I was looking over some lecture videos on YouTube the other day and came across this good one on effective field theory in physics. It's a graduate level course, but the introductory lecture shouldn't be too difficult to follow even if you haven't taken a lot of physics ‒ most of the theories are just mentioned by name. Be warned: it is a genuine physics lecture so it's just a professor with a chalkboard. I thought it might give some insight into my frequent references to effective theory (e.g. here) in how I think about economics. Here's a translation/dictionary for some of the terms Iain Stewart uses from physics to one way you could think about them in economics:
high energy theory → "fundamental theory", agents/microeconomics
low energy theory → "effective theory", aggregates/macroeconomics
quantum field theory → framework (e.g. DSGE)
Iain Stewart begins with "the big picture" at 6:49. At 40:00 he goes into the two ways effective theories can be used: "top-down" versus "bottom-up". Top-down for economics would be starting with e.g. individual agents and performing some sort of expansion (i.e. deriving macroeconomic theory from microeconomics). One could say this is a possible microfoundations approach ‒ at least assuming you know what the fundamental theory of human behavior is. However, in economics (macro or micro) we are probably looking at the "bottom up" approach (at 49:00) where the "true economic theory" is unknown, so I'd recommend skipping to there.
One thing Stewart does mention is that effective theory is the modern way physicists look at their field. He points out that "the Standard model is an effective field theory that has an infinite number of operators" which is to say that what in the 1960s might have been thought of as part of a fundamental theory of physics is really just an effective theory for something we don't yet understand (e.g. string theory).
Now there are some definite issues one must deal with in order to try and apply the effective theory approach to economics. For one, we do not have any well-established symmetries in economics. As noted in the lecture, symmetries are extremely important to the effective theory approach. I've proposed that there is a scale invariance in economics (which is at the heart of the information equilibrium approach) that can be used as a symmetry. This is far from a settled question, though.
But even if you don't understand the symmetries, the scales (and "power counting" in the lecture, i.e. determining what is important) can be used to try and get a handle on the system. For example, I use an "effective theory" approach in this post to understand the volume problem in finance.
Anyway, I hope this lecture provides some insight into how I think about economics. You don't need to look at the later lectures as they get more into the details relevant to particle physics, but the introduction shows a little bit of the modern view of mathematical theories in physics.