Specifically, in the state-of-the-art attention-based NMT model (Bahdanau et al., 2015), generating a target word heavily depends on the relevant parts of the source sentence, and a source word is involved in generation of all target words.
over-translation and under-translation inevitably happen because of ignoring the "coverage" of source words (i.e., number of times a source word is translated to a target word).