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EFFICIENT ESTIMATION OF FACTOR MODELS

Published online by Cambridge University Press:  02 August 2011

In Choi
In Choi*
Affiliation:
Sogang University
*
*Address correspondence to In Choi, Department of Economics, Sogang University, #1 Shinsu-dong, Mapo-gu, Seoul, Korea; e-mail: inchoi@google.com, inchoi@sogang.ac.kr.
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Abstract

This paper considers the factor model Xt = ΛFt + et. Assuming a normal distribution for the idiosyncratic error et conditional on the factors {Ft}, conditional maximum likelihood estimators of the factor and factor-loading spaces are derived. These estimators are called generalized principal component estimators (GPCEs) without the normality assumption. This paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces. It is shown that variance of the GPCE of the common component is smaller than that of the principal component estimator studied in Bai (2003, Econometrica 71, 135–172). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component estimator. The feasible GPCE (FGPCE) of the factor space is shown to be asymptotically equivalent to the GPCE. The GPCE and FGPCE are shown to be more efficient than the principal component estimator in finite samples.

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Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 274 - 308
Copyright
Copyright © Cambridge University Press 2011

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