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This paper proposes a new method for estimating linear dynamic structural models. 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-form 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-run and long-run frequencies are included. The forward-looking component and the inflation inertia are relatively stable and equally quantitatively important. Overall, our estimates present much less sampling uncertainty than the corresponding generalized method of moment (GMM) estimates, both in extensive Monte Carlo simulations and the empirical application, and they provide formal empirical support for misspecification of the NKPC as a model for all frequencies.