Estimating the rank of a beta matrix: a GMM approach1

A full-rank beta matrix is a necessary condition for correctly estimating the risk premia in linear asset pricing models. However, the true values of betas are unobserved in practice and must be estimated. In this paper, we propose a straightforward testing method based on the generalised method of moments to assess whether the beta matrix is of full rank. We show that our method has desirable finite sample properties and performs better than available alternatives. We apply our method to several popular factor models and find that most models have rank deficiency in several datasets.