We have studied the electrocaloric response of the archetypal antiferroelectric PbZrO3 as a function of voltage and temperature in the vicinity of its antiferroelectric-paraelectric phase transition. Large electrocaloric effects of opposite signs, ranging from an electrocooling of -3.5 K to an electroheating of +5.5K, were directly measured with an infrared camera. We show by calorimetric and electromechanical measurements that the large negative electrocaloric effect comes from an endothermic antiferroelectric-ferroelectric switching, in contrast to dipole destabilization of the antiparallel lattice, previously proposed as an explanation for the negative electrocaloric effect of antiferroelectrics.