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Second-order approximation of dynamic models with time-varying risk

  • Benigno, Gianluca
  • Benigno, Pierpaolo
  • Nisticò, Salvatore

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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 37 (2013)
Issue (Month): 7 ()
Pages: 1231-1247

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Handle: RePEc:eee:dyncon:v:37:y:2013:i:7:p:1231-1247
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. 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.
  2. 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.
  3. 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.).
  4. 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.
  5. Andreasen, Martin, 2011. "How non-Gaussian shocks affect risk premia in non-linear DSGE models," Bank of England working papers 417, Bank of England.
  6. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramírez & Martin Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," PIER Working Paper Archive 09-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Nicholas Bloom & Max Floetotto & Nir Jaimovich & Itay Saporta-Eksten & Stephen J. Terry, 2014. "Really Uncertain Business Cycles," Working Papers 14-18, Center for Economic Studies, U.S. Census Bureau.
  8. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  9. Alejandro Justiniano & Giorgio E. Primiceri, 2006. "The Time Varying Volatility of Macroeconomic Fluctuations," NBER Working Papers 12022, National Bureau of Economic Research, Inc.
  10. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  11. Glenn D. Rudebusch & Eric T. Swanson, 2008. "The bond premium in a DSGE model with long-run real and nominal risks," Working Paper Series 2008-31, Federal Reserve Bank of San Francisco.
  12. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," FRB Atlanta Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  13. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
  14. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
  15. 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.
  16. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers 5964, C.E.P.R. Discussion Papers.
  17. 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 10-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  18. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  19. 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.
  20. 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.
  21. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  22. 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.
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