arXiv 27 Aug 2019 · Econometrics · publishedEconometrica (2021) · 3 citations (OpenAlex)
arXiv:1908.10478 · PDF · DOI · OpenAlex · Extracted main text
We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, i.e., when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of sufficiency and minimality help pin down a desirable one. If estimation of minimal sufficient underlying parameters is inefficient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao-Blackwellization. We call an estimator weakly efficient if it does not admit such improvement. New weakly efficient estimators are presented in linear IV and nonlinear regression models. Simulation of a linear IV model demonstrates how 2SLS and optimal IV estimators are improved.
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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 | van der Vaart, A. W (1998) Asymptotic Statistics | 0.961 | 9 | 5 | 89% |
| 2 | Bickel, P. J., C. A. J. Klaassen, Y. Ritov, and J. A. Wellner (1993) Efficient and Adaptive Estimation for Semiparametric Models | 0.928 | 4 | 3 | 100% |
| 3 | Staiger, D. and J. H. Stock (1997) Instrumental Variables Regression with Weak Instruments | 0.874 | 5 | 2 | 100% |
| 4 | Dufour, J.-M (1997) Some Impossibility Theorems in Econometrics With Applications to Structural and Dynamic Models | 0.811 | 4 | 2 | 100% |
| 5 | Stock, J. H. and J. H. Wright (2000) GMM with Weak Identification | 0.811 | 4 | 2 | 100% |
| 6 | Andrews, D. W. K. and X. Cheng (2012) Estimation and Inference With Weak, Semi-Strong, and Strong Identification | 0.737 | 3 | 2 | 100% |
| 7 | Hirano, K. and J. R. Porter (2015) Location Properties of Point Estimators in Linear Instrumental Variables and Related Models | 0.737 | 3 | 2 | 100% |
| 8 | van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence and Empirical Processes: With Applications to Statistics | 0.714 | 11 | 3 | 36% |
| 9 | Andrews, I. and T. B. Armstrong (2017) Unbiased Instrumental Variables Estimation Under Known First-Stage Sign | 0.644 | 2 | 2 | 100% |
| 10 | Newey, W. K (1994) Series Estimation of Regression Functionals | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 21 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Quasi-Bayesian Hierarchical Models | 0.811 | 4 | 2 |
| 2 | Locally regular and efficient tests in non-regular semiparametric models | 0.737 | 3 | 2 |
| 3 | Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models | 0.405 | 1 | 1 |
| 4 | Ill-Conditioned Orthogonal Scores in Double Machine Learning | 0.405 | 1 | 1 |
| 5 | Inference under First-Order Degeneracy | 0.405 | 1 | 1 |