The article compares two ways of estimating the New Keynesian Phillips Curve (NKPC) to understand inflation dynamics. One way uses a standard difference equation, while the other uses a closed form that considers past inflation and current/future costs. The closed form method gives more efficient estimates in simulations and real data analysis. The findings suggest that lagged inflation still influences inflation dynamics even when trend inflation is considered, showing that trend inflation alone may not fully explain inflation patterns.