Shifts in the composition of the workforce meaningfully affect the cyclicality of average wages. This paper argues that such shifts manifest as a representative agent shock to either labor supply or the labor wedge, which are known to be crucial for labor market fluctuations. I develop a tractable model with multidimensional skill heterogeneity and heterogeneous industries to study when composition bias materially impacts aggregate wages. The aggregate impact of sectoral labor demand shocks is mediated by the level and transferability of its workers’ skills. Wages are flexible and the only shock in the model is to labor demand; nevertheless, the model replicates the fact that average wages rose during the Great Recession even as employment collapsed. Reduced form composition-adjustment methods recover positive comovements between employment and wages in recent periods suggesting an increasing role for composition effects through time, which the model rationalizes through changes in the skill distribution and composition of sectoral shocks.