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Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions

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  • Martin Wagner

    (University of Klagenfurt
    Bank of Slovenia
    Institute for Advanced Studies)

Abstract

Cointegrating polynomial regressions (CPRs), i.e., regressions that include deterministic terms, integrated processes and powers of integrated processes as explanatory variables and stationary errors, have become prominent in several fields of applications, e.g., in the analysis of environmental Kuznets curves. A key issue, as always in cointegration analysis, is testing for the presence or absence of a cointegrating relationship. This paper discusses two complementary tests: one with the null hypothesis of cointegration and one with the null hypothesis of the absence of cointegration. It is shown that (inter alia) for the empirically most relevant case, in which only one of the integrated regressors occurs as regressor also with higher powers, critical values can be simulated and are provided for a variety of specifications. Finally, the usage of the tests is illustrated for the environmental Kuznets curve for carbon and sulfur dioxide emissions. The illustration also investigates the sensitivity of the test decisions with respect to kernel and bandwidth choices, sample size and data vintage.

Suggested Citation

  • Martin Wagner, 2023. "Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions," Empirical Economics, Springer, vol. 65(1), pages 1-31, July.
    • Handle: RePEc:spr:empeco:v:65:y:2023:i:1:d:10.1007_s00181-022-02332-3
    DOI: 10.1007/s00181-022-02332-3
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    References listed on IDEAS

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    2. Wagner, Martin, 2008. "The carbon Kuznets curve: A cloudy picture emitted by bad econometrics?," Resource and Energy Economics, Elsevier, vol. 30(3), pages 388-408, August.
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    More about this item

    Keywords

    Cointegrating polynomial regression; Cointegration; Unit root; Testing; Environmental Kuznets curve; Material Kuznets curve; Exchange rate target-zone;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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