This article considers testing the hypothesis that errors in a panel data model are weakly cross-sectionally dependent, using the exponent of cross-sectional dependence α, introduced recently in Bailey, Kapetanios, and Pesaran (2012). It is shown that the implicit null of the cross-sectional dependence (CD) test depends on the relative expansion rates of N and T. When T = O(N ^ε), for some 0 < ε ≤1, then the implicit null of the CD test is given by 0 ≤ α < (2 − ε)/4, which gives 0 ≤ α <1/4, when N and T tend to infinity at the same rate such that T/N → κ, with κ being a finite positive constant. It is argued that in the case of large N panels, the null of weak dependence is more appropriate than the null of independence which could be quite restrictive for large panels. Using Monte Carlo experiments, it is shown that the CD test has the correct size for values of α in the range [0, 1/4], for all combinations of N and T, and irrespective of whether the panel contains lagged values of the dependent variables, so long as there are no major asymmetries in the error distribution.