Taisuke Otsu, Kazuhiko Shinoda and Mengshan Xu

Published 6 October 2025

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This paper proposes a semiparametric and a nonparametric instrumental variable (IV) estimator, under the assumption that the conditional mean of the endogenous variable, given the instrumental variable, is known to be monotone increasing. We employ isotonic estimation to obtain the fitted instruments in the first stage of a two-stage semiparametric or nonparametric estimation procedure. We show that the proposed semiparametric IV estimator is tuning-parameter-free and achieves the semiparametric efficiency bound. Moreover, we show that compared to the nonparametric two-stage least squares estimator (Blundell, Chen and Kristensen, 2007; Horowitz, 2011, 2012), our 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.