Symmetrically normalized instrumental-variable estimation using panel data

We discuss the estimation of linear panel-data models with sequential moment restrictions using symmetrically normalized generalized method of moments (GMM) estimators (SNM) and limited information maximum likelihood (LIML) analogues. These estimators are asymptotically equivalent to standard GMM but are invariant to normalization and tend to have a smaller finite-sample bias, especially when the instruments are poor. We study their properties in relation to ordinary GMM and minimum distance estimators for AR(1) models with individual effects by mean of simulations. Finally, as empirical illustrations, we estimate by SNM and LIML employment and wage equations using panels of U.K. and Spanish firms.