Accounting for Unobservable Heterogeneity in Cross Section Using Spatial First Differences

TL;DR

This paper introduces a spatial first differences method for identifying causal effects in cross-sectional data with unobservable heterogeneity, especially useful when units are spatially dense, without needing instruments.

Contribution

It proposes a novel cross-sectional design using spatial first differences to control for unobservable heterogeneity, applicable to geographic and environmental studies.

Findings

New estimates of geographic factors on agricultural productivity.

Method effectively isolates causal effects without instruments.

Applicable to land management and climate policy decisions.

Abstract

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.