IDEAS home Printed from https://ideas.repec.org/p/ekd/008007/8359.html
   My bibliography  Save this paper

A penalty function approach to occasionally binding credit constraints

Author

Listed:
  • Marcin Kolasa
  • Michal Brzoza-Brzezina
  • Krzysztof Makarski

Abstract

A substantial part of the literature using dynamic stochastic general equilibrium (DSGE) models features financial frictions in the form of credit constraints. In this concept some agents (entrepreneurs or households) are limited in their borrowing capacity by the amount of collateral that they can provide to the lender. The constraint is assumed to be eternally binding, which facilitates the model solution as standard perturbation techniques can be applied. A number of papers used this approach to model frictions in the housing market. However, while conceptually and computationally attractive, the eternally binding constraint (EBC) setup suffers from a major shortcoming. The permanent nature of collateral constraints generates strong, short-lived and symmetric reactions of macroeconomic variables to shocks. This means in particular that the EBC modeling strategy does not allow to distinguish between “normal” and “stress” periods. This model feature seems inconsistent with empirical evidence, which shows that residential investment, housing stock, change in mortgage loans and house price inflation are all skewed downwards, i.e. left tail events are relatively more frequent. This suggests either that shocks affecting the housing market are asymmetric, or that it responds to symmetric shocks in a skewed fashion. In this paper we consider a model in which asymmetries emerge endogenously from constraints facing the agents. The discussion presented above suggests that the collateral constraints should not be applied in a permanently and symmetrically binding fashion. A preferred specification would feature constraints that do not matter under normal circum-stances (from the modeling perspective: in the vicinity of the steady state), but become binding occasionally, i.e. during episodes of unfavorable economic conditions (e.g. after a series of negative macroeconomic or financial shocks). The idea of occasionally binding constraints (OBC) is not new. However, given their highly non-linear nature, they should ideally be solved with global methods. Due to the curse of dimensionality, however, these can be applied only to relatively small models with a limited number of state variables. In spite of the progress achieved in the area of global solution techniques in recent years, such methods are still out of range for models of the size used for practical policymaking, i.e. featuring a number of real and nominal rigidities. Adding these frictions seems indispensable when the models are to be applied for instance for analyzing business cycle consequences of macroprudential policies. For such models, local solution methods are still the only feasible option. For these reasons, we thoroughly investigate a potentially attractive shortcut to approximate occasionally binding constraints, i.e. the so-called barrier or penalty function method. This approach essentially consists in converting inequality constraints into equality constraints, making the use of standard perturbation techniques possible. To this end, we construct a DSGE model with a standard set of rigidities and collateral constraints, except that the latter are introduced in the form of a smooth penalty function. We parametrize the model in such a way that the constraint does not play an important role close to the steady state, but becomes binding when the economy is hit by sufficiently large negative shocks. Next, we investigate the main features of the model both under per-fect foresight and in a stochastic setting using its local approximations of various orders. Our main findings are as follows. First, the introduction of occasionally binding con-straints via the penalty function approach allows to generate asymmetric and non-linear reactions of the economy to shocks. Second, this feature can be also reproduced for local approximations, though only for orders higher than two. Third, and less optimistic, stochastic simulations for 2nd, 3rd and 4th order approximations suffer from serious stability problems that make them inapplicable in practice. Approximations of order higher than four are, on the other hand, prohibitively expensive in terms of storing and computing power for medium-sized business cycle models. All in all, while being practical for non-stochastic models, the penalty function approach unfortunately fails to fulfill our expectations in a stochastic environment. This makes it an attractive way of introducing financial frictions into deterministic models like GEM or EAGLE. However, a fully-fledged application in a realistic stochastic framework seems currently out of range.

Suggested Citation

  • Marcin Kolasa & Michal Brzoza-Brzezina & Krzysztof Makarski, 2015. "A penalty function approach to occasionally binding credit constraints," EcoMod2015 8359, EcoMod.
  • Handle: RePEc:ekd:008007:8359
    as

