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Selective school admissions give rise to a Regression Discontinuity (RD) design that non-parametrically identifies causal effects for marginal applicants. Without stronger assumptions nothing can be said about causal effects for inframarginal applicants. Estimates of causal effects for inframarginal applicants are valuable for many policy questions, such as affirmative action, that substantially alter admissions cutoffs. This paper develops a latent factor-based approach to RD extrapolation that is then used to estimate effects of Boston exam schools away from admissions cutoffs. Achievement gains from Boston exam schools are larger for applicants with lower English and Math abilities. I also use the model to predict the effects of introducing either minority or socioeconomic preferences in exam school admissions. Affirmative action has modest average effects on achievement, while increasing the achievement of the applicants who gain access to exam schools as a result.