At what age are children responsible before God?

This text is from a transcript of a talk by David Gooding, entitled ‘God’s Glorious Plan for Creation’ (2007).

As far as I know, the Bible does not discuss the matter. The Jews, whose book the Old Testament is, to this day regard twelve as the age at which at least a boy assumes responsibility for his own sins, and then they'll have a ceremony called the Bar Mitzvah at that stage. I think we're not called upon to decide. This is for God to decide, surely, for he knows the hearts.