Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol62.Issue3.Dec1999:

Agricultural Systems 62 (1999) 159±168
www.elsevier.com/locate/agsy

Eciency of government-supported horticulture:
the case of Oman
L. Zaibet a, P.S. Dharmapala b,*
a
College of Agriculture, Sultan Qaboos University, Oman
College of Commerce and Economics, Sultan Qaboos University, Oman

b

Received 4 December 1998; received in revised form 24 June 1999; accepted 17 September 1999

Abstract
This paper analyzes technical eciency in Oman using the stochastic production frontier and the data envelopment
analysis (DEA) methods. Di€erent methods are used because the determinants of technical eciency may be in¯uenced
by the method used and also by the assumptions (such as returns to scale) maintained. Results from the stochastic
parametric frontier (SPF) and DEA±Charnes, Cooper, Rhodes (CCR) models show that the percentage of farmers that
could qualify as technically ecient is as low as 17%. When the DEA±Banker, Charnes, Cooper (BCC) method was
used, this percentage increased to about 46%. Factors such as o€-farm income and soil quality were found to be

positively correlated to productivity. On the other hand, small farm size and farmer's age showed a negative relationship with productivity. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Technical eciency; Stochastic production frontier; Data envelopment analysis; Agriculture; Oman

1. Introduction
In the Arab Gulf countries, agriculture has
enjoyed a substantial output growth due to signi®cant government support. In the Sultanate of
Oman, the area under cultivation has moved from
41,000 ha in 1987 to 71,000 ha in 1994, an increase
of 73%, and output has increased by 43% during
the same period (CBO, 1995). A range of policies
has been implemented aiming at creating employment for the national workforce, diversifying the
sources of revenues and achieving a sucient level
of food security. Support programs included direct
free services, heavily subsidized inputs, and free
* Corresponding author.
E-mail addresses: lzaibet@squ.edu.om (L. Zaibet), sunilda
@squ.edu.om (P.S. Dharmapala).

and easy credit guaranteed above market prices
for some products (Mahdi, 1996). Moreover, the

government of Oman has imposed import restrictions to protect local producers (JICA, 1990) and
supported marketing facilities such as the Public
Authority for Marketing and Produce (PAMAP)
to help farmers to market their products more
eciently.
A major support program, and maybe the most
signi®cant of all support programs in the oilexporting Arab Gulf countries, in general, comes
from the current land policies and unrestricted
access to groundwater resources (Mahdi, 1996).
Substantial drilling of wells was carried out after
the oil boom to expand agricultural lands and
boost agricultural production beyond the traditional small farms (Al-Kuwari, 1996). In Oman,
approximately half of the irrigated area utilizes

0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00061-X

160

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

wells and pumps to extract groundwater (AbdelRahman and Abdel-Majid, 1993). During the last
two decades traditional wells have been replaced
by motorized pumps and virtually all wells in the
coastal belt were mechanized (Stranger, 1985).
This resulted in water extraction more than tripling. As a result of this expansion it was noticeable that the adverse e€ects of increasing the
number of wells was re¯ected in increased salinity
levels in the groundwater reservoir as well as in
the soils in the Batinah region (Northern coastal
area).
Ad hoc expansion of this type ought to be controlled and not tolerated. In 1989, the government
started a national campaign for water conservation (Royal decree 72/89). Various water-use regulations have been put into force and all wells
have had to be registered. Since then, the objective of the government has been to achieve
sustainable agricultural growth that precludes
horizontal expansion and additional water extraction. E€orts, therefore, should be directed to
vertical expansions, i.e. increased agricultural
productivity and farmers' eciency.
New programs to introduce modern irrigation
techniques were promoted to improve irrigation eciency. As of 1995, 1800 farms were equipped with new irrigation systems and more than
2500 farms are currently at the design stage. This

program was supported with a subsidy scheme
ranging from 30 to 75% of the installation cost
depending on the farm size (Zaibet and Omezzine,
1997). Currently 5±6% of the agricultural area is
equipped with modern irrigation systems (Zaibet
and Omezzine, 1997). But even where advanced
techniques have been adopted, irrigation eciency
at the farm level remains low (MAF, 1993).
The problem of agricultural development in the
Arab Gulf countries is primarily a problem of
management of irrigation water and production
eciency. The above-described set of support
policies (direct payments and protection) would
not be e€ective without programs to increase
managerial skills and production eciency at the
farm level. Despite all the support policies it is
recognized that agricultural productivity has
remained relatively low (Zaibet and Omezzine,
1997; Omezzine et al., 1999).

