[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/eie/wpaper/1021.html
   My bibliography  Save this paper

Second-Order Approximation of Dynamic Models with Time-Varying Risk

Author

Listed:
  • Gianluca Benigno

    (London School of Economics)

  • Pierpaolo Benigno

    (LUISS "Guido Carli" and EIEF)

  • Salvatore Nisticò

    (Università di Roma "Tor Vergata" and LUISS "Guido Carli")

Abstract
This paper provides first and second-order approximation methods for the solution of non-linear dynamic stochastic models in which the exogenous state variables follow conditionally-linear stochastic processes displaying time-varying risk. The first-order approximation is consistent with a conditionally-linear model in which risk is still time-varying but has no distinct role - separated from the primitive stochastic disturbances - in influencing the endogenous variables. The second-order approximation of the solution, instead, is sufficient to get this role. Moreover, risk premia, evaluated using only a first-order approximation of the solution, will be also time varying.

Suggested Citation

  • Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2010. "Second-Order Approximation of Dynamic Models with Time-Varying Risk," EIEF Working Papers Series 1021, Einaudi Institute for Economics and Finance (EIEF), revised Dec 2010.
    • Handle: RePEc:eie:wpaper:1021
    as

    Download full text from publisher

    File URL: http://www.eief.it/files/2012/09/wp-21-second-order-approximation-of-dynamic-models-with-time-varying-risk.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    2. Glenn D. Rudebusch & Eric T. Swanson, 2012. "The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 105-143, January.
    3. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    4. Juan Rubio-Ramirez & Jesus Fernandez-Villaverde & Pablo A. Guerron-Quintana, 2010. "Fortune or Virtue: Time Variant Volatilities versus Parameter Drifting in U.S. Data," 2010 Meeting Papers 270, Society for Economic Dynamics.
    5. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta†Eksten & Stephen J. Terry, 2018. "Really Uncertain Business Cycles," Econometrica, Econometric Society, vol. 86(3), pages 1031-1065, May.
    6. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    7. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    8. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    9. Benigno, Pierpaolo & Benigno, Gianluca, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
    10. Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
    11. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    12. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 247-309.
    13. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
    14. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
    15. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    16. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    17. 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.
    18. Martin M. Andreasen, 2010. "How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models," CREATES Research Papers 2010-63, Department of Economics and Business Economics, Aarhus University.
    19. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramirez, 2010. "Fortune or virtue: time-variant volatilities versus parameter drifting," Working Papers 10-14, Federal Reserve Bank of Philadelphia.
    20. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
    21. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    22. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    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. Yusuf Soner Başkaya & Timur Hülagü & Hande Küçük, 2013. "Oil Price Uncertainty in a Small Open Economy," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 61(1), pages 168-198, April.
    2. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    3. Oliver de Groot, 2014. "The Risk Channel of Monetary Policy," International Journal of Central Banking, International Journal of Central Banking, vol. 10(2), pages 115-160, June.
    4. Gross, Isaac & Hansen, James, 2021. "Optimal policy design in nonlinear DSGE models: An n-order accurate approximation," European Economic Review, Elsevier, vol. 140(C).
    5. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    6. Charles Engel, 2011. "Comment on "Risk, Monetary Policy and the Exchange Rate"," NBER Chapters, in: NBER Macroeconomics Annual 2011, Volume 26, pages 310-314, National Bureau of Economic Research, Inc.
    7. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    8. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
    9. Castelnuovo, Efrem & Pellegrino, Giovanni, 2018. "Uncertainty-dependent effects of monetary policy shocks: A new-Keynesian interpretation," Journal of Economic Dynamics and Control, Elsevier, vol. 93(C), pages 277-296.
    10. Meyer-Gohde, Alexander, 2015. "Risk-Sensitive Linear Approximations," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113057, Verein für Socialpolitik / German Economic Association.
    11. Pablo Guerrón-Quintana & Alexey Khazanov & Molin Zhong, 2023. "Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model," Finance and Economics Discussion Series 2023-027, Board of Governors of the Federal Reserve System (U.S.).
    12. Rizvanoghlu, Islam, 2011. "Oil Price Shocks and Macroeconomy: The Role for Precautionary Demand and Storage," MPRA Paper 42351, University Library of Munich, Germany, revised 01 Jun 2012.
    13. Gorodnichenko, Yuriy & Ng, Serena, 2017. "Level and volatility factors in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 91(C), pages 52-68.
    14. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    15. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 247-309.
    16. Borovicka, J. & Hansen, L.P., 2016. "Term Structure of Uncertainty in the Macroeconomy," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1641-1696, Elsevier.
    17. Valerio Scalone, 2015. "Estimating Non-Linear DSGEs with the Approximate Bayesian Computation: an application to the Zero Lower Bound," Working Papers 6/15, Sapienza University of Rome, DISS.
    18. Husted, Lucas & Rogers, John & Sun, Bo, 2018. "Uncertainty, currency excess returns, and risk reversals," Journal of International Money and Finance, Elsevier, vol. 88(C), pages 228-241.
    19. Malkhozov, Aytek, 2014. "Asset prices in affine real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 180-193.
    20. Ana Maria Santacreu, 2015. "Monetary Policy in Small Open Economies: The Role of Exchange Rate Rules," Review, Federal Reserve Bank of St. Louis, vol. 97(3), pages 217-232.
    21. Jochen Michaelis, 2013. "Und dann werfen wir den Computer an – Anmerkungen zur Methodik der DSGE-Modelle," MAGKS Papers on Economics 201323, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

