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The Stata Journal
Volume 18 Number 4: pp. 937-950

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Nonparametric instrumental-variable estimation

Denis Chetverikov
Department of Economics
University of California, Los Angeles
Los Angeles, CA
Dongwoo Kim
Department of Economics
University College London
London, UK
Daniel Wilhelm
Department of Economics
University College London
London, UK
Abstract.  In this article, we introduce the commands npiv and npivcv, which implement nonparametric instrumental-variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands can impose the constraint that the resulting estimated function is monotone. Using such a shape restriction may significantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm, 2017, Econometrica 85: 1303–1320) because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as high variance. However, the constrained estimator that imposes the monotonicity significantly reduces variance by removing nonmonotone oscillations of the estimator. We provide a small Monte Carlo experiment to study the estimators' finite-sample properties and an application to the estimation of gasoline demand functions.
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