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Existence and uniqueness of solutions to dynamic models with occasionally binding constraints

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  • Holden, Tom D.

Abstract

Policy makers would like to prevent self-fulfilling fluctuations. Given the prevalence of occasionally binding constraints (OBCs) such as the zero lower bound (ZLB), this requires understanding the determinacy of models with OBCs. To this end, we derive existence and uniqueness conditions for otherwise linear models with OBCs. Our main result gives necessary and sufficient conditions for such a model to have a unique perfect foresight solution returning to a given steady state, for any initial condition. We show that while standard New Keynesian models with a ZLB possess multiple perfect-foresight paths eventually escaping the ZLB, price level targeting restores determinacy.

Suggested Citation

  • Holden, Tom D., 2019. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 144570, ZBW - Leibniz Information Centre for Economics.
  • Handle: RePEc:zbw:esprep:144570
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    1. Guido Ascari & Tiziano Ropele, 2009. "Trend Inflation, Taylor Principle, and Indeterminacy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(8), pages 1557-1584, December.
    2. Tom Holden, 2010. "Products, patents and productivity persistence: A DSGE model of endogenous growth," Economics Series Working Papers 512, University of Oxford, Department of Economics.
    3. Anton Nakov, 2008. "Optimal and Simple Monetary Policy Rules with Zero Floor on the Nominal Interest Rate," International Journal of Central Banking, International Journal of Central Banking, vol. 4(2), pages 73-127, June.
    4. Stefan Laséen & Lars E.O. Svensson, 2011. "Anticipated Alternative policy Rate Paths in Plicy Simulations," International Journal of Central Banking, International Journal of Central Banking, vol. 7(3), pages 1-35, September.
    5. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    6. Olivier Coibion & Yuriy Gorodnichenko & Johannes Wieland, 2012. "The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?," Review of Economic Studies, Oxford University Press, vol. 79(4), pages 1371-1406.
    7. Bernardino Adao & Isabel Correia & Pedro Teles, 2011. "Unique Monetary Equilibria with Interest Rate Rules," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(3), pages 432-442, July.
    8. Carlstrom, Charles T. & Fuerst, Timothy S. & Paustian, Matthias, 2015. "Inflation and output in New Keynesian models with a transient interest rate peg," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 230-243.
    9. Guerrieri, Luca & Iacoviello, Matteo, 2015. "OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 22-38.
    10. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2010. "Generalizing the Taylor Principle: Comment," American Economic Review, American Economic Association, vol. 100(1), pages 608-617, March.
    11. Gavin, William T. & Keen, Benjamin D. & Richter, Alexander W. & Throckmorton, Nathaniel A., 2015. "The zero lower bound, the dual mandate, and unconventional dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 14-38.
    12. Jean Barthélemy & Magali Marx, 2011. "State-Dependent Probability Distributions in Non Linear Rational Expectations Models," Sciences Po publications 347, Sciences Po.
    13. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 565-615.
    14. Schmitt-Grohé, Stephanie & Uribe, Martín, 2012. "The Making Of A Great Contraction With A Liquidity Trap and A Jobless Recovery," CEPR Discussion Papers 9237, C.E.P.R. Discussion Papers.
    15. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    16. Bodenstein, Martin, 2010. "Trade elasticity of substitution and equilibrium dynamics," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1033-1059, May.
    17. Jung, Taehun & Teranishi, Yuki & Watanabe, Tsutomu, 2005. "Optimal Monetary Policy at the Zero-Interest-Rate Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 813-835, October.
    18. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    19. Olivier Coibion & Yuriy Gorodnichenko & Johannes Wieland, 2012. "The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?," Review of Economic Studies, Oxford University Press, vol. 79(4), pages 1371-1406.
    20. Barthélemy, Jean & Marx, Magali, 2017. "Solving endogenous regime switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 1-25.
    21. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    22. S Borağan Aruoba & Pablo Cuba-Borda & Frank Schorfheide, 2018. "Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 87-118.
    23. Alisdair McKay & Emi Nakamura & Jón Steinsson, 2017. "The Discounted Euler Equation: A Note," Economica, London School of Economics and Political Science, vol. 84(336), pages 820-831, October.
