IDEAS home Printed from https://ideas.repec.org/p/bca/bocadp/21-5.html
   My bibliography  Save this paper

Occasionally Binding Constraints in Large Models: A Review of Solution Methods

Author

Listed:
  • Jonathan Swarbrick

Abstract

This practical review assesses several approaches to solving medium- and large-scale dynamic stochastic general equilibrium (DSGE) models featuring occasionally binding constraints. In such models, global solution methods are not possible because of the curse of dimensionality. This causes the modeller to look elsewhere for methods that can handle the significant non-linearities and non-differentiable functions that inequality constraints represent. The paper discusses methods—including Newton-type solvers under perfect foresight, the piecewise linear algorithm (OccBin), regime-switching models (RISE) and the news shocks approach (DynareOBC)—and compares the results from a simple borrowing constraints model obtained using projection methods, providing example MATLAB code. The study focuses on the news shocks method, which I find produces higher accuracy than other methods and allows the modeller to study multiple equilibria and determinacy issues.

Suggested Citation

  • Jonathan Swarbrick, 2021. "Occasionally Binding Constraints in Large Models: A Review of Solution Methods," Discussion Papers 2021-5, Bank of Canada.
    • Handle: RePEc:bca:bocadp:21-5
    as

    Download full text from publisher

    File URL: https://www.bankofcanada.ca/wp-content/uploads/2021/03/sdp2021-5.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guerrieri, Luca & Iacoviello, Matteo, 2017. "Collateral constraints and macroeconomic asymmetries," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 28-49.
    2. Christopher Erceg & Jesper Lindé, 2014. "Is There A Fiscal Free Lunch In A Liquidity Trap?," Journal of the European Economic Association, European Economic Association, vol. 12(1), pages 73-107, February.
    3. Jonathan H. Wright, 2012. "What does Monetary Policy do to Long‐term Interest Rates at the Zero Lower Bound?," Economic Journal, Royal Economic Society, vol. 122(564), pages 447-466, November.
    4. Jonathan Swarbrick, 2019. "Lending Standards, Productivity and Credit Crunches," Staff Working Papers 19-25, Bank of Canada.
    5. Leonardo Gambacorta & Boris Hofmann & Gert Peersman, 2014. "The Effectiveness of Unconventional Monetary Policy at the Zero Lower Bound: A Cross‐Country Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(4), pages 615-642, June.
    6. 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.
    7. Holden, Tom D., 2016. "Computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 144569, ZBW - Leibniz Information Centre for Economics.
    8. James D. Hamilton & Jing Cynthia Wu, 2012. "The Effectiveness of Alternative Monetary Policy Tools in a Zero Lower Bound Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(s1), pages 3-46, February.
    9. Eric T. Swanson & John C. Williams, 2014. "Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates," American Economic Review, American Economic Association, vol. 104(10), pages 3154-3185, October.
    10. Simon Gilchrist & David López-Salido & Egon Zakrajšek, 2015. "Monetary Policy and Real Borrowing Costs at the Zero Lower Bound," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 77-109, January.
    11. Hong Lan & Alexander Meyer-Gohde, 2013. "Pruning in Perturbation DSGE Models - Guidance from Nonlinear Moving Average Approximations," SFB 649 Discussion Papers SFB649DP2013-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Collard, Fabrice & Juillard, Michel, 2001. "A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model," Computational Economics, Springer;Society for Computational Economics, vol. 17(2-3), pages 125-139, June.
    13. Brzoza-Brzezina, Michał & Kolasa, Marcin & Makarski, Krzysztof, 2015. "A penalty function approach to occasionally binding credit constraints," Economic Modelling, Elsevier, vol. 51(C), pages 315-327.
    14. Tom Holden & Michael Paetz, 2012. "Efficient Simulation of DSGE Models with Inequality Constraints," Quantitative Macroeconomics Working Papers 21207b, Hamburg University, Department of Economics.
    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. Benhabib, Jess & Evans, George W. & Honkapohja, Seppo, 2014. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 220-238.
    17. Dixon, Huw & Pourpourides, Panayiotis M., 2016. "On imperfect competition with occasionally binding cash-in-advance constraints," Journal of Macroeconomics, Elsevier, vol. 50(C), pages 72-85.
    18. Eggertsson, Gauti B. & Singh, Sanjay R., 2019. "Log-linear approximation versus an exact solution at the ZLB in the New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 105(C), pages 21-43.
    19. Braun, R. Anton & Körber, Lena Mareen, 2011. "New Keynesian dynamics in a low interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2213-2227.
    20. 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.
    21. Andrew Binning & Junior Maih, 2017. "Modelling Occasionally Binding Constraints Using Regime-Switching," Working Paper 2017/23, Norges Bank.
    22. 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?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1371-1406.
    23. Stanley Fischer, 2016. "Monetary Policy, Financial Stability, and the Zero Lower Bound," American Economic Review, American Economic Association, vol. 106(5), pages 39-42, May.
    24. 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.
    25. 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.
    26. Benhabib, Jess & Evans, George W. & Honkapohja, Seppo, 2014. "Liquidity traps and expectation dynamics: Fiscal stimulus or fiscal austerity?," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 220-238.
