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

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Author Info

  • Gianluca Benigno

    (London School of Economics)

  • Pierpaolo Benigno

    (LUISS "Guido Carli" and EIEF)

  • Salvatore Nisticò

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

Abstract

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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Bibliographic Info

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. 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.
  2. 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.
  3. Alejandro Justiniano & Giorgio E. Primiceri, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," NBER Working Papers 12022, National Bureau of Economic Research, Inc.
  4. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
  5. Jules van Binsbergen & Jesús Fernández-Villaverde & Ralph S.J. Koijen & Juan F. Rubio-Ramírez, 2010. "The Term Structure of Interest Rates in a DSGE Model with Recursive Preferences," NBER Working Papers 15890, National Bureau of Economic Research, Inc.
  6. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers 5964, C.E.P.R. Discussion Papers.
  7. 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.
  8. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
  9. Andreasen, Martin, 2011. "How non-Gaussian shocks affect risk premia in non-linear DSGE models," Bank of England working papers 417, Bank of England.
  10. 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.
  11. Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A. & Rubio-Ramirez, Juan Francisco & Uribe, Martín, 2009. "Risk Matters: The Real Effects of Volatility Shocks," CEPR Discussion Papers 7264, C.E.P.R. Discussion Papers.
  12. 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.
  13. 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.
  14. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  15. 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.
  16. 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.
  17. 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.
  18. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  19. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  20. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  21. 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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Citations

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Cited by:
  1. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2011. "Risk, Monetary Policy and the Exchange Rate," NBER Working Papers 17133, National Bureau of Economic Research, Inc.
  2. Jaroslav Borovicka & Lars Hansen, 2012. "Examining macroeconomic models through the lens of asset pricing," Working Paper Series WP-2012-01, Federal Reserve Bank of Chicago.
  3. Yusuf Soner Baskaya & Timur Hulagu & Hande Kucuk, 2013. "Oil Price Uncertainty in a Small Open Economy," Working Papers 1309, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
  4. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
  5. Jochen Michaelis, 2013. "Und dann werfen wir den Computer an – Anmerkungen zur Methodik der DSGE-Modelle," MAGKS Papers on Economics 201323, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
  6. Rizvanoghlu, Islam, 2011. "Oil Price Shocks and Macroeconomy: The Role for Precautionary Demand and Storage," MPRA Paper 42351, University Library of Munich, Germany, revised 01 Jun 2012.
  7. Charles Engel, 2011. "Comment on "Risk, Monetary Policy and the Exchange Rate"," NBER Chapters, in: NBER Macroeconomics Annual 2011, Volume 26, pages 310-314 National Bureau of Economic Research, Inc.
  8. DeGroot, Oliver, 2014. "The Risk Channel of Monetary Policy," Finance and Economics Discussion Series 2014-31, Board of Governors of the Federal Reserve System (U.S.).

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