The main aim of this paper is to compare two alternative methods for estimating frontier functions and measuring efficiency in production. The application of Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) to the same data panel provides insights in estimating technical efficiency of producersâ€™ organizations in selected regions in Bulgaria.DEA, SFA, technical efficiency, frontier production, farm efficiency, Community/Rural/Urban Development, International Development, C14, C23, C51, C61, C67, D24,

Zaimova, Darina

English

Research Papers in Economics

Perspectives of Innovations, Economics & Business, Volume 4, Issue 1, 2010          
www.pieb.cz 
 
 
International Cross-Industry Journal  
41 
Yit = f(xit) + vit - uit        (1) 
INDUSTRIES AND SECTORS: ISSUES AND POLICIES 
EFFICIENCY ANALYSIS OF PRODUCERS’ 
ORGANIZATIONS (CASE OF SOUTH EASTERN 
AND CENTRAL PLANNING REGIONS OF 
BULGARIA) 
  DARINA ZAIMOVA, PH.D. 
 
 
Management Department, Faculty of Economics  
Trakia University, Bulgaria 
JEL Classifications: C14, C23, C51, C61, C67, D24 
Key words: DEA, SFA, technical efficiency, frontier production, farm efficiency 
Abstract: The main aim of this paper is to compare two alternative methods for estimating frontier functions and measuring 
efficiency in production. The application of Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) to the 
same data panel provides insights in estimating technical efficiency of producers’ organizations in selected regions in Bulgaria. 
ISSN: 1804-0527 (online)  1804-0519 (print)    PP. 41-44 
 
 
Introduction 
Adaptation  of the  organizational  structure is  focused  on 
market imperfections, defining them as obstacle for achieving 
the optimal production process and scale. Production function 
includes  not  only  conventional  production  factors  but  also 
variables that can represent the effect of institutional changes. 
Comparing  production  function  to  the  demand  function 
defines  sources  of  influence  over  production  factors, 
differentiating  them  from  those  that  reflect  on  productivity 
itself.  This  approach  distinguishes  market  effect  from  the 
effect of government regulation and institutional policy line. 
Theory on Stochastic Frontier Analysis                                   
and Data Envelopment Analysis 
Stochastic  Frontier  Analysis  (SFA)  represents 
parametric, econometric techniques for estimating efficiency 
coefficients. The production function can be expressed in the 
following form: 
where  Yi  is  the  production  of  the  i-th  producer;  xi  is  a 
vector of input quantities; vi is the random variable; ui  is non-
negative  random  variable  which  is  assumed  to  account  for 
technical  inefficiency.  The  benefits  of  this  approach  result 
from decomposing the error term into two components - one 
to  account  for  random  effects  and  another  to  account  for 
technical inefficiency. 
The stochastic frontier production function to be estimated 
is 
ln  (Yit)  =  b0  +b1  ln  (Landit)  +b2  ln  (Laborit)  +b3  ln 
(Production  costsit)  +b4  ln  (Indirect  costsit)  +b5  ln  (Yearit) 
+b6 ln (Landit)
2 +b7 ln (Laborit)
2 +b8 ln (Production costsit)
2 
+b9 ln (Indirect costsit)
2 +b10 ln (Landit)ln (Laborit) +b11 ln 
(Landit)  ln  (Production  costsit)  +b12  ln  (Landit)ln  (Indirect 
costsit)  +b13  ln  (Laborit)ln  (Production  costsit)  +b14  ln 
(Laborit)  ln  (Indirect  costsit) +b15  ln  (Production  costsit) ln 
(Indirect costsit)+ vit - uit 
 
 
Technical inefficiency effects are defined by 
uit = δ0 + δ1 (Membership in Producer organization) +  
+ δ2 (Specialization level) + δ3 (Soil bonitet) + 
+ δ4 (Rainfall quantity)                         (3) 
Likelihood  ratio  (LR)  tests  are  performed  to  test 
hypothesis  that  there  is  no  technical  inefficiency  (uit  =  0). 
Three hypotheses are formulated in order to be studied the 
effect from membership in producers’ organizations: 
1.Н0:  “There  is  no  technical  inefficiency  in  the  formulated 
empirical model.” 
In  the  Cobb-Douglas  production  function  land  variable 
includes  arable  land;  labor  variable  is  the  total  number  of 
hired seasonally and full-time workers; production costs are 
represented by the value of the expenses made in the farm; 
indirect costs are organized by the organization itself - value 
of the fertilizer, manure, pesticides, machinery, marketing and 
administrative expenses. 
2.Н0: “The technical inefficiency level of the i-th producer is 
not relevant to the inefficiency coefficients of the variables 
in the empirical model. 
The  formulated  translog  production  function  in  (2) 
accounts  for  technical  change  and  time-varying  technical 
inefficiency effects. The variable year in the model specifies 
that joining producers’ organization has direct influence over 
inefficiency effects. 
3.Н0: “Membership in producers’ organizations, specialization 
level, soil bonitet and rainfall quantity have no influence 
over technical inefficiency.” 
The values of the two parameters σ
2 and g(gamma) =σu
2/ 
σ
2 are associated with the variances of the random variables vit 
and uit in the inefficiency model (3). Perspectives of Innovations, Economics & Business, Volume 4, Issue 1, 2010          
www.pieb.cz 
 
