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 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 on employment. I find that weak instruments and strong violations of the exclusion restriction do not worsen the performance of the estimators. In both applications, the coefficients change considerably but this is reconcilable with the arguments made in the literature .