Panel data consist of measurements taken from several individuals over time. Correlation among measurements taken from the same individual are often accounted for using random effect and random coefficient models. Panel data analysis that accounts for measurement error in the explanatory variables has not been thoroughly studied. This dissertation investigates statistical issues associated with two types of measurement error models for panel data;The first paper considers identification and estimation of a random effect model when some explanatory variables are measured with error. Here, individual heterogeneity is assumed to be manifested in intercepts that randomly differ across individuals. Identification of model parameters given the first two moments of observed variables is examined, and relatively unrestrictive sufficient conditions for identification are obtained. Estimation based on maximum normal likelihood is proposed. This method can be easily implemented using available computer packages that perform moment structure analysis. Compared to the only existing procedure based on instrumental variables, the new method is shown to be more efficient and to have much wider applicability. Standard error estimates and goodness-of-fit statistics obtained under the assumption of normally distributed observations are shown to be asymptotically valid for a broad class of non-normal observations. Simulation results demonstrating the efficiency and usefulness of the new procedure are presented;The second paper deals with the random coefficient model with measurement error, where all regression coefficients randomly differ across individuals. Two procedures are proposed for model fitting and estimation. The generalized least squares method is developed for the first two sample moments with a distribution-free estimate of the weight. Since this method tends to yield very variable estimates in small samples, an alternative method, the pseudo maximum normal likelihood procedure is also developed. The latter, obtained by maximizing a hypothetical normal likelihood for the first two sample moments, produces relative stable estimates in most samples. Asymptotic properties of the two procedures are derived and are used to obtain valid standard errors of the estimators. Numerical results showing the finite-sample properties of these estimators are also reported.