Debates in education policy draw on different theories about how to raise children's achievement. The "school competition" theory holds that achievement rises when families can choose among competing schools. The school resource theory holds that achievement rises with school spending and resources that spending can buy. The "family resources" theory holds that children's achievement rises with parental education and income. We test all three theories in Chile between 2002 and 2013, when reading and math scores rose by 0.2-0.3 standard deviations, while school competition, school resources, and family resources all increased. In a difference in differences analysis, we ask which Chilean municipalities saw the greatest increases in test scores. Test scores did not rise faster in municipalities with greater increases in competition, but did rise faster in municipalities with greater increases in school resources (teachers per student) and especially family resources (parental education, not income). Student grade point averages show similar patterns. Results contradict the school competition theory but fit the family resource theory and, to a lesser extent, the school resource theory.