Selection into private schools is the principal cause of bias when estimating the effect of private schooling on academic achievement. By exploiting the generous public subsidizing of private high schools in the province of Quebec, the second most populous province in Canada, we identify the causal impact of attendance in a private high school on achievement in mathematics. Because the supply of highly subsidized spaces is much higher at the high school level than at the grade school level, 94% of transitions from the public to the private sector occur at the end of primary school, we assume that these transitions are exogenous with respect to changes in transitory unobserved variables affecting math scores conditional on variables such as changes in income and child fixed effects. Using 7 cycles of data from Statistics Canada's National Longitudinal Survey on Children and Youth (NLSCY), we estimate the effect of attending a private high school on the percentile rank and a standardized math test score with different models (child fixed effects, random effects and a pooled OLS) and restricted samples to control for the degree of selection. The results, interpreted as a treatment on the treated effect show that the effect of changing schools, from a public grade school to a private high school, increases the percentile rank of the math score between 4 and 10 points and by between 0.12 and 0.36 of a standard deviation depending on the specification and samples. (Contains 1 figure and 14 tables.)