It is common knowledge that the standard New Keynesian model is not able to generate a persistent response in output to temporary monetary shocks. We show that this shortcoming can be remedied in a simple and intuitively appealing way through the introduction of labor turnover costs (such as hiring and firing costs). Assuming that it is costly to hire and fire workers implies that the employment rate is slow to converge to its steady state value after a monetary shock. The after-effects of a shock continue to exert an effect on the labor market even long after the shock is over. The sluggishness of the labor market translates to the product market and thus the output effects of the monetary shock become more persistent. Under reasonable calibrations our model generates hump-shaped output responses. In addition, it is able to replicate the Beveridge curve relationship and a negative correlation between job creation and job destruction.