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Estimating the Relative Efficiency of Highway Safety Investments on Commercial Transportation.

Abstract

Highway safety has been one of the most important public policy issues discussed in recent years. Accidents involving commercial vehicles result in many negative effects, both personal and economic. Although the numbers of highway accidents have been declining in the past decade, many people still suffer from the effects of severe highway accidents. As public policymakers struggle to improve safety on our highway system, they are looking for analytical tools to help them assess and leverage the impact of scarce public resources. This research effort used data envelopment analysis (DEA) for benchmarking the efficiency of public policy factors (regulatory and financial) known to have an influence on safety performance. The results of this research can provide objective safety performance and improvement recommendations for commercial transportation and therefore serve to be instructive to those states with lower levels of safety performance. Our findings suggest that government agencies could focus on more effective policymaking (emphasizing road condition improvement and capital outlay utilization vs. other investments) to reduce highway fatality rates.

Introduction

Commercial motor carriers play an important role in providing transportation services in any modern industrialized economy. Accidents involving commercial motor vehicles (CMVs) have a twofold penalty: first, the direct loss of resources as a result of the accident, and second, the indirect loss of efficiency as goods are slowed and damaged in transit. Commercial motor vehicles accident costs can include increased travel time, a large property damage penalty, and the loss of human life. The major difference between driving CMVs and driving non-CMVs is the complex operational environment required of commercial drivers, including work requirements, government regulations, and company practices; company practices require optimal safety with consistent productivity (Zogby, Knipling, and Werner 2000).

In 2013 nearly 4,000 people were killed and 95,000 were injured in highway crashes involving CMVs (large trucks in this study) in the United States (National Highway Traffic Safety Administration 2013). For motor carriers, safety related vehicle technologies are changing rapidly, and firms could accelerate their adoption to increase their safety performance (Cantor, Corsi, and Grimm 2006, 2009; Cantor et al. 2013, 2016). In addition, adopting more practical safety training and awareness programs could help drivers operate vehicles in a safer manner (Swartz and Douglas 2009; Douglas and Swartz 2015, 2016a, 2016b). Technology (engineering) and training (behaviorism) have been two fundamental approaches to improved safety for many decades.

Government agencies, on the other hand, try to improve highway safety by regulating driver and carrier operations and investing in infrastructure and enforcement (public policy choices). While the focus on training practices and vehicle technologies have dramatically cut the number of truck-involved fatalities by 21 percent, from 2003 to 2013 (America Trucking Association 2013), there is still a long way to go to achieve the ultimate safety goals: eliminate all losses of life and decrease the number of injuries. As such, this research recommends that decision-makers in government agencies could focus on leveraging public policy choices to achieve this goal. Although a wide variety of CMV accident research has been conducted to identify critical risk factors and improve CMV safety (Federal Motor Carrier Safety Administration 2007a, b), it is also important to analyze and compare safety performance from a public policy perspective in order to better understand how to continue to reduce CMV fatalities effectively.

In terms of highway safety, the relationship between a set of safety performance inputs (factors) and outcomes needs to be determined carefully. A safety performance input (or "indicator") is defined as "any measurement that is causally related to crashes or injuries, used in addition to a count of crashes or injuries to indicate safety performance or understand the process that leads to accidents" by the European Transport Safety Council (2001). The purpose of this study was to investigate the relative effectiveness of a number of promising public policy choices (inputs) in improving safety performance.

Data envelopment analysis (DEA) is a methodology that can be used to measure operational efficiency. In recent years, DEA has been used to rank organizational safety performance in several fields (Beriha, Patnaik, and Mahapatra 2011; Mejza and Corsi 1999; Reiman and Pietikainen 2012; Tinmannsvik and Hovden 2003). Generally, DEA provides nonbiased results without the problem of assigning statistical weights. Traditionally, DEA has been used by researchers to "benchmark" the contribution of various inputs among firms or organizations to improve an output in order to assess how effective each input will be in improving the outcome sought.

Currently, there has not been extensive research studying the role of regulations or investments in infrastructure ("public policy choices") in improving CMV safety. Although some CMV safety research has been studied from the carriers perspective (Weber and Weber 2004), the main target of this research was focused on revenue and cost domains rather than safety exclusively. The role of relative public policy choices has not been well studied, and DEA would seem to a good analytical fit to study the issue from the public policy perspective.

The remainder of this article is organized as follows. First, findings from previous literature on the link between CMV safety performance and DEA will be presented and discussed. Next, the concepts of the DEA model and the Malmquist index are introduced. This will be followed by a description of the safety indicators and outcomes. The final sections present and discuss the results and limitations of the study. Concluding remarks and future directions of research are summarized in the last section.

Literature Review

Safety performance has been an important issue for organizations and government agencies to evaluate. Rodriguez, Rocha, and Belzer (2004) used negative binomial regression models to examine the effects of various types of truck driver compensation and trucking firm financial performance on driver safety. They concluded that small trucking firms can invest in driver compensation to improve safety outcomes. In addition, the coefficients for the direct compensation variable were not statistically significant. Corsi, Barnard, and Gibney (2002) explored the linkage between safety and financial performance among 656 motor carriers. The financial variables such as operating ratio and return on assets were not significantly correlated to the safety performance.

Britto, Corsi, and Grimm (2010) investigated the relationship between motor-carrier financial performance and safety performance. They collected a sample of 657 carriers with complete matched data from the Motor Carrier Safety Status Measurement System (SafeStat) and explored the relationship between 2002 financial data and 2003 safety performance. They analyzed the data by using count regression models and multivariate analysis and found a significant relationship between motor carriers' strong financial performance in one year and better safety performance in the subsequent year. These studies tend to examine the relationship between financial and safety performance; however, the results cannot provide suggestions for performance improvement.

