  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.
