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

Author

Listed:
  • Gianluca Benigno

  • Pierpaolo Benigno

  • Salvatore Nistico

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 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 alsotime varying.

Suggested Citation

  • Gianluca Benigno & Pierpaolo Benigno & Salvatore Nistico, 2011. "Second-Order Approximation of Dynamic Models with Time-Varying Risk," FMG Discussion Papers dp677, Financial Markets Group.
    • Handle: RePEc:fmg:fmgdps:dp677
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    2. Yusuf Soner Başkaya & Timur Hülagü & Hande Küçük, 2013. "Oil Price Uncertainty in a Small Open Economy," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 61(1), pages 168-198, April.
    3. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    4. Oliver de Groot, 2014. "The Risk Channel of Monetary Policy," International Journal of Central Banking, International Journal of Central Banking, vol. 10(2), pages 115-160, June.
    5. Gross, Isaac & Hansen, James, 2021. "Optimal policy design in nonlinear DSGE models: An n-order accurate approximation," European Economic Review, Elsevier, vol. 140(C).
    6. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    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. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    9. Michael Hatcher, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
    10. Meyer-Gohde, Alexander, 2015. "Risk-Sensitive Linear Approximations," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113057, Verein für Socialpolitik / German Economic Association.
    11. Pablo Guerrón-Quintana & Alexey Khazanov & Molin Zhong, 2023. "Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model," Finance and Economics Discussion Series 2023-027, Board of Governors of the Federal Reserve System (U.S.).
    12. 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.
    13. Gorodnichenko, Yuriy & Ng, Serena, 2017. "Level and volatility factors in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 91(C), pages 52-68.
    14. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    15. 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.
    16. Borovicka, J. & Hansen, L.P., 2016. "Term Structure of Uncertainty in the Macroeconomy," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1641-1696, Elsevier.
    17. Valerio Scalone, 2015. "Estimating Non-Linear DSGEs with the Approximate Bayesian Computation: an application to the Zero Lower Bound," Working Papers 6/15, Sapienza University of Rome, DISS.
    18. Castelnuovo, Efrem & Pellegrino, Giovanni, 2018. "Uncertainty-dependent effects of monetary policy shocks: A new-Keynesian interpretation," Journal of Economic Dynamics and Control, Elsevier, vol. 93(C), pages 277-296.
    19. Malkhozov, Aytek, 2014. "Asset prices in affine real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 180-193.
    20. Ana Maria Santacreu, 2015. "Monetary Policy in Small Open Economies: The Role of Exchange Rate Rules," Review, Federal Reserve Bank of St. Louis, vol. 97(3), pages 217-232.
    21. 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).
    22. Husted, Lucas & Rogers, John & Sun, Bo, 2018. "Uncertainty, currency excess returns, and risk reversals," Journal of International Money and Finance, Elsevier, vol. 88(C), pages 228-241.

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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