This article uses a replication experiment of ninety-four specifications from sixteen different studies to show the severity of the problem of selection on unobservables. Using a variety of approaches, it shows that membership in the General Agreement on Tariffs and Trade/World Trade Organization has a significant effect on a surprisingly high number of dependent variables (34 per cent) that have little or no theoretical relationship to the WTO. To make the exercise even more conservative, the study demonstrates that membership in a low-impact environmental treaty, the Convention on Trade in Endangered Species, yields similarly high false positive rates. The authors advocate theoretically informed sensitivity analysis, showing how prior theoretical knowledge conditions the crucial choice of covariates for sensitivity tests. While the current study focuses on international institutions, the arguments also apply to other subfields and applications.