The objective of Weber and Weber's 2004 study was to measure how highway-related factors (maintenance expenditures, miles of highways) and company-related factors (labor, fuel, and trucks) contributed to incomes of trucking and warehousing industry within 48 states between 1994 and 2000. They collected data from FHWA, the Fatality Analysis Reporting System (FARS), and the Bureau of Economic Analysis. The results of using DEA found that efforts to reduce inefficiency by the states could increase incomes and reduce traffic fatalities. They also found different performance in different regions. For example, the West and Southwest have more consistent efficiency than other regions. Although fatalities were considered in the analysis, the primary consideration was the evaluation of economic performance of trucking and warehousing industries.

Other researchers have begun to investigate the role of government action (law) and public policy choices (funding) on CMV safety. Of particular interest is the overlap between law/public policy and human incentives in smaller firms (Corsi et. al. 2012, 2014; Cantor et al 2013). This three-article series investigated the type of firm and driver from unionized, larger firms to smaller firms employing independent owner-operators. While "the firm as unit of analysis" is a very popular, traditional approach to understanding the effect of policy and regulation on safety, recent work in "behavioral safety" emphasizing the role of the driver was implicitly included.

The study of Shen et al. (2012) discussed the road safety benchmark from examining the number of inhabitants, passenger-kilometer traveled, and passenger cars in 27 European countries by using DEA model. They clustered countries into different groups for better identification. The study estimated the efficiency of and the setting of targets for policymakers based on the limitations of current operations. Nevertheless, it did not provide practical recommendations for future improvements. For example, how the targeted fatalities will be reduced was not clearly explained in the study. In addition, these four studies only provided one-year data comparison. The results cannot provide long-term directions for policymakers.

In Egilmez and McAvoy's study (2013), highway expenditures, vehicle miles traveled (VMT) intensity, road condition, road length, and seatbelt usage were included in the analysis. The unit of this study was 50 US states, and the findings suggested that the majority of the states had decreasing safety performance from 2002 to 2008. The results also indicated that the safety belt usage, highway expenditure, and road condition have to be improved in a more effective manner. In terms of highway expenditures and road conditions, different categories should be dismantled and addressed for a better funding utilization.

DEA has been used to measure motor-carrier operation/safety performance. Mejza and Corsi (1999) applied DEA to examine a set of safety inputs that generates safety-related outcomes for motor carriers. They used driver and vehicle performance collected from SafeStat as safety-output variables. The five safety inputs were average compensation per driver, average number of drivers per annual vehicle-mile, vehicle parts expense per annual vehicle-mile, tire and tube expense per annual vehicle-mile, and average number of tractors per annual vehicle-mile. The results can identify the efficient and inefficient performing carriers, and provide safety improvement objectives as well as recommendations for continuous improvement of their safety processes.

The application of DEA has been used to measure road safety performance in European countries (Hermans et al. 2009; Shen et al. 2012). It has recently been applied to compare US states' road safety performance by Egilmez and McAvoy (2013). In Hermans et al.'s (2009) study, the objective was to minimize fatalities with a certain level of safety indicators including the percentage of road users respecting the blood alcohol concentration (BAC) limit, speed limits, seatbelt laws, the age of the vehicles under six years old, motorway density, and trauma management. These variables are all strong safety predictors of safety performance. The findings provide priorities for improving the efficiency of road safety investments. For example, in many European countries infrastructure investment is the most important priority for enhancing road safety. Nevertheless, US government agencies did not provide a comprehensive database for these indicators.

The previous literature review leads to the following research question: Can DEA help governments to evaluate CMV safety performance, utilize investments, and make future policy priorities? Motor carriers' financial performance has been validated as a strong predictor of safety performance. However, there is a lack of knowledge about how well government investments can result in improvements in CMV safety. For the public sector, only a limited number of studies investigated the relationship between financial investments and safety performance among the states. This research can contribute by providing long-term investment-spending priority to government agencies with state comparison.

Methodology

Basic Data Envelopment Analysis Model

The proposed methodology uses DEA for benchmarking the safety performance of CMV transportation in the southeastern states of the United States. Data envelopment analysis is a linear programming approach for measuring the relative efficiency of a set of comparable groups called decision-making units (DMUs), in this case, the state governments. The idea was initially used by Farrell (1957) for evaluating economic productivity, but only to measure the efficiency of a single output.

The definition of efficiency, or productivity, is to evaluate how well the resources are used to produce the outputs in organizations. The difficulty of the original use was the selection of inputs, outputs, and the weights for measuring single input to single output ratio for multiple times. DEA was used for assessing multiple inputs and outputs by Charnes, Cooper, and Rhodes (1978) in the approach designated the "Charnes, Cooper and Rhodes" (CCR) model. The major benefit of using DEA is that it does not require the user to assign a complete specification for the functional form of the production frontier (between investment choices and safety results); the conversion process of inputs to outputs does not need to be completely understood a priori. In addition, the distribution of inefficient deviations from the frontier need not be assumed in advance. Data envelopment analysis requires general production and distribution assumptions only; it is very robust in that it eliminates the need to apply restrictive requirements of formulated assumptions and variations compared to other regression models (Cooper, Seiford, and Zhu 2011). It is therefore particularly useful in investigating the efficiency of inputs against outputs in complex adaptive systems such as those that exist outside of the laboratory or on the factory floor.

