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Econometric Issues when Modelling with a Mixture of I(1) and I(0) Variables


  • Lance A Fisher

    () (Macquarie University)

  • Syeon-seung Huh

    () (Yonsei University)

  • Adrian Pagan

    () (University of Sydney)


This paper considers structural models when both I(1) and I(0) variables are present. It is necessary to extend the traditional classification of shocks as permanent and transitory, and we do this by introducing a mixed shock. The extra shocks coming from introducing I(0) variables into a system are then classified as either mixed or transitory. Conditions are derived upon the nature of the SVAR in the event that these extra shocks are transitory. We then analyse what happens when there are mixed shocks, finding that it changes a number of ideas that have become established from the cointegration literature. The ideas are illustrated using a well-known SVAR where there are mixed shocks. This SVAR is re-formulated so that the extra shocks coming from the introduction of I(0) variables do not affect relative prices in the long-run and it is found that this has major implications for whether there is a price puzzle. It is also shown how to handle long-run parametric restrictions when some shocks are identified using sign restrictions.

Suggested Citation

  • Lance A Fisher & Syeon-seung Huh & Adrian Pagan, 2013. "Econometric Issues when Modelling with a Mixture of I(1) and I(0) Variables," NCER Working Paper Series 97, National Centre for Econometric Research.
  • Handle: RePEc:qut:auncer:2013_9

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    References listed on IDEAS

    1. Fabio Canova & Luca Gambetti & Evi Pappa, 2007. "The Structural Dynamics of Output Growth and Inflation: Some International Evidence," Economic Journal, Royal Economic Society, vol. 117(519), pages 167-191, March.
    2. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    3. Fank Smets, 1997. "Measuring Monetary Policy Shocks in France, Germany and Italy: The Role of The Exchange Rate," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 133(III), pages 597-616, September.
    4. Renée Fry & Adrian Pagan, 2011. "Sign Restrictions in Structural Vector Autoregressions: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 938-960, December.
    5. Gert Peersman, 2005. "What caused the early millennium slowdown? Evidence based on vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 185-207.
    6. Pagan, A.R. & Pesaran, M. Hashem, 2008. "Econometric analysis of structural systems with permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3376-3395, October.
    7. Matthew Shapiro & Mark Watson, 1988. "Sources of Business Cycles Fluctuations," NBER Chapters,in: NBER Macroeconomics Annual 1988, Volume 3, pages 111-156 National Bureau of Economic Research, Inc.
    8. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
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    Cited by:

    1. Mardi Dungey & Denise Osborn & Mala Raghavan, 2014. "International Transmissions to Australia: The Roles of the USA and Euro Area," The Economic Record, The Economic Society of Australia, vol. 90(291), pages 421-446, December.

    More about this item


    Mixed models; transitory shocks; mixed shocks; long-run restrictions; sign restrictions; instrumental variables;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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