Prove non-Gaussian validity of the bootstrap over-identification test

Prove that the Gaussian multiplier-bootstrap procedure for the over-identification statistic remains asymptotically valid when the observed data are non-Gaussian.

Background

The proposed bootstrap over-identification test is constructed from Gaussian multiplier-bootstrap draws and is designed to work well when the real data are Gaussian. The paper argues heuristically that asymptotic pivotality of the statistic should imply validity under non-Gaussianity as well.

A formal proof is not provided. Establishing this result would justify using the bootstrap critical value beyond the Gaussian-data case and would strengthen the inferential claims for the model-specification test.

References

Being based on Gaussian draws, this procedure is designed to work well when the real data is Gaussian, but we conjecture it remains asymptotically valid even if the real data is non-Gaussian.

— Limited-Information Estimation of Heterogeneous Agent Models  (2608.13953 - Liu et al., 14 Aug 2026) in Appendix A, subsection “Over-identification test”