On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test
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...
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| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/154887 |
| _version_ | 1826127182959738880 |
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| author | Wang, Wenjie |
| author2 | School of Social Sciences |
| author_facet | School of Social Sciences Wang, Wenjie |
| author_sort | Wang, Wenjie |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:04:36Z |
| format | Journal Article |
| id | ntu-10356/154887 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:04:36Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1548872022-01-13T03:00:06Z On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test Wang, Wenjie School of Social Sciences Social sciences::Economic theory Nonparametric Bootstrap Weak Identification 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. Nanyang Technological University This work was supported by NTU SUG Grant No.M4082262.SS0. 2022-01-13T03:00:05Z 2022-01-13T03:00:05Z 2020 Journal Article Wang, W. (2020). On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test. Economics Letters, 191, 109157-. https://dx.doi.org/10.1016/j.econlet.2020.109157 0165-1765 https://hdl.handle.net/10356/154887 10.1016/j.econlet.2020.109157 2-s2.0-85083319288 191 109157 en M4082262.SS0 Economics Letters © 2020 Elsevier B.V. All rights reserved. |
| spellingShingle | Social sciences::Economic theory Nonparametric Bootstrap Weak Identification Wang, Wenjie On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title | On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title_full | On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title_fullStr | On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title_full_unstemmed | On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title_short | On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test |
| title_sort | on the inconsistency of nonparametric bootstraps for the subvector anderson rubin test |
| topic | Social sciences::Economic theory Nonparametric Bootstrap Weak Identification |
| url | https://hdl.handle.net/10356/154887 |
| work_keys_str_mv | AT wangwenjie ontheinconsistencyofnonparametricbootstrapsforthesubvectorandersonrubintest |