Symmetrically Normalized Instrumental-Variable Estimation Using Panel Data

TLDR

The paper addresses estimation of linear panel‑data models with sequential moment restrictions using symmetrically normalized GMM (SNM) and LIML analogues. The authors evaluate SNM and LIML properties via simulations comparing them to ordinary GMM and minimum‑distance estimators for AR(1) models with individual effects. SNM and LIML estimators are asymptotically equivalent to standard GMM, invariant to normalization, and exhibit smaller finite‑sample bias with weak instruments, as shown in simulations and empirical wage and employment equation estimates for UK and Spanish firms. Keywords: autoregressive models, dynamic panel data, employment equations, generalized method of moments, Monte Carlo methods, symmetric normalization.

Abstract

Abstract 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. KEY WORDS: Autoregressive modelsDynamic panel dataEmployment equationsGeneralized method of momentsMonte Carlo methodsSymmetric normalization