The investigated DMUs, processes, and organizational units are characterized by the conversion of multiple disproportionate inputs to outputs. For given inputs and outputs with unknown weights, each DMU will be assessed for a relative efficiency score, which is called technical efficiency (TE). In general, a DMU with an efficiency score of 1 is considered a relatively efficient unit, and a relatively inefficient unit is the DMU with a score less than 1. The basic assumption of the CCR model is that the returns to scale are constant (a stable underlying process). However, an increase in inputs does not always have the same proportional change in outputs; therefore, another model was developed by Banker, Charnes, and Cooper (the BCC model). This improved model explicitly considers variable returns to scale (Banker, Charnes, and Cooper 1984).

Instead of measuring the technical efficiency, the BCC model decomposes the technical efficiency into pure technical efficiency (PTE) and scale efficiency (SE). In terms of variable return to scale, the PTE only measures the managerial efficiency of the allocation of inputs or the capacity of outputs in the organization, and the SE indicates the ability of choosing the optimal scale. The use of the SE makes it possible to determine whether the relationships between input and output variables involved increasing, constant (the nominal CCR assumption), or decreasing returns to scale. Two terms considered for scale efficiency are increasing return-to-scale (IRS) and decreasing return-to-scale (DRS). Cooper, Seiford, and Zhu (2011) provide a comprehensive discussion for returns to scale in DEA. The general output-oriented BBC multiplier model is presented symbolically:

Objective function:

min z = [m.summation over (i=1)] [v.sub.i][x.sub.ij] + [u.sub.o] (1)

subject to:

[m.summation over (i=1)] [v.sub.i][x.sub.ij] - [s.summation over (r=1)] [u.sub.r][y.sub.rj] + [u.sub.0] [greater than or equal to] 0, for j = 1, ..., n, (2)

[m.summation over (i=1)] [u.sub.i][y.sub.i0] = 1 (3)

[v.sub.1], [u.sub.r] [greater than or equal to] [epsilon], [u.sub.0] free in sign (4)

where r = output 1 to output s; i = input 1 to input m; [y.sub.rj] = amount of output r from unit j; [x.sub.ij] = amount of input i from unit j; [u.sub.r] = the variable weight given to output r; [v.sub.i] = the variable weight given to input i. [epsilon] is a small non-Archimedean number (Charnes, Cooper, and Rhodes 1979) in order to prevent the DMUs from assigning a weight of zero. It is noted that the objective function in an output-oriented DEA model is to maximize the outputs. In contrast, the multiplier model, for an easier way to solve, transforms the function to minimize the inputs.

For each inefficient unit, a peer group is assigned from a set of corresponding efficient units. These efficient units are able to be the reference points to those inefficient units. Meanwhile, the efficient units can be said to have the same inputs and outputs orientation as inefficient units, but the difference is the weight. The aspect of peer group can help other units with lower efficiency to improve. Nevertheless, these efficient units usually do not have same importance even though they are all shown in the peer groups. The key features presented by Norman and Stoker (1991) provide insights to identify the efficient units appearing in the peer groups in an input-oriented model:

* The robustly efficient units are emerged many times from different peer groups. These types of efficient units are more likely to remain efficient unless huge shifts of inputs and outputs occur. The value of the units is larger than any other efficient units because these units can offer more information of improvement than others.

* The weakly efficient units are revealed few times in the peer groups, usually only one or two counts. These units may become inefficient after a minor change in inputs, or the outputs may shift with a small increase in an input or decrease of an output.

* The marginal inefficient units are those with an efficient score in excess of 0.9 and less than 1.0. These units are potentially efficient units in the future with a small amount of improvement.

* Medium inefficient units have efficiency between 0.7 and 0.9.

* Distinctively inefficient units have difficulties to improve their performance from under 0.7 to 1 in a short period, unless some major shifts of inputs and outputs are made.

As a result, DEA can be used in number of ways to determine how the units can be more efficient. The processes can be illustrated as the following (Boussofiane, Dyson, and Thanassoulis 1991):
   using peer groups;
   identifying efficient operating practices;
   setting targets;
   identifying efficient strategies; and
   monitoring efficiency changes over time.


After performing DEA and obtaining the performance by each DMU, the Malmquist index is used to measure whether the productivity of DMUs increase or decrease over time.

Malmquist Index

A quantity index was introduced to analyze data in a consumption framework by Malmquist (1953), and then the developed index was applied to a production analysis to measure the productivity change over time by Caves, Christensen, and Diewert (1982). Fare et al. (1992) defined the Malmquist index (MI) as the geometric mean of the two indices as shown in eq. 5-7. In Fare's definition, [D.sup.t.sub.0]([x.sup.t], [y.sup.t]) denotes the output distance function that presents the transformation of the inputs into the outputs in time period t. [d.sup.t+1.sub.0]([x.sup.t+1], [y.sup.t+1]) presents the efficiency in time period t+1. [D.sup.t.sub.0] ([x.sup.t+1], [y.sup.t+1]) is defined as the measure of the maximal proportion change in outputs required to make ([x.sup.t+1], [y.sup.t+1]) feasible in relation to the technology in time period t. Similarly, [D.sup.t+1.sub.0], ([x.sup.t], [y.sup.t]) is the function to measure the maximal proportion change in outputs required to make ([x.sup.t], [y.sup.t]) feasible in relation to the technology in time period t+1. A more comprehensive explanation can be seen in Fare's study.

