Nonlinear regression with measurement error is important for estimation from microeconomic data. One approach to identification and estimation is a causal model, in which the unobserved true variable is predicted by observable variables. This paper details the estimation of such a model using simulated moments and a flexible disturbance distribution. An estimator of the asymptotic variance is given for parametric models. Also, a semiparametric consistency result is given. The value of the estimator is demonstrated in a Monte Carlo study and an application to estimating Engel Curves.