Semiparametric Efficiency in Nonlinear LATE Models

Joint with: Denis Nekipelov

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, 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 multi-step semiparametric efficient estimators that achieve the semiparametric efficiency bound. Using data from the Florida Family Transition Program, we apply the suggested

estimation procedure to analyze the effect of the parent’s employment on children’s achievement for single-parent households who applied for state welfare support. We find that the linear regression estimate of the treatment effect has a substantial attenuation bias as compared to instrument-based methods. In general, parent’s employment

adversely affects child’s achievement. Our result suggests that ignoring the selection effect indeed leads to substantial bias in the estimate of effect of parent’s employment.

For more information, contact Frank Schorfheide.