Testing slope homogeneity in large panels

This paper proposes a standardized version of Swamyʹs 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, denoted by Δ ˜ , exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors, but with non-normally distributed errors, the test is shown to have a standard normal distribution as ( N , T ) → j ∞ such that N / T 2 → 0 . When the errors are normally distributed, a mean-variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of N and T . The test is also applied to stationary dynamic models, and shown to be valid asymptotically so long as N / T → κ , as ( N , T ) → j ∞ , where 0 ⩽ κ < ∞ . 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 . Similar results are also obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and so long as T ⩾ N .