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

Author

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  • Benigno, Gianluca
  • Benigno, Pierpaolo
  • Nisticò, Salvatore
Abstract
This paper provides first and second-order approximation methods for the solution of nonlinear 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 timevarying 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.

Suggested Citation

  • Benigno, Gianluca & Benigno, Pierpaolo & Nisticò, Salvatore, 2010. "Second-order approximation of dynamic models with time-varying risk," LSE Research Online Documents on Economics 121707, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:121707
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    Cited by:

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    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. Gross, Isaac & Hansen, James, 2021. "Optimal policy design in nonlinear DSGE models: An n-order accurate approximation," European Economic Review, Elsevier, vol. 140(C).
    8. 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.
    9. 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.
    10. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    11. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
    12. 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.
    13. 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.
    14. 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.
    15. 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.).
    16. 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.
    17. 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.
    18. Malkhozov, Aytek, 2014. "Asset prices in affine real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 180-193.
    19. 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.
    20. Gorodnichenko, Yuriy & Ng, Serena, 2017. "Level and volatility factors in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 91(C), pages 52-68.
    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).

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    More about this item

    Keywords

    stochastic volatility; second order approximation;

    JEL classification:

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

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