Telekinesis

Ok, so I just watched this film for the first time. I'm wondering: did Riggan really have telekinesis? Was he moving things with his mind? Or is that just part of his mental fantasy breakdown? I would think that if he could really do half of that stuff he would become an even bigger star than he already is. (If it is just a fantasy then the light falling onto the actor's head was a huge coincidence.)

Why would he hide it? Because he doesn't want to be poked and prodded by a thousand scientists and government agents? So he is not forced into performing tricks constantly?

I dunno. Birdman is one of the oddest films I've seen and I'm just not sure what to make of it or the events in it.