The impacts of international migration on development in the sending countries, and especially the effects on remaining household members, are increasingly studied. However, comparisons of households in developing countries with and without migrants are complicated by a double-selectivity problem: households self-select into migration, and among households involved in migration, some send a subset of members with the rest remaining whilst other households migrate en masse. We address these selectivity issues using the randomization provided by an immigration ballot under the Pacific Access Category (PAC) of New Zealand's immigration policy. We survey applicants to the 2002-05 PAC ballots in Tonga and compare outcomes for the remaining household members of emigrants with those for members of similar households who were unsuccessful in the ballots. The immigration laws determine which household members can accompany the principal migrant, providing an instrument to address the second selectivity issue. Using this natural experiment we examine the myriad impacts that migration has on remaining household members, focussing on labor supply, income, durable assets, financial service usage, diet and physical and mental health and use multiple hypothesis testing procedures to examine which impacts are robust. We find the overall impact on households left behind to be largely negative. We also find evidence that both sources of selectivity matter, leading studies which fail to adequately address them to misrepresent the impact of migration.