Even with a complex hierarchy, a rig is useless without positioning the proper pivot points. This will allow the puppet's pieces to rotate correctly. The arm needs to rotate from the shoulder and stay attached to the torso, so its pivot point needs to be positioned accordingly. A good way to achieve this is to position the pivot point exactly in the center of the articulation.
The initial position of the pivot point is always at the center of the scene. Sometimes there will not be an obvious place of rotation to place the pivot point, but it's a good idea to reposition the pivot to the best transformation point. For instance, the master peg, which generally controls the entire rig, is often best positioned between the character's feet.