This paper develops methods for assessing the sensitivity of empirical conclu-
sions regarding conditional distributions to departures from the missing at ran-
dom (MAR) assumption. We index the degree of nonignorable selection governing
the missing data process by the maximal Kolmogorov–Smirnov distance between
the distributions of missing and observed outcomes across all values of the co-
variates. Sharp bounds on minimum mean square approximations to conditional
quantiles are derived as a function of the nominal level of selection considered in
the sensitivity analysis and a weighted bootstrap procedure is developed for con-
ducting inference. Using these techniques, we conduct an empirical assessment
of the sensitivity of observed earnings patterns in U.S. Census data to deviations
from the MAR assumption. We find that the well documented increase in the re-
turns to schooling between 1980 and 1990 is relatively robust to deviations from
the missing at random assumption except at the lowest quantiles of the distribu-
tion, but that conclusions regarding heterogeneity in returns and changes in the
returns function between 1990 and 2000 are very sensitive to departures from ig-
norability.
Keywords. Quantile regression, missing data, sensitivity analysis, wage structure.
JEL classification. C01, C80, J31.