Inferring Networks of Interdependent Labor Skills to Illuminate Urban Economic Structure

Cities are among the best examples of complex systems. The adaptive components of a city, such as its people, firms, institutions, and physical structures, form intricate and often non-intuitive interdependencies with one another. These interdependencies can be quantified and represented as links of a network that give visibility to otherwise cryptic structural elements of urban systems. Here, we use aspects of information theory to elucidate the interdependence network among labor skills, illuminating parts of the hidden economic structure of cities. Using pairwise interdependencies we compute an aggregate, skills-based measure of system “tightness” of a city’s labor force, capturing the degree of integration or internal connectedness of a city’s economy. We find that urban economies with higher tightness tend to be more productive in terms of higher GDP per capita. However, related work has shown that cities with higher system tightness are also more negatively affected by shocks. Thus, our skills-based metric may offer additional insights into a city’s resilience. Finally, we demonstrate how viewing the web of interdependent skills as a weighted network can lead to additional insights about cities and their economies.


S1. Further network analysis/visualizations Importance Network
There are two different measure of the O*Net elements, levels and importance. Despite measuring different aspects of the elements, the resulting networks are qualitatively similar. Figure S1-1 displays the network created from the importance measure of the element. We applied the Louvain community detection algorithm (1) and, like the element network, found three communities. After removing edges less than zero, the overall network is polarized into two main groups, "sensory-physical" and "socio-cognitive" skills. As with the network created using the level measure instead of importance, the socio-cognitive lobe was found to have two sub-components illustrative of technical skills (green) and more general socio-cognitive skills (red). Sensory-physical elements are yellow.
Figure S1-1. Importance Network. Elements are nodes with color indicating community: yellow = sensory-physical skills; green = technical socio-cognitive skills; and red = general sociocognitive skills.

Network Statistics
Looking at two broad measures, density and average degree, further supports that the two element networks are similar to one another and different from the IWA network (Table S1-1). Consistent with reported figures, the networks analyzed exclude edges with weights below zero. Density is the number of edges present as a share of all possible edges and average degree is the average of how many edges each node has. The two element networks have slightly over half of all possible edge present while the IWA network has slightly under half of all possible edges present. The average degree of the element networks, however, is substantially lower than the IWA network which has substantially more nodes than the element networks. For each network, the nodes (elements or IWAs) with the highest degrees are reported in table S1-2. A nodes degree is simply the number of other nodes it is connected to. While the two element networks are visually similar to one another, the top five nodes differ with only oral comprehension appearing in both. The closeness centrality of a node is a measure of distance to all other nodes. The 5 nodes with the highest closeness centrality are reported in table S1-3. Closeness centrality for any given node is the number of nodes divided by the sum of all the shortest path lengths from that node to all other nodes. The measure ranges from zero to one with one representing a direct link to all other nodes. Closeness centrality has been identified as a measure of the ease at which a node can obtain information (2). In contrast to degree, the two element networks have three common nodes among the highest in the network: speech clarity, oral comprehension, and oral expression. Nodes in the socio-cognitive: general group account for nine of the top ten nodes in terms of element (level) closeness centrality. In stark contrast, nodes in the sensory-physical community account entirely for the nodes with the lowest closeness centrality for levels. Finally, the highest betweenness centrality scores are reported in table S1-4. Betweenness centrality measures the share of shortest paths that include the node. The highest betweenness measures are notably higher in the element networks, reflecting the polarized nature of these networks. The nodes with the highest betweenness are located at the narrow points in between the two polarized portions of the network. These are skills that may be able to bridge the gap between the polarized regions of the networks and allow workers with these skills to easily transition between the two substantially different portions of the network.

S2. Mapping O*NET occupation codes to BLS occupation codes
In our analysis we paired O*NET version 24.2 (3) with the Bureau of Labor Statistics (BLS) 2018 occupational employment statistics (4). These two entities use slightly different occupation codes. In particular, the BLS uses the federal standard 6-digit code, while O*NET adds an extra 2-digits so that occupations may be further divided. Here we describe in detail our procedure for linking the two data sets.
With two exceptions, every O*NET occupation code can be mapped to one BLS occupation code. In most cases, one O*NET code maps to one and only one BLS code, as in the following example: This leaves the two exceptions requiring further processing. O*NET version 24.2 still uses one occupation code that the was retired by the BLS after its 2016 data release: 25-3099 -Miscellaneous Teaching Occupations. In 2017 the BLS replaced this occupation code with two new codes, 25-3097 -Teachers and Instructors, All Other, Except Substitute Teachers, and 25-3098 -Substitute Teachers. O*Net 24.2 continues to use the older code. Therefore, first map O*Net values to the old BLS code 25-3099, and then apply those element averages to the two BLS occupations that replaced 25-3099, namely 25-3097 and 25-3098.
The full mapping is included in the accompanying file: bls_onet_crosswalk_2018.csv

S3. Mapping Metropolitan Statistical Areas
Despite using the term metropolitan statistical area (MSA) to describe its geographical areas of aggregation, the Bureau of Labor (BLS) statistics actually uses an alternative geospatial unit in the six New England states. These units are known at New England City and Town Areas or NECTAs (5). This presents problems of matching labor data to almost every other federal data set, including GDP data we take from the U.S. Bureau of Labor Statistics (BEA). Thus, we created a mapping of areas used by the BLS to corresponding areas used by the BEA. These units have similar names but do not cover the same geographical areas. However, as we are using rates (e.g. per capita GDP) and not gross numbers, we accept these as generally applicable to their NECTA counterparts. Table S3-2 presents the metropolitan areas used by the BLS (NECTAs) to aggregate labor data and how we mapped them to metropolitan areas used by the BEA (MSAs).

S4. List of O*NET elements and individual work activities (IWAs) used
The O*Net dataset decomposes occupations into a set of attributes called elements, which are assigned values for dimensions such as importance and level. The full list of these elements is shown in Table S4-1. O*Net additional decomposes occupations into a set of individual work activities (IWAs), which are either present or absent for each occupation. The complete list of IWAs is presented in Table S4-2. In both tables, each element's assigned cluster, as determined by the Louvain community detection algorithm, is show.

S5. Further statistical analysis
The correlation between skills tightness and GDP per capita remain positive and significant when controlling for MSA population. As correlations are reported in the paper, regressions analysis of GDP Per Capita are reported in Table S0-1.