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THREE-DIMENSIONAL FACTOR MODELS WITH GLOBAL AND LOCAL FACTORS

Published online by Cambridge University Press:  11 August 2025

Xun Lu ,
Sainan Jin  and
Liangjun Su
Xun Lu
Affiliation:
https://ror.org/00t33hh48 Chinese University of Hong Kong
Sainan Jin
Affiliation:
https://ror.org/03cve4549 Tsinghua University
Liangjun Su*
Affiliation:
https://ror.org/03cve4549 Tsinghua University
*
Address correspondence to Liangjun Su, School of Economics and Management, Tsinghua University, Beijing, China, e-mail: sulj@sem.tsinghua.edu.cn.
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Abstract

This article considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We show that the numbers of global and local factors can be estimated uniformly and consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA) and establish the asymptotic properties of the PCA estimators. Monte Carlo simulations demonstrate that they perform well in finite samples. An application to the dataset of international trade reveals the relative importance of different types of factors.

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ARTICLES
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Econometric Theory , First View , pp. 1 - 47
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

The authors thank the Editor, Peter C.B. Phillips, a Co-Editor, and two anonymous referees for their constructive comments. Lu acknowledges support from the Hong Kong Research Grants Council (RGC) under grant number 14500121 and Chinese University of Hong Kong for the start-up fund. Su thanks the National Natural Science Foundation of China (NSFC) for financial support under the grant number 72133002. All errors are the authors’ sole responsibilities.

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