Estimation of Nonlinear Models with Measurement Error Using Marginal Information

We consider the problem of consistent estimation of nonlinear models with mismeasured explanatory variables, when marginal information on the true values of these variables is available. The marginal distribution of the true variables is used to identify the distribution of the measurement error, and the distribution of the true variables conditional on the mismeasured and the other explanatory variables. The estimator is shown to be root-n consistent and normally distributed. The simulation results are in line with the asymptotic results. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of welfare benefits is obtained from an administrative source