Panel data dynamics with mis-measured variables: modeling and GMM estimation

Generalized Method of Moments (GMM) estimation is discussed under the joint occurrence of fixed effects and random measurement errors in an autoregressive panel data model. Finite memory of measurement errors is allowed for. Two GMM specializations are considered: (i) using instruments (IVs) in levels for a differenced version of the equation and (ii) using IVs in differences for the level version. Index sets for lags and leads are convenient in examining how the potential IV-set is affected by changes in the memory pattern. While measurement errors with long memory may give an IV-set too small for identification, problems of "IV proliferation" and "weak IVs" may arise unless the panel is short. An application based on data for (log-transformed) capital stock and output from Norwegian manufacturing firms, supplemented with Monte Carlo simulations, to illustrate finite sample biases, is considered. Overall, with respect to bias and IV strength, GMM specialization (ii) seems superior to inference using GMM specialization (i).