    27. Florin O. Bilbiie & Tommaso Monacelli & Roberto Perotti, 2019. "Is Government Spending at the Zero Lower Bound Desirable?," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(3), pages 147-173, July.
    28. Adam, Klaus & Billi, Roberto M., 2007. "Discretionary monetary policy and the zero lower bound on nominal interest rates," Journal of Monetary Economics, Elsevier, vol. 54(3), pages 728-752, April.
    29. Tom D. Holden, 2023. "Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints," The Review of Economics and Statistics, MIT Press, vol. 105(6), pages 1481-1499, November.
    30. John B. Taylor, 1999. "A Historical Analysis of Monetary Policy Rules," NBER Chapters, in: Monetary Policy Rules, pages 319-348, National Bureau of Economic Research, Inc.
    31. Johannes F. Wieland, 2019. "Are Negative Supply Shocks Expansionary at the Zero Lower Bound?," Journal of Political Economy, University of Chicago Press, vol. 127(3), pages 973-1007.
    32. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 1-49.
    33. Tom D. Holden & Paul Levine & Jonathan M. Swarbrick, 2020. "Credit Crunches from Occasionally Binding Bank Borrowing Constraints," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 52(2-3), pages 549-582, March.
    34. 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?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1371-1406.
    35. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    36. 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.
    37. Gauti B. Eggertsson & Michael Woodford, 2003. "The Zero Bound on Interest Rates and Optimal Monetary Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(1), pages 139-235.
    38. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Crescentini, Alex & Giri, Federico, 2023. "Dynare replication of "A Model of Secular Stagnation: Theory and Quantitative Evaluation" by Eggertsson et al. (2019)," I4R Discussion Paper Series 56, The Institute for Replication (I4R).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lansing, Kevin J., 2021. "Endogenous forecast switching near the zero lower bound," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 153-169.
    2. Tom D. Holden, 2023. "Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints," The Review of Economics and Statistics, MIT Press, vol. 105(6), pages 1481-1499, November.
    3. Jesper Lindé & Mathias Trabandt, 2018. "Should we use linearized models to calculate fiscal multipliers?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 937-965, November.
    4. Andrew Binning & Junior Maih, 2017. "Modelling Occasionally Binding Constraints Using Regime-Switching," Working Paper 2017/23, Norges Bank.
    5. Andrew Binning & Junior Maih, 2016. "Implementing the zero lower bound in an estimated regime-switching DSGE model," Working Paper 2016/3, Norges Bank.
    6. Lepetyuk, Vadym & Maliar, Lilia & Maliar, Serguei, 2020. "When the U.S. catches a cold, Canada sneezes: A lower-bound tale told by deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    7. Benjamin D. Keen & Alexander W. Richter & Nathaniel A. Throckmorton, 2017. "Forward Guidance And The State Of The Economy," Economic Inquiry, Western Economic Association International, vol. 55(4), pages 1593-1624, October.
    8. Andrew Binning & Junior Maih, 2016. "Forecast uncertainty in the neighborhood of the effective lower bound: How much asymmetry should we expect?," Working Paper 2016/13, Norges Bank.
    9. Martin Slanicay & Jan Čapek & Miroslav Hloušek, 2016. "Some Notes On Problematic Issues In Dsge Models," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 61(210), pages 79-100, July - Se.
    10. William T. Gavin & Benjamin D. Keen & Alexander W. Richter & Nathaniel A. Throckmorton, 2013. "Global Dynamics at the Zero Lower Bound," Auburn Economics Working Paper Series auwp2013-17, Department of Economics, Auburn University.
    11. Vadym Lepetyuk & Lilia Maliar & Serguei Maliar, 2017. "Should Central Banks Worry About Nonlinearities of their Large-Scale Macroeconomic Models?," Staff Working Papers 17-21, Bank of Canada.
    12. Gauti Eggertsson & Sergey Egiev & Alessandro Lin & Josef Platzer & Luca Riva, 2021. "A Toolkit for Solving Models with a Lower Bound on Interest Rates of Stochastic Duration," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 121-173, July.
    13. Hills, Timothy S. & Nakata, Taisuke & Schmidt, Sebastian, 2019. "Effective lower bound risk," European Economic Review, Elsevier, vol. 120(C).
    14. 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.
    15. Cars Hommes & Domenico Massaro & Isabelle Salle, 2019. "Monetary And Fiscal Policy Design At The Zero Lower Bound: Evidence From The Lab," Economic Inquiry, Western Economic Association International, vol. 57(2), pages 1120-1140, April.
    16. Tom Holden & Michael Paetz, 2012. "Efficient Simulation of DSGE Models with Inequality Constraints," Quantitative Macroeconomics Working Papers 21207b, Hamburg University, Department of Economics.
    17. S. Bogan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2021. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 96-120, July.
    18. Yasuo Hirose & Takeki Sunakawa, 2019. "Review of Solution and Estimation Methods for Nonlinear Dynamic Stochastic General Equilibrium Models with the Zero Lower Bound," The Japanese Economic Review, Japanese Economic Association, vol. 70(1), pages 51-104, March.
    19. Taisuke Nakata, 2018. "Reputation and Liquidity Traps," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 252-268, April.
    20. Morris, Stephen D., 2020. "Is the Taylor principle still valid when rates are low?," Journal of Macroeconomics, Elsevier, vol. 64(C).

    More about this item

    Keywords

    Business fluctuations and cycles; Economic models;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bca:bocadp:21-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bocgvca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.