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

  • Gianluca Benigno
  • Pierpaolo Benigno
  • Salvatore Nisticò

This paper provides first and second-order approximation methods for the solution of nonlinear 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 timevarying 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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File URL: http://cep.lse.ac.uk/pubs/download/dp1033.pdf
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Paper provided by Centre for Economic Performance, LSE in its series CEP Discussion Papers with number dp1033.

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Date of creation: Dec 2010
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Handle: RePEc:cep:cepdps:dp1033
Contact details of provider: Web page: http://cep.lse.ac.uk/_new/publications/series.asp?prog=CEP

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  1. 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.
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  3. 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.
  4. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
  5. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  11. 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.
  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. 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.
  14. 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.
  15. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," NBER Working Papers 12672, National Bureau of Economic Research, Inc.
  16. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  17. 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.
  18. 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.
  19. Andreasen, Martin, 2011. "How non-Gaussian shocks affect risk premia in non-linear DSGE models," Bank of England working papers 417, Bank of England.
  20. Collard, Fabrice & Juillard, Michel, 1999. "Accuracy of stochastic perturbuation methods: the case of asset pricing models," CEPREMAP Working Papers (Couverture Orange) 9922, CEPREMAP.
  21. Giorgio Primiceri & Alejandro Justiniano, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," 2006 Meeting Papers 353, Society for Economic Dynamics.
  22. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
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