Abundance and Economic diversity as a descriptor of cities' economic complexity

Intricate interactions among firms, institutions, and spatial structures shape urban economic systems. In this study, we propose a framework based on three structural dimensions – abundance, diversity, and longevity (ADL) of economic units – as proxies of urban economic complexity and resilience. Using a decade of georeferenced firm-level data from Mexico City, we analyze the relationships among ADL variables using regression, spatial correlation, and time-series clustering. Our results reveal nonlinear dynamics across urban space, with powerlaw behavior in central zones and logarithmic saturation in peripheral areas, suggesting differentiated growth regimes. Notably, firm longevity modulates the relationship between abundance and diversity, particularly in periurban transition zones. These spatial patterns point to an emerging polycentric restructuring within a traditionally monocentric metropolis. By integrating economic complexity theory with spatial analysis, our approach provides a scalable method to assess the adaptive capacity of urban economies. This has implications for understanding informality, designing inclusive urban policies, and navigating structural transitions in rapidly urbanizing regions.

💡 Research Summary

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The paper introduces a novel framework for quantifying urban economic complexity based on three structural dimensions of economic units: Abundance (the count of firms and institutions within a spatial unit), Diversity (the number of distinct economic activities, measured by NAICS 1‑level codes), and Longevity (the average lifespan of firms, calculated as the number of years each firm appears in the DENUE database). Using a decade of georeferenced firm‑level data for Mexico City (2015‑2024), the authors overlay the data on Uber’s H3 hierarchical hexagonal grid with a 600 m radius (≈1.2 km), yielding 9,644 hexagons, of which 3,988 contain sufficient observations.

The methodological pipeline consists of: (1) constructing annual Abundance and Diversity series for each hexagon, (2) computing average Longevity per hexagon, (3) applying Dynamic Time Warping (DTW) clustering to the 14‑point time series (2010‑2024) to uncover common temporal patterns, (4) performing linear regression and spatial autocorrelation (Moran’s I, LISA) to assess relationships among the ADL variables, and (5) fitting non‑linear models to explore how Abundance and Diversity interact across space.

DTW clustering reveals that Abundance follows a highly homogeneous trajectory: virtually all hexagons belong to a single cluster, indicating a city‑wide, steady increase in the number of firms. Diversity, however, splits into two dominant clusters—approximately 29 % of hexagons show modest, stable diversity, while the remaining 70 % exhibit a stronger upward trend. This bifurcation aligns with a spatial gradient: central districts maintain a richer mix of activities, whereas peripheral zones experience slower diversification.

Regression analyses show that within a hexagon, the correlation between Abundance and Diversity does not explain Longevity. In contrast, the Abundance and Diversity of neighboring hexagons are significant predictors of a hexagon’s average Longevity (positive coefficients, p < 0.01). Spatial autocorrelation metrics confirm clustering of high‑Abundance/High‑Diversity neighborhoods, suggesting that firms’ survival prospects are enhanced by the economic density and variety of adjacent areas—a clear spill‑over effect.

Non‑linear fitting uncovers distinct functional forms across the urban core and periphery. In the central zones, Abundance and Diversity follow a power‑law relationship (D ≈ k·A^α, α≈1.2), implying that each additional firm contributes disproportionately to activity variety. In the outskirts, the relationship saturates logarithmically (D ≈ ln A + c), indicating diminishing returns to diversity as firm counts rise. This dual regime points to differentiated growth dynamics: a “fast‑track” of simultaneous firm creation and diversification in the core, versus a “slow‑track” where firm proliferation outpaces diversification in peripheral districts.

The authors interpret these patterns as evidence of an emerging polycentric restructuring of Mexico City, moving away from its historically monocentric configuration. The modulation of the Abundance‑Diversity link by Longevity, especially pronounced in peri‑urban transition zones, suggests that firm survival is contingent on both local density and the broader spatial context.

Policy implications are threefold: (i) targeted support for peripheral transition zones can boost firm longevity and thus urban resilience; (ii) fostering a polycentric network of activity hubs may enhance overall economic complexity and adaptive capacity; (iii) incorporating Longevity into spatial risk assessments can help identify vulnerable informal sectors and guide inclusive urban planning.

In sum, the ADL framework provides a scalable, data‑driven method to assess the structural underpinnings of urban economies. By integrating economic complexity theory with spatial econometrics, the study offers a nuanced view of how firm abundance, activity diversity, and survival interact across space and time, delivering actionable insights for scholars and policymakers confronting rapid urbanization and structural transitions.