Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

est of the system. The rate equations were then substituted into the
system to derive a linear structure of the first order. The reduced
form of this structure was then obtained and utilized in estimating
demand equations for the individual transport models.
Prior to our study a few simple estimating equations for rail and
motor rates existed. These usually expressed the rates as linear func-
tions of distance and, perhaps, distance squared for individual com-
modities. By utilizing published sources of rail data, and obtaining
comprehensive shipment data from private sources for motor and water
transport, we were able to conduct a thorough analysis of transport
rates for these three modes. Our approach was to relate the average
revenue per ton of the commodity shipped to the distance it was shipped ;
the quantity variable was the total annual tonnage shipped between the
two markets. For motor and water transport the size of the individual
shipments was available. The carload waybill statistics yielded ob-
servations on the average density and estimated prices of the com-
modities. These were used as product attributes.
Rate regressions were estimated for all five of the major MR com-
modity groupings. Then, after conversion of the commodity groups, rate
parameters were estimated for the four STCC groups selected for reduced
form estimation.
Distance proved to be the best single explanatory variable for
rail and water transport, whereas shipment size was the most important
for motor transport. The quantity variable also proved significant in
explaining water rates, whereas its effects were quite mixed for rail.
These quantity relationships for rail transport were explored further
a quantity variable and several product attributes. For rail shipments
187