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Accounting for Unobservable Heterogeneity in Cross Section Using Spatial First Differences

Author

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  • Hannah Druckenmiller
  • Solomon Hsiang
Abstract
We develop a simple cross-sectional research design to identify causal effects that is robust to unobservable heterogeneity. When many observational units are dense in physical space, it may be sufficient to regress the “spatial first differences” (SFD) of the outcome on the treatment and omit all covariates. This approach is conceptually similar to first differencing approaches in time-series or panel models, except the index for time is replaced with an index for locations in space. The SFD design identifies plausibly causal effects, even when no instruments are available, so long as local changes in the treatment and unobservable confounders are not systematically correlated between immediately adjacent neighbors. We demonstrate the SFD approach by recovering new cross-sectional estimates for the effects of time-invariant geographic factors, soil and climate, on long-run average crop productivities across US counties — relationships that are notoriously confounded by unobservables but crucial for guiding economic decisions, such as land management and climate policy.

Suggested Citation

  • Hannah Druckenmiller & Solomon Hsiang, 2018. "Accounting for Unobservable Heterogeneity in Cross Section Using Spatial First Differences," NBER Working Papers 25177, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25177
    Note: DEV ED EEE EFG EH IO ITI LS PE POL
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    References listed on IDEAS

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    Cited by:

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    5. Ariel Ortiz-Bobea, 2021. "Climate, Agriculture and Food," Papers 2105.12044, arXiv.org.
    6. Richard S.J. Tol, 2020. "The Economic Impact of Weather and Climate," Video Library 2094, Department of Economics, University of Sussex Business School.
    7. Linsenmeier, Manuel, 2021. "Temperature variability and long-run economic development," SocArXiv xvucn, Center for Open Science.
    8. Diane Alexander & Hannes Schwandt, 2022. "The Impact of Car Pollution on Infant and Child Health: Evidence from Emissions Cheating," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 2872-2910.
    9. Justin B. Winikoff & Dominic P. Parker, 2024. "Farm size, spatial externalities, and wind energy development," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(4), pages 1518-1543, August.
    10. Robert Gonzalez, 2022. "Mobile phone access and insurgent violence: Evidence from a radio wave propagation model in Afghanistan," HiCN Working Papers 370, Households in Conflict Network.
    11. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
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    13. Albouy, David & Christensen, Peter & Sarmiento-Barbieri, Ignacio, 2020. "Unlocking amenities: Estimating public good complementarity," Journal of Public Economics, Elsevier, vol. 182(C).
    14. Sayed Morteza Malaekeh & Layla Shiva & Ammar Safaie, 2024. "Investigating the economic impact of climate change on agriculture in Iran: Spatial spillovers matter," Agricultural Economics, International Association of Agricultural Economists, vol. 55(3), pages 433-453, May.

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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • I26 - Health, Education, and Welfare - - Education - - - Returns to Education
    • Q15 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Land Ownership and Tenure; Land Reform; Land Use; Irrigation; Agriculture and Environment
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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