We estimate peer effects in two datasets with non-overlapping peer groups: golfers who play tournaments randomized in groups of three; and students who are randomly paired for in-class computer-assisted learning. In such data, existing instrumental variable methods to address bias in peer effect estimation do not apply. Alternative estimation methods exist that do not require instruments, but they fail to correct for one understudied but important source of bias, which we call ‘exclusion bias.’ We provide formulas for the magnitude of this bias when fixed effects are included at the level of selection pools. We then derive a consistent estimator that corrects for this bias and propose a simple method for testing the presence of endogenous peer effects. Using this novel method, we find positive peer effects in the first case – consistent with emulation between golfers during the tournament – and negative peer effects in the other – consistent with congestion or wasteful competition for the computer between students. These results differ markedly from existing methods in terms of magnitude, significance, and inference.