Pesaran CD Test: Cross-Sectional Dependence Diagnostic for Panel Data
Also known as: CD Test, Cross-Sectional Dependence Test, Pesaran General CD Test, Kesitsel Bağımlılık Testi
The Pesaran CD test is a general diagnostic procedure for detecting cross-sectional dependence in panel data models. Developed by M. Hashem Pesaran (2021), it is applicable to both balanced and unbalanced panels with large N and T, and retains validity under heterogeneous slope coefficients. The test is widely adopted in empirical economics, finance, and political economy as a prerequisite check before selecting appropriate estimators or unit-root tests for panel datasets.
Key highlights
- Valid under both large N and large T asymptotics, making it suitable for macro-panels and micro-panels alike.
- Robust to slope heterogeneity and applicable to fixed-effects, random-effects, and pooled panel specifications.
- Computationally simple: requires only OLS residuals and standard normal critical values.
- Performs well even under non-normal disturbances due to its reliance on pairwise correlations rather than distributional assumptions.
Intuition
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How it works
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When to use it
Apply the Pesaran CD test as a diagnostic step before estimating panel models or performing panel unit-root and cointegration tests when the panel contains a moderately large number of cross-sectional units (N ≥ 10) and sufficient time periods (T ≥ 4). The test is particularly suited when slope heterogeneity is suspected and when the panel may be affected by common factors, global shocks, or spatial spillovers. It is recommended over the Breusch–Pagan LM test when N is large relative to T, since the LM test requires T > N. If cross-sectional dependence is confirmed, researchers should switch to second-generation unit-root tests (e.g., CIPS) and cross-sectionally robust estimators (e.g., CCE, AMG). The test assumes that the time dimension T is at least moderately large and that residuals are stationary.
Strengths & limitations
- Valid under both large N and large T asymptotics, making it suitable for macro-panels and micro-panels alike.
- Robust to slope heterogeneity and applicable to fixed-effects, random-effects, and pooled panel specifications.
- Computationally simple: requires only OLS residuals and standard normal critical values.
- Performs well even under non-normal disturbances due to its reliance on pairwise correlations rather than distributional assumptions.
- Loses power against weak cross-sectional dependence when N is very large but individual pairwise correlations are small.
- Requires residuals from a consistently estimated model; misspecification of the conditional mean can distort the test.
- Assumes stationarity of residuals; applying the test to non-stationary panels may yield misleading results.
- Does not identify the source or structure of dependence—only its presence—so further modeling (e.g., factor structure) is needed.
Common pitfalls
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Applications
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Frequently asked
How does the CD test differ from the Breusch–Pagan LM test?
The Breusch–Pagan LM test statistic is the scaled sum of squared pairwise correlations and diverges as N grows with fixed T, making it unsuitable for large-N panels. The CD test uses the unscaled sum of correlations, which has mean zero under the null even for large N, and follows a standard normal distribution in large N, large T settings. The CD test is therefore preferred whenever N is substantial.
What should I do if the CD test rejects cross-sectional independence?
Rejection indicates that standard first-generation estimators and unit-root tests (LLC, IPS) are invalid. Researchers should switch to second-generation procedures: use CIPS or CADF for unit-root testing, apply CCE (Common Correlated Effects) or AMG (Augmented Mean Group) estimators for slope estimation, and consider factor-augmented or spatial panel models to model the dependence structure explicitly.
Can the CD test be used with unbalanced panels?
Yes. Pesaran (2021) derives the asymptotic theory for unbalanced panels by computing each pairwise correlation over the subset of time periods for which both units have observations. The standard normal limit continues to hold as long as the minimum overlap across pairs is sufficient for correlation estimation, though power may be reduced when the panel is severely unbalanced.
Sources
- 1.Pesaran, M. H. (2021). General diagnostic tests for cross-sectional dependence in panels. Empirical Economics, 60(1), 13–50.
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Cite this page
ScholarGate. (2026, June 2). Pesaran CD Test. ScholarGate. https://scholargate.app/econometrics/pesaran-cd-test