Public transit cost efficiency studies: The impact of non-contracting regulations

Transportation Research Part A 126 (2019) 247–258

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Public transit cost efficiency studies: The impact of non-contracting regulations

T

K. Obeng College of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, United States

ABSTRACT

This paper studies the effects of non-contracting regulations on the efficiency of U.S. public transit systems. First, it estimates a system of cost and input demand equations and second, a frontier equation with technical inefficiency a function of regulation and heterogeneity variables. It finds that bus useful-life regulation makes transit systems overuse capital relative to labor, contracting out entire service is 7.2% cheaper than direct operation, and a mixed operation that combines direct operations with contracting-out has no statistically significant effect on cost. Also, according to the study’s results, the U.S. labor protection regulation (Section 13c) and contracting out entire service make transit systems overuse capital and nonlabor inputs relative to labor respectively. Overall the study finds that the regulations increase technical change by a small amount and make transit systems perceive their costs as low, which in turn makes them produce more output. Other findings are, the average transit system is 73% technically efficient, 68% allocative efficient and 50% cost efficient. Finally, incentive regulation increases technical inefficiency, bus useful-life regulation reduces technical inefficiency, and transit systems that contract-out their entire services have high levels of technical inefficiency.

1. Introduction In recent years there have been many studies that evaluate public transit regulations in terms of their effects on cost efficiency. For example, Margari et al. (2007) studied the effect of regulation and environmental variables on the efficiency of Italian public transit systems using panel data and a three-step methodology that combined stochastic frontier and Data Envelopment Analysis (DEA). In the first step, they used DEA to calculate input slacks followed in the second step by a stochastic frontier estimation with the slacks as dependent variables and regulations and managerial variables as independent variables. In the third step, they re-run the DEA using the original inputs less the slacks and concluded that regulations played less role in public transit efficiency than managerial skills. Instead of DEA, Piacenza (2006) used a stochastic cost frontier model, panel data and an inefficiency equation to study the effects of cost-plus contracts and fixed price subsidies on the efficiency of Italian transit systems and found significant impacts of regulations on x-inefficiency and lower cost distortions in transit systems operating under fixed-price subsidy regulations. Adding to these studies but in a contextually different environment Holmgren (2013) studied cost efficiency of public transit systems in Sweden using a stochastic frontier model in which inefficiency was a function of time, differences in production environment and factors external to the organization. He found that cost efficiency decreased over time and attributed it to restrictions on network design and vehicles. In a similar study in terms of Swedish bus transit systems, Vigren (2016) used a stochastic frontier model that distinguished between gross technical efficiency and net technical efficiency devoid of internal and environmental variables and found lower cost efficiency for contractors that operated in high density areas and services operated without contracting. Another study, Urdanoz and Vibes (2013), found that after the liberalization (deregulation) of European railroads firms exerted more effort to reduce cost inefficiency. Additionally, Gagnepain and Ivaldi (2002) studied the effect of regulations on bus transit efficiency in France using a model that included a labor-inefficiency parameter reflecting the factors not under the control of management, and a parameter reflecting the actions management could take to counterbalance this inefficiency. They then derived a set of equations to compare cost-plus

E-mail address: [email protected]. https://doi.org/10.1016/j.tra.2019.06.010 Received 31 August 2017; Received in revised form 26 April 2019; Accepted 8 June 2019 0965-8564/ © 2019 Elsevier Ltd. All rights reserved.

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contracts and fixed price contracts and found lower marginal and average costs under fixed price contracts and managers exerting the optimal level of effort under cost-plus contracts. Another study of French bus transit systems by Kerstens (1996) using a stochastic frontier found risk sharing characteristics and contract duration affected efficiency. For Norwegian public transit systems, Dalen and Gomez-Lobo (2002) did not find yardstick and subsidy-cap contracts affected efficiency nor did Odeck and Alkadi (2001) find regulatory contracts affected efficiency. Moving away from these European studies Zhang et al. (2015) found that management contract, net cost contract and gross cost contract positively affected technical efficiency in Chinese bus transit systems. While these studies provide information useful to understand the efficiency of various contractual agreements used in public transit, an observation is that many convey to readers that transit regulation is about different contractual practices. Certainly, this may be true in some contexts but it must be recognized that transit regulations are not only contracts but also provisions in laws that affect how transit services are provided. Therefore, a need exists to widen the scope of public transit efficiency studies to include these provisions. Furthermore, while many of these studies are from European countries, there are few if any current studies that address public transit regulations using U.S. data. The reason is that the context is different in the U.S. as there are no established federal or state administrative agencies charged with regulating public transit, though in the past when public transit systems were privately owned or operated by public utilities they were regulated at state levels. In fact, since after the Urban Mass Transportation Act of 1964 transit systems in the U.S. have been owned by state and local governments and public agencies, and it was not until the 1980s that private companies found their way back into providing transit services mostly under contract. In the absence of formal regulations and agencies to administer them, U.S. transit regulations take the form of provisions in Executive Orders, federal laws (see 49 U.S.C. Chapter 53 which codifies all U.S. laws regarding transit), government policies, rules and funding requirements of the U.S. Department of Transportation and the Federal Transit Administration (FTA). For example, Section 5333(b) of Title 49 of U.S. Code (Section 13 (c) of the FTA Act) requires that transit systems receiving federal capital subsidies cannot use the money to buy equipment to replace labor. Grant applicants are required to estimate its impacts on labor and propose remedies to be certified by the U.S. Department of Labor as fair and equitable. The 1964 Urban Mass Transportation Act also contained provisions for private sector participation in providing public transit services (contracting out services). However, a more formal process of contracting out transit services in the U.S. did not develop until the passage of the Surface Transportation Assistance Act of 1982. Two years after this act was passed, the Urban Mass Transportation Administration (UMTA) adopted guidelines for contracting out transit services to private sector companies to be used by those applying for federal discretionary funds. Other requirements are that FTA Circular 9030.1c (U.S. Federal Transit Administration, 1998) specifies that transit systems must maintain a bus spare ratio of 20%, and the reporting instructions for the FTA Section 5309 capital investment program, which is discretionary, stipulates a bus useful life of 12 years (U.S. Federal Transit Administration, 2017). Though this section also specifies that project sponsors can claim a useful life between 12 years and 18 years, those doing so must “provide documentation demonstrating experience maintaining buses beyond 12 years” (U.S. Federal Transit Administration, 2017, p. 8). Still, other requirements are that each transit system must have a Transportation Asset Management Plan, transit services must be wheelchair accessible and must conform to the Americans with Disabilities Act by not discriminating on the basis of disabilities. Certainly, not all these regulations affect input levels. Those that do include the bus useful life regulation which discourages using reliable vehicles beyond their regulated useful lives and prevents disposing of problem vehicles which are below their said useful lives without penalty. Others are the incentive regulation in Section 5307 of the Urbanized Area Formula grant which Obeng and Azam (1995) show theoretically that it has the unintended effect of encouraging capital-for-labor substitution by penalizing transit systems with high operating costs, and the contracting requirement which has potential to increase labor-for-capital substitution because the contractors can use low wage part-time labor. An essential point about contracting is that U.S. transit agencies do not necessarily select low bid contracts but must select the best value contract which FTA Circular 4220.1F defines as the “most advantageous offer by evaluating and comparing factors in addition to cost or price” (p. 5). Thus, the winning contract maximizes effectiveness and does not minimize cost, implying inherent allocative distortions in the contracts. Despite being around for many years these regulations are seldom studied in terms of their impacts on cost efficiency though in the 1980s several studies using U.S. transit data pointed to the cost savings of contracting. However, since 2012 few studies have appeared in the transit economics literature addressing how U.S. federal requirements and regulations affect efficiency. In one such study Obeng (2011) used an indirect production function and decomposed the changes in output into the lump-sum, subsidy, cost and inefficiency effects. In another, Obeng (2013) used a latent class model to identify two classes of transit systems based on variables which affected technical inefficiency. He found that in one class the regulations regarding useful life and contracting lowered technical inefficiency, and in another the incentive tier regulation lowered it. In a follow-up study also using an indirect production function Obeng et al. (2016) studied the effects of both regulations and subsidies on allocative distortion and technical inefficiency and decomposed overall output efficiency among its sources. They found that bus useful life regulation and contracting out some services to private companies reduced non-labor-labor allocative distortion while bus spare ratio regulation increased it. For capitallabor allocative distortion, contracting out some passenger service to private sector companies and the spare ratio regulation reduced it and the incentive tier regulation increased it. Also, they found that the spare ratio regulation increased technical inefficiency and that the contribution of regulations to overall output efficiency was negative. These studies clearly show lack of focus on cost efficiency and its dynamic changes from regulations, thus leaving a gap in the transit economics literature. This study fills this gap in the following ways. First, we focus on cost efficiency, which is the ratio of minimum actual cost to total actual cost, and use an unbalanced time series data spanning five years and 1029 observations to study dynamic changes in cost efficiency, allocative distortion and technical change. Second, in specifying an empirical model for this study, we include regulations, technical change and ownership variables, and methods of service delivery such as directly operated services, entirely contracted-out services and their combination. This allows us to identify regulation-induced rate of technical change 248

