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Properties of the Conditional Likelihood Ratio Test under Discrete Approximation

Marcelo J. Moreira, Mahrad Sharifvaghefi

arXiv 5 Jul 2026 · Econometrics

arXiv:2607.04380 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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11
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36
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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
1Isaiah Andrews and Anna Mikusheva Conditional Inference with a Functional Nuisance Parameter1.000154100%
2Moreira, M. J. and W. Newey and M. Sharifvaghefi Robust GMM estimation and testing in a weak instrument setting: bridging theory and practice self1.00075100%
3Andrews, D. W. K. and M. J. Moreira and J. H. Stock (2006) Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression self0.64422100%
4H. Moreira and M. J. Moreira Optimal Two-Sided Tests for Instrumental Variables Regression with Heteroskedastic and Autocorrelated Errors self0.64422100%
5Moreira, Marcelo J and Ridder, Geert and Sharifvaghefi, Mahrad Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression self0.64422100%
6Motohiro Yogo Estimating the Elasticity of Intertemporal Rate of Substitution When Instruments Are Weak0.58531100%
7Chao, John C and Hausman, Jerry A and Newey, Whitney K and Swanson,… (2014) Testing overidentifying restrictions with many instruments and heteroskedasticity0.40511100%
8Moreira, M. J A Conditional Likelihood Ratio Test for Structural Models self0.40511100%
9Moreira, M. J. and G. Ridder and M. Sharifvaghefi Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors self0.40511100%
10Moreira, M. J. and M. Sharifvaghefi Corrigendum to the Online Supplement for “Conditional Inference with a Functional Nuisance Parameter” by Andrews and Mikusheva self0.40511100%

Showing the top 10 of 11 scored citations.