ONLINE - Identification through Sparsity in Factor Models: the l1-Rotation Criterion

24.09.2021 15:15 – 16:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT

We show that sparsity in the loading matrix can solve the rotational indeterminacy in factor models, allowing a researcher to recover how individual factors relate to the observed variables. The key insight is that any rotation of a sparse loading vector will be less sparse. While a rotation criterion based on the l0-norm of the loading matrix is infeasible, we prove that a rotation criterion based on the l1-norm will consistently recover the individual loading vectors under sparsity in the loading matrix. Existing rotation criteria (e.g. the Varimax rotation, \cite{kaiser1958}) lack such theoretical guarantees.

We further show that the assumption of sparsity in the loading matrix is testable, and develop such a test. Our l1-rotation performs better than existing rotation criteria in our simulations, and we find strong evidence for the presence of local factors in two economic applications.

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