Local Estimation of Spatial Autocorrelation Processes

  • Fernando LópezEmail author
  • Jesús Mur
  • Ana Angulo
Part of the Advances in Spatial Science book series (ADVSPATIAL)


The difficulties caused by the lack of stability in the parameters of an econometric model are well known: biased and inconsistent estimators, misleading tests and, in general, wrong inference. Their importance explains the attention that the literature has dedicated to the problem. The first formal test of parameter stability is that of Chow (1960), which considers only one break point, known a priori, under the assumption of constant variances. Dufour (1982) extends the discussion to the case of multiple regimes and Phillips and Ploberger (1994) and Rossi (2005) place it in a context of model selection. Simultaneously, Quandt (1960) started another line of research in which the break point is unknown and the variance can change. The CUSUM test, based on recursive residuals (Brown et al. 1975), the various methods for endogenizing the choice of the break point (as in Banerjee et al. 1992), and the extension to multiple structural changes in a system of equations (Qu and Perron 2007) are natural proposals in this line. Other more peculiar approaches include the tests for continuous parameter variation (Hansen 1996), the Markov switching regression (García and Perron 1996) and the Bayesian approaches (e.g., Salazar 1982; Zivot and Phillips and Ploberger 1994; Koop and Potter 2007).


Spatial Dependence Gaussian Mixture Model Structural Break Local Estimation Geographically Weight Regression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been carried out with the financial support of project SEJ2006–02328/ECON of the Ministerio de Ciencia y Tecnología of the Reino de España.


