Hi Guys,
I have a large Macaw and have been researching this quite closely (I'm in the UK). First up, researchers have tracked Parrots in the wild with VHF transmitters over up to 3 years including Hyacinth Macaws, so tracking your/my Parrot IS possible, however a suitable VHF transmitter for your Parrot will cost you around $260/£160, you'll then need a VHF receiver unit which will cost you around $850/£570 to $2,000/£1,400 (depending on its size and sensitivity) and then a suitable directional antennae for the above at a cost of around $250/£160 (looks like an old style TV aerial).
Recommendations are: For larger Parrots the VHF transmitter (which can be around the size of a partially squashed Walnut

) should be mounted at the base of the Tail feathers with a combination of glue and dental floss/cotton (I know - sounds awful and it's permanent) - the unit is attached to the Feathers and this is how they tracked the wild Hyacinths. Alternatively, you can look for the transmitter to be located behind the head using a harness which is clearly much more prone to beak attack! However in any event, both solutions will feature a 10cm aerial which will need to be either attached to a feather 'stem' with glue or bounce loose on the back . . . On the wild Hyacinths, they actually glued the aerial all the way along one of the tail feathers - but all this is pretty extreme!
Now onto GPS, there is a firm that is about to release (Sept 2015) the Worlds first live time GPS tracker which will tell you exactly where your bird is, provided you also have their VHF transmitter etc. etc. but I'm not sure of the cost. The Quail GPS system mentioned in the thread above won't help you track your Parrot practically, as it is designed to record the movement of a Bird and then ONCE YOU HAVE GOT WITHIN RANGE OF THE BIRD download it's movements. Infact, up to now that is ALL GPS tracking devices have done this on birds - you retrieve HISTORICAL data either by catching the bird and downloading it, or in the case of the Quaill system it transmits the data wirelessly from the bird, but will only tell you where the Quail has been. Upshot of the situation is, if you've lost your bird/Quail then the GPS recorder won't help you at all, but if you do find him you'll at least know where he's been hiding!
So, in summary what we have here is:
a) Permanent attached VHF transmitter to the top of your Parrots tail complete with Super Glue and string - aerial taped to a tail feather :-( (worked on wild Hyacinths)
b) Neck and back based rucksack style transmitter with a long and highly chewable aerial presumably boucing around unless we revert to Glue again . .
and finally:
c) A set-up bill of around $2,000 - $3,000 (£1,400 - £1,900)
I do free fly my Parrot now and he's given me a few heart attacks, but mid term I will be investing in a VHF transmitter/receiver/aerial system once I can stump up the money . . not keen on the Glue though
Take care
Mark