![Sample our Built Environment journals, sign in here to start your access, Latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5926/TOC-Subject-Sample-2021-Built-Environment.jpg"})
Abstract
Dynamic factor adjustment models are applied to analyse input inflexibilities in public transit systems. Based on a panel data of 44 U.S. single mode bus transit systems, labour input is found to be the most flexible with an adjustment speed of 17.8% annually while non-labour and capital inputs do not adjust. However, it is found that transit systems tend to increase non-labour and capital inputs when labour inputs are less than the optimal quantity, indicating short-run substitution of inputs. Furthermore, it examines internal and external factors affecting the adjustment process and finds that transit systems that operate most of their fleet at the peak and others providing their services without contacting-out adjust labour inputs faster. Among current regulations, it finds evidence that the bus useful life regulation decreases the adjustment speed of non-labour inputs in the short run.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 For example, Li, Kahn, and Nickelsburg (Citation2014) note that they increase the scrappage of old buses, and in air quality non-attainment areas, as established by the Environmental Protection Agency, increase how fast diesel buses are scrapped for low polluting ones.
2 Regulations intended to affect input allocation include the Buy America programme, the Section 13c labour protection clause, the spare bus ratio requirement, and the bus useful life requirement.
3 For example, the penalties for violating the U.S. Section 13c federal labour protection requirement, which are prohibiting transit systems from using federal capital subsidy to make labour worse off than before and requiring six-years of salary to be paid to those made worse off, make the cost of adjusting transit labour very high and slow the adjustment process to cost minimization levels. Similarly, the cost of adjusting capital would be likely high and its adjustment process slow if buses are bought with federal money, and if the federal bus useful life regulation and the spare bus ratio regulation which restrict bus replacement or acquisition are binding.
4 For example, the Washington Metropolitan Area Transit Authority and the Metropolitan Transit Authority of New York hedge fuel prices (Canes Citation2016). In 2009 Nashville Metropolitan Transit Authority implemented a fuel-hedging programme that by 2012 had saved it $12.5 million (Metro Citation2012).
5 This study focuses on bus transit systems to avoid mixing the technologies of different transit modes (e.g. bus, rail, ferry) and to limit its focus on regulations specific to bus transit systems. To address these issues, the data used in this study exclude those transit systems which provide multiple transit modes such as the Metropolitan Authority of New York which is the most dominant public transportation in the U.S. in terms of bus services. Excluding this transit system, annual bus ridership in the U.S. was about 4 billion in 2016 compared to less than 2 billion rail passengers (Mallett Citation2018).
6 The translog cost function is often used in economics to approximate an unknown true functional form as the second-order Taylor expansion of the unknown function. The cross-product terms represent the second-order approximations. Viton (Citation1981) first introduced the translog cost function to analyse costs of operating urban bus transit in the transportation literature.
7 Non-labour input includes all other inputs which cannot be classified as labour or capital. For transit system the major items in non-labour input are fuel, tires, lubricants, materials, supplies and utilities. Also, it includes overhead costs. Other studies often use three types of inputs, labour, capital, and energy to specify production technology (e.g. Tian et al. Citation2017). To capture all costs of operation, the third input in the cost function includes all other types of inputs rather than being limited to energy.
8 This transformation has two benefits in the empirical section. First, adjustment speed is expected to be very slow for some inputs such as capital and close to zero based on preliminary estimation of the first-generation model. An almost zero adjustment speed makes more difficult to find statistically significant factors which explain it. Also, there were convergence problems in the non-linear system of equations and in obtaining significant coefficients in the adjustment equations when estimating βii. Possibly, this indicates the iteration process reached a local instead of a global maximum in the likelihood function making it harder to proceed beyond that point.
9 These variables, representing internal factors and regulations, are chosen, based on the availability of data. Many other regulations may directly and indirectly affect operations of public transportation, in particular environmental regulations. Some transportation literature looked at various environmental effects of transportation sectors (e.g. Tian et al. Citation2017). Due to lack of system-specific data of other regulations, we limit our scope to examining effects of these five regulations which directly affect bus operations. However, although the empirical work is limited to these five regulation, our theoretical model and empirical approach can be applied to a wide variety of regulations including command-and-control types and market-incentive types.
10 Drobetz and Wanzenried (Citation2006) use a firm-specific fixed effects to capture variation in adjustment speed among firms. Our approach extends their model by explaining this variation of adjustment speed among transit systems by various adjustment impediment sources.
