We compare the total flux density variations and the VLBI structural variations in a sample of 27 gamma-ray blazars. We find that all the radio variations are due to shocks; the flux of the underlying jet remains constant. A large fraction of the shocks grow and fade within the innermost 0.1 mas, appearing only as ‘core flares’. Comparisons with the EGRET data show that gamma-ray flares must come from the shocks, not from the jet. At the time of an EGRET flare, the shock is typically already over a parsec downstream from the radio core, beyond the accretion disk and/or the broad line region (BLR) photon fields. Thus, present models for gamma-ray production are inadequate, since they typically model the gamma-ray inverse Compton flux as coming from the jet, with significant disk or BLR external Compton components.