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Theory of Weak Identification in Semiparametric Models

Tetsuya Kaji

arXiv 27 Aug 2019 · Econometrics · publishedEconometrica (2021) · 3 citations (OpenAlex)

arXiv:1908.10478 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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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
1van der Vaart, A. W (1998) Asymptotic Statistics0.9619589%
2Bickel, P. J., C. A. J. Klaassen, Y. Ritov, and J. A. Wellner (1993) Efficient and Adaptive Estimation for Semiparametric Models0.92843100%
3Staiger, D. and J. H. Stock (1997) Instrumental Variables Regression with Weak Instruments0.87452100%
4Dufour, J.-M (1997) Some Impossibility Theorems in Econometrics With Applications to Structural and Dynamic Models0.81142100%
5Stock, J. H. and J. H. Wright (2000) GMM with Weak Identification0.81142100%
6Andrews, D. W. K. and X. Cheng (2012) Estimation and Inference With Weak, Semi-Strong, and Strong Identification0.73732100%
7Hirano, K. and J. R. Porter (2015) Location Properties of Point Estimators in Linear Instrumental Variables and Related Models0.73732100%
8van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence and Empirical Processes: With Applications to Statistics0.71411336%
9Andrews, I. and T. B. Armstrong (2017) Unbiased Instrumental Variables Estimation Under Known First-Stage Sign0.64422100%
10Newey, W. K (1994) Series Estimation of Regression Functionals0.64422100%

Showing the top 10 of 21 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Quasi-Bayesian Hierarchical Models0.81142
2Locally regular and efficient tests in non-regular semiparametric models0.73732
3Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models0.40511
4Ill-Conditioned Orthogonal Scores in Double Machine Learning0.40511
5Inference under First-Order Degeneracy0.40511