Nonparametric Instrumental Regression


  • S. Darolles,

    1. DRM—Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France and Lyxor Asset Management;
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  • Y. Fan,

    1. Dept. of Economics, Vanderbilt University, VU Station B 351819, 2301 Vanderbilt Place, Nashville, TN 37235-1819, U.S.A.;
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  • J. P. Florens,

    1. Toulouse School of Economics, Université Toulouse 1 Capitole, Manufacture des Tabacs, 21 Allée de Brienne, 31000 Toulouse, France;
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  • E. Renault

    1. Dept. of Economics, P.O. Box B, Brown University, Providence, RI 02912, U.S.A. and CENTER, Tilburg;
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    • We first want to thank our coauthors on papers strongly related with this one: M. Carrasco, C. Gourieroux, J. Johannes, J. Heckman, C. Meghir, S. Van Bellegem, A. Vanhems, and E. Vytlacil. We also acknowledge helpful comments from a co-editor, the referees, and D. Bosq, X. Chen, L. Hansen, P. Lavergne, J. M. Loubes, W. Newey, and J. M. Rolin. We thank the participants at conferences and seminars in Chicago, Harvard–MIT, London, Louvain-la-Neuve, Montreal, Paris, Princeton, Santiago, Seattle, Stanford, Stony Brook, and Toulouse. We also thank R. Lestringand, who performed the numerical illustration given in Section 5.


The focus of this paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model E[Yϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The function ϕ is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyzes identification and overidentification of this model, and presents asymptotic properties of the estimated nonparametric instrumental regression function.