    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. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    2. Andreasen, Martin, 2011. "An estimated DSGE model: explaining variation in term premia," Bank of England working papers 441, Bank of England.
    3. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 247-309.
    4. 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.
    5. Kyle Jurado, 2016. "Advance Information and Distorted Beliefs in Macroeconomic and Financial Fluctuations," 2016 Meeting Papers 154, Society for Economic Dynamics.
    6. Amisano, Gianni & Tristani, Oreste, 2010. "Euro area inflation persistence in an estimated nonlinear DSGE model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 1837-1858, October.
    7. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," EconStor Preprints 269876, ZBW - Leibniz Information Centre for Economics.
    8. Andreasen, Martin M., 2012. "An estimated DSGE model: Explaining variation in nominal term premia, real term premia, and inflation risk premia," European Economic Review, Elsevier, vol. 56(8), pages 1656-1674.
    9. Alali, Walid Y., 2009. "Solution Strategies of Dynamic Stochastic General Equilibrium (DSGE) models," MPRA Paper 116480, University Library of Munich, Germany.
    10. Benchimol, Jonathan & Ivashchenko, Sergey, 2021. "Switching volatility in a nonlinear open economy," Journal of International Money and Finance, Elsevier, vol. 110(C).
    11. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    12. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    13. Francesco Bianchi & Leonardo Melosi, 2017. "Escaping the Great Recession," American Economic Review, American Economic Association, vol. 107(4), pages 1030-1058, April.
    14. Andreasen, Martin M. & Caggiano, Giovanni & Castelnuovo, Efrem & Pellegrino, Giovanni, 2024. "Does risk matter more in recessions than in expansions? Implications for monetary policy," Journal of Monetary Economics, Elsevier, vol. 143(C).
    15. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    16. Doh, Taeyoung, 2011. "Yield curve in an estimated nonlinear macro model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1229-1244, August.
    17. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    18. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    19. 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.
    20. Anh Nguyen, 2015. "Financial frictions and the volatility of monetary policy in a DSGE model," Working Papers 75949436, Lancaster University Management School, Economics Department.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:eie:wpaper:1021. 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: Facundo Piguillem (email available below). General contact details of provider: https://edirc.repec.org/data/einauit.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.