arXiv 20 Aug 2024 · Econometrics
arXiv:2408.11193 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chao, J. C., N. R. Swanson, J. A. Hausman, W. K. Newey, and T. Woute… (2012) Asymptotic distribution of JIVE in a heteroskedastic IV regression with many instruments | 1.000 | 6 | 3 | 100% |
| 2 | Matsushita, Y. and T. Otsu (2022) A jackknife Lagrange multiplier test with many weak instruments | 0.950 | 7 | 3 | 86% |
| 3 | Crudu, F., G. Mellace, and Z. Sándor (2021) Inference in instrumental variable models with heteroskedasticity and many instruments | 0.941 | 6 | 4 | 83% |
| 4 | Evdokimov, K. S. and M. Kolesár (2018) Inference in Instrumental Variables Analysis with Heterogeneous Treatment Effects | 0.909 | 8 | 4 | 75% |
| 5 | Mikusheva, A. and L. Sun (2022) Inference with many weak instruments | 0.874 | 6 | 2 | 100% |
| 6 | Angrist, J. D. and A. B. Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.855 | 8 | 3 | 62% |
| 7 | Lee, D. S., J. McCrary, M. J. Moreira, J. R. Porter, and L. Yap (2023) What to do when you can't use '1.96' Confidence Intervals for IV, Working Paper 31893, National Bureau of Economic Research | 0.843 | 3 | 3 | 100% |
| 8 | Staiger, D. and J. H. Stock (1997) Instrumental Variables Regression with Weak Instruments | 0.811 | 4 | 2 | 100% |
| 9 | Agan, A., J. L. Doleac, and A. Harvey (2023) Misdemeanor prosecution | 0.811 | 4 | 2 | 100% |
| 10 | Anatolyev, S. and M. Slvsten (2023) Testing many restrictions under heteroskedasticity | 0.811 | 4 | 2 | 100% |
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