Interval estimation of potentially misspecified quantile models in the presence of missing data

"This paper develops practical methods for relaxing the missing at random assumption when estimating models of conditional quantiles with missing outcome data and discrete covariates. We restrict the degree of non-ignorable selection governing the missingness process by imposing bounds on the Kolmogorov-Smirnov (KS) distance between the distribution of outcomes among missing observations and the overall (unselected) distribution. Two methods are developed for conducting inference in this environment. The first allows us to perform finite sample inference on the identified set and is well suited to tests of model specification. The second enables us to conduct inference on the parameters of potentially misspecified models. To illustrate our techniques, we revisit the results of Angrist, Chernozhukov, and Fernandez-Val (2006) regarding changes across Decennial Censuses in the quantile specific returns to schooling"--National Bureau of Economic Research web site