We introduce two empirical strategies harnessing the randomness in school assignment mechanisms to measure school value-added. The first estimator controls for the probability of school assignment, treating take-up as ignorable. We test this assumption using randomness in assignments. The second approach uses assignments as instrumental variables (IVs) for low-dimensional models of value-added and forms empirical Bayes posteriors from these IV estimates. Both strategies solve the underidentification challenge arising from school undersubscription. Models controlling for assignment risk and lagged achievement in Denver and New York City yield reliable value-added estimates. Estimates from models with lower-quality achievement controls are improved by IV.

The H-1B Visa Reform Act of 2004 dictates an annual allocation of 85,000 visas with 20,000 reserved for advanced-degree applicants. We represent the main requirements of this legislation as formal axioms and characterize visa allocation rules consistent with the axioms. Despite the precise number reserved, we show that the range of implementations satisfying these axioms can change the allocation of advanced-degree visas by as much as 14,000 in an average year. Of all rules satisfying these axioms, the 2019 rule imposed by executive order is most favorable to advanced-degree holders. However, two earlier modifications resulted in larger changes, possibly unintentionally.