Identification through sparsity in factor models: The ℓ1-rotation criterion

• 成果类型: Article
• 署名作者: Freyaldenhoven, Simon
• 署名单位: Federal Reserve System - USA; Federal Reserve Bank - Philadelphia
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2369
• 发表日期: 2026
• 关键词: INDEPENDENT COMPONENT ANALYSIS; analytic rotation; number; arbitrage; VARIMAX

摘要

Linear factor models are generally not identified. We provide sufficient conditions for identification: Under a natural sparsity assumption (the presence of local factors that affect only subsets of observables), the true loading matrix is the sparsest rotation and can be recovered by minimizing the & ell; 1-norm of the loading matrix. This enables economically meaningful interpretation of the individual factors. More generally, our & ell; 1-rotation criterion offers a novel approach to simplify the loading matrix and performs well relative to existing methods (e.g., Varimax, Kaiser (1958)) in our simulations. We illustrate our method in two economic applications. The R package l1rotation implements the method and facilitates adoption.