Do asset pricing models change over time?

The literature commonly evaluates factor models based on their unconditional performance. This paper proposes a novel method to identify time-varying factor models, examining whether these models change over time. Our method estimates the conditional stochastic discount factor (SDF) model by accounting for time variation in both factor sets and their SDF loadings. Our empirical results reject the hypothesis of a time-invariant factor model, instead supporting time-varying sparsity in the SDF. Our conditional SDF model accommodates sparse risk prices and explains various anomalies with time-varying, potentially nonzero premia. We recommend prioritizing testing risk price over risk premia to evaluate pricing factors.