We propose and estimate a dynamic stochastic general equilibrium model featuring search and matching frictions, deep habits and a CES production function. The model successfully replicates the cyclical properties of labour market variables in the US economy for three main reasons. First, the endogenous mechanisms of the model-factor complementarity, deep habits and unemployment benefits-play a key role for explaining the amplification in unemployment and vacancies. Second, factor-biased productivity innovations are important exogenous sources of labour market dynamics. Third, demand-side innovations induce markup fluctuations consistent with the deep habits mechanism.