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

Author

Listed:
  • Gianluca Benigno
  • Pierpaolo Benigno
  • Salvatore Nisticò

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

  • Gianluca Benigno & Pierpaolo Benigno & Salvatore Nisticò, 2010. "Second-Order Approximation of Dynamic Models with Time-Varying Risk," CEP Discussion Papers dp1033, Centre for Economic Performance, LSE.
  • Handle: RePEc:cep:cepdps:dp1033
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. repec:eee:macchp:v2-1641 is not listed on IDEAS
    7. repec:eee:dyncon:v:80:y:2017:i:c:p:1-16 is not listed on IDEAS
    8. Hatcher, Michael, 2011. "Time-varying volatility, precautionary saving and monetary policy," Bank of England working papers 440, Bank of England.
    9. Borovicka, J. & Hansen, L.P., 2016. "Term Structure of Uncertainty in the Macroeconomy," Handbook of Macroeconomics, Elsevier.
    10. 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.
    11. Malkhozov, Aytek, 2014. "Asset prices in affine real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 180-193.
    12. repec:eee:moneco:v:91:y:2017:i:c:p:52-68 is not listed on IDEAS
    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. 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).

    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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