Differences in labour market institutions and regulations between countries of the monetary union can cause divergent responses even to a common shock. We augment a multi-country model of the euro area with search and matching framework that differs across Ricardian and hand-to-mouth households. In this setting, we investigate the implications of crosscountry heterogeneity in labour market institutions for the conduct of monetary policy in a monetary union. We compute responses to an expansionary demand shock and to an inflationary supply shock under the Taylor rule, asymmetric unemployment targeting, and average inflation targeting. For each rule we distinguish between cases with zero weight on the unemployment gap and a negative response to rising unemployment Across all rules, responding to unemployment leads to lower losses of employment and higher inflation. Responding to unemployment reduces cross-country differences within the monetary union and the differences in consumption levels of rich and poor households.