Two-stage Liu estimator in a simultaneous equations model

ABSTRACT

Two-stage least squares estimation in a simultaneous equations model has several desirable properties under the problem of multicollinearity. So, various kinds of improved estimation techniques can be developed to deal with the problem of multicollinearity. One of them is ridge regression estimation that can be applied at both stages and defined in Vinod and Ullah [Recent advances in regression methods. New York: Marcel Dekker; 1981]. We propose three different kinds of Liu estimators that are named by their implementation stages. Mean square errors are derived to compare the performances of the mentioned estimators and two different choices of the biasing parameter are offered. Moreover, a numerical example is given with a data analysis based on the Klein Model I and a Monte Carlo experiment is conducted.

KEYWORDS:

• Liu estimator
• multicollinearity
• ridge estimator
• simultaneous equations model
• two-stage estimation

2010 AMS SUBJECT CLASSIFICATIONS:

• 62H12
• 62J05
• 62J07
• 62P20

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Selma Toker http://orcid.org/0000-0002-4557-1646

Additional information

Funding

Selma Toker was supported by Çukurova University Scientific Research Projects Unit (project number 2852).