Using rich panel data from Pakistan, we compute test score based measures of quality (School Value-Addeds or SVAs) for more than 800 schools across 112 villages and verify that they are valid and unbiased. With the SVA measures, we then document three striking features of the schooling environment. First, there is substantial within-village variation in quality. The annualized difference in learning between the best and worst performing school in the same village is 0.4 sd; compounded over five years of primary schooling, this difference is similar in size to the test score gap between low- and high-income countries. Second, students learn more in private schools (0.15 sd per year on average), but substantial within-sector variation in quality means that the effects of reallocating students from public to private schools can range from -0.35 sd to +0.65 sd. Thus, there is a range of possible causal estimates of the private premium, a feature of the environment we illustrate using three different identification approaches. Finally, parents appear to recognize and reward SVA in the private sector, but the link between parental demand and SVA is weaker in the public sector. These results have implications for both the measurement of the private premium and how we design and evaluate policies that reallocate children across schools, such as school closures and vouchers.