Vector autoregressive methods have been used to model the interrelationships between job vacancy rates, job separation rates and job‐finding rates using tools such as impulse response analysis. We investigate whether such impulse responses change across the business cycle or over time, by estimating time‐varying parameter–vector autoregressions for data from North America (the USA and Canada) and Europe (France, Spain and the UK). While the adjustment process of the labour market to shocks in Canada and the USA is similar, we find the adjustment process differs much more across the European countries, with greater persistence in shocks relative to the USA and Canada. Copyright © 2012 John Wiley & Sons, Ltd.