The efficiency change measures the distance from the observed production to the optimal maximum production between period t and t+1 (eq. 5). The technical change (TECHCFf) measures the shift in the frontier (innovation) over time (eq. 6). The Malmquist index can be expressed by eq. 7. When a value of MI is equal to 1, there is no productivity change between inputs and outputs across the periods. A value of MI less than 1 indicates a decreasing productivity, whereas a value more than 1 denotes productivity growth.

efficiency change = [D.sup.t+1.sub.0]([x.sup.t+1], [y.sup.t+1])/[D.sup.t.sub.0])([x.sup.t], [y.sup.t]) (5)

[mathematical expression not reproducible] (6)

[mathematical expression not reproducible] (7)

This version of the Malmquist index, known as the FGLR model, is based on constant return to scale. The assumption of the CRS model does not reflect the real situation, which is that the proportion of input change does not usually change the same proportion of an output. Fare et al. (1994) introduced a VRS Malmquist model (FGNZ model) to further decompose the efficiency change into pure efficiency change (PECH) and scale change (SECH). The model is formulated as follows (eq. 8). The first expression measures the PECHCH, the second expression measures the SECH, and the third expression measures the TC.

[mathematical expression not reproducible]. (8)

Data

Selections of DMUs

This study focuses on the CMV safety performance in 12 southeastern US states: Alabama, Kentucky, Mississippi, South Carolina, North Carolina, Georgia, Florida, West Virginia, Virginia, Tennessee, Arkansas, and Louisiana. Specifically, the unit of analysis for this research is the safety performance of these states over time. The results describe the annual efficiency change. More importantly, the suggestion of assigned targets can offer future direction for decision makers.

The purpose of selecting these particular states is one of pseudoexperimental control (Cook, Campbell, and Shadish 2002), attempting to hold three of the most serious confounds to inference "constant." The mix of traffic by type of vehicle, cargo, and mode; type of road surface, and weather externalities are similar among the states chosen. With the exception of Arkansas and Louisiana, the states are classified as "southeastern states" by the Association of American Geographers. Arkansas and Louisiana were added to the selection of DMUs to increase the analytical strength of the data set with minimal impact from the effects of differences in climate.

Regarding the analysis, data included the years 2003-2011. Due to the limited data sources and the lack of data for some years, data for the years 2003, 2005, 2007, 2009, and 2011 (every two years) are considered in the analysis. Hence, a total of 60 DMUs are evaluated by designated inputs and outputs. The raw data was provided by the Federal Motor Carrier Safety Administration (FMCSA) in the Motor Carrier Management Information System (MCMIS), where CMV inspections and crash data were collected. It was provided by the Highway Statistics from the Federal Highway Administration (FHWA), which contained statistical information for highway finance and highway infrastructure. More detail is presented in the subsection.

Identification of Safety Performance Indicators

The dependent variable of interest in this study was the "Fatality Rate," defined by the FMCSA as the fatalities per 100 million vehicle miles traveled (MVMT). The fatality rate is a commonly used variable in the highway safety literature. The objective function of an output-oriented DEA model requires values to be maximized. Consequently, an inverse value transformation was performed, since our objective was to reduce the fatality rate. Therefore, the minimization of the fatality rate was represented as the maximization of the mean travel distance between fatalities. To select the most appropriate input variables, some critical factors from the previous research were chosen. Egilmez and McAvoy (2013) considered four main safety performance indicators (SPIs): economic investment on the system, the usage of the system, the condition of the system, and the personal safety in the system. Hermans et al. (2009) defined alcohol and drugs, speed, protective systems, trauma management, infrastructure, and vehicle life as SPIs. Although some significant variables were applied from earlier studies (Tsai et al. 2015), not all can be incorporated in our DEA model. Nevertheless, some new factors related to CMV were imported.

It is almost impossible to collect data from every truck driver and company, due to the issue of time consumption and large costs. For example, lower seatbelt usage is one of the critical factors that increases the probability of fatal crashes. According to Cook, Hoggins, and Olson (2008), the CMV seatbelt usage is lower than passenger vehicle seatbelt usage. Still, there is no existing database to record or compare CMV seatbelt usage. Two steps were followed to choose the inputs. Because we want to provide southeastern state governments with an easy conductible tool to analyze and monitor safety performance, the inputs should choose from data that can be collected easily as the initial step. In addition, these factors must be controllable for improving the safety performance.

The inputs were collected from two online databases, MCMIS and FMCSA; the highway statistics were collected from the FHWA. In this study, four main subject areas were evaluated: the economic investment on the system, the condition of the system, the inspection status, and the level of traffic enforcement. The economic investment on the system and the condition of the system were extended from the work of Egilmez and McAvoy (2013). Because federal and state agencies may concentrate on different categories of highway expenditures, the economic investments on the system were detailed into three categories: capital outlay, maintenance and services, and highway law enforcement and safety.

Capital outlays are expenditures associated with highway improvements. Maintenance and traffic services include road maintenance, traffic control operations, snow and ice removal, and other items. Highway law enforcement and safety consists of state agencies, inspection programs, safety programs, and other items. These variables were standardized by dividing road lengths. We also separated the condition of the system into rural system and urban system. Road condition was categorized on scale-based data as "very good," "good," "fair," "mediocre," and "poor," which was determined by the FHWA in 2014 (Federal Highway Administration 2014). The road condition score is transformed into a value between o and 1, which is defined as the total weighted-miles of road divided by the total graded road length (Egilmez and McAvoy 2013).

