Universal resilience patterns in labor markets

Cities are the innovation centers of the US economy, but technological disruptions can exclude workers and inhibit a middle class. Therefore, urban policy must promote the jobs and skills that increase worker pay, create employment, and foster economic resilience. In this paper, we model labor market resilience with an ecologically-inspired job network constructed from the similarity of occupations’ skill requirements. This framework reveals that the economic resilience of cities is universally and uniquely determined by the connectivity within a city’s job network. US cities with greater job connectivity experienced lower unemployment during the Great Recession. Further, cities that increase their job connectivity see increasing wage bills, and workers of embedded occupations enjoy higher wages than their peers elsewhere. Finally, we show how job connectivity may clarify the augmenting and deleterious impact of automation in US cities. Policies that promote labor connectivity may grow labor markets and promote economic resilience.

In this section, we consider the job network constructed with an alternative skill similarity metric.
Specifically, we measure the Jaccard similarity of the O*NET skills required by each occupation according to where O(i, s) is the relative weight of skill s in job i. The universality of the skill complexity of cities is consistent for this alternative job network construction (see Fig. S3 and Fig. S4). represent total employment in the city. As an alternative method, we consider the job-job network constructed from Jaccard skill similarity. City Total Employment Figure S4: The equilibrium solutions of our model for each city while varying γ and the rate of job match dissolution λ after controlling for the skill matching complexity in each city w c eff . Each panel represents a difference choice of γ. As an alternative method, we consider the job-job network constructed from Jaccard skill similarity. Symbol size and color represent total employment in the city. Solid line is the analytically-derived equilibrium solution e c eff .

Supplementary Note 3: Robustness of the job network connectivity definition
Our job network connectivity w eff depends on the definition of the job network w i j . Here we study the robustness of w eff with respect to the different assumptions made to build the job network.
Firstly we made w c i j = 0 in city c for jobs i with the number of jobs E c j = 0 in the BLS data. Since BLS does not report occupations i that have less than 30 people employed by city we are effectively using a threshold in our definition, i.e. w c i j = 0 if E c j < θ . Figure S5 shows that w eff does not change when that threshold is increased beyond 30. In fact, cross-correlation of the values are pretty high  Figure S6 shows that the values of w eff are pretty robust against the actual set of skills used to calculate the job network.
In summary, both tests performed in this section show that our definition of w eff and, in turn, our results do not depend critically on the assumptions made to construct the job network.

Supplementary Note 7: Simulating Labor Flows within City
For a given city c, we simulate the employment of occupation E i and the flow of workers between unemployment U i and another occupation j using eq. (2) from the main text: Here, λ captures the exogenous rate of job match dissolution, w i j measures skill matching between occupations based on occupations' required O*NET skills, and α captures exogenous forces aside from skill matching that shape inter-occupational career mobility.
The simulation starts using the empirical employment distribution on c according to Occupational Employment Statistics (OES) from the US Bureau of Labor Statistics (BLS). We integrate the system using 10,000 iterations of Forward Euler integration with a time step of ∆t = 0.5 to allow the system to reach a steady state. The system is evaluated once it reaches a steady state at the end of the simulation to avoid transient dynamics.
For simulations of employment shocks from automation, the system is integrated for an additional 1,000 iterations after the removal of occupations with exposure to automation above some threshold θ . An occupation's exposure to automation is determined using estimates from 2 .
If occupation i has exposure to automation above θ , then we simulate that systemic shock by setting     Table S1 for variable definitions and data sources.           The percentage change in job connectivity w c eff (see main text for definition) in city c in year2 compared to in year1. 100 · (w c year2,eff − w c year1,eff )/w c year1,eff  Year