Accounting for Unobservable Heterogeneity in Cross Section Using Spatial First Differences

We develop a cross-sectional research design to identify causal effects in the presence of unobservable heterogeneity without instruments. When 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. The identifying assumptions of SFD are similar in mathematical structure and plausibility to other quasi-experimental designs. We use SFD to obtain new estimates for the effects of time-invariant geographic factors, soil and climate, on long-run agricultural productivities --- relationships crucial for economic decisions, such as land management and climate policy, but notoriously confounded by unobservables.