"... when it is difficult to measure what managers do, it can be tricky to design incentives to reward them."
Why would it be difficult to measure what managers do? Measure the total output of their team. That's it.
Why would it be difficult to measure what managers do? Measure the total output of their team. That's it.
measure: how does one truly measure anything related to a team or individual? Just as lines of code is a bad measure of a developer, even very quantifiable things like sales numbers don't tell the whole story. A salesperson who hooks clients on promises that can't be kept is not doing a good job, no matter how it might look in one quarter. Goodhart's law exists for a reason.
total: a team that appears to be high performing but depends on the output of a small portion of that team, or that is high performing despite several team members, is not a success. People who carry a team often leave for better compensation or challenge. People who appear to have high output themselves at the expense of others should be removed from the team. People who are ineffective on a particular team should find a new environment where they can achieve more success.
output: Not all teams exist to produce specific output. An IT department might replace 50 broken keyboards across the company in a quarter, but it would be foolish to ask "what can we do to get that number to 75?"
their team: A manager usually exists both to help direct reports do a better job, but also to provide timely and pertinent information to other teams, and many organizations have teams that primarily serve "internal customers". An operations team could be given a goal of "zero new bugs or outages" and freeze all new deployments to achieve it. But the development teams would obviously be upset, and the entire company would likely suffer.