We develop a multivariate dynamic factor model that exploits euro area country-specific information on output and inflation for estimating an area-wide measure of the output gap. In the proposed multi-country framework we moreover allow for flexible stochastic volatility specifications for both the error variances and the innovations to the latent quantities in order to deal with potential changes in the commonalities of business cycle movements. By tracing the relative importance of the common euro area output gap component as a means to explaining movements in both output and inflation over time, the paper provides valuable insights in the evolution of the degree of synchronicity of the country-specific business cycles. In an out-of-sample forecasting exercise, the paper shows that the proposed approach performs well as compared to other well-known benchmark specifications.