We focus on a quantitative assessment of rigid labor markets in an environment of stable monetary policy. We ask how wages and labor market shocks feed into the inflation process and derive monetary policy implications. Towards that aim, we structurally model matching frictions and rigid wages in line with an optimizing rationale in a New Keynesian closed economy DSGE model. We estimate the model using Bayesian techniques for German data from the late 1970s to present. Given the pre-euro heterogeneity in wage bargaining we take this as the first-best approximation at hand for modelling monetary policy in the presence of labor market frictions in the current European regime. In our framework, we find that labor market structure is of prime importance for the evolution of the business cycle, and for monetary policy in particular. Yet shocks originating in the labor market itself may contain only limited information for the conduct of stabilization policy.