This paper analyzes horticultural growers' technical eciency in Oman, a country where agriculture is substantially subsidized. The paper
focuses on the Batinah region, which represents
about 50% of the total cultivated area in Oman
and where the problems of water scarcity and soil
salinity as a result of excessive pumping of
groundwater are acute. We use di€erent methods
to estimate eciency indexes: (1) the stochastic
production frontier (SPF); (2) the data envelopment analysis±Charnes, Cooper, Rhodes (DEA±
CCR) model; and (3) the DEA±Banker, Charnes,
Cooper (BCC) model. The DEA models (CCR,
BCC) allow the investigation of returns to scale
for individual farms. We are interested, in particular, in the e€ects of structural variables such as
farm size, o€-farm income and soil type on productivity and on the level of eciency. If signi®cant ineciencies exist the identi®cation of
factors contributing to such ineciencies is very
important for policy decisions.
1.1. Data description
The study was conducted in the Batinah region
as a major agricultural area of Oman. This region has bene®ted the most from government programs to install new irrigation systems (drips and
sprinklers). Farm data were collected through a
questionnaire. A total of 50 farmers selected randomly were interviewed, but only 35 observations

were used because of missing information. Farmers were growing a variety of horticultural crops
throughout the year: tomato, water melon, sweetmelon, cucumber and potato. Output prices were
collected for individual farms; thus, we aggregated
all outputs into one output value (the dependent
variable). In this study we used three endogenous
variables: labor, capital and water.
Water quantity (in m3) was estimated based on
irrigation application design and farmer's irrigation schedule. Irrigation schedule (interval and
period of irrigation) for each crop was collected
by interviews. Drip emitters on each farm are
designed to deliver a ¯ow rate of 4 l hÿ1. Capital
was measured as an aggregate value of cash
expenditure on fertilizers, insecticides, plowing
and harvesting. Labor was measured in total days

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

of occasional and permanent labor. Finally, we
included land (total plot size) as an exogenous
input in the production function.

Other explanatory variables were measured
as dummies to explain agricultural productivity as
measured by (log) total output. Farmer's age
is included as a dummy variable equal to 1 if age is
less than 30 years and 0 otherwise. The age variable serves to test the hypothesis that younger
people are more receptive to innovations and
therefore a positive impact on productivity results.
Farm size is included as a dummy, which is equal
to 1 if the size is less than 10 feddan (1 feddan=0.42 ha) and 0 otherwise. The relation
between farm size and eciency has received a
great deal of attention among economists but the
empirical evidence is not conclusive (Bagi, 1982;
Ellis, 1992; Kalaitzandonakes et al., 1992).
We also included o€-farm income in the analysis
of farmers' eciency. It is hypothesized that
farmers having extra-farm income would spend
less time on the farm (Kumbhakar et al., 1989).
On the other hand, we can posit that the existence
of o€-farm income may increase farmers' eciency as o€-farm income may provide farmers
with cash which is necessary to buy inputs and

hire adequate labor. The nature of the soil may
also a€ect eciency. Adequate soils are more
likely to yield a higher eciency than soils which
are not adequate (salinity or other problems). We
also included the farmer's experience as a dummy
variable that equals 1 for more than 5 years and
is 0 otherwise. In fact, many farmers in Oman,
mainly the youngest, have not grown up on farms.
Lack of experience may be a source of ineciency.

2. The stochastic frontier and eciency measures
The SPF was ®rst introduced by Aigner et al.
(1977), and Meeusen and van de Broeck (1977).
Jondrow et al. (1982), who extended the SPF to
allow for the estimation of individual ®rmeciency levels with cross-sectional data, introduced a major development in the SPF. Since
then, the SPF has been widely used in empirical
work. Recent applications include the estimation
of farm eciency in US dairy farms (Kumbhaker

161

et al., 1989), and technical eciency in commercial
®sheries (Kirkley et al., 1995), and technical eciency in banking (Caudill et al., 1995).
The SPF approach assumes that ®rms deviate
from the production frontier due to ineciencies.
The starting point to formulate our model is a
traditional Cobb±Douglas production function,
which is an excellent candidate for SPF (Kirkley et
al., 1995; Kumbhaker et al., 1989):
Y ˆ AX exp…†

…1†

In this equation, Y is output, X denotes a vector
of inputs (endogenous and exogenous), and  is a
vector of parameters. A is the eciency parameter
and  is the error term. But farms may deviate
from the production frontier not only because of
the usual random noise but also because of technical ineciency. To accomplish the link between
the eciency parameter and the SPF, A is speci®ed as (Aigner et al., 1977):

