We consider current-induced domain wall motion and, the reciprocal process, moving domain wall-induced current. The associated Onsager coefficients are expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the effective Gilbert damping coefficient alphaw and the effective out-of-plane spin-transfer torque parameter betaw are dominated by spin-orbit interaction in combination with scattering off the domain wall, and not scattering off extrinsic impurities. Numerical calculations give alphaw approximately 0.01 and betaw approximately 1 in dirty (Ga,Mn)As. The extraordinarily large betaw parameter allows experimental detection of current or voltage induced by domain wall motion in (Ga,Mn)As.