"In reporting correlations between unionization and managerial pay, we are not necessarily able to establish whether unions cause differences" Yes, but that's

"In reporting correlations between unionization and managerial pay, we are not necessarily able to establish whether unions cause differences" Yes, but that's a different correlation vs causation issue. The point is, the phenomenon of unions equalizing pay, on the company (micro) level (which has been reproduced in other countries and time periods), can be considered to be a causal explanation for the phenomenon of rising inequality when unions decline, in the society at large.