Labour market institutions are a crucial determinant of wage inequality, the wage share in aggregate income, and the unemployment rate. Since these variables affect, in turn, the distribution of income across households, the question arises of whether stronger labour market institutions have an impact on income inequality. Institutions can in principle have conflicting effects. For example, a higher unemployment benefit tends to increase the wage share, which in turn reduces inequality, but it also increases the unemployment rate thus making the distribution of income more unequal. This paper examines what is the overall impact of labour market institutions on household income inequality. The evidence indicates that stronger institutions are associated with lower income inequality, but in some cases also with higher rates of unemployment. We explore the magnitude of this trade-off, and quantify the changes in inequality and unemployment that we would observe if a common labour standard were imposed on members of the European Union.