Improving education quality is an important concern in many countries around the world. Over the last few decades, many governments have introduced market mechanisms in education with the objectives of enhancing choice and encouraging competition. In theory, increased competition between educational establishments should result in the provision of better quality education services to attract students. These reforms have given rise to fierce debates in political and scientific circles. In the first chapter I study the mechanisms that underlie student sorting in a mixed public-private system using a 2008 education reform implemented in Chile aimed at decreasing education inequality. Specifically, I exploit the shock to schools’ incentives to test for whether schools select students based on socioeconomic characteristics. I show that low-SES parent’s school choices are restricted by private school cream-skimming behavior. I estimate a demand model incorporating these admission restrictions to capture parental preferences for different school characteristics and peer composition. I show that ignoring cream-skimming leads to underestimating poor parents' preferences for school quality. I find that the decrease in cream-skimming induced by the reform led to lower public school enrollment and that strong preferences for high-income peers drove increased enrollment in schools that opted out of the reform. Overall, this led to increased segregation with higher impacts in markets with greater competition. In the second chapter I study the consequences of increased competition and geographic differentiation resulting from the deregulation of the Chilean college market and the increase in government scholarships and loans. We study the effects of these changes in market characteristics on the efficiency of the higher education system and the accessibility and quality of colleges. We estimate a sorting model to account for vertical and horizontal dimensions of differentiation and quantify the quality of public and private colleges. We find that most of the growth in enrollment comes from elite institutions that expand the size of existing programs and private universities that almost doubled their enrollment and at the same time doubling on average the number of programs offered. We calculate substitution patterns for when a program increase its quality. We find significant substitution between middle tier programs, whereas top tier universities tend to substitute mainly from other programs in that same range.