  The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.
