Patrik Guggenberger, Frank Kleibergen, Sophocles Mavroeidis
arXiv 21 Mar 2021 · Econometrics · publishedEconometric Theory (2023) · 2 citations (OpenAlex)
arXiv:2103.11371 · PDF · DOI · OpenAlex · Extracted main text
We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger et al. (2019), GKM19 from now on, introduce a subvector Anderson-Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity. The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests conditional homoskedasticity. The new test equals this adaption when the data is consistent with AKP structure as decided by a model selection procedure. Otherwise the test equals the AR/AR test in Andrews (2017) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.
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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 | Andrews, D. W (2017) Identification-robust subvector inference | 0.961 | 36 | 7 | 89% |
| 2 | Dufour, J.-M. and M. Taamouti (2005) Projection-based statistical inference in linear structural models with possibly weak instruments | 0.737 | 3 | 2 | 100% |
| 3 | Stock, J. H. and J. H. Wright (2000) GMM with weak identification | 0.693 | 10 | 1 | 100% |
| 4 | Andrews, D. W. and G. Soares (2010) Inference for parameters defined by moment inequalities using generalized moment selection | 0.644 | 2 | 2 | 100% |
| 5 | Guggenberger, P., F. Kleibergen, and S. Mavroeidis (2019) A more powerful subvector Anderson Rubin test in linear instrumental variables regression self | 0.644 | 2 | 2 | 100% |
| 6 | Guggenberger, P., F. Kleibergen, S. Mavroeidis, and L. Chen (2012) On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression self | 0.644 | 2 | 2 | 100% |
| 7 | Kleibergen, F (2021) Efficient size correct subset inference in homoskedastic linear instrumental variables regression self | 0.644 | 2 | 2 | 100% |
| 8 | van Loan, C. F. and N. Pitsianis (1993) Approximation with Kronecker products | 0.606 | 6 | 2 | 33% |
| 9 | Anderson, T. W. and H. Rubin (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations | 0.405 | 1 | 1 | 100% |
| 10 | Andrews, D. W. and X. Cheng (2014) GMM estimation and uniform subvector inference with possible identification failure | 0.405 | 1 | 1 | 100% |
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