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The zero lower bound: frequency, duration, and numerical convergence

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  • Richter Alexander W.

    (Department of Economics, Auburn University, 0332 Haley Center, Auburn, AL, USA)

  • Throckmorton Nathaniel A.

    (Department of Economics, Indiana University and DePauw University, 7 E Larabee St, Harrison Hall, Greencastle, IN, USA)

Abstract

When monetary policy faces a zero lower bound (ZLB) constraint on the nominal interest rate, a minimum state variable (MSV) solution may not exist even if the Taylor principle holds when the ZLB does not bind. This paper shows there is a clear tradeoff between the expected frequency and average duration of ZLB events along the boundary of the convergence region – the region of the parameter space where our policy function iteration algorithm converges to an MSV solution. We show this tradeoff with two alternative stochastic processes: one where monetary policy follows a 2-state Markov chain, which exogenously governs whether the ZLB binds, and the other where ZLB events are endogenous due to discount factor or technology shocks. We also show that small changes in the parameters of the stochastic processes cause meaningful differences in the decision rules and where the ZLB binds in the state space.

Suggested Citation

  • Richter Alexander W. & Throckmorton Nathaniel A., 2015. "The zero lower bound: frequency, duration, and numerical convergence," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 1-26, January.
  • Handle: RePEc:bpj:bejmac:v:15:y:2015:i:1:p:26:n:7
    DOI: 10.1515/bejm-2013-0185
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    Cited by:

    1. Morris, Stephen D., 2020. "Is the Taylor principle still valid when rates are low?," Journal of Macroeconomics, Elsevier, vol. 64(C).
    2. Schmidt, Sebastian & Nakata, Taisuke & Hills, Timothy, 2016. "The risky steady state and the interest rate lower bound," Working Paper Series 1913, European Central Bank.
    3. Masolo, Riccardo M. & Winant, Pablo E., 2019. "The Stochastic Lower Bound," Economics Letters, Elsevier, vol. 180(C), pages 54-57.
    4. Michael Plante & Alexander W. Richter & Nathaniel A. Throckmorton, 2018. "The Zero Lower Bound and Endogenous Uncertainty," Economic Journal, Royal Economic Society, vol. 128(611), pages 1730-1757, June.
    5. Atkinson, Tyler & Richter, Alexander W. & Throckmorton, Nathaniel A., 2020. "The zero lower bound and estimation accuracy," Journal of Monetary Economics, Elsevier, vol. 115(C), pages 249-264.
    6. Taisuke Nakata & Sebastian Schmidt & Paul Yoo, 2018. "Speed Limit Policy and Liquidity Traps," IMES Discussion Paper Series 18-E-06, Institute for Monetary and Economic Studies, Bank of Japan.
    7. Iiboshi, Hirokuni & Shintani, Mototsugu, 2016. "Zero interest rate policy and asymmetric price adjustment in Japan: an empirical analysis of a nonlinear DSGE model," MPRA Paper 93868, University Library of Munich, Germany.
    8. Alexander Richter & Nathaniel Throckmorton & Todd Walker, 2014. "Accuracy, Speed and Robustness of Policy Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 445-476, December.
    9. Robert Amano & Thomas Carter & Sylvain Leduc, 2019. "Precautionary Pricing: The Disinflationary Effects of ELB Risk," Working Paper Series 2019-26, Federal Reserve Bank of San Francisco.
    10. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 182-204.
    11. Nakata, Taisuke & Schmidt, Sebastian, 2019. "Conservatism and liquidity traps," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 37-47.
    12. Tambakis, Demosthenes N., 2014. "On the risk of long-run deflation," Economics Letters, Elsevier, vol. 122(2), pages 176-181.
    13. Tambakis, Demosthenes N., 2015. "Determinate liquidity traps," Economics Letters, Elsevier, vol. 135(C), pages 126-132.
    14. Volker Hahn, 2017. "Policy Effects in a Simple Fully Non-Linear New Keynesian Model of the Liquidity Trap," Working Paper Series of the Department of Economics, University of Konstanz 2017-05, Department of Economics, University of Konstanz.
    15. Holden, Thomas, 2016. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130142, ZBW - Leibniz Information Centre for Economics.
    16. Taisuke Nakata, 2017. "Uncertainty at the Zero Lower Bound," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(3), pages 186-221, July.
    17. Hills, Timothy S. & Nakata, Taisuke & Schmidt, Sebastian, 2019. "Effective lower bound risk," European Economic Review, Elsevier, vol. 120(C).
    18. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - Leibniz Information Centre for Economics.
    19. Fernando M. Duarte & Anna Zabai, 2015. "An interest rate rule to uniquely implement the optimal equilibrium in a liquidity trap," Staff Reports 745, Federal Reserve Bank of New York.
    20. Roulleau-Pasdeloup, Jordan, 2020. "Optimal monetary policy and determinacy under active/passive regimes," European Economic Review, Elsevier, vol. 130(C).
    21. Javier Andrés & Pablo Burriel & Wenyi Shen, 2020. "Debt sustainability and fiscal space in a heterogeneous Monetary Union: normal times vs the zero lower bound," Working Papers 2001, Banco de España.
    22. Yoichiro Tamanyu, 2020. "The Role of Nonlinearity in Indeterminate Models: An Application to Expectations-Driven Liquidity Traps," Keio-IES Discussion Paper Series 2020-023, Institute for Economics Studies, Keio University.

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    More about this item

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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