    24. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    25. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    26. Wieland, Volker & Cwik, Tobias & Müller, Gernot J. & Schmidt, Sebastian & Wolters, Maik, 2012. "A new comparative approach to macroeconomic modeling and policy analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 523-541.
    27. Stefan Laséen & Lars E.O. Svensson, 2009. "Anticipated Alternative Instrument-Rate Paths in Policy Simulations," NBER Working Papers 14902, National Bureau of Economic Research, Inc.
    28. Brendon, Charles & Paustian, Matthias & Yates, Tony, 2013. "The pitfalls of speed-limit interest rate rules at the zero lower bound," Bank of England working papers 473, Bank of England.
    29. Stephanie Schmitt-Grohe & Jess Benhabib & Martin Uribe, 2001. "Monetary Policy and Multiple Equilibria," American Economic Review, American Economic Association, vol. 91(1), pages 167-186, March.
    30. Tom Holden & Michael Paetz, 2012. "Efficient simulation of DSGE models with inequality constraints," School of Economics Discussion Papers 1612, School of Economics, University of Surrey.
    31. Nakata, Taisuke & Schmidt, Sebastian, 2019. "Conservatism and liquidity traps," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 37-47.
    32. Lawrence J. Christiano & Martin S. Eichenbaum & Mathias Trabandt, 2015. "Understanding the Great Recession," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 110-167, January.
    33. Lawrence J. Christiano & Massimo Rostagno, 2001. "Money Growth Monitoring and the Taylor Rule," NBER Working Papers 8539, National Bureau of Economic Research, Inc.
    34. Rupert, Peter & Šustek, Roman, 2019. "On the mechanics of New-Keynesian models," Journal of Monetary Economics, Elsevier, vol. 102(C), pages 53-69.
    35. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    36. Marco Del Negro & Marc Giannoni & Christina Patterson, 2012. "The forward guidance puzzle," Staff Reports 574, Federal Reserve Bank of New York.
    37. Farmer, Roger E.A. & Khramov, Vadim & Nicolò, Giovanni, 2015. "Solving and estimating indeterminate DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 17-36.
    38. Julio J. Rotemberg, 1982. "Monopolistic Price Adjustment and Aggregate Output," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 517-531.
    39. Susanto Basu & Brent Bundick, 2015. "Endogenous Volatility at the Zero Lower Bound: Implications for Stabilization Policy," NBER Working Papers 21838, National Bureau of Economic Research, Inc.
    40. 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.
    41. Takashi Kamihigashi, 2014. "Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 251-273, June.
    42. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    43. Evans, George W & McGough, Bruce, 2018. "Equilibrium selection, observability and backward-stable solutions," Journal of Monetary Economics, Elsevier, vol. 98(C), pages 1-10.
    44. Paul Beaudry & Franck Portier, 2006. "Stock Prices, News, and Economic Fluctuations," American Economic Review, American Economic Association, vol. 96(4), pages 1293-1307, September.
    45. Refet S Gürkaynak & Andrew Levin & Eric Swanson, 2010. "Does Inflation Targeting Anchor Long-Run Inflation Expectations? Evidence from the U.S., UK, and Sweden," Journal of the European Economic Association, MIT Press, vol. 8(6), pages 1208-1242, December.
    46. 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.
    47. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    48. Karel R. S. M. Mertens & Morten O. Ravn, 2014. "Fiscal Policy in an Expectations-Driven Liquidity Trap," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1637-1667.
    49. Boneva, Lena Mareen & Braun, R. Anton & Waki, Yuichiro, 2016. "Some unpleasant properties of loglinearized solutions when the nominal rate is zero," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 216-232.
    50. Roc Armenter, 2018. "The Perils of Nominal Targets," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 50-86.
    51. Bodenstein, Martin & Guerrieri, Luca & Gust, Christopher J., 2013. "Oil shocks and the zero bound on nominal interest rates," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 941-967.
    52. Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008. "Linear-quadratic approximation, external habit and targeting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3315-3349, October.
    53. Roc Armenter, 2013. "The perils of nominal targets," Working Papers 14-2, Federal Reserve Bank of Philadelphia.
    54. Mendes, Rhys R., 2011. "Uncertainty and the Zero Lower Bound: A Theoretical Analysis," MPRA Paper 59218, University Library of Munich, Germany.
    55. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    56. Vestin, David, 2006. "Price-level versus inflation targeting," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1361-1376, October.
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    More about this item

    Keywords

    occasionally binding constraints; zero lower bound; existence; uniqueness; price targeting;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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