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

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  • Gianluca Benigno
  • Pierpaolo Benigno
  • Salvatore Nisticò

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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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 16633.

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Date of creation: Dec 2010
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Publication status: published as Benigno, Gianluca & Benigno, Pierpaolo & Nisticò, Salvatore, 2013. "Second-order approximation of dynamic models with time-varying risk," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1231-1247.
Handle: RePEc:nbr:nberwo:16633

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  1. 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, C.E.P.R. Discussion Papers 7264, C.E.P.R. Discussion Papers.
  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, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 10-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers, C.E.P.R. Discussion Papers 5964, C.E.P.R. Discussion Papers.
  4. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1997-37, Carnegie Mellon University, Tepper School of Business.
  5. Glenn Rudebusch & Eric Swanson, 2008. "The bond premium in a DSGE model with long-run real and nominal risks," Working Paper Series, Federal Reserve Bank of San Francisco 2008-31, Federal Reserve Bank of San Francisco.
  6. 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, Elsevier, vol. 30(12), pages 2477-2508, December.
  7. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0282, National Bureau of Economic Research, Inc.
  8. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  9. 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, Society for Computational Economics 162, Society for Computational Economics.
  10. Jules H. 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," PIER Working Paper Archive, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 10-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Gianluca Benigno & Pierpaolo Benigno & Salvatore Nistic�, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, University of Chicago Press, vol. 26(1), pages 247 - 309.
  12. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  13. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen Terry, 2013. "Really Uncertain Business Cycles," CEP Discussion Papers, Centre for Economic Performance, LSE dp1195, Centre for Economic Performance, LSE.
  14. Paul Gomme & Paul Klein, 2009. "Second-order approximation of dynamic models without the use of tensors," Working Papers, Concordia University, Department of Economics 09004, Concordia University, Department of Economics, revised 28 Apr 2010.
  15. 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.
  16. Giorgio Primiceri & Alejandro Justiniano, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," 2006 Meeting Papers, Society for Economic Dynamics 353, Society for Economic Dynamics.
  17. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  18. 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.
  19. Martin M. Andreasen, 2010. "How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models," CREATES Research Papers 2010-63, School of Economics and Management, University of Aarhus.
  20. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(6-7), pages 979-999, June.
  21. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2807, C.E.P.R. Discussion Papers.
  22. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, 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 Nistic�, 2012. "Risk, Monetary Policy, and the Exchange Rate," NBER Macroeconomics Annual, University of Chicago Press, University of Chicago Press, vol. 26(1), pages 247 - 309.
  2. Charles Engel, 2011. "Comment on "Risk, Monetary Policy and the Exchange Rate"," NBER Chapters, National Bureau of Economic Research, Inc, in: NBER Macroeconomics Annual 2011, Volume 26, pages 310-314 National Bureau of Economic Research, Inc.
  3. 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.
  4. Yusuf Soner Başkaya & Timur H�lag� & Hande K���k, 2013. "Oil Price Uncertainty in a Small Open Economy," IMF Economic Review, Palgrave Macmillan, Palgrave Macmillan, vol. 61(1), pages 168-198, April.
  5. Oliver de Groot, 2014. "The Risk Channel of Monetary Policy," International Journal of Central Banking, International Journal of Central Banking, International Journal of Central Banking, vol. 10(2), pages 115-160, June.
  6. Jaroslav Borovicka & Lars Hansen, 2012. "Examining macroeconomic models through the lens of asset pricing," Working Paper Series, Federal Reserve Bank of Chicago WP-2012-01, Federal Reserve Bank of Chicago.
  7. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers, Bank of England 440, Bank of England.
  8. Jochen Michaelis, 2013. "Und dann werfen wir den Computer an – Anmerkungen zur Methodik der DSGE-Modelle," MAGKS Papers on Economics, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung) 201323, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

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