The next subject area is the inspection status, which consists of three variables: drivers with a bad inspection status per MVMT, vehicles with a bad inspection status per MVMT (number of out-of-service driver and vehicle violations), and full inspection rates. It was expected that fatigued drivers and vehicles with bad maintenance records would lead to a higher crash risk. The effect of inputs on the outputs has to have the same direction of impact; therefore, a transformation is used. These two variables are calculated as one divided by the number of out-of-service violations per MVMT. In terms of CMV inspections, there are six levels. Full inspection rates represent the rates of comprehensive inspection of CMVs per MVMT. The last SPI index is traffic enforcement. The evidence shows that some types of moving violations are highly correlated with future crash involvement (Murray, Lantz, and Keppler 2006). It is also suggested that more traffic tickets reduce accidents (Luca 2015). Therefore, the number of operation violations per MVMT was included in the study. Four SPI indices are listed in table 1.

For our variable selection, the variables belonging to the first SPI, the economic investments on the system, indicate the impact of investment on highway to fatalities. It is a premise of a public policy that effective spending on highway improvements, maintenance, and law enforcement and safety have a positive effect on lowering the fatality rate. Therefore, there should be a positive relationship in our model. The same assumption can be applied to the second SPI, the condition of the system, which is that better road conditions lead to a lower fatality rate. The third SPI, inspection status, was also expected to have a positive relationship based on our transformation. The last SPI, traffic enforcement, should have a positive impact in reducing the risk of traffic crashes.

To investigate our assumption, the next step is to perform a correlation analysis to find the relationship between the inputs and the output. The variables with significant positive coefficient values are the valid inputs in the model. The results are provided in table 2. With the exceptions of full inspection rates (Full_ins) and operation violations per MVMT (Violations), other inputs have a significant positive linear sense to the output. There could be a reversal of causality in the model at work. States with worse vehicle inspection results would place an emphasis on increased enforcement in this area. This concept could also be at work in the case of the violations. Hence, these two variables should be investigated further; the a priori expectation would be for improvements in those variables to have a positive impact on the output.

Based on the Pearson product moment correlation coefficient, maintenance, and traffic enforcement and safety expenditures have the most significant relationship with the fatality rate. It is noted that the number of DMUs should be at least twice the number of inputs and outputs multiplied to sustain the accuracy of the results (Golany and Roll 1989). Bowlin (1998) suggested having three times the number of DMUs as there are input and output variables. In our study, a total number of 60 DMUs satisfied these assumptions.

Results and Discussion

The results of using DEA to examine the efficiency of the data collected from the seven inputs and one output for 12 southeastern states from 2003 to 2011 are presented as follows: (a) identification of road safety scores and relevant benchmarks, (b) an overall efficiency score based on the Malmquist index, and (c) a sensitivity analysis.

Identification of Relevant Benchmarks

The results of solving the proposed model provided two efficiency indices (PTE and SE) for each DMU, as well as the returns to scale. As previously stated, the PTE measures the managerial efficiency in increasing the outputs by allocating the inputs in the organization. This study reflects the safety performance of a state under the variable returns to scale. The SE indicates the ability of the model to select the optimal scale under the variable returns to scale. TE is the overall efficiency under constant returns to scale; in this study, it represents the overall safety performance of a state.

In the output-oriented DEA model, a DMU with a value greater than 1 is relatively inefficient, as compared to other efficient DMUs. The results are shown in table 3. In 2003 only two states were observed as "technically efficient" (Mississippi and Tennessee). Four other states were identified as efficient states under increasing returns to scale. The results showed that four states (Arkansas, Georgia, Louisiana, and South Carolina) utilized their resources well, but they could adjust the size of their resources to reach constant returns to scale. For other inefficient states, the focus would be the target setting of reducing the fatality rates without changing the current resource allocation.

In 2005 only two states had a pure technical efficiency equal to 1: Arkansas and Georgia. In 2003 six states had increasing returns to scale; therefore, a DMU should reconsider its funding strategy and law enforcement operations for reducing the fatality rates to obtain the optimal return to scale. In 2005 the four states with decreasing returns to scale should have considered utilizing the inputs to have better safety performance. In 2007 only three states were relatively efficient, as compared to the other DMUs. It is noted that 10 states demonstrated pure technical efficiency out of the 12 states in 2009, which means the resources allocation and traffic enforcement reduced the fatality rates without wasting money. The values of the PTE in 2011 had a slight increase; regardless, more than half of the states still remained relatively efficient. In terms of efficiency, there were several efficient units on the frontier. These efficient units can still be compared for the best practice performance.

The peer group is an efficiency reference set in which the members are identified as similar efficient performance units; inefficient DMUs are compared directly with these efficient DMUs in the group. When a DMU is referred to more times by other inefficient DMUs in the group, the input utilization and the produced outputs have more importance. The reference of the DMUs can be used as realistic targets for other DMUs for efficiency improvements. The results are illustrated in figure 1. The performance of Mississippi in 2009 were compared 17 times to the other inefficient units; Tennessee in 2009 was compared 16 times. How these two state governments utilized the resources and operated their enforcement would be the targets for other state governments.

Road Safety Performance Scores Based on the Matmquist Index

By solving the Malmquist-VRS model, road safety performance scores are shown in figure 2. The values are the means of the biennial periods between 2003 and 2011. Three metrics (i.e., PECH, TECHCH, and SECH) represent the components of the DEA model as introduced in the Methodology section. Regarding road safety performance, PECH measures the positive/negative efficiency growth of the fatality rate affected by the composition of the inputs. During the periods of 2003-2005 and 2007-2009, the average safety performance had a positive efficiency growth level of 2.5 percent and 2.1 percent respectively. Although the fatality rate decreased from 2005 to 2007, the negative efficiency growth indicated that the fatality rates should have decreased more in terms of the amounts of resource allocation. This could indicate that spending was misallocated during that period. Another negative efficiency growth level occurred during the period of 2009-2011 (-0.6%). During that time, the auto industry was starting to recover; shifting the expansion to the Southeast might have increased the highway driving risk.

