In a parametric conditional moment model with time-varying parameters, we develop a new integrated conditional moment (ICM) estimator which uses all information from conditional restrictions seamlessly. Our approach builds on the ICM principle originally proposed by Bierens (1982) and combines it with local smoothing to deliver estimates of the time-varying parameters. Under general regularity conditions - including local stationarity and restrictions on plysical dependence - we show that our estimator is consistent and asymptotically normally distributed. Importantly, our approach is a one-step approach that is robust to parametrizing - and estimating - the relationship between endogenous variables and instruments. Our simulation study document the reliability and power of our approach in a variety of cases - and, especially, when the underlying relationship between the endogenous variables and the instruments cannot be reliably estimated - even with exible time-varying approaches. Our estimation of the traditional Phillips curve that links in ation to unemployment with US data from 1960 to 2024 reveals important uctuations over time, including the diminishing importance of unemployment, especially after 2006.