We analyse the determinants of unemployment persistence in four OECD countries by estimating a structural Bayesian VAR with an informative prior based on an insiders/outsiders model. We explicitly insert unemployment benefits and labour taxes so that our identification is not affected by the Faust and Leeper (1997) critique. We find widespread hysteresis: demand shocks play a dominant role in explaining unemployment also in the medium-run. Moreover real wages have low sensitivity to cyclical fluctuations and to labour market disequilibria. Our results emphasise the real power of the unions and their interactions with structural shocks and other institutions as crucial determinants of hysteresis.