Panel data with measurement errors : instrumental variables and GMM procedures combining levels and differences

The estimation of linear, static regression equations from panel data with measurement errors in the regressors is considered. If the latent regressor is autocorrelated or non-stationary, several consistent instrumental variables (IV) and generalized method of moments (GMM) estimators usually exist, provided some structure is imposed on the disturbances and measurement errors. Applications of GMM procedures (i) on equations in differences with IV's in levels and (ii) on equations in levels with IV's in differences - the difference transformations eliminating unobserved individual heterogeneity - are considered. The IV's may be constructed from values of the regressors or the regressand. Some of the orthogonality conditions delimiting the valid IV's are redundant. Illustrations based on data on inputs and outputs from an eight year panel of manufacturing firms are given.