The usual problem when doing empirical work is that you don't have an important variable in your data. Very, very occasionally, you have the opposite problem: Lots of different highly correlated variables measuring pretty much the same thing. What to do? How to choose?
I would say that if the variable is typically measured in a specific way in the (economics) literature, maybe go with that one for your main specification unless you have reason to believe you have a better one. Either way, include a table in the appendix showing that your results are robust across measures. Don't freak out if you fail to see a star for one or two of them. This will happen if you have enough different measures and not a large enough sample size.
Another good option to choosing just one for your main specification is to include a summary measure of all of the different measures. Of course, many ways to create summary measures. Have a look here for a nice discussion of this.
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