Modeling and Estimation of the Vehicle-Miles Traveled Tax Rate Using Stochastic Differential Equations

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The mismatch in demand and supply of the revenue for improving highway infrastructure and maintenance is an area of growing concern. In various studies, it has been found that the existing revenue collection system based on gas/fuel tax is not an appropriate model for highway funding. Some of the main drawbacks of the current system include no effective tax process for vehicles based on alternative fuel, no effective changes to the tax rate due to economic inflation, and more highway expenditure than generated revenue. A revenue model based on vehicle-miles traveled (VMT) has been identified as a potential alternative by various studies. For this new revenue model, it is extremely important to develop the required mathematical framework and estimate an effective VMT tax rate that addresses the current gap between generated and required revenue. The main objective of this paper was to estimate what VMT tax rate should be charged in order to generate the same amount of revenue that is being generated by the gas tax or to generate some specific required revenue. To this purpose, mathematical models for motor gasoline (gas) prices, gas consumption, and VMT based on stochastic differential equations were developed. Parameters for all the developed models then were estimated based on the maximum likelihood principle (maximum likelihood estimation) technique using relevant past data for each variable. The validity of the models was analyzed using the mean square errors which were found to be low. Numerical simulations were performed, and the effective VMT tax rate was estimated. To the best knowledge of authors this is the first attempt to model VMT and the VMT tax rate using stochastic dynamical models hence this is a novel contribution to the field. © 2015 IEEE.