The results of TECHCH show inconsistent performance over time. A negative growth of TECHCH was observed from 2003 to 2005, but there was more than 20 percent positive growth from the periods of 2005-2007 and 2007-2009. After that, a downward trend of TECHCH was detected from 2009 to 2011. A positive technical change implies an innovation or technology improvement over time such as new roadside technology corridors and safety program campaigns. Decreasing technological efficiency denotes that government agencies did not use the technology effectively. The value of the MI was significantly affected by the TECHCH since it is the multiplication of SECH, PECH, and TECHCH.

Results of the Malmquist Index

In terms of TECHCH, nine states showed constant efficiency, two states (i.e., Alabama and Florida) had increasing performances in efficiency, and only one state, South Carolina, was observed to have a decreasing performance in efficiency. The results of TC indicate a positive safety improvement from resource allocation and technology within the period of 2003-2011 in 12 states. Mississippi was observed to have a decreasing technological change over time. In terms of the overall productivity index (MI), only Mississippi and South Carolina had negative growth from the inefficient technology use and resource utilization (see table 4).

Sensitivity Analysis

A sensitivity analysis was performed to test the robustness of the model by selecting different numbers of inputs. In the study, the VRS-DEA model was solved seven times by only selecting six out of seven inputs to measure the variation in the efficiency. Also of note and requiring further investigation are the mediocre associations between and among the CMV operations-related inputs, which display a moderately strong association with fatality rates in the biserial correlations that are not supported by the sensitivity analysis.

Figure 3 presents the average sensitivity of each input variable on the impact of the efficiency of DMUs for each period. The highest variation occurs when the rural road condition, urban road condition, or capital outlay expenditure is dropped, especially within the first three periods. For the first two inputs, the average variation is around 6 percent for the entire period. When the urban road condition is dropped, eight of the weakly efficient units of 28 efficient units become inefficient units. When the rural road condition is unselected, five of the weakly efficient units become inefficient units. The capital outlay is ranked third among all the variables. Therefore, it can be concluded that the road condition (rural/urban) and the capital outlay are the most significant inputs out of the seven inputs. From the biserial correlations (table 2 above), this is supported by the effect sizes of Rural 0.332, Urban 0.286 and Capitol 0.392, which are robust factors. An increased investment in these areas has a strong likelihood of reducing fatalities. Highway law enforcement and safety is found to be the least significant factor. This relationship is contradicted by the simple biserial correlation data and merits further investigation. This could be an anomalous result of a restriction of the range and variation of the input variable relative to the outcome variable, which would indicate a consistent contribution from government agencies over the time period investigated. Also of note and requiring further investigation are the mediocre associations between the CMV operations-related inputs, which display a moderately strong association with fatality rates in the biserial correlations but that are not supported by sensitivity analysis.

Issues and Limitations

Several limitations to inferences must be applied to the results of this study. First, the inputs were collected from public datasets. All research relying on government-collected archival data suffer from the obvious restrictions to inference resulting from how the variables were defined, and how the data were collected and "pre-processed" by the system set up to collect the data. Archival data may be easily and readily available; but the numbers might not represent the actual variables of interest to the researcher in the study. Many times the measures used are "proxy" in nature. In addition, much of the data used in this study were reported from lower-level (local and regional) government agencies, and many of the accident reports contained missing values. For an original DEA model, missing values in inputs or outputs cannot be handled. The exclusion of records containing partial data for the variables of interest, while a common limitation for research of this type, still confounds the generalizability of the results somewhat. As with any research using archival, proxy measures, there will be inconsistencies between how the data descriptions are interpreted by the people entering the data vs. those using the data for analysis. In addition, during data entry the exclusion of some values and variables is not random, but researchers must presume there is no significant nonresponse pattern. The results hold for the sample, but caution must be exercised when extending the implications into practice without further validation.

In addition, government agencies update the collecting method for data every several years. This frequently involves changing how variables are defined, classified, and measured. Most often, the change takes place and historical data are not adjusted to bring them into harmony with the new interpretation; a "discontinuity" in the data exists. While the researchers are not aware that any of the primary variables of interest in this study were changed substantively inside the time range of data collected, this can still present subtle changes in the response of variables to each other. Thus, it is problematic to monitor a longer safety performance change due to data accuracy.

The most significant common threat to inference is, of course, the "unmeasured variables" or "externalities" problem. There are many public policy choices that were not represented in this dataset. A well-designed and -executed review of previous factors studied in the literature helps guard against the possibility of missing an important factor; however, it is still important to keep in mind the contributions to variance in the output variable are only relevant compared amongst the factors studied. For example, a "public awareness" campaign on the importance of seatbelt usage may become a "historical confound" if it also biases local law enforcement to begin including the use of seat belts (or not) as a contributing factor to accidents in a way they had not been doing prior to the implementation of the awareness campaign. If the absence/presence of (or level of) this externality was not formally recognized and controlled for, its contribution to variance would be transferred (erroneously) to other variables. While the researchers were diligent (through the review of literature and analysis of contemporaneous potential confounds), this problem still exists.

Implications for Research and Practice

In this study, the CMV highway safety performance was measured every two years from 2003 to 2011. The fatality rates dramatically decreased during this time frame. Among the contributing factors for consideration were the adoption of new safety programs, innovative vehicle technology, and investments on highway maintenance and condition. The state government agencies also set up their own strategies to reduce the rate of CMV fatalities from different safety projects. The purpose of this research was to try to assess the relative contributions of the various programs to the reduction seen.

