Malte Londschien, Peter Bühlmann
arXiv 21 Jul 2024 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2026) · 1 citations (OpenAlex)
arXiv:2407.15256 · PDF · DOI · OpenAlex · Extracted main text
We propose a weak-instrument-robust subvector Lagrange multiplier test for instrumental variables regression. We show that it is asymptotically size-correct under a technical condition. This is the first weak-instrument-robust subvector test for instrumental variables regression to recover the degrees of freedom of the commonly used non-weak-instrument-robust Wald test. Additionally, we provide a closed-form solution for subvector confidence sets obtained by inverting the subvector Anderson-Rubin test. We show that they are centered around a k-class estimator. Also, we show that the subvector confidence sets for single coefficients of the causal parameter are jointly bounded if and only if Anderson's likelihood-ratio test rejects the hypothesis that the first-stage regression parameter is of reduced rank, that is, that the causal parameter is not identified. Finally, we show that if a confidence set obtained by inverting the Anderson-Rubin test is bounded and nonempty, it is equal to a Wald-based confidence set with a data-dependent confidence level. We explicitly compute this Wald-based confidence 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 | Tanaka, T., C. F. Camerer, and Q. Nguyen (2010) Risk and time preferences: Linking experimental and household survey data from vietnam | 1.000 | 17 | 3 | 100% |
| 2 | Kleibergen, F (2021) Efficient size correct subset inference in homoskedastic linear instrumental variables regression | 1.000 | 16 | 4 | 100% |
| 3 | Card, D (1995) Using geographic variation in college proximity to estimate the return to schooling | 1.000 | 14 | 3 | 100% |
| 4 | Anderson, T. W (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions | 0.959 | 34 | 5 | 88% |
| 5 | Staiger, D. O. and J. H. Stock (1997) Instrumental variables regression with weak instruments | 0.956 | 8 | 3 | 88% |
| 6 | Londschien, M (2025) A statistician's guide to weak-instrument-robust inference in instrumental variables regression with illustrations in Python self | 0.941 | 12 | 3 | 83% |
| 7 | 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 | 0.927 | 49 | 6 | 80% |
| 8 | Guggenberger, P., F. Kleibergen, and S. Mavroeidis (2019) A more powerful subvector Anderson Rubin test in linear instrumental variables regression | 0.888 | 10 | 3 | 70% |
| 9 | Kleibergen, F (2002) Pivotal statistics for testing structural parameters in instrumental variables regression | 0.874 | 10 | 2 | 100% |
| 10 | Moreira, M. J (2003) A conditional likelihood ratio test for structural models | 0.874 | 6 | 2 | 100% |
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