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as an additional component of allocative efficiency and calculate its effect on cost efficiency. More specifically, we show that with regulations the components of cost efficiency are the effects of regulation-induced technical change, the scale, lump-sum, budget (cost) and input price effects, technical efficiency and random error. Thus, the focus on cost efficiency and the attribution of its decomposition to the sources noted, makes the present paper different from the earlier works already mentioned. Additionally, the use of unbalanced panel data that allow us to determine dynamic changes in cost efficiency and technical efficiency and assess the role of technical change resulting from regulation-induced innovation contrasts this paper and earlier works. An important finding is that the transit systems analyzed are 73% technically efficient after accounting for inefficiencies from regulations and heterogeneity, 68% allocative efficient and 50% cost efficient. The next section deals with methodology and it is followed by data, results and conclusion respectively. 2. Methodology The methodology for this study is informed by earlier works of Obeng et al. (2016), Kumbhakar et al. (2014), Kumbhakar (1997), Obeng et al. (1997) and many others. These studies are parametric and use nonlinear models. Although Data Envelopment Analysis (DEA) could have been used, its assumptions are restrictive making it unsuitable for this study. For example, it assumes perfect technology, that external factors do not affect the position of the frontier, and that the inclusion of many variables reduces the solution space and increases the efficiency scores especially in small samples (Ayadi and Hammami, 2015). Similarly, the stochastic frontier models used in current studies in which the estimation is done in one step by maximum likelihood method cannot be used to estimate highly non-linear multi-equation models. Using the above discussion as background, let a transit system’s wage rate in any period t be wn1t where n = 1, 2, 3 indexes transit systems, its proxy price of all other inputs wn2t and its rental price of capital wn3t . Further, let a transit system minimize its actual cost Cnt = i wnit xnit subject to the production function constraint Qnt = f (xn1t , xn2t , ...xnit ) where x nit refers to the quantities of inputs i = 1, 2, 3 that a transit system uses in producing outputQnt . Then the Lagrangian of this minimization isMinimizeL= i wnit xnit + (Qnt f (x n1t , x n2t , ...x nit )) and taking its partial derivative with respect to input levels, setting the results equal to zero and then solving gives,

MPxnit

MPxn1t

=

wnit wn1t

where MPxn1t and MPxnit are the marginal

products of the reference input and another input respectively. When there is a regulation that affects public transit inputs, it changes this ratio which measures allocative distortion. To account for this change, let regulations affect the optimal combination of the inputs and distort the relative price ratios as MPxnit

in MP

xn1t

=

wnit e ni1t wn1t

where e

ni1t

is the measure of allocative distortion from regulations. From this expression, we define the after-

regulation input price perceived by the transit system as wnit = wnit e ni1 where n11 = 0 and the after-regulation or perceived cost which the transit system minimizes as Cnt = i xnit wnit . Taking the logarithm of the after-deregulation input prices, if ni1t > 0 then lnwnit = lnwnit + ni1t , implying that regulations make the price of x nit more expensive relative to the price of x n1t resulting in substituting x n1t for the other inputs and the transit system perceiving a large after-regulation cost and producing less. If ni1t < 0 thenlnwnit = lnwnit ni1t implying that regulations make the price of x nit less expensive relative to the price of x n1t resulting in substituting x nit for x n1t and the transit system perceiving its after-regulation cost as low and producing more. Finally, if ni1t = 0 thenlnwnit = lnwnit so the transit system correctly perceives its input prices and this leaves the optimal rate of input substitution unchanged. Thus, we can distinguish both the distortionary price effect and the cost effect of the regulations. Next assume that in addition to the regulation there is technical change which causes shifts in the transit system’s cost function. This technical change may be affected by input regulations since they restrict the choices of inputs to be used and the innovations affecting these inputs. Granderson (1999) argues that regulations alter the choice of innovations and McCauley (1986a,b) shows that regulations other than rate of return regulation alter the rate of technical change. Lee et al. (2011) show that regulations make firms become innovative and that performance-based regulation has greater potential for technological innovations. However, they argue against technology-based regulation, reasoning that once the target-based technology is achieved there is no incentive in pursuing other cost-saving innovations. Some of these results align with those of Smith (1974) who shows that regulations cause distortions in innovations. For example, if regulations disfavor some specific inputs, they will prevent innovations in those inputs and instead create innovations in substitute inputs as happened in the U.S. electric utility industry where emissions control led to innovations in alternative energy (i.e., switch from coal to gas and solar), and is happening in the automobile industry with the C.A.F.E. (Combined Average Fuel Efficiency) regulations leading to smaller fuel-efficient engines and electric cars. In transit systems, such distortions likely occur because some regulations target specific inputs. For example, the Section 13(c) labor protection requirement possibly restricts labor-saving innovations, therefore affecting the rate of technical change. And the incentive regulation in the Federal Urbanized Area Formula Grant by rewarding transit systems for maximizing a performance measure negatively weighted against higher operating cost encourages labor-saving and non-labor-saving innovations, which also could impact the rate of technical change. To account for technical change and the distortionary price effects, we assume an after-regulation cost frontier C (w , Q, t , z ) eu v whose composed error is separable from its deterministic component and approximate it by the translog function below,

