Urban Sprawl in Shrinking Cities: Causal Evidence from Brazil

Across many urban systems, cities continue to expand physically even as their populations decline. This spatial-demographic mismatch, which we refer to as shrinking but sprawling cities, raises important questions about the economic consequences of urban expansion under demographic contraction. Using data for more than 5,500 Brazilian municipalities between 2010 and 2022, we estimate the causal impact of urban sprawl on labor productivity in municipalities experiencing population decline. To address endogeneity, we implement a two-stage least squares strategy that instruments population shrinkage using a SPEI-based shift-share design and urban sprawl using spatial diffusion in urban expansion across neighboring municipalities. We find that urban sprawl significantly reduces labor productivity growth in municipalities experiencing population decline. The negative interaction between shrinkage and sprawl is robust across sectors and to multiple robustness checks. These findings suggest that spatial expansion under demographic contraction weakens agglomeration forces and generates significant productivity losses in urban systems.