Based on the wide-ranging liberal reforms introduced in the early 1990s, Sweden has become one of the most prominent realizations of Milton Friedman's proposal for market-based schooling. From 1991 to 2012, the percentage of Swedish ninth-grade students attending independent, voucher-financed, private schools increased from 2.8% to 14.2%. A recent study using municipality-level data claimed that the resulting increase in school competition positively affected student performance in both private and public schools. In this study, using data on 2,154,729 school leavers, we show that this result does not hold when controlling for individual-level background factors and differences in the peer composition of schools.