Recent theoretical and empirical advances have renewed interest in monopsonistic models of the labor market. However, there is little direct empirical support for these models. We use an exogenous change in wages at Department of Veterans Affairs (VA) hospitals as a natural experiment to investigate the extent of monopsony in the nurse labor market. We estimate that labor supply to individual hospitals is quite inelastic, with short‐run elasticity around 0.1. We also find that non‐VA hospitals responded to the VA wage change by changing their own wages.