The purpose of this study is to investigate the issue of efficiency in the U.S. motor carrier industry using DEA and SFA. While both methods used the same variables, the resulting efficiency scores were significantly different. This leads to the question of which method is a better measure of efficiency.Public Economics,

Allen, Albert J.

Estrada, Joselito K.

Shaik, Saleem

English

Research Papers in Economics

 
An Assessment of the Efficiency of Agribusiness Trucking Companies 
A Data Envelopment Analysis Approach 
 
 
Albert J. Allen 
Department of Agricultural Economics 
Mississippi State University 
P.O. Box 5187 
Mississippi State, MS 39762 
Phone: (662) 325-2883 
E-mail: allen@agecon.msstate.edu
 
Saleem Shaik 
Department of Agricultural Economics 
Mississippi State University 
P.O. Box 5187 
Mississippi State, MS 39762 
Phone: (662) 325-7992 
E-mail: shaik@agecon.msstate.edu
 
and 
 
Joselito K. Estrada 
Department of Business Administration 
University of Texas at Brownsville 
80 Fort Brown 
Brownsville, TX 78520 
Phone: (956) 983-7151 
E-mail: jkestrada@utb.edu
 
 
 
 
Selected Paper prepared for presentation at the 
Southern Agricultural Economics Association Annual Meetings 
Little Rock, Arkansas, February 5-9, 2005 
 
 
 
 
 
 
Copyright 2005 by Albert J. Allen, Saleem Shaik, and Joselito K. Estrada. Readers may 
make verbatim copies of this document for non-commercial purposes by any means, 
provided that this copyright notice appears on all such copies. ABSTRACT 
 
  The purpose of this study is to investigate the issue of efficiency in the U.S. motor 
carrier industry using DEA and SFA. While both methods used the same variables, the 
resulting efficiency scores were significantly different. This leads to the question of 
which method is a better measure of efficiency. 
INTRODUCTION 
The motor carrier industry occupies an important position in the movement of 
goods and services. Given its advantages in the areas of accessibility to points of origin 
and final destination and the relatively low capital requirements for industry entry, motor 
carriers have overshadowed other transportation modes in terms of the market share, 
employment, and the number of firms.  
In 2002, motor carrier employment accounted for 37 percent of the 3,581,013 
persons employed in the overall transportation industry. In terms of payroll, this sector’s 
share of the industry’s $127 billion annual payroll was estimated at 35 percent. As far as 
market share was concerned, motor carriers accounted for roughly 57 percent of the 
195,143 firms in the transportation industry (County Business Patterns, 2002). 
In an era of rising fuel costs, transportation deregulation, and competition from 
foreign motor carrier operators, the issue of efficiency becomes important. Understanding 
the factors that allow firms to become efficient would be helpful in trying to alleviate the 
possibility of reduced domestic motor carrier transportation capability. 
The purpose of this study is to investigate the issue of efficiency in the U.S. motor 
carrier industry. Specifically, the objective of this endeavor is to estimate the relative 
efficiency of U.S. agribusiness trucking firms using Data Envelopment Analysis (DEA). 
While the measurement of efficiency in the agribusiness trucking industry has been conducted previously (Allen, Fuentes, and Shaik, 2004), the present study differs with 
respect to how efficiency is estimated.  
One appealing characteristic of DEA is the fact that there is no need to specify the 
functional form of the production function to be used (Pedraja-Chaparro, Salinas-
Jimenez, and Smith, 1999). Despite its appeal, the question of whether the DEA model 
being used is correctly specified becomes an issue. DEA does not have any statistical 
tests for goodness-of-fit or misspecification that parametric statistical methods, such as 
regression, have (Van der Meer, Quigley, and Storbeck, 2004).  
In order to avoid the problem of model misspecification, the present study follows 
the procedure established by Van der Meer, Quigley, and Storbeck (2004). To test their 
DEA model of operational efficiency among Coastguard coordination centers in the UK 
was correctly specified, the DEA efficiency scores were compared and ranked with 
efficiency scores from a stochastic frontier analysis (SFA) model that they developed for 
the same purpose. The results obtained in both models were similar. 
This study compared efficiency scores from the DEA model with SFA efficiency 
scores. To test for similarities, correlation coefficients were estimated for both sets of 
efficiency scores.  
The results of this study could present some interesting considerations for 
decision-makers who use DEA in their activities. Specification of the most appropriate 
variables to use in order to maximize/minimize a given objective is of importance. In a 
highly competitive industry, such as the U.S. motor carrier industry, this can spell the 
difference between choices that lead to the continuation or the cessation of a firm’s 
operations. DATA AND METHODS 
DEA is a mathematical technique that allows for the assessment of the operating 
efficiency of each firm, which is called a decision-making unit (DMU) in DEA, relative 
to other DMUs in the same industry. Using a set of inputs and outputs that are common to 
each DMU, a “virtual” DMU is generated and serves as the basis of comparison for each 
DMU in the industry. This “virtual” DMU embodies the most relatively efficient firm in 
terms of input use and output production. If a DMU’s input use and output production are 
the same as that of the “virtual” DMU, that DMU is said to be efficient. DMUs that fall 
short of the “virtual” DMU in terms of input use and output production are deemed to be 
inefficient. 
This non-parametric method for estimating frontier functions represents one of 
two principal methods. The other method, which is econometric in nature, is referred to 
as Stochastic Frontier Analysis or SFA (Coelli, 1996). A description of these two 
efficiency models is presented below. 
EFFICIENCY MODELS  
STOCHASTIC FRONTIER ANALYSIS [SFA] 
The technology transforming input vector X= (x1....x4) into output denoted by Y can be 
represented by Cobb-Douglas and the Translog stochastic production function as: 
(1) Yi = xiβ + (Vi - Ui)   ,i=1,...,N, 
where Yi is the production (or the logarithm of the production) of the i-th firm; 
 x i is a k×1 vector of (transformations of the) input quantities of the i-th firm;
1
  β is a vector of unknown parameters; 
                                                 
