Maki Cointegration Test
Also known as: Structural-break cointegration test
The Maki cointegration test extends cointegration testing to allow for an unknown number of endogenously-determined structural breaks in the cointegrating relationship. Introduced by Maki (2012), it builds on Gregory and Hansen (1996), enabling detection of cointegration even when relationships shift due to policy changes, institutional reforms, or fundamental regime shifts. This is essential for applied time-series work where structural change is common.
Key highlights
- Endogenously determines number and location of breaks
- Accounts for break estimation uncertainty (unlike ad hoc break dates)
- More powerful than traditional tests when breaks are present
- Produces economically interpretable break dates
Intuition
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How it works
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When to use it
Use Maki test when studying long time series (30+ years) with suspected regime shifts—e.g., policy changes, institutional reforms, technological transitions. It is particularly useful in international finance (post-liberalization relationships), labor economics (post-reform wage structures), and environmental economics (post-regulation effects). Requires sufficient data and clear motivation for expected breaks.
Strengths & limitations
- Endogenously determines number and location of breaks
- Accounts for break estimation uncertainty (unlike ad hoc break dates)
- More powerful than traditional tests when breaks are present
- Produces economically interpretable break dates
- Computationally intensive for many potential breaks or long series
- Small samples can reduce power; requires T > 50 or so for reliable inference
- Assumes breaks are few (1-5); many breaks lead to over-parameterization
- Critical values require interpolation or simulation when series length not in tables
Common pitfalls
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Applications
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Frequently asked
How do I choose the maximum number of breaks?
Use parsimony: start with 0 breaks, then test 1, 2, 3, 4 breaks. Stop when additional breaks cease improving fit significantly (use LR tests). Rule of thumb: T/30 is an upper bound.
What trimming parameter should I use?
Standard choice is 15% trimming on each end (0.15), ensuring breaks are not too close to sample endpoints. Sensitivity-check: repeat with 10% and 20% trimming.
How do I distinguish between Maki and Gregory-Hansen tests?
Gregory-Hansen (1996) tests for one unknown break. Maki (2012) allows multiple unknown breaks via sequential testing. Use Maki if unsure of break numbers; use Gregory-Hansen if convinced of exactly one break.
Are breaks economically interpretable?
Yes, typically. Examine break dates against known policy changes, crises, or reforms. Align dates with economic events for validity checks.
Sources
- 1.Maki, D. (2012). Tests for cointegration allowing for an unknown number of breaks. Economic Modelling, 29(5), 2011-2015.
- 2.Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99-126.
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ScholarGate. (2026, June 3). Maki Cointegration Test. ScholarGate. https://scholargate.app/econometrics/maki-cointegration-test