We establish that season of birth is related to educational attainment because of school start age policy and compulsory school attendance laws. Individuals born in the beginning of the year start school at an older age, and can therefore drop out after completing less schooling than individuals born near the end of the year. Roughly 25 percent of potential dropouts remain in school because of compulsory schooling laws. We estimate the impact of compulsory schooling on earnings by using quarter of birth as an instrument for education. The instrumental variables estimate of the return to education is close to the ordinary least squares estimate, suggesting that there is little bias in conventional estimates.

Conventional value-added models (VAMs) compare average test scores across schools after regression-adjusting for students’ demographic characteristics and previous scores. This article tests for VAM bias using a procedure that asks whether VAM estimates accurately predict the achievement consequences of random assignment to specific schools. Test results from admissions lotteries in Boston suggest conventional VAM estimates are biased, a finding that motivates the development of a hierarchical model describing the joint distribution of school value-added, bias, and lottery compliance. We use this model to assess the substantive importance of bias in conventional VAM estimates and to construct hybrid value-added estimates that optimally combine ordinary least squares and lottery-based estimates of VAM parameters. The hybrid estimation strategy provides a general recipe for combining nonexperimental and quasi-experimental estimates. While still biased, hybrid school value-added estimates have lower mean squared error than conventional VAM estimates. Simulations calibrated to the Boston data show that, bias notwithstanding, policy decisions based on conventional VAMs that control for lagged achievement are likely to generate substantial achievement gains. Hybrid estimates that incorporate lotteries yield further gains.