When regressors of interest are interval-censored, knowledge of their marginal distribution implies additional restrictions, which, combined with shape restrictions, lead to tighter bounds on the regression function. We show how to estimate these bounds, as well as bounds on any linear functional, using a linear programming formulation and establish consistency. Valid Bayesian and frequentist inference can be performed using the computationally attractive Bayesian bootstrap. An application to age-earnings profiles illustrates the usefulness of distribution information.

We present a semiparametric method to estimate group-level dispersion, which is particularly effective in the presence of censored data. We apply this procedure to obtain measures of occupation-specific wage dispersion using top-coded administrative wage data from the German IAB Employment Sample (IABS). We then relate these robust measures of earnings risk to the risk attitudes of individuals working in these occupations. We find that willingness to take risk is positively correlated with the wage dispersion of an individual's occupation.