Do greasy wheels curb inequality?

I document a disparity in the cyclicality of the allocative wage-the labor costs considered when deciding to form or dissolve an employment relationship-across levels of educational attainment. Specifically, workers with a bachelors degree or more exhibit an allocative wage that is highly pro-cyclical while high school dropouts exhibit no statistically discernible cyclical pattern. I also assess the response to monetary policy shocks of both employment and allocative wages across education groups. The less educated respond to monetary policy shocks on the employment margin while the more educated respond on the wage margin. An important takeaway is that conventional monetary policy easing reduces employment inequality but increases wage inequality. I embed these findings in a New Keynesian framework that includes price and heterogeneous wage rigidity and show that heterogeneity results in welfare losses due to fluctuations that exceed those of the output-gap and p rice-level equivalent representative agent economy. The excess welfare loss is borne by the least educated