1For example, if Yi is the log of output and xi contains the logs of the input quantities, then the Cobb-
Douglas production function is obtained. Vi are random variables which are assumed to be iid. N(0,σV
2), and independent 
of the 
Ui which are non-negative random variables which are assumed to account for 
technical inefficiency in production and are often assumed to be iid. |N(0,σU
2)|. 
 
The term exp{- Ui } corresponds to the technical efficiency [TE] measure.  In the 
case of the production function TE will take the value between zero and one.  The 
unobservable Ui being predicated from the estimation is conditional upon the observed 
value of ( Vi - Ui ) 
DATA ENVELOPMENT ANALYSIS [DEA] 
The technology that transforms inputs x = (x1.......xI)  0  ⎥
I
+ into outputs yg = 
(y1.......yG) 0 ⎥
G, can be represented by output, input and graph sets.  These sets can be 
effectively utilized to compute efficiency measures. 
  Input oriented definition of efficiency is the multiple by which year t input can be 
decreased at a later point in time, producing the year t outputs.  Following Fare, 
Grosskopf and Lovell (1994 pp 62-63), the input reference set satisfying constant return 
to scale and strong disposability of inputs can be defined as: 
(2)       L (y)  =  { x :  y produced by x in year T;   y  
T
+
J ∈ℜ}
  
This concept can be represented by an input distance function evaluated for any year t 
using a reference production possibilities set T, as: 
            D (y ,x )   =  min  {  :     y  P (x ) }
                              or
            min      s.t.             y    Y z
(3)                                        x    X z
                                              z     0 
i
Ttt - 1 t Tt
, z
t
t
λλ
λ
λ
λ
∈
≤
≤
≥
             where X  =  (x
12 T , ,....., ) xxHere, the second expression identifies the linear program that is used to calculate the 
distance function, with the z's being a Tx1 vector of intensity variables that identify the 
constant return to scale boundaries of the reference set. 
  This study used operational data for agricultural commodities and refrigerated 
food carriers, which was obtained from the Technical Transportation Services Blue Book 
of Trucking Companies, for the years 1994 to 2002. The input and output variables that 
were used in conducting the data envelopment analysis were the same variables utilized 
in a study conducted by Allen, Fuentes, and Shaik (2004).   
Descriptions of these variables are presented in Table 1. 
 
RESULTS 
 
  Estimated results of the DEA and SFA models for the refrigerated foods and 
agricultural commodities carriers are presented in Tables 3 and 4, respectively. Between 
1994 and 2002, mean efficiency scores for both carrier sectors using the DEA and SFA 
models have been consistent, wherein the DEA mean scores exhibiting slightly values 
than the SFA scores. 
  A cursory inspection of the data may show that both measures of efficiency seem 
to produce similar results. When we tried to correlate the DEA and SFA scores for all 
firms in all years for each sector, a different picture emerged. 
  Table 4 shows us the correlation coefficients between the DEA and SFA 
efficiency scores for refrigerated foods and agricultural commodities carriers. In both 
types of carriers, the correlation coefficients were too close to zero to merit any distinct 
type of linear relationship.   SUMMARY AND CONCLUSIONS 
 
  This paper sought out to investigate the efficiency of several sectors within the 
U.S. trucking industry. Data envelopment analysis (DEA) was used as a means of testing 
the level of efficiency of these firms. 
  Since the DEA model does not necessarily call for the specification of the input 
and output variables in the model, we decided to use variables that were obtained from a 
prior efficiency study using stochastic frontier analysis (SFA). Given the fact that 
econometric models such as SFA have to specify the functional form of the model, it was 
assumed that this would give us a DEA model whose variables are appropriately 
specified. Essentially, the input and output variables in the SFA are the same as in the 
DEA model. Results from the DEA and SFA models illustrated that the efficiency scores 
from both models were significantly different from each other. 
  This allows us to raise an important issue regarding the measurement of 
efficiency. While we do not profess to know which efficiency estimation model or 
approach would be superior, does an approach or method exist for testing the accuracy of 
these estimation methods? 
  
