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

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  • Holden, Tom D.

Abstract

We present the first necessary and sufficient conditions for the existence of a unique perfect-foresight solution, returning to a given steady-state, in an otherwise linear model with occasionally binding constraints. We derive further conditions on the existence of a solution in such models, and provide a proof of the inescapability of the “curse of dimensionality” for them. We also construct the first solution algorithm for these models that is guaranteed to return a solution in finite time, if one exists. When extended to allow for other non-linearities and future uncertainty, our solution algorithm is shown to produce fast and accurate simulations. In an application, we show that widely used New Keynesian models with endogenous states possess multiple perfect foresight equilibrium paths when there is a zero lower bound on nominal interest rates. However, we show that price level targeting is sufficient to restore determinacy in these situations.

Suggested Citation

  • Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - German National Library of Economics.
  • Handle: RePEc:zbw:esprep:127430
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    File URL: https://www.econstor.eu/bitstream/10419/127430/1/paper.pdf
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    References listed on IDEAS

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    1. 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.
    2. Tom Holden & Michael Paetz, 2012. "Efficient Simulation of DSGE Models with Inequality Constraints," Quantitative Macroeconomics Working Papers 21207b, Hamburg University, Department of Economics.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    8. 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.
    9. Basu, Susanto & Bundick, Brent, 2015. "Endogenous volatility at the zero lower bound: implications for stabilization policy," Research Working Paper RWP 15-1, Federal Reserve Bank of Kansas City.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    19. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    20. 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.
    21. 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.
    22. 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.
    23. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    24. 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.
    25. 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.
    26. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2012. "Merging simulation and projection approaches to solve high-dimensional problems," Working Papers. Serie AD 2012-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    27. Tibor Illés & Marianna Nagy & Tamás Terlaky, 2010. "A polynomial path-following interior point algorithm for general linear complementarity problems," Journal of Global Optimization, Springer, vol. 47(3), pages 329-342, July.
    28. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    29. 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.
    30. Julio J. Rotemberg, 1982. "Monopolistic Price Adjustment and Aggregate Output," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 517-531.
    31. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Tom D. Holden & Paul Levine & Jonathan M. Swarbrick, 2017. "Credit Crunches from Occasionally Binding Bank Borrowing Constraints," Staff Working Papers 17-57, Bank of Canada.
    2. Darracq Pariès, Matthieu & Kühl, Michael, 2016. "The optimal conduct of central bank asset purchases," Working Paper Series 1973, European Central Bank.
    3. William John Tayler & Roy Zilberman, 2017. "Taxation, Credit Spreads and Liquidity Traps," Working Papers 173174116, Lancaster University Management School, Economics Department.

    More about this item

    Keywords

    occasionally binding constraints; zero lower bound; existence; uniqueness; price targeting; DSGE; linear complementarity problem;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • 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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