Journal of Geographical Systems

, Volume 14, Issue 1, pp 5–28 | Cite as

Dynamic spatial panels: models, methods, and inferences

  • J. Paul Elhorst
Original Article


This paper provides a survey of the existing literature on the specification and estimation of dynamic spatial panel data models, a collection of models for spatial panels extended to include one or more of the following variables and/or error terms: a dependent variable lagged in time, a dependent variable lagged in space, a dependent variable lagged in both space and time, independent variables lagged in time, independent variables lagged in space, serial error autocorrelation, spatial error autocorrelation, spatial-specific and time-period-specific effects. The survey also examines the reasoning behind different model specifications and the purposes for which they can be used, which should be useful for practitioners.


Dynamic effects Spatial spillover effects Identification Estimation methods Stationarity conditions 

JEL Classification

C21 C23 C51 



The author would like to thank Jan Jacobs, three anonymous referees, the editor of this journal, and the participants of the 5th World Conference of the Spatial Econometrics Association in Toulouse 2011 for valuable comments on a previous version of this paper.


  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer, DordrechtGoogle Scholar
  2. Anselin L, Le Gallo J, Jayet H (2008) Spatial panel econometrics. In: Mátyás L, Sevestre P (eds) The econometrics of panel data, fundamentals and recent developments in theory and practice, 3rd edn. Kluwer, Dordrecht, pp 627–662Google Scholar
  3. Arrelano M (2003) Panel data econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  4. Arrelano M, Bond S (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev Econ Stud 58(2):277–297CrossRefGoogle Scholar
  5. Balestra P, Nerlove M (1966) Pooling cross-section and time-series data in the estimation of a dynamic model: the demand for natural gas. Econometrica 34(3):585–612CrossRefGoogle Scholar
  6. Baltagi BH (2005) Econometric analysis of panel data, 3rd edn. Wiley, ChichesterGoogle Scholar
  7. Baltagi BH, Song SH, Koh W (2003) Testing panel data models with spatial error correlation. J Econom 117(1):123–150CrossRefGoogle Scholar
  8. Baltagi BH, Song SH, Jung BC, Koh W (2006) Testing for serial correlation, spatial autocorrelation and random effects using panel data. J Econom 140(1):5–51CrossRefGoogle Scholar
  9. Baltagi BH, Egger P, Pfaffermayr M (2007) A generalized spatial panel data model with random effects.
  10. Beck N (2001) Time-series-cross-section data: what have we learned in the past few years? Ann Rev Polit Sci 4:271–293CrossRefGoogle Scholar
  11. Beenstock M, Felsenstein D (2007) Spatial vector autoregressions. Spatial Econ Anal 2(2):167–196CrossRefGoogle Scholar
  12. Bhargava A, Sargan JD (1983) Estimating dynamic random effects models from panel data covering short time periods. Econometrica 51(6):1635–1659CrossRefGoogle Scholar
  13. Blanchard OJ, Katz LF (1992) Regional evolutions. Brookings Pap Econ Act 23(1):1–75CrossRefGoogle Scholar
  14. Blundell R, Bond S (1998) Initial conditions and moment restrictions in dynamic panel data models. J Econom 87(1):115–143CrossRefGoogle Scholar
  15. Brady RR (2011) Measuring the diffusion of housing prices across space and time. J Appl Econom 26(2):213–231CrossRefGoogle Scholar
  16. Bun M, Carree M (2005) Bias-corrected estimation in dynamic panel data models. J Bus Econ Stat 3(2):200–211CrossRefGoogle Scholar
  17. Burridge P (1981) Testing for a common factor in a spatial autoregression model. Environ Plan A 13(7):795–800CrossRefGoogle Scholar
  18. Cressie N, Wikle CK (2011) Statistics for spatial-temporal data. Wiley, BlackwellGoogle Scholar
