Cross-sectional dependence means that the residuals (errors) from different cross-sectional units (e.g., countries, firms) are correlated. This can bias standard errors and inference in panel data models.

The Breusch-Pagan LM test is suitable for small N and large T and sums squared pairwise residual correlations, the Pesaran Scaled LM test suits moderate N and T with a scaled version of the LM test, while the Pesaran CD test is ideal for large N and T and relies on average pairwise residual correlations.

The Pesaran CD and Scaled LM tests are not the same—while the CD test is based on average pairwise residual correlations and suits large N and T, the Scaled LM test modifies the Breusch-Pagan LM for moderate N and T using a standardized LM statistic, though both handle fixed effects well and are asymptotically normally distributed.

Stata's xtcsd, pesaran command implements the Pesaran (2004) CD test, which is based on the average of pairwise correlation coefficients of residuals across cross-sectional units. It does not compute the Pesaran scaled LM test, which must be calculated manually or through other packages like xttest2 or user-written commands.

With N = 23 and T = 30, your panel data falls into a moderate, nearly balanced range where both the Pesaran CD test and the scaled LM test can be informative. Use the Pesaran CD test (xtcsd, pesaran) for a quick check under the assumption of weak cross-sectional dependence, but if you're concerned about stronger dependence or need more precision, consider also computing the scaled LM test manually or using xtcd for Driscoll and Kraay-style robust standard errors.

Azza Alaa

To detect cross-sectional dependence in panel data, you can use tests like Pesaran’s CD test, Breusch-Pagan LM test, or Friedman’s test; presence of dependence indicates that shocks in one cross-sectional unit affect others, which can bias standard errors if not accounted for.

To determine the presence of cross-sectional dependence in panel data, you can use statistical tests such as Pesaran’s CD test, Breusch-Pagan LM test, or Friedman’s test. These tests check whether the residuals across cross-sectional units (e.g., countries, firms) are correlated, which, if true, violates the assumption of independence and may bias your estimates. You can perform these tests in Stata using commands like xttest2 (for Breusch-Pagan) or xtcd (for Pesaran CD).

Detect using Pesaran CD, LM, or Bias-Corrected LM tests. Crucial to adjust standard errors in presence of dependence.