A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

10 Pages Posted: 8 Nov 2016

See all articles by Namhyun Kim

Namhyun Kim

University of Exeter Business School

Winfried Pohlmeier

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE)

Date Written: December 2016

Abstract

The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.

Suggested Citation

Kim, Namhyun and Pohlmeier, Winfried, A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments (December 2016). Oxford Bulletin of Economics and Statistics, Vol. 78, Issue 6, pp. 915-924, 2016, Available at SSRN: https://ssrn.com/abstract=2866090 or http://dx.doi.org/10.1111/obes.12144

Namhyun Kim (Contact Author)

University of Exeter Business School ( email )

Streatham Court
Xfi Building, Rennes Dr.
Exeter, EX4 4JH
United Kingdom

Winfried Pohlmeier

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE) ( email )

Konstanz, D-78457
Germany

HOME PAGE: http://econometrics.wiwi.uni-konstanz.de

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
2
Abstract Views
171
PlumX Metrics