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

TL;DR

This study introduces an Abundance-Diversity-Longevity ($ADL$) framework to characterize urban economic complexity and resilience using a decade of DENUE firm data for Mexico City mapped onto a hexagonal grid. By combining Dynamic Time Warping clustering, non-linear regression, and spatial analyses, the work reveals nonlinear, scale-dependent relationships: central areas exhibit power-law growth in abundance and diversity, while peripheral areas tend toward logarithmic saturation, with longevity modulated by spatial context. The findings highlight the importance of neighbor effects and suggest an emergent polycentric restructuring in a traditionally monocentric metropolis, with implications for informality and inclusive urban policy. Overall, the ADL approach offers a scalable, spatially explicit lens to assess urban adaptive capacity and the dynamics of structural transitions in rapidly urbanizing regions.

Abstract

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.

Figures (9)

• Figure 1: Workflow for the spatial and statistical analysis of firm-level data in Mexico City. The diagram summarizes the integration of geospatial and statistical procedures, beginning with combining the DENUE (National Statistical Directory of Economic Units) point layer with the Uber H3 hexagonal grid to generate polygonal spatial layers for analysis. Using INEGI’s georeferenced DENUE catalog of economic units, three properties—abundance, diversity, and longevity (ADL)—were derived for each economic unit. These properties were calculated based on the composition of the units within a homogeneous or one-dimensional spatial analysis unit (H3) for each of the ten years analyzed. Subsequently, these three properties were aggregated for each hexagon: (1) abundance, defined as the total number of economic units within the hexagon; (2) diversity, defined as the number of distinct economic activities present; and (3) longevity, calculated as the average number of years each economic unit appears within the same hexagon. Using this information, a database was constructed in which each record corresponds to a uniquely identified hexagon in Mexico City and contains the three variables representing the ADL properties.
• Figure 2: The total number of units registered DENUE (INEGI) between 2015 and 2024 (left). We can observe a clear upward trend, with a peak in 2017, followed by a period of lower variation beginning in 2019. (right) New economic units registered vs those that disappeared from the directory each year .
• Figure 3: Time Series clusters for abundance (Figure B) and diversity (Figure D). In Figure A, $H_i$ diversity DTW clusters. The stable diversity throughout the city is evident. -say something about the three clusters in the middle. And, in Figure B, the three obtained clusters for the abundance time series. The monocentric nature of Mexico City is depicted in the concentric pattern observed.
• Figure 4: Correlation between the abundance and diversity variables, all periods. Each point represents an $H_i$, and each line represents the obtained fit with the: -Ordinary least squares (OLS), Statmodels Python function used for the fit. Although a global non-linear trend is observed, three regimes, based on the abundance, are also identified, ranging from 1) $0$ to $1000$, 2) $1000$ to $2000$, and 3) from abundance $>2000$.
• Figure 5: Mexico City abundance-diversity bivariate map. Explain something about the monocentric and ring structure observed. Also, what is in the North red Hexagons?