  1. Anselin L (1988a) Spatial econometrics: methods and models. Kluwer, DordrechtGoogle Scholar
  2. Anselin L (1988b) Lagrange multiplier test diagnostics for spatial dependence and spatial heterogeneity. Geogr Anal 20:1–17CrossRefGoogle Scholar
  3. Anselin L (1990) Spatial dependence and spatial structural instability in applied regression analysis. J Reg Sci 30:185–207CrossRefGoogle Scholar
  4. Anselin L (1995) Local indicators of spatial association. Geogr Anal 27:93–115CrossRefGoogle Scholar
  5. Anselin L, Bera A (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah A, Giles D (eds) Handbook of applied economic statistics. Marcel Dekker, New York, pp 237–289Google Scholar
  6. Banerjee A, Lumsdaine R, Stock J (1992) Recursive and sequential tests of the unit root and trend break hypotheses: theory and international evidence. J Bus Econ Stat 10:271–287Google Scholar
  7. Battisti M, Di Vaio G (2007) A spatially filtered mixture of P-convergence regressions for EU regions, 1980–2002. Empir Econ 34:105–121CrossRefGoogle Scholar
  8. Baumol W (1986) Productivity growth, convergence, and welfare: what the long-run data show. Am Econ Rev 76:1072–1085Google Scholar
  9. Bloom D, Canning D, Sevilla J (2003) Geography and poverty traps. J Econ Growth 8:355–378CrossRefGoogle Scholar
  10. Breusch T, Pagan A (1979) A simple test for heteroscedasticity and random coefficient variation. Econometrica 47:1287–1294CrossRefGoogle Scholar
  11. Brown R, Durbin J, Evans J (1975) Techniques for testing the constancy of regression relationships over time. J Roy Stat Soc B 37:149–192Google Scholar
  12. Brunsdom C, Fotheringham S, Charlton M (1996) Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal 28:281–298CrossRefGoogle Scholar
  13. Brunsdom C, Fotheringham S, Charlton M (1998) Spatial nonstationarity and autoregresive models. Environ Plann A 30:957–973CrossRefGoogle Scholar
  14. Casetti E (1972) Generating models by the expansion method. application to geographical research. Geogr Anal 4:81–91CrossRefGoogle Scholar
  15. Casetti E (1991) The investigation of parameter drift by expanded regressions: generalities and a family planning example. Environ Plann A 23:1045–1051CrossRefGoogle Scholar
  16. Chow G (1960) Tests of equality between sets of coefficients in two linear regressions. Econometrica 28:591–605CrossRefGoogle Scholar
  17. Cleveland W (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74:829–836CrossRefGoogle Scholar
  18. Cleveland W, Devlin S (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83:596–610CrossRefGoogle Scholar
  19. Cressie N (1991) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  20. Davidson J (2000) Econometric theory. Blackwell, New YorkGoogle Scholar
  21. Di Giacinto V (2003) Differential regional effects of monetary policy: a geographical SVAR approach. Int Reg Sci Rev 7:313–341CrossRefGoogle Scholar
  22. Dufour J (1982) Recursive stability analysis of linear regression relationships. J Econometrics 19:21–76CrossRefGoogle Scholar
  23. Ertur C, LeGallo J, Baumond C (2006) The regional convergence process, 1980–1995: do spatial regimes and spatial dependence matter? Int Regional Sci Rev 29:3–34CrossRefGoogle Scholar
  24. Ertur C, LeGallo J, LeSage J (2007) Local versus global convergence in Europe: a Bayesian spatial econometric approach. Rev Reg Stud 37:82–108Google Scholar
  25. Fisher M, Stirböck C (2006) Pan-European regional income growth and club-convergence. Insights from a spatial econometric perspective. Ann Reg Sci 40:693–721Google Scholar
  26. Florax R, de Graaff T (2004) The performance of diagnostics tests for spatial dependence in linear regression models: a meta-analysis of simulation studies. In: Anselin L, Florax R, Rey S (eds) Advances in spatial econometrics: methodology, tools and applications. Springer, Berlin, pp 29–65Google Scholar
  27. Florax R, Folmer H, Rey S (2003) Specification searches in spatial econometrics: the relevance of Hendry’s methodology. Reg Sci Urban Econ 33:557–579CrossRefGoogle Scholar
  28. García R, Perron P (1996) An analysis of the real interest rate under regime shifts. Rev Econ Stat 78:111–125CrossRefGoogle Scholar
  29. Getis A, Ord J (1992) The analysis of spatial association by use of distance statistics. Geog Anal 24:189–206CrossRefGoogle Scholar
  30. Greene W (2003) Econometric analysis. Prentice Hall, New YorkGoogle Scholar
  31. Hansen B (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64:413–430CrossRefGoogle Scholar
  32. Huang J (1984) The autoregressive moving average model for spatial analysis. Aust J Stat 26:169–178CrossRefGoogle Scholar
  33. Koop G, Potter S (2007) Estimation and forecasting in models with multiple breaks. Rev Econ Stud 74:763–789CrossRefGoogle Scholar
  34. Lacombe D (2004) Does econometric methodology matter? An analysis of public policy using spatial econometric techniques. Geogr Anal 36:105–118Google Scholar
  35. LeGallo J, Dall’erba S (2006) Evaluating the temporal and spatial heterogeneity of the European convergence process, 1980–1999. J Reg Sci 46:269–288CrossRefGoogle Scholar
  36. LeGallo J, Ertur C, Baumont C (2003) A spatial econometric analysis of convergence across European regions, 1980–1995. In: Fingleton B (ed) European regional growth. Springer, Berlin, pp 99–130Google Scholar
  37. McLachlan G, Peel D (2000) Finite mixture models. Wiley, New YorkCrossRefGoogle Scholar
  38. McMillen D (1996) One hundred fifty years of land values in chicago: a nonparametric approach. J Urban Econ 40:100–124CrossRefGoogle Scholar
  39. McMillen D (2004) Employment densities, spatial autocorrelation, and subcenters in large metropolitan areas. J Reg Sci 44:225–244CrossRefGoogle Scholar
  40. McMillen D, McDonald J (1997) A nonparametric analysis of employment density in a policentric city. J Reg Sci 37:591–612CrossRefGoogle Scholar
  41. Mur J, López F, Angulo A (2008) Symptoms of instability in models of spatial dependence. Geogr Anal 40:189–211CrossRefGoogle Scholar
  42. Pace K, Lesage J (2004) Spatial autoregressive local estimation. In: Getis A, Mur J, Zoller H (eds) Spatial econometrics and spatial statistics. Palgrave, London, pp 31–51Google Scholar
  43. Páez A, Uchida T, Miyamoto K (2002a) A general framework for estimation and inference of geographically weighted regression models: 1: location-specific kernel bandwidth and a test for locational heterogeneity. Environ Plann A 34:733–754CrossRefGoogle Scholar
  44. Páez A, Uchida T, Miyamoto K (2002b) A general framework for estimation and inference of geographically weighted regression models: 2: spatial association and model specification tests. Environ Plann A 34:883–904CrossRefGoogle Scholar
  45. Parent O, Riou S (2005) Bayesian analysis of knowledge: spillovers in European regions. J Reg Sci 45:747–775CrossRefGoogle Scholar
  46. Phillips P, Ploberger W (1994) Posterior odds testing for a unit root with data-based model selection. Economet Theor 10:774–808CrossRefGoogle Scholar
  47. Quah D (1986) Regional convergence clusters across Europe. Eur Econ Rev 40:951–958CrossRefGoogle Scholar
  48. Quandt R (1960) Tests of the hypothesis that a linear regression system obeys two separate regimes. J Am Stat Assoc 55:324–330CrossRefGoogle Scholar
  49. Qu Z, Perron P (2007) Estimating and testing structural changes in multivariate regressions. Econometrica 75:459–502CrossRefGoogle Scholar
  50. Ramajo J, Márquez M, Hewings G, Salinas M (2008) Spatial heterogeneity and interregional spillovers in the European Union: do cohesion policies encourage convergence across regions? Eur Econ Rev 52:551–567CrossRefGoogle Scholar
  51. Rietveld P, Wintershoven H (1998) Border effects and spatial autocorrelation in the supply of network infrastructure. Paper Reg Sci 77:265–276CrossRefGoogle Scholar
  52. Rossi B (2005) Optimal tests for nested model selection with underlying parameter instability. Econ Theor 21:962–990Google Scholar
  53. Salazar D (1982) Structural changes in time series models. J Econometrics 19:147–163CrossRefGoogle Scholar
  54. Seber G (1984) Multivariate observations. Wiley, New YorkCrossRefGoogle Scholar
  55. Titterington D, Smith A, Makov U (1985) Statistical analysis of finite mixture distributions. Wiley, New YorkGoogle Scholar
  56. Tsionas E (2000) Regional growth and convergence: evidence from the United States. Reg Stud 34:231–238CrossRefGoogle Scholar
  57. Zivot E, Phillips P (1994) A Bayesian analysis of trend determination in economic time series. Economet Rev 13:291–336CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Quantitative Methods and ComputingTechnical University of CartagenaCartagenaSpain

Personalised recommendations