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The Four Equation New Keynesian Model

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  • Eric R. Sims
  • Jing Cynthia Wu

Abstract

This paper develops a New Keynesian model featuring financial intermediation, short and long term bonds, credit shocks, and scope for unconventional monetary policy. The log-linearized model reduces to four key equations – a Phillips curve, an IS equation, and policy rules for the short term nominal interest rate and the central bank's long bond portfolio (QE). The four equation model collapses to the standard three equation New Keynesian model under a simple parameter restriction. Credit shocks and QE appear in both the IS and Phillips curves. Optimal monetary policy entails adjusting the short term interest rate to offset natural rate shocks, but using QE to offset credit market disruptions. The ability of the central bank to engage in QE significantly mitigates the costs of a binding zero lower bound.

Suggested Citation

  • Eric R. Sims & Jing Cynthia Wu, 2019. "The Four Equation New Keynesian Model," NBER Working Papers 26067, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:26067
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    1. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-254, April.
    2. Sarah Mouabbi & Jean‐Guillaume Sahuc, 2019. "Evaluating the Macroeconomic Effects of the ECB's Unconventional Monetary Policies," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(4), pages 831-858, June.
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    Cited by:

    1. Karadi, Peter & Nakov, Anton, 2021. "Effectiveness and addictiveness of quantitative easing," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 1096-1117.
    2. Bailey, Andrew & Bridges, Jonathan & Harrison, Richard & Jones, Josh & Mankodi, Aakash, 2020. "The central bank balance sheet as a policy tool: past, present and future," Bank of England working papers 899, Bank of England.
    3. Joshua Brault & Hashmat Khan & Louis Phaneuf & Jean Gardy Victor, 2021. "Did the Fed Remain at the ZLB Long Enough? Lessons from the 2008-2019 Period," Working Papers 21-09, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    4. Cantore, Cristiano & Freund, Lukas B., 2021. "Workers, capitalists, and the government: fiscal policy and income (re)distribution," Journal of Monetary Economics, Elsevier, vol. 119(C), pages 58-74.
    5. Bletzinger, Tilman & von Thadden, Leopold, 2021. "Designing QE in a fiscally sound monetary union," European Economic Review, Elsevier, vol. 132(C).
    6. Garriga, Carlos & Kydland, Finn E. & Šustek, Roman, 2021. "MoNK: Mortgages in a New-Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    7. Jing Cynthia Wu & Fan Dora Xia, 2020. "Negative interest rate policy and the yield curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 653-672, September.
    8. Boehl, Gregor, 2022. "Monetary policy and speculative asset markets," European Economic Review, Elsevier, vol. 148(C).
    9. Roulleau-Pasdeloup, Jordan, 2023. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    10. Philippe Goulet Coulombe, 2022. "A Neural Phillips Curve and a Deep Output Gap," Working Papers 22-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    11. Böhl, Gregor & Lieberknecht, Philipp, 2021. "The hockey stick Phillips curve and the effective lower bound," Discussion Papers 55/2021, Deutsche Bundesbank.
    12. Eric R. Sims & Jing Cynthia Wu, 2020. "Wall Street vs. Main Street QE," NBER Working Papers 27295, National Bureau of Economic Research, Inc.
    13. Tarron Khemraj & Sherry Yu, 2023. "Inflation Dynamics and Quantitative Easing," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 49(4), pages 613-638, October.
    14. Ani Asoyan & Vahagn Davtyan & Haykaz Igityan & Hasmik Kartashyan & Hovhannes Manukyan, 2020. "Modelling the Effects of a Health Shock on the Armenian Economy," Russian Journal of Money and Finance, Bank of Russia, vol. 79(4), pages 18-44, December.
    15. Donato Masciandaro & Romano Vincenzo Tarsia, 2021. "Society, Politicians, Climate Change and Central Banks: An Index of Green Activism," BAFFI CAREFIN Working Papers 21167, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    16. Cardamone, Dario & Sims, Eric & Wu, Jing Cynthia, 2023. "Wall Street QE vs. Main Street Lending," European Economic Review, Elsevier, vol. 156(C).
    17. Eric Schaling & Kgotso Morema, 2022. "Optimalinterestrategapsforflexibleinflationtargeting," Working Papers 11037, South African Reserve Bank.
    18. Ani Asoyan & Vahagn Davtyan & Haykaz Igityan & Hasmik Kartashyan & Hovhannes Manukyan, 2020. "Modelling the Effects of a Health Shock on the Armenian Economy," Working Papers 15, Central Bank of the Republic of Armenia, revised Dec 2020.
    19. Cantore, Cristiano & Meichtry, Pascal, 2023. "Unwinding quantitative easing: state dependency and household heterogeneity," Bank of England working papers 1030, Bank of England.
    20. Jordan Roulleau-Pasdeloup, 2022. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Papers 2209.05081, arXiv.org, revised Feb 2023.
    21. Philippe Goulet Coulombe, 2022. "A Neural Phillips Curve and a Deep Output Gap," Papers 2202.04146, arXiv.org.
    22. Sims, Eric & Wu, Jing Cynthia, 2021. "Evaluating Central Banks’ tool kit: Past, present, and future," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 135-160.

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    More about this item

    JEL classification:

    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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