On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test

Wenjie Wang

Economics Letters, 2020, vol. 191, issue C

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. bootstrap 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 test can be very conservative even under strong IVs.

Keywords: Nonparametric bootstrap; Weak identification; Weak instrument; Subvector inference; Anderson–Rubin test (search for similar items in EconPapers)
JEL-codes: C12 C13 C26 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Working Paper: On the Inconsistency of Nonparametric Bootstraps for the Subvector Anderson-Rubin Test (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:191:y:2020:i:c:s0165176520301245

DOI: 10.1016/j.econlet.2020.109157

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