Econometrica: Jul 2012, Volume 80, Issue 4

Nonparametric Instrumental Variable Estimation of Structural Quantile Effects

https://doi.org/10.3982/ECTA7937
p. 1533-1562

Patrick Gagliardini, Olivier Scaillet

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.

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Supplement to "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects"

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