We use a migration lottery program to overcome the double-selectivityproblems posed by migration. We compare a wide range ofoutcomes for the remaining household members of Tongan emigrantswith those of members of similar households who were unsuccessful inthe lottery, with the policy rules determining which household memberscan move. Multiple hypothesis testing procedures are used to examinerobustness. The overall impact on households left behind is largely negativein terms of resource availability, and both sources of selectivity matter,leading studies that fail to address them adequately to misrepresentthe impact of migration on households.