Weak-Instrument-Robust Subvector Inference in Instrumental Variables Regression: A Subvector Lagrange Multiplier Test and Properties of Subvector Anderson-Rubin Confidence Sets
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SeriesEconometrics Seminars and Workshop Series
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SpeakersMalte Londschien (ETH Zurich, Switzerland)
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FieldEconometrics, Data Science and Econometrics
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LocationUniversity of Amsterdam, room E5.22
Amsterdam -
Date and time
October 11, 2024
12:30 - 13:30
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 Wald test, which is not robust to weak instruments. 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. Joint paper with Peter Bühlmann.