 
International Cross-Industry Journal  
42 
Data  Envelopment  Analysis  (DEA)  is  a  deterministic 
approach  based  on  linear  programming  techniques.  This 
approach  introduces  a  piecewise  linear  envelopment  of  the 
data  and  constructs  a  best-practice  frontier.  Regarding  the 
existence of random error DEA is very sensitive because any 
random  error is  counted  as difference in  efficiency.  In this 
present analysis is used input-oriented variable returns to scale 
(VRS) DEA model (Färe, 1994): 
minθλθ        (5) 
  s.t.         -qit + Qλ ≥ 0 
θxit – Xλ ≥ 0 
I1′λ = 1 
λ ≥ 0, 
where input and output vectors are presented by vectors xit 
and  qit,  respectfully  for  the  i-th  producer  in  the  t-th  time 
period. The data for all of the producers is denoted by input 
matrix X and output matrix Q. The input technical efficiency 
is represented by θ and has value 0≤θ≤1. Applying DEA is 
bound to preliminary condition that technical efficiency is a 
relative  measure,  because  producer’s  technical  efficiency  is 
relative to other producers in the sample. 
The inputs used to measure technical efficiency are: land - 
agricultural  land  under  usage  by  producers,  members  of 
producers’  organizations;  labor  -  the  number  of  workers, 
employed  in  a  farm;  production  costs  -  value  of  expenses 
made  in  the  farm;  indirect  costs  -  value  of  the  fertilizer, 
manure, pesticides, machinery, marketing and administrative 
expenses in the organization. Output is represented by gross 
value of production by each producer and sales revenue. 
Results from applying Stochastic Frontier Analysis 
The  present  research  includes  data  of  130  agricultural 
producers,  members  in  producers’  organizations  that  are 
registered  in  South  Central  and  South  Eastern  planning 
regions.  Maximum  likelihood  estimates  are  obtained  using 
computer program Frontier 41 by Tim Coelli (Coelli, 1998). 
The upper boundaries for mixed c
2 distribution are employed 
from Kodde and Palm (Kodde, Palm, 1986). 
The  first  null  hypothesis  H0  is  given  by  Cobb-Douglas 
technology and implies that there is no technical inefficiency 
in the empirical model. The results show technical efficiency 
coefficients  in  the  range  between  0.530  and  0.586.  The 
hypothesis is rejected for the four years and this means that 
the additional parameters of the translog function, compared 
to the Cobb-Douglas function will bring significant additional 
information about scale economies between producers.  
The  second  hypothesis  states  that  there  is  no  relation 
between coefficients of technical inefficiency of the farmers 
and coefficients of technical inefficiency of the 15 parameters 
included in the translog model. The hypothesis is accepted for 
the first two years in the analysis. A conclusion can be drawn 
that  production  behavior  of  the  farms  could  be  adequately 
described  by  the  translog  function.  The  proportion  of  the 
inefficiency effect on the total variability of the random effect 
is given by the estimates of the g parameters that are close to 1 
and shows that the total variability is explained essentially by 
the  technical  efficiency.  For  the  last  two  years  the  null 
hypothesis is rejected and ordinary least-squares estimates are 
accepted. 
According to the third null hypothesis coefficients of the 
explanatory variables in the inefficiency model (3) have no 
influence over technical efficiency of the producers. For the 
four years in the analysis the null hypothesis is rejected. This 
means that the joint effect of the coefficients associated with 
membership  in  the  producers’  organizations,  specialization 
level,  soil  bonitet  and  rainfall  is  significant,  although  the 
individual  effects  of  the  variables  may  not  be  statistically 
significant. This implies that there is positive effect and strong 
relation  between  technical  efficiency  of  the  farmers  and 
variables in the inefficiency model. The main tool used for the 
production technology is partial output elasticities. This way 
is represented to what extent of the proportional input change, 
keeping  the  other  inputs  constant  is  decisive  for  the 
proportional change in the output quantity and returns.  
TABLE 1. OUTPUT ELASTICITIES AND RETURNS TO SCALE 
  2005  2006  2007  2008 
Partial output elasticities 
Land  0.039  0.035  0.037  0.038 
Labor  0.079  0.087  0.040  0.037 
Direct expenses  0.316  0.377  0.303  0.298 
Indirect expenses  0.207  0.371  0.503  0.480 
Scale elasticities  0.641  0.870  0.883  0.853 
Source: own estimations 
The magnitudes of the output elasticities presented in the 
Table 1 indicate that the utilized proportional change of direct 
and  indirect  expenses  have  the  highest  proportional 
contribution to the production and revenue generation when 
keeping other variables constant. This implies that expenses 
arranged by producers’ organization such as seed, chemicals, 
fertilizers,  have  positive  effect  on  the  efficiency  of  its 
members. Although the investigated period is medium-term 
oriented there is a pronounced tendency for more than 50% 
increase  of  the  elasticity  of  indirect  expenses.  The  output 
elasticities  with  respect  to  land  and  labor  imply  that  the 
proportional increase of these variables results in a relatively 
low proportional increase in production and revenue. The low 
average  values  running  up to  0.050 for  land  and 0.069 for 
labour  indicate  low  capacity  utilization  of  these  inputs. 
Regarding  the  scale  elasticities  represented  in  Table  1,  the 
sum  of  production  elasticities  is  less  than  one.  The 
proportional  increase  of  all  input  will  result  in  a  lower 
proportional increase of revenue thus the production extension 
is  not  required.  The  producers  are  not  achieving  the  scale 
optimum although there is a tendency for increase of the scale 
elasticities. 
Results from applying Data Envelopment Analysis 
Table 2 presents the average slacks for each input for the 
total technical efficiency. As can be seen from Table 2 the 
most inefficiently used input is labor. For the first year labor 
could be unproportionally decreased by 6%. Perspectives of Innovations, Economics & Business, Volume 4, Issue 1, 2010          
www.pieb.cz 
 
