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Interpretation and Computation of Estimates from Regression Models using Spatial Filtering

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  • R. Kelley Pace
  • James P. Lesage
  • Shuang Zhu

Abstract

Spatial filtering in various forms has become a popular way to address spatial dependence in statistical models (Griffith, 2003; Tiefelsdorf & Griffith, 2007). However, spatial filtering faces computational challenges for large n as the current method requires order of n-super-3 operations. This manuscript demonstrates how using iterative eigenvalue routines on sparse weight matrices can make filtering feasible for data sets involving a million or more observations and empirically estimates an operation count on the order of n-super- 1.1 . Moreover, we show that filtering performs better, both statistically and numerically, for spatial weight matrices with more neighbours. Finally, we show that although filtering out spatial aspects of the data reduces bias in parameter estimates for the spatially lagged dependent variable DGP, it also filters out spatial aspects of interest such as spillovers.

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  • R. Kelley Pace & James P. Lesage & Shuang Zhu, 2013. "Interpretation and Computation of Estimates from Regression Models using Spatial Filtering," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 352-369, September.
  • Handle: RePEc:taf:specan:v:8:y:2013:i:3:p:352-369
    DOI: 10.1080/17421772.2013.807355
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    References listed on IDEAS

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    1. Kelley Pace, R. & LeSage, James P., 2008. "A spatial Hausman test," Economics Letters, Elsevier, vol. 101(3), pages 282-284, December.
    2. Daniel A. Griffith, 2000. "A linear regression solution to the spatial autocorrelation problem," Journal of Geographical Systems, Springer, vol. 2(2), pages 141-156, July.
    3. Daniel A. Griffith, 2003. "Spatial Autocorrelation and Spatial Filtering," Advances in Spatial Science, Springer, number 978-3-540-24806-4.
    4. James P. LeSage & R. Kelley Pace & Nina Lam & Richard Campanella & Xingjian Liu, 2011. "New Orleans business recovery in the aftermath of Hurricane Katrina," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(4), pages 1007-1027, October.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach," Environment and Planning A, , vol. 39(5), pages 1193-1221, May.
    7. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    8. Griffith, Daniel A., 2002. "A spatial filtering specification for the auto-Poisson model," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 245-251, July.
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    Cited by:

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    2. Dargel, Lukas & Thomas-Agnan, Christine, 2022. "A generalized framework for estimating spatial econometric interaction models," TSE Working Papers 22-1312, Toulouse School of Economics (TSE).
    3. Di Cagno, Daniela & Fabrizi, Andrea & Meliciani, Valentina & Wanzenböck, Iris, 2016. "The impact of relational spillovers from joint research projects on knowledge creation across European regions," Technological Forecasting and Social Change, Elsevier, vol. 108(C), pages 83-94.
    4. Thomas-Agnan, Christine & Dargel, Lukas, 2023. "Efficient Estimation of Spatial Econometric Interaction Models for Sparse OD Matrices," TSE Working Papers 23-1409, Toulouse School of Economics (TSE).
    5. Christoph Hammer & Aurélien Fichet de Clairfontaine, 2016. "Trade Costs and Income in European Regions," Department of Economics Working Papers wuwp220, Vienna University of Economics and Business, Department of Economics.
    6. Yongwan Chun & Daniel A. Griffith & Monghyeon Lee & Parmanand Sinha, 2016. "Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters," Journal of Geographical Systems, Springer, vol. 18(1), pages 67-85, January.
    7. Donegan, Connor & Chun, Yongwan & Hughes, Amy E., 2020. "Bayesian estimation of spatial filters with Moran's eigenvectors and hierarchical shrinkage priors," OSF Preprints fah3z, Center for Open Science.
    8. Chao Wu & Yu Hua, 2023. "Does Environmental Regulation Have an Employment Dividend? Evidence from China," Sustainability, MDPI, vol. 15(7), pages 1-20, April.
    9. Miguel Gómez-Antonio & Miriam Hortas-Rico & Linna Li, 2016. "The Causes of Urban Sprawl in Spanish Urban Areas: A Spatial Approach," Spatial Economic Analysis, Taylor & Francis Journals, vol. 11(2), pages 219-247, June.
    10. Crespo Cuaresma, Jesus & Doppelhofer, Gernot & Huber, Florian & Piribauer, Philipp, 2015. "Growing Together? Projecting Income Growth in Europe at the Regional Level," Department of Economics Working Paper Series 198, WU Vienna University of Economics and Business.
    11. Aurélien Fichet de Clairfontaine & Manfred Fischer & Rafael Lata & Manfred Paier, 2015. "Barriers to cross-region research and development collaborations in Europe: evidence from the fifth European Framework Programme," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 577-590, March.
    12. Philipp Piribauer, 2016. "Heterogeneity in spatial growth clusters," Empirical Economics, Springer, vol. 51(2), pages 659-680, September.
    13. Daisuke Murakami & Daniel Griffith, 2015. "Random effects specifications in eigenvector spatial filtering: a simulation study," Journal of Geographical Systems, Springer, vol. 17(4), pages 311-331, October.
    14. Daniel A. Griffith & Yongwan Chun, 2016. "Evaluating Eigenvector Spatial Filter Corrections for Omitted Georeferenced Variables," Econometrics, MDPI, vol. 4(2), pages 1-12, June.

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