Identication robust inference in multivariate reduced rank regression and factor models

We propose identi…cation robust inference methods for multivariate reduced rank (MRR) regressions. Such models involve nonlinear restrictions on the coe¢ cients of a multivariate linear regression (MLR), whose identi…cation may raise serious non-regularities leading to the failure of standard asymptotics. To circumvent such problems, we propose con…dence set estimates for parameters of interest based on inverting Hotelling-type pivotal statistics. We provide analytical solutions to the latter problem which hold exactly (or asymptotically) imposing (or relaxing) Gaussian error distributions. Simulation-based counterparts are also suggested for non-Gaussian parametric hypotheses. Hotelling’s T criterion, which may be seen as the multivariate counterpart of the student-t statistic, is a widely used pivot in MLR contexts and mostly serves for multivariate test purposes. Our proposed con…dence sets have much more informational content than such tests and have various useful applications in statistics, econometrics and …nance. Our approach further provides multivariate extensions of the classical Fieller problem. Proposed inference methods are applied to a multi-factor Capital Asset Pricing model with unobservable risk-free rates and an Arbitrage Pricing Theory based model with Fama-French factors. Results reveal dramatic di¤erences between the standard Wald-type con…dence set estimates and our proposed identi…cation robust ones and illustrate the severe implications of redundant factors.