Before revision:  I apply the methods to simulated data and the estimation of the effects of trade exposure and immigration on wages . After removing shares selected as endogenous, the positive effects of immigration decrease while the effects of Chinese import exposure are not affected .
After revision:  I apply the methods in simulations and two empirical examples: the effect of immigration on wages . After removing shares selected as endogenous, the positive effects of immigration decrease while the effects of Chinese import exposure are not affected .