Spanning latent and observable factors

E. Andreou, P. Gagliardini, E. Ghysels and M. Rubin

Journal of Econometrics, 2025, vol. 248, issue C

Abstract: Factor analysis is a widely used tool to summarize high dimensional panel data via a small dimensional set of latent factors. Many applications in finance and macroeconomics, are often focused on observable factors with an economic interpretation. The objective of this paper is to provide a test to answer a question which naturally comes up in discussions regarding latent versus observable factors: do latent and observable factors span the same space? We derive asymptotic properties of a formal test and propose a bootstrap version with improved small sample properties. We find empirical evidence for a small number of factors common between a small number of traditional Fama–French risk factors – or returns on a few stocks (i.e. “magnificent” 5 or 7) – and large panels of US, North American and international portfolio returns.

Keywords: Latent pervasive factors; Observable factors; Canonical correlations; Spanning; PCA (search for similar items in EconPapers)
JEL-codes: C12 C23 C38 C55 E32 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:248:y:2025:i:c:s0304407624000897

DOI: 10.1016/j.jeconom.2024.105743

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