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Spatial Differencing: Estimation and Inference

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Abstract

Spatial differencing is a spatial data transformation pioneered by Holmes (1998) increasingly used to estimate casual effects with non-experimental data. Recently, this transformation has been widely used to deal with omitted variable bias generated by local or site-specific unobservables in a “boundary-discontinuity” design setting. However, as well known in this literature, spatial differencing makes inference problematic. Indeed, given a specific distance threshold, a sample unit may be the neighbor of a number of units on the opposite side of a specific boundary inducing correlation between all differenced observations that share a common sample unit. By recognizing that the spatial differencing transformation produces a special form of dyadic data, we show that the dyadic-robust variance matrix estimator proposed by Cameron and Miller (2014) is, in general, a better solution compared to the most commonly used estimators.

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  • Federico Belotti & Edoardo Di Porto & Gianluca Santoni, 2017. "Spatial Differencing: Estimation and Inference," CSEF Working Papers 474, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  • Handle: RePEc:sef:csefwp:474
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    1. Federico Belotti & Edoardo Di Porto & Gianluca Santoni, 2018. "Spatial Differencing: Estimation and Inference," CESifo Economic Studies, CESifo Group, vol. 64(2), pages 241-254.
    2. Sandra E. Black, 1999. "Do Better Schools Matter? Parental Valuation of Elementary Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 577-599.
    3. Chirinko, Robert S. & Wilson, Daniel J., 2008. "State investment tax incentives: A zero-sum game?," Journal of Public Economics, Elsevier, vol. 92(12), pages 2362-2384, December.
    4. Gilles Duranton & Laurent Gobillon & Henry G. Overman, 2011. "Assessing the Effects of Local Taxation using Microgeographic Data," Economic Journal, Royal Economic Society, vol. 121(555), pages 1017-1046, September.
    5. Elias Einiö & Henry G. Overman, 2016. "The (Displacement) Effects of Spatially Targeted Enterprise Initiatives: Evidence from UK LEGI," SERC Discussion Papers 0191, Centre for Economic Performance, LSE.
    6. Gibbons, Stephen & Machin, Stephen & Silva, Olmo, 2013. "Valuing school quality using boundary discontinuity," LSE Research Online Documents on Economics 45246, London School of Economics and Political Science, LSE Library.
    7. Gibbons, Stephen & Machin, Stephen & Silva, Olmo, 2013. "Valuing school quality using boundary discontinuities," Journal of Urban Economics, Elsevier, vol. 75(C), pages 15-28.
    8. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    9. Fack, Gabrielle & Grenet, Julien, 2010. "When do better schools raise housing prices? Evidence from Paris public and private schools," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 59-77, February.
    10. Federico Belotti & Edoardo Di Porto & Gianluca Santoni, 2021. "The effect of local taxes on firm performance: Evidence from geo‐referenced data," Journal of Regional Science, Wiley Blackwell, vol. 61(2), pages 492-510, March.
    11. Oskari Harjunen & Mika Kortelainen & Tuukka Saarimaa, 2018. "Best Education Money Can Buy? Capitalization of School Quality in Finland," CESifo Economic Studies, CESifo Group, vol. 64(2), pages 150-175.
    12. Kahn, Matthew E., 2004. "Domestic pollution havens: evidence from cancer deaths in border counties," Journal of Urban Economics, Elsevier, vol. 56(1), pages 51-69, July.
    13. Thomas J. Holmes, 1998. "The Effect of State Policies on the Location of Manufacturing: Evidence from State Borders," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 667-705, August.
    14. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
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    Cited by:

    1. Augusto Cerqua & Guido Pellegrini, 2020. "Local multipliers at work," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 29(4), pages 959-977.
    2. Federico Belotti & Edoardo Di Porto & Gianluca Santoni, 2018. "Spatial Differencing: Estimation and Inference," CESifo Economic Studies, CESifo Group, vol. 64(2), pages 241-254.
    3. Federico Belotti & Edoardo Di Porto & Gianluca Santoni, 2021. "The effect of local taxes on firm performance: Evidence from geo‐referenced data," Journal of Regional Science, Wiley Blackwell, vol. 61(2), pages 492-510, March.

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    More about this item

    Keywords

    Spatial differencing; Boundary discontinuity; robust inference; dyadic data.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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