How does multicollinearity between some variables affect non-collinear ones?

Question

In a multiple regression model, i.e. $y \sim x_1 + x_2 + x_3$, where $x_1$ and $x_2$ are collinear (e.g. present high correlation around 0.8), it is well known that many problems arise regarding parameter estimation or hypothesis testing (on $x_1$ and $x_2$). But how does collinearity affect the third non-collinear variable, $x_3$?

Answer 1

(Assume a linear model, OLS.)

Multicollinearity has its bad effects through the variance inflation factor (VIF), which is calculated by using all but one of the regression features to predict the remaining regression feature. That regression has its $R^2$ calculated, and then $\frac{1}{1-R^2}$ is the VIF.

If that remaining variable is independent of the others, then that $R^2=0$, and the $VIF=1$. Thus, the multicollinearity does not cross-contaminate the standard error for the coefficient of that independent variable.