Measurement error causes a downward bias when estimating a panel data linear regression model. The panel data context offers various opportunities to derive moment conditions that result in consistent GMM estimators. We consider three sources of moment conditions: (i) restrictions on the intertemporal covariance matrix of the errors in the equations, (ii) heteroskedasticity and nonlinearity in the relation between the error-ridden covariate and another, error-free, covariate in the equation, and (iii) nonzero third moments of the covariates. In a simulation study we show that these approaches work well.
measurement error panel data third moments heteroskedasticity GMM