 
International Cross-Industry Journal  
43 
TABLE 2. AVERAGE SLACK FOR INPUTS (%) 
 
2005  2006  2007  2008 
CRS  VRS  CRS  VRS  CRS  VRS  CRS  VRS 
Inputs 
Land  0.78  -  2.27  3.69  2.27  -  2.27  - 
Labor  5.92  11.70  23.14  31.86  36.20  33.90  36.30  32.80 
Production costs  0.01  0.21  -  -  -  -  -  - 
Indirect costs  0.01  0.21  -  -  -  -  -  - 
Output 
Gross value of 
production  8.37  6.37  19.95  -  14.00  -  14.00  - 
Sales revenue  0.03  0.19  -  0.69  -  13.00  -  13.00 
Source: own calculations 
   
TABLE 3. INPUT EFFICIENCY COEFFICIENTS 
  
2005  2006  2007  2008 
CRS  VRS  CRS  VRS  CRS  VRS  CRS  VRS 
Land  0.67  0.72  0.78  0.74  0.80  0.64  0.77  0.60 
Labor  0.31  0.70  0.20  0.68  0.64  0.68  0.20  0.65 
Production costs  0.80  0.82  0.88  0.89  0.80  0.80  0.87  0.76 
Indirect costs  0.80  0.82  0.88  0.89  0.80  0.80  0.87  0.76 
Source: own calculations 
 
 
TABLE 4. EFFICIENCY COEFFICIENT ACCORDING TO THE FARM SIZE 
  2005  2006  2007  2008 
CRS  VRS  CRS  VRS  CRS  VRS  CRS  VRS 
Land 
>5 ha  0.671  0.924  0.548  1  0.517  1  0.52  1 
<5 ha  0.715  0.716  0.777  0.745  0.806  0.636  0.787  0.623 
Labor 
>5 ha  0.681  0.685  0.865  0.865  0.865  0.865  0.865  0.865 
<5 ha  0.314  0.314  0.204  0.684  0.164  0.68  0.165  0.68 
Source: own calculations 
   
TABLE 5. EFFICIENCY COEFFICIENTS ACCORDING TO THE FARM OWNERSHIP TYPES 
  
2005  2006  2007  2008 
CRS  VRS  CRS  VRS  CRS  VRS  CRS  VRS 
Land 
Partnership  0.478  0.689  0.556  0.556  0.721  0.920  0.730  0.897 
Individual 
producers  0.671  0.716  0.777  0.745  0.797  0.635  0.787  0.731 
Labor 
Partnership  0.725  0.625  0.458  0.96  0.455  0.672  0.455  0.672 
Individual 
producers  0.314  0.704  0.204  0.684  0.164  0.68  0.165  0.680 
Source: own calculations Perspectives of Innovations, Economics & Business, Volume 4, Issue 1, 2010          
www.pieb.cz 
 
