No need for me to trot out my dusty economics textbook, as The Economist provides essentially the same definition as the one presented to me in my economics class:
"“The setting up of mathematical models describing economic relationships (such as that the quantity demanded of a good is dependent positively on income and negatively on price), testing the validity of such hypotheses and estimating the parameters in order to obtain a measure of the strengths of the influences of the different independent variables.”
In what way does this definition contradict what I said about econometrics? You either use statistical data to test an economic theory, or you form an economic theory to try and explain statistical data, hence the preponderence of functions found in both econometrics and macroeconomics courses.
Is there ever a situation where a theory based on unrealistic assumptions can be logically cohesive?
Is there ever a situation where a theory based on unrealistic assumptions can be logically cohesive?
No, that’s why a lot of mainstream models tend to gain popularity when they “predict” something, and then become worthless when they fail to predict everything else they should have predicted. The lack of a rigorous logical structure is another shortcoming of mainstream economic theory, and you don’t have to be a praxeologist to recognize this.
I have a family friend who took graduate-level economics courses in college who once told me, “In econometrics, you’ll find that there are as many functions as there are economists”. This statement is almost a truism, especially considering how, like you said, models come and go so quickly in the economics field. This no doubt also contributes to the ridicule economics receives from practitioners of other sciences.