arXiv 28 Jun 2021 · Econometrics
arXiv:2106.15003 · PDF · DOI · OpenAlex · Extracted main text
The finite sample properties of estimators are usually understood or approximated using asymptotic theories. Two main asymptotic constructions have been used to characterize the presence of many instruments. The first assumes that the number of instruments increases with the sample size. I demonstrate that in this case, one of the key assumptions used in the asymptotic construction may imply that the number of “effective" instruments should be finite, resulting in an internal contradiction. The second asymptotic representation considers that the number of instrumental variables (IVs) may be finite, infinite, or even a continuum. The number does not change with the sample size. In this scenario, the regularized estimator obtained depends on the topology imposed on the set of instruments as well as on a regularization parameter. These restrictions may induce a bias or restrict the set of admissible instruments. However, the assumptions are internally coherent. The limitations of many IVs asymptotic assumptions provide support for finite sample distributional studies to better understand the behavior of many IV estimators.
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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 | Harding, Hausman, and Palmer (2016) Finite sample bias corrected IV estimation for weak and many instruments | 0.928 | 4 | 3 | 100% |
| 2 | Carrasco (2012) A regularization approach to the many instruments problem | 0.874 | 7 | 2 | 100% |
| 3 | Bekker (1994) Alternative approximations to the distributions of instrumental variable estimators | 0.511 | 2 | 1 | 100% |
| 4 | Phillips and Moon (1999) Linear regression limit theory for nonstationary panel data | 0.511 | 2 | 1 | 100% |
| 5 | Staiger and Stock (1997) Instrumental Variables Regression with Weak Instruments | 0.405 | 1 | 1 | 100% |
| 6 | Anatolyev and Gospodinov (2011) Specification testing in models with many instruments | 0.405 | 1 | 1 | 100% |
| 7 | Andrews and Stock (2007) Testing with many weak instruments | 0.405 | 1 | 1 | 100% |
| 8 | Belloni, Chen, Chernozhukov, and Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.405 | 1 | 1 | 100% |
| 9 | Bun and Windmeijer (2011) A comparison of bias approximations for the two-stage least squares (2SLS) estimator | 0.405 | 1 | 1 | 100% |
| 10 | Carrasco and Tchuente (2016) Efficient estimation with many weak instruments using regularization techniques | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 14 scored citations.