Download This PaperOn the Inconsistency of Nonparametric Bootstraps for the Subvector Anderson-Rubin Test
12 Pages Posted: 9 Apr 2020 Last revised: 20 Apr 2020
Date Written: March 7, 2020
Abstract
Bootstrap procedures based on instrumental variable (IV) estimates or t-statistics are generally invalid when the instruments are weak. The bootstrap may even fail when applied to identification-robust test statistics. For subvector inference based on the Anderson-Rubin (AR) statistic, Wang and Doko Tchatoka (2018) show that the residual bootstrap is inconsistent under weak IVs. In particular, the residual bootstrap depends on certain estimator of structural parameters to generate bootstrap pseudo-data, while the estimator is inconsistent under weak IVs. It is thus tempting to consider nonparametric bootstrap. In this note, under the assumptions of conditional homoskedasticity and one nuisance structural parameter, we investigate the bootstrap consistency for the subvector AR statistic based on the nonparametric i.i.d. bootstap and its recentered version proposed by Hall and Horowitz (1996). We find that both procedures are inconsistent under weak IVs: although able to mimic the weak-identification situation in the data, both procedures result in approximation errors, which leads to the discrepancy between the bootstrap world and the original sample. In particular, both bootstrap tests can be very conservative under weak IVs. The pairs bootstrap can be very conservative even under strong IVs.
Keywords: Nonparametric Bootstrap; Weak Identification; Weak Instrument; Subvector Inference; Anderson-Rubin Test
JEL Classification: C12; C13; C26
Suggested Citation: Suggested Citation