Non-Math Classes Shouldn't Give Homework

One of the classroom issues I've always wrestled with is homework. For one, I find it very difficult to prevent cheating when students are not in my classroom. Also, at least half of my regular students do not do homework. Ever. That's certainly not a reason to abandon homework, but it is a major drain on student grades (and a hassle for teachers). Lastly, most students have huge time commitments outside of school like sports, work, and family. So, should I give homework? Here's a study:

Following an identification strategy that allows us to largely eliminate unobserved student and teacher traits, we examine the effect of homework on math, science, English and history test scores for eighth grade students in the United States. Noting that failure to control for these effects yields selection biases on the estimated effect of homework, we find that math homework has a large and statistically meaningful effect on math test scores throughout our sample. However, additional homework in science, English and history are shown to have little to no impact on their respective test scores.

This goes along with my current classroom expectations. I give a closing question that requires a large paragraph to answer. Half of the students finish it in class, a fourth of them do it at home, and about a fourth don't do it at all. That is for non-honors/AP classes (I give extensive reading and questions for my AP Microeconomics and AP US classes). It seems like a healthy compromise and since homework only seems to help students learn technical content like math, I'll stick with it for now. Though I'm not sure if economics is more of a math or more social science.