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.


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