What does it say about the data if ridge regression is not reducing multicollinearity? I am predicting the salary to be offered to a new candidate for which I am concentrating on just continuous (9 in number) variables. Variables are as attached. When I ran OLS the coefficient for total experience came out negative but it is not expected to have a negative coefficient for total experience when "salary to be offered" is the dependent variable. Then, I removed the current salary and then ran OLS and the coefficient of total experience turned positive.
This clearly aligns with the fact that current salary and total experience are correlated therefore multicollinearity is present. Now I can't drop the variables because they are important.
I intend to build a linear equation that can explain the impact of every important predictor on the dependent variable and I thought ridge regression can help me with this problem but even in the presence of ridge regression the sign of the coefficient for total experience is negative which I think implies the multicollinearity is still present.
But even after ridge regression, the sign of the coefficient for total experience is negative.
In other words, shrinkage of the coefficients is not happening.
Can anyone suggest what might have happened?

There could be something funky happening from the standpoint of statistics, but it seems like, for a given current salary, having more experience is a detriment future prospects. I kind of understand that; if you’ve been working twenty years and still make the salary of a junior employee, maybe you’re not very good at your job and should not expect much of a salary increase at your next job (maybe even a pay cut if the high-end firms won’t hire you).
This could mean that you are witnessing Simpson’s Paradox, and there is an economic interpretation that could be valuable. Rather than be frustrated, I would prefer to take pride in uncovering this interesting economic phenomenon!
