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Residual based tests for cointegration in dependent panels

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  • Chang, Yoosoon
  • Nguyen, Chi Mai

Abstract

In the paper, we propose residual based tests for cointegration in general panels with cross-sectional dependency, endogeneity and various heterogeneities. The residuals are obtained from the usual least squares estimation of the postulated cointegrating relationships from each individual unit, and the nonlinear IV panel unit root testing procedure is applied to the panels of the fitted residuals using as instruments the nonlinear transformations of the adaptively fitted lagged residuals. The t-ratio, based on the nonlinear IV estimator, is then constructed to test for unit root in the fitted residuals for each cross-section. We show that such nonlinear IV t-ratios are asymptotically normal and cross-sectionally independent under the null hypothesis of no cointegration. The average or the minimum of the IVt-ratios can, therefore, be used to test for the null of a fully non-cointegrated panel against the alternative of a mixed panel, i.e., a panel with only some cointegrated units. We also consider the maximum of the IV t-ratios to test for a mixed panel against a fully cointegrated panel. The critical values of the minimum, maximum as well as the average tests are easily obtained from the standard normal distribution function. Our simulation results indicate that the residual based tests for cointegration perform quite well in finite samples.

Suggested Citation

  • Chang, Yoosoon & Nguyen, Chi Mai, 2012. "Residual based tests for cointegration in dependent panels," Journal of Econometrics, Elsevier, vol. 167(2), pages 504-520.
    • Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:504-520
    DOI: 10.1016/j.jeconom.2011.09.032
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    8. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    9. Francesca Di Iorio & Stefano Fachin, 2022. "Fiscal reaction functions for the advanced economies revisited," Empirical Economics, Springer, vol. 62(6), pages 2865-2891, June.
    10. Omay, Tolga & Emirmahmutoglu, Furkan & Denaux, Zulal S., 2017. "Nonlinear error correction based cointegration test in panel data," Economics Letters, Elsevier, vol. 157(C), pages 1-4.
    11. Francesca Di Iorio & Stefano Fachin, 2014. "Dealing with unobservable common trends in small samples: a panel cointegration approach," DSS Empirical Economics and Econometrics Working Papers Series 2014/5, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.

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    More about this item

    Keywords

    Panel cointegration tests; Testing instruments; Nonstationary panel; Cross-sectional dependency;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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