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Second Order Approximation of Dynamic Models with Time-Varying Risk

  • Benigno, Gianluca
  • Benigno, Pierpaolo
  • Nisticò, Salvatore

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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8177.

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Date of creation: Jan 2011
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Handle: RePEc:cpr:ceprdp:8177
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  1. 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.
  2. 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.
  3. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2004. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Econometric Society 2004 North American Winter Meetings 411, Econometric Society.
  4. Jesús Fernández-Villaverde & Pablo A. Guerrón-Quintana & Juan Rubio-Ramírez & Martín Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," NBER Working Papers 14875, National Bureau of Economic Research, Inc.
  5. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-quadratic approximation of optimal policy problems," Discussion Papers 0607-02, Columbia University, Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  10. Alejandro Justiniano & Giorgio E. Primiceri, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," NBER Working Papers 12022, National Bureau of Economic Research, Inc.
  11. 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.
  12. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen Terry, 2013. "Really Uncertain Business Cycles," CEP Discussion Papers dp1195, Centre for Economic Performance, LSE.
  13. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  14. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  15. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  16. Andreasen, Martin, 2011. "How non-Gaussian shocks affect risk premia in non-linear DSGE models," Bank of England working papers 417, Bank of England.
  17. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  18. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  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. 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.
  21. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  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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