Does Instrumental variable address selection bias?

Hello Everyone,

I am using two main explanatory variables in my study, one is continues variable, and one is dummy variable. I take an simple example here:

If I want to address the relationship between democracy degree and salary in different country. I have :

Democracy degree= alpha + beta* salary + u

This is basic OLS model.

Then I set salary scales from 1 to 10, where 1 is the lowest and 10 is the highest, I will use this as my continues variable; then I set a dummy variable equals to 1 if the salary levels ranging from 5 to 10, otherwise is 0.

Now I would argue that a country's education level can affect the people's salary level. So I will use a variable called " Education level" to address salary level ( Taking an example here, please forget about the potential relationship between Democracy and Education level).

Well, I firstly run IV model in stata with salary level( continues variable) with education level, and I find the variable is endogenous; then I use dummy variable instead of continues variable to run IV model and use the same IV ( Education level). But this time I did not find endogenous. Can I conclude that the way of using dummy variable to measure salary level does not related to endogeneity and I will use OLS with the dummy variable measurement?

Actually my main question is , both my two measures are related to salary level, and one is continues variable and one is dummy variable. Can I use the same IV for both measures?

Thank you very much for all your help!

Chen