Spurious Inference in Unidentified Asset-Pricing Models

This paper studies some seemingly anomalous results that arise in possibly misspecified and uniden-tified linear asset-pricing models estimated by maximum likelihood and one-step generalized method of moments. Strikingly, when useless factors (that is, factors that are independent of the returns on the test assets) are present, the models exhibit perfect fit, as measured by the squared correlation between the model’s fitted expected returns and the average realized returns, and the tests for cor-rect model specification have asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large. We also derive the highly non-standard limiting be-havior of these invariant estimators and their t-tests in the presence of identification failure. These results reveal the spurious nature of inference as factors that are useless are selected with hig