This paper presents results on the stability of the wage dispersion model presented in Mortensen (2003). Specifically, we test four 'positive definite' learning processes on a single parameterisation of the underlying model, and submit the most successful to a thorough sensitivity analysis. The general result of existing studies of the stability of price dispersion models is that learning processes can converge on limiting distributions that qualitatively match the equilibrium distribution. In contrast, the most successful process considered in this paper can converge on a limiting distribution that quantitatively matches the equilibrium distribution. financial stability?