Partly linear instrumental variables regressions without smoothing on the instruments

We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber–Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normali...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2024-09, Vol.33 (3), p.897-920
Main Authors: Florens, Jean-Pierre, Lapenta, Elia
Format: Article
Language:English
Subjects:
Asymptotic methods
Economics
Finance
Insurance
Management
Mathematics and Statistics
Normality
Original Paper
Parameter estimation
Parameter identification
Regularization
Statistical Theory and Methods
Statistics
Statistics for Business
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Summary:We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber–Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rate for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-024-00931-z