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Ride-sourcing or transportation network companies (TNCs) provide on-demandtransportation service for compensation, connecting drivers of personalvehicles with passengers through smartphone applications. In this study, weconsider the problem of estimating a spatiotemporally varying probabilitydistribution for the productivity of a TNC driver, using data on more than 1.2million TNC trips in Austin, Texas. We propose a graph-based smoothing approachthat allows for distinct spatial and temporal dynamics, including differentdegrees of smoothness, spatio-temporal interactions, and interpolation inregions with little or no data. For such a goal, we introduce the Graph-fusedElastic Net (GFEN) and use it in combination with a dyadic tree decompositionfor density estimation. In addition, we present an optimization-driven approachfor fast point estimates scalable to massive graphs. Bayesian inference anduncertainty quantification with MCMC are also illustrated. The main resultsdemonstrate that the optimization strategy is an effective exploration tool forselecting adequate regularization schemes using Bayesian optimization of thecross-validation loss. Two key empirical findings made possible by our methodinclude: 1) the probability that a TNC driver can expect to earn a living wagein Austin exhibits high variability in space and time, from as low as 25% to ashigh as 85%; and 2) some drivers suffer considerable "tail risk", with thebottom 10% of the earnings distribution falling below $10 per hour -- grosslybelow a living wage in Austin for a single adult -- for specific times andlocations. All code and data for the paper are publicly available, as a Shinyapp for visualizing the results and a software package in Julia forimplementing the GFEN.

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