Talented students compete fiercely for seats at Boston and New York exam schools. These schools are characterized by high levels of peer achievement and a demanding curriculum tailored to each district's highest achievers. While exam school students clearly do very well in school, the question of whether an exam school education adds value relative to a regular public education remains open. We estimate the causal effect of exam school attendance using a regression-discontinuity design, reporting both parametric and non-parametric estimates. We also develop a procedure that addresses the potential for confounding in regression-discontinuity designs with multiple, closely-spaced admissions cutoffs. The outcomes studied here include scores on state standardized achievement tests, PSAT and SAT participation and scores, and AP scores. Our estimates show little effect of exam school offers on most students' achievement in most grades. We use two-stage least squares to convert reduced form estimates of the effects of exam school offers into estimates of peer and tracking effects, arguing that these appear to be unimportant in this context. On the other hand, a Boston exam school education seems to have a modest effect on high school English scores for minority applicants. A small group of 9th grade applicants also appears to do better on SAT Reasoning. These localized gains notwithstanding, the intense competition for exam school seats does not appear to be justified by improved learning for a broad set of students.