EconBase
← All papers

Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets

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

Abstract

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.

Citation extraction

22
references
203
in-text mentions
22
distinct cited
1
self-citations
12,513
main-text words

appendix boundary found by appendix_command · 45% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Tanaka, T., C. F. Camerer, and Q. Nguyen (2010) Risk and time preferences: Linking experimental and household survey data from vietnam1.000173100%
2Kleibergen, F (2021) Efficient size correct subset inference in homoskedastic linear instrumental variables regression1.000164100%
3Card, D (1995) Using geographic variation in college proximity to estimate the return to schooling1.000143100%
4Anderson, T. W (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions0.95934588%
5Staiger, D. O. and J. H. Stock (1997) Instrumental variables regression with weak instruments0.9568388%
6Londschien, M (2025) A statistician's guide to weak-instrument-robust inference in instrumental variables regression with illustrations in Python self0.94112383%
7Guggenberger, 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 regression0.92749680%
8Guggenberger, P., F. Kleibergen, and S. Mavroeidis (2019) A more powerful subvector Anderson Rubin test in linear instrumental variables regression0.88810370%
9Kleibergen, F (2002) Pivotal statistics for testing structural parameters in instrumental variables regression0.874102100%
10Moreira, M. J (2003) A conditional likelihood ratio test for structural models0.87462100%

Showing the top 10 of 22 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1A statistician's guide to weak-instrument-robust inference in instrumental variables regression with illustrations in Python0.899225
2The exact distribution of the conditional likelihood-ratio test in instrumental variables regression0.64422