Highway Hierarchies and the Efficient Provision of Road Services

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Highway Hierarchies and the Efficient Provision
of Road Services
Pacific Regional Science Conference, Portland 2002

• -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
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Introduction

• Hierarchies in Highways and Governments
• Government layers responsible for a Highway class
• Scale Economies?

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Figure 1 Functional Highway Classification and
Type of Service Provided
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Theory

• A third dimension to the problem - Costs

Figure 2 Schematic representation of three
dimensional structure of highways, costs and
government layers
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Theory Contd.

• Parabolic variation of Cost with Expenditure
  share by state government

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Theory Contd.

• Existing Expenditure Structure

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Theory Contd.
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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

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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
• Zipfs law
• Model generalized for all states

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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

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Data Contd.

• Results

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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.

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Model

• Cost variables

Table 4 Table explaining the relationship
between cost variables
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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.

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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.

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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?

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Model Contd.

• Quasi Cobb-Douglas function
• as and bs are regression coefficients
• Only two regression functions since the degrees
  of freedom of the problem is 4

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Model Contd.

• Why variables (p/l) and (t/pt) are used?
• Multicollinearity
• Cost functions has an optimal expenditure share
  (convex function) if and only if
• for total expenditure function
• for capital outlay function

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Results
Table 5 Regression results for Total expenditure
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Results Contd.
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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

Table 7 Table showing optimal vales and 95
confidence interval for state expenditure share
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Results Contd.

• Marginal and Average Costs

Table 8 Marginal and Average costs for Total
Expenditure and Capital Outlay
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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