Weak Identification with Many Instruments
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916105106227200 |
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| author | Mikusheva, Anna Sun, Liyang |
| author_facet | Mikusheva, Anna Sun, Liyang |
| contents | Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and summarizes ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak identification-robust inference under heteroskedasticity. We establish new results for a jack-knifed version of the Lagrange Multiplier (LM) test statistic. Furthermore, we extend the weak-identification-robust tests to settings with both many exogenous regressors and many instruments. We propose a test that properly partials out many exogenous regressors while preserving the re-centering property of the jack-knife. The proposed tests have correct size and good power properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09535 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weak Identification with Many Instruments Mikusheva, Anna Sun, Liyang Econometrics Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and summarizes ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak identification-robust inference under heteroskedasticity. We establish new results for a jack-knifed version of the Lagrange Multiplier (LM) test statistic. Furthermore, we extend the weak-identification-robust tests to settings with both many exogenous regressors and many instruments. We propose a test that properly partials out many exogenous regressors while preserving the re-centering property of the jack-knife. The proposed tests have correct size and good power properties. |
| title | Weak Identification with Many Instruments |
| topic | Econometrics |
| url | https://arxiv.org/abs/2308.09535 |