Friedman (1962) observed that the ability of firms to acquire and maintain reputations for quality is a key ingredient for the efficient provision of goods and services in a market economy. This paper explores the implications of school reputation for skill acquisition and labor market outcomes in an otherwise competitive market. We find that reputation effects can explain several puzzling findings in the economics of education, including the fact that competition can, but does not always, improve skill acquisition. This result follows from an anti-lemons effect (in contrast to Akerlof's lemons effect) that arises when schools can enhance their reputation by positively selecting their students. This leads to excess demand for "high quality" selective schools that drive out non-selective schools. This in turn reduces "relative diversity", a measure of ability dispersion in a school, leading to lower skill acquisition.