ahsanullah mohsen · ahsanullah mohsen keywords: technical efficiency, fruit production, stochastic...
TRANSCRIPT
Ahsanullah Mohsen
The technical efficiency of fruit production in
Afghanistan - A case study of Logar province
Volume | 018 Bochum/Kabul | 2017 www.afghaneconomicsociety.org
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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The technical efficiency of fruit production in
Afghanistan - A case study of Logar province
Ahsanullah Mohsen
Keywords: Technical Efficiency, Fruit Production, Stochastic Frontier Production
Function, Logar, Afghanistan.
Abstract
“Efficiency is doing things right; effectiveness is doing the right things” (Peter Drucker).
Horticultural activity is among the focal sources of income for the residents of Afghanistan. Hence,
those families which largely rely on their agricultural and/or garden outputs require efficient
gardening (fruit producing) activities to be in a position to live a comfortable life.
The key motivation for this paper is the absence of research in this area. For this reason, the
results of this paper could be used as vital background information to ensure strategies aimed at
productivity gain.
Gardening activities in Afghanistan are conducted in the traditional manner. Customary methods
of horticulture are typical causes of low productivity. The study included 196 fruit producers and
intended to find the mean technical efficiency of fruit gardeners in the Logar province of
Afghanistan, which will highlight the potential opportunities for increasing the yields.
To approach these economic issues, several methods of technical efficiency estimation were
used. One of them is Stochastic Frontier Analysis (SFA). The maximum likelihood estimation
method is utilized to estimate the coefficients and predict the parameters of inefficiency equation.
The mean technical efficiency was found to be very low, namely 43.42% on average for the
participants. This equally means that orchard owners are not operating in a technically efficient
manner. Based on the findings in this paper, the output of the fruit producers could be increased
by almost 67 % with the same amount of resources.
Description of Data
The analysis in this paper contains both primary and secondary data. The secondary data was
collected from scientific journal articles, books, and the internet. Whereas, the primary data which
makes the core basis of this study was collected from 196 fruit producers in Logar province using
a carefully structured questionnaire. Data collection covers six districts (Mohammad Agha, Pole
Alam, Khawrwar, Charkh, Baraki Barak, Azra) in Logar province, including the center of the
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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territory. The majority of interviewees were from the Mohammad Agha district. This area borders
Kabul province and has relatively more varieties of fruits. Moreover, the Mohammad Agha district
has the advantage of being near to the Kabul and therefore has a better access to markets, which
turn the attention of many inhabitants toward fruit production.
All the data were collected for the year 2015-16. The Solar Hijri calendar is adjusted to the
Gregorian calendar.
Prior to collecting data from the fruit producers, around 10 questionnaires were distributed to them
for pre-testing the questionnaire. This was done to find the potential problems that the
respondents might have faced while filling the forms. Due to the fact that all fruit producers are
not registered in Logar province, the data was not collected through a random sampling. After the
pre-test, 200 questionnaires were distributed and 196 were received back. To obtain precise
predictions and estimations, it is necessary to structure the data and organize it for the analysis.
Thus, data analyzed in this study were thoroughly inspected and cleaned for the analysis.
Research Question/Theoretical contextualization
In Afghanistan agriculture is the primary source of income, economic growth, and food security.
The agriculture sector contributes 22% of GDP and 76.8% labor force is engaged in agricultural
activities (Central Intelligence Agency, 2015). Nonetheless, Afghan farmers and fruit producers
are unequipped with technology and have a low level of expertise to enhance the output through
the expanding land. Thus, increasing the productivity of the yield per unit of land area is crucial
to the gardeners in the Logar province. The above-mentioned argument signifies the importance
of this analysis, which mainly aims at assessing the technical efficiency of gardeners. This study
will help to find the determinants of technical efficiency.
The study is thoroughly hypothesized, every assumption in their turn being tested for making the
decision of acceptance or rejection. The first hypothesis is that all parameters of the stochastic
frontier are equal to zero, which also means that output is unaffected by input variables. The
second hypothesis is that socioeconomic and demographic variables do not affect the technical
efficiency of gardeners.
The logic behind measuring efficiency is to find how far a firm is producing output relative to its
maximum capacity. In other words, it is to find an extra amount of potentially producible production
with the same quantity of inputs. For example, a company produces eighty-five units of an output
and if the efficiency calculation comes up with the potential output of one hundred items given the
inputs set, then this firm is said to be inefficient. This implies that this particular firm can increase
its output by fifteen percent with the same amount of resources. The loss of fifteen units is the
result of inefficiency.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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A brief overview of efficiency measurements will be discussed in this section. A number of books
and studies have discussed this issue in more detail such as (Farrell, 1957) and (Färe, Grosskopf,
& Lovell, 1994).
The efficiency of a firm is said to be a composite of technical and price efficiencies1. The technical
efficiency means maximal output quantity obtained from a given set of inputs. Whereas allocative
or price efficiency is the ability of the producer in order to use inputs optimally. The combination
of these two efficiency measures is, therefore, named overall efficiency or economic efficiency.
(Farrell, 1957)
In measuring the efficiency, production technology is assumed to be known. However, this is not
the case in the real world. It is necessary to estimate the efficient isoquant from the data under
study. The identification of the production frontier involves complicated procedures which will be
discussed later in this paper.
Technical efficiency is output oriented, whereas allocative efficiency is input oriented. In input-
oriented technical efficiency, the aim is to reduce all inputs proportionally without decreasing the
quantity of output. Whereas in output-oriented measures, the objective is to proportionally
increase the production quantities with the same amount of resources. In both cases, the firm
benefits without losing something and this results in increasing the efficiency of that company.