REFERENCES 
 
Allen, Albert, Porfirio Fuentes, and Saleem Shaik (2004). Stochastic Frontier Analysis of 
Agribusiness Trucking Companies. Selected paper presented at the American 
Agricultural Economics Association Annual Meeting, Denver, CO, August 2004. 
 
Coelli, Tim (1996). A Guide to DEAP Version 2.1: A Data Development Analysis 
(Computer) Program. CEPA Working Paper 96/08. Center for Efficiency and 
Productivity Analysis, Department of Econometrics, University of New England. 
 
Fare, R., S. Grosskopf, and C.A.K. Lovell (1994). Production Frontiers, Cambridge 
University Press.  
Pedraja-Chaparro F, Salinas-Jimenez J and Smith P (1999). On the quality of the data 
envelopment analysis model. Journal of the Operational Research Society 50: 636-644. 
 
Van der Meer, R.B., J. Quigley, and J.E. Storbeck (2004). Using Data Envelopment 
Analysis to Model the Performance of UK Coastguard Centres. Working paper. 
University of Stratchclyde (Glasgow, UK) and University of Texas at Brownsville. 
 
U.S. Census Bureau (2002). County Business Patterns. U.S. Department of Commerce, 
U.S. Census Bureau. Washington, D.C. Available at http://censtats.census.gov/ 
(Accessed: January 2005). 
  
 
 
Table 1: Input and Output Variables in the DEA and SFA Models. 
Variable Description 
Labor Variables 
1.  Number of drivers and helpers 
2.  Number of cargo handlers 
3.  Number of officers, supervisors, 
clerical and administrative staff 
4.  Total number of other laborers 
Capital Variables 
1.  Number of tractors owned 
2.  Number of trucks owned 
3.  Number of tractors leased 
4.  Number of trucks leased 
5.  Other equipment 
Operating Variable 
Costs 
1.  Fuel – gallons, oil, and lubricants 
2.  Total maintenance 
Input 
Operating Fixed 
Costs 
1.  Total operating taxes and licenses 
2.  Total insurance 
3.  Depreciation and amortization 
Output Total  Ton-Miles 
Source: Allen, Fuentes, and Shaik (2004). 
 
 
 
 
 
 
 
 
 
 
 
 
 Table 2: DEA and SFA Efficiency Scores for Refrigerated Food Carriers (1994-2002). 
1994 1995 1996  1997  1998  1999  2000  2001  2002  DMU 
DEA  SFA  DEA  SFA  DEA  SFA  DEA SFA  DEA SFA  DEA  SFA DEA SFA DEA SFA DEA SFA 
1  0.988 0.753 0.998 0.920 0.972 0.937 0.976  0.775  0.937 0.797 0.986 0.852  0.984 0.910  0.894 0.798  0.938 0.825 
2  0.976 0.887  1 0.832 0.986 0.791  1  0.829  0.952 0.820  1 0.831  0.982 0.906  0.898 0.900  0.938 0.857 
3  1 0.699 0.975 0.829 0.990 0.866 0.987  0.843  0.946 0.825 0.994 0.913  0.999 0.843  0.888 0.865  1 0.819 
4  1 0.716 0.830 0.870  1 0.917 0.998  0.883  0.974 0.946  1 0.996  1 0.881  0.937 0.813  1 0.905 
5  0.963 0.804  1 0.694  1 0.851 0.990  0.686  1 0.858  1 0.811  1 0.914  0.874 0.775  0.998 0.854 
6  0.963 0.854 0.993 0.762  1 0.871  1  0.748  1 0.820  1 0.861  1 0.825  1 0.886  1 0.816 
7  1 0.748 0.999 0.873 0.973 0.830  1  0.785  0.932 0.836 0.992 0.820  1 0.775  0.839 0.779  1 0.919 
8  0.962 0.886  1 0.850 0.989 0.820 0.982  0.750  0.995 0.822 0.980 0.890  0.978 0.813  0.844 0.909  1 0.810 
9  1 0.794 0.985 0.810 0.996 0.787 0.982  0.766  1 0.927 0.978 0.844  0.989 0.844  0.784 0.841  1 0.757 
10  0.980 0.906 0.978 0.821 0.984 0.892  1  0.890  0.938 0.902  1 0.992  0.979 0.841  0.763 0.814  0.996 0.902 
11  1 0.706  1 0.792 0.971 0.745 0.992  0.923  1 0.788  1 0.891  1 0.891  0.725 0.822  0.984 0.850 
12  0.990 0.920 0.991 0.834  1 0.795 0.975  0.803  1 0.871 0.979 0.862  1 0.850  0.668 0.796  1 0.802 
13  0.997 0.977 0.986 0.943  1 0.826 0.998  0.772  0.931 0.801 0.974 0.900  0.995 0.948  0.713 0.852  1 0.784 
14  1 0.834  1 0.898  1 0.648 0.963  0.811  0.898 0.706  1 0.878  0.995 0.675  0.753 0.774  0.976 0.825 
15  1 0.817 0.989 0.773 0.985 0.841  1  0.827  1 0.858  1 0.897  1 0.854  1 0.689  0.972 0.871 
16  0.997 0.936 0.968 0.884 0.990 0.777 0.920  0.966  0.969 0.880 0.994 0.922  0.999 0.774  0.999 0.729  1 0.834 
17                0.989  0.855 1  0.892  0.999  0.644 1  0.845 
18                1  0.969  0.981  0.874 1  0.940 1  0.924 
19                0.956  0.993 1  0.854  0.964  0.874 1  0.761 
20                0.978  0.834  0.929  0.878  0.941  0.960 1  0.845 
21                     0.950  0.742 1  0.919 
 
