Time Series Analysis for Toll Road Data

One important reason for imposing tolls on roadways is to help reduce traffic congestion by giving an incentive to drivers to carpool, drive at non-toll times, or to seek alternate routes. While there are correlations between traffic volumes and toll rates, many other factors also influence driver decisions, including gas prices, availability of alternate routes, road construction, family income, and many others. Hence, management and analysis of a toll structure for a roadway can require a complex analysis. In Seoul, South Korea, tolls were imposed on two roadways between the Han River and the Central Business District (CBD) beginning in November, 1996. These were at the Namsan 1st and Namsan 3rd tunnels. Both roadways are supplied by similar suburb regions and are the main gateways to the CBD. The toll structure provided several different incentives to drivers. Vehicles with more than two passengers were admitted toll-free. In addition, vehicles participating in a “do not drive one day in seven” program received coupons for some tolls. Other vehicles paid a nearly constant toll rate of 2000 won (approximately US $2.50). An important measure indicating to what degree the toll price affects driver decision is the elasticity of demand, defined as the percentage change in demand resulting from a percentage change in price. Although the toll rate has remained constant since 1996, the value of the toll to users has changed due to inflation. In order to take this effect into account, a common practice is to convert historical prices to equivalent present market prices, and for the data presented here, this has been done using the consumer price index (CPI) for Seoul. Thus, all prices in the database are Korean Won in 2007 equivalent market values, and the elasticity of demand can be estimated based on these prices. If the elasticity is assumed constant, then the demand function can be specified as