Conventional value-added models (VAMs) compare average test scores across schools after regression-adjusting for students’ demographic characteristics and previous scores. This article tests for VAM bias using a procedure that asks whether VAM estimates accurately predict the achievement consequences of random assignment to specific schools. Test results from admissions lotteries in Boston suggest conventional VAM estimates are biased, a finding that motivates the development of a hierarchical model describing the joint distribution of school value-added, bias, and lottery compliance. We use this model to assess the substantive importance of bias in conventional VAM estimates and to construct hybrid value-added estimates that optimally combine ordinary least squares and lottery-based estimates of VAM parameters. The hybrid estimation strategy provides a general recipe for combining nonexperimental and quasi-experimental estimates. While still biased, hybrid school value-added estimates have lower mean squared error than conventional VAM estimates. Simulations calibrated to the Boston data show that, bias notwithstanding, policy decisions based on conventional VAMs that control for lagged achievement are likely to generate substantial achievement gains. Hybrid estimates that incorporate lotteries yield further gains.

We develop a theory of endogenous uncertainty and business cycles in which short-lived shocks can generate long-lasting recessions. In the model, higher uncertainty about fundamentals discourages investment. Since agents learn from the actions of others, information flows slowly in times of low activity and uncertainty remains high, further discouraging investment. The economy displays uncertainty traps: self-reinforcing episodes of high uncertainty and low activity. Although the economy recovers quickly after small shocks, large temporary shocks may have long-lasting effects on the level of activity. The economy is subject to an information externality but uncertainty traps may remain in the efficient allocation. Embedding the mechanism in a standard business cycle framework, we find that endogenous uncertainty increases the persistence of large recessions and improves the performance of the model in accounting for the Great Recession.