Regularized LIML for many instruments

Tchuente, Guy and Carrasco, Marine (2015) Regularized LIML for many instruments. Journal of Econometrics, 186 (2). pp. 427-442. ISSN 0304-4076. (doi:https://doi.org/10.1016/j.jeconom.2015.02.018) (Full text available)

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http://dx.doi.org/10.1016/j.jeconom.2015.02.018

Abstract

The use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators. However, in finite samples, the inclusion of an excessive number of moments increases the bias. To solve this problem, we propose regularized versions of the limited information maximum likelihood (LIML) based on three different regularizations: Tikhonov, Landweber–Fridman, and principal components. Our estimators are consistent and asymptotically normal under heteroskedastic error. Moreover, they reach the semiparametric efficiency bound assuming homoskedastic error. We show that the regularized LIML estimators possess finite moments when the sample size is large enough. The higher order expansion of the mean square error (MSE) shows the dominance of regularized LIML over regularized two-staged least squares estimators. We devise a data driven selection of the regularization parameter based on the approximate MSE. A Monte Carlo study and two empirical applications illustrate the relevance of our estimators.

Item Type: Article
Uncontrolled keywords: Heteroskedasticity, High-dimensional models, LIML, Many instruments, MSE, Regularization methods
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HB Economic Theory
Divisions: Faculties > Social Sciences > School of Economics
Depositing User: Guy Tchuente
Date Deposited: 20 Jan 2016 12:53 UTC
Last Modified: 07 Dec 2017 13:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/53782 (The current URI for this page, for reference purposes)
Tchuente, Guy: https://orcid.org/0000-0001-8507-3337
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