This article estimates a stylised search‐and‐matching model on data for Australia, covering the period 1978–2008. Using Bayesian methods, I find that the model does a fairly good job in replicating the data. Surprisingly, I find a large value for the worker's bargaining power and low vacancy‐posting costs. The model generates a strong Beveridge curve and matches the standard deviations of all variables but vacancies. I identify technology and separation shocks to be the main drivers of fluctuations.