The traditional New Keynesian dynamic stochastic general equilibrium model of business cycle fluctuations generally abstracts from fluctuations in unemployment and employment. We propose a model that incorporates a labor market with wage and matching frictions into a New Keynesian sticky price model. We analyze the effect of a monetary policy shock on unemployment and investigate how labor market frictions in turn affect the transmission process of monetary policy on inflation. The model allows wage rigidities to interact with adjustments in employment and hours affecting inflation dynamics via marginal costs. We find a significant impact of the degree of wage rigidity on the response of unemployment and inflation to an interest rate innovation. Moreover, the impact of a monetary policy shock on unemployment and inflation depends not just on the degree of wage persistence but also on labor market fundamentals such as bargaining power and the flows in and out of employment.