Recently Andrle (2012) demonstrates a strong, stable and positive comovement between the cyclical component of output and deviation of core inflation from long-term inflation expectations in the U.S. starting from the 1960’s through the Great Recession. This paper documents strong comovement of output and inflation using a set of nonrestrictive assumptions, rather than constructing a formal semi-structural model of the Phillips curve, with many restrictive assumptions as in Basistha and Nelson (2007) for instance.5 Recently, Basturk and others (2013) proposed a complex nonparametric model of the semi-structural New-Keynesian Phillips curve for the U.S. estimated by computational intensive Bayesian methods. Our approach avoids the restrictive parametric assumptions of previous studies and by being formulated in frequency domain it requires only straightforward and transparent calculations.