Invisible Aviary?

While I was passing the time unloading my slingshot at pigeons roosting under the eaves, I began to consider whether it might not be more efficient to simply keep a predatory bird as a pet that could handle the pigeon population for me. Of course, this would introduce problems of keeping the predatory bird from simply flying off, which introduced a whole new line of logic to me: An Invisible Aviary! We already have cheap technology available to create an invisible fence for dogs. Why not an invisible dome for birds? Let your birds wander the confines of your own aviary without having to fork out for the actual construction of a physical one. Figure as a bird attains enough height to cross the boundary, it gets a mild electric shock that momentarily stuns it into falling back below the threshold. At that point, it can regain stabilization and avoid crashing. My mind was consequently filled with visions of immensely populated invisible aviaries sprouting up all over teh country...