Panel Cointegration Tests (Pedroni, Kao, Westerlund)
Also known as: Pedroni cointegration test, Kao cointegration test, Westerlund cointegration test, panel long-run equilibrium tests, Panel Eşbütünleşme Testleri (Pedroni, Kao, Westerlund)
Panel cointegration tests check whether a set of integrated variables share a stable long-run equilibrium relationship across a panel of cross-sectional units. Pedroni (1999, 2004) provides heterogeneous-panel tests with seven statistics, Kao (1999) gives an ADF-based homogeneous-panel test, and Westerlund (2007) adds error-correction-based tests robust to structural breaks and cross-sectional dependence.
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When to use it
Use panel cointegration tests with panel data where the variables are continuous and individually integrated of order one, I(1), confirmed first by panel unit-root tests such as IPS, LLC or CIPS. A reasonably long panel (at least about 50 observations) is needed. Choose Pedroni when slopes may differ across units, Kao when a common homogeneous slope is plausible, and Westerlund when cross-sectional dependence or structural breaks are a concern. If more than one cointegrating vector is expected, move to a panel VECM instead.
Strengths & limitations
- Pools information across cross-sectional units, gaining power to detect long-run relationships that single time-series tests would miss.
- Offers a family of complementary statistics: Pedroni's seven heterogeneous tests, Kao's homogeneous ADF-based test, and Westerlund's error-correction tests.
- Westerlund's tests can be made robust to cross-sectional dependence through bootstrap critical values and accommodate structural breaks.
- Requires the variables to be I(1); if they are stationary or of mixed integration order the tests are invalid.
- Cross-sectional dependence biases the standard Pedroni and Kao tests unless a robust variant is used.
- Establishing cointegration alone does not estimate the long-run coefficients, and more than one cointegrating vector requires a panel VECM.
Frequently asked
Which test should I choose among Pedroni, Kao, and Westerlund?
Use Pedroni when the long-run slopes may differ across units, Kao when a common homogeneous slope is plausible, and Westerlund when you suspect cross-sectional dependence or structural breaks, since its error-correction tests offer bootstrap-robust critical values.
Do I need to test for unit roots first?
Yes. Panel cointegration is only meaningful when the variables are integrated of order one, I(1). Confirm this beforehand with panel unit-root tests such as IPS, LLC, or CIPS; if the series are stationary or of mixed order the cointegration tests are invalid.
What is cross-sectional dependence and why does it matter?
Cross-sectional dependence means the units in the panel are correlated, for example through common global shocks. It biases the standard Pedroni and Kao tests, so a robust variant such as Westerlund's bootstrap test or a CSD-corrected Pedroni test should be used.
What happens if there is more than one cointegrating relationship?
These tests detect whether a cointegrating relationship exists but assume a single cointegrating vector. When several long-run relationships are expected, a panel vector error-correction model (VECM) is required to estimate them jointly.
Sources
- Pedroni, P. (2004). Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis. Econometric Theory, 20(3), 597–625. DOI: 10.1017/S0266466604203073 ↗
- Westerlund, J. (2007). Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and Statistics, 69(6), 709–748. DOI: 10.1111/j.1468-0084.2007.00477.x ↗
How to cite this page
ScholarGate. (2026, June 1). Panel Cointegration Tests (Pedroni, Kao, Westerlund). ScholarGate. https://scholargate.app/en/econometrics/panel-cointegration
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