We estimate peer effects for fourth graders in six European countries. The identification relies on variation across classes within schools. We argue that classes within primary schools are formed roughly randomly with respect to family background. Similar to previous studies, we find sizeable estimates of peer effects in standard OLS specifications. The size of the estimate is much reduced within schools. This could be explained either by selection into schools or by measurement error in the peer background variable. When we correct 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. We find no significant evidence of non-linear peer effects.