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

  • Gianluca Benigno

    (London School of Economics)

  • Pierpaolo Benigno

    (LUISS "Guido Carli" and EIEF)

  • Salvatore Nisticò

    (Università di Roma "Tor Vergata" and LUISS "Guido Carli")

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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File URL: http://www.eief.it/files/2012/09/wp-21-second-order-approximation-of-dynamic-models-with-time-varying-risk.pdf
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Paper provided by Einaudi Institute for Economics and Finance (EIEF) in its series EIEF Working Papers Series with number 1021.

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Length: 24 pages
Date of creation: 2010
Date of revision: Dec 2010
Handle: RePEc:eie:wpaper:1021
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  1. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Fortune or Virtue: Time-Variant Volatilities Versus Parameter Drifting in U.S. Data," NBER Working Papers 15928, National Bureau of Economic Research, Inc.
  2. 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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  7. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  8. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 247 - 309.
  9. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-61, October.
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  12. 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.
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  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. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
  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. 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).
  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. 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.
  20. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  21. Martin M. Andreasen, 2010. "How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models," CREATES Research Papers 2010-63, Department of Economics and Business Economics, Aarhus University.
  22. 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.
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