lnCnt =

0

+ m

i

i lnwnit

m z nmt

+ unt

+

i

iq lnwnit lnQnt

+ 0.5

i

j

ij lnwnit lnwnjt

vnt forj = 1, 2, 3.

+

tt

+ 0.5

tt t

2

+

i

it

× t × lnw nit + t × lnQnt + (1)

where t is defined already and it is used to show shifts (up or down) in the cost function over time; z m is a set of regulation and 249

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heterogeneity variables; ni1t = f (ykt ) and yk is a subset of the regulation variables, u = |U |and v iidN (0, 2) . For homogeneity of degree one in after-regulation factor prices the following restrictions are imposed: i i = 1, i ij = i it = i iq = 0;and for symmetry, ij = ji . Differentiating Eq. (1) with respect to time and expanding the terms through substitution gives the rate of technical change,

lnCnt = t

{

t

+

tt t

+

it lnwnit

i

+

tq lnQnt

}+{

i

it ni1t

}

(2)

Eq. (2) shows that the effect of regulation on the rate of technical change can be determined from the sign of the term in the second set of braces. If negative it shows that over time regulations make firms seek innovative ways to increase the rate of technical growth and reduce cost; and if positive it shows that the regulations increase the rate of technical decline and cost. Thus,

< 0 shows technical growth and t nt > 0 shows technical decline. Additionally, expanding Eq. (1) through substitution, rearranging and classifying the terms, we rewrite it as,

lnCnt t

lnC

(3)

lnCnt = lnCmin + lnCalt + lnCalw + lnCalq + lnCalump + unt + vnt ,

{

where lnCmin =

+

0

t2 +

lnCalt =

{

i

it ni1t

{

lnCalw = 0.5

lnCalq =

{

lnCalump =

i

{

it

i

i

+

i

× t × lnwnit +

iq lnwnit lnQnt

tq

+ 0.5

i

j

ij lnwnit lnwnjt

+

m

m z nmt

+

tt

+ 0.5

tt

}

× t × lnQnt ,

}

×t ,

j

ij ( ni1t lnwnjt

iq ni1t lnQnt

i

i lnwnit

i

i1 ni1t

+

nj1t lnwnit )

}

}

+ 0.5

i

j

ij ( ni1t nj1t )

}

Suppressing the last two terms, the first term is the logarithm of deterministic minimum actual cost without regulations (lnCmin) ; the second is the effect of the shift in the cost function from the regulations (lnCalt ) ; the third is the effect of regulations through input prices (lnCalw ) ; the fourth is the scale effect of the regulations through output(lnCalq) ; and the fifth is the lump-sum effect of the regulations (lnCalump ). The second through fifth terms are the components of the logarithm of gross allocative inefficiency nt so termed because they exclude the cost effect of the regulations. Substituting, we rewrite this equation aslnCnt = lnCmin + nt + unt + vnt . Since the translog function is an expansion around the mean the output and price effects are zero (and their exponentials are one), showing that they do not affect the mean of allocative efficiency. In Kumbhakar (1997) this gross allocative inefficiency is the sum of the third, fourth and fifth terms. If technical inefficiency and random error are suppressed then the deterministic component of this equation is the same as Obeng et al. (1997) derived in subsidy context for cross-sectional data. An important point to make is that this equation ignores the cost effect of the regulations. Recall that the regulations may make transit systems perceive their cost as increasing or decreasing because it changes perceived input prices. To account for this cost effect, subtract lnCnt from both sides of Eq. (3) and solve for ln

ln

Cmint Cnt

= ln

Cnt Cnt

nt

unt + vnt

( )to get, Cmint Cnt

(4)

The left-hand-side of this equation is the logarithm of the ratio of minimum actual cost to actual total cost; that is, the logarithm of cost efficiency. The first term on the right-hand-side is the logarithm of the cost effect of regulation or the proportion of actual total cost minimized after regulation. This is a part of allocative efficiency and it is equal toln i Snit e ni1t . If it is positive then the transit system perceives an after-regulation cost larger than its actual total cost, the reverse being also true. The other part of allocative efficiency is the second term and together with the first, measure net allocative efficiencye nt . While the exponentials of some of the components of net allocative efficiency may be greater than one, by definition, cost efficiency and technical efficiency are positive and less than one. Therefore, e nt must also be positive and less than one for each transit system. To satisfy this condition the value of the exponential of each firm’s net allocative efficiency is normalized by dividing it by its largest value in the observations so that the most allocative efficient transit system has a value of one. We would like to calculate cost efficiency and its components using Eq. (4) and that means estimating equations to obtain the parameters above. To obtain these equations we take the derivative of Eq. (1) with respect to the logarithm of the after-regulation w x input price to give the after-regulation input share in cost, Snit = nit nit . Then, taking its logarithm, solving for input demand and Cnt performing substitutions gives, 250

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lnxnit = ln

{

i

+

t + 0.5

j tt

t2

ij lnwnjt

+

+

+

it t

}+

+

0

× t × lnw nit + t × lnQnt +

it

i

iq lnQnt

{

i lnwnit

i

m z nmt

m

+

i

iq lnwnit lnQnt

lnwnit + unt

+ 0.5

i

j

ij lnwnit lnwnjt

vnt

+

t

(5)

}

where lnSnit = ln i + j ij lnwnjt + iq lnQnt + it t and all the restrictions on the coefficients in Eq. (1) apply. The system of input demand equations based on this equation can then be estimated to obtain the coefficients of the deterministic component of the frontier. To improve this estimation and make it easier to extract cost residuals, which we need later in the analysis, the fourth equation below is added,

lnCnt = lnCnt =

0

ln

+ m

i

(

i

Snit e

i lnwnit

m z nmt

ln

ni1t

+

(

) iq lnwnit lnQnt

i i

Snit e

ni1t

+ 0.5

)+u

nt

i

ij lnwnit lnwnjt

j

+

tt

+ 0.5

tt t

2

+

i

it

× t × lnw nit + t × lnQnt +

vnt .

