Frees Cross-Sectional Dependence Test for Panel Data
Also known as: Frees CD Test, Frees Q-statistic Test, Cross-Sectional Dependence Test (Frees), Frees Bağımlılık Testi
The Frees test, introduced by Edward Frees in 1995, is a non-parametric diagnostic procedure for detecting cross-sectional dependence in panel data. It is designed for settings where N (number of units) is large and T (time periods) is moderate, making it a standard pre-estimation check before applying panel regression methods that assume cross-sectional independence. Applied economists and social scientists routinely use it to verify whether units in the panel share common shocks or spatial linkages.
Key highlights
- Non-parametric: based on Spearman ranks, so it does not require normally distributed residuals.
- Directly targets all forms of cross-sectional dependence, not just pairwise linear correlation.
- Provides tabulated critical values derived from first principles, avoiding reliance on asymptotic normality that may fail in small samples.
- Complements Pesaran's CD test and Breusch-Pagan LM test, offering a fuller diagnostic picture.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Apply the Frees test before estimating any panel model when you suspect that units share common shocks, spatial spillovers, or network linkages. It is most appropriate when N > 2 and T is moderate (the asymptotic tables require at least T = 3). The test is distribution-free and does not assume normally distributed residuals, making it suitable for macro panels with fat-tailed errors. If cross-sectional dependence is confirmed, standard OLS, fixed-effects, or random-effects estimators will produce inefficient or inconsistent inference; Driscoll-Kraay or FGLS corrections become necessary. For short panels where T is very small, Pesaran's CD test may be preferred.
Strengths & limitations
- Non-parametric: based on Spearman ranks, so it does not require normally distributed residuals.
- Directly targets all forms of cross-sectional dependence, not just pairwise linear correlation.
- Provides tabulated critical values derived from first principles, avoiding reliance on asymptotic normality that may fail in small samples.
- Complements Pesaran's CD test and Breusch-Pagan LM test, offering a fuller diagnostic picture.
- Critical values are tabulated for specific (N, T) combinations; interpolation is needed for cases not in Frees' original tables.
- Power can be lower than Pesaran's CD test in panels where dependence is one-directional or heterogeneous across pairs.
- The test is designed for balanced panels; application to severely unbalanced panels requires modification.
- Like all residual-based diagnostics, test validity depends on correct specification of the regression model.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How does the Frees test differ from the Pesaran CD test?
Both detect cross-sectional dependence in panel residuals, but they use different statistics. The Frees test uses the average of squared Spearman rank correlations and compares it to tabulated Q critical values, while Pesaran's CD test uses the average of plain Pearson correlations and follows a standard normal distribution. Frees' approach is non-parametric and more sensitive to dependence that is symmetric or bidirectional, whereas Pesaran's CD test has higher power when the net average correlation is large and one-directional.
What should I do if the Frees test rejects the null?
Rejection means residuals are cross-sectionally correlated, so standard errors from OLS, FE, or RE estimators are invalid. Common remedies include Driscoll-Kraay standard errors (robust to cross-sectional and serial dependence), feasible GLS with a cross-sectionally correlated error structure, or two-way fixed effects with clustered standard errors. The choice depends on panel dimensions and the source of dependence.
Is the Frees test suitable for unbalanced panels?
The original Frees (1995) framework assumes a balanced panel where all N units are observed over the same T periods. For unbalanced panels, the pairwise Spearman correlations can still be computed over the common time periods shared by each pair, but the tabulated critical values may no longer apply exactly. Researchers typically either balance the panel by restricting the sample or treat non-rejection cautiously in severely unbalanced settings.
Sources
- 1.Frees, E. W. (1995). Assessing cross-sectional correlation in panel data. Journal of Econometrics, 69(2), 393–414.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 2). Frees Test. ScholarGate. https://scholargate.app/econometrics/frees-test