Abstract.Error Correction Models (ECMs) have proved a popular organising principle in applied econometrics, despite the lack of consensus as to exactly what constitutes their defining characteristic, and the rather limited role that has been given to economic theory by their proponents. This paper uses a historical survey of the evolution of ECMs to explain the alternative specifications and interpretations and proceeds to examine their implications for estimation. The various approaches are illustrated for wage equations by application to UK labour market data 1855–1987. We demonstrate that error correction models impose strong and testable non‐linear restrictions on dynamic econometric equations, and that they do not obviate the need for modelling the process of expectations formation. With the exception of a few special cases, both the non‐linear restrictions and the modelling of expectations have been ignored by those who have treated ECMs as merely reparameterisations of dynamic linear regression models or vector autoregres