Panel KPSS Test (Hadri Panel Stationarity Test)
Also known as: KPSS panel stationarity test, panel stationarity test, Hadri LM test, panel KPSS
The Panel KPSS test, introduced by Hadri (2000), tests the null hypothesis that all series in a panel are stationary against the alternative that some or all contain a unit root. It extends the univariate KPSS framework to panel data by aggregating individual LM statistics, providing higher power than unit-root tests when most series are in fact stationary.
Key highlights
- Null hypothesis is stationarity, providing a confirmatory check complementary to ADF-type panel unit-root tests.
- Straightforward standardised normal limiting distribution facilitates inference without simulation-based critical values.
- Accommodates both level-stationary and trend-stationary alternatives via optional linear trend specification.
- Aggregating individual LM statistics exploits the panel dimension, yielding higher power than applying the univariate KPSS test series by series.
- Well-documented and widely implemented in econometric software (Stata, R, EViews, Python statsmodels).
Intuition
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How it works
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When to use it
Use the Panel KPSS test when you want to confirm stationarity rather than merely failing to reject a unit root, or as a complement to Panel ADF/PP tests to verify conclusions from both sides. It is appropriate for balanced or mildly unbalanced panels with moderate to large T (at least 20-30 periods) and N of any practical size. It is most informative when used alongside panel unit-root tests: if Panel ADF fails to reject non-stationarity and Panel KPSS also rejects stationarity, the evidence of a unit root is strong. Do not rely on this test alone when T is small (below 20), when cross-sectional dependence is strong and uncorrected, or when the panel has heterogeneous break patterns, as the Hadri statistic is known to over-reject in the presence of cross-sectional dependence.
Strengths & limitations
- Null hypothesis is stationarity, providing a confirmatory check complementary to ADF-type panel unit-root tests.
- Straightforward standardised normal limiting distribution facilitates inference without simulation-based critical values.
- Accommodates both level-stationary and trend-stationary alternatives via optional linear trend specification.
- Aggregating individual LM statistics exploits the panel dimension, yielding higher power than applying the univariate KPSS test series by series.
- Well-documented and widely implemented in econometric software (Stata, R, EViews, Python statsmodels).
- Severely over-rejects the null when cross-sectional dependence is present and not corrected; corrections (e.g., Hadri-Kurozumi) are needed.
- Power can be low against near-unit-root alternatives when T is small.
- Assumes homogeneous long-run variances across units in its basic form; heterogeneity may distort size.
- Does not identify which specific cross-section units are non-stationary when the null is rejected.
Common pitfalls
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Applications
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Frequently asked
How does Panel KPSS differ from Panel ADF or Panel PP?
Panel ADF and PP tests take the null hypothesis to be a unit root (non-stationarity) and try to reject it in favour of stationarity. Panel KPSS reverses this: the null is stationarity and the alternative is a unit root. Because the tests have complementary nulls, running both and comparing conclusions gives a more complete picture of the data's integration order.
Why does Hadri's test over-reject when cross-sectional dependence is present?
The original Hadri (2000) derivation assumes cross-sectionally independent errors. When units share common factors or correlated shocks, the LM statistics across units co-move, inflating the standardised statistic and causing spurious rejection of stationarity. Corrections using HAC long-run variance estimators that account for cross-unit dependence (Hadri-Kurozumi 2012) alleviate this problem.
Should I demean or detrend before running the test?
The choice depends on whether you expect a deterministic linear trend. If the series exhibits a clear upward or downward drift over time, use the trend-stationary specification. If the series fluctuates around a fixed mean, the level-stationary specification is appropriate. Mis-specifying the deterministic component changes the limiting distribution and can distort test size.
What do I do if Panel ADF fails to reject a unit root but Panel KPSS also rejects stationarity?
This combination is the strongest evidence of non-stationarity: both the unit-root-null test (ADF) and the stationarity-null test (KPSS) point to the same conclusion. Proceed by differencing the series to achieve stationarity, or investigate panel cointegration if theory suggests a long-run equilibrium relationship among the variables.
What if Panel ADF rejects the unit root but Panel KPSS also rejects stationarity?
Contradictory outcomes (both nulls rejected) often signal that the series is neither purely I(0) nor purely I(1), or that some cross-section units differ in their order of integration. Investigate heterogeneity across units, check for structural breaks, or consider that the panel may contain a mix of stationary and non-stationary units.
Sources
- 1.Hadri, K. (2000). Testing for stationarity in heterogeneous panel data. Econometrics Journal, 3(2), 148-161.
- 2.Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178.
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ScholarGate. (2026, June 3). Panel KPSS test. ScholarGate. https://scholargate.app/econometrics/panel-kpss-test