Decomposing and Interpreting Spatial Effects in Spatio-Temporal Analysis: Evidences for Spatial Data Pooled Over Time

Chapter
Part of the Advances in Geographic Information Science book series (AGIS)

Abstract

Empirical applications using individual spatial data pooled over time usually neglect the fact that such data are not only spatially localized: they are also collected over time, i.e. temporally localized. So far, little effort has been devoted to proposing a global way for dealing with spatial data (cross-section) pooled over time, such as real estate transactions, business start-up, crime and so on. However, the spatial effect, in such a context, can be decomposed in two different components: a multidirectional spatial effect (same time period) and a unidirectional spatial effect (previous time period). Based on real estate literature, this chapter presents different spatio-temporal autoregressive (STAR) models and shows how spatial econometrics models can be extended for empirical investigation. Using a Monte Carlo experiment, we underline the effect of neglecting the decomposition of the spatial effect on the bias of the autoregressive coefficients as well as on the interpretation of the marginal effect. An empirical experiment using apartment sales in Paris between 1990 and 2003 supports the global results obtained through the Monte Carlo experiment.

Keywords

Spatio-temporal data Weights matrix Spatial econometric Real estate Data generating process (DGP) 

Notes

Acknowledgement

This research was funded by the Fonds de recherche québécois sur la société et la culture (FRQSC).

