Deep habits and the cyclical behaviour of equilibrium unemployment and vacancies

We extend the standard textbook search and matching model by introducing deep habits in consumption. The cyclical fluctuations of vacancies and unemployment in our model can replicate those observed in the US data, with labour market tightness being 20 times more volatile than consumption. Vacancies display a hump-shaped response to technology shocks as well as autocorrelation coefficients that are in line with the empirical evidence. Our model preserves the assumption of fully flexible wages for the new hires and the calibration is consistent with the estimated elasticity of unemployment to unemployment benefits. The numerical simulations generate an artificial Beveridge curve which is in line with the data.