This paper presents a new mechanism through which monetary policy rules affect inflation persistence. When assuming that price reset hazard functions are not constant, backward- looking dynamics emerge in the NKPC. This new mechanism makes the traditional demand channel of monetary transmission have a long-lasting effect on inflation dynamics. The Calvo model fails to convey this insight, because its constant hazard function leads those important backward-looking dynamics to be canceled out. I first analytically show how it works in a simple setup, and then solve a log-linearized model numerically around positive trend inflation. With realistic calibration of trend inflation and the monetary policy rule, the model can account for the pattern of changes in inflation persistence observed in the post-wwii U.S. data. In addition, with increasing hazard functions, the "Taylor principle" is sufficient to guarantee the determinate equilibrium even under extremely high trend inflation.