Hemibel Thinking

Don't go away. Stick around for some useful insights about social-science research.

First, what is "hemibel thinking"? Philip M. Morse and George E. Kimball, pioneers in the field of military operations research, wrote in their classic Methods of Operations Research (1951) that the

successful application of operations research usually results in improvements by factors of 3 or 10 or more....In our first study of any operation we are looking for these large factors of possible improvement....They can be discovered if the [variables] are given only one significant figure,…any greater accuracy simply adds unessential detail.

One might term this type of thinking "hemibel thinking." A bel is defined as a unit in a logarithmic scale corresponding to a factor of 10. Consequently a hemibel corresponds to a factor of the square root of 10, or approximately 3.

This is science-speak for the following proposition: Things are rarely clear cut in the "real" world, especially in the realm of human behavior, where there's a lot of uncertainty about which events contribute to particular outcomes, about the relative importance of those events, and about the appropriate numerical values to assign to them. Anyone who aspires to be a social scientist, should therefore be humble about claiming precision for quantitative estimates that are probably very imprecise.

Exhibit A: Prof. Ray Fair's macroecnomic model of the U.S. It consists of 131 equations, each of which has several independent variables. No wonder Fair's model, in its various incarnations, has done such a lousy job of forecasting changes in real GDP.

You might say that Fair's model is an extreme case. There are, after all, many simpler models in the social sciences. Yes, but all models in the social sciences rely on inevitably imprecise estimates of the events arising from human behavior -- even when those events are economic ones. Indeed, many social-science models are incomplete because many crucial events are unknown, unquantifiable, or both. In the case of the minimum wage, about which I have written recently, a professional economist echoes my views.

Hemibel thinking takes on great importance in light of the imprecision inherent in complex social-science models. Consider a model with only 10 variables. Even if the model doesn't omit crucial variables, its results must be taken with large doses of salt. An error of about 25 percent in the value of each variable can produce a result that is off by a factor of 10; an error of about 12 percent in the value of each variable can produce a result that is off by a factor of 3 (a hemibel). (By the way, if you think that social-science data aren't that bad, you haven't seen how such data are collected and reported.) Of course, the errors might (miraculously) be offsetting, but don't bet on it. It's not that simple: Some errors will be large and some errors will be small (but which are which), and the errors may lie in either direction (but in which direction?).

So, the next time you read about research that purports to "prove" or "predict" such-and-such about a social phenomenon -- the effect of the minimum wage on employment, the influence of "nature" vs. "nurture" in child-rearing, the inflationary effect of government deficits -- take a deep breath and ask yourself "does this make sense?"