How Likely are Ride-share Drivers to Earn a Living Wage? Large-scale Spatio-temporal Density Smoothing with the Graph-fused Elastic Net

Ride-sourcing or transportation network companies (TNCs) provide on-demand transportation service for compensation, connecting drivers of personal vehicles with passengers through smartphone applications. In this study, we consider the problem of estimating a spatiotemporally varying probability distribution for the productivity of a TNC driver, using data on more than 1.2 million TNC trips in Austin, Texas. We propose a graph-based smoothing approach that allows for distinct spatial and temporal dynamics, including different degrees of smoothness, spatio-temporal interactions, and interpolation in regions with little or no data. For such a goal, we introduce the Graph-fused Elastic Net (GFEN) and use it in combination with a dyadic tree decomposition for density estimation. In addition, we present an optimization-driven approach for fast point estimates scalable to massive graphs. Bayesian inference and uncertainty quantification with MCMC are also illustrated. The main results demonstrate that the optimization strategy is an effective exploration tool for selecting adequate regularization schemes using Bayesian optimization of the cross-validation loss. Two key empirical findings made possible by our method include: 1) the probability that a TNC driver can expect to earn a living wage in Austin exhibits high variability in space and time, from as low as 25% to as high as 85%; and 2) some drivers suffer considerable "tail risk", with the bottom 10% of the earnings distribution falling below $10 per hour -- grossly below a living wage in Austin for a single adult -- for specific times and locations. All code and data for the paper are publicly available, as a Shiny app for visualizing the results and a software package in Julia for implementing the GFEN.