How to deal with multicollinearity issue when analyzing survey results?

Question

I recently conducted my first study looking at parental education as a determinant of risk. I conducted a survey which measured risk in several contexts and also recorded information about the individuals such as gender, height and all the other usual suspects. Little work has been done on the effect of ethnicity on risk and also country of origin/residence on risk (an interesting secondary research question). The issue is that parents nationality are very highly correlated with their children (as one would expect) to the extent that Minitab has discarded various determinants for being highly correlated. Due to the nature of the sample (students in the UK) correlation is something that it unavoidable.

I don't wish to discard variables just because they are highly correlated, although I have seen a few suggestions to do so. Is there a way to overcome this issue? Otherwise how else would one look at the marginal effect of country of birth/parents nationality on their risk preferences? Am I overlooking something simple?

Answer 1

This is a great question, here's my intuition:

The sort of problem you're talking about has to do with identification: when we conduct causal analysis, we'd like to be able to make claims about the effects of several different variables. However, in cases of high dependence amongst the variables (like this), our ability to make separate claims about the variables is heavily restricted.

I'll try to give an example using your data. (I may have the wrong idea, here, though – please correct me if I misstate your case):

Parents' ethnicity and children's ethnicity are very closely bound in your sample – another way of saying this is that you have very few (if any) observations where these are different. This means that (statistically speaking) you'll be unable to differentiate the causal impact of parents vs. children's ethnicity.

The sort of data you'd need to make claims like this, would be observations where these variables are different from one another (perhaps by looking at multi-racial couples, or adopted children). In the absence of this data, you'll be unable to differentiate these impacts.

In a sense, this is disheartening news (since we'd like to be able to estimate separate effects), but in another way, this result is entirely sensible. If we think of ethnicity being generally a stable trait at the family level, then it may make sense to think of ethnicity as sort of a bundle of effects – knowing a child's ethnicity may tell you something meaningful as well about their parents' ethnicity, so in a sense, it'd be unusual to report on a heavy distinction between these constructs.

In summary, you're not doing anything wrong (at least in my mind)… The sort of problem you've identified has to do with a property of the data that's tricky to get around, rather than a problem with the way the analysis is being conducted.