Identification through sparsity in factor models: The ℓ ₁ ‐rotation criterion

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 ℓ 1 ‐norm of the loading matrix. This enables economically meaningful interpretation of the individual factors. More generally, our ℓ 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.