This paper applies a unified methodology to multiple data sets to estimate both the levels and trends in U.S. high school graduation rates. We establish that (a) the true rate is substantially lower than widely used measures, (b) it peaked in the early 1970s, (c) majority-minority differentials are substantial and have not converged for 35 years, (d) lower post-1970 rates are not solely due to increasing immigrant and minority populations, (e) our findings explain part of the slowdown in college attendance and rising college wage premiums, and (f) widening graduation differentials by gender help explain increasing male-female college attendance gaps.

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models, including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters.