Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels

Authors


J. Paul Elhorst, Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlandse-mail: j.p.elhorst@eco.rug.nl

Abstract

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.

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