Reduced-Rank Regression: A Useful Determinant Identity

Abstract

We derive an identity for the determinant of a product involving non-squared matrices. The identity can be used to derive the maximum likelihood estimator in reduced-rank regressions with Gaussian innovations. Furthermore, the identity sheds light on the structure of the estimation problem that arises when the reduced-rank parameters are subject to additional constraints.

Keywords: Determinant Identity, Reduced Rank Regression, Least Squares

JEL Classification: C3, C32