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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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  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.
  2. Giorgio Primiceri & Alejandro Justiniano, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," 2006 Meeting Papers 353, Society for Economic Dynamics.
  3. 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.
  4. Paul Gomme & Paul Klein, 2009. "Second-order approximation of dynamic models without the use of tensors," Working Papers 09004, Concordia University, Department of Economics, revised 28 Apr 2010.
  5. Pablo Guerron & Martin Uribe & Juan Rubio-Ramirez & Jesus Fernandez-Villaverde, 2010. "Risk Matters: The Real Effects of Volatility Shocks," 2010 Meeting Papers 281, Society for Economic Dynamics.
  6. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  7. 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.
  8. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  9. 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.
  10. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Fortune or Virtue: Time-Variant Volatilities Versus Parameter Drifting in U.S. Data," PIER Working Paper Archive 10-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  12. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  13. 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 105-43, January.
  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. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-quadratic approximation of optimal policy problems," Discussion Papers 0607-02, Columbia University, Department of Economics.
  16. 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.
  17. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  18. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  19. Collard, Fabrice & Juillard, Michel, 1999. "Accuracy of stochastic perturbuation methods: the case of asset pricing models," CEPREMAP Working Papers (Couverture Orange) 9922, CEPREMAP.
  20. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  21. Martin M. Andreasen, 2010. "How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models," CREATES Research Papers 2010-63, School of Economics and Management, University of Aarhus.
  22. 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.
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Cited by:
  1. Jaroslav Borovicka & Lars Hansen, 2012. "Examining macroeconomic models through the lens of asset pricing," Working Paper Series WP-2012-01, Federal Reserve Bank of Chicago.
  2. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  5. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
  6. 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).
  7. 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.
  8. 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.

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