Identification Through Sparsity in Factor Models

Factor models are generally subject to a rotational indeterminacy, meaning that individual factors are only identified up to a rotation. In the presence of local factors, which only affect a subset of the outcomes, we show that the implied sparsity of the loading matrix can be used to solve this rotational indeterminacy. We further prove that a rotation criterion based on the 1-norm of the loading matrix can be used to achieve identification even under approximate sparsity in the loading matrix. This enables us to consistently estimate individual factors, and to interpret them as structural objects. Monte Carlo simulations suggest that our criterion performs better than widely used heuristics, and we find strong evidence for the presence of local factors in financial and macroeconomic datasets.