Accounting for Unobservable Heterogeneity in Cross Section Using Spatial First Differences

Hannah Druckenmiller, Solomon Hsiang

NBER Working Paper No. 25177
Issued in October 2018, Revised in June 2019
NBER Program(s):Development Economics Program, Economics of Education Program, Environment and Energy Program, Economic Fluctuations and Growth Program, Health Economics Program, Industrial Organization Program, International Trade and Investment Program, Labor Studies Program, Public Economics Program, Political Economy Program

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.

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Document Object Identifier (DOI): 10.3386/w25177

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