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We consider the semiparametric regression Xtβ + φ (Z) where β and φ(.) are unknown slope coefficient vector and function, and where the variables (X, Z) are endogeneous. We propose necessary and sufficient conditions for the identification of the parameters in the presence of instrumental variables. We also focus on the estimation of β. An incorrect parametrization of φ generally leads to an inconsistent estimator of β, whereas consistent nonparametric estimators for β have…

This paper considers a semi‐parametric version of the transformation model φ (Y) =β′X+U under exogeneity or instrumental variables assumptions (E(U∣X) = 0 or . This model is used as an example to illustrate the practice of the estimation by solving linear functional equations. This paper is specially focused on the data‐driven selection of the regularization parameter and of the bandwidths. Simulations experiments illustrate the relevance of this approach.