Intelligence and consciousness of self is not self-awareness. They are different things. Parrots are, without a doubt, highly intelligent. They can learn, they figure things out -they reason and reach conclusions-, they understand and use the concept of a proper name (identity) and even intangible things like the concept of zero, they can count and might even have a sense of time but none of those things represents self-awareness.
The thing is that when we say that a parrot understands something, in reality, unless there is a precise action that can only be explained by this, there is nothing to tell us that this has happened but our gut feeling. It's not that I have anything against gut feelings, mind you! Sometimes, there is nothing else that we can go by. I call them my 'off-the-wall' theories but they are the same thing. Birds are not easy to understand because they have no eyebrows and they can't move their beaks or cheeks the way we move them so there is no real facial expression to go by (which is what we use with human beings) - this, added to the fact that they cannot tell us if they really and truly get something or not makes this kind of thing impossible to tell one way or the other with any certainty UNLESS there is precise and exact proof - and we don't have those yet.
Wolf, you started the thread but I don't think you have said whether you believe they are or not...