Strength and weakness of instruments in IV and GMM estimation of dynamic panel data models

It is shown that e¢ cient GMM (generalized method of moments) estimation of a linear model corresponds to standard IV (instrumental variables) estimation of this model, after transforming it such (as in GLS) that its resulting disturbances have a scalar covariance matrix, while using as instruments the original instruments linearly transformed by the transpose of the inverse of the matrix used to transform the model. This correspondence between e¢ cient GMM and classic IV can be exploited to convert IV measures for the strength of instrumental variables in terms of concentration parameters for use in the more complex GMM context. For ine¢ cient IV estimates in models where the disturbances are dependent, and more generally for GMM employing a suboptimal weighting matrix, such measures can be developed by referring to the asymptotic precision matrix of particular coe¢ cient estimates. These measures for (marginal) instrument strength are then established for various particular implementations of IV and GMM for dynamic panel data models with time-invariant unobserved heterogeneity. Calculations for particular parametrizations allow to better understand aspects of the actual performance of the popular Anderson-Hsiao, Arellano-Bond and Blundell-Bond (system) estimators in samples of empirically relevant sizes. Department of Quantitative Economics, Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands ([email protected]).