11 The authors appreciate the comments of the reviewer who pointed out that the components of non-labour cost input include overhead. Since most transit systems in our sample are small (less than 50 vehicles), overhead cost may be a large share of non-labour inputs than fuels and materials when compared to large systems.
12 The average bus age of U.S. transit systems was between 6.8 and 7.0 years in 2007 through 2011 (Rogoff Citation2012). In our sample, the average bus age was between 5.7 and 6.0 years in the same period which is slightly less than the national average. However, the maximum of the average bus age was between 10.4 and 11.5 years, indicating some transit systems used buses for more than 10 years on average. Due to bus useful life regulation, some buses are held for 12 years before being sold especially those bought with non-federal monies. These buses are auctioned off to private operators in the secondhand market who operate them many more years. Lever et al. (Citation2007) reported that the average retirement age of these ‘12-year’ buses was 15.1 years.
13 U.S. transit systems do not have shared ownership (e.g., joint MPO-City, City-State or State-MPO ownership).
14 An average fleet age of more than 6 years means many of the vehicles were not bought with federal government funds. The federal bus useful life regulation does not permit vehicles bought with federal funds to be operated for more than 12 years (Obeng and Sakano Citation2020). A transit system wanting to do so must demonstrate its capability in operating and maintaining buses longer than 12 years. The regulation also requires detailed accounting of the age of each vehicle bought with federal money each year.
15 This ratio is calculated with each year’s data and not relative to a base year fleet size. This introduces inflexibility into the calculation which could likely affect the results. We are thankful to a reviewer for pointing this out to us.
16 Although the estimates of adjustment speeds of inputs in transit systems in this study cannot be compared directly with those from other empirical studies in other industries due to different external and internal factors affecting speed of adjustment, Nadiri and Rosen (Citation1969) estimate the adjustment speed in U.S. manufacturing sector from 1947 to 1962 as 0.35 for labour inputs and 0.05 for capital inputs. Rungsuriyawiboon and Stefanou (Citation2007) find 3% annual adjustment of capital (quasi-fixed input) for U.S. electric utility companies from 1986 to 1999. On the other hand, Asche and Salvanes (Citation1996) report much faster adjustment speeds for U.S. manufacturing sector from 1948 to 1981, 0.741 or 0.549 for labour, 0.868 or 0.847 for materials, 0.139 or 0.286 for capital, and 0.674 or 0.626 for energy (normalized quadratic/generalized Leontief). Although these estimates of adjustment speed vary largely, capital is always found slowest in adjustment, materials the fastest, and labour and fuel in middle. Our estimate confirms these relative adjustment speeds among inputs.
17 The bounds on own-adjustment are not imposed since they are parameterized and vary from one transit system to another.
18 Convergence failed when all the variables were included in the adjustment equations. To address this problem, for each adjustment impediment equation, the internal and external variables were added one at a time until better results were obtained from the estimation, following Drobetz and Wanzenried (Citation2006).
19 From Equations (3) and (4), an actual change in input quantities from year (t - 1) to (t) is a fraction of the change that a transit system needs to make to achieve its optimal input quantity where this fraction, represented by the speed of adjustment, depends on the conditions of the transit system in year (t) including if or not it meets a particular regulation. Because the enforcement or penalty for violating a regulation will be imposed in the following year (t + 1) based on the data reported in year (t), the decision and action taken by a transit system each year reflects its condition that year and the change in the quantity of its input. For example, if a transit system wants to increase its incentive subsidy in year (t), it must reduce its cost or increase its output in year (t - 1) which would involve changing its inputs. Thus, meeting a regulation in year (t) should have a direct effect on a transit system’s input allocation that year, and this will be reflected in a change in the speed of its input adjustment from year t - 1 to t. On the other hand, if a transit system did not meet the regulation in year t - 1, it would be forced to change its inputs to meet the regulation. Thus, not meeting a particular regulation in year (t - 1) might affect the speed of input adjustment in year (t). Because Equation (4) does not include the previous year’s conditions, observed changes in input quantities are not a result of enforcing the regulations each year. The effect of such an enforcement and the actions taken by a transit system to meet the regulations each year will be reflected in the following year’s data.
20 For example, the penalty to stop a fuel delivery contract may not be substantial compared to the adjustment costs of capital and labour.