On inflation expectations in the NKPC model

To create an estimable version for annual data of the hybrid new Keynesian Phillips curve, one needs an expression for the expectation of next year's inflation. The rational expectations literature assumes that this expectation is equal to the realization in the next year and an associated forecast error. This paper argues that this assumption goes against the Wold decomposition theorem, and that it introduces correlation between the error and a regressor. A more appropriate approach resorts to a MIDAS type of model, where forecast updates for next year are created when for example monthly inflation rates come in. An illustration to annual USA inflation, 1956-2016, shows the merits of this MIDAS approach.