  19. Debarsy N, Ertur C, LeSage JP (2011) Interpreting dynamic space-time panel data models. Stat Methodol. doi: 10.1016/j.stamet.2011.02.002
  20. De Groot AJ, Elhorst JP (2010). Labour market effects of flexicurity from a regional perspective. Tijdschrift voor Economische en Sociale Geografie [J Econ Soc Geogr] 101(4):392–408Google Scholar
  21. Driscoll JC, Kraay AC (1998) Consistent covariance matrix estimation with spatially dependent data. Rev Econ Stat 80(4):549–560CrossRefGoogle Scholar
  22. Elhorst JP (2001) Dynamic models in space and time. Geogr Anal 33(2):119–140CrossRefGoogle Scholar
  23. Elhorst JP (2003) Specification and estimation of spatial panel data models. Int Reg Sci Rev 26(3):244–268CrossRefGoogle Scholar
  24. Elhorst JP (2005) Unconditional maximum likelihood estimation of linear and log-linear dynamic models for spatial panels. Geogr Anal 37(1):62–83CrossRefGoogle Scholar
  25. Elhorst JP (2008a) Serial and spatial autocorrelation. Econ Lett 100(3):422–424CrossRefGoogle Scholar
  26. Elhorst JP (2008b) A spatiotemporal analysis of aggregate labour force behaviour by sex and age across the European Union. J Geogr Syst 10(2):167–190CrossRefGoogle Scholar
  27. Elhorst JP (2010a) Spatial panel data models. In: Fischer MM, Getis A (eds) Handbook of applied spatial analysis. Springer, Berlin, Heidelberg and New York, pp 377–407CrossRefGoogle Scholar
  28. Elhorst JP (2010b) Matlab software for spatial panels. Paper presented at 4th world conference of the spatial econometric association, ChicagoGoogle Scholar
  29. Elhorst JP (2010c) Applied spatial econometrics: raising the bar. Spatial Econ Anal 5(1):9–28CrossRefGoogle Scholar
  30. Elhorst JP (2010d) Dynamic panels with endogenous interaction effects when T is small. Reg Sci Urban Econ 40(5):272–282CrossRefGoogle Scholar
  31. Elhorst JP, Piras G, Arbia G (2010a) Growth and convergence in a multi-regional model with space-time dynamics. Geogr Anal 42(3):338–355CrossRefGoogle Scholar
  32. Elhorst JP, Zandberg E, De Haan J (2010b) The impact of interaction effects among neighboring countries on financial reform: a dynamic spatial panel data approach. Mimeo, GroningenGoogle Scholar
  33. Enders W (1995) Applied econometric time series. Wiley, New YorkGoogle Scholar
  34. Ertur C, Koch W (2007) Growth, technological interdependence and spatial externalities: theory and evidence. J Appl Econom 22(6):1033–1062CrossRefGoogle Scholar
  35. Fingleton B, Le Gallo J (2008) Estimating spatial models with endogenous variables, a spatial lag en spatially dependent disturbances: finite sample properties. Pap Reg Sci 87(3):319–339CrossRefGoogle Scholar
  36. Franzese RJ Jr, Hays JC (2007) Spatial econometric models of cross-sectional interdependence in political science panel and time-series-cross-section data. Political Anal 15(2):140–164CrossRefGoogle Scholar
  37. Greene WH (2005) Econometric analysis, 6th edn. Pearson Prentice Hall, New JerseyGoogle Scholar
  38. Hahn J, Kuersteiner G (2002) Asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and T are large. Econometrica 70(4):1639–1657CrossRefGoogle Scholar
  39. Hamilton JD (1994) Time series analysis. Princeton University Press, New JerseyGoogle Scholar
  40. Hendry DF (1995) Dynamic econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  41. Hsiao C (2003) Analysis of panel data, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  42. Hsiao C, Pesaran MH, Tahmiscioglu AK (2002) Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. J Econom 109(1):107–150CrossRefGoogle Scholar
  43. Jacobs JPAM, Ligthart JE, Vrijburg H (2009) Dynamic panel data models featuring endogenous interaction and spatially correlated errors.
  44. Kapoor M, Kelejian HH, Prucha IR (2007) Panel data models with spatially correlated error components. J Econom 140(1):97–130CrossRefGoogle Scholar
