Inference with Many Weak Instruments and Heterogeneity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908333681672192 |
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| author | Yap, Luther |
| author_facet | Yap, Luther |
| contents | This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. I first show that existing test procedures, including those that are robust to either weak instruments or heterogeneous treatment effects, can be arbitrarily oversized. I propose a novel and valid test based on a score statistic and a ``leave-three-out" variance estimator. In the presence of heterogeneity and within the class of tests that are functions of the leave-one-out analog of a maximal invariant, this test is asymptotically the uniformly most powerful unbiased test. In two applications to judge and quarter-of-birth instruments, the proposed inference procedure also yields a bounded confidence set while some existing methods yield unbounded or empty confidence sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inference with Many Weak Instruments and Heterogeneity Yap, Luther Econometrics This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. I first show that existing test procedures, including those that are robust to either weak instruments or heterogeneous treatment effects, can be arbitrarily oversized. I propose a novel and valid test based on a score statistic and a ``leave-three-out" variance estimator. In the presence of heterogeneity and within the class of tests that are functions of the leave-one-out analog of a maximal invariant, this test is asymptotically the uniformly most powerful unbiased test. In two applications to judge and quarter-of-birth instruments, the proposed inference procedure also yields a bounded confidence set while some existing methods yield unbounded or empty confidence sets. |
| title | Inference with Many Weak Instruments and Heterogeneity |
| topic | Econometrics |
| url | https://arxiv.org/abs/2408.11193 |