Marcelo J. Moreira, Mahrad Sharifvaghefi
arXiv 5 Jul 2026 · Econometrics
arXiv:2607.04380 · PDF · DOI · OpenAlex · Extracted main text
The conditional likelihood ratio (CLR) test is a valuable tool for inference under weak identification, with appealing theoretical properties in both linear and non-linear settings. Its implementation nevertheless requires minimizing a non-convex objective function, a difficulty long recognized even in the linear IV setting. While grid-based methods that provide a practical approximation may perform well in particular designs, such procedures do not guarantee that the resulting test preserves the theoretical properties of the CLR test uniformly across a class of data-generating processes. This paper examines the implementation challenges and their consequences for test size and power. In the linear IV settings, we contrast the grid-based method with the polynomial approach of Moreira, Newey, and Sharifvaghefi(2024), which guarantees global minimization and aligns computation with the theoretical properties of the CLR 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 | Isaiah Andrews and Anna Mikusheva Conditional Inference with a Functional Nuisance Parameter | 1.000 | 15 | 4 | 100% |
| 2 | Moreira, M. J. and W. Newey and M. Sharifvaghefi Robust GMM estimation and testing in a weak instrument setting: bridging theory and practice self | 1.000 | 7 | 5 | 100% |
| 3 | Andrews, D. W. K. and M. J. Moreira and J. H. Stock (2006) Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression self | 0.644 | 2 | 2 | 100% |
| 4 | H. Moreira and M. J. Moreira Optimal Two-Sided Tests for Instrumental Variables Regression with Heteroskedastic and Autocorrelated Errors self | 0.644 | 2 | 2 | 100% |
| 5 | Moreira, Marcelo J and Ridder, Geert and Sharifvaghefi, Mahrad Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression self | 0.644 | 2 | 2 | 100% |
| 6 | Motohiro Yogo Estimating the Elasticity of Intertemporal Rate of Substitution When Instruments Are Weak | 0.585 | 3 | 1 | 100% |
| 7 | Chao, John C and Hausman, Jerry A and Newey, Whitney K and Swanson,… (2014) Testing overidentifying restrictions with many instruments and heteroskedasticity | 0.405 | 1 | 1 | 100% |
| 8 | Moreira, M. J A Conditional Likelihood Ratio Test for Structural Models self | 0.405 | 1 | 1 | 100% |
| 9 | Moreira, M. J. and G. Ridder and M. Sharifvaghefi Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors self | 0.405 | 1 | 1 | 100% |
| 10 | Moreira, M. J. and M. Sharifvaghefi Corrigendum to the Online Supplement for “Conditional Inference with a Functional Nuisance Parameter” by Andrews and Mikusheva self | 0.405 | 1 | 1 | 100% |
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