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The proposed generalized band spectrum estimator (GBSE) generalizes band spectrum regression to simultaneously account for endogeneity and nonlinearities of unknown form in the first stage, while having a computationally convenient closed\u2010form expression in the time domain. We apply the GBSE to the hybrid New Keynesian Phillips curve (NKPC) with U.S. postwar data. We find a stable marginal cost coefficient in the short run, with relatively large and statistically significant values, and small and insignificant values when both short\u2010run and long\u2010run frequencies are included. The forward\u2010looking component and the inflation inertia are relatively stable and equally quantitatively important. 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