Before revision:  Our estimator converges at parametric rate and has asymptotic normality properties. It may be useful for labor economics applications that involve bracketed salaries and rich, high-dimensional demographic data about the subjects of the study .
After revision:  I apply this result to estimate sharp nonparametric bounds on the average treatment effect in Lee (2008)'s model of endogenous selection and substantially tighten the bounds on this parameter in Angrist et al. (2006)'s empirical setting. I also apply this result to estimate sharp identified sets for two other parameters - a new parameter, called a partially linear predictor, and the average partial derivative when the outcome variable is recorded in intervals .