Abstract: Researchers often confront regressions where key covariates are missing or only interval-observed. Standard remedies, such as imputation or auxiliary modeling assumptions, resolve ambiguity at the expense of credibility. Instead, we derive the sharp identified set, the smallest parameter set consistent with both the incomplete data and the maintained model, for a class of conditional expectation models without auxiliary assumptions. A computationally tractable Hausdorff consistent estimator for this set is provided with associated asymptotic uniformly valid confidence regions for the true parameter. This is achieved by extending an existing random set framework to infinite-dimensional Polish spaces. We apply our method to a multiple price list survey design measuring discount rates and document substantial sensitivity with respect to interval width.

For Information contact angela.baldassarre@unibocconi.it or giulia.zenoni@unibocconi.it