Regularized LIML for many instruments

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: School of Economics Discussion Papers ; No. 1515

Classification and Topics

• Classification: Wirtschaft ; Estimation: General
• Subject: heteroskedasticity ; high-dimensional models ; LIML ; many instruments ; MSE ; regularization methods

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Carrasco, Marine ; Tchuente, Guy
• Event: Veröffentlichung
• (who): University of Kent, School of Economics
• (where): Canterbury
• (when): 2015

Further information

• Handle: http://hdl.handle.net/10419/129982
• Last update: 10.03.2025, 11:43 AM CET