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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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  4. Jinill Kim & Sunghyun Henry 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. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
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  7. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  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. Andreasen, Martin, 2011. "How non-Gaussian shocks affect risk premia in non-linear DSGE models," Bank of England working papers 417, Bank of England.
  11. 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.
  12. 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.
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  14. Collard, Fabrice & Juillard, Michel, 1999. "Accuracy of stochastic perturbuation methods: the case of asset pricing models," CEPREMAP Working Papers (Couverture Orange) 9922, CEPREMAP.
  15. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  16. Alejandro Justiniano & Northwestern University, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," Computing in Economics and Finance 2006 219, Society for Computational Economics.
  17. 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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  20. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  21. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen J. Terry, 2012. "Really Uncertain Business Cycles," NBER Working Papers 18245, National Bureau of Economic Research, Inc.
  22. 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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