Semiparametric nonlinear panel data models with measurement error

This paper develops the identification and estimation of nonlinear semi-parametric panel data models with mismeasured variables and their corresponding average partial effects using only three periods of data. The past observables are used as instruments to control the measurement error problem, and the time averages of perfectly observed variables are used to restrict the unobserved individual-specific effect by a correlated random effects specification. The proposed approach relies on the Fourier transforms of several conditional expectations of observable variables. We then estimate the model via the semi-parametric sieve Generalized Method of Moments estimator. The finite-sample properties of the estimator are investigated through Monte Carlo simulations. We use our method to estimate the effect of the wage rate on labor supply using PSID.