It's hard for me to think about how else to measure manager productivity. Managers don't usually submit code themselves.

Lots of people in a business aren't submitting code, but that's not really my point. Depending on a manager's style they can increase synchronization overhead between team members and different teams to the point that everyone's productivity is reduced while the manager has never been busier or productive on paper.

A manager's productivity IS the team's productivity, and should be measured in results.

A "productive" manager that slows down the team isn't an effective manager at all, no matter how hard he or she is working.

The manager might be able to scapegoat a poor team member or two when poor results become evident, but sooner or later, he or she will have to pay the piper.