Engle-Granger Cointegration Test
Also known as: EG cointegration test, Engle-Granger two-step method, residual-based cointegration test, EG test
The Engle-Granger two-step method tests whether two or more non-stationary I(1) time series share a common stochastic trend — that is, whether a linear combination of them is stationary. If cointegration is confirmed, an error-correction model (ECM) can be estimated to capture both short-run dynamics and long-run equilibrium adjustment.
Key highlights
- Simple two-step procedure that is easy to implement and interpret.
- Produces the cointegrating vector directly as the OLS slope from the first-step regression.
- Immediately yields the error-correction term for ECM estimation if cointegration is found.
- Widely cited and computationally inexpensive, making it a practical first-pass test for bilateral long-run relationships.
- Applicable in both small and large samples, though power improves with longer time spans.
Intuition
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How it works
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When to use it
Use the Engle-Granger test when you have two (or a small number of) I(1) time series and wish to determine whether they share a long-run equilibrium. It suits bilateral relationships — one dependent and one independent variable — examined in a single-equation framework. Do not use it when: (a) the series may be I(0) or I(2), since the test requires matching integration orders; (b) you suspect more than one cointegrating relationship among three or more variables — use the Johansen trace or maximum-eigenvalue test instead; (c) the sample is very short (fewer than ~50 observations), as the test has low power; or (d) the relationship is nonlinear, in which case nonlinear or threshold cointegration methods are more appropriate.
Strengths & limitations
- Simple two-step procedure that is easy to implement and interpret.
- Produces the cointegrating vector directly as the OLS slope from the first-step regression.
- Immediately yields the error-correction term for ECM estimation if cointegration is found.
- Widely cited and computationally inexpensive, making it a practical first-pass test for bilateral long-run relationships.
- Applicable in both small and large samples, though power improves with longer time spans.
- Restricted to testing a single cointegrating vector; cannot detect multiple cointegrating relationships among three or more I(1) variables.
- Results are sensitive to the choice of dependent variable: regressing y on x can yield different conclusions than regressing x on y.
- Requires pre-testing for the order of integration, and any misclassification (e.g., treating an I(0) variable as I(1)) invalidates inference.
- Non-standard critical values must be used for the residual-based ADF step; using standard Dickey-Fuller tables leads to over-rejection of the null.
- Low power in small samples and when the speed of adjustment to equilibrium is slow.
Common pitfalls
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Applications
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Frequently asked
What critical values should I use for the residual ADF test?
Use MacKinnon (1991, 2010) critical values, not the standard Dickey-Fuller tables. These non-standard values account for the fact that the residuals are estimated, not directly observed, and depend on the number of I(1) variables in the cointegrating regression.
How does the Engle-Granger test differ from the Johansen test?
The Engle-Granger test is a single-equation, residual-based procedure suited for two variables and a single cointegrating vector. The Johansen test uses a full-system VAR framework and can detect multiple cointegrating relationships among several variables simultaneously. For three or more I(1) series, the Johansen approach is generally preferred.
What does the error-correction term tell me?
The error-correction term is the lagged residual from the first-step cointegrating regression. Its coefficient in the ECM represents the speed of adjustment: how quickly the dependent variable corrects deviations from the long-run equilibrium each period. A coefficient of −0.3, for example, means 30% of last period's disequilibrium is corrected within one period.
Does the order of variables matter in the cointegrating regression?
Yes — which variable is placed on the left-hand side can affect the estimated residuals and, therefore, the test outcome. It is good practice to run the test in both directions and check whether conclusions are robust to the choice of dependent variable.
Can I apply the Engle-Granger test to panel data?
Residual-based cointegration tests have been extended to panel settings (e.g., Pedroni 1999, Kao 1999), which provide more power by exploiting the cross-sectional dimension. These panel cointegration tests are distinct from the bivariate Engle-Granger procedure and should be used instead when you have a panel of country or firm observations.
Sources
- 1.Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.
- 2.Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.ISBN 978-0691042893
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ScholarGate. (2026, June 3). Engle-Granger Cointegration Test. ScholarGate. https://scholargate.app/econometrics/engle-granger-cointegration-test