Question on Variance Inflation Factor (Intuitively correlated but VIF is not high)

[Jun Park]

Hi, I am trying to run the following regressions
1. Preferences for redistribution = debt/financial_assets + debt/realestate_assets + someothercontrols + e.
2. Preferences for redistribution = debt/financial_assets + financial_assets + someothercontrols + e.

The first equation has two ratio variables with the same numerator.
The second equation has a ratio variable and a level variable which is the denominator of that ratio variable.

Intuitively, it makes sense that both equations might somewhat be problematic because the variables are correlated. But when I calculate the VIF, at most it's 1.5-2. Which I think it means they are still moderately correlated but not so problematic.
Does this mean running those regressions are fine? Or should I still follow my intuition and not include both of them in the same model.

[Jeff Wooldridge]

The answer to your question has little to do with the value of VIF. You need to ask whether the ceteris paribus thought experiment makes sense. In the first equation, do you want to know the partial effects of your debt variables on the preference outcome holding the other one fixed? If you do, then estimate that model, and forget about VIF. The question is whether you get meaningful coefficients with standard errors small enough to produce confidence intervals that rule out certain values.

In the second equation, I think it makes sense to hold financial assets fixed and ask whether the ratio of debt to financial assets matters. But that ratio can only change if debt changes if you're holding financial assets fixed. So you could just put debt in by itself. This is really a functional form issue.