Panel Engle-Granger Cointegration Test
Also known as: panel cointegration test, panel EG cointegration, Pedroni cointegration test, residual-based panel cointegration
The Panel Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure to panel data, allowing researchers to detect long-run equilibrium relationships among integrated variables across multiple cross-sectional units simultaneously. Pedroni (1999) developed panel statistics that pool information across units while allowing heterogeneous short-run dynamics and individual-specific intercepts and trends.
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When to use it
Use the Panel Engle-Granger test when you have a balanced or moderately unbalanced panel of at least 10-15 cross-sectional units and a sufficiently long time dimension (T > 20) for the asymptotic approximations to be reliable, and when all variables of interest are confirmed I(1). It is well-suited when you suspect the long-run slope may differ across units (heterogeneous cointegration). Do not use it when variables are I(0) or I(2), when T is very short (T < 10), or when cross-sectional dependence across units is strong — in that case prefer second-generation tests such as Westerlund's panel cointegration tests that explicitly account for cross-sectional correlation.
Strengths & limitations
- Extends the simple, intuitive two-step Engle-Granger framework to panels, increasing statistical power by pooling cross-sectional information.
- Allows heterogeneous long-run slope coefficients across units, making it suitable for macro panels where country-specific relationships differ.
- Provides seven complementary test statistics, enabling triangulation of evidence and more nuanced conclusions.
- Well-established critical values and asymptotic theory developed by Pedroni (1999, 2004) make implementation straightforward.
- Group-mean statistics (group rho, group PP, group ADF) are consistent under heterogeneous alternatives and often recommended as the primary statistics.
- Directly indicates whether to proceed with a panel error-correction model, linking the test to subsequent dynamic analysis.
- Assumes cross-sectional independence; when cross-sectional dependence is present the test is severely size-distorted and over-rejects the null.
- Requires both a sufficiently large N and T; small T or small N undermines the asymptotic normality of the panel statistics.
- The first step OLS regression does not yield super-consistent estimates of the cointegrating vector in small T panels, potentially inflating residual non-stationarity.
- Cannot identify the number of cointegrating vectors when more than two variables are involved; for that purpose the panel Johansen approach is more appropriate.
- Power can be limited when the cointegrating relationship is heterogeneous across units and T is moderate.
Frequently asked
How many of Pedroni's seven statistics should I report?
Report all seven but give particular attention to the three group-mean statistics (group rho, group PP, group ADF), which are consistent under the alternative of heterogeneous cointegrating vectors. If a majority of statistics reject the null, evidence for cointegration is generally considered strong.
What is the difference between panel Engle-Granger and panel Johansen cointegration?
Both test for long-run relationships among I(1) variables, but panel Johansen (Larsson et al., 2001) is based on the full-information maximum likelihood approach and can identify the rank (number) of cointegrating vectors when three or more variables are modelled jointly. Panel Engle-Granger is residual-based and is limited to testing whether at least one cointegrating relationship exists.
Can I apply this test when my panel has cross-sectional dependence?
No — standard Pedroni tests assume cross-sectional independence. When units share common factors (e.g., global shocks), use second-generation tests such as Westerlund's (2007) error-correction-based panel cointegration tests, which are robust to cross-sectional dependence.
What do I do after finding panel cointegration?
Estimate a Panel Vector Error Correction Model (Panel VECM) to quantify the speed of adjustment toward the long-run equilibrium and to test for short-run dynamics. You can also use Fully Modified OLS (FMOLS) or Dynamic OLS (DOLS) to obtain efficient long-run coefficient estimates in the presence of endogenous regressors.
What if my panel is unbalanced?
Pedroni's asymptotic results extend to mildly unbalanced panels, but severely unbalanced panels can distort the statistics. In practice, keep the degree of imbalance modest and consider bootstrap critical values if the imbalance is severe.
Sources
- Pedroni, P. (1999). Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics, 61(S1), 653-670. DOI: 10.1111/1468-0084.0610s1653 ↗
- Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251-276. DOI: 10.2307/1913236 ↗
How to cite this page
ScholarGate. (2026, June 3). Panel Engle-Granger Cointegration Test. ScholarGate. https://scholargate.app/en/econometrics/panel-engle-granger-cointegration
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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