I have found that throughout my career, I routinely have a great deal of responsibility, with much less direct authority. As people often say, "I know how to read an org chart." and I'm typically not above most of the people who I need to contribute to my projects. I have do have a lot of indirect authority, provided that I am providing wise council to senior stakeholders. I have built a reputation as someone to ignore at your own peril if you choose to ignore my warnings about the likely outcomes on the current path, and how I can change that path to avoid risks and capitalize on opportunities. Having the ear of people with authority means that when I ask, they will either step in to provide direct help, or explain to me why there is a strategic plan happening in the background where I should back off.
My authority comes from influence. If I tell an executive sponsor that Team X said I have no authority to tell them what to do, the response is often an emphatic (and humerus) "* **I*** have the authority to tell them and I'm delegating that authority to YOU. If they have a problem with that, tell them I will have a closed door meeting to explain it to their bosses personally." That gets the point across quickly.
I rarely have to do that. I follow a carrot and stick approach for motivation. At the worker level, the carrot is that I'll make them look good by building a plan where they get the credit for strong performance. The stick is that I might have that other conversation. At the executive level, the carrot is still that I'll make them look good, and the stick is a well thought out explanation of the business implications of failure. Using that approach, what I lack in direct authority, I more than make up for in influence.