Our paper provides a consistent framework to study the structural or cyclical nature of Beveridge curve (BC) dynamics: We connect equilibrium unemployment theory to a flexible multivariate unobserved components model. We disentangle permanent and transitory components of all series determining the BC and its position. Cointegration and identification are addressed. The German curve is an ideal illustration as reforms of the institutional setting and the Great Recession were accompanied by a remarkable labour market development. We find an extraordinary increase in trend matching efficiency after the reforms, which testifies to a permanent improvement. Matching efficiency accounts for about half of the BCś inward shift. As tightness also increased, a persistent upward movement masked the inward shift.