Price Stability in Economies with Habit Persistence

Abstract

This paper shows that the divine-coincidence does not hold in a sticky price model with external habit if a time-varying tax rate on labor income is not implemented to fully eliminate the time-varying distortions associated with external habit and monopoly power in goods market. The required labor income tax rate is inversely related to the risk-free real interest rate and the markup in the goods market, but it is proportional to the degree of external habit. Under this circumstance, the optimal monetary policy commands a countercyclical interest rate, having a perfect negative correlation with tax rate in the sticky price model with external habit. If a time-invariant tax is the only fiscal instrument, then the degree of 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, price stability is not the optimal policy. The monetary policy authority should optimally try to undo the time-varying distortions associated with external habit and monopoly power in goods market by deviating from price stability.