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 unified 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.