The weak instrument problem of the system GMM estimator in dynamic panel data models

The system GMM estimator for dynamic panel data models combines momentconditions for the model in first differences with moment conditions for the model inlevels. It has been shown to improve on the GMM estimator in the first differencedmodel in terms of bias and root mean squared error. However, we show in this paperthat in the covariance stationary panel data AR(1) model the expected values ofthe concentration parameters in the differenced and levels equations for the crosssectionat time t are the same when the variances of the individual heterogeneityand idiosyncratic errors are the same. This indicates a weak instrument problemalso for the equation in levels. We show that the 2SLS biases relative to that of theOLS biases are then similar for the equations in differences and levels, as are thesize distortions of the Wald tests. These results are shown to extend to the paneldata GMM estimators.JEL Classification: C12, C13, C23Keywords: Dynamic Panel Data, System GMM, Weak Instruments