Is Completeness Necessary? Estimation in Nonidentified Linear Models

53 Pages Posted: 13 Sep 2017 Last revised: 10 Nov 2021

See all articles by Andrii Babii

Andrii Babii

University of North Carolina at Chapel Hill

Jean-Pierre Florens

University of Toulouse

Date Written: September 11, 2017

Abstract

We show that estimators based on spectral regularization converge to the best approximation of a structural parameter in a class of nonidentified linear ill-posed inverse models. Importantly, this convergence holds in the uniform and Hilbert space norms. We describe several circumstances when the best approximation coincides with a structural parameter, or at least reasonably approximates it, and discuss how our results can be useful in the partial identification setting. Lastly, we document that identification failures have important implications for the asymptotic distribution of a linear functional of regularized estimators, which can have a weighted chi-squared component. The theory is illustrated for various high-dimensional and nonparametric IV regressions.

Keywords: completeness condition, weak identification, nonparametric IV regression, high-dimensional regressions, spectral regularization

JEL Classification: C14, C26

Suggested Citation

Babii, Andrii and Florens, Jean-Pierre, Is Completeness Necessary? Estimation in Nonidentified Linear Models (September 11, 2017). Available at SSRN: https://ssrn.com/abstract=3035393 or http://dx.doi.org/10.2139/ssrn.3035393

Andrii Babii (Contact Author)

University of North Carolina at Chapel Hill ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27514
United States

Jean-Pierre Florens

University of Toulouse ( email )

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+33(0)5 61 12 85 96 (Phone)
+33(0)5 61 12 86 37 (Fax)

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