In an attempt to estimate the relative effectiveness of various government effort with the aim of reducing crashes involved in CMVs, DEA was successfully used to analyze safety performance and public policy choices among several similar states. DEA and the Malmquist index were applied to measure the efficiency over time. Seven safety performance indicators were included in the model: capital outlay, maintenance and service expenditures, highway law enforcement and safety spending, rural road conditions, urban road conditions, number of out-of-service driver violations per MVMT, and the number of out-of-service vehicle violations per MVMT. The only outcome was (the inverse of) the fatality rate. The southeastern states were selected for the period between 2003 and 2011. This study found that it is indeed practical to analyze safety investments this way, and we recommend that this type of analysis become a regular practice among regions (to account for difference in hazard profiles due to weather, geography, density, and so on). A determination of which factors are more or less effective in reducing highway fatalities should be assessed, evaluated, and potentially acted upon.

The results of the DEA analysis and Malmquist index values indicated an overall positive efficiency growth among the southeastern states. The findings of the research present different results comparing to Egilmez and McAvoy's study that the main measure unit is all vehicles on the road. The inconsistent results may indicate that the CMV safety and resource utilization has been monitored more effectively by companies and government agencies than overall road safety over time. The majority of overall safety performance is affected by the change of technology. Rather than a consistent increasing or decreasing trend in efficiency from the period by period analysis, the unstable performance change raised two concerns. First, the utilization of inputs from the stakeholders should be improved (better use of investments), and second, how the economic issues play a role in affecting the efficiency. Although each indicator should be improved for better CMV safety, some factors have to be prioritized, such as rural road condition, urban road condition, and capital outlay. This study found that differences between/among factors do exist, and additional factors must be included in future analyses of this type. Follow-up research is needed both to validate the factors found to be significant in this study for this (southeastern) region and to identify additional public policy choice/investments for data collection and analysis.

This research developed a framework for evaluating southeast CMV highway safety. There were several studies addressing the road safety problems, and some indicators were selected. It must be noted that CMV safety is another lesson that needs to be analyzed as a separate category. There is still more work to do in studies. First, the injury rate should be considered as a potential output. Second, a more detailed investment on highways, particularly for CMV, should be considered for a more precise result. Finally, a regional comparison should be obtained for federal agencies.

Note

This work was supported by the NIOSH Deep South Center for Occupational Safety and Ergonomics, under grant number: T42OH008436. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of CDC-NIOSH.

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Yao-Te Tsai

Feng Chia University

Stephen M. Swartz

Corresponding Author

Auburn University

steve.swartz@auburn.edu

Fadel M. Megahed

Miami University

Caption: Figure 1 Peer Count Summary

Caption: Figure 3 Sensitivity Analysis
Table 1/Input and Output Variables for Safety Performance

Inputs    [SPI.sub.1]: The economic investment on system (expenditure)
             [I.sub.1] capital outlay
             [I.sub.2] maintenance and services
             [I.sub.3] highway law enforcement and safety
          [SPI.sub.2]: The condition of system
             [I.sub.4] Rural road condition
             [I.sub.5] Urban road condition
          [SPI.sub.3]: Inspection status
             [I.sub.6] 1/Out of service driver violations per MVMT
             [I.sub.7] 1/Out of service vehicle violations per MVMT
             [I.sub.8] Full inspection per MVMT
          [SPI.sub.4]: Traffic enforcement
             [I.sub.9] Operation violations per MVMT
Outputs   [O.sub.1]1/Fatality rates

Table 2/Correlation Analysis

                                          Capital      Maint

Capital           Pearson Correlation     1           0.453 **
                  Sig. (2-tailed)                     0.000
Maint             Pearson Correlation     0.453 **    1
                  Sig. (2-tailed)         0.000
Law_Safety        Pearson Correlation     0.572 **    0.815 **
                  Sig. (2-tailed)         0.000       0.000
Urban             Pearson Correlation     0.195       0.086
                  Sig. (2-tailed)         0.135       0.514
Rural             Pearson Correlation     0.369 **    0.116
                  Sig. (2-tailed)         0.004       0.377
Full_ins          Pearson Correlation    -0.115      -0.235
                  Sig. (2-tailed)         0.381       0.07
DOOS              Pearson Correlation     0.178       0.403 **
                  Sig. (2-tailed)         0.173       0.001
voos              Pearson Correlation     0.106       0.184
                  Sig. (2-tailed)         0.422       0.159
Violations        Pearson Correlation    -0.178      -0.135
                  Sig. (2-tailed)         0.173       0.304
Fatality_rates    Pearson Correlation     0.392 **    0.611 **
                  Sig. (2-tailed)         0.002       0.000

                  Law_Safety      Urban       Rural      Full_ins

Capital            0.572 **      0.195       0.369 **    -0.115
                   0.000         0.135       0.004        0.381
Maint              0.815 **      0.086       0.116       -0.235
                   0.000         0.514       0.377        0.07
Law_Safety         1             0.111       0.145       -0.402 **
                                 0.4         0.27         0.001
Urban              0.111         1           0.808 **    -0.203
                   0.4                       0.000        0.12
Rural              0.145         0.808 **    1           -0.239
                   0.27          0.000                    0.066
Full_ins          -0.402 **     -0.203      -0.239        1
                   0.001         0.12        0.066
DOOS               0.437 **     -0.039      -0.013       -0.403 **
                   0.000         0.77        0.924        0.001
voos               0.221         0.169       0.297 *     -0.553 **
                   0.089         0.197       0.021        0.000
Violations        -0.088        -0.375 **   -0.514 **     0.143
                   0.505         0.003       0.000        0.276
Fatality_rates     0.663 **      0.286 *     0.332 **    -0.25
                   0.000         0.027       0.01         0.054

