Structural Break Engle-Granger Cointegration Test
Also known as: Gregory-Hansen cointegration test, cointegration with structural break, EG cointegration with regime shift, residual-based cointegration with break
The structural break Engle-Granger cointegration test, most commonly implemented via the Gregory-Hansen (1996) procedure, extends the classical Engle-Granger two-step test to allow for a single unknown structural break in the long-run cointegrating relationship. It tests whether two or more integrated series share a common stochastic trend even when that relationship may have shifted at some point in the sample.
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When to use it
Use this test when you suspect a long-run equilibrium relationship between I(1) variables but also believe a structural change (policy reform, financial crisis, institutional shift) may have altered the relationship at an unknown date. It is preferable to the standard Engle-Granger test whenever there is any prior reason to suspect parameter instability. Do not use it when: the series are not all I(1); you expect more than one structural break (consider Hatemi-J two-break test instead); the sample is short (fewer than roughly 50 observations), as break-date estimation is unreliable; or when theory strongly supports break-free stability.
Strengths & limitations
- Allows cointegration to be detected even when the long-run relationship has shifted, avoiding spurious rejection of a genuine cointegrating link.
- Does not require the analyst to know or specify the break date — it is estimated endogenously from the data.
- Three model variants (level shift, level shift with trend, regime shift) provide flexibility to match different types of structural change.
- Well-developed non-standard critical values (Gregory & Hansen, 1996) ensure correct size.
- Widely implemented in econometric software (R: strucchange/gets, Stata: egranger with break option, EViews).
- Identifies the most likely break date as a by-product, aiding economic interpretation.
- Restricted to a single structural break; if the true DGP has two or more breaks, power falls and results can be misleading.
- Retains the two-step OLS framework of Engle-Granger, which has lower power than Johansen's system-based approach in multivariate settings.
- Break-date estimation is imprecise in short samples; the trimming convention (discarding the outer 15% of the sample) further reduces usable observations.
- Does not handle asymmetric or nonlinear cointegration; for those cases, nonlinear ARDL or threshold cointegration is more appropriate.
- Inference is on a bivariate (or limited multivariate) system; Johansen-based break extensions are preferred for systems with three or more variables.
Frequently asked
How does this test differ from the standard Engle-Granger test?
The standard Engle-Granger test estimates a single cointegrating regression and tests its residuals for a unit root using standard ADF critical values. The Gregory-Hansen extension estimates the regression separately for every candidate break date, takes the most favourable (most negative) ADF statistic across all those dates, and compares it to larger non-standard critical values that adjust for the implicit data-mining over break dates.
Which model variant should I choose — level shift, trend shift, or regime shift?
Choose based on economic theory. A level shift (C model) allows only the intercept to change — appropriate when the equilibrium level shifts but the slope relationship remains stable. Adding a trend (C/T model) suits series with deterministic trends. The regime shift (C/S model) allows both intercept and slope to change, appropriate when the sensitivity of y to x is itself believed to have changed. Report all three for robustness if theory is ambiguous.
What if both the standard Engle-Granger and the Gregory-Hansen tests fail to reject?
This indicates no evidence of cointegration even allowing for one structural break. Consider whether more than one break may be present (use Hatemi-J two-break test), whether the variables are truly I(1), or whether a nonlinear cointegration framework is more appropriate.
Can this test handle more than two variables?
Yes, in principle — the cointegrating regression can include multiple I(1) regressors. However, for systems with three or more variables the Johansen-based break extensions (e.g., Johansen, Mosconi & Nielsen 2000) are generally preferred because the Engle-Granger two-step approach discards information by ignoring feedback from the regressors.
Is the estimated break date statistically reliable?
It should be treated with caution. The break date is the τ that minimises the ADF statistic, but confidence intervals around it are typically wide, especially in samples under 100 observations. Use the point estimate to guide interpretation but do not treat it as precisely identified.
Sources
- Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99-126. link ↗
- 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). Structural Break Engle-Granger Cointegration Test. ScholarGate. https://scholargate.app/en/econometrics/structural-break-engle-granger-cointegration
Which method?
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