Endogeneity in Spatial Models

  • Julie Le Gallo
  • Bernard FingletonEmail author
Living reference work entry


The objective of this chapter is to provide an overview of estimation methods of spatial regression models including endogenous variables in addition to the spatial lag variable. We first provide evidence that spatial autocorrelation matters when dealing with endogenous variables. In particular, in terms of estimation, omitting a spatial lag and using spatially autocorrelated instruments induces bias in instrumental variables estimates. In terms of testing, wrongly omitted spatial autocorrelation under the form of a spatial lag or a spatial error significantly decreases the power of Hausman and Sargan tests, which are widely used in applied microeconometrics. We then describe instrumental variables, generalized method of moments and maximum likelihood procedures for cross-sectional and panel spatial models including endogenous variables, and suggest how standard diagnostics might be adapted given the presence of spatial error dependence. We finish by presenting other identification strategies, drawing from the impact evaluation econometrics literature, and discuss how they can be adapted in a spatial context.


Spatial autocorrelation Endogenous variables Instrumental variables Hausman test Sargan test Stable unit treatment value assumption 

JEL Classification

C21 C23 C26 C31 C33 C36 


  1. Anselin L, Kelejian HH (1997) Testing for spatial error autocorrelation in the presence of endogenous regressors. Int Reg Sci Rev 20(1–2):153–182CrossRefGoogle Scholar
  2. Arellano M, Bond S (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev Econ Stud 58(5):277–297CrossRefGoogle Scholar
  3. Baltagi B (ed) (2013) Econometric analysis of panel data, 5th edn. Wiley, New YorkGoogle Scholar
  4. Baltagi B, Fingleton B, Pirotte A (2019) A time-space dynamic panel data model with spatial moving average errors. Reg Sci Urban Econ. 76:13–31. Scholar
  5. Betz T, Cook SJ, Hollenbach FM (2019) Spatial interdependence and instrumental variable models. Polit Sci Res Methods. (forthcoming)
  6. Bond S (2002) Dynamic panel data models: a guide to micro data methods and practice. Port Econ J 1(2):141–162CrossRefGoogle Scholar
  7. Bowsher C (2002) On testing overidentifying restrictions in dynamic panel data models. Econ Lett 77(2):211–220CrossRefGoogle Scholar
  8. Cerulli G (2017) Identification and estimation of treatment effects in the presence of (correlated) neighborhood interactions: model and Stata implementation via ntreated. Stata J 17(4):803–833CrossRefGoogle Scholar
  9. Delgado MS, Florax RJGM (2015) Difference- in-differences techniques for spatial data: local autocorrelation and spatial interaction. Econ Lett 137:123–126CrossRefGoogle Scholar
  10. Drukker DM, Egger P, Prucha IR (2013) On two-step estimation of a spatial autoregressive model with autoregressive disturbances and endogenous regressors. Econ Rev 32(5–6):686–733CrossRefGoogle Scholar
  11. Fingleton B, Le Gallo J (2007) Finite sample properties of estimators of spatial models with autoregressive, or moving average, disturbances and system feedback. Ann Econ Stat (87/88):39–62Google Scholar
  12. Fingleton B, Le Gallo J (2008) Estimating spatial models with endogenous variables, a spatial lag and spatially dependent disturbances: finite sample properties. Pap Reg Sci 87(3):319–339CrossRefGoogle Scholar
  13. Keele L, Titiunik R (2018) Geographic natural experiments with interference: the effect of all-mail voting on turnout in Colorado. CESifo Econ Stud 64(2):127–149CrossRefGoogle Scholar
  14. Kelejian HH, Prucha IR (2004) Estimation of simultaneous systems of spatially interrelated cross sectional equations. J Econ 118(1-2):27–50CrossRefGoogle Scholar
  15. Kelejian HH, Prucha IR (2007) HAC estimation in a spatial framework. J Econ 140(1):131–154CrossRefGoogle Scholar
  16. Lee L-f (2007) GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. J Econ 137(2):489–514CrossRefGoogle Scholar
  17. Le Gallo J, Fingleton B (2012) Measurement errors in a spatial context. Reg Sci Urban Econ 42(1-2):114–125CrossRefGoogle Scholar
  18. Le Gallo J, Mutl J (2014) Autocorrélation spatiale des erreurs et erreurs de mesure: quelles interactions? Rég Dév 40-2014:37–52Google Scholar
  19. Liu X (2012) On the consistency of the LIML estimator of a spatial autoregressive model with many instruments. Econ Lett 116(3):472–475CrossRefGoogle Scholar
  20. Liu X, Saraiva P (2015) GMM estimation of SAR models with endogenous regressors. Reg Sci Urban Econ 55(5–6):68–79CrossRefGoogle Scholar
  21. Liu X, Saraiva P (2019) GMM estimation of spatial autoregressive models in a system of simultaneous equations with het-eroskedasticity. Econ Rev 38(4):359–385CrossRefGoogle Scholar
  22. Pesaran MH (ed) (2015) Time series and panel data econometrics. Oxford University Press, OxfordGoogle Scholar
  23. Yang K, Lee L-f (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models. J Econ 196(1):196–214CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.CESAER UMR 1041AgroSup Dijon, INRA, Université de Bourgogne Franche-ComtéDijonFrance
  2. 2.Department of Land EconomyUniversity of CambridgeCambridgeUK

Personalised recommendations