Nonparametric Instrumental Variable Estimation of Structural Quantile Effects


  • Patrick Gagliardini,

    1. Faculty of Economics, University of Lugano, Via Buffi 13, 6900 Lugano, Switzerland and Swiss Finance Institute;
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  • Olivier Scaillet

    1. GFRI, University of Geneva, Bd du Pont d'Arve 40, CH-1211 Genève 4, Suisse and Swiss Finance Institute;
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    • We are very grateful to Victor Chernozhukov, who was a co-author of the original version. We also thank him for providing the tightness argument for the consistency proof. We thank the editor and referees for helpful suggestions. We thank J. Hausman and G. Sidak for generously providing us with the data on telecommunications services in the United States. We are especially grateful to X. Chen for comments that have led to major improvements in the paper. We also thank G. Dhaene, R. Koenker, O. Linton, E. Mammen, M. Wolf, and seminar participants at Athens University, Zurich University, Bern University, Boston University, Queen Mary, Greqam Marseille, Mannheim University, Leuven University, Toulouse University, ESEM 2008, and SITE 2009 workshop for helpful comments. The authors acknowledge the support provided by the Swiss National Science Foundation through the National Center of Competence in Research: Financial Valuation and Risk Management (NCCR FINRISK).


We study the asymptotic distribution of Tikhonov regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill-posed, and we consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the asymptotic variance. We study the small sample properties via simulation results and provide an empirical illustration of estimation of nonlinear pricing curves for telecommunications services in the United States.