Tikhonov regularization for nonparametric instrumental variable estimators

Patrick Gagliardini () and Olivier Scaillet

Journal of Econometrics, 2012, vol. 167, issue 1, 61-75

Abstract: We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives. After showing its consistency in the Sobolev norm and uniform consistency under an embedding condition, we derive the expression of the asymptotic Mean Integrated Square Error and the rate of convergence. The optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical findings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.

Keywords: Nonparametric estimation; Ill-posed inverse problems; Tikhonov regularization; Endogeneity; Instrumental variable (search for similar items in EconPapers)
JEL-codes: C13 C14 C15 D12 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (48)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407611002375
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:167:y:2012:i:1:p:61-75

DOI: 10.1016/j.jeconom.2011.08.006

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().