How do minimum wages (MW) shape the aggregate wage dynamics when wage adjustment is lumpy? In this paper, we document new empirical findings on the effect of MW on wage rigidity using quarterly micro wage data matched with sectoral bargained MW. We estimate a micro empirical model of wage rigidity taking into account minimum wage dynamics and we use a simulation method to investigate implications of lumpy micro wage adjustment for the aggregate wage dynamics. Our main findings are the following. Both national and sectoral MW have a large effect on the timing and on the size of wage adjustments. At the aggregate level, MW contribute to amplify, by a factor of 1.7, the response of wages to past inflation. Ignoring MW leads to underestimate the speed of aggregate wage adjustment by about a year. The elasticities of wages with respect to past inflation, the national MW and industry-level MW are respectively 0.42, 0.17 and 0.16. Finally, there are significant spillover effects of the NMW on higher wages transiting through industry-level MW.