Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-21T16:17:09.375Z Has data issue: false hasContentIssue false
  • English
  • Français

IMPLEMENTING STOCHASTIC VOLATILITY IN DSGE MODELS: A COMMENT

Published online by Cambridge University Press:  29 November 2018

Lorenzo Bretscher ,
Alex Hsu  and
Andrea Tamoni
Lorenzo Bretscher
Affiliation:
London Business School
Alex Hsu*
Affiliation:
Georgia Institute of Technology
Andrea Tamoni
Affiliation:
London School of Economics and Political Science
*
Address correspondence to: Alex Hsu, Scheller College of Business, Georgia Institute of Technology, USA. e-mail: alex.hsu@scheller.gatech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We highlight a state variable misspecification with one accepted method to implement stochastic volatility (SV) in DSGE models when transforming the nonlinear state-innovation dynamics to its linear representation. Although the technique is more efficient numerically, we show that it is not exact but only serves as an approximation when the magnitude of SV is small. Not accounting for this approximation error may induce substantial spurious volatility in macroeconomic series, which could lead to incorrect inference about the performance of the model. We also show that, by simply lagging and expanding the state vector, one can obtain the correct state-space specification. Finally, we validate our augmented implementation approach against an established alternative through numerical simulation.

Keywords

Dynamic Equilibrium EconomiesStochastic VolatilityPerturbation
Type
Articles
Information
Macroeconomic Dynamics , Volume 24 , Issue 4 , June 2020 , pp. 935 - 950
Copyright
© Cambridge University Press 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We would like to thank two anonymous referees and the associate editor for their valuable comments. We are also grateful to Wouter den Haan and Martin Andreasen for helpful discussions.

References

Adjemian, S., Bastani, H., Juillard, M., Karamé, F., Maih, J., Mihoubi, F., Perendia, G., Pfeifer, J., Ratto, M. and Villemot, S. (2011) Dynare: Reference Manual Version 4. Dynare Working Papers 1, CEPREMAP.Google Scholar
Andreasen, M. (2012) On the effects of rare disasters and uncertainty shocks for risk premia in non-linear DSGE models. Review of Economic Dynamics 15(3), 295–316.CrossRefGoogle Scholar
Andreasen, M. M., Fernández-Villaverde, J. and Rubio-Ramírez, J. F. (2017) The pruned state-space system for non-linear DSGE models: Theory and empirical applications. The Review of Economics Studies 28(4), 755–775.Google Scholar
Basu, S. and Bundick, B. (2017) Uncertainty shocks in a model of effective demand. Econometrica 85(3), 937–958.CrossRefGoogle Scholar
Bloom, N. (2009) The impact of uncertainty shocks. Econometrica 77(3), 623–685.Google Scholar
Bloom, N., Floetotto, M., Jaimovich, N., Saporta-Eksten, I. and Terry, S. J. (2012) Really Uncertain Business Cycles. National Bureau of Economic Research, Inc., NBER Working Papers 18245.CrossRefGoogle Scholar
Bretscher, L., Hsu, A. and Tamoni, A. (2017) Risk Aversion and the Response of the Macroeconomy to Uncertainty Shocks. Georgia Institute of Technology, Scheller College of Business, Working Paper Series 17–13.Google Scholar
den Haan, W. J. and de Wind, J. (2010) How well-behaved are higher-order perturbation solutions? Netherlands Central Bank, Research Department, DNB Working Papers 240.Google Scholar
Fernández-Villaverde, J. and Levintal, O. (2017) Solution methods for models with rare disasters. Quantitative Economics 9, 903–944.CrossRefGoogle Scholar
Fernández-Villaverde, J., Guerrón-Quintana, P., Rubio-Ramírez, J. F. and Uribe, M. (2011) Risk matters: The real effects of volatility shocks. American Economic Review 101(6), 2530–2561.CrossRefGoogle Scholar
Fernández-Villaverde, J., Guerrón-Quintana, P. and Rubio-Ramírez, J. F. (2015a) Estimating dynamic equilibrium models with stochastic volatility. Journal of Econometrics 185(1), 216–229.CrossRefGoogle Scholar
Fernández-Villaverde, J., Guerrón-Quintana, P., Kuester, K. and Rubio-Ramírez, J. (2015b) Fiscal volatility shocks and economic activity. American Economic Review 105(11), 3352–3384.CrossRefGoogle Scholar
Judd, K. (1998) Numerical Methods in Economics, 1st edition, Volume 1. Cambridge, MA: The MIT Press.Google Scholar
Justiniano, A. and Primiceri, G. E. (2008) The time-varying volatility of macroeconomic fluctuations. American Economic Review 98(3), 604–641.CrossRefGoogle Scholar
Kung, H. (2015) Macroeconomic linkages between monetary policy and the term structure of interest rates. Journal of Financial Economics 115(1), 42–57.CrossRefGoogle Scholar
Levintal, O. (2017) Fifth-order perturbation solution to DSGE models. Journal of Economic Dynamics and Control 80(C), 1–16.CrossRefGoogle Scholar
Schmitt-Grohe, S. and Uribe, M. (2004) Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control 28(4), 755–775.CrossRefGoogle Scholar
Swanson, E. T., Anderson, G. S. and Levin, A. T. (2006) Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models. Federal Reserve Bank of San Francisco, Working Paper Series 2006-01.Google Scholar