mean 0.989 0.827 0.981 0.837 0.990 0.825 0.985  0.816  0.967  0.841 0.990 0.891 0.991  0.852  0.878  0.819  0.991  0.844  
Table 3: DEA and SFA Efficiency Scores for Agricultural Commodity Carriers (1994-2002). 
1994  1995  1996 1997 1998 1999  2000  2001  2002  DMU 
DEA SFA DEA  SFA  DEA SFA DEA SFA DEA SFA DEA SFA  DEA  SFA  DEA  SFA  DEA  SFA 
1  1 0.870  1  0.790 0.999 0.731 0.983 0.829  1 0.856 0.966 0.805  0.969 0.906  0.983 0.694  0.929 0.898 
2  1 0.898 0.989  0.726  1 0.822 0.979 0.763  1 0.924 0.982 0.945  1 0.706  0.974 0.762  1 0.773 
3  1 0.716  1  0.823 0.997 0.793  1 0.857 0.987 0.874 0.986 0.778  1 0.920  0.973 0.874  0.911 0.885 
4  1 0.849  1 0.8290 0.998 0.801 0.977 0.781 0.985 0.782 0.973 0.753  1 0.977  1 0.851  1 0.937 
5  0.989 0.854 0.999  0.775  1 0.775  1 0.535  1 0.873  1 0.887  0.996 0.834  1 0.811  0.935 0.791 
6  1 0.776  1  0.835  1 0.823  1 0.730  1 0.808 0.989 0.670  1 0.818  1 0.822  1 0.866 
7  1 0.828  1  0.914  1 0.866 0.935 0.812  1 0.859 0.988 0.716  0.998 0.936  1 0.792  0.997 0.917 
8  1 0.837  1  0.836  1 0.841 0.966 0.723 0.986 0.807  1 0.804  0.965 0.920  0.993 0.834  1 0.851 
9  0.995 0.673  1  0.882  1 0.793 0.983 0.821 0.980 0.820  1 0.854  0.955 0.832  0.932 0.943  0.970 0.871 
10              1  0.748  0.964  0.829       
11              0.967  0.886  0.962  0.870       
12              0.994  0.794          
 
mean 0.998 0.811 0.999  0.823 0.999 0.805 0.980 0.761 0.993 0.845 0.987 0.803  0.983 0.868  0.984 0.820  0.971 0.865 
 
 
Table 4: Correlation Coefficients For DEA and SFA Models 
Type of Carrier  Coefficient 
Refrigerated Foods  0.040978 
Agricultural Commodities  -0.126118 
 

A Guide to DEAP Version 2.1: A Data Development Analysis (Computer) Program. CEPA Working Paper 96/08. Center for Efficiency and Productivity Analysis,

County Business Patterns.

On the quality of the data envelopment analysis model.

Production Frontiers,

Stochastic Frontier Analysis of Agribusiness Trucking Companies. Selected paper presented at the American Agricultural Economics Association Annual Meeting,

Using Data Envelopment Analysis to Model the Performance of UK Coastguard Centres. Working paper.

An Assessment of the Efficiency of Agribusiness Trucking Companies: A Data Envelopment Analysis Approach

An Assessment of the Efficiency of Agribusiness Trucking Companies: A Data Envelopment Analysis Approach

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