Journal of Real Estate Finance and Economics, Vol. 17:1, 99±121 (1998)
# 1998 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
A Generalized Spatial Two-Stage Least Squares
Procedure for Estimating a Spatial Autoregressive
Model with Autoregressive Disturbances
HARRY H. KELEJIAN
INGMAR R. PRUCHA
Department of Economics, University of Maryland, College Park, MD 20742
Cross-sectional spatial models frequently contain a spatial lag of the dependent variable as a regressor or a
disturbance term that is spatially autoregressive. In this article we describe a computationally simple procedure
for estimating cross-sectional models that contain both of these characteristics. We also give formal large-sample
Key Words: Spatial autoregressive model, two-stage least squares, generalized moments estimation
Cross-sectional spatial regression models are often formulated such that they permit
interdependence between spatial units. This interdependence complicates the estimation
of such models. One form of interdependence arises when the value of the dependent
variable corresponding to each cross-sectional unit is assumed, in part, to depend on a
weighted average of that dependent variable corresponding to neighboring cross-sectional
units. This weighted average is often described in the literature as a spatial lag of the
dependent variable, and the model is then referred to as a spatially autoregressive model
(see, e.g., Bloomestein, 1983, and Anselin, 1988, p. 35).
The spatially lagged dependent
variable is typically correlated with the disturbance term (see, e.g., Ord 1975, and Anselin,
1988, p. 58), and hence the ordinary least squares estimator is typically not consistent in
such situations. Another form of interdependence that arises in such models is that the
disturbance term is often assumed to be spatially autoregressive. Consistent procedures,
other than maximum liklihood, have been suggested in the literature for models that
contain one of these interdependencies.
Unfortunately, such procedures are not available
for models that have both of these characteristics. This shortcoming is of consequence
because maximum likelihood procedures are often computationally very challenging
when the sample size is large.
Furthermore, the maximum likelihood procedure requires
distributional assumptions that the researcher may not wish to specify.
The purpose of this article is to suggest an estimation procedure for cross-sectional
spatial models that contain a spatially lagged dependent variable as well as a spatially