Are teachers' impacts on students' test scores (value-added) a good measure of their quality? This question has sparked debate partly because of a lack of evidence on whether high value-added (VA) teachers improve students' long-term outcomes. Using school district and tax records for more than one million children, we find that students assigned to high-VA teachers are more likely to attend college, earn higher salaries, and are less likely to have children as teenagers. Replacing a teacher whose VA is in the bottom 5 percent with an average teacher would increase the present value of students' lifetime income by approximately $250,000 per classroom.

Are teachers' impacts on students' test scores (value-added) a good measure of their quality? One reason this question has sparked debate is disagreement about whether value-added (VA) measures provide unbiased estimates of teachers' causal impacts on student achievement. We test for bias in VA using previously unobserved parent characteristics and a quasi-experimental design based on changes in teaching staff. Using school district and tax records for more than one million children, we find that VA models which control for a student's prior test scores provide unbiased forecasts of teachers' impacts on student achievement.

Using 41 million observations on savings for the population of Denmark, we show that the effects of retirement savings policies on wealth accumulation depend on whether they change savings rates by active or passive choice. Subsidies for retirement accounts, which rely on individuals to take an action to raise savings, primarily induce individuals to shift assets from taxable accounts to retirement accounts. We estimate that each $1 of government expenditure on subsidies increases total saving by only 1 cent. In contrast, policies that raise retirement contributions if individuals take no action—such as automatic employer contributions to retirement accounts—increase wealth accumulation substantially. We estimate that approximately 15% of individuals are “active savers” who respond to tax subsidies primarily by shifting assets across accounts; 85% of individuals are “passive savers” who are unresponsive to subsidies but are instead heavily influenced by automatic contributions made on their behalf. Active savers tend to be wealthier and more financially sophisticated. We conclude that automatic contributions are more effective at increasing savings rates than subsidies for three reasons: (i) subsidies induce relatively few individuals to respond, (ii) they generate substantial crowd-out conditional on response, and (iii) they do not increase the savings of passive individuals, who are least prepared for retirement.