Panel Geary's C Spatial Autocorrelation

Both test global spatial autocorrelation in panels, but they use different formulas. Moran's I measures the cross-product of mean deviations between neighbors; Geary's C measures squared differences between neighboring pairs. Geary's C is more sensitive to local dissimilarities and can distinguish positive from negative autocorrelation more clearly in some datasets. Using both together gives a more complete diagnostic.

C < 1 indicates positive spatial autocorrelation: neighboring units tend to have more similar values than would be expected under spatial randomness. A value of 0.7 pooled across time periods suggests consistent clustering of similar values across the panel. The further C is from 1, the stronger the autocorrelation signal.

Common choices are queen or rook contiguity (binary neighbor indicators), k-nearest neighbors, or inverse-distance weights. Row-standardize the matrix. Run sensitivity checks with at least two different specifications; if conclusions change substantially, report both and discuss the spatial structure of your data.

In principle yes, but implementation is more complex because units present in some periods but not others complicate the aggregation step. Standard software implementations assume a balanced panel. For unbalanced panels, compute per-period Geary's C only for periods and units with complete data, then average carefully.

Rejection is a diagnostic signal, not a final result. It means your panel data violates the independence assumption of standard panel estimators. The appropriate next step is to fit a spatial panel model — such as a Spatial Lag Panel Model or Spatial Error Panel Model — that explicitly accounts for the spatial dependence in the data.