Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Londschien, Malte Bühlmann, Peter |
| author_facet | Londschien, Malte Bühlmann, Peter |
| contents | We propose a weak-instrument-robust subvector Lagrange multiplier test for instrumental variables regression. We show that it is asymptotically size-correct under a technical condition or as the number of instruments grows to infinity. This is the first weak-instrument-robust subvector test for instrumental variables regression to recover the degrees of freedom of the commonly used non-weak-instrument-robust Wald test. Additionally, we provide a closed-form solution for subvector confidence sets obtained by inverting the subvector Anderson-Rubin test. We show that they are centered around a k-class estimator. We show that the subvector confidence sets for single coefficients of the causal parameter are jointly bounded if and only if Anderson's likelihood-ratio test rejects the null hypothesis that the first-stage regression parameter is of reduced rank, that is, that the causal parameter is not identified. Finally, we show that if a confidence set obtained by inverting the Anderson-Rubin test is bounded and nonempty, it is equal to a Wald-based confidence set with a data-dependent confidence level. We explicitly compute this Wald-based confidence set and its confidence level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets Londschien, Malte Bühlmann, Peter Statistics Theory Econometrics We propose a weak-instrument-robust subvector Lagrange multiplier test for instrumental variables regression. We show that it is asymptotically size-correct under a technical condition or as the number of instruments grows to infinity. This is the first weak-instrument-robust subvector test for instrumental variables regression to recover the degrees of freedom of the commonly used non-weak-instrument-robust Wald test. Additionally, we provide a closed-form solution for subvector confidence sets obtained by inverting the subvector Anderson-Rubin test. We show that they are centered around a k-class estimator. We show that the subvector confidence sets for single coefficients of the causal parameter are jointly bounded if and only if Anderson's likelihood-ratio test rejects the null hypothesis that the first-stage regression parameter is of reduced rank, that is, that the causal parameter is not identified. Finally, we show that if a confidence set obtained by inverting the Anderson-Rubin test is bounded and nonempty, it is equal to a Wald-based confidence set with a data-dependent confidence level. We explicitly compute this Wald-based confidence set and its confidence level. |
| title | Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets |
| topic | Statistics Theory Econometrics |
| url | https://arxiv.org/abs/2407.15256 |