An academic whose research consists of the stata commands reg, ivregress, robust, and vce().
The term is a reference to the old adage, "Infinite monkey theorem", that a million monkeys randomly typing at a million typewriters would eventually produce Shakespeare. To understand the term, just replace typewriters with "computers with stata" and shakespeare with "insightful economics."
A Regression Monkey hitting keys at random on a computer with Stata for an infinite amount of time will almost surely type any given text, such as the complete works of insightful economics.