recent studies. Potential bias from invisible sample selection can be large, but transparent assumptions regarding behaviors of household members and selectivity of migrants allow identification of informative bounds.