A ˆ  exp…†
So, Eq. (1) becomes:
Y ˆ X exp… ‡ †

…2†

In Eq. (2)  is a parameter common to all farms
and  is the technical ineciency measure that
varies across farms. The ®rst error term  is
assumed to be a two-sided error that accounts for
factors outside the farm control, whereas the second, , is assumed to be a one-sided error associated with factors under the control of the farm.
Estimation of Eq. (2) is based on a speci®c
assumption about the distributions of the error
terms  and . The most common distributional
assumptions made are the normal and half-normal
distributions for  and , respectively.
Let  ˆ  ‡ ; the density function for  could be
written as (Weinstein, 1964):
     
2



 l ;
…3†

f…† ˆ



1

where  ˆ …2 ‡ 2 †2 ; l ˆ  = and , and  are
the standard normal density and distribution
functions, respectively.

162

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

Following Jondrow et al. (1982) the technical
ineciency is estimated as the conditional expected value of  given :
 
‰…l=† ‡ …l=†=…l=†Š
E…= ˆ


…4†

The log likelihood function of Eq. (3) for a
sample of N farms is:
    
N
X
X
1
2
 2
ÿ
ÿ ln  ÿ ln
Li ˆ
2


i
i


 
l
N
2
‡ ln  ÿ
ˆ log
ÿ N log 

2





X
l
1 X
‡
i :
ÿ 2
log  ÿ

2
i

ln L ˆ

…5†

l
‰…l=† ‡ …l=†=…l=†Š:
1 ‡ l2

Variablea

Parameter
estimate

Standard
error

T-statistic

Intercept
Capital
Water
Labor
Land
Age
Exp.
Income
Size
Soil


ÿ2.86
0.30
0.66
0.85
0.03
ÿ0.42
ÿ1.07
0.75
ÿ0.49
0.40
0.18

0.63*
0.02*
0.02*
0.08*
0.07
0.15*
0.07*
0.14*
0.12*
0.11*
0.001*

ÿ4.50
11.07
22.41
9.72
0.52
ÿ2.76
ÿ13.39
5.28
ÿ4.06
3.5
116.7

lˆ

The parameters of this model are , , , and l.
We can also transform Eq. (4) to be a function of
 and l instead of   and  . After algebraic
transformation, Eq. (4) could be written as:
ˆ

Table 1
Maximum likelihood parameter estimates of SPF

2


1.39

0.51*

2.72

2

0.118

±

±

2

0.06

±

±

Log likelihood function=2112
a
Endogenous variables are in natural logarithms and exogenous variables are dummies.
* Statistically signi®cant at 5%.

…6†

Eq. (5) is estimated using TSP 4.3 (Time Series
Processor). Then, the parameter estimates, l, ,
and , are used to estimate , as in Eq. (6). Technical eciency measures are then derived as
exp(ÿ).
The stochastic production frontier method
allows for technical eciency to be measured for
individual farmers from the statistical noise as
shown in Eq. (6). Such measures will provide
important information on the level of eciency.
Moreover, estimation of Eq. (5) would show
the sources of ineciency, namely the e€ect of the
di€erent exogenous variables, such as farm size,
farmer's age, o€-farm income, quality of soil, on
productivity and eciency.
2.1. Estimation and results
Maximum likelihood estimates of Eq. (5) are
presented in Table 1. There are three endogenous
variables, i.e. capital, labor, and water, and
one exogenous variable, i.e. land, all in natural

logarithms. Exogenous variables which a€ect
productivity are included as dummies, so special
attention should be given to the interpretation of
these variables given the semi-logarithmic nature
of the overall equation (Kennedy, 1982).
All parameter estimates were statistically signi®cant at the 5% signi®cance level except for
land. The coecient of labor has the highest value
(elasticity) followed by irrigation water and capital. This suggests that productivity would be
higher when more hired labor exists. All four exogenous variables a€ecting productivity have signi®cant coecients. The coecient of variable age
suggests that productivity for young farmers is
34% [1ÿexp(ÿ0.42)] lower than that for older
ones. So, contrary to what could be expected,
young farmers are not more productive.
In the context of Oman, farming does not depend
on the expertise of the owner, but rather on hired
labor. Most young farmers have extra-farming
occupations, which may explain the negative relationship between age and productivity. The same
could be said about the variable experience (EXP)

