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

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  • Sergio A. Lago Alves

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.

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  • Sergio A. Lago Alves, 2013. "Is the Divine Coincidence Just a Coincidence? The Implications of Trend Inflation," Working Papers Series 329, Central Bank of Brazil, Research Department.
  • Handle: RePEc:bcb:wpaper:329
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    Cited by:

    1. Buckle, Robert A., 2018. "Thirty years of inflation targeting in New Zealand: The origins, evolution and influence of a monetary policy innovation," Working Paper Series 8086, Victoria University of Wellington, Chair in Public Finance.
    2. Yasufumi Gemma & Takushi Kurozumi & Mototsugu Shintani, 2023. "Trend Inflation and Evolving Inflation Dynamics:A Bayesian GMM Analysis," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 506-520, December.
    3. Haque, Qazi & Groshenny, Nicolas & Weder, Mark, 2021. "Do we really know that U.S. monetary policy was destabilizing in the 1970s?," European Economic Review, Elsevier, vol. 131(C).
    4. Machado, Vicente da Gama & Portugal, Marcelo Savino, 2014. "Measuring inflation persistence in Brazil using a multivariate model," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 68(2), June.
    5. Sergio A. Lago Alves, 2018. "Monetary Policy, Trend Inflation, and Unemployment Volatility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(4), pages 637-673, June.
    6. Cho, Daeha & Han, Yoonshin & Oh, Joonseok & Rogantini Picco, Anna, 2021. "Uncertainty shocks, precautionary pricing, and optimal monetary policy," Journal of Macroeconomics, Elsevier, vol. 69(C).
    7. Ravenna, Federico & Walsh, Carl, 2020. "Worker heterogeneity, selection, and employment dynamics in the face of aggregate demand and pandemic shocks," CEPR Discussion Papers 15043, C.E.P.R. Discussion Papers.
    8. Guido Ascari & Argia M. Sbordone, 2014. "The Macroeconomics of Trend Inflation," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 679-739, September.
    9. repec:zbw:bofrdp:2019_020 is not listed on IDEAS
    10. Ulrich Gunter, 2019. "Estimating and forecasting with a two-country DSGE model of the Euro area and the USA: the merits of diverging interest-rate rules," Empirical Economics, Springer, vol. 56(4), pages 1283-1323, April.
    11. Haque, Qazi & Groshenny, Nicolas & Weder, Mark, 2021. "Do we really know that U.S. monetary policy was destabilizing in the 1970s?," European Economic Review, Elsevier, vol. 131(C).
    12. Buckle, Robert A., 2018. "Thirty years of inflation targeting in New Zealand: The origins, evolution and influence of a monetary policy innovation," Working Paper Series 20927, Victoria University of Wellington, Chair in Public Finance.
    13. International Monetary Fund, 2016. "Brazil: Selected Issues," IMF Staff Country Reports 2016/349, International Monetary Fund.
    14. Takushi Kurozumi & Willem Van Zandweghe, 2020. "Output-Inflation Trade-offs and the Optimal Inflation Rate," Working Papers 20-20, Federal Reserve Bank of Cleveland.
    15. Hasui, Kohei, 2020. "A Note On Robust Monetary Policy And Non-Zero Trend Inflation," Macroeconomic Dynamics, Cambridge University Press, vol. 24(6), pages 1574-1594, September.
    16. Zhao, Hong, 2022. "On the impacts of trend inflation in an open economy," Journal of International Economics, Elsevier, vol. 138(C).
    17. Kim, Bae-Geun, 2016. "Supply shocks and the divine coincidence," Economics Letters, Elsevier, vol. 145(C), pages 210-213.

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