Answer
This slows down the Earth's rotation, lengthening the day by a tiny, tiny amount.
Work Step by Step
This situation is similar to the one shown in Figure 8.52, but in reverse. If everyone moved closer to the equator, they would be farther from the Earth’s rotational axis. Moving mass away from the axis of rotation increases the rotational inertia of the system.
No external torques act on the system (Earth + inhabitants), so angular momentum is conserved. The product of rotational inertia and rotational speed stays constant. Since the first went up, the second must go down.
The rotational speed slows down, making the day longer.
