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arXiv · 2302.14396

A specification test for the strength of instrumental variables

Zhenhong Huang·Chen Wang·Jianfeng Yao
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Abstract

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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Zhenhong Huang, Chen Wang, Jianfeng Yao. 2023-02-28. A specification test for the strength of instrumental variables. https://arxiv.org/abs/2302.14396

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