When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

Frühwirth-Schnatter, Sylvia; Hosszejni, Darjus; Lopes, Hedibert Freitas

doi:10.3390/econometrics11040026

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When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

by

Sylvia Frühwirth-Schnatter

¹

,

Darjus Hosszejni

^1,*

and

Hedibert Freitas Lopes

^2,3

¹

Department of Finance, Accounting, and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria

²

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA

³

Insper Institute of Education and Research, São Paulo 04546-042, Brazil

^*

Author to whom correspondence should be addressed.

Econometrics 2023, 11(4), 26; https://doi.org/10.3390/econometrics11040026

Submission received: 24 February 2023 / Revised: 29 October 2023 / Accepted: 1 November 2023 / Published: 20 November 2023

(This article belongs to the Special Issue High-Dimensional Time Series in Macroeconomics and Finance)

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Abstract

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis.

Keywords: identifiability; sparsity; rank deficiency; rotational invariance; variance identification

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MDPI and ACS Style

Frühwirth-Schnatter, S.; Hosszejni, D.; Lopes, H.F. When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures. Econometrics 2023, 11, 26. https://doi.org/10.3390/econometrics11040026

AMA Style

Frühwirth-Schnatter S, Hosszejni D, Lopes HF. When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures. Econometrics. 2023; 11(4):26. https://doi.org/10.3390/econometrics11040026

Chicago/Turabian Style

Frühwirth-Schnatter, Sylvia, Darjus Hosszejni, and Hedibert Freitas Lopes. 2023. "When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures" Econometrics 11, no. 4: 26. https://doi.org/10.3390/econometrics11040026

APA Style

Frühwirth-Schnatter, S., Hosszejni, D., & Lopes, H. F. (2023). When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures. Econometrics, 11(4), 26. https://doi.org/10.3390/econometrics11040026

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

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