Revisiting the empirical fundamental relationship of traffic flow for highways using a causal econometric approach

The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted variables such as driving behaviour and weather. To this end, this paper adopts a causal approach to obtain an unbiased estimate of the fundamental flow-density relationship using traffic detector data. In particular, we apply a Bayesian non-parametric spline-based regression approach with instrumental variables to adjust for the aforementioned confounding bias. The proposed approach is benchmarked against standard curve-fitting methods in estimating the flow-density relationship for three highway bottlenecks in the United States. Our empirical results suggest that the saturated (or hypercongested) regime of the estimated flow-density relationship using correlational curve fitting methods may be severely biased, which in turn leads to biased estimates of important traffic control inputs such as capacity and capacity-drop. We emphasise that our causal approach is based on the physical laws of vehicle movement in a traffic stream as opposed to a demand-supply framework adopted in the economics literature. By doing so, we also aim to conciliate the engineering and economics approaches to this empirical problem. Our results, thus, have important implications both for traffic engineers and transport economists.