Don't say begs the question.

For one thing, it's likely that you don't even know what it means. And if you do know, it's likely that your reader does not.

On the high plains of academia, in such lofty locales as philosophy and rhetoric, "begging the question" means leaving it begging for an answer (another form is "beggaring the question," or making a beggar of it). A common way to beg a question is to answer by simply restating the question in different words. [Question: Why does opium make you sleepy? Answer: Because it is a soporific.] Another common way to beg questions is to answer them with circular arguments. To add to the confusion, academics often use the phrase when there is no question, referring, for example, to any circular argument as "begging the question." So simply understanding this confusing phrase is a challenge. 

In recent years, many writers and speakers have tried to sound erudite by using this phrase, but they misuse it to mean "raises the question". ["Discovery of one catalytic RNA begs the question of whether RNA catalysis is widespread."]  The same misuse of the phrase occurs in a fiction story in the latest New Yorker—so it's very fashionable right now, which is never a good sign.

So what should you say?

A good replacement for the misused phrase is raises the question. ["Discovery of one catalytic RNA raises the question of whether RNA catalysis is widespread."]

A good replacement for the properly used phrase is simply to state how and why the purported answer fails to answer the question. There are all kinds of ways to beg a question, so tell your reader what, specifically, the problem is. It's always better to be specific.

You don't want your writing to look as if you are laboring in vain to sound erudite, do you? Then avoid the phrase begs the question. Avoid it altogether. With either the original or the new trendy meaning, it has no place in clear, understandable writing.