This paper proposes a modified version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). We exploit the cross section dispersion of individual slopes weighted by their relative precision. Using Monte Carlo experiments, we show that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. For autoregressive (AR) models the test performs well for moderate values of the root of the autoregressive process, but with roots near unity a bias-corrected bootstrapped version performs well even if N is large relative to T. The cross section dispersion tests are used to test the homogeneity of slopes in autoregressive models of individual earnings using the PSID data and show statistically significant evidence of slope heterogeneity in the earnings dynamics.