Dumitrescu-Hurlin Panel Granger Causality Test

Standard panel Granger causality tests typically assume homogeneous slope coefficients across all units, meaning the same causal structure is imposed on every cross-section. The DH test estimates separate regressions for each unit and averages the resulting Wald statistics, allowing each unit to have its own causal relationship. This makes it more flexible and better suited for macro-panels where heterogeneity is expected.

The Z-bar statistic relies on the large-T asymptotic distribution of each individual Wald statistic and is valid when both N and T are large. The Z-bar-tilde applies a degrees-of-freedom correction to account for finite-sample bias in the individual Wald distributions. In empirical practice with moderate T, the Z-bar-tilde is preferred because it provides better size control and more reliable p-values.

The DH test in its standard form assumes cross-sectional independence. When common shocks or spatial spillovers are present, the test can suffer from size distortions. Recommended remedies include using cross-sectionally demeaned data before applying the test, bootstrapping critical values under cross-sectional dependence, or employing the Konya (2006) bootstrap panel causality framework, which is designed to handle dependence explicitly.