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On (bootstrapped) cointegration tests in partial systems

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  • Sven Schreiber

Abstract

As applied cointegration analysis faces the challenge that (a) potentially relevant variables are unobservable and (b) it is uncertain which covariates are relevant, partial systems are often used and potential (stationary) covariates are ignored. Recently it has been argued that a nominally significant cointegration outcome using the bootstrapped rank test (Cavaliere, Rahbek, and Taylor, 2012) in a bivariate setting might be due to test size distortions when a larger data-generating process (DGP) with covariates is assumed. This study reviews the issue systematically and generally finds noticeable but only mild size distortions, even when the specified DGP includes a large borderline stationary root. The previously found drastic test size problems in an application of a long-run Phillips curve (inflation and unemployment in the euro area) appear to hinge on the particular construction of a time series for the output gap as a covariate. We conclude that the problems of the bootstrapped rank test are not severe and that it is still to be recommended for applied research.

Suggested Citation

  • Sven Schreiber, 2019. "On (bootstrapped) cointegration tests in partial systems," IMK Working Paper 199-2019, IMK at the Hans Boeckler Foundation, Macroeconomic Policy Institute.
    • Handle: RePEc:imk:wpaper:199-2019
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    References listed on IDEAS

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    1. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2014. "Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 606-650, August.
    2. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    3. Swensen, Anders Rygh, 2011. "A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables," Journal of Econometrics, Elsevier, vol. 165(2), pages 152-162.
    4. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-399, October.
    5. Benati, Luca, 2015. "The long-run Phillips curve: A structural VAR investigation," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 15-28.
    6. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575.
    7. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
    8. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2012. "Bootstrap Determination of the Co‐Integration Rank in Vector Autoregressive Models," Econometrica, Econometric Society, vol. 80(4), pages 1721-1740, July.
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    More about this item

    Keywords

    bootstrap; cointegration rank test; empirical size;
    All these keywords.

    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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