(6)

Again, all the restrictions on the coefficients noted earlier apply here too. Of course, one could also use the actual i 1input cost 1 S share equations given bySnit = Snit ni11t and Eq. (6) as a system in the analysis. Doing so, however, introduces more i nit ni1t nonlinearities and complexities into the system of equations which could affect the estimation and the results. Thus, we use the system of input demand and cost equations recognizing that the cost and share equations also can be used. A problem with trying to estimate this system of input demand and cost equations to obtain technical efficiency is that standard stochastic frontier estimation techniques based on maximum likelihood methods cannot be used as noted earlier since the equations are nonlinear and have many variables. However, there are some approaches that can be adapted to extract information about technical inefficiency from the residuals of Eq. (6). In one such approach Kumbhakar et al. (2014) distinguish between persistent firm-specific technical efficiency and a time-varying technical efficiency. To estimate them using panel data, they suggest first, estimating a random effects model to obtain firm-specific constants; second, using the constants which are in logarithms to calculate persistent technical efficiency for each firm by subtracting the values for each firm from the largest value and calculating the negative exponential of the result; third, using the residual from the first step as a dependent variable in a stochastic frontier model in which technical inefficiency is parameterized and estimating it by maximum likelihood to obtain residual technical efficiency. If persistent technical efficiency is suppressed then this approach reduces into the two-step method in Bhattachryya et al. (1995). In the latter study, also using panel data, the authors use the maximum likelihood method to estimate a weighted regression that corrects for heteroscedasticity and calculate the residual of this regression. Then, they use this residual as a dependent variable in a stochastic frontier regression in which technical inefficiency is a function of firm characteristics including ownership. This parameterization allowed them to separate out the effects of internal factors from the calculation of technical efficiency. This latter approach was used by Obeng et al. (2016) in a single period analysis of overall output efficiency using cross-sectional data. A competing approach is the three-step method in Margari et al. (2007) noted earlier which can be adapted by replacing the slacks with residuals. We follow Obeng et al. (2016), Kumbhakar et al. (2014) and Bhattachryya et al. (1995) in extracting technical efficiency from the residual of Eq. (6). Thus, in the first step we use iterative seemingly unrelated equations method to estimate a system of weighted nonlinear regression equations based upon Eqs. (5) and (6) to account for heteroscedasticity. Then, we calculate the residual nt of the cost function (Eq. (6)) and use it as the dependent variable in the frontier equation nt = h (z nmt ; ) + nt vnt where h (·) is inefficiency due to firm characteristics (heterogeneity), regulations and other variables, z nmt . nt is a one-sided positive measure of net technical efficiency so termed because it excludes heterogeneity. Before estimating it, we make assumptions about the distribution of nt . Commonly, in the stochastic frontier literature, three distributions are assumed: half normal, truncated at zero from below, and exponential.1 In this study, we assume that the distribution of nt is exponential and its log-likelihood is,

logL = constant

n

2

2 v 2 u

+

n n

u

+

n

ln

n

v

v

u

.

(7)

where is the cumulative normal distribution function, n = n vn and to make the equation easily understood some subscripts are suppressed. Maximizing this equation with respect to and and taking the sum of the results across observations gives consistent estimates of the coefficients. Using the results, we calculate the mean technical efficiency of each transit system by the Battese and Coelli (1988) approach as,

En {u } = where z =

(

v

+

v

1 v

(z ) (z )

)and

(8)

is the standard normal density function.

3. Data The application of the methods above requires data to estimate the cost, demand and stochastic frontier equations. The data are 1

Initial estimation using the other distributions did not give good results in terms of the value of technical efficiency. 251

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an unbalanced panel of U.S. transit systems with 1029 observations spanning 2007–2011 and are from the National Transit Database (NTD). This data source provides detailed information on transit systems including cost, revenue, output, performance and background data, which transit systems receiving federal funding must submit to the Federal Transit Administration (FTA) annually. Upon receipt, the data are used to monitor and audit transit performance, and to allocate the Federal Urbanized Area Formula Grant to transit systems. To include a transit system from this database in the study, it must operate bus modes only and not rail, monorail, inclined planes or ferry boats. Initially, all single mode bus systems that submitted their data to the FTA each year were included in the sample. Then, those missing relevant data on inputs, cost and other data which the study requires were deleted. This deletion resulted in unequal numbers of qualifying transit systems each year and an unbalanced panel of bus systems. For example the respective observations for 2007, 2008, 2009, 2010 and 2011 are 277, 126, 170, 193 and 263. In this paper, the data are limited to operating cost and its components such as wages and benefits, the quantities of the inputs used, output, background data and others describing the environments where the selected transit systems operate. For output, this paper follows convention in using the produced output, annual vehicle miles. Labor is measured in terms of hours worked(xn1t ) , fleet size (xn3t ) is used as a proxy for capital, and the total gallons of fuel (xn2t ) are a proxy for all other types of inputs. The price of labor (wn1t ) for each transit system each year is total labor compensation including fringe benefits divided by hours worked. For each transit system each year, the proxy price of the other inputs (wn2t )is the result of total operating cost less total labor compensation divided by gallons of fuel (xn2t ),and the rental price of capital each year for a transit system is calculated using the formula: wn3t = Pt (rnt + d) exp ( d ×Ant ). In this formula (Pt ) is the average price of a new transit bus each year and it is obtained from various issues of Transit Fact Book published by American Public Transit Association; rnt is each year’s interest rate on the highest-yield bond of the municipality or county where a transit system is located; d is a straight-line rate of depreciation assuming a bus useful life of 20 years; and Ant is the average age of a transit system’s bus fleet each year. Each transit system’s capital cost each year is the product of its fleet size and the rental price of its capital, i.e., wn3t xn3t . This is then added to total operating cost (Cnot ) to obtain total cost (Cnt ) w xnit .Of note is that all the which in turn is used to calculate the actual shares of the inputs in cost for each transit system as Snit = nit Cnt prices and cost are adjusted by consumer price index and are in constant 1982 dollars. Besides the cost information we also developed measures for the different federal regulations in Table 1. For the requirement that transit systems must purchase some of their services from private sector companies, U.S. transit systems use three approaches to provide services: they may provide the service directly, purchase the entire service from private sector sources, or use a mixed approach wherein they combine direct service provision with contracting-out part of the service to the private sector. In this paper, we define variables to represent each approach. For direct provision of services, it is represented by the binary variable (Dnt ) which takes a value of one if true and a zero otherwise; the binary variable (PURnt ) takes a value of one if a transit system buys all its services from a private sector company (contracting out the entire service) and a zero otherwise; and for the mixed approach the binary variable, Mnt takes a value of one if true and a zero otherwise. Another regulation is the bus useful life regulation, which requires that transit systems must use the buses they purchase with federal money for at least 12 years. Using the binary variable FAGEnt ,a transit system is coded as one if its average fleet age meets this regulation and a zero otherwise. Yet, another regulation is that transit systems cannot have a bus spare ratio of more than 20%. For this, we calculated the ratio of fleet size to the total number of vehicles available for maximum service and created a binary variable SPnt which takes a value of one if its value is at most 1.2 and a zero otherwise. The incentive tier component of the federal Urbanized Area Formula Grant penalizes transit systems with high operating cost and rewards those with large passenger miles. To capture it, we use a binary variableFEDnt which takes a value of one each time a transit system receives a federal formula grant. Finally, we account for the federal labor protection requirement in Section 13(c) of the Federal Transit Act by defining a binary variable CAPnt to take a value of one each year a transit system receives federal capital grants and a zero otherwise. We assume that the transit systems receiving this grant certified they met this regulation as they must do. A Table 1 Examples of federal regulations affecting public transit. Regulations and Laws 1. Years of vehicle use regulation

