D5 Annex report WP 3: ETIS Database methodology ... - ETIS plus

D5 Annex WP 3: DATABASE METHODOLOGY AND DATABASE USER
MANUAL – FREIGHT TRANSPORT DEMAND
Step 3: Appraising the Results
This data is represented below in graphical form: m versus n.
The more negative n is, the quicker the function goes to zero because of the d to the power of n
term. The more positive m is the quicker the function goes to zero because of the exponential
term. The difference is in the shape of the curve:
· An exponential curve behaves sensibly near zero ­ starting at 1 and gradually decreasing.
Then at high distance it becomes very small.
· A power­n (n negative) curve starts at infinity (at distance = zero) and quickly comes
down but is less active than the exponential term at higher distances.
If n is positive, the seeding graph of trade vs distance initially goes up from zero (for small d ­
while the exponential term is negligible). As the exponential term catches up and becomes
dominant at larger d, trade falls back down again to approach zero at high distances.
A large positive n keeps the exponential term negligible until higher distance so the graph
continues to rise for longer. A large positive m allows the exponential term to quickly dominate,
keeping the peak close to zero distance.
The variable m should not be negative. Where it is, n should always be negative and the
exponential term does not become dominant until beyond the fitted points. Although this may fit
the data for the distances fitted, it is unrealistic for larger distances. Negative m should only
result where the data is very sparse.
Most commodities fit into the n negative, m positive position in mn space. The actual position
depends on the shape of the trade vs distance curve. A highly negative n shows that the graph
quickly descends within relatively small distances without giving much information as to trade
at large distances. A large m shows that there is very little trade at large distances without
giving much information about the small distance trade.
So on the graphs below; negative n is a measure of the speed of descent of the curve at short
distances. Positive m is a measure of the speed of descent of the curve at larger distances.
The apparently anomalous value for ‘90 Others’ is not necessarily wrong ­ it is just based on
very sparse data and is the best estimate.
11 Beverage has a high value of m. As it’s n is not very negative, this shows that at small
distances, there is little dependence of trade on distance but at high distances, the trade quickly
decreases.
00 Animals again suffers from sparse data. This point suggests that the trade has a non­zerodistance
peak before descending rapidly at high distance.
Document2
27 May 2004
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