                   DOOS        VOOS      Violations    Fatality_rates

Capital            0.178       0.106       -0.178         0.392 **
                   0.173       0.422        0.173         0.002
Maint              0.403 **    0.184       -0.135         0.611 **
                   0.001       0.159        0.304         0.000
Law_Safety         0.437 **    0.221       -0.088         0.663 **
                   0.000       0.089        0.505         0.000
Urban             -0.039       0.169       -0.375 **      0.286 *
                   0.77        0.197        0.003         0.027
Rural             -0.013       0.297 *     -0.514 **      0.332 **
                   0.924       0.021        0.000         0.010
Full_ins          -0.403 **   -0.553 **     0.143        -0.250
                   0.001       0.000        0.276         0.054
DOOS               1           0.806 **     0.054         0.344 **
                               0.000        0.681         0.007
voos               0.806 **    1           -0.12          0.287 *
                   0.000                    0.36          0.026
Violations         0.054      -0.12         1            -0.338 **
                   0.681       0.36                       0.008
Fatality_rates     0.344 **    0.287 *     -0.338 **      1
                   0.007       0.026        0.008

** Correlation is significant at the 0.01 level (2-tailed).

* Correlation is significant at the 0.05 level (2-tailed).

Table 3/Efficiency Scores for 12 States

States(year)     TE      PTE       SE     RTS

AL03           1.610    1.597    1.007    drs
AR03           1.038    1.000    1.038    irs
FL03           2.028    1.869    1.086    drs
GA03           1.003    1.000    1.003    irs
KY03           1.381    1.339    1.032    irs
LA03           1.672    1.000    1.672    irs
MS03           1.000    1.000    1.000     --
NC03           1.433    1.427    1.004    drs
SC03           1.319    1.000    1.319    irs
TN03           1.000    1.000    1.000     --
VA03           1.346    1.321    1.018    drs
WV03           2.033    1.873    1.087    irs
AL05           1.479    1.464    1.009    drs
AR05           1.018    1.000    1.018    irs
FL05           2.092    1.946    1.075    drs
GA05           1.000    1.000    1.000     --
KY05           1.376    1.319    1.043    irs
LA05           1.718    1.477    1.164    irs
MS05           1.244    1.215    1.024    irs
NC05           1.704    1.689    1.009    drs
SC05           1.698    1.678    1.012    irs
TN05           1.425    1.420    1.002    irs
VA05           1.252    1.230    1.016    drs
WV05           1.980    1.789    1.107    irs
AL07           1.684    1.667    1.010    drs
AR07           1.198    1.000    1.198    irs
FL07           1.412    1.389    1.016    drs
GA07           1.056    1.013    1.043    irs
KY07           1.272    1.247    1.020    drs
LA07           1.346    1.140    1.179    irs
MS07           1.000    1.000    1.000     --
NC07           1.277    1.276    1.001    drs
SC07           1.167    1.101    1.059    irs
TN07           1.253    1.000    1.253    irs
VA07           1.074    1.074    1.000     --
WV07           1.458    1.233    1.181    irs
AL09           1.000    1.000    1.000     --
AR09           1.000    1.000    1.000     --
FL09           1.000    1.000    1.000     --
GA09           1.000    1.000    1.000     --
KY09           1.054    1.000    1.054    irs
LA09           1.000    1.000    1.000     --
MS09           1.000    1.000    1.000     --
NC09           1.043    1.041    1.002    drs
SC09           1.095    1.087    1.008    irs
TN09           1.000    1.000    1.000     --
VA09           1.000    1.000    1.000     --
WV09           1.060    1.000    1.060    irs
AL11           1.013    1.001    1.012    irs
AR11           1.082    1.000    1.082    irs
FL11           1.117    1.109    1.007    irs
GA11           1.078    1.047    1.030    irs
KY11           1.000    1.000    1.000     --
LA11           1.000    1.000    1.000     --
MS11           1.152    1.000    1.152    irs
NC11           1.000    1.000    1.000     --
SC11           1.200    1.193    1.007    drs
TN11           1.034    1.013    1.021    drs
VA11           1.000    1.000    1.000     --
WV11           1.221    1.000    1.221    irs

Note: DRS = Decreasing return-to-scale,
IRS = increasing return-to-scale.

Table 4/Malmquist Index

States                TC       PECHCH     SCH        MI

Alabama              1.058     1.084     1.003     1.150
Arkansas             1.024     1.000     1.000     1.024
Florida              1.083     1.033     1.029     1.151
Georgia              1.043     1.000     1.000     1.043
Kentucky             1.116     1.000     1.000     1.116
Louisiana            1.088     1.000     1.050     1.142
Mississippi          0.977     1.000     0.993     0.970
North Carolina       1.082     1.000     1.000     1.082
South Carolina       1.030     0.975     0.994     0.998
Tennessee            1.022     1.000     1.000     1.022
Virginia             1.105     1.000     1.000     1.105
West Virginia        1.069     1.000     1.041     1.114

Figure 2 The Overall Trend Performance

            MI      SECH    PECH    TECHCH

2009-2011   0.915   0.981   0.994   0.939
2007-2009   1.327   1.064   1.025   1.217
2005-2007   1.17    0.964   0.991   1.225
2003-2005   0.939   1.03    1.021   0.893

Note: Table made from bar graph.
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Author:Tsai, Yao-Te; Swartz, Stephen M.; Megahed, Fadel M.
Publication:Transportation Journal
Date:Mar 22, 2018
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