Marcelo J. Moreira, Whitney K. Newey, Mahrad Sharifvaghefi
arXiv 29 Sep 2026 · Econometrics
arXiv:2609.36445 · PDF · Extracted main text
This paper characterizes the global minimum of the continuously updating generalized method of moments (CU-GMM) objective in linear instrumental variables models. We allow optimal weighting matrices under heteroskedasticity, autocorrelation, or clustering. We show that the objective is a ratio of polynomials. For one endogenous regressor, stationary points of CU-GMM objective function are real eigenvalues of a companion matrix. Comparing their objective values with the value at infinity gives the global minimum, extending the classical eigenvector approach to limited information maximum likelihood. With multiple endogenous regressors, algebraic elimination and checks for real solutions identify the minimum among finitely many candidate objective values, including boundary values. Galois theory rules out general formulas by radicals even with one endogenous regressor and two instruments, while numerical root finding remains possible. Finding the global minimum allows us to compute overidentification and likelihood ratio tests, including the conditional likelihood ratio (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 | Whitney K. Newey and Frank Windmeijer (2009) Generalized Method of Moments with Many Weak Moment Conditions self | 1.000 | 6 | 4 | 100% |
| 2 | Paul A. Bekker Alternative Approximations to the Distributions of Instrumental Variables Estimators | 0.843 | 3 | 3 | 100% |
| 3 | Moreira, M. J A Conditional Likelihood Ratio Test for Structural Models self | 0.843 | 3 | 3 | 100% |
| 4 | Moreira, Marcelo J and Ridder, Geert and Sharifvaghefi, Mahrad Power Bounds and Efficiency Loss for Asymptotically Optimal Tests in IV Regression self | 0.843 | 3 | 3 | 100% |
| 5 | Moreira, Marcelo J and Sharifvaghefi, Mahrad (2026) Properties of the Conditional Likelihood Ratio Test under Discrete Approximation self | 0.843 | 3 | 3 | 100% |
| 6 | Lars Peter Hansen and John Heaton and Amir Yaron (1996) Finite-Sample Properties of Some Alternative GMM Estimators | 0.737 | 3 | 2 | 100% |
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| 10 | Melvin Stephens and Dou-Yan Yang (2014) Compulsory Education and the Benefits of Schooling | 0.693 | 5 | 1 | 100% |
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