2023/02/28 by Zhenhong Huang, Chen Wang, Huang, Zhenhong +3
Economics, Econometrics and Finance · #Econometrics (econ.EM) #Economic Policies and Impacts #FOS: Economics and business #Fiscal Policy and Economic Growth #Monetary Policy and Economic Impact
paper · pdf · doi:10.48550/arxiv.2302.14396
openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops a new specification test for the instrument weakness when the number of instruments Kn 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.