It shows that the divine-coincidence does not hold in a sticky price model with external habit.

What is it about?

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 counter-cyclical 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.

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