We investigate the roles of a time-varying inflation target and monetary and fiscal policy stances on the dynamics of inflation in a DSGE model. Under an active monetary and passive fiscal policy regime, inflation closely follows the path of the inflation target and a stronger reaction of monetary policy to inflation decreases the equilibrium response of inflation to non-policy shocks. In sharp contrast, under an active fiscal and passive monetary policy regime, inflation moves in an opposite direction from the inflation target and a stronger reaction of monetary policy to inflation increases the equilibrium response of inflation to non-policy shocks. Moreover, a weaker response of fiscal policy to debt decreases the response of inflation to non-policy shocks. These results are due to variation in the value of public debt that leads to wealth effects on households. Finally, under a passive monetary and passive fiscal policy regime, both monetary and fiscal policy stances affect inflation dynamics, but because of a role for self-fulfilling beliefs due to equilibrium indeterminacy, theory provides no clear answer on the overall behavior of inflation. We characterize these results analytically in a simple model and numerically in a richer quantitative model.