Lottery-based estimates suggest that Boston's charter schools produce large achievement gains for their applicants. The consequences of charter school expansion are less clear. In this paper I develop econometric methods that allow me to extrapolate from lottery estimates for current cohorts and predict the effects of policy changes on citywide achievement gaps. I show that among lottery applicants, non-white students benefit much more than white students from attending Boston's charter schools. I then use a model of selection into charter application and attendance to extrapolate from the lottery-based results and predict charter attendance effects for non-charter students. Simulation results suggest that realistic expansions of the city's charter network are likely to reduce achievement gaps significantly.