Regarding multicollinearity, is it recommended to use ridge-regression if you have some covariates with VIF values around 10 in the OLS model? What would be the best VIF level to use to decide whether or not to do ridge-regression?
For collinearity diagnosis, I prefer to use condition indices.
Ridge regression is one possible solution to collinearity. However, deciding what to do about collinearity is a two-step process:
1) Diagnosis if it's a problem 2) Decide what to do
Ridge regression helps solve the problem by accepting a biased but lower variance solution. Other possible solutions include dropping a variable from the model, combining variables (e.g with Partial Least Squares), getting more data, and probably other things that I am not thinking of at the moment.
EDIT per @gung 's comment
Condition index is better than VIF for some technical reasons (if you want details, see books by David Belsley) but more practically because they give you information on which sets of variables are causing the collinearity. Belsley suggests 10 for moderate collinearity and 30 for severe. But you also want to look at the proportion of variance explained.