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Analyzing I(2) Systems by Transformed Vector Autoregressions

Author

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  • Hans Christian Kongsted

    (Institute of Economics, University of Copenhagen)

  • Heino Bohn Nielsen

    (Institute of Economics, University of Copenhagen)

Abstract

We characterize the restrictions imposed by the minimal I(2)-to-I(1) transformation that underlies much applied work, e.g. on money demand relationships or open-economy pricing relationships. The relationship between the parameters of the original I(2) vector autoregression, including the coefficients of polynomially cointegrating relationships, and the transformed I(1) model is characterized. We discuss estimation of the transformed model subject to restrictions as well as the more commonly used approach of unrestricted reduced rank regression. Only a minor loss of efficiency is incurred by ignoring the restrictions in the empirical example and a simulation study. A properly transformed vector autoregression thus provides a practical and effective means for inference on the parameters of the I(2) model.

Suggested Citation

  • Hans Christian Kongsted & Heino Bohn Nielsen, 2002. "Analyzing I(2) Systems by Transformed Vector Autoregressions," Discussion Papers 02-20, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:0220
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2002/0220.pdf/
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    References listed on IDEAS

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    1. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
    2. repec:bla:jecsur:v:12:y:1998:i:5:p:573-93 is not listed on IDEAS
    3. G. Coenen & J.-L. Vega, 2001. "The demand for M3 in the euro area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 727-748.
    4. Anindya Banerjee & Lynne Cockerell & Bill Russell, 2001. "An I(2) analysis of inflation and the markup," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 221-240.
    5. William J. Crowder & Dennis L. Hoffman & Robert H. Rasche, 1999. "Identification, Long-Run Relations, and Fundamental Innovations in a Simple Cointegrated System," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 109-121, February.
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    Cited by:

    1. Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, vol. 124(2), pages 205-225, February.
    2. Hans Christian Kongsted, 2002. "Testing the Nominal-to-Real Transformation," Discussion Papers 02-06, University of Copenhagen. Department of Economics.

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    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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