Identifying the new Keynesian Phillips curve

"Phillips curves are central to discussions of inflation dynamics and monetary policy. New Keynesian Phillips curves describe how past inflation, expected future inflation, and a measure of real marginal cost or an output gap drive the current inflation rate. This paper studies the (potential) weak identification of these curves under generalized methods of moments (GMM) and traces this syndrome to a lack of persistence in either exogenous variables or shocks. The authors employ analytic methods to understand the identification problem in several statistical environments: under strict exogeneity, in a vector autoregression, and in the canonical three-equation, New Keynesian model. Given U.S., U.K., and Canadian data, they revisit the empirical evidence and construct tests and confidence intervals based on exact and pivotal Anderson-Rubin statistics that are robust to weak identification. These tests find little evidence of forward-looking inflation dynamics"--Federal Reserve Bank of Atlanta web site.