Following insights by Bewley (1999a), this paper analyses a model with downward rigidities in which firms cannot pay discriminate based on a year of entry to a firm, and develops an equilibrium model of wages and unemployment. We solve for the dynamics of wages and unemployment under conditions of downward wage rigidity, where forward looking firms take into account these constraints. Using simulated productivity data based on the post-war US economy, we analyse the ability of the model to match certain stylised labour market facts.