Babii, Andrii and Florens, Jean-Pierre (2020) Is completeness necessary? Estimation in nonidentified linear models. TSE Working Paper, n. 20-1091, Toulouse

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This paper documents the consequences of the identification failures in a class of linear ill-posed inverse models. The Tikhonov-regularized estimator converges to a well-defined limit equal to the best approximation of the structural parameter in the orthogonal complement to the null space of the operator. We illustrate that in many instances the best approximation may coincide with the structural parameter or at least may reasonably approximate it. We obtain a new nonasymptotic risk bounds in the uniform and the Hilbert space norms for the best approximation. Nonidentification has important implications for the large sample distribution of the Tikhonov-regularized estimator, and we document the transition between the Gaussian and the weighted chi-squared
limits. The theoretical results are illustrated for the nonparametric IV and the functional linear IV regressions and are further supported by the Monte Carlo experiments.

Item Type: Monograph (Working Paper)
Language: English
Date: April 2020
Place of Publication: Toulouse
Uncontrolled Keywords: nonidentified linear models, weak identification, nonparametric IV regression, functional linear IV regression, Tikhonov regularization.
JEL Classification: C14 - Semiparametric and Nonparametric Methods
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 21 Apr 2020 08:03
Last Modified: 08 Apr 2021 12:48
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