Identification-Robust Factor Pricing: Canadian Evidence

Abstract

We analyze factor models based on the Arbitrage Pricing Theory (APT). using identification-robust inference methods. Such models involve nonlinear reduced-rank restrictions whose identification may raise serious non-regularities and lead to a failure of standard asymptotic theory. We build confidence sets for structural parameters based on inverting Hotelling-type pivotal statistics. These confidence sets provide much more information than the corresponding tests. Our approach may be interpreted as a multivariate extension of the Fieller method for inference on mean ratios. We also introduce a formal definition for a redundant factor linking the presence of such factors to unbounded confidence sets, and we document their perverse effects on minimum-root-based model tests. Results are applied to multifactor asset-pricing models with Canadian data, the Fama-French-Carhart benchmarks and monthly returns of 25 portfolios from 1991 to 2010. Despite evidence of weak identification, several findings deserve notice when data are analyzed over ten-year subperiods. With equally weighted portfolios, the three-factor model is rejected before 2000, but weakly supported thereafter. In contrast, the three-factor model is not rejected with value-weighted portfolios. Interestingly in this case, the market factor is priced before 2000 along with size, while both Fama-French factors are priced thereafter. The momentum factor severely compromises identification, which calls for caution in interpreting existing work documenting momentum effects on the Canadian market. This empirical analysis underscores the practical usefulness of our analytical confidence sets.