Phillips curves are central to discussions of inflation dynamics and monetary policy. The hybrid new Keynesian Phillips curve (NKPC) describes how past inflation, expected future inflation, and a measure of real aggregate demand drive the current inflation rate. This paper studies the (potential) weak identification of the NKPC under Generalized Method of Moments and traces this syndrome to a lack of higher-order dynamics in exogenous variables. We employ analytic methods to understand the economics of the NKPC identification problem in the canonical three-equation, new Keynesian model. We revisit the empirical evidence for the USA, the UK, and Canada by constructing tests and confidence intervals based on the Anderson and Rubin (1949) statistic, which is robust to weak identification. We also apply the Guggenberger and Smith (2008) LM test to the underlying NKPC pricing parameters. Both tests yield little evidence of forward-looking inflation dynamics.