1 INTRODUCTION
Spatial dependence models deal with spatial interaction (spatial autocorrelation) and spatial
structure (spatial heterogeneity) primarily in cross-section data, see Anselin (1988, 1999).
Spatial dependence models use a metric of economic distance, see Anselin (1988) and Conley
(1999) to mention a few. This measure of economic distance provides cross-sectional data with
a structure similar to that provided by the time index in time series. There is an extensive
literature estimating these spatial models using maximum likelihood methods, see Anselin
(1988). More recently, generalized method of moments have been proposed by Kelejian and
Prucha (1999) and Conley (1999). Testing for spatial dependence is also extensively studied
by Anselin (1988, 1999), Anselin and Bera (1998), Anselin, Bera, Florax and Yoon (1996) to
mention a few.
With the increasing availability of micro as well as macro level panel data, spatial panel data
models studied in Anselin (1988) are becoming increasingly attractive in empirical economic
research. See Case (1991), Kelejian and Robinson (1992), Case, Hines and Rosen (1993),
Holtz-Eakin (1994), Driscoll and Kraay (1998), Baltagi and Li (1999) and Bell and Bockstael
(2000) for a few applications. Convergence in growth models that use a pooled set of countries
over time could have spatial correlation as well as heterogeneity across countries to contend
with, see Delong and Summers (1991) and Islam (1995) to mention a few studies. County
level data over time, whether it is expenditures on police, or measuring air pollution levels can
be treated with these models. Also, state level expenditures over time on welfare benefits,
mass transit, etc. Household level survey data from villages observed over time to study
nutrition, female labor participation rates, or the effects of education on wages could exhibit
spatial correlation as well as heterogeneity across households and this can be modeled with
a spatial error component model.
Estimation and testing using panel data models have also been extensively studied, see Hsiao
(1986) and Baltagi (2001), but these models ignore the spatial correlation. Heterogeneity
across the cross-sectional units is usually modeled with an error component model. A La-
grange multiplier test for random effects was derived by Breusch and Pagan (1980), and an
extensive Monte Carlo on testing in this error component model was performed by Baltagi,
Chang and Li (1992). This paper extends the Breusch and Pagan LM test to the spatial
error component model. First, a joint LM test is derived which simultaneously tests for the
existence of spatial error correlation as well as random region effects. This LM test is based
on the estimation of the model under the null hypothesis and its computation is simple requir-
ing only least squares residuals. This test is important, because ignoring spatial correlation
and heterogeneity due to the random region effects will result in ine¢cient estimates and