• Open Access

Semiparametric efficiency in nonlinear LATE models


  • The authors acknowledge generous research supports from the NSF and excellent research assistance from Tim Armstrong. The usual disclaimer applies. We would like to thank Alberto Abadie, Shakeeb Khan, Guido Imbens, Bernard Salanié, Ed Vytlacil, conference participants in the 2007 NASM meeting in Duke University, and seminar participants at Columbia University, University of Pennsylvania, Harvard, and MIT for helpful comments. The authors have made use of the FTP data without representing positions by the State of Florida and MDRC.


In this paper we study semiparametric efficiency for the estimation of a finite-dimensional parameter defined by generalized moment conditions under the local instrumental variable assumptions. These parameters identify treatment effects on the set of compliers under the monotonicity assumption. The distributions of covariates, the treatment dummy, and the binary instrument are not specified in a parametric form, making the model semiparametric. We derive the semiparametric efficiency bounds for both conditional models and unconditional models. We also develop multistep semiparametric efficient estimators that achieve the semiparametric efficiency bound. To illustrate the efficiency gains from using the optimal semiparametric weights, we design a Monte Carlo study. It demonstrates that our semiparametric estimator performs well in nonlinear models.