We revisit the issue of the high cyclicality of wages of new hires. We show that after controlling for composition effects likely involving procyclical upgrading of job match quality, the wages of new hires are no more cyclical than those of existing workers. The key implication is that the sluggish behavior of wages for existing workers is a better guide to the cyclicality of the marginal cost of labor than is the high measured cyclicality of new hires wages unadjusted for composition effects. Key to our identification is distinguishing between new hires from unemployment versus those who are job changers. We argue that to a reasonable approximation, the wages of the former provide a composition-free estimate of the wage flexibility, while the same is not true for the latter. We then develop a quantitative general equilibrium model with sticky wages via staggered contracting, on-the-job search, and heterogeneous match quality, and show that it can account for both the panel data evidence and aggregate evidence on labor market volatility.