    Download full text from publisher

    File URL: http://ecomod.net/system/files/Kolasa.ecomod_final.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    2. 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.
    3. Julio J. Rotemberg & Michael Woodford, 1999. "Interest Rate Rules in an Estimated Sticky Price Model," NBER Chapters,in: Monetary Policy Rules, pages 57-126 National Bureau of Economic Research, Inc.
    4. Matteo Iacoviello, 2005. "House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle," American Economic Review, American Economic Association, vol. 95(3), pages 739-764, June.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    6. Kiyotaki, Nobuhiro & Moore, John, 1997. "Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-248, April.
    7. Kim, Sunghyun Henry & Kollmann, Robert & Kim, Jinill, 2010. "Solving the incomplete market model with aggregate uncertainty using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 50-58, January.
    8. Gomes, S. & Jacquinot, P. & Pisani, M., 2012. "The EAGLE. A model for policy analysis of macroeconomic interdependence in the euro area," Economic Modelling, Elsevier, vol. 29(5), pages 1686-1714.
    9. Charles T. Carlstrom & Timothy S. Fuerst & Matthias Paustian, 2010. "Optimal Monetary Policy in a Model with Agency Costs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 37-70, September.
    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. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    12. Helbling, Thomas & Huidrom, Raju & Kose, M. Ayhan & Otrok, Christopher, 2011. "Do credit shocks matter? A global perspective," European Economic Review, Elsevier, vol. 55(3), pages 340-353, April.
    13. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
    14. Sylvia Kaufmann & Maria Teresa Valderrama, 2010. "The Role Of Credit Aggregates And Asset Prices In The Transmission Mechanism: A Comparison Between The Euro Area And The Usa," Manchester School, University of Manchester, vol. 78(4), pages 345-377, July.
    15. Roeger, Werner & in 't Veld, Jan, 2004. "Some selected simulation experiments with the European commission's QUEST model," Economic Modelling, Elsevier, vol. 21(5), pages 785-832, September.
    16. Hubrich, Kirstin & Tetlow, Robert J., 2015. "Financial stress and economic dynamics: The transmission of crises," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 100-115.
    17. Brzoza-Brzezina, Michał & Makarski, Krzysztof, 2011. "Credit crunch in a small open economy," Journal of International Money and Finance, Elsevier, vol. 30(7), pages 1406-1428.
    18. Dewachter, Hans & Wouters, Raf, 2014. "Endogenous risk in a DSGE model with capital-constrained financial intermediaries," Journal of Economic Dynamics and Control, Elsevier, vol. 43(C), pages 241-268.
    19. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    20. Matteo Iacoviello & Stefano Neri, 2010. "Housing Market Spillovers: Evidence from an Estimated DSGE Model," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 125-164, April.
    21. Andrea Gerali & Stefano Neri & Luca Sessa & Federico M. Signoretti, 2010. "Credit and Banking in a DSGE Model of the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 107-141, September.
    22. Marcin Kolasa & Giovanni Lombardo, 2014. "Financial Frictions and Optimal Monetary Policy in an Open Economy," International Journal of Central Banking, International Journal of Central Banking, vol. 10(1), pages 43-94, March.
    23. Enrique G. Mendoza, 2010. "Sudden Stops, Financial Crises, and Leverage," American Economic Review, American Economic Association, vol. 100(5), pages 1941-1966, December.
    24. Den Haan, Wouter J. & De Wind, Joris, 2012. "Nonlinear and stable perturbation-based approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1477-1497.
    25. Fiorella De Fiore & Oreste Tristani, 2013. "Optimal Monetary Policy in a Model of the Credit Channel," Economic Journal, Royal Economic Society, vol. 123(571), pages 906-931, September.
    26. Aliaga-Díaz, Roger & Olivero, María Pía, 2012. "Do Bank Capital Requirements Amplify Business Cycles? Bridging The Gap Between Theory And Empirics," Macroeconomic Dynamics, Cambridge University Press, vol. 16(03), pages 358-395, June.
    27. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    28. 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.
    29. Lombardo, Giovanni & McAdam, Peter, 2012. "Financial market frictions in a model of the Euro area," Economic Modelling, Elsevier, vol. 29(6), pages 2460-2485.
    30. Angeloni, Ignazio & Faia, Ester, 2013. "Capital regulation and monetary policy with fragile banks," Journal of Monetary Economics, Elsevier, vol. 60(3), pages 311-324.
    31. Simon Gilchrist & Egon Zakrajsek, 2012. "Credit Spreads and Business Cycle Fluctuations," American Economic Review, American Economic Association, vol. 102(4), pages 1692-1720, June.
    32. Ratto, Marco & Roeger, Werner & Veld, Jan in 't, 2009. "QUEST III: An estimated open-economy DSGE model of the euro area with fiscal and monetary policy," Economic Modelling, Elsevier, vol. 26(1), pages 222-233, January.
    33. Meh, Césaire A. & Moran, Kevin, 2010. "The role of bank capital in the propagation of shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 555-576, March.
    34. Katrin Assenmacher-Wesche & Stefan Gerlach, 2008. "Monetary policy, asset prices and macroeconomic conditions : a panel-VAR study," Working Paper Research 149, National Bank of Belgium.
    35. Tamim Bayoumi & Hamid Faruqee & Douglas Laxton & Philippe D Karam & Alessandro Rebucci & Jaewoo Lee & Benjamin L Hunt & Ivan Tchakarov, 2004. "GEM; A New International Macroeconomic Model," IMF Occasional Papers 239, International Monetary Fund.
    36. Brzoza-Brzezina, Michał & Kolasa, Marcin & Makarski, Krzysztof, 2013. "The anatomy of standard DSGE models with financial frictions," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 32-51.
    37. 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.
    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. Krzysztof Makarski, 2017. "Mnożniki fiskalne w modelu z ograniczeniami kredytowymi," GRAPE Working Papers 13, GRAPE Group for Research in Applied Economics.
    2. Karmakar, Sudipto, 2016. "Macroprudential regulation and macroeconomic activity," Journal of Financial Stability, Elsevier, vol. 25(C), pages 166-178.
    3. Laséen, Stefan & Pescatori, Andrea & Turunen, Jarkko, 2017. "Systemic risk: A new trade-off for monetary policy?," Journal of Financial Stability, Elsevier, vol. 32(C), pages 70-85.
    4. Andrew Binning & Junior Maih, 2017. "Modelling Occasionally Binding Constraints Using Regime-Switching," Working Papers No 9/2017, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    5. Torój, Andrzej, 2017. "Managing external macroeconomic imbalances in the EU: the welfare cost of scoreboard-based constraints," Economic Modelling, Elsevier, vol. 61(C), pages 293-311.

    More about this item

    Keywords

    general; United States; General equilibrium modeling; Modeling: new developments;

    JEL classification:

    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

    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:ekd:008007:8359. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Theresa Leary). General contact details of provider: http://edirc.repec.org/data/ecomoea.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.