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

  • Gianluca Benigno

    ()

  • Pierpaolo Benigno

    ()

  • Salvatore Nistico

    ()

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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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
Contact details of provider: Web page: http://www.lse.ac.uk/fmg/

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  1. 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.
  2. 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.
  3. Fernández-Villaverde, Jesús & Koijen, Ralph & Rubio-Ramírez, Juan Francisco & van Binsbergen, Jules H., 2010. "The Term Structure of Interest Rates in a DSGE Model with Recursive Preferences," CEPR Discussion Papers 7781, C.E.P.R. Discussion Papers.
  4. Jinill Kim & Sunghyun 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.).
  5. 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.
  6. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-quadratic approximation of optimal policy problems," Discussion Papers 0607-02, Columbia University, Department of Economics.
  7. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. 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.
  9. 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).
  10. Giorgio Primiceri & Alejandro Justiniano, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," 2006 Meeting Papers 353, Society for Economic Dynamics.
  11. 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.
  12. Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A. & Rubio-Ramírez, Juan Francisco & Uribe, Martín, 2009. "Risk Matters: The Real Effects of Volatility Shocks," CEPR Discussion Papers 7264, C.E.P.R. Discussion Papers.
  13. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  14. 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.
  15. An, Sungbae & Schorfheide, Frank, 2005. "Bayesian Analysis of DSGE Models," CEPR Discussion Papers 5207, C.E.P.R. Discussion Papers.
  16. 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.
  17. 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.
  18. 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.
  19. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  20. 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.
  21. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  22. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
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