This paper examines the impact of peer ability on student achievement, using a unique matched panel data set of students and schools. The authors argue that peer effects on student achievement are often confounded by omitted and mismeasured variables, and that fixed effects models can help isolate these effects. They find that peer achievement has a positive effect on achievement growth, and that students throughout the school test score distribution benefit from higher achieving schoolmates. However, the variance in achievement appears to have no systematic effect. The study addresses the reciprocal nature of peer interactions and the interpretation of estimates based on past achievement as a measure of peer group quality. The authors use a fixed effects framework to control for student and school-by-grade fixed effects, as well as observable family and school characteristics. They find that peer effects are more accurately estimated using lagged peer achievement rather than contemporaneous achievement, as lagged achievement avoids the problem of simultaneous equations bias. The study also considers the role of peer group composition in school choice and the potential for peer effects to influence classroom instruction. The authors find that peer effects are more pronounced for students who have been in a group for a longer period, and that the variance in achievement is not systematically affected by peer group characteristics. However, the study notes that the measurement of peer income is noisy and may confound actual income differences with differences in school efforts to classify children as disadvantaged. The results suggest that peer ability has a strong and direct influence on learning, but the exact causal mechanism remains ambiguous. The study concludes that the use of fixed effects models and lagged measures of peer achievement provides a valid source of identification for the estimation of peer group effects. The results also indicate that average income or peer heterogeneity in terms of achievement levels does not significantly affect growth in mathematics achievement.This paper examines the impact of peer ability on student achievement, using a unique matched panel data set of students and schools. The authors argue that peer effects on student achievement are often confounded by omitted and mismeasured variables, and that fixed effects models can help isolate these effects. They find that peer achievement has a positive effect on achievement growth, and that students throughout the school test score distribution benefit from higher achieving schoolmates. However, the variance in achievement appears to have no systematic effect. The study addresses the reciprocal nature of peer interactions and the interpretation of estimates based on past achievement as a measure of peer group quality. The authors use a fixed effects framework to control for student and school-by-grade fixed effects, as well as observable family and school characteristics. They find that peer effects are more accurately estimated using lagged peer achievement rather than contemporaneous achievement, as lagged achievement avoids the problem of simultaneous equations bias. The study also considers the role of peer group composition in school choice and the potential for peer effects to influence classroom instruction. The authors find that peer effects are more pronounced for students who have been in a group for a longer period, and that the variance in achievement is not systematically affected by peer group characteristics. However, the study notes that the measurement of peer income is noisy and may confound actual income differences with differences in school efforts to classify children as disadvantaged. The results suggest that peer ability has a strong and direct influence on learning, but the exact causal mechanism remains ambiguous. The study concludes that the use of fixed effects models and lagged measures of peer achievement provides a valid source of identification for the estimation of peer group effects. The results also indicate that average income or peer heterogeneity in terms of achievement levels does not significantly affect growth in mathematics achievement.