References

  1. 1.
    Student (1914) The elimination of spurious correlation due to position in time or space. Biometrika 5:351–360CrossRefGoogle Scholar
  2. 2.
    Anselin L, Bera AK (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
  3. 3.
    Griffith DA (2005) Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Am Geogr 95:740–760CrossRefGoogle Scholar
  4. 4.
    LeSage J, Pace RK (2009) Introduction to spatial econometrics. Taylor & Francis Group, Boca RatonCrossRefGoogle Scholar
  5. 5.
    LeSage J, Pace RK (2004) Models for spatially dependent missing data. J Real Estate Financ Econ 29(2):233–254CrossRefGoogle Scholar
  6. 6.
    Anselin L (2010) Thirty years of spatial econometrics. Pap Reg Sci 89:3–25CrossRefGoogle Scholar
  7. 7.
    Arbia G (2011) A lustrum of SEA: recent research trends following the creation of the spatial econometrics association (2007–2011). Spat Econ Anal 6(4):376–395CrossRefGoogle Scholar
  8. 8.
    Dubé J, Legros D (2013) Dealing with spatial data pooled over time in statistical models. Lett Spat Resour Sci 6:1–18CrossRefGoogle Scholar
  9. 9.
    Rosen S (1974) Hedonic prices and implicit markets: product differentiation in pure competition. J Polit Econ 82:34–55CrossRefGoogle Scholar
  10. 10.
    Can A (1992) Specification and estimation of hedonic housing price models. Reg Sci Urban Econ 22:453–474CrossRefGoogle Scholar
  11. 11.
    Dubin RA (1998) Spatial autocorrelation: a primer. J Hous Econ 7:304–327CrossRefGoogle Scholar
  12. 12.
    Dubin RA, Sung C-H (1987) Spatial variation in the price of housing: rent gradients in non-monocentric cities. Urban Stud 24:193–204CrossRefGoogle Scholar
  13. 13.
    Krige DG (1966) Two-dimensional weighted moving average trend surfaces for ore valuation. J South Afr Inst Min Metall 67:13–38Google Scholar
  14. 14.
    Trigg DW, Leach AG (1967) Exponential smoothing with an adaptive response rate. J Oper Res Soc 18:53–59CrossRefGoogle Scholar
  15. 15.
    Widrow B, Hoff ME (1960) Adaptive switching circuits. In: IRE WESCON Convention Record, Part 4. IRE, New York, pp 96–104Google Scholar
  16. 16.
    Casetti E (1972) Generating models by the expansion method: applications to geographical research. Geogr Anal 4:81–91CrossRefGoogle Scholar
  17. 17.
    Casetti E (1997) The expansion method, mathematical modeling, and spatial econometrics. Int Reg Sci Rev 20:9–33CrossRefGoogle Scholar
  18. 18.
    Cleveland WS, Devlin SJ (1988) Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83:596–610CrossRefGoogle Scholar
  19. 19.
    Fotheringham AS, Brunsdon C, Charlton M (2002) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, LondonGoogle Scholar
  20. 20.
    Fotheringham AS, Charlton ME, Brunsdon C (1998) Geographically weighted regression: a natural evolution of the expansion method for spatial data analysis. Environ Plann A 30: 1905–1927CrossRefGoogle Scholar
  21. 21.
    McMillen DP (1996) One hundred fifty years of land values in Chicago: a nonparametric approach. J Urban Econ 40:100–124CrossRefGoogle Scholar
  22. 22.
    Anselin L (1988) Spatial econometrics: methods and models. Springer, BostonCrossRefGoogle Scholar
  23. 23.
    Dubin R, Pace RK, Thibodeau TG (1999) Spatial autoregression techniques for real estate data. J Real Estate Lit 7:79–96CrossRefGoogle Scholar
  24. 24.
    Ord K (1975) Estimation methods for models of spatial interaction. J Am Stat Assoc 70: 120–126CrossRefGoogle Scholar
  25. 25.
    Gibbons S, Overman HG (2012) Mostly pointless spatial econometrics? J Reg Sci 52:172–191CrossRefGoogle Scholar
  26. 26.
    Corrado L, Fingleton B (2012) Where is the economics in spatial econometrics? J Reg Sci 52:210–239CrossRefGoogle Scholar
  27. 27.
    Small KA, Steimetz SSC (2012) Spatial hedonics and the willingness to pay for residential amenities. J Reg Sci 52:635–647CrossRefGoogle Scholar
  28. 28.
    Dubé J, Legros D (2013) A spatio-temporal measure of spatial dependence: an example using real estate data. Paper Reg Sci 92:19–30Google Scholar
  29. 29.
    Can A, Megbolugbe I (1997) Spatial dependence and house price index construction. J Real Estate Financ Econ 14:203–222CrossRefGoogle Scholar
  30. 30.
    Pace RK, Barry R, Clapp JM, Rodriquez M (1998) Spatiotemporal autoregressive models of neighborhood effects. J Real Estate Financ Econ 17:15–33CrossRefGoogle Scholar
  31. 31.
    Pace RK, Barry R, Gilley OW, Sirmans CF (2000) A method for spatial-temporal forecasting with an application to real estate prices. Int J Forecast 16:229–246CrossRefGoogle Scholar
  32. 32.
    Gelfand AE, Ecker MD, Knight JR, Sirmans CF (2004) The dynamics of location in home price. J Real Estate Financ Econ 29:149–166CrossRefGoogle Scholar
  33. 33.
    Tu Y, Yu SM, Sun H (2004) Transaction-based office price indexes: a spatiotemporal modeling approach. Real Estate Econ 32:297–328CrossRefGoogle Scholar
  34. 34.
    Sun H, Tu Y, Yu SM (2005) A Spatio-temporal autoregressive model for multi-unit residential market analysis. J Real Estate Financ Econ 31:155–187CrossRefGoogle Scholar
  35. 35.
