In this paper we use optimal-instrument and new finite-sample methods to test the empirical relevance of the New Keynesian Phillips curve (NKPC) equation. Unlike generalized method of moments-based methods, these generalized Anderson-Rubin tests are immune to the presence of weak instruments, and allow, by construction, to assess the identification status of a model. Our results are illustrated using the Gali-Gertler (1999) NKPC specifications and data, as well as a survey-based inflation expectation series from the Philadelphia Fed. Our test rejects the reported Gali-Gertler estimates, conditional on their choice of instruments. Nevertheless, and in contrast to Ma (2002), we do obtain relatively informative confidence sets. This provides support for NKPC equations and illustrates the usefulness of using exact procedures and optimal instruments in IV-based estimations. In particular, our results reveal that firms fix prices in a predominantly backward-looking manner, but that they adjust prices every quarter or so. Furthermore, the outcomes indicate that it is difficult to pin-point the extent of the importance of marginal costs for the inflation process.
