Zhenhong Huang, Chen Wang, Jianfeng Yao
arXiv 28 Feb 2023 · Econometrics
arXiv:2302.14396 · PDF · DOI · OpenAlex · Extracted main text
This paper develops a new specification test for the instrument weakness when the number of instruments $K_n$ is large with a magnitude comparable to the sample size $n$. The test relies on the fact that the difference between the two-stage least squares (2SLS) estimator and the ordinary least squares (OLS) estimator asymptotically disappears when there are many weak instruments, but otherwise converges to a non-zero limit. We establish the limiting distribution of the difference within the above two specifications, and introduce a delete-$d$ Jackknife procedure to consistently estimate the asymptotic variance/covariance of the difference. Monte Carlo experiments demonstrate the good performance of the test procedure for both cases of single and multiple endogenous variables. Additionally, we re-examine the analysis of returns to education data in Angrist and Keueger (1991) using our proposed test. Both the simulation results and empirical analysis indicate the reliability of the test.
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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 | Mikusheva, A. and L. Sun (2022) Inference with many weak instruments | 0.874 | 5 | 2 | 100% |
| 2 | Angrist, J. D. and A. B. Keueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.843 | 3 | 3 | 100% |
| 3 | Chao, J. C. and N. R. Swanson (2005) Consistent estimation with a large number of weak instruments | 0.737 | 3 | 3 | 67% |
| 4 | Anatolyev, S. and N. Gospodinov (2011) Specification testing in models with many instruments | 0.737 | 3 | 2 | 100% |
| 5 | Anderson, T., N. Kunitomo, and Y. Matsushita (2010) On the asymptotic optimality of the liml estimator with possibly many instruments | 0.644 | 2 | 2 | 100% |
| 6 | Angrist, J. D. and A. B. Krueger (1995) Split-sample instrumental variables estimates of the return to schooling | 0.644 | 2 | 2 | 100% |
| 7 | Bekker, P. A (1994) Alternative approximations to the distributions of instrumental variable estimators | 0.644 | 2 | 2 | 100% |
| 8 | Bound, J., D. A. Jaeger, and R. M. Baker (1995) Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory vari… | 0.644 | 2 | 2 | 100% |
| 9 | Chao, J. C. and R. Swanson (2006) Asymptotic normality of single-equation estimators for the case with a large number of weak instruments | 0.644 | 2 | 2 | 100% |
| 10 | Lee, Y. and R. Okui (2012) Hahn–Hausman test as a specification test | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 35 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | The First-stage F Test with Many Weak Instruments | 0.000 | 1 | 1 |