  We describe double Hurwitz numbers as intersection numbers on the moduli
space of curves. Assuming polynomiality of the Double Ramification Cycle (which
is known in genera 0 and 1), our formula explains the polynomiality in chambers
of double Hurwitz numbers, and the wall crossing phenomenon in terms of a
variation of correction terms to the {\psi} classes. We interpret this as
suggestive evidence for polynomiality of the Double Ramification Cycle.