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

which shows a negative sign as well. The number
of years in farming does not seem to lead to better managerial skills as acquired over the years.
O€-farm income, however, indicates a gain in
productivity. Previous studies focused on the
negative e€ects of o€-farm activities as an indication of e€ort spent on non-farm activity (Kumbhaker et al., 1989). In our case, farmers with o€farm activities tended to hire more labor, available
at low wages, to compensate for the time they
spent outside the farm, which tends to increase
eciency. Another outcome of the model is the
negative sign associated with the variable size.
Smaller farms (less than 10 feddans) are 38%
[1ÿexp(ÿ0.49] less ecient than larger farmers.
Finally, soil type indicated a positive e€ect on
productivity. Loss in productivity due to inadequate soils is evaluated at 49%.
The other parameters of the model, l and
, are
also signi®cantly di€erent from zero at the 5%
level. The ratio of standard errors l is found to be
greater than one (1.39) and signi®cantly di€erent
from zero, indicating that the residual of the
production frontier is dominated by technical
ineciency. Technical eciency measures are
derived using Eq. (6) and are reported in Table 2.
Frequency analysis shows that there is a group of
farmers (about 50%) where technical eciency
falls below 40%, whereas only 20% of farmers
have a technical eciency level of more than
70%. Parameter estimates (Table 1) show that
factors such as o€-farm income and soil quality
positively in¯uence the level of productivity,
whereas small farm size and age showed negative
relationships with productivity. Further insights
into the e€ects of these factors are explored using
the DEA method. In particular, the e€ect of farm
size could be in¯uenced by the presence of returns
to scale.
2.2. DEA approach
DEA is a nonparametric data-based methodology that provides measures of optimal pro®t ratios
and best-practice eciency. It identi®es the bestpractice ®rms on the ecient productivity frontier
(ecient ®rms) and ®rms that are interior to that
frontier (inecient ®rms). Many outputs and

163

inputs can be analyzed simultaneously for an
arbitrary number of observations, also called
decision-making units (DMUs). Relative eciency
characterizations can be made DMU-by-DMU
across all of the DMUs under consideration, for
the same inputs and outputs of data. The selected
DMU for comparison is denoted by DMUc. The
input/output data entries must be non-negative,
with zero entries allowed.
Two DEA models (input-oriented) of relevance
for a wide range of applications are: (1) the ratio
model, which assumes constant returns to scale;
and (2) the convex model, which allows increasing and decreasing returns to scale. In DEA literature, the ®rst is CCR model (Charnes et al., 1978),
and the second is the BCC model (Banker et al.,
1984). Both models are linear programming (LP)
formulations. In this part of the paper we compare and contrast technical eciency measures in
CCR and BCC models and investigate returns to
scale associated with the sample of farms. As discussed earlier, here we also show the e€ects of o€farm income, farm size, and soil type on the eciency measures, using experimental designs.
2.3. Fundamentals and concepts
A DEA data domain consists of n DMUs. The
selected DMUc (c=1,2,. . .,n) is characterized by
an input vector Xc and an output vector Yc. (All
vectors are column vectors, and [. . .]T stands for
transpose.) For the rest of the paper we use the
following de®nitions and notations:
Yc=[ y1c,y2c,. . .,yrc]T, r-dimensional non-negative
output vector, where c=1,2,. . .,n.
Xc=[x1c,x2c,. . .,xmc]T, m-dimensional nonnegative input vector, where c=1,2,. . .,n.
U=[u1,u2,. . .,ur]T, r-dimensional non-negative
output multiplier.
V=[v1,v2,. . .,vm ]T, m-dimensional non-negative
input multiplier.
l=[l1,l2,. . .,ln]T, n-dimensional vector of real
scalars.
I=[1,1,. . .,1]T, n-dimensional vector of 1s.
X=[X1,X2,. . .,Xn], input data matrix.
Y=[Y
 1,Y2,. . .,Yn], output data matrix.
w= U
V , virtual multiplier.

164

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

Table 2
Eciency measures from SPF, CCR and BCC modelsa
Farmer

 (SPF)

 (CCR)

Class

(BCC)

Class

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

0.2523
0.0342
0.2036
0.2797
0.3572
0.6336
0.3676
0.0361
0.0351
0.3427
0.8902
0.5307
0.1718
0.1141
0.3057
0.9744
0.4138
0.8209
0.0460
0.2568
0.4126
0.4029
0.9493
0.9583
0.9804
0.6676
0.4288
0.4107
0.4795
0.4400
0.2112
0.0815
0.9532
0.1557
0.1787

0.364135
0.238095
0.132683
0.713443
0.344912
0.466889
0.477821
0.021719
0.082039
0.184336
0.443661
0.154745
0.210767
0.536298
0.235349
0.915631
0.744705
0.252826
0.098799
1
0.599027
0.489796
0.214119
1
1
0.776303
1
1
0.972378
0.35458
0.399863
0.21335
1
0.556212
0.214664

N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
E
N
N
N
E
E
N
E
E
N
N
N
N
E
N
N

0.877842
1
0.840312
1
0.558796
1
0.735618
0.832573
0.737607
1
0.520437
0.244985
1
1
0.519075
0.978353
0.759211
1
1
1
0.879788
0.782011
0.259071
1
1
0.823893
1
1
1
1
0.721441
0.605688
1
0.727466
0.62489

N
E
N
E
N
E
N
N
N
E
N
N
E
E
N
N
N
E
E
E
N
N
N
E
E
N
E
E
E
E
N
N
E
N
N

LB±RTS

UB±RTS

Returns

0.927536

1

Incr.

