Instrumental Variable Estimation of Nonlinear Models with Nonclassical Measurement Error Using Control Variates∗

We consider nonlinear models with an independent variable that is measured with error. The measurement error can be correlated with the true value, i.e. the measurement error is allowed to be nonclassical. We show that we can use a control variate estimator to estimate the parameters of interest. If we are prepared to make an assumption of the joint distribution of the first-stage and measurement errors the estimator is parametric. If we are only willing to specify the marginal distribution of the measurement error (up to a finite dimensional parameter vector), the estimator is semi-parametric. In the semi-parametric case the instrument must be sufficiently powerful, it must have a sufficiently large support. We derive the influence function of the semi-parametric estimator that properly account for the estimation of the control variates in the first stage.