Cross-Section Spatial Regression Models

  • Julie Le GalloEmail author
Living reference work entry


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.


Cross-section spatial regression Spatial autocorrelation Heteroskedasticity Parameter instability Spatial specification tests 


  1. Anselin L (1988) Spatial econometrics, methods and models. Kluwer, DordrechtCrossRefGoogle Scholar
  2. Anselin L (2001) Rao’s score test in spatial econometrics. J Statist Plann Inference 97:113–139CrossRefGoogle Scholar
  3. Anselin L (2010) Thirty years of spatial econometrics. Pap Reg Sci 89:3–25CrossRefGoogle Scholar
  4. 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
  5. 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
  6. Anselin L, Bera A, Florax RGJM, Yoon M (1996) Simple diagnostic test for spatial dependence. Reg Sci Urban Econ 26:77–104CrossRefGoogle Scholar
  7. 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
  8. Casetti E, Can A (1999) The econometric estimation and testing of DARP models. J Geogr Syst 1:91–106CrossRefGoogle Scholar
  9. Cliff A, Ord JK (1972) Testing for spatial autocorrelation among regression residuals. Geogr Anal 4:267–284CrossRefGoogle Scholar
  10. Conley TG (1999) GMM estimation with cross-sectional dependence. J Econ 92:1–44CrossRefGoogle Scholar
  11. Elhorst JP (2010) Applied spatial econometrics: raising the bar. Spat Econ Anal 5:9–28CrossRefGoogle Scholar
  12. Florax RJGM, Folmer H, Rey SJ (2003) Specification searches in spatial econometrics: the relevance of Hendry’s methodology. Reg Sci Urban Econ 33:557–579CrossRefGoogle Scholar
  13. Fotheringham AS, Brundson C, Charlton M (2004) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, ChichesterGoogle Scholar
  14. Halleck Vega S, Elhorst JP (2015) The SLX model. J Reg Sci 55:339–363CrossRefGoogle Scholar
  15. Kelejian HH (2016) Critical issues in spatial models: error term specifications, additional endogenous variables, pre-testing, and Bayesian analysis. Lett Spat Resour Sci 9:113–136CrossRefGoogle Scholar
  16. Kelejian HH, Piras G (2011) An extension of Kelejian’s J-test for non-nested spatial models. Reg Sci Urban Econ 41:281–292CrossRefGoogle Scholar
  17. Kelejian HH, Piras G (2017) Spatial econometrics. Elsevier, AmsterdamGoogle Scholar
  18. Kelejian HH, Prucha I (2007) HAC estimation in a spatial framework. J Econ 140:131–154CrossRefGoogle Scholar
  19. Kelejian HH, Robinson DP (1995) Spatial correlation: a suggested alternative to the autoregressive model. In: Anselin L, Florax RJGM (eds) Advances in spatial econometrics. Springer, HeidelbergGoogle Scholar
  20. Kelejian HH, Robinson DP (1998) A suggested test for spatial autocorrelation and/or heteroskedasticity and corresponding Monte-Carlo results. Reg Sci Urban Econ 28:389–417CrossRefGoogle Scholar
  21. LeSage J, Pace KP (2009) Introduction to spatial econometrics. CRC Press, Boca RatonCrossRefGoogle Scholar
  22. McMillen DP (2003) Spatial autocorrelation or model misspecification? Int Reg Sci Rev 26: 208–217CrossRefGoogle Scholar
  23. Moran P (1950) A test for the serial dependence of the residuals. Biometrika 35:255–260Google Scholar
  24. Mur J, Lopez F, Angulo A (2010) Instability in spatial error models: an application to the hypothesis of convergence in the European case. J Geogr Syst 12:259–280CrossRefGoogle Scholar
  25. Pace RK, LeSage JP (2004) Spatial autoregressive local estimation. In: Getis A, Mur J, Zoller H (eds) Recent advances in spatial econometrics. Palgrave Macmillan, BasingstokeGoogle Scholar
  26. Pace RK, LeSage JP (2008) A spatial Hausman test. Econ Lett 101:282–284CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CESAER UMR1041AgroSup Dijon, INRA, Université de Bourgogne Franche-ComtéDijonFrance

Personalised recommendations