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Unit Root and Cointegration Tests in Spatial Cross-Section Data

  • Michael Beenstock
  • Daniel Felsenstein
Chapter
  • 566 Downloads
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

Although nonstationarity arises in time series data, it may also arise in spatial cross-section data. A definition of spatial nonstationarity is provided in which spatial impulse responses do not weaken with distance. Hence, remote shocks have the same effect on outcomes in a location, as do shocks in its immediate neighbors. This definition implies that the SAR coefficients tends to unity. Analytical methods are used to derive spatial impulse responses when space is lateral (east–west), and simulation methods are used when space is bilateral (east–west, north–south). A lattice based spatial unit root test is proposed to test for spatial nonstationarity, and its critical values are calculated using Monte Carlo simulation methods. We show that these critical values depend on the specification of W.

Since space is finite, the asymptotic properties of spatial unit root tests are undefined. Specifically, because finite space has edges, unit roots that would arise if space was infinite, do not arise when space is finite, because locations on the edge of space are less spatially connected than their counterparts in the epicenter of space. We use simulation methods to show how edge effects weaken spatial unit roots.

If spatial cross-section data are nonstationary, spatial cross-section regression parameter estimates may be spurious or nonsense. A spatial cointegration test is proposed in which, under the null, the variables concerned are not spatially cointegrated, in which event the parameter estimates are genuine. They are spatially cointegrated if the residual errors are spatially stationary. If they are spatially cointegrated, their parameter estimates are super-consistent. Monte Carlo methods are used to calculate critical values to test for spatial cointegration in cross-section data.

References

  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic, DordrechtCrossRefGoogle Scholar
  2. Beenstock M, Felsenstein D (2012) Nonparametric estimation of the spatial connectivity matrix using spatial panel data. Geogr Anal 44(4):386–397CrossRefGoogle Scholar
  3. Beenstock M, Feldman D, Felsenstein D (2012) Testing for unit roots and cointegration in spatial cross-section data. Spat Econ Anal 7(2):203–222CrossRefGoogle Scholar
  4. Cressie NAC (1993) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  5. Davidson R, MacKinnon JG (2009) Econometric theory and methods. Oxford University Press, New YorkGoogle Scholar
  6. Engle R, Granger CWJ (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 35:251–276CrossRefGoogle Scholar
  7. Fingleton B (1999) Spurious spatial regression: some Monte Carlo results with spatial unit roots and spatial cointegration. J Reg Sci 39:1–19CrossRefGoogle Scholar
  8. Florax RJGM, Folmer H, Rey SJ (2003) Specification searches in spatial econometrics: the relevance of Hendry’s methodology. Reg Sci Urban Econ 33:557–559CrossRefGoogle Scholar
  9. Granger CWJ (1969) Spatial data and time series analysis. In: Scott A (ed) Studies in regional science, London papers in regional science. Pion, London, pp 1–24Google Scholar
  10. Hendry DF (1995) Dynamic econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  11. Lauridsen J, Kosfeld R (2004) A Wald test for spatial nonstationarity. Estudios de Economia Aplicada 22:475–486Google Scholar
  12. Lauridsen J, Kosfeld R (2006) A test strategy for spurious spatial regression, spatial nonstationarity, and spatial cointegration. Pap Reg Sci 85:363–377CrossRefGoogle Scholar
  13. Lauridsen J, Kosfeld R (2007) Spatial cointegration and heteroscedasticity. J Geogr Syst 9:253–265CrossRefGoogle Scholar
  14. Lee L-F, Yu J (2009) Spatial nonstationarity and spurious regression: the case with a row-normalized spatial weights matrix. Spat Econ Anal 4:301–327CrossRefGoogle Scholar
  15. Mur J, Trivez FJ (2003) Unit roots and deterministic trends in spatial econometric models. Int Reg Sci Rev 26:289–312CrossRefGoogle Scholar
  16. Sargent TJ (1979) Macroeconomic theory. Academic, New YorkGoogle Scholar
  17. Stakhovych S, Bijmolt THA (2008) Specification of spatial models: a simulation study on weights matrices. Pap Reg Sci 88:389–409CrossRefGoogle Scholar
  18. Yule GU (1926) Why do we sometimes get nonsense-correlations between time series? A study in sampling and the nature of time series. J R Stat Soc 89:1–64CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Beenstock
    • 1
  • Daniel Felsenstein
    • 2
  1. 1.Department of EconomicsHebrew University of JerusalemJerusalemIsrael
  2. 2.Department of GeographyHebrew University of JerusalemJerusalemIsrael

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