Measurement Errors in Dynamic Panel Data Analysis: a Synthesis on Modeling and Gmm Estimation

A panel data model which combines an autoregressive fixed effects panel data equation and a static equation with measurement errors is considered. Examples of models for pure time series data with errors in variables are the starting point. Two versions of the Generalized Method of Moments (GMM) for this panel data model are considered, with fixed effects accounted for by, respectively, (i) transforming the equation to differences and keeping the instruments in levels, (ii) keeping the equation in levels and transforming the instruments to differences. In specifying the set of valid moment conditions and instrument sets, patterns with finite memory of disturbances, of latent regressors and of the measurement errors are discussed. Focus is on examining how the potential instrument sets which satisfy both the rank conditions for the instrumented variables and the orthogonality conditions for the composite errors and disturbances, change when the model’s memory pattern changes. Sometimes the joint occurrence of measurement errors and long memories implies that the potential instrument sets becomes too small to make consistent estimation possible. An application based on panel data for capital stock and output from Norwegian manufacturing firms is presented.