    Smith TE, Wu P (2009) A spatio-temporal model of housing prices based on individual sales transactions over time. J Geogr Syst 11(4):333–355CrossRefGoogle Scholar
  36. 36.
    Nappi-Choulet I, Maury T-P (2009) A spatiotemporal autoregressive price index for the paris office property market. Real Estate Econ 37(2):305–340CrossRefGoogle Scholar
  37. 37.
    Huang B, Wu B, Barry M (2010) Geographically and temporally weighted regression for modeling spatiotemporal variation in house prices. Int J Geogr Inf Sci 24(3):383–401CrossRefGoogle Scholar
  38. 38.
    Nappi-Choulet I, Maury T-P (2011) A spatial and temporal autoregressive local estimation for the paris housing market. J Reg Sci 51(4):732–750CrossRefGoogle Scholar
  39. 39.
    Thanos S, Bristow AL, Wardman MR (2012) Theoretically consistent temporal ordering specification in spatial hedonic pricing models applied to the valuation of aircraft noise. J Environ Econ Policy 1(2):103–126CrossRefGoogle Scholar
  40. 40.
    Liu X (2013) Spatial and temporal dependence in house price prediction. J Real Estate Financ Econ 47:341–369CrossRefGoogle Scholar
  41. 41.
    Dubé J, Legros D (2014) Spatial econometrics and spatial data pooled over time: towards an adapted modelling approach. J Real Estate Lit 22(1):101–125Google Scholar
  42. 42.
    Dubé J, Legros D (2014) Spatial econometrics using microdata. Wiley, LondonCrossRefGoogle Scholar
  43. 43.
    Dubé J, Baumont C, Legros D (2013) Matrices de pondérations et contexte spatio-temporel en économétrie spatiale. Revue Canadienne de science régionale 36(1/3):57–75Google Scholar
  44. 44.
    Des Rosiers F, Dubé J, Thériault M (2011) Do peer effects shape property values? J Property Invest Financ 29(4/5):510–528CrossRefGoogle Scholar
  45. 45.
    LeSage J (2014) What regional scientists need to know about spatial econometrics. Rev Reg Stud 44:13–32Google Scholar
  46. 46.
    Getis A, Aldstadt J (2004) Constructing the spatial weights matrix using a local statistic. Geogr Anal 36:90–104CrossRefGoogle Scholar
  47. 47.
    Haining RP (2009) Spatial autocorrelation and the quantitative revolution. Geogr Anal 41: 364–374CrossRefGoogle Scholar
  48. 48.
    Pinkse J, Slade ME (2010) The future of spatial econometrics. J Reg Sci 50:103–117CrossRefGoogle Scholar
  49. 49.
    McMillen DP (2010) Issues in spatial data analysis. J Reg Sci 50:119–141CrossRefGoogle Scholar
  50. 50.
    Legendre P (1993) Spatial autocorrelation: trouble or new paradigm? Ecology 74(6): 1659–1673CrossRefGoogle Scholar
  51. 51.
    Pace RK, Barry R (1997) Quick computation of spatial autoregressive estimators. Geogr Anal 29:232–246CrossRefGoogle Scholar
  52. 52.
    Dubé J, Legros D, Thériault M, Des Rosiers F (2014) A spatial difference-in-differences estimator to evaluate the effect of change in public mass transit systems on house prices. Transp Res B 64:24–40CrossRefGoogle Scholar
  53. 53.
    LeSage J (1999) Applied econometrics using Matlab. www.spatial-econometrics.com
  54. 54.
    Anselin L, Florax R (1995) New directions in spatial econometrics. Springer, New YorkCrossRefGoogle Scholar
  55. 55.
    Lee L-F (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925CrossRefGoogle Scholar
  56. 56.
    Kelejian HH, Prucha IR (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):99–121CrossRefGoogle Scholar
  57. 57.
    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
  58. 58.
    Kelejian HH, Prucha IR (2007) The relative efficiencies of various predictors in spatial econometric models containing spatial lags. Reg Sci Urban Econ 37(3):363–374CrossRefGoogle Scholar
  59. 59.
    Kelejian HH, Prucha IR (2007) HAC estimation in a spatial framework. J Econ 140(2007): 131–154CrossRefGoogle Scholar
  60. 60.
    Kelejian HH, Prucha IR (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. J Econ 140(1):53–130CrossRefGoogle Scholar
  61. 61.
    Adkins LC, Gade MN (2012) Monte Carlo experiments using stata: a primer with examples. Working paper. http://learneconometrics.com
  62. 62.
    Dubé J, Legros D (2015) Modeling spatial data pooled over time: schematic representation and Monte Carlo evidences. Theor Econ Lett 5:132–154CrossRefGoogle Scholar
  63. 63.
    Smith TE (2009) Estimation bias in spatial models with strongly connected weight matrices. Geogr Anal 41:307–332CrossRefGoogle Scholar
  64. 64.
    Hamilton JD (1994) Time series analysis. Princeton University Press, PrincetonGoogle Scholar
  65. 65.
    Dubé J, Legros D (2014) Spatial econometrics and the hedonic pricing model: what about the temporal dimension? J Prop Res 31(4):333–359CrossRefGoogle Scholar
  66. 66.
    Dubé J, Baumont C, Legros D (2011) Utilisation des matrices de pondérations en économétrie spatiale: Proposition dans un contexte spatio-temporel, Documents de travail du Laboratoire d’Économie et de Gestion (LEG), Université de Bourgogne, e2011–01, 33pGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Université LavalQuébecCanada
  2. 2.Université de BourgogneDijonFrance

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