 
International Cross-Industry Journal  
44 
For the next three years the average percentage of labor 
that could be decreased and still achieve the same output is 
25.4%.  There  are  insignificant  opportunities  to 
unproportionally  decrease  the  utilized  land  and  the  two 
categories of the costs without bearing negative results for the 
released production and sales revenue. Results from applying 
variable returns to scale (VRS) DEA model show that there is 
a potential to increase percentage of sales revenue. 
Results  from  sensitivity  analysis  of  the  inputs  are 
presented on Table 3. 
Efficiency  coefficients  of  production  and  indirect  costs 
take values from 0.80 to 0.88 under assumption for constant 
returns  to  scale  (CRS)  and  from  0.79  to  0.88  under 
assumption for variable returns to scale (VRS). Membership 
in producers’ organizations is an opportunity for producers to 
adjust the usage of their inputs. The results indicate positive 
relation between producers’ membership and relative share of 
producers’ costs. There is a possibility to decrease the two 
categories cost with average 17% and still achieve the same 
output. 
Under  common  definition  “members  in  organizations” 
there are presented different farm types according to their size 
and  ownership.  In  order  to  be  studied  the  influence  of 
institutional factors analysis is decomposed into two separate 
levels. The relation between size of the arable land and the 
efficiency coefficient is developed on the first level; and on 
the second level the criterion for studying producers is their 
form for ownership.  
Efficiency coefficients of land and labor for each producer 
in the sample are presented by there relation with the best-
practice  frontier  (Table  4).  Under  assumption  for  constant 
returns to scale the farmers with arable land less than 5 ha can 
decrease the used land with average 34% and still achieve the 
same  level  of  the  output.  This  suggests  that  intensive 
production  technologies  are  not  necessarily  resulting  in 
increasing  of  the  final  output.  Applying  variable  returns  to 
scale model results that the largest farms are more efficient. 
 
TABLE 6. TECHNICAL EFFICIENCY COEFFICIENTS 
 
 
 
 
 
 
 
 
 
           Source: own calculations 
 
Labour  is  the  other  main  factor  that  is  studied  in  it’s 
relation to efficiency. Values of the efficiency coefficients of 
labour  for  producers  with  arable  land  less  than  5  ha 
significantly decreases from 0.31 for the first year to 0.16 for 
the year 2008. For the largest farmers the tendency is contrary 
and  the  efficiency  coefficient  increases  with  21%  for  the 
whole period.  Incensement of the land efficiency coefficients 
results  in  increasing  of  labor  efficiency  coefficients  under 
assumption of variable returns to scale. The results show that 
the  share  of  the  hired  labor  has  significant  influence  on 
technical efficiency. 
On the second level of the analysis producers are divided 
in  two  categories  -  individual  producers  and  partnership 
(Table 5). 
The commonly accepted view that family farms are more 
efficient  than  wage-labor  farms  because  of  the  lower 
transaction costs could be supported by the results. The values 
of  the  labor  efficiency  coefficients  are  decreasing  for  the 
period under assumption for constant and variable returns to 
scale. Under assumption for variable returns to scale for the 
both  categories  values  of  labor  efficiency  coefficients  are 
close for the last two years of the period. 
Conclusion 
There are several positive signals about the future and the 
role of producers’ organizations. The results from Stochastic 
Frontier  analysis  and  Data  Envelopment  analysis  indicate 
relatively high technical efficiency coefficients (Table 6). 
Results  from  DEA  under  assumption  for  constant  and 
variable returns to scale show very low technical inefficiency 
level, varying between 0.11 and 0.06. SFA results define this 
coefficient  between  0.13  and  0.27.  The  difference  between 
results is due to the different treatment of the standard error 
term  according  to  the  methodology  of  the  two  analyses. 
Producers’ organizations show a satisfactory efficiency level, 
their  productivity  rose  over  analyzed  period  that  might 
suggest  managerial  efficiency  and  technological 
improvements.  These  results  indicate  that  the  producer 
organizations  increase  their  competitiveness  and  follow  the 
continuous  changes  in  consumption  model  by  improving 
managerial capabilities and by investing in technology. 
References 
Coelli, T., Rao, D., Battesse, G., 1998. An introduction to efficiency 
and productivity analysis, Kluwer Academic Publishers. 
Färe, R. and Shawna, G., 1994, “Estimation of returns to scale using 
Data Envelopment Analysis: A comment”, European Journal of 
Operational Research 79(2), pp. 379-382. 
Kodde, D., Palm, F., 1986. Notes and comments: Wald Criteria for 
Jointly Testing Inequality Restrictions, Econometrica, Vol.54, 5, 
pp.1243-1248. 
 
 
 
  DEA/CRS/  DEA/VRS/  SFA 
2005  0.884  0.914  0.733 
2006  0.895  0.919  0.734 
2007  0.908  0.938  0.878 
2008  0.906  0.866  0.810 

Efficiency analysis of producersâ€™ organizations (Case of South Eastern and Central planning regions of Bulgaria)

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