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We document new empirical findings on the effects of wage setting institutions on wage rigidity using quarterly micro wage data matched with sectoral minimum wages. We first estimate a micro empirical model of wage rigidity that takes into account minimum wage dynamics. We then use a simulation method to investigate the implications of lumpy micro wage adjustment for aggregate wages. Both national and sectoral minimum wages have a large effect on the timing and on the size of wage adjustments. Minimum wage setting institutions contribute to increasing the time it takes to fully absorb a shock to wages by one year, although the resulting wage changes are significantly higher. Minimum wages contribute to amplifying, by a factor of 1.7, the response of wages to past inflation. The elasticities of wages with respect to past inflation, the national minimum wage and sectoral minimum wages are 0.42, 0.17 and 0.16 respectively. Finally, there are significant spillover effects of the national minimum wage on higher wages passing through from sectoral minimum wages.