The leap from "controlled experiments are not possible" to "one has to deduce from first principles" is huge and unsupported. The results of controlled experiments do not exhaust the available empirical evidence by a long shot. We have a lot of data about the effects of monetary policy from around the world. True, inferring causality from this data is not nearly as straightforward as inferring causality from a randomized controlled trial, but it's still a lot more reliable than deduction from first principles, I would think.
Think about how your argument sounds when applied to cosmological theories about the very early universe. We have a number of different theories that cannot be simultaneously right, and we cannot conduct controlled experiments. Would you endorse deduction from first principles in this instance as well?
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If I replace "economic variables" with "astronomy" what part of this sentence changes in implication? Why is this incoherent for some fields? The level of rigor cannot be the only difference: Physics and astronomy have become more rigorous over time, not by discussing first principles, even when moving from Aristotle to Medieval physics to Newtonian physics, but rather by adopting principles based on the empirical data. The same goes for the switch from Ptolemaic systems to Copernicus and then Kepler. It is the empirical data that matters, the apparent time-series of planetary and stellar motion.
Does arguing over this definition pay any rent?
Re Physics, please correct me as required but in the way I use the phrase "first principles" here, Physics does not have any first principles. Physics is observation, hypothesis, experimentation and repeat. After a certain hypothesis has sufficient amount of experimental proof behind it, it becomes a theory and thus the foundation for further work. And occasionally, we find that there is a variable missing in the theory as the experiments did not test the situations that that variable speaks to. Then we test to tease out the nuances of that aspect of reality. And so on.
Economics has first principles, in the sense I use the phrase. Thus the Q: What is an economy? It leads to those first principles and then deduction covers the rest. But one can of course get the first principles wrong and the deduction is then useless.