"The control function in the semiparametric selection model is zero at infinity. This paper proposes additional restrictions of the same type and shows how to use them to test assumed exclusion restrictions necessary for root N estimation of the model. The test is based on the estimated control function and its derivative and takes the form of a GMM step that occurs at infinity. Alternative estimation of the parameters are proposed which do not rely on exclusion restrictions, extending available results for the estimation of the intercept at infinity. Simulations are implemented"--Forschungsinstitut zur Zukunft der Arbeit web site.