This paper sets up a canonical new Keynesian model with habit persistence in
consumption. The paper estimates key parameters using maximum likelihood and shows
that the habit persistence improves the explanatory power of the model over the business
cycle, irrespective of habit formation way. If the distortions associated with external habit
are not completely eliminated by the fiscal policy, then the remaining external habit entails
a gap between the private marginal rate of substitution between consumption and labor and
the social marginal rate of substitution, generating an endogenous trade-off between the
stabilization of welfare-relevant output gap and inflation. Under this circumstance,
discretion, partially taking into account the trade-off between output gap and inflation, can
be better than a strict inflation targeting rule in welfare dimension if the fiscal authority
does not implement any tax policy to eliminate the distortions associated with external habit.
The monetary policy to deal with distortions associated with external habit is less effective in
the ratio external habit model than in the difference habit model, resulting in a higher the
inflation rate in the ratio external habit model than the inflation rate in the difference habit
model.