Assessing cross-sectional correlation in panel data

Consider drawing a sample of ‘n’ experimental units where each unit is observed over ‘T’ time periods. Are the draws independent? A test statistic introduced by Breusch and Pagan (1980) is one measure used to quantify the amount of cross-sectional correlation. It is effective when T is large relative to n and, as shown by Breusch and Pagan, has desirable asymptotic (in T) properties. In this paper, we consider the case often encountered in the analysis of panel data, where n is large relative to T. Here, the Breusch and Pagan statistic does not enjoy the same desirable asymptotic (in n) properties. In fact, we show that the asymptotic distribution depends on the parent population even under the hypothesis of no cross-sectional correlations. Thus, we introduce a distribution-free statistic that does not have this drawback. Asymptotic properties of the new statistic are established, when the data are drawn from identical distributions and when the statistic is evaluated using residuals from a complex model. Both the Breusch and Pagan statistic and the new statistic are shown to be members of a more general family. By considering this generalization, finite-sample properties of members of the family are easily established. Further, it turns out that a statistic introduced by Friedman (1937) is another special case of this family.