Advertisement

Cliometrica

, Volume 2, Issue 1, pp 49–83 | Cite as

Minimum distance estimation of the spatial panel autoregressive model

  • Théophile AzomahouEmail author
Original Paper
  • 139 Downloads

Abstract

This paper contributes to the interface literature of new methodological foundation of analyzing historical data with space and spatio-temporal phenomena. In particular, I consider estimating the spatial panel autoregressive model using the minimum distance estimator. Spatial autoregression has important implications for economic system that typifies correlatedness across many spatial locations and which could evolve over long span of time. To overcome computational difficulties, I suggest a two-stage estimation procedure based on minimum distance estimators. A striking feature of the proposed model is that minimum distance estimates are derived under common slopes and complete equality of parameters across spatial units. Assumption of common slopes across spatial units is an empirical and theoretical plausibility as many spatial units are observed to share common trend and typology of changes occurring to the individual system under which equality of parameters are possibilities. The estimation strategy allows various restrictions on time-varying vector parameters. Moreover, those restrictions can easily be tested. I apply this procedure to the residential demand for water of 115 French municipalities over the biannual period 1988–1993. The primary contribution of the paper is to the methodological side of cliometrics while the empirical application (with shorter time period) has been presented for illustrative purpose although, it can nonetheless be readily applied to historical data with long-time horizon allowing for restrictions such as spatio-temporal common vector and structural break in parameter estimates.

Keywords

Spatial dependence Panel data Minimum distance estimator Residential demand for water 

JEL Classification

C13 C23 D12 Q25 

Notes

Acknowledgments

I gratefully acknowledge François Laisney, two referees and the editor of this journal for comments leading to improvements in the paper. The usual disclaimer applies.

References

  1. Akerlof G (1997) Social distance and social choice. Econometrica 65:1005–1027Google Scholar
  2. Anselin L (1988a) Lagrange multiplier test diagnostics for spatial dependence and spatial heterogeneity. Geogr Anal 20:1–17Google Scholar
  3. Anselin L (1988b) Spatial econometrics methods and models. Kluwer, DordrechtGoogle Scholar
  4. Anselin L, Bera A (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Truchmuche A (ed) Handbook of applied economic statistics, pp 237–289Google Scholar
  5. Baltagi BH, Li D (2002) Prediction in the panel data model with spatial correlation. In: Luc Anselin, Raymon Florax (eds) New advances in spatial econometrics (forthcoming)Google Scholar
  6. Bell KP, Bockstael NE (2000) Applying the generalized-moments estimation approach to spatial problems involving microlevel data. Rev Econ Stat 82(1):72–82Google Scholar
  7. Case A (1987) On the use of spatial autoregressive models in demand analysis. Discussion papers, Princeton University, Woodrow Wilson School, p 135Google Scholar
  8. Case A (1991) Spatial patterns in household demand. Econometrica 59:953 –965Google Scholar
  9. Chen X, Conley T (2001) A new semiparametric spatial model for panel time series. J Econ 105:59–83Google Scholar
  10. Cliff AD, Ord JK (1981) Spatial processes models and applications. Pion, LondonGoogle Scholar
  11. Conley T (1999) Generalized method of moments estimation with cross sectional dependence. J Econ 92:1–45Google Scholar
  12. Cressie N (1991) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  13. Deaton A (1990) Price elasticities from survey data: extensions and Indonesian results. J Appl Econ 44:281–309Google Scholar
  14. Driscoll JC, Kraay AC (1998) Consistent covariance matrix estimation with spatially dependent panel data. Rev Econ Stat 80(4):549–560Google Scholar
  15. Getis A, Ord JK (1992) The analysis of spatial association by use of distance statistics. Geogr Anal 24:189–206Google Scholar
  16. Gouriéroux C, Monfort A (1989) Statistiques et Modèles Économétriques, vol. 1–2. Économica, ParisGoogle Scholar
  17. Gouriéroux C, Monfort A, Trognon A (1985) Moindres Carrés Asymptotiques. Annale de l’INSEE 58:91–122Google Scholar
  18. Griffith DA (1988) Advanced spatial statistics. Kluwer, DordrechtGoogle Scholar
  19. Hanke SH, de Maré (1982) Residential water demand a pooled times series and cross-section study of Malmö, Sweden. Water Resour Bull 18(4):621–625Google Scholar
  20. Hansen L (1982) Large sample properties of generalized method of moments estimators. Econometrica 50:1029–1054Google Scholar
  21. Hansen LG (1996) Water and energy price impacts on residential water demand in Copenhagen. Land Econ 72(1):66–79Google Scholar
  22. Hewitt JA, Hanemann WM (1995) A discret continuous choice approach to residential water demand under block rate pricing. Land Econ 71(2):173–192Google Scholar
  23. Howe CW (1982) The impact of price on residential water demand new insights. Water Resour Res 18(4):713–716Google Scholar
  24. INSEE (1998) Tableaux de l’Économie Lorraine. Institut National de la Statistique et des Études ÉconomiquesGoogle Scholar
  25. Kelejian H, Prucha I (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbance. J Real Estate Financ Econ 17(1):99–121Google Scholar
  26. Kelejian H, Prucha I (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. Int Econ Rev 40:509–533Google Scholar
  27. Kodde DA, Palm FC, Pfann GA (1990) Asymptotic least-squares estimation: efficiency considerations and applications. J Appl Econ 5:229–243Google Scholar
  28. Lee L-F (2004) Asymptotic Distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72:1899–1925CrossRefGoogle Scholar
  29. LeSage JP, Dowd MR (1997) Analysis of spatial contiguity influences on state price level formation. Int J Forcast 2:245–253Google Scholar
  30. Nauges C, Thomas A (2000) Privately operated water utilities, municipal price negotiation, and estimation of residential water demand: the case of France. Land Econ 76(81):68–85Google Scholar
  31. Pinkse J, Slade ME, Brett C (2002) Spatial price competition: a semiparametric approach. Econometrica 70:1111–1153CrossRefGoogle Scholar
  32. Silverman BW (1986) Density estimation for statistics and data analysis, 1st edn. Chapman & Hall, LondonGoogle Scholar
  33. Valiron F (1994) Memento du Gestionnaire de l’Eau et de l’Assainissement, Tome 1, Eau dans la ville. Lavoisier—Technique et Documentation, ParisGoogle Scholar
  34. Wand MP, Jones M (1995) Kernel smoothing. Chapman and Hall, LondonGoogle Scholar
  35. Yoo S-H, Yang C-Y (2000) Dealing with bottled water expenditures data with zero observations: a semiparametric specification. Econ Lett 66:151–157Google Scholar
  36. Ziliak JP, Wilson BA, Stones JA (1999) Spatial dynamics and heterogeneity in the cyclicality of real wages. Rev Econ Stat 81(2):227–236Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Bureau d’Économie Théorique et Appliquée (BETA-Theme)Université Louis PasteurStrasbourg CedexFrance

Personalised recommendations