WP 20-25/R – Using a novel rotation criterion, we show that sparsity in the loading matrix is sufficient to recover individual loading vectors in a factor model. This enables economic interpretation of the factors.
Previous versions of this working paper were originally published as Identification Through Sparsity in Factor Models in June 2020 and as Identification Through Sparsity in Factor Models: The ℓ1 -Rotation Criterion in November 2021.
Linear factor models are generally not identified. We provide sufficient conditions for identification: Under a sparsity assumption, we can estimate the individual loading vectors using a novel rotation criterion that minimizes the ℓ1-norm of the loading matrix. This enables economic interpretation of the factors. The assumption of sparsity in the loading matrix is testable, and we propose such a test. Existing rotation criteria are theoretically unjustified and perform worse in our simulations. We illustrate our method in two economic applications.