[beefman]

Productivity is measured by dividing GDP by total hours worked, with the assumptions that GDP is caused by work and that the relationship is linear. The latter assumption is false and the former is highly suspect.

You raise a good question about localization of GDP. The global economy is a highly-connected network. It's often unclear how to draw valid conclusions from national accounts, let alone the local accounting attempted here.

That said, I think there most likely is a trend of the kind imagined by the authors and that it's showing up in these figures. Showing up is the most it's doing though.