Macroeconomic theory is chock full of mathiness. It’s not just Lucas and Prescott, it’s the whole scientific culture of the field.
I think you find this going all the way back to John Hicks’ famous 1937 paper, “Mr. Keynes and the Classics.”
The “i” in this model could be a short-term interest rate, or it could be a long-term interest rate. It could be a risk-free rate, or it could be a risky rate. It could be a nominal rate, or it could be a real rate.
And, as Smith points out once again, none of the equations in the IS-LM model, or any other mathematical macro model, has any demonstrated empirical validity. The equations are, at best, a way of organizing and expressing the economist’s opinions about macro.
My own opinion, as you know, is that thinking about the economy as if it were a single business (or as a single consumer who also runs a single business) is wrong-footed from the very start. Instead, I believe that it is in the shifting kaleidoscope of patterns of specialization and trade among multitudes of businesses that employment fluctuations take place.
It is fascinating to me that there are critics who will not buy the PSST story until they see it expressed using math. To me, that is as beside the point as arguing that it has no validity unless it can be told in Latin or Swahili or Yiddish.