Highway Hierarchies and the Efficient Provision of Road Services -David Levinson -Bhanu Yerra...
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Highway Hierarchies and the Efficient Provision of Road
Services
-David Levinson
-Bhanu Yerra
Levinson, David and Bhanu Yerra (2002) Highway Costs and the Efficient Mix of State and Local Funds Transportation Research Record: Journal of the Transportation Research Board 1812 27-36. http://nexus.umn.edu/Papers/Hierarchy.pdf
Pacific Regional Science Conference, Portland 2002
Introduction
• Hierarchies in Highways and Governments
• Government layers responsible for a Highway class
• Scale Economies?
Access
Movement Limited Access
Locals
SPEED
FLOW
slow fast
high
low
Arterials
Figure 1: Functional Highway Classification and Type of Service Provided
Theory
• A third dimension to the problem - Costs
CostsGovernment
Local Streets
Collectors
Arterials
Interstate
LocalState
Federal
CapitalOperation
Others
Figure 2: Schematic representation of three dimensional structure of highways, costs and government layers
Theory Contd.
• Parabolic variation of Cost with Expenditure share by state government
State Share of expenditure
Cost spent on ahighway class
Minimum Cost
Optimal expenditure share
Figure 3: Parabolic variation of cost with respect to state's expenditure share
0% 100%
Theory Contd.
• Existing Expenditure Structure
StateTotal Expenditure
(000's of $)
Total Expenditure byState government
(000's of $)
ExpenditureShare byState And
Federal Govt.Minnesota 2138205 739068 0.35
Colorado 1336351 558925 0.42
New York 6477788 2883818 0.45
New J ersey 2186140 1014999 0.46
Wisconsin 1713293 821911 0.48
Table 1: Top five states financed by Local Government
Theory Contd.
StateTotal Expenditure
(000's of $)
Total Expenditure byState government
(000's of $)
ExpenditureShare byState And
Federal GovtDelaware 315239 301532 0.96
West Virginia 851186 805161 0.95
Rhode Island 252608 225050 0.89
Kentucky 1038414 917451 0.88
North Carolina 1712137 1472088 0.86
Table 2: Top five states financed by State Government
Data• Variables considered in this study
– Cost variables– Expenditures- Capital Outlay, Maintenance and
Total Expenditure per year in a state
– Expenditure Share
– Network variables– Length of highways in a state
– Output variables– Vehicle miles traveled (VMT) by Passenger cars
– Vehicle miles traveled (VMT) by trucks
Data Contd.
• Instrumental Variables (IV)– Necessity of IV model
– Percentage of VMT by a vehicle type is not available for lower highway classes
– Issues in formulating IV model– Model generalized for all roadway classes
» Rank of a roadway class as a variable
» Zipf’s law
– Model generalized for all states
Data Contd.
• IV Model
– i represents state,
– j represents highway class, j - 1 .. 12,
– is the estimated % of VMT by the passenger cars in ith state on jth highway class,
– is the estimated % of VMT by the trucks in ith state on jth highway class,
– Rj represents the rank of the jth class of highway,
– vij represents the % of total VMT in jth class of highway, in ith state,
– lij represents the % of road length of jth roadway class in ith state,
's, 's, 's, 's are coefficients from the regression
ˆ p ij =δpRjα p (vij )
βp (lij)γp
ˆ t ij =δtRjαt (vij )
βt (lij )γt
ˆ p ij
ˆ t ij
Data Contd.
• ResultsPassenger cars Trucks
VariableCoefficient Standard Error Coefficient Standard Error
ln(Rj) - 0.092 0.011 -0.65 0.08
l (n vij) - 0.037 0.0089 -0.28 0.066
l (n lij) - -0.041 0.0069 0.28 0.05
Constan t - -0.337 0.029 -1.011 0.209
Numbe r ofobservations
300 333
-R Squared 0.20 0.17
Adj. R-Squared 0.20 0.17
Note : All variables are significant at 99% confidence interval
Table 3: Regression results for percentage vehicle miles traveled onjth class of roadway by passenger cars and trucks
Data Contd.
• Calculating output variables using IV model
– pi represents millions of VMT by passenger cars in ith state,
– ti represents millions of VMT by trucks in ith state,
– Vj is total vehicle miles traveled by all vehicle types on the jth class of roads.
pi = ˆ p ijVjj
∑
ti = ˆ t ijVjj
∑
Model• Cost variables
StateGovt.
LocalGovt.
All Govt.Layers
CapitalOutlay
cs cl c
Mainten ance ms ml m
To tale xpendi t ure
es el e
Table 4: Table explaining the relationship between cost variables
Model Contd.
