How big is it?

A question that comes up (or that should come up!) in empirical research is: How big is the effect? How important? How does this effect compare with that one? Deirdre McCloskey calls it the question of "oomph." For example, in explaining variation in earnings across individuals, which has more oomph: differences in gender, in education, or in work experience?

To answer, we need estimates of the partial effects, but also a way to scale the units to make comparisons between apples and oranges. One conventional way to do this is to standardize regression coefficients by calculating the effect of a one-standard-deviation change in each variable. But as I realized while teaching this to my econometrics students this week, the comparison is tricky when some of your explanatory variables are qualitative (0-1), such as gender. What does it mean to predict the effect of a standard deviation of female-ness? (Yeah, OK, maybe something, but still...)

During my midterm today I started reading Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models (they really could have used a catchier title!). It's interesting to read a first-rate non-economist statistician on the techniques we economists use routinely. I have already gained one tip that helps with the problem at hand- the problem of oomph. Whereas standardized coefficients usually look at the effect of a one standard deviation change in X, Gelman recommends scaling regression coefficients by two s.d. Why? This makes comparison with the 0-1 effects of dummy variables more reasonable. When the mean of a dummy variable is around 0.5 (e.g., female), then one s.d. of it is also 0.5, so a 0-1 switch is 2 standard deviations of the dummy. And it's pretty close even when p = 0.2: s.d. = 0.4. Voila! I can compare the size of the effect of gender on earnings with the effect of experience or education.

Nifty! And practical! And easy... And did I mention that all their examples are cleanly coded in R? That's especially handy for ECON 41/42 at Santa Clara University. It's a fat book, and it gets harder, but I'll keep reading.