Nonparametric instrumental-variable estimation

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.

本文中，我们介绍了npiv与npivcv两个命令，二者分别实现了不带交叉验证选择调优参数的非参数工具变量（nonparametric instrumental-variable，NPIV）估计方法，以及带交叉验证选择调优参数的NPIV估计方法。上述两个命令均可施加约束，使得最终估计得到的函数具备单调性。此类形状约束可显著提升NPIV估计量的性能（Chetverikov与Wilhelm，2017，《计量经济学》（Econometrica）第85卷：1303–1320），原因在于NPIV估计问题的不适定性会导致无约束估计量出现诸如方差过高这类极差的统计特性。而施加单调性约束的受限估计量，则可通过消除估计量的非单调震荡，显著降低估计方差。本文通过小型蒙特卡洛实验探究了该类估计量的有限样本性质，并将其应用于汽油需求函数的估计。