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 FundsHighway Costs and the Efficient Mix of State and Local Funds Transportation Research Record: Journal of the Transportation Research Board Pacific Regional Science Conference, Portland 2002

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

Figure 1: Functional Highway Classification and Type of Service Provided

Theory A third dimension to the problem - Costs CostsGovernment Local Streets Collectors Arterials Interstate Local State Federal Capital Operation 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 a highway 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 Table 1: Top five states financed by Local Government

Theory Contd. 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 , – 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, –R j represents the rank of the jth class of highway, –v ij represents the % of total VMT in jth class of highway, in ith state, –l ij represents the % of road length of jth roadway class in ith state, –  's,  's,  's,  's are coefficients from the regression

Data Contd. Results

Data Contd. Calculating output variables using IV model –p i represents millions of VMT by passenger cars in ith state, –t i represents millions of VMT by trucks in ith state, –V j is total vehicle miles traveled by all vehicle types on the jth class of roads.

Model Cost variables 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, –e s is total cost financed by state and federal government, –e l is total cost financed by local government, –c s is capital outlay financed by state and federal government, –c l is capital outlay financed by local government, –m s is maintenance cost financed by state and federal government, –m l is maintenance cost financed by the local government.

Model Contd. Expenditure share variables q s,e is expenditure share of total cost by state and federal government, q s,c is expenditure share of capital outlay by state and federal government, q s,m is expenditure share of maintenance costs by state and federal government.

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?

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

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

Results Table 5: Regression results for Total expenditure

Results Contd. Table 6: Regression results for Capital Outlay

Results Contd. Optimal Expenditure share q s,e,min is the optimal total expenditure share by state q s,c,min is the optimal capital outlay share by state Table 7: Table showing optimal vales and 95% confidence interval for state expenditure share

Results Contd. Marginal and Average Costs 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