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

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  • Gianluca Benigno

    ()

  • Pierpaolo Benigno

    ()

  • Salvatore Nistico

    ()

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 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 alsotime varying.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/DP677_2011_SecondOrder.pdf
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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp677.

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Date of creation: Mar 2011
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Handle: RePEc:fmg:fmgdps:dp677

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Web page: http://www.lse.ac.uk/fmg/

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  1. 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.
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  3. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen J. Terry, 2014. "Really Uncertain Business Cycles," Working Papers 14-18, Center for Economic Studies, U.S. Census Bureau.
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  5. Jesus Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Fortune or virtue: time-variant volatilities versus parameter drifting," Working Papers 10-14, Federal Reserve Bank of Philadelphia.
  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 2530-61, October.
  7. Glenn Rudebusch & Eric Swanson, 2008. "The bond premium in a DSGE model with long-run real and nominal risks," Working Paper Series 2008-31, Federal Reserve Bank of San Francisco.
  8. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
  9. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Chapters, in: NBER Macroeconomics Annual 2011, Volume 26, pages 247-309 National Bureau of Economic Research, Inc.
  10. 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.
  11. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  12. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
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  14. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  15. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  16. Giorgio Primiceri & Alejandro Justiniano, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," 2006 Meeting Papers 353, Society for Economic Dynamics.
  17. 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.
  18. Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A. & Rubio-Ramírez, Juan Francisco, 2010. "Fortune or Virtue: Time-Variant Volatilities Versus Parameter Drifting in U.S. Data," CEPR Discussion Papers 7813, C.E.P.R. Discussion Papers.
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Cited by:
  1. Jaroslav Borovicka & Lars Peter Hansen, 2011. "Examining Macroeconomic Models Through the Lens of Asset Pricing," Working Papers 2011-012, Becker Friedman Institute for Research In Economics.
  2. Yusuf Soner Baskaya & Timur Hulagu & Hande Kucuk, 2013. "Oil Price Uncertainty in a Small Open Economy," Working Papers 1309, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
  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. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
  5. 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).
  6. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  7. 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.
  8. 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.

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