Before revision:  In this paper we give results for the valid inference of a treatment effect after selecting from among very many control variables and the estimation of instrumental variables with potentially very many instrumentswhen post- or orthogonal L_2-Boosting is used for the variable selection.
After revision:  In this paper , we provide results for valid inference after post- or orthogonal L_2-Boosting is used for variable selection. We consider treatment effects after selecting among many control variables and the estimation of instrumental variables with potentially very many instrumentswhen post- or orthogonal L_2-Boosting is used for the variable selection.