We study the long-run relation between money, measured by inflation or interest
rates, and unemployment. We first document in the data a positive relation
between these variables at low frequencies. We then develop a framework where
unemployment and money are both modeled using microfoundations based on
search and bargaining theory, providing a united theory for analyzing labor
and goods markets. The calibrated model shows that money can account for a
sizable fraction of trends in unemployment. We argue it matters, qualitatively
and quantitatively, whether one uses monetary theory based on search and
bargaining, or an alternative ad hoc specification.