Most quizzes that I have seen used in economics only test the most basic skills of memorization and regurgitation. Therefore, I am generally not a proponent of using conventional quizzes as any substantial part of assessment.
I have heard of promising alternative forms, such as unlimited try quizzes – where the quiz serves to promote mastery, that I would be open to experimenting with.
Another scenario in which I might employ a quiz as if I was teaching a class that was very dependent on student contribution and student work prior to the class. If I was having difficulty ensuring that students did the required readings prior to class and that harmed discussion, I would consider implementing a quiz to motivate students to properly prepare.