The reason given in the movie Looper for sending targets to the past is that it is difficult to dispose bodies.
Thirty years into the future in 2074, time travel is invented, but is immediately outlawed. However, because by that point tracking technology has rendered it nearly impossible to dispose of bodies secretly, crime bosses turn to time travel to send their targets to the past to be killed using "loopers": hired guns paid in silver to kill whoever is sent to them.
When trying to capture old Joe, they kill his wife. So how did they dispose the body of his wife? Or is it difficult to dispose bodies only in US and not in China? And they came for old Joe only because the Rainmaker wanted to close the loops?
Could someone explain? What am I missing?