Conditional Agglomeration in China’s Northeast Rust Belt: Density, Structural Orientation, and Ownership-Mixing Entropy

Northeast China’s rust-belt cities have faced persistent concerns about stagnating labor productivity amid structural change. This paper examines how the productivity payoff to urban density depends on local economic structure and ownership composition using an annual panel of prefecture-level cities. We estimate two-way fixed-effects models with city and year effects and city-clustered standard errors, complemented by dynamic specifications and additional robustness checks. The results show a robust positive within-city association between population density and labor productivity. This density premium is structure-conditioned: the productivity payoff to density is significantly larger in city-years that are more industry-oriented. Information-theoretic measures further show that sectoral and ownership composition matter in distinct ways. A normalized entropy measure based on 19 all-city sectoral employment categories is positively associated with labor productivity, while its interaction with density is negative and significant, indicating that the density premium is weaker in more sectorally balanced city-years. A normalized four-category ownership entropy measure, constructed from SOE, private/self-employed, collective, and other employment shares, is positively associated with labor productivity and interacts positively with density, indicating a stronger density–productivity association in city-years with a more balanced ownership composition. Collectively, the findings suggest that urban density is not a uniform engine of productivity: its payoff depends on whether dense city economies are organized around productive sectoral linkages and a sufficiently balanced ownership environment. Overall, the evidence supports a conditional agglomeration view in which productivity dynamics in Northeast China reflect the interaction of density, structural orientation, sectoral dispersion, and ownership mixing.