2. Spare ratio regulation 3. Section 13(c) labor production clause

4. Contracting 5. Federal incentive tier Subsidy

Effect on Transit Systems Vehicles partially funded with federal subsidies: > 35–40 feet: must be used for at least 12 years, or at least 500,000 miles Small heavy-duty buses (approximately 30 feet in length): more than 10 years or 350,000 miles Buses 25–35 feet in length: used for at least 7 years or 200,000 miles Medium light-duty buses 25–35 feet in length: used for at least 5 years or more than 150,000 miles Transit systems operating 50 or more vehicles must keep 20% of their vehicles as spare if they were bought with federal aid. Can be forced to dispose of excess vehicles. Capital subsidies cannot be used to worsen the employment situation of workers. Job training and retraining for displaced workers Displaced workers to receive compensation equal to six years pay. Compensation also for those whose jobs are downgraded. Transit systems must contract-out portions of their services to private sector companies. Penalizes transit systems receiving operating subsidies for high cost Rewards recipients of federal operating subsidy for more passenger miles

• • • • • • • • • • • • •

Sources: a: USDOT, FTA Circular FTA C 9030.1D. Urbanized area formula program: Program guidance and application instructions (Revised 8/27/ 2012). b: http://publictransport.about.com. 252

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Table 2 Descriptive statistics. Variable

N

Mean

Std. Dev

Share of labor in actual total cost Share of non-labor inputs in actual total cost Share of capital in actual total cost Logarithm of total cost Logarithm of labor price Logarithm of non-labor price Logarithm of rental price of capital Logarithm of annual vehicle miles Logarithm of gallons of fuel Logarithm of labor hours worked Logarithm of fleet size Logarithm of average fleet age Controlled right-of-way (yes 1, no = 0) FAGEnt :Meets years-of-use regulation (yes = 1, no = 0) SPnt :Meets spare ratio regulation (yes = 1, no = 0) CAPnt :Labor protection requirements (yes = 1, no = 0) Dedicated local funding source (yes = 1, no = 0) FEDnt :Incentive tier regulation (yes = 1, no = 0) Transit system owned by city (yes = 1, no = 0) Transit system owned by Metropolitan Planning Organization (yes = 1, no = 1) Transit system owned by a transit agency (yes = 1, no = 0) (Dnt ):Directly operates entire transit system (yes = 1, no = 0) (PURnt ):Entire transit service purchased from private sector companies (yes = 1, no = 0) Mnt :Mixed operation involving direct provision and contracting out some service to private sector companies (yes = 1, no = 0) Number of transit systems in 2007 Number of transit systems in 2008 Number of transit systems in 2009 Number of transit systems in 2010 Number of transit systems in 2011

1029 1029 1029 1029 1029 1029 1029 1029 1029 1027 1029 1029 1029 1029 1029 1029 1029 1029 1029 1029 1029 1029 1029 1029 277 126 170 193 263

0.4920 0.2792 0.2288 15.4909 2.5167 0.8594 9.6493 14.4748 12.5379 12.2263 4.2873 1.6791 0.0276 0.0126 0.2410 0.9767 0.3882 0.8863 0.6589 0.2838 0.0350 0.4601 0.4276 0.1118

0.1151 0.0922 0.0934 1.1605 0.3291 0.9436 0.1641 1.1118 1.3874 1.0896 1.0088 0.4014 0.1639 0.1117 0.4279 0.1510 0.4876 0.3176 0.4743 0.4510 0.1838 0.4987 0.4950 0.3152

cautionary note about FEDnt and CAPnt is that they also capture federal operating and capital subsidies so it is difficult to separate the effects of these regulations from their corresponding subsidies. Therefore, we refer to them as capturing both effects. Table 2 shows descriptive statistics about the data. A key observation in this table is the dominance of small transit systems in the sample. For example 63.4%, 27.1% and 7.8% operate less than 50, 50 to 199 and between 200 and 499 vehicles in maximum service respectively. The rest, 1.7%, operate 500 or more vehicles in maximum service. Others are the bold-face entries which are the regulations addressed in this paper. They show that 24.1% of the transit systems meet the spare ratio regulation, 88.6% are affected by the incentive tier regulation and 42.8% contract-out their entire services to private sector companies; 11.2% use the mixed approach of combining direct operations with contracting; and 46% provide the services themselves. This latter percentage is quite surprising since we thought that all transit systems would contract out some passenger services to the private sector. In addition, the data show that 97.7% certified to have met the Section 13(c) labor protection requirement and received federal capital subsidies. In terms of who owns the service, the data also show that 65.9% is owned by cities, 28.4% by Metropolitan Planning Organizations, and 3.5% by transit agencies. The rest 2.2% is owned by non-profit agencies, for-profit organizations and universities among others. Of note also are the cost shares of labor, non-labor and capital of 49.2%, 27.9% and 22.9% respectively. 4. Results The empirical equations to be estimated in the first stage using the data are the system of cost and the input demand equations for labor, capital and non-labor inputs based on Eqs. (5) and (6), and in the second stage, the stochastic frontier equation, nt = h (z nmt ; ) + nt + vnt . In these equations, the logarithms of the continuous variables are mean centered and the other variables are as defined earlier. To correct for heteroscedasticity, we estimated a system of weighted input demand and cost equations using nonlinear iterative seemingly unrelated equations methods. The results in Table 3 show adjusted coefficients of determination of 0.38, 0.78, 0.92 and 0.94 respectively for the cost, labor, non-labor and capital equations indicating a good fit of the model. Additionally, most of the coefficients are statistically significant at the 0.05 probability level. Examining non-labor-labor allocative distortion, it is negatively related to contracting out the entire service to private sector companies, spare ratio regulation and the incentive regulation whereas its relationship with bus useful life regulation is statistically weak. Thus, the after-regulation price of non-labor inputs becomes small relative to the price of labor leading to its substitution for labor. Confirming this finding, the calculated mean of the logarithm of non-labor-labor allocative distortion is −1.13. Similarly, the calculated mean of the logarithm of capital-labor allocative distortion is −1.47 showing that the after-regulation price of capital becomes small and leads to overuse of capital relative to labor. Because these mean values are negative, they show that the average transit system in receiving subsidies conforms to these regulations and minimizes a cost lower than actual total cost. Using Cnt = Cnt i Snit e ni1t and evaluating the term affected by the summation, at the mean, transit systems perceive their after-regulation 253

