Zhenhong Huang, Chen Wang, Jianfeng Yao
arXiv 28 Feb 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2302.14423 · PDF · DOI · OpenAlex · Extracted main text
A widely adopted approach for detecting weak instruments is to use the first-stage $F$ statistic. While this method was developed with a fixed number of instruments, its performance with many instruments remains insufficiently explored. We show that the first-stage $F$ test exhibits distorted sizes for detecting many weak instruments, regardless of the choice of pretested estimators or Wald tests. These distortions occur due to the inadequate approximation using classical noncentral Chi-squared distributions. As a byproduct of our main result, we present an alternative approach to pre-test many weak instruments with the corrected first-stage $F$ statistic. An empirical illustration with Angrist and Keueger (1991)'s returns to education data confirms its usefulness.
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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 | Angrist, J. D. and A. B. Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.928 | 4 | 3 | 100% |
| 2 | Wang, Q., Z. Su, and J. Yao (2014) Joint clt for several random sesquilinear forms with applications to large-dimensional spiked population models | 0.737 | 4 | 2 | 75% |
| 3 | Chao, J. C. and N. R. Swanson (2005) Consistent estimation with a large number of weak instruments | 0.737 | 3 | 3 | 67% |
| 4 | Angrist, J. D. and A. B. Krueger (1995) Split-sample instrumental variables estimates of the return to schooling | 0.644 | 2 | 2 | 100% |
| 5 | Hansen, C., J. Hausman, and W. Newey (2008) Estimation with many instrumental variables | 0.511 | 2 | 2 | 50% |
| 6 | Hausman, J. A., W. K. Newey, T. Woutersen, J. C. Chao, and N. R. Swa… (2012) Instrumental variable estimation with heteroskedasticity and many instruments | 0.511 | 2 | 2 | 50% |
| 7 | Stock, J. H. and M. Yogo (2005) Testing for weak instruments in linear iv regression | 0.511 | 2 | 2 | 50% |
| 8 | Wang, W. and M. Kaffo (2016) Bootstrap inference for instrumental variable models with many weak instruments | 0.511 | 2 | 2 | 50% |
| 9 | Anatolyev, S. and N. Gospodinov (2011) Specification testing in models with many instruments | 0.405 | 1 | 1 | 100% |
| 10 | Anatolyev, S. and P. Yaskov (2017) Asymptotics of diagonal elements of projection matrices under many instruments/regressors | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.