• Cost variables Contd.– e is total cost of capital outlay and maintenance,
– c is capital outlay cost,
– m is maintenance cost,
– es is total cost financed by state and federal government,
– el is total cost financed by local government,
– cs is capital outlay financed by state and federal government,
– cl is capital outlay financed by local government,
– ms is maintenance cost financed by state and federal government,
– ml is maintenance cost financed by the local government.
Model Contd.
• Expenditure share variables
• qs,e is expenditure share of total cost by state and federal government,
• qs,c is expenditure share of capital outlay by state and federal government,
• qs,m is expenditure share of maintenance costs by state and federal government.
qs,e =es
eqs,c =
cs
cqs,m =
ms
m
Model Contd.
• Cost functions
– l is length of highways in a state in thousands of miles,
– p is millions of vehicle miles traveled by passenger cars in a state,
– t is millions of vehicle miles traveled by trucks in a state.
• Why Square of expenditure share by state a variable in the model?
e= f(qs,e,qs,e2 ,l,p,t)
c = f (qs,e,qs,e2 ,l,p,t)
m= f(qs,m,qs,m2 ,l,p,t)
Model Contd.
• Quasi Cobb-Douglas function
• a’s and b’s are regression coefficients
• Only two regression functions since the degrees of freedom of the problem is 4
ln(e) =a1qs,e +a2qs,e2 +a3 ln(l)+a4 ln(
pl) +a5(
tp+t
) +a6
ln(c) =b1qs,c +b2qs,c2 +b3ln(l)+b4 ln(
pl)+b5(
tp+t
)+b6
Model Contd.
• Why variables (p/l) and (t/p+t) are used?• Multicollinearity
• Cost functions has an optimal expenditure share (convex function) if and only if
for total expenditure function
for capital outlay function
a2 >0;
b2 >0;
ResultsTotal Expenditure
VariableCoefficient
StandardError
P-value
Expenditure share a1 -5.00 2.20 0.029
Square ofExpenditure share by
state governmenta2 3.28 1.67 0.057
Natural Logarithm oflength
a3 0.90 0.06 0.000
Natural logarithm of(VMT by passenger
cars/ length)a4 0.66 0.12 0.000
Fraction of VMT byTrucks
a5 17.84 9.59 0.071
Constant a6 4.48 1.54 0.006
No. of Observations 43
R-Squared 0.93
Adj. R-Squared 0.91
Table 5: Regression results for Total expenditure
Results Contd.Capital Outlay
VariableCoefficient
StandardError
P-value
Expenditure share b1 -5.75 2.21 0.013
Square ofExpenditure share by
state governmentb2 3.55 1.60 0.032
Natural Logarithm oflength
b3 0.92 0.07 0.000
Natural logarithm of(VMT by passenger
cars/ length)b4 0.64 0.13 0.000
Fraction of VMT byTrucks
b5 17.79 10.46 0.097
Constant b6 4.24 1.68 0016
No. of Observations 43
R-Squared 0.91
Adj. R-Squared 0.90
Table 6: Regression results for Capital Outlay
Results Contd.
• Optimal Expenditure share
qs,e,min is the optimal total expenditure share by state
qs,c,min is the optimal capital outlay share by state
qs,e,min =−a1
2a2
qs,c,min =−b1
2b2
Expenditure ShareOptimalValue
StandardDeviation
Lower limit(2.5%)
Upper limit(97.5%)
Total expenditure share 0.76 0.043 0.67 0.84
Capital Outlay Share 0.81 0.045 0.72 0.96
Maintenance Share 0.67 0.064 0.54 0.79
Table 7: Table showing optimal vales and 95% confidence interval for state expenditure share
Results Contd.
• Marginal and Average CostsCost
Passengercars
Trucks
Marginal Cost ($/ VMT) 0.023 0.51
Average Cost ($/ VMT) 0.035 0.32
Elasticity 0.66 1.59Total Expenditure
Economies of scale Increasing Decreasing
Marginal Cost ($/ VMT) 0.014 0.33
Average Cost ($/ VMT) 0.023 0.21
Elasticity 0.64 1.57Capital Outlay
Economies of scale Increasing Decreasing
Marginal Cost ($/ VMT) 0.009 0.18
Average Cost ($/ VMT) 0.013 0.11
Elasticity 0.69 1.64Maintenance
Economies of scale Increasing Decreasing
Table 8: Marginal and Average costs for Total Expenditure and Capital Outlay
Conclusion and Recommendations• Parabolic nature of cost functions
• Most of the states are within the 95% confidence interval of optimal expenditure share of capital outlay
• Most of the states are out of the 95% confidence interval of optimal expenditure share of Total expenditure
• All states together can save $10 billion if all of them are at optimal point.
• Financial policies