This chapter provides a selective survey of specification issues in spatial econometrics. We first present the most commonly used spatial specifications in a cross-sectional setting in the form of linear regression models including a spatial lag and/or a spatial error term, heteroskedasticity or parameter instability. Second, we present a set of specification tests that allow checking deviations from a standard, i.e., non-spatial, regression model. Focus is on unidirectional, multidirectional and robust LM tests, since these require only the estimation of the model under the null. Because of the complex links between spatial autocorrelation and spatial heterogeneity, we devote attention to the specifications incorporating both aspects and to the associated specification tests.
Anselin L, Bera AK (1998) Spatial dependence in linear regression models with an application to spatial econometrics. In: Ullah A, Giles DEA (eds) Handbook of applied economics statistics. Springer, BerlinGoogle Scholar
Anselin L, Florax RGJM (1995) Small sample properties of tests for spatial dependence in regression models: some further results. In: Anselin L, Florax RJGM (eds) New directions in spatial econometrics. Springer, BerlinCrossRefGoogle Scholar
Anselin L, Bera A, Florax RGJM, Yoon M (1996) Simple diagnostic test for spatial dependence. Reg Sci Urban Econ 26:77–104CrossRefGoogle Scholar
Arbia G (2011) A lustrum of SEA: recent research trends flowing the creation of the spatial econometrics association (2007–2011). Spat Econ Anal 6:377–395CrossRefGoogle Scholar
Casetti E, Can A (1999) The econometric estimation and testing of DARP models. J Geogr Syst 1:91–106CrossRefGoogle Scholar
Cliff A, Ord JK (1972) Testing for spatial autocorrelation among regression residuals. Geogr Anal 4:267–284CrossRefGoogle Scholar