The main finding is that e-hail (e.g., Uber and Lyft) may not scale as well as street-hailing taxi.  In other words, a thicker market may help improve the performance of taxi more than that of e-hail. We develop a physical model to describe the matching process of both modes. Using the model, we then derive the production function and measure the returns to scale in the matching process.  It indicates that taxi has returns to scale of  2 (implying increasing returns to scale) whereas e-hail has returns to scale of 1 (constant returns to scale).   Empirical data collected in Shenzhen, China largely confirm the theory.

While this paper has yet to be published, I must have spent more time writing and revising it than any of my other papers.  Hongyu convinced me to write it  for a general journal, which, with the benefit of hindsight, might have caused us to oversell an otherwise fine idea.   That being said, I did learn a lot from the process, and I still think it is one of my better works.   The preprint is here, and the abstract follows.

Uberization promises to transform society based on an intuitive proposition: Advanced peer-to-peer matching guarantees greater overall efficiency. Here we show a paradox challenging this proposition in uberized ride-hail service, known as e-hail. By analyzing hundreds of local markets in Shenzhen, China, we discover e-hail is outperformed—in terms of wait time and trip production—by taxis hailed off street in areas with high densities of passengers and drivers. This paradox arises because a quicker match does not always expedite and enhance a service. On the contrary, it can induce competition that undermines the network effect, making a passenger less likely to benefit from more drivers, and vice versa, in e-hail than in taxi service. Consequently, simply attracting more users may not improve e-hail’s efficiency (defined as trip production at a given density of passengers and drivers), because its competitive edge diminishes with scale. The finding implies uberization has a limited impact on efficiency and is unlikely to create a “winner-take-all” in transportation