An influential strand of research has tested for the effects of immigration on natives’ wages and employment using exogenous refugee supply shocks as natural experiments. Several studies have reached conflicting conclusions about the effects of noted refugee waves such as the Mariel Boatlift in Miami and post-Soviet refugees to Israel. We show that conflicting findings on the effects of the Mariel Boatlift can be explained by a large difference in the pre- and post-Boatlift racial composition in subsamples of the Current Population Survey extracts. This compositional change is specific to Miami, unrelated to the Boatlift, and arises from selecting small subsamples of workers. We also show that conflicting findings on the labor market effects of other important refugee waves are caused by spurious correlation between the instrument and the endogenous variable introduced by applying a common divisor to both. As a whole, the evidence from refugee waves reinforces the existing consensus that the impact of immigration on average native-born workers is small, and fails to substantiate claims of large detrimental impacts on workers with less than high school.