Just got to Paul Krugman’s criticism of Economics in the Sunday New York Times magazine. Members of the profession are excoriated for being beguiled beyond the bounds of decency by mathematics. Groan! Why do mid-life crisis always lead to proclamations that theory is dead? The militantly middle of the road columnist David Brooks has also joined in while promoting the behavioral cause. I suppose being middle of the road is hard since one has to avoid oncoming traffic in both directions.
These and other criticisms brought to mind Capra’s series of WWII films, `Why We Fight.’ They were conceived to convince an isolationist nation about the need to fight the Nazis. No, I’m not comparing the atheoretical unwashed to the Nazi’s. But it did inspire a desire to take up my puny cudgels in defence of mathematical modeling. Herewith, 3 of the usual objections to quantitative models and responses.
Objection #1: Not everything can be reduced to numbers.
True. But a great deal of importance can.
Objection #2: Workable Quantitative models cannot capture the complexities of real life.
So what? The question is not whether a particular quantitative model accurately represents reality but whether there is an alternative model that is more accurate. How do we know that a decision arrived at by what we are pleased to call instinct, intuition or experience has really acknowledged all the complexities of reality? Indeed, one of the beauties of quantitative models is their explicitness. Like Cromwell’s portrait they appear warts and all.
Simple quantitative models frequently provide profound qualitative insights into the process being modeled. Thus, one may wish to build a model not so much to decide what to do, but to test and refine ones intuition about what is going on.
Objection #3: Quantitative models ignore the context.
Yes. However, there is no law that obliges one to follow the recommendations of a quantitative model that is not appropriate to the context. Second, ignoring the context can be a good thing because the context of the decision is irrelevant. A quantitative model often captures the essence of a decision, say, the choice between a gamble and a sure thing. It does not matter whether the context is the stock market, a medical diagnosis or wildcatting. This allows for the transfer of insight from one setting to another.