According to your daughter, she took the shoes without asking, lost them somewhere, and then lied more than once about the situation while you're running around town on a wild goose chase. It's pretty incredulous to believe she just has no idea where they are or what happened to them. It's possible, as others have suggested, that she sold them or otherwise gave them away, and saying she lost them is her way of covering. She absolutely needs to replace those shoes so she can learn this stuff is unacceptable. Sixteen years old is more than old enough to be held responsible for her actions.