On the bias caused by spatial aggregation of flows on the estimation of the degree of scale economies

From an economic viewpoint, transportation supply has been historically characterized through very aggregated descriptions of the output of a transportation firm. The use of measures like ton-miles or passenger-kilometers was standard practice through the end of the 1970’s. Currently, the accepted description of transportation output is in terms of a vector of flows; aggregate measures have empirically been shown to be the source of significant problems in the economic analysis of transportation systems. In particular, the scarce empirical work on multioutput cost functions shows that the scalar volume-distance measure generates biased estimates of both marginal costs and degree of scale economies. In this paper, these biases are analyzed from an econometric viewpoint, using linear cost functions as first order approximations. Biases are expressed as differences of weighted sums, which are then used to show that, under reasonable statistical assumptions, the aggregated model causes a systematic overestimation of the degree of scale economies. This phenomenon is generalized to include a fairly general dependence of marginal costs on flows and distances.