Gustavo Schlemper, Marcelo J. Moreira
arXiv 5 Apr 2026 · Econometrics
arXiv:2604.04279 · PDF · DOI · OpenAlex · Extracted main text
We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In practice, researchers typically recover such sets by grid search, a procedure that can miss parts of the confidence region, truncate unbounded sets, and deliver misleading inference. We replace grid inversion with exact and approximation-based methods that are both reliable and computationally efficient. Our approach exploits the polynomial and rational structure of the Anderson-Rubin and Lagrange multiplier statistics to obtain exact confidence sets via polynomial root finding. For the conditional quasi-likelihood ratio test, we derive an exact inversion algorithm based on the geometry of the statistic and its critical value function. For more general conditional tests, we construct polynomial approximations whose coverage error vanishes with approximation degree, allowing numerical accuracy to be made arbitrarily high. In many empirical applications with weak instruments, standard grid methods produce incorrect confidence regions, while our procedures reliably recover sets with correct nominal coverage. The framework extends beyond linear IV to models with piecewise polynomial or rational moment conditions, offering a general tool for reliable weak-identification robust inference.
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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 | Motohiro Yogo Estimating the Elasticity of Intertemporal Rate of Substitution When Instruments Are Weak | 1.000 | 17 | 3 | 100% |
| 2 | Kleibergen, F Testing Parameters in GMM without Assuming that they are Identified | 1.000 | 6 | 3 | 100% |
| 3 | Moreira, M. J A Conditional Likelihood Ratio Test for Structural Models self | 1.000 | 6 | 3 | 100% |
| 4 | Stock, J. H. and J. Wright GMM with Weak Identification | 0.928 | 4 | 3 | 100% |
| 5 | Isaiah Andrews and Anna Mikusheva Conditional Inference with a Functional Nuisance Parameter | 0.843 | 3 | 3 | 100% |
| 6 | Moreira, M. J Tests with Correct Size in the Simultaneous Equations Model self | 0.843 | 3 | 3 | 100% |
| 7 | H. Moreira and M. J. Moreira Optimal Two-Sided Tests for Instrumental Variables Regression with Heteroskedastic and Autocorrelated Errors self | 0.843 | 3 | 3 | 100% |
| 8 | Anna Mikusheva Robust Confidence Sets in the Presence of Weak Instruments | 0.811 | 4 | 2 | 100% |
| 9 | Andrews, D. W. K. and M. J. Moreira and J. H. Stock Optimal Invariant Similar Tests for Instrumental Variables Regression self | 0.737 | 3 | 2 | 100% |
| 10 | Moreira, M. J. and W. Newey and M. Sharifvaghefi Robust GMM estimation and testing in a weak instrument setting: bridging theory and practice self | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 32 scored citations.