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Table 3 System of equations results. Nonlinear ITSUR Summary of Residual Errors Equation

DF Model

DF Error

SSE

MSE

Root MSE

R-Square

Adj. R-Sq.

ln (C ) ln (x n1t )

7.5 7.5

1020 1020

2561.3 800.9

2.5123 0.7856

1.585 0.8863

0.3853 0.7821

0.3813 0.7808

7.5

1020

284.3

0.2789

0.5281

0.9381

0.9377

ln (x n3t )

ln (x n2t )

7.5

1020

264.3

0.2593

0.5092

0.9156

0.9151

Nonlinear ITSUR Parameter Estimates Parameter

Estimate

Approx. Std. Err

t Value

Approx. Pr. > |t|

Non-labor-labor allocative distortion from regulation FAGEnt :Bus useful life regulation (yes = 1, no = 0) SPnt :Spare ratio regulation (yes =1, no = 0) (PURnt ):Purchases entire service (yes = 1, no = 0) FEDnt :Incentive regulation (yes = 1, no = 0)

−0.6502 −0.1382 −0.4396 −1.0108

0.3860 0.0762 0.0767 0.0747

−1.6800 −1.8100 −5.7300 −13.5300

0.0924 0.0701 < 0.0001 < 0.0001

Capital-labor allocative distortion from regulation FAGEnt :Bus useful life regulation (yes = 1, no = 0) SPnt :Spare ratio regulation (yes =1, no = 0) PURnt :Purchases entire service (yes = 1, no = 0) FEDnt :Incentive regulation (yes = 1, no = 0) CAPt :Meets labor protection regulation (yes = 1, no = 0)

0.8228 −0.0775 −1.1900 −0.0156 −0.9264

0.3698 0.0761 0.0908 0.1018 0.0730

2.2200 −1.0200 −13.1100 −0.1500 −12.6900

0.0263 0.3087 < 0.0001 0.8786 < 0.0001

Cost and Input Demand Equations Constant term ln (wn1t ) ln (wn2t ) ln (wn3t ) ln (Qnt )

0.5(ln (wn1t ))2 ln (wn1t ) × ln (wn2t ) ln (wn1t ) × ln (Qnt ) ln (wn1t ) × t 0.5(ln (w 2t ))2 ln (wn2t ) × ln (Qnt ) ln (wn2t ) × t 0.5 × (lnQnt ) 2 t × ln (Qnt ) ln (Ant )

0.5(ln (wn3t )) 2 ln (wn2t ) × ln (wn3t )

1.1965 0.3281 0.3710 0.3008 0.8982 0.1870

0.0469 0.0122 0.0118 0.0126 0.0182 0.0043

25.5000 26.8200 31.5000 23.8400 49.4200 43.7400

0.0261 0.0012 0.0533

0.0023 0.0016 0.0082

11.3500 0.7800 6.4900

−0.1013 −0.0250 −0.0008 0.1107

0.0057 0.0038 0.0951

−0.0094

0.0041 0.0029 0.0022 0.0051

0.0043 0.0129 0.0061

< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001

−24.8100 −8.6100 −0.3800 21.7700

< 0.0001 < 0.0001 0.7041 < 0.0001

1.3100 0.2900

0.1908 0.7687

< 0.0001 0.4339 < 0.0001

15.6200

0.0032

< 0.0001

−2.8900

0.0039

Parameter

Estimate

Approx. Std. Err

t Value

Approx.

ln (wn3t ) × ln (Qnt ) ln (wn1t ) × ln (wn3t ) ln (wn3t ) × t t

−0.0011 −0.0857 −0.0004 0.0065 −0.0004

0.0016 0.0052 0.0012 0.0267 0.0080

−0.6700 −16.5200 −0.3400 0.2400 −0.0500

0.5003 < 0.0001 0.7352 0.8066 0.9579

0.5t 2 Heterogeneity Variables

Controlledrightofway (yes = 1, no = 0) Incentiveregulation (yes = 1, no = 0) Ln (averagefleetage) Purchasesentireservice (yes = 1, no = 0) Mixedoperation: directprovisionandcontracting (yes = 1, no = 0)

−0.0105 −0.1103 0.1434 −0.0720 −0.0110

0.0399 0.0242 0.0165 0.0167 0.0200

−0.2600 −4.5600 8.6800 −4.3200 −0.5500

0.7917 < 0.0001 < 0.0001 < 0.0001 0.5825

cost as 64.4% of actual total cost. This counterintuitive result (since we expected otherwise) is, again, explained by the fact that transit systems that must meet the labor protection and incentive regulations receive capital subsidy and operating subsidy. Obeng et al. (2016) find that these input subsidies reduce perceived input prices and lead to lower perceived cost than total actual cost. Also, most of the variables in the equation for capital-labor allocative distortion have statistically significant coefficients at the 0.05 254

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probability level except the spare ratio regulation and the incentive regulation whose coefficients are not statistically significant. On the other hand, the Section 13(c) labor protection regulation and contracting an entire service to a private sector company make the after-regulation price of capital small relative to that of labor resulting in substituting capital for labor. More information about the effect of the regulations on inputs can be gleaned from the optimal factor cost shares. From Eq. (3) it can be shown that the after-regulation optimal share of an input in cost is

