In this paper we study semiparametric efficiency for the estimation of a finite-
dimensional parameter defined by generalized moment conditions under the lo-
cal instrumental variable assumptions. These parameters identify treatment ef-
fects on the set of compliers under the monotonicity assumption. The distrib-
utions 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 uncondi-
tional 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 mod-
els.
Keywords. Semiparametric efficiency bound, local treatment effect, FTP, child
achievement, unemployment benefits.
JEL classification. C25, C26, C31.