Do Greasy Wheels Curb Inequality?

I document a disparity in the cyclically 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 college 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 more educated respond on the wage margin. An important takeaway: conventional monetary policy easing reduces employment inequality but increases wage inequality. I embed thesefindings in a New Keynesian framework including price and heterogeneous wage rigidity and show that heterogeneity results in welfare losses resulting from fluctuations that exceed those of the output-gap and price-level equivalent representative agent economy. The excess welfare loss is borne by the least educated. An implication is that the welfare performance of a Taylor-type rule can be improved by including a feedback on the unemployment gap which overweights the unemployment gap.