Snit =

lnCnt lnwnit

=

i

+

ij lnwnjt

j

+

iq lnQnt

+

it t

=

i

+

j

ij lnwnjt

+

iq lnQnt

+

it t

+

j

ij nj1t where

the term in braces is the

optimal share Snit of an input in actual total cost and the last term is how the regulations affect it. Rewriting this expression asSnit = Snit + j ij nj1t and evaluating the last term, the regulations reduce the optimal share of labor in cost by 24%, increase the optimal share of non-labor inputs in cost by 11.4% and the optimal share of capital in cost by 12.6%. That is, with regulations, the perceived price of labor becomes high reducing its quantity demanded and its cost share, while the perceived prices of the other inputs fall resulting in increases in their quantities demanded and cost shares. Hence, together, the regulations are labor-saving though their individual impacts may be different. Additionally, the increases in the costs of capital and non-labor inputs from the regulations were not enough to offset the large decrease in labor cost resulting in lower after-regulation total cost. For the cost equation, the heterogeneity variables that have statistically significant coefficients are incentive regulation, contracting-out the entire service and average fleet age. It is found that the transit systems that receive federal operating subsidies and must abide by the incentive regulation have 11% lower cost; those that contract-out their entire passenger service to private sector companies have 7.2% lower cost; and a percentage increase in fleet age increases cost by 0.14%. Besides these results, the information in the table allows us to calculate economies of scale and the rate of technical change. Taking the derivative of the logarithm of the after-regulation cost in Eq. (3) with respect to the logarithm of output, substituting the relevant coefficients into the result and rearranging the terms gives the following equation for returns to scale,

lnCnt = 0.8982 lnQnt

0.0250lnwn1t + 0.0261lnwn2t

= {0.8924

0.0011lnwn3t + 0.0533lnQnt + 0.0057t

0.0250lnwn1t + 0.0261lnwn2t

+ {0.0261 × ( 1.1254)

0.0011lnwn3t + 0.0533lnQnt + 0.0057t } (9)

0.0011 × ( 1.4743)}.

The terms in the first set of braces show the elasticity of cost with respect to output without regulations, and those in the second set of braces show the effects of regulations on this elasticity. If this elasticity is less than one, it shows economies of scale; if it is one, it shows constant returns to scale; and if it is greater than one, it shows diseconomies of scale. Evaluating this equation gives a value 0.87 indicating economies of scale. The sources of the economies of scale are increases in the prices of labor and capital inputs whose coefficients are negative. Additionally, the sum of the effects of the regulations in the second set of braces is negative (−0.0278), indicating that it is a source of the economies of scale; that is, it reduces the elasticity of cost with respect to output. Comparatively, this elasticity increases with time and higher prices of the non-labor input. In addition to the finding of economies of scale, we calculate technical change by substituting the relevant estimated coefficients into Eq. (2). This substitution gives the rate of technical change as,

lnCnt t =

{0.0065

0.0008lnwn1t + 0.0012lnwn2t

0.0004lnwn3t + 0.0057lnQnt

0.0004 × t } (10)

{0.0012 × ( 1.1254) + 1.4743 × 0.0004}.

A positive value of the right-hand-side of this equation when evaluated shows technical growth and a negative value technical decline, and the term unassociated with variables in the first set of braces measures pure technical change. Since the value of this term is −0.0065 it shows a pure technical decline of 0.65%. Evaluating all the terms in the first set of braces gives a value of −0.004 thus showing a 0.4% rate of technical decline. On the other hand the value of the terms inside the second set of braces is −0.0008, thus making its effect positive and indicating 0.08% pure technical growth. The source of this latter growth is non-labor-labor allocative distortion from regulations (the first term in the second braces) which increases pure technical growth by 0.14%, a value larger than the 0.06% pure technical decline from capital-labor allocative distortion from regulations (the second term). When all the terms in this equation are evaluated and the result multiplied by 100, the rate of technical decline is 0.32%, which is attributed to increases in the prices of labor and capital inputs and time. Shifting the discussion to technical efficiency, the results of the frontier estimation in Table 4 show that most of the coefficients are statistically significant at the 0.05 probability level and bus useful life regulation decreases technical inefficiency whereas the transit systems that contract-out their entire services have higher technical inefficiency. In comparison, the incentive regulation and an increase in fleet age increase technical inefficiency, and over time technical inefficiency decreased by 24.1%. Furthermore, the results do not show statistically significant effects of the labor protection regulation on technical inefficiency. And, after factoring out technical inefficiency from regulations and heterogeneity, at the mean, the studied transit systems achieve 73% technical efficiency (with a standard error of 0.0005) as the last row of the table shows. This low standard error explains the very little variation in efficiency by transit system size in Table 5. Table 5 also shows cost efficiency and its components based upon Eq. (3). Here, we show the mean for all the transit systems and then by transit system size in terms of vehicles operated in maximum service. A striking result is the consistent pattern of the relative 255

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Table 4 Frontier estimation of technical efficiency. Parameter Estimates Parameter

Estimate

Standard Error

Approx. Pr. > |t|

Intercept FAGEnt :Bus Useful life regulation (yes = 1, no = 0) Ant :Ln(average fleet age) PURnt :Contracts out entire Service (yes = 1, no = 0) Mnt :Mixed operation involving direct provision and contracting out some service to private sector companies (yes = 1, no = 0) FEDnt :Incentive regulation (yes = 1, no = 0) CAPnt :Labor protection requirements (section 13c) t:Time in years

−1.6468 −0.5107 0.2068 0.2791 0.0204

0.0713 0.1754 0.0483 0.0392 0.0645

< 0.0001 0.0036 < 0.0001 < 0.0001 0.7517

0.5127 0.1082 −0.2410 0.5901 0.0211 0.3121

0.0607 0.1326 0.0122 0.0088

< 0.0001 0.4148 < 0.0001 < 0.0001

0.0713

< 0.0001

v u

µ Model Fit Summary Number of Endogenous Variables Endogenous Variable Number of Observations Missing Values Log Likelihood Maximum Absolute Gradient Number of Iterations Optimization Method AIC Schwarz Criterion

1 C 1027 2 −918.59 8.31 16 Quasi-Newton 1859 1913 0.59 0.04

Efficiency

Mean

Standard Deviation

Stochastic technical efficiency

0.7226

0.0006

Table 5 Cost Efficiency. System Size: Vehicles Operate in Maximum Service Variable Allocative Distortions in Inputs from Regulations Non-labor-Labor Allocative Distortion Capital-Labor Allocative Distortion Net Allocative Efficiency Efficiency effect of regulation induced rate of technical change Lump-sum Effect of Regulation Scale/Output effect of Regulation Regulation effect on cost/budget Regulation effect on input price Technical Efficiency Cost Efficiency:Allocativeefficiency × TechnicalEfficiency

• • • • • • •

All Systems Mean (N = 1029)

< 50 Mean (N = 654)

50 – 199 Mean (N = 279)

200–499 Mean (N = 80)

499–999 Mean (N = 12)

1000+ Mean (N = 4)

