AbstractWe develop an equilibrium model of labour force participation to examine the labour market business cycle. The model remains agnostic about unemployment inflows and outflows, modelling these flows with a structural moving average representation derived from a factor‐augmented vector autoregression model. Estimating the augmented dynamic stochastic general equilibrium model on data for the USA, we identify the structural shocks and parameters driving business cycle fluctuations, avoiding misspecified job‐finding and job‐separation rates. Our results show that real wage rigidities play a minor role, labour force participation is mildly procyclical, and transitions between employment, unemployment and non‐participation are strongly cyclical.