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 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 response of inflation to non-policy shocks. Moreover, a higher level of government debt leads to a greater response of inflation while 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 parameters matter for inflation dynamics, but because of 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 quantitative model.