  45. Kelejian HH, Prucha IR (1998) A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. J Real Estate Finance Econ 17(1):99–121CrossRefGoogle Scholar
  46. Kelejian HH, Prucha IR (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. Int Econ Rev 40(2):509–533CrossRefGoogle Scholar
  47. Kelejian HH, Prucha IR (2002) 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Reg Sci Urban Econ 32(6):691–707CrossRefGoogle Scholar
  48. Kelejian HH, Prucha IR (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. J Econom 157(1):53–67CrossRefGoogle Scholar
  49. Kelejian HH, Prucha IR, Yuzefovich Y (2006) Estimation problems in models with spatial weighting matrices which have blocks of equal elements. J Reg Sci 46(3):507–515CrossRefGoogle Scholar
  50. Kholodilin KA, Siliverstovs B, Kooths S (2008) A dynamic panel data approach to the forecasting of the GDP of German Länder. Spatial Econ Anal 3(2):195–207CrossRefGoogle Scholar
  51. Kiviet JF (1995) On bias, inconsistency and efficiency of some estimators in dynamic panel data models. J Econom 68(1):53–78CrossRefGoogle Scholar
  52. Korniotis GM (2010) Estimating panel models with internal and external habit formation. J Bus Econ Stat 28(1):145–158CrossRefGoogle Scholar
  53. Kukenova M, Monteiro JA (2009) Spatial dynamic panel model and system GMM: a Monte Carlo investigation.
  54. Lee LF (2004) Asymptotic distribution of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925CrossRefGoogle Scholar
  55. Lee LF, Yu J (2010a) Some recent developments in spatial panel data models. Reg Sci Urban Econ 40(5):255–271CrossRefGoogle Scholar
  56. Lee LF, Yu J (2010b) Estimation of spatial autoregressive panel data models with fixed effects. J Econom 154(2):165–185CrossRefGoogle Scholar
  57. Lee LF, Yu J (2010c). Efficient GMM estimation of spatial dynamic panel data models with fixed effects.
  58. Lee LF, Yu J (2010d) A spatial dynamic panel data model with both time and individual fixed effects. Econom Theory 26(2):564–597CrossRefGoogle Scholar
  59. LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press Taylor & Francis Group, Boca RatonCrossRefGoogle Scholar
  60. Nerlove M (1999) Properties of alternative estimators of dynamic panel models: an empirical analysis of cross-country data for the study of economic growth. In: Hsiao C, Lahiri K, Lee LF, Pesaran MH (eds) Analysis of panels and limited dependent variable models. Cambridge University Press, Cambridge, pp 136–170CrossRefGoogle Scholar
  61. Nerlove M, Balestra P (1996) Formulation and estimation of econometric models for panel data. In: Mátyás L, Sevestre P (eds) The econometrics of panel data, 2nd revised edition. Dordrecht, Kluwer, pp 3–22Google Scholar
  62. Newey W, West K (1987) A simple positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55(3):703–708CrossRefGoogle Scholar
  63. Nickell S (1981) Biases in dynamic models with fixed effects. Econometrica 49(6):1417–1426CrossRefGoogle Scholar
  64. Parent O, LeSage JP (2010) A spatial dynamic panel model with random effects applied to commuting times. Transp Res Part B 44(5):633–645CrossRefGoogle Scholar
  65. Parent O, LeSage JP (2011) A space-time filter for panel data models containing random effects. Comput Stat Data Anal 55(1):475–490CrossRefGoogle Scholar
  66. Pesaran MH, Tosetti E (2011) Large panels with common factors and spatial correlation. J Econom 161(2):182–202CrossRefGoogle Scholar
  67. Yang Z, Li C, Tse YK (2006) Functional form and spatial dependence in spatial panels. Econ Lett 91(1):138–145CrossRefGoogle Scholar
  68. Yu J, De Jong R, Lee L (2008) Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large. J Econom 146(1):118–134CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Economics and EconometricsUniversity of GroningenGroningenThe Netherlands

Personalised recommendations