I don't see a very high frequency of people answering their own questions, despite the FAQ mentioning it as a welcome practice. However, is it effective?
Does answering your own question discourage other answers or help get more a answers?
Regarding how effective is answering your own question, you can see the other way around:
Nobody was able to answer your question or those who did not answer it perfectly (something was missing). You decid to search on your own and you find the appropriate answer and you want to share it with us.
Again your answer might not be complete but it will be a better starting point than having only a question (It might be worth updating the question instead if you feel your answer is not perfect).
Does answering your own question discourage other answers or help get answers?
In a way yes, It will decrease the pool of people able/willing to answer. It is like refining your question or being very precise, the target people get thinner. I do not think this is a bad thing.
It depends. Answering your own question very well, and covering all bases in a clearly expert manner could well discourage other answers, since others may think that they don't really have anything to add.
But is that really a bad thing? Personally I'd have that reaction to any expert answer covering all bases, it's just that self answered questions tend to be more thorough (because presumably it'd be silly to start a question and answer it if you've only got a half-baked answer.)