If you're a journalist and simply phone a few institutional investors who make up the bulk of this kind of trading and with who you have a trusting relationship

If you're a journalist and simply phone a few institutional investors who make up the bulk of this kind of trading and with who you have a trusting relationship, they'll tell you. If they all mostly agree, that's your answer. And it's almost always what you assumed anyways from the news, because this stuff isn't rocket science. So for all practical purposes, yes actually you usually do know, whenever a stock movement is large enough that it's clearly outside the normal noise of day trading. I mean, can you prove the reason with 100% mathematical certainty? No. But can you be 99% sure? Of course.