Validity of sequential multiple change-point tests under near-weak instruments

Establish that the sequential testing methods of Hall, Han, and Boldea (2012) for detecting multiple change points in linear models with endogenous regressors remain valid when instruments exhibit near-weak identification; specifically, demonstrate that these sequential sup-Wald tests maintain asymptotic validity under near-weak instruments as they do in the zero-versus-one change case shown in this paper.

Background

The paper develops inference for structural changes in linear IV/GMM models under near-weak instruments and proves that the sup-Wald test of zero versus one change remains valid in this setting. To handle multiple changes, the authors recommend the sequential testing framework of Hall, Han, and Boldea (2012) but do not provide a formal proof of its validity under near-weak instruments.

This leaves open whether the sequential procedure (which iteratively applies change-point tests to identify multiple breaks) preserves correct asymptotic properties, such as size control and limiting behavior, when identification is near-weak. Formalizing this extension would strengthen the multi-break inference procedure proposed in the paper.