Estimation methods for models using lattice data and taking spatial dependence into account are as mature as global statistics for spatial autocorrelation (Ord, 1975, Hepple, 1976); the form of model most commonly used is known as the simultaneous autoregression (SAR). Ten years have now passed since Anselin and Griffith (1988) surveyed the regional science and economic geography literature to see how far these methods were being applied to data sets for which they should have been suited. The low penetration they reported seemed related to the lack of access to these tools in standard statistical packages, addressed subsequently by Anselin and Hudak (1992), Griffith (1993), Bivand (1992), and others. The most substantial effect has been achieved by Anselin's ``SpaceStat'' program, permitting the estimation of most of the specification tests and models described in the literature (1995b).
Examples of the application of these methods by economists are Dubin's estimation of a hedonic regression with cross-section data (1988), an analysis of spatial patterns in household demand by Case (1991), and two detailed studies of fiscal policy interdependence between U.S. states (Case, Rosen and Hines, 1993, Besley and Case, 1995). In addition, mention can be made of some recent studies taking up location problems: Anselin, Varga and Acs (1997) challenge and refine Jaffe's conceptual framework for the analysis of local geographical spillovers between university research and high technology innovations, modifying previous conclusions. Bernat (1996) evaluates manufacturing and regional economic growth across U.S. states in relation to hypotheses based on Kaldor's laws. Bivand and Szymanski (1997) have investigated the attenuation of neighbourhood effects, suggested to stem from local yardstick competition, following the introduction of compulsory competitive tendering for refuse disposal services in English local authorities. A classic study on price autocorrelation in space is reported in Haining (1983, 1984). In all of these examples, the inclusion of information about the mutual location of the observations makes a difference to the conclusions drawn.
We will now present briefly the basic models of spatial econometrics. Assuming that the variance of the disturbance term is constant, we start from the standard linear regression model:
where 
is an 
vector of observations on a dependent variable taken at each of N locations, 
is an 
matrix of exogenous variables, 
is an 
vector of parameters, and 
is an vector of disturbances. The two alternative forms of spatial dependence models are the spatial lag model:
and the spatial error model:
where 
is a scalar spatial error parameter, and 
is a spatially autocorrelated disturbance vector. These two models can also be related through the Common Factor model (see Burridge, 1981, Bivand, 1984). The use of the non-spatial linear model with spatial data is equivalent to assuming, in the above parameterisation, that 
. The spatial lag and spatial error models can only be combined for estimation if the neighbourhood specifications, here the 
matrices, of the lag and error components differ; for testing, however, the same matrix may be employed.
Dependence between observations in econometrics can stem both from a hypothesised data generation process, such as the kind presented above, and from omitted variable biases, possible even both simultaneously. The spatial lag model is clearly related to a distributed lag interpretation, in that the lagged dependent variable, 
, can be seen as equivalent to the sum of a power series of lagged independent variables stepping out across the map, with the impact of spillovers declining with successively higher powers of 
. This may be termed a structural autoregressive relationship, and one would expect it to be based on economic processes. The alternate model presupposes a shared spatial process affecting all of the variables, and is perhaps more often to be interpreted as indicating missing variables.