Monday, September 10, 2012

My Bid for Immortality: Dorman’s Law

Why do writers get to name laws after themselves, when explorers can’t put their own name to mountains, and field biologists can’t do it for new species?  I don’t know, but I’ll take advantage of the loophole to promulgate my own deep discovery:

The sum of a reliable number and an unreliable number is an unreliable number.

Commentary on the law would emphasize that the extent of joint unreliability depends on how unreliable the second number is and how large relative to the first.

This bit of wisdom, hidden in plain sight for eons, has particular relevance to the practice of economics.  Economists are constantly estimating the size and value of bundles of things, whether direct and indirect employment effects of a program, the benefits and costs of a particular project, or the value of the output of an entire economy.  When they do this they encounter some items that they can put a fairly precise number on and others where even the most sophisticated techniques offer little more than a wild guess.

What my eponymous law says is that, when faced with this situation, an economist should distinguish between reliably and unreliably measured elements in the bundle and, as one output, provide a composite total for just the first set.

Here is an example.  A miracle feed supplement is developed that increases a cow’s production of milk by 25% but leads to a greater incidence of coronary disease in the dairy-consuming population.  As an economist, you are asked to provide an estimate of the total cost of this excess disease.  Some aspects can be measured precisely, like additional costs of hospitalization and medication or the excess work absences that will result from more widespread illness.  Others are unavoidably loosy-goosy, like the subjective disutility of those suffering heart conditions or the disutility induced in their friends and family.

My law doesn’t tell you not to try to put numbers on the ineffable.  What it does say is that, if you do a good job on the first set of outcomes, add them to the second and report the total, you lose the benefit of the precision with which you measured the “hard” items.  The message is, whatever else you do, report the subtotal of reliably measured costs separately.  If you want, you can also throw in the other stuff, total up a composite estimate, and let the reader decide what to do with it.

Being clearer about what we know pretty well and what we don’t is a first step toward winning, and deserving, respect for the way we do economics.


Barkley Rosser said...

I hate to break it to you, Peter, but nobody gets to name laws after themselves. It only works when others name them after you. Sorry, but nice try, :-).

Noah Smith said...

WAIT...are you saying that...if X and Y are two random variables...that Var(X+Y) >= max(Var(X),Var(Y))???


Peter Dorman said...


Say it ain't so! If you're right, I may need some help on this, bro.


Wait a moment.... I didn't say anything about dispersion. "Reliable" is a more qualitative notion. The problem with estimations of the WTP or WTA of a physical impairment are not simply that there's a lot of spread around a point estimate. It's that there is a lot that can go wrong when we try to impose a particular model (like well-behaved preference maps) on psychological processes we don't understand very well. This is much closer to Knightian uncertainty than parametric risk.

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