alternative estimating criteria that produce asymptotically equivalent estimators for fixed T and large N. Finally ... concern with heteroskedasticity has lead to consider alternative GMM .... present two-step SN-GMM estimators and test statistics of over .... concentrated NLS criterion that only depends on o, which gives 0NLS as.
Working Paper 96-45
Departamento de Economía
Statistics and Econometrics Series 16
Universidad Carlos III de Madrid
July, 1996
Calle Madrid, 126 28903 Getafe (Spain) Fax (341) 624-98-75
SYMMETRICALLy NORMALIZED INSTRUMENT AL-VARIABLE
ESTIMATION USING PANEL DATA
César Alonso-Borrego* and Manuel Arellano •• Abstract _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ In this paper we discuss the estimation of panel data models with sequential moment restrictions using symmetrically normalized GMM estimators. These estimators are asymptotically equivalent to standard GMM but are invariant to normalization and tend to have a smaller finite sample bias. They also have a very different behaviour compared to standard GMM when the instruments are poor. We study the properties of SN-GMM estimators in relation to GMM, minimum distance and pseudo maximum likelihood estimators for various versions of the AR(1) model with individual effects by mean of simulations. The emphasis is not in assessing the value of enforcing particular restrictions in the model; rather, we wish to evaluate the effects in small samples of using alternative estimating criteria that produce asymptotically equivalent estimators for fixed T and large N. Finally, as an empírical illustration, we estimate by SN-GMM employment and wage equations using panels of UK and Spanish firms.
Keywords: Panel data, instrumental variables, symmetric normalization, autoregressive models, employment equations. • Departamento de Economía, Departamento de Estadística y Econometría de la Universidad Carlos III de Madrid .•• CEMFI, Madrid We thank Richard Blundell, Gary Chamberlain, Guido Imbens, Whitney Newey, Enrique Sentana, Jim Stock an seminar audiences at Harvard, Princeton and Northwestern for useful comments. An earlier version of this paper was presented at the ESRC Econometric Study Group Annual Conference, Bristol, July 1994, and at the Econometric Society European Meeting in Maastricht, August 1994.
1. Introduction
In this paper we present instrumental variable estimators of panel data models with predetermined variables subject to a symmetric normalization rule of the coefficients of the endogenous variables. We also evaluate the performance of these techniques for first-order autoregressive models with individual effects by mean of simulations. Lastly, an empirical illustration is provided. This work is motivated by a concern with the biases of ordinary IV estimators when the instruments are poor. A linear panel data model wl th predetermined variables, typically estlmated by IV techniques, takes the form
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