Marcelo J. Moreira, Geert Ridder, Mahrad Sharifvaghefi
arXiv 22 Mar 2026 · Econometrics
arXiv:2603.21004 · PDF · OpenAlex · Extracted main text
We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic frontier of the testing problem. We show that Lagrange multiplier and conditional quasi likelihood ratio tests can have power arbitrarily close to size even when the null and alternative are well separated, because they do not fully exploit the reduced-form likelihood. In contrast, the conditional likelihood ratio (CLR) test uses the full reduced-form likelihood. We prove that the power-size gap of CLR converges to one if and only if the testing problem becomes trivial in total variation distance, so that CLR attains the decision theoretic frontier whenever any test can. An empirical illustration based on Yogo (2004) shows that these failures arise in empirically relevant configurations.
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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 | Kraft,C Some Conditions for Consistency and Uniform Consistency of Statistical Procedures | 1.000 | 9 | 3 | 100% |
| 2 | Andrews, D. W. K. and M. J. Moreira and J. H. Stock (2006) Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression self | 0.928 | 4 | 3 | 100% |
| 3 | Motohiro Yogo Estimating the Elasticity of Intertemporal Rate of Substitution When Instruments Are Weak | 0.928 | 4 | 3 | 100% |
| 4 | Isaiah Andrews Conditional Linear Combination Tests for Weakly Identified Models | 0.843 | 3 | 3 | 100% |
| 5 | 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% |
| 6 | Moreira, M. J A Conditional Likelihood Ratio Test for Structural Models self | 0.737 | 3 | 2 | 100% |
| 7 | Staiger, D. and J. H. Stock Instrumental Variables Regression with Weak Instruments | 0.737 | 3 | 2 | 100% |
| 8 | Isaiah Andrews and Anna Mikusheva Conditional Inference with a Functional Nuisance Parameter | 0.644 | 2 | 2 | 100% |
| 9 | M. Bertanha and M.J. Moreira Impossible Inference in Econometrics: Theory and Applications self | 0.644 | 2 | 2 | 100% |
| 10 | Dufour, J-M Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 24 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Properties of the Conditional Likelihood Ratio Test under Discrete Approximation | 0.644 | 2 | 2 |