Nous nous intéressons à l'estimation non paramétrique d'une fonction de régression instrumentale ϕ .Cette fonction est définie à l'aide de conditions de moment provenant d'un modèle économétrique structurel de la forme ( )des variables endogènes et les W des instruments.La fonction ϕ est alors la solution d'un problème inverse mal posé, et nous proposons une procédure d'estimation utilisant la régularisation de Tikhonov.Le papier analyse l'identification et la suridentification du modèle et donne les propriétés asymptotiques de l'estimateur de la régression instrumentale non paramétrique.

We use the control function approach to identify the average treatment effect and the effect of treatment on the treated in models with a continuous endogenous regressor whose impact is heterogeneous. We assume a stochastic polynomial restriction on the form of the heterogeneity, but unlike alternative nonparametric control function approaches, our approach does not require large support assumptions.

Different definitions of noncausality (according to Granger, Sims, Haugh and Pierce,...) are analyzed in terms of orthogonality in the Hilbert space of square integrable variables. Conditions, when necessary, are given for their respective equivalence. Some problems of testability are mentioned. Finally noncausality is also analyzed in terms of rational expectations, extending previous results of Sims. (Author)

In this note the relationship between alternative concepts of noncausality is analyzed using the tool of conditional independence among a-fields. (For the reader who is unfamiliar with this technique, the Appendix sketches the proofs and the basic technical apparatus, along with some basic motivations.) Furthermore, the relationship between the concepts of noncausality and transitivity is made explicit in order to facilitate, in econometric modelling, the use of results already obtained in sequential analysis.