0.442355

0.483790

Incr.

0.624223

0.770309

Incr.

0.883091

1

Incr.

0.960638
0.485160

1
1

Incr.
Incr.

0.760520
0.911489
ÿ0.481842

1
1
0.225143

Incr.
Incr.
Const.

ÿ1.483871
ÿ7.07E+16

0.171692
1

Const.
Const.

ÿ0.964678
ÿ0.778442
0.041950
0.708078

0.204244
0.900360
0.896381
1

Const.
Const.
Incr.
Incr.

ÿ7.07E+16

0.203094

Const.

a
SPF, stochastic parametric frontier; CCR, Charnes, Cooper, Rhodes; BCC, Banker, Charnes, Cooper; LB, lower bound; UB,
upper bound; RTS, returns to scale; Incr., increasing returns; const., constant returns;  is the optimal value of  in CCRE and BCCE
models, as de®ned in the last paragraph, column one, next page.

fc(w)=UTYc, virtual bene®t to DMUc,
c=1,2,. . .,n.
gc(w)=VT Xc, virtual cost to DMUc,
c=1,2,. . .,n.
fc(w)/gc(w), DEA bene®t-to-cost ratio for DMUc
with respect to multiplier w, where gc (w)>0;
Wc is the set of all such multipliers, and
dim(Wc)4r+m.

Thompson et al. (1993) introduced the following
eciency measure for DMUc under the CCR ratio
(multiplier) model:
Max ‰ fc …w†=gc …w†Š
s:t: fj …w†4gj …w†; w50;
where j=1,2,. . .,c,. . .,n.

…7†

165

L. Zaibet, P.S. Dharmapala / Agricultural Systems 62 (1999) 159±168

Using the Charnes±Cooper transformation
(Charnes and Cooper, 1985), one can obtain the
following LP formulations:
1. Input-oriented CCR ratio model for DMUc
CCRE: envelopment
(primal)
Min: 
s.t.
Xc ÿ Xl50
Yl5Yc
 unrestricted; l50

CCRM: multiplier
(dual)
Max: z ˆ UT Yc
s.t.
VT Xc ˆ 1
UT Y ÿ VT X40
U50; V50

…8†

2. Input-oriented BCC convex model for DMUc
BCCE: envelopment
(primal)
Min: 
s.t.
Xc ÿ Xl50
Yl5Yc
IT l ˆ 1
 unrestricted; l50

BCCM: multiplier
(dual)
Max: z ˆ UT Yc ‡ u
s.t.
VT Xc ˆ 1
UT Y ÿ VT X ‡ u I40
u unrestricted
U50; V50
…9†

Now, we state the CCRE and CCRM models
with slack variables added to the constraints.
Similar formulations can be done for BCCE and
BCCM models.
Min: 
s.t.
n
xic ÿ  xij lj ˆ sÿ
i
jˆ1

r

Max: z ˆ  uk ykc
kˆ1
s.t.
i 50

…i ˆ 1; 2; . . . ; m†
n

 ykj lj ÿ ykc ˆ s‡
k

jˆ1

…k ˆ 1; 2; . . . ; r†
lj 50 … j ˆ 1; 2; . . . ; n†
 unrestricted

3. Returns to scale (RTS) for DMUo can be
found by solving the following LP models
(Banker and Thrall, 1992):
u‡ ˆ Max: u
s.t.
VT Xc ˆ 1
U T Y c ‡ u ˆ 1
UT Y ÿ VT X ‡ u I40
u unrestricted;
U50; V50

uk 50
r

m

kˆ1
m

iˆ1

 uk yrj ÿ  vi xij ‡ tj ˆ 0

 vi xic ˆ 1

iˆ1

and in class RE. This class can be partitioned
into three sub-classes: (1) DEA-extreme-ecient
DMUs in class E, which are at the vertices on the
frontier; (2) DEA-non-extreme-ecient DMUs in
class E0 , which are on the frontier between vertices; and (3) DEA-inecient DMUs in class F
which are on the extended frontier. Firms with
0