−1.13 −1.47 0.68 1.00 2.02 1.00 0.66 1.00 0.73 0.50

−1.09 −1.39 0.66 1.00 1.97 0.98 0.66 1.00 0.73 0.48

−1.18 −1.59 0.71 0.99 2.08 1.03 0.65 0.96 0.73 0.52

−1.24 −1.70 0.79 0.98 2.15 1.11 0.67 0.92 0.73 0.58

−1.30 −1.83 0.77 0.98 2.22 1.16 0.61 0.88 0.73 0.56

−0.94 −1.18 0.67 0.98 1.83 1.16 0.68 0.92 0.73 0.49

contributions of the sources to allocative efficiency regardless transit system size. Because the continuous variables are mean centered the contributions of output and prices, as noted earlier, take values of one when all transit systems are considered. Also, the very small effect of technical change on cost efficiency through input prices makes the exponential of its contribution close to one. As a result of this consistency we focus on the overall mean values by source in column 2 in the following discussion. We find that when all the transit systems are considered, the lump-sum effect of the regulations has the largest impact on allocative efficiency by increasing it appreciably (2.02). Comparatively, the cost effect is 0.66 and because it is less than one, it contributes less to allocative efficiency. Multiplying the values of the components of net allocative efficiency, normalizing the results as discussed earlier and taking the mean 256

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gives 68% net allocative efficiency. Next, because we found that the transit systems are 73% technically efficient, multiplying it by net allocative efficiency gives 0.4964. This shows that the transit systems studied are approximately 50% cost efficient because of technical inefficiency and the regulations distorting their optimal input combinations. 5. Conclusion This paper decomposed cost efficiency, allocative and technical efficiencies among their sources including technical change, regulations, service delivery methods and ownership variables. Its results show that except the bus spare ratio regulation and contracting-out the entire service, the regulations examined do not affect non-labor-labor and capital-labor allocative distortions in the same way. For example, bus useful life regulation increases capital-labor allocative distortion implying that they make transit systems overuse labor relative to capital and has a statistically weak effect on non-labor-labor allocative distortion. Other results are that incentive regulation reduces cost by 11.2%. Regardless their individual effects, overall, the regulations make transit systems perceive their costs as low, which is contrary to what we had expected but can be explained that the subsidies attached to both the incentive and labor protection regulations reduce perceived cost (Obeng et al. 2016). So, our results may be capturing this effect, which means that we should be cautious in attributing them to regulations only. They also mean that the effects of the incentive and labor protection regulations dominate those of the others. This perception of a lower cost makes transit system produce more output which from our results contributes somewhat to economies of scale. Also, the study permits a comparison of the costs of a transit system contracting-out its entire passenger service to a private sector company and a mixed operation to direct operation. Our results show that the cost of contracting out the entire service is 7.2% cheaper than direct operation, and a mixed operation has no statistically significant effect on cost. These results are partially consistent with previous U.S. research results of Iseki (2010) who found 5.5% cost savings from contracting out entire service but inconsistent with his finding of 7.8% cost saving from mixed operation. This inconsistency suggests that more research should be done about the factors which increase the cost of contracting. It suggests also that type of contract affects its cost saving potential and cautions against generalizing the effects of contracting. In addition, we found that the regulations increase pure technical change by 0.08% and in doing so expand innovation choices in how inputs are combined. Though small, this increase is consistent with the literature on regulations and technical change, which argues that they induce firms to become innovative (Lee et al. 2011). Also, the results show that at the mean the effects of regulations through output and the rate of technical change leave the level of allocative efficiency unchanged since the continuous variables are mean centered, thus making the budget and lump-sum effects of the regulations the main sources of lower allocative efficiency. For technical inefficiency, we found that bus useful life regulation reduces it, contracting-out the entire service increases it, and over time it has declined implying that transit systems are producing more output with their inputs. This increased production contributes to our finding of 73% technical efficiency in the transit systems studied after accounting for the inefficiency effects of regulations and heterogeneity. The product of this technical efficiency and the 68% allocative efficiency found gives 50% cost efficiency. A reason for this low cost efficiency is the incentive regulation attached to federal operating subsidy which creates large nonlabor-labor allocative distortion and large technical inefficiency though the latter is wiped out by the effects of other regulations. Although bus useful life regulation also creates large capital-labor allocative distortion, it has the advantage of reducing technical inefficiency by a large amount, according to our results, and should be maintained. Another reason is that, as noted earlier, the regulations make transit systems perceive their costs lower than actual total cost. While this makes them produce large outputs, they do not combine their inputs optimally leading them to overuse some inputs relative to labor. Managerial implications: The question we ask is what are the managerial implications of these findings? Certainly, being cost efficient is important to management and requires it to pay attention to its input proportions (allocative efficiency) and how much of those inputs it uses in producing a given level of output (technical efficiency). Our results provide some directions for management to address both issues. For allocative efficiency the results suggest that management should reduce its use of capital and non-labor inputs because the regulations make them perceive their costs so low that they are overused relative to labor. An example of an action that could be taken to reduce these inputs is increasing headways on routes with low demand. Another is for some of the affected companies to re-examine their practices of purchasing all their passenger services from private companies since we find that it is a source of allocative inefficiency. While not explicitly examined, a possible explanation for this finding is that the results may have captured the practice of using management contracts to operate transit systems. Since such contracts are paid for with federal capital subsidy, the contractor cannot layoff excess employees because the federal labor protection rule still applies, but can reduce capital and non-labor inputs and this leads to allocative distortion. To address this problem management might consider reducing its nonessential labor through attrition and retirements. For technical inefficiency the study suggests that management should focus on meeting the bus useful-life regulation because transit systems that do so have lower technical inefficiency. Meeting this regulation allows management to dispose of old unreliable vehicles timely, avail itself to new and improved vehicles, reduce maintenance cost and use the available vehicles to provide its services efficiently. Complementing this result is the finding that an increase in average fleet age increases technical inefficiency. Both findings are consistent with the premise of the bus useful-life regulation and its requirement that transit systems operating their vehicles bought with federal funds beyond 12 years must provide evidence of their experience and capability in doing so. An additional area for management to focus on to improve technical efficiency is to balance its efficiency and effectiveness in providing its service. For, our finding that those transit systems that meet the incentive regulation have higher levels of technical inefficiency suggests that they may be focusing more on the effectiveness part of that regulation in increasing passenger miles than on the efficiency part of reducing operating cost. 257

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Limitation: The two-step approach used in this paper is its limitation. As there is no readily available program to estimate a system of nonlinear frontier equations, future research in this direction is needed. Also, the fact that the transit systems studied receive input subsidies which we did not explicitly consider in calculating allocative distortion is a limitation of this study and an area for future research to focus. Particularly, future research should focus on developing continuous measures of these regulations and using them in the models in this paper. This will enable researchers to determine how the levels at which transit systems meet these regulations affect allocative, technical and cost efficiencies as well as distinguish the effects of these regulations from those of subsidies. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.tra.2019.06.010. References American Public Transit Association, 2011. 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