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

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

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

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term contains one bracketed expression, (8b 1-1), which is negative<br />

by assumption. If this expression dominates, the overall intercept<br />

term will be negative. It should also be noted that whenever the in-<br />

tercept is estimated as negative the dummy variable coefficient is es-<br />

timated to be positive.<br />

In general we expected the mileage coefficients to be negative.<br />

Our theory assumes that <strong>for</strong> each commodity group the total amount<br />

transported would decrease with distance. This assumption was valid.<br />

However, if one mode enjoys a great advantage in the shorter hauls and<br />

another in the longer ones, the latter mode may display a positive dis-<br />

tance coefficient and remain consistent with our theory so long as<br />

this positive effect is more than compensated <strong>for</strong> by the reduction in<br />

tonnage <strong>for</strong> the <strong>for</strong>mer mode. Two of the nine estimated coefficients<br />

came out positive and both of these were offset by negative intercept<br />

terms. <strong>Water</strong> shipments of Group 29, Petroleum and Coal Products, in-<br />

creased rather largely with distance and rail shipments of Group 30,<br />

Rubber and Miscellaneous Plastics Products, increased a very small<br />

amount. However, all of the statistically significant estimates showed<br />

a negative mileage effect.<br />

Without exception the signs of the estimated coefficients of the .<br />

square of distance were the opposite of the sign of the distance co-<br />

efficients. This coefficient, however, was never large enough in value<br />

to completely override the influence of the first degree term. That<br />

is, if the distance coefficient was negative and the distance squared<br />

coefficient positive, <strong>for</strong> the relevant range, the net effect of dis-<br />

tance on quantity was negative.<br />

169

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