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LARGE SYSTEM OF SEEMINGLY UNRELATED REGRESSIONS: A PENALIZED QUASI-MAXIMUM LIKELIHOOD ESTIMATION PERSPECTIVE

Published online by Cambridge University Press:  27 May 2019

Qingliang Fan ,
Xiao Han ,
Guangming Pan  and
Bibo Jiang
Qingliang Fan*
Affiliation:
Xiamen University
Xiao Han
Affiliation:
Nanyang Technological University
Guangming Pan
Affiliation:
Nanyang Technological University
Bibo Jiang
Affiliation:
Pennsylvania State University
*
*Address correspondence to Qingliang Fan, MOE Key Lab of Econometrics, Wang Yanan Institute of Studies in Economics (WISE) and School of Economics, Xiamen University, D312 Economics Bldg, Xiamen University, Xiamen 361005, China; e-mail: michaelqfan@gmail.com.
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Abstract

In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate of the estimated covariance matrix in terms of the Frobenius norm. The model selection consistency of the covariance matrix estimator is also established. Simulation results show that when the number of equations is large relative to the sample size and the error covariance matrix is sparse, the PQMLE outperforms other contemporary estimators.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 3 , June 2020 , pp. 526 - 558
Copyright
Copyright © Cambridge University Press 2019 

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Footnotes

Thanks to Liangjun Su (co-editor) and two anonymous referees for their insightful comments and references, which have helped to greatly improve the earlier version of this article. We are grateful to Peter C. B. Phillips, M. Hashem Pesaran and seminar and conference participants from Singapore Management University, Peking University, SETA 2014, 4th IAAE conference, etc., for their helpful comments. Qingliang Fan acknowledges support of the National Natural Science Foundation of China (NSFC) grant 71671149, 71631004 (Key Project), and the Fundamental Research Funds for the Central Universities (Project No. 20720171042).

References

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