A1422
Title: Semiparametric and nonparametric instrumental variable estimation with first-stage isotonic regression
Authors: Mengshan Xu - University of Mannheim (Germany) [presenting]
Taisuke Otsu - London School of Economics (United Kingdom)
Kazuhiko Shinoda - Nagoya University (Japan)
Abstract: A semiparametric and a nonparametric instrumental variable (IV) estimators are proposed under the assumption that the conditional mean of the endogenous variable, given the instrumental variable, is known to be monotone increasing. Isotonic estimation is employed to obtain the fitted instruments in the first stage of a two-stage semiparametric or nonparametric estimation procedure. It is shown that the proposed semiparametric IV estimator is tuning-parameter-free and achieves the semiparametric efficiency bound. Moreover, it is shown that compared to the nonparametric two-stage least squares estimator, the proposed nonparametric IV estimator requires notably fewer tuning parameters and achieves the same convergence rate. Additionally, it exhibits greater stability, as evidenced by Monte Carlo simulations.
