Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/129982
Authors: 
Carrasco, Marine
Tchuente, Guy
Year of Publication: 
2015
Series/Report no.: 
School of Economics Discussion Papers 1515
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.
Subjects: 
heteroskedasticity
high-dimensional models
LIML
many instruments
MSE
regularization methods
JEL: 
C13
Document Type: 
Working Paper

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