A new estimator is proposed for linear triangular systems, where identification results from the model errors following a bivariate and diagonal GARCH(1,1) process with potentially time-varying error covariances. This estimator applies when traditional instruments are unavailable. I demonstrate its usefulness on asset pricing models like the capital asset pricing model and Fama–French three-factor model. In the context of a standard two-pass cross-sectional regression approach, this estimator improves the pricing performance of both models. Set identification bounds and an associated estimator are also provided for cases where the conditions supporting point identification fail. Copyright © 2013 John Wiley & Sons, Ltd.