This paper focuses on a three-dimensional model that combines two different
types of spatial interaction effects, i.e. endogenous interaction effects via a spatial
lag on the dependent variable and interaction effects among the disturbances via a
spatial moving average (SMA) nested random effects errors. A three-stage procedure
is proposed to estimate the parameters. In a first stage, the spatial lag panel data model
is estimated using an instrumental variable (IV) estimator. In a second stage, a generalized
moments (GM) approach is developed to estimate the SMA parameter and the
variance components of the disturbance process using IV residuals from the first stage.
In a third stage, to purge the equation of the specific structure of the disturbances a
Cochrane–Orcutt-type transformation is applied combined with the IV principle. This
leads to the GM spatial IV estimator and the regression parameter estimates. Monte
Carlo simulations show that our estimators are not very different in terms of root mean
square error from those produced by maximum likelihood. The approach is applied to
European Union regional employment data for regions nested within countries