We identify the causal effect of out-of-school suspensions on student outcomes. Suspension policies are controversial among education policy-makers who seek to balance deterrence and the need for a peaceful classroom against keeping at-risk students in school where they can learn. There is a racial component to this debate, as black students are suspended at much higher rates than white students. Our identification comes from quasi-experimental variation in the impact of a policy change in 2012 in a large urban school district, which eliminated suspensions for minor offenses such as smoking or using obscene language. For the majority of schools, in which suspensions for minor infractions were used extremely rarely, the new suspension policy necessarily had no impact. However, it led to a sharp reduction in the total suspension rate in schools that had previously used them. Despite the strong association in our data between low test scores and high rates of suspension for minor offenses, our quasi-experimental results for students in grades 6 to 8 indicate that the policy change had no causal impact on test scores. This remains true when the sample is restricted to black students, or students who had been suspended in the past. Our calculations therefore suggest that differences in suspension rates for minor offenses are unlikely to contribute meaningfully to the racial achievement gap observed in our sample.