Working Paper: NBER ID: w25177
Authors: 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.
Keywords: unobservable heterogeneity; spatial first differences; causal inference; agricultural productivity
JEL Codes: C21; I26; Q15; Q51; Q54
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| SFD approach (B51) | unbiased estimates of causal relationships (C51) |
| SFD approach (B51) | causal estimates for relationships confounded by unobservables (C21) |
| geographic factors (R12) | agricultural productivity (Q11) |
| long-term climate and soil conditions (Q54) | maize yields (Q11) |
| unobserved factors shared by adjacent observational units (C21) | estimates of causal relationships (C51) |