We develop and estimate a medium scale macroeconomic model that allows for unemployment and staggered nominal wage contracting. In contrast to most existing quantitative models, the employment and hours of existing workers are efficient. Wage rigidity, however, affects the hiring of new workers. The former is introduced via the staggered Nash bargaing setup of Gertler and Trigari (2006). A robust finding is that the model with wage rigidity provides a better description of the data than does a flexible wage version. In addition, we are able to quantify the effect of wage rigidity on output and inflation dynamics. More work is necessary, however, to ensure a robust identification of the key labor market parameters.