Standard models of equilibrium unemployment assume exogenous labour market institutions and flexible wage determination. This paper models wage rigidity and collective bargaining endogenously, when workers differ by observable skill and may adopt either individualised or collective wage bargaining. In the calibrated model, a substantial fraction of workers and firms as well as the median voter prefer collective bargaining to the decentralised regime. A fundamental distortion of the separation decision represented by employment protection (a firing tax) is necessary for such preferences to emerge. Endogenizing collective bargaining can significantly modify comparative statics effects of policy arising in a single-regime setting.