Jesse Hoekstra, Frank Windmeijer
arXiv 25 Jan 2026 · Econometrics
arXiv:2601.17843 · PDF · DOI · OpenAlex · Extracted main text
For subvector inference in the linear instrumental variables model under homoskedasticity but allowing for weak instruments, Guggenberger, Kleibergen, and Mavroeidis (2019) (GKM) propose a conditional subvector Anderson and Rubin (1949) (AR) test that uses data-dependent critical values that adapt to the strength of the parameters not under test. This test has correct size and strictly higher power than the test that uses standard asymptotic chi-square critical values. The subvector AR test is the minimum eigenvalue of a data dependent matrix. The GKM critical value function conditions on the largest eigenvalue of this matrix. We consider instead the data dependent critical value function conditioning on the second-smallest eigenvalue, as this eigenvalue is the appropriate indicator for weak identification. We find that the data dependent critical value function of GKM also applies to this conditioning and show that this test has correct size and power strictly higher than the GKM test when the number of parameters not under test is larger than one. Our proposed procedure further applies to the subvector AR test statistic that is robust to an approximate kronecker product structure of conditional heteroskedasticity as proposed by Guggenberger, Kleibergen, and Mavroeidis (2024), carrying over its power advantage to this setting as well.
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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 | Guggenberger, Patrik and Kleibergen, Frank and Mavroeidis, Sophocles (2024) A powerful Subvector Anderson-Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity | 0.843 | 4 | 4 | 75% |
| 2 | Patrik Guggenberger and Frank Kleibergen and Sophocles Mavroeidis (2019) A More Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression | 0.843 | 3 | 3 | 100% |
| 3 | James H. Stock and Motohiro Yogo (2005) Testing for Weak Instruments in Linear IV Regression | 0.737 | 3 | 2 | 100% |
| 4 | T. W. Anderson and Herman Rubin (1949) Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations | 0.644 | 2 | 2 | 100% |
| 5 | John G. Cragg and Stephen G. Donald (1993) Testing Identifiability and Specification in Instrumental Variable Models | 0.644 | 2 | 2 | 100% |
| 6 | James, Alan T (1964) Distributions of Matrix Variates and Latent Roots Derived from Normal Samples | 0.511 | 3 | 2 | 33% |
| 7 | Muirhead, Robb J (2009) Aspects of Multivariate Statistical Theory | 0.511 | 2 | 2 | 50% |
| 8 | T. W. Anderson (1977) Asymptotic Expansions of the Distributions of Estimates in Simultaneous Equations for Alternative Parameter Sequences | 0.405 | 1 | 1 | 100% |
| 9 | R. L. Basmann (1960) On Finite Sample Distributions of Generalized Classical Linear Identifiability Test Statistics | 0.405 | 1 | 1 | 100% |
| 10 | Patrik Guggenberger and Frank Kleibergen and Sophocles Mavroeidis an… (2012) On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression | 0.405 | 1 | 1 | 100% |
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