This paper develops identification and estimation of the parameters of a nonlinear semi-parametric panel data model with mismeasured variables as well as the 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 estimate the model via the semi-parametric sieve minimum distance 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 data.