Identification Through Sparsity in Factor Models: the l1-rotation criterion

Simon Freyaldenhoven

Abstract:

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. Existing rotation criteria (e.g. VARIMAX, Kaiser 1958) are theoretically unjustified and perform worse in our simulations. We illustrate our method in two economic applications.