Q: Is a minor or someone who is mentally incompetent liable for damage they do?

A: A child under bar mitzvah or a mentally incompetent person who damaged is legally exempt, since he has no legal culpability. Even when the child matures, he is not legally accountable for the damages of his childhood (C.M. 424:8).

Beis din or his parents should discipline the child for having damaged, though, so that he should not continue damaging (C.M. 349:3,5).

Nonetheless, Rav Ashi was made to pay for a loan document that he destroyed when he was a child (B.K. 98b; Rashi). Many authorities derive from this that the child has a moral responsibility to pay when he matures. Nowadays, the parents usually pay instead, to relieve him of that responsibility (see Pischei Choshen, Nezikin 10:[115]).

Rema (O.C. 343:1) also writes that if a child sinned, it is proper that he do something for atonement when he matures. Thus, if he damaged, it is proper to pay (Mishnah Berurah 343:9). Some infer that it is not necessary to pay the full amount, but Sefer Chassidim advocates paying fully to achieve complete atonement (Pischei Teshuvah, C.M. 349:2; Yechaveh Daas 8:6).