Abstract
This paper develops inference for a cross-sectional R^2 constructed from estimated intercepts in multivariate time-series regressions and for differences in this measure across competing linear factor models. In traded-factor asset pricing, the statistic measures the fraction of cross-sectional dispersion in mean returns explained by the model. We show that its asymptotic behavior is regime dependent: under interior configurations it is T^0.5-Gaussian with feasible HAC variance estimation, whereas at perfect fit and related boundary cases it is nonregular and converges at rate T to quadratic-form limits. We develop feasible inference for each regime and comparison tests for nested and non-nested models. Simulations and empirical applications show that apparent differences in model fit often reflect substantial sampling uncertainty.