What makes a piece of mathematical economics not only mathematics but also economics is, I believe, this: When we set up a system of theoretical relationships and use economic names for the otherwise purely theoretical variables involved, we have in mind some actual experiment, or some design of an experiment, which we could at least imagine arranging, in order to measure those quantities in real economic life that we think might obey the laws imposed on their theoretical namesakes.
Trygve Haavelmo, "The probability approach in econometrics" in: Supplement to Econometrica. 12 91944), p. 5; Cited in Pearl (2012, 1-2)