Invariant Inference and Efficient Computation in the Static Factor Model

Abstract

Factor models are used in a wide range of areas. Two issues with Bayesian versions of these models are a lack of invariance to ordering of and scaling of the variables and computational inefficiency. This article develops invariant and efficient Bayesian methods for estimating static factor models. This approach leads to inference that does not depend upon the ordering or scaling of the variables, and we provide arguments to explain this invariance. Beginning from identified parameters which are subject to orthogonality restrictions, we use parameter expansions to obtain a specification with computationally convenient conditional posteriors. We show significant gains in computational efficiency. Identifying restrictions that are commonly employed result in interpretable factors or loadings and, using our approach, these can be imposed ex-post. This allows us to investigate several alternative identifying (noninvariant) schemes without the need to respecify and resample the model. We illustrate the methods with two macroeconomic datasets.