This point is actually addressed in the introduction of the study.

> These checks notwithstanding, an obvious concern with our estimates is the endogeneity of the decision to appoint a business manager—perhaps firms turn to business managers when they need to cut labor costs. To bolster the argument that our results capture causal effects of business managers on wages and the labor share, we use two strategies. First, we obtain very similar estimates when we focus on manager retirements and deaths, which are arguably less endogenous than other switches from non-business to business managers. Second, we develop an instrumental variable (IV) strategy (...)