with Pierluigi Balduzzi, 2008, Journal of Business and Economic Statistics 26, pp. 354-368. [Paper]. We consider two formulations of the linear factor model with non-traded factors. In the first formulation (LFM), risk premia and alphas are estimated by a cross-sectional regression of average returns on betas. In the second formulation (LFM*), the factors are replaced by their projections on the span of excess returns, and risk premia and alphas are estimated by time-series regressions. We compare the two formulations and study the small-sample properties of estimates and test statistics. We conclude that the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.