Factor models with local factors — Determining the number of relevant factors

We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We derive which factors are pervasi...

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Bibliographic Details
Published in:Journal of econometrics Vol. 229; no. 1; pp. 80 - 102
Main Author: Freyaldenhoven, Simon
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.07.2022
Elsevier Sequoia S.A
Subjects:
Analysis of covariance
econometrics
Eigenvalues
Estimating techniques
Factor models
High-dimensional data
Local factors
mathematical theory
Principal components analysis
Sparsity
Variables
variance covariance matrix
Weak factors
High-dimensional data
C52
C55
Weak factors
Sparsity
C38
Factor models
Local factors
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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Summary:We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We derive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. We then introduce a new class of estimators to determine the number of those relevant factors. Unlike existing estimators, our estimators use not only the eigenvalues of the covariance matrix, but also its eigenvectors. We find that incorporating partial sums of the eigenvectors into our estimators leads to significant gains in performance in simulations.
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2021.04.006