Testing Slope Homogeneity in Large Panels

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). The proposed test exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors and normally distributed errors, the test is shown to have a standard normal distribution as (N, T) →^j ∞. Under non-normal errors and in the case of stationary dynamic models, the condition on the relative expansion rates of N and T for the test to be valid is given by √N /T → 0, as (N, T) →^j ∞. Using Monte Carlo experiments, it is shown 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 proposed test performs well for moderate values of the root of the autoregressive process. But for AR models with roots near unity a bias-corrected bootstrapped version of the test is proposed which performs well even if N is large relative to T. The proposed cross section dispersion tests are applied to testing the homogeneity of slopes in autoregressive models of individual earnings using the PSID data. The results show statistically significant evidence of slope heterogeneity in the earnings dynamics, even when individuals with similar educational backgrounds are considered as sub-sets.