We propose alternative single-equation semi-structural models for forecasting inflation in Canada, whereby structural New Keynesian models are combined with time-series features in the data. Several marginal cost measures are used, including one that in addition to unit labour cost also integrates relative price shocks known to play an important role in open-economies. Structural estimation and testing is conducted using identification-robust methods that are valid whatever the identification status of the econometric model. We find that our semi-structural models perform better than various strictly structural and conventional time series models. In the latter case, forecasting performance is significantly better, both in the short run and in the medium run.