Before revision:  All products must fulfill the exclusion restriction, for the instrument to be valid. I propose applying methods which can preselect invalid products when either more than half or the largest group of products is valid. I discuss extensions of these methods for fixed effects models. I illustrate the procedures with three applications: a simulation study, the labor market effect of Chinese import competition and the effect of immigration to the US. My results help explain why previous studies have found low effects of immigration  .
After revision:  All products must fulfill the exclusion restriction, making the identifying assumption very strict. In this paper, I propose the use of machine learning methods that allow to substantially relax the exclusion restriction, by selecting invalid shares. 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 .