Develop sampling theory and inference for the identified set

Develop sampling theory and inference procedures for the sharp identified sets in linear panel quantile models with unrestricted individual heterogeneity and fixed time dimension.

Background

The paper establishes population identification and computational characterizations of sharp identified sets for linear panel quantile models under quantile strict exogeneity, including coupling representations, observable duality, finite-support linear programs, and dual-sieve procedures for continuous designs. It explicitly limits its scope to population analysis and does not address estimation of the identified set or inferential procedures based on finite samples.

Consequently, a concrete unresolved task is to develop sampling theory and formal inference methods—such as confidence regions or confidence sets—for the identified sets and related projections produced by the paper’s population characterizations. The same issue applies to the continuous-design dual-sieve procedures, whose population outer-set properties do not by themselves provide finite-sample statistical guarantees.

References

The paper is limited to identification and population computation. We do not estimate the individual effects, use a large-$T$ approximation, or develop confidence regions for the identified set. The finite-support criterion gives an exact population optimization characterization. The continuous-design criteria give population outer approximations whose limiting intersection is sharp. Sampling theory and inference are left for future work.

— Identification in Linear Quantile Panel Models  (2609.10925 - Khan et al., 10 Sep 2026) in Section 1, Introduction; paragraph beginning “The paper is limited to identification and population computation”