## Marginal and marginal

Statistics and economics have similar, but not identical, jargon, that overlap in various confusing ways (consider “OLS,” “endogeneity,” “ignorability,” etc., not to mention the implicit assumptions about the distributions of error terms in models).

To me, the most interesting bit of terminological confusion is that the word “marginal” has opposite meanings in statistics and economics. In statistics, the margin (as in “marginal distribution”) is the average or, in mathematical terms, the integral. In economics, the margin (as in “marginal cost”) is the change or, in mathematical terms, the derivative. Things get more muddled because statisticians talk about the marginal effect of a variable in a regression (using “margin” as a derivative, in the economics sense), and econometricians work with marginal distributions (in the statistical sense). I’ve never seen any confusion in any particular example, but it can’t be a good thing for one word to have two opposite meanings.

P.S. I assume that the derivation of “margin,” in both senses, is from the margin of a table, in which case either interpretation makes sense: you can compute sums or averages and place them on the margin, or you can imagine the margin to represent the value at the next value of x, in which case the change to get there is the “marginal effect.”

1. Anonymous says:

I wonder whether it's actually better for a word to have two opposite meanings, than two similar, but not identical ones. In most cases, the appropriate meaning of marginal is obvious from context, but that's less likely to be true if the two meanings are similar.

2. As an economist, I would argue that a variable is endogenous if it is not independent of the error term. Endogeneity mostly arises due to simultaneity, omitted variables, and measurement error.

What's the problem with OLS?

3. dsquared says:

I will certainly put my hand up on this one; "marginal distributions" never fail to confuse me and I always waste about half an hour believing that the conditional distribution is the marginal distribution exactly because I am going by analogy with "marginal effect".

4. Andrew says:

Michael,

The issue with "endogeneity" is that people often seem sure about what it means, but it's hard to pin down a definition. In the context of a specific model, you can use your definition above, but people commonly use the term without reference to any particular model.

The problem with "OLS" is that I'm never sure what's "ordinary" about it. Is it being compared to weighted least squares, instrumental variables, or something else? More generally, I avoid the term because it focuses on the estimation method rather than what is more important, which is the model. I prefer the term "linear regression" because it focuses on the linearity of the model, which is the key assumption, I think.

5. David says:

I actually read a paper that used 'marginal' in the statistics sense and it confused the crap out of me. Now, it makes a lot more sense. [The usage; I'm still struggling to believe the paper]