Panel data with errors-in-variables: essential and redundant orthogonality conditions in GMM-estimation

General Method of Moments (GMM) estimation of a linear one-equation model using panel data with errors-in-variables is considered. To eliminate fixed individual heterogeneity, the equation is differenced across one or more than one periods and estimated by means of instrumental variables. With non-autocorrelated measurement error, we show that only the one-period and a few two-period differences are essential, i.e. relevant for GMM-estimation. GMM estimation based on all orthogonality conditions on the basis of a generalized inverse formulation is shown to be equivalent to estimation using only the essential orthogonality conditions.