We estimate peer effects for fourth graders in six European countries. The identification relies on variation across classes within schools, which we argue are formed roughly randomly. The estimates are much reduced within schools compared to the standard ordinary least squares (OLS) results. This could be explained either by selection into schools or by measurement error in the peer variable. Correcting for measurement error, we find within‐school estimates close to the original OLS estimates. Our results suggest that the peer effect is modestly large, measurement error is important in our survey data, and selection plays little role in biasing peer effects estimates.