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Results of the Frontier Cost Function
Table 1 presents the results of the SFCF and accompanying inefficiency effects
model. The coefficient for the variable Riders (1.074) is statistically significantly
greater than one, indicating that the “average” school district is operating at a
point of diseconomies of scale. Mathematically this indicates that a 1.0% increase
in riders would lead to a 1.07% increase in transportation costs, holding all else
constant. In a more practical sense, this result may suggest that the average
district is operating at a point beyond its efficient capacity. With no additional
slack in its transportation system, even a small (unexpected) increase in riders
may lead to a greater than proportional increase in costs.
Table 1: Estimation Results of Frontier Cost Function and
Inefficiency Effects Model
Variable
Coefficient
Standard
Error
t-ratio
P-value
Constant 1.544 0.120 12.851 0.000
LN(Riders) 1.074 0.009 116.805 0.000
LN(Bus Cost Per Rider) 0.615 0.078 7.871 0.000
LN(Fuel Cost Per Rider) 0.266 0.013 19.818 0.000
LN(Wage Cost Per Rider) 0.119 0.075 1.592 0.111
Trend -0.022 0.003 -6.861 0.000
SERS Percent 0.064 0.015 4.331 0.000
2001-02 School Year 0.104 0.021 5.058 0.000
Parameters in One-Sided Inefficiency Effects Model
Constant -11.333 68.548 -0.165 0.869
LN(Square Miles) 1.809 3.831 0.472 0.637
LN(Average Commute Distance) 2.220 5.725 0.388 0.698
LN(Per Capita Personal Income) 1.192 8.663 0.138 0.891
Variance Parameters for Compound Errors
Lambda
Sigma
6.538 13.410 0.488 0.626
1.159 2.341 0.495 0.621
Log Likelihood Function 173.5
Source: ECONorthwest analysis of ODE and other sources of data
School Transportation ECONorthwest January 2009 Page 55