# Highly Collinear Independent Variables of Interest

Suppose I am interested in the follows: I have county-level data. For each county, I know the share of the population that was born from one parent and the share of the population that was born from two. Suppose I am interested in the impact of the black population on tax revenues. In particular, suppose I am also interested in the impact of the share of the population born from two black parents separately from the share born from one black parent. I am using OLS.

The problem is that the share of the population born from one and two black parents is highly correlated, resulting in a near multicollinearity problem.

Of course I can proceed by just testing the total share of the black population, and that is a result in which I am inherently interested. However, if I include the 1 and 2 parents as together as two regressors, the results seem meaningless relative to the total share because the 1 and 2 parent variables produce a near multicollinearity.

Should I run two separate regression? A regression on the share with 1 parent and a regression on the share with 2 parents? Or is there nothing that can be done because of the near multicollinearity?

Thank you very much for any help you can provide.

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Why not have "Number of Black parents" as a single IV, with three levels (0, 1, 2)? –  Peter Flom Oct 28 '12 at 19:12
I don't follow the complete design, but if you are interested in a set of proportions that sum to one, you can include 1 fewer variables in the model & the last becomes the reference level. EG, if there are 1 & 2-parent families only, you could use the 2-parent proportion as the reference & only include a variable for the % of 1-parent families. –  gung Oct 28 '12 at 19:19
@PeterFlom The data are at the county level, so I don't see how I can do that. I can have 1 IV: share of population with at least 1 black parent (with excluded category being 0). Or, I can have 2 IV: share of population with exactly 1 black parent and share of population with exactly 2 (with excluded category being 0). The problem with the 2 IV set up is the near multi-collinearity. The first set-up is fine, but it does not get at the underlying question of interest. –  user1690130 Oct 28 '12 at 19:35
@Gung. There are three categories: share of population with exactly 0 black parents, share with exactly 1, and share with exactly 2. The excluded category is 0. The problem is that the share with exactly 1 and share with exactly 2 are highly correlated. So, I worry about including them together. One alternative is to collapse the variable into share with at least 1, but that does not fully get at what I want. –  user1690130 Oct 28 '12 at 19:38
I gather the problem is that the % of children born to 0 parents is not quite 0, but so close that % 1 is almost perfectly predictable from % 2. If that's true, one possibility is to exclude all 0's from your analysis (obviously, this approach & the constraints it places on interpretation need to be made clear to readers), then use, say, 2 as the reference category & have just one variable w/ % 1's (out of the total of 1's + 2's). –  gung Oct 28 '12 at 19:41
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