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. This setting allows for valid inference on low-dimensional components in a regression estimated with L_2-Boosting .
After 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 in a high-dimensional setting similar to Lasso, i.e., under approximate sparsity without assuming the beta-min condition. These results are extended to the 2SLS framework and valid inference is provided for treatment effect analysis .