Abstract: In economic applications with missing or set-valued data, standard assumptions like missing-at-random are untestable and often difficult to justify. In this paper, I study identification in mean regression models with incomplete covariate data under "worst-case" conditions: the process determining observability is unknown and unrestricted. To make progress, I develop a new methodology inspired by the panel literature. I represent model features with minimal assumptions as unobserved heterogeneity, and I then target a minimal collection of functions which have non-negative expectations with respect to the heterogeneity. This approach turns out to be tractable, and I obtain conditional moment inequalities which completely characterize identification in the incomplete data models. The method is also versatile; I illustrate how it can be used in other settings. Finally, numerical exercises demonstrate the identification potential of the derived moment inequalities, as well as their feasibility for use in environments which are close to empirical practice.