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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. 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.
  2. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nistic�, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 247 - 309.
  3. 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.
  4. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  5. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-41, June.
  6. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-quadratic approximation of optimal policy problems," Discussion Papers 0607-02, Columbia University, Department of Economics.
  7. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen Terry, 2013. "Really uncertain business cycles," LSE Research Online Documents on Economics 51526, London School of Economics and Political Science, LSE Library.
  8. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  9. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  10. Henry Kim & Jinill Kim & Ernst Schaumburg & Christopher A. Sims, 2005. "Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models," Discussion Papers Series, Department of Economics, Tufts University 0505, Department of Economics, Tufts University.
  11. 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.
  12. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  13. An, Sungbae & Schorfheide, Frank, 2005. "Bayesian Analysis of DSGE Models," CEPR Discussion Papers 5207, C.E.P.R. Discussion Papers.
  14. Pablo A. Guerron-Quintana & Martin Uribe & Juan Rubio-Ramirez & Jesús Fernández-Villaverde, 2009. "Risk Matters: The Real E¤ects of Volatility Shocks," 2009 Meeting Papers 237, Society for Economic Dynamics.
  15. 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.
  16. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  17. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  18. Glenn D. Rudebusch & Eric T. Swanson, 2008. "The bond premium in a DSGE model with long-run real and nominal risks," Working Paper Research 143, National Bank of Belgium.
  19. 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.
  20. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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Cited by:
  1. 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.
  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. 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.
  4. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
  5. 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.
  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).

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