Is the Divine Coincidence Just a Coincidence? The Implications of Trend Inflation

No 329, Working Papers Series from Central Bank of Brazil, Research Department

Abstract: In standard New Keynesian models, in which staggered pricing is the only nominal rigidity and shocks to preferences or technology are the only source of fluctuations, the literature has long agreed that the divine coincidence holds: the monetary authority is able to simultaneously stabilize the inflation rate and the output gap. I show that the divine coincidence holds only when the inflation rate is stabilized at exactly zero. Even a small deviation of trend (steady-state) inflation from zero generates a policy trade-off. I demonstrate this result using the model's non-linear equilibrium conditions to avoid any bias arising from log-linearization. When the model is log-linearized in line with common practice, a non-zero trend inflation gives rise to what I call an endogenous trend inflation cost-push shock. This shock enters the New Keynesian Phillips curve whenever the steady state level of inflation (trend inflation) deviates from zero. To assess the impact of trend inflation, I derive the welfare-based loss function under trend inflation and characterize optimal policy rules. Optimal policy is able to reduce the volatility of inflation and the output gap but can never fully stabilize them under non-zero trend inflation.

Date: 2013-10
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Related works:
Journal Article: Lack of divine coincidence in New Keynesian models (2014)
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