The output-oriented and input-oriented efficiency measures will be equal if the production function
has the constant return to scale. As the name indicates, the output-oriented measure is the
opposite of input-oriented. With an example of single input and one output, it is easy to show the
difference between these two measures.
1 In recent literature, allocative efficiency and economic efficiency is used instead of price efficiency and overall
efficiency respectively.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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In figure 1 (a), f (x) is a production function with the technology of decreasing return to scale.
Additionally, a firm is located in point P which operates inefficiently. According to Farrell input-
oriented measure, technical efficiency is represented by the ratio AB/AP. On the other hand, an
output-oriented measure of technical efficiency is given by CP/CD. Only when a corporation has
the condition of CRS, then the output and input-oriented measures of technical efficiency
converge to the equivalent value (Färe & Lovell, 1978). In figure 1 (b), an inefficient firm having
a CRS is located at point P. It can be depicted on the graph that output and input-oriented
measures of technical efficiency are the same. Meaning AB/AP=CD/CP, for the firm P which has
technically inefficient production.
Beside others, the DEA and Stochastic Frontier Analysis (SFA) are two methods of estimating
the efficiency and obtaining frontier. The former method is non-parametric where the latter is a
parametric approach. One way to estimate the frontier for cross-sectional data of “I” number of
firms is to sketch a subjective-chosen function and envelop all the data points by this function.
(Aigner & Chu, 1968) used this method considering an equation of Cobb-Douglas which has the
following form:
ln 𝑦𝑖 = 𝑥𝑖′𝛽 − 𝑢𝑖 i=1… I, (1)
Where yi is the output of the producer I; xi is a k×1 vector of input factors; ln is the natural
logarithms of inputs and/or output; β is the unknown parameter to be estimated and ui is a random
variable, which explains inefficiency of the firm having non-negative value. The inefficiency term
is nonnegative for if it is negative the net result would be positive. The inefficiency cannot be
added, but it is to be reduced. There are many approaches in order to estimate the unknown
parameters. Aigner and Chu preferred estimating the model by linear programming and also
suggested the quadratic programming for estimating the model. (Afriat, 1972) utilized the
maximum likelihood method. This method was used based on the assumption that the inefficiency
A
0 C
q
D
B
x
f(x)
P
(a) DRS
q
A P
C
f(x) D
B
0 x
(b) CRS
(Coelli, Prasada, O'Donnell, &
Battesse, 1998)
Figure 1. Technical Efficiency of Input and Output-Oriented Measures and
Return to Scale
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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term has a gamma distribution. On the other hand, (Richmond, 1974) applied the least squares
technique which is sometimes referred to as the Modified Ordinary Least Squares (MOLS).
Equation 1 is restricted by non-stochastic quantity exp (xi’β) and is, therefore, a deterministic.
Moreover, all errors, such as measurement errors, statistical noise and other sources of errors
are considered to be due to the inefficiency of the firm. This problem could be solved by adding
another random variable in the model which counts for statistical noise. After adding a variable to
the statistical noise, the representation is not deterministic anymore. The new model is known as
a stochastic production frontier.
(Aigner, Charles Albert Knox, & Schmidt, 1977) also (Meeusen & Broeck, 1977) simultaneously
and independently suggested the stochastic frontier production function having the form
ln qi = xi’β + vi - ui (2)
which has an additional random variable vi responsible for statistical noise in the data, otherwise
it is the same as equation 1. Statistical noises are the result of neglecting an important variable,
measurement error, and model misspecification. Unlike before, equation 2 is regarded as a
stochastic frontier production function. Due to the fact that the production is bounded from above
not only by deterministic part of the equation but now with the deterministic plus a random error
term vi, i.e. exp (xi’β+ vi). Added random error can take the value of either sign, the positive or
negative.
The last term in equation 2 can also be written as 𝑢𝑖 = 𝛿𝑧𝑖 + 𝑤𝑖, where z is the socioeconomic
and demographic factor influencing the technical efficiency. In addition to that, the delta is an
unknown parameter to be predicted. Finally, the last term is accountable for errors.
One of the key motives for using the stochastic frontier is to find the inefficiency effects of the
firms. Therefore, output-oriented technical efficiency is the most commonly applied method. This
can be computed using the result of actual or observed production divided by deterministic frontier
or qi divided by its stochastic frontier output.
𝑇𝐸 =𝑞𝑖
exp(𝑥𝑖′𝛽+𝑣𝑖)
=exp(𝑥𝑖
′𝛽+𝑣𝑖−𝑢𝑖)
exp(𝑥𝑖′𝛽+𝑣𝑖)
= exp(𝑢𝑖). (3)
This fraction computes the production of a particular organization with respect to the output of a
fully efficient firm using the same resource. The result of the technical efficiency TE is a value
between one and zero due to the fact that the fraction is the outcome of dividing the whole by its
part. If the result is one, it indicates the firm is perfectly technically efficient. The opposite is true
if the result of the fraction is zero. To calculate the technical efficiency of a producer, it is
necessary to estimate the parameters in equation 3 the stochastic frontier production function.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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(Aigner, Charles Albert Knox, & Schmidt, 1977) applied the MLE method, assuming ui and vi are
independently and identically distributed normal and half-normal random variables respectively
with zero means and 𝜎𝑣2, 𝜎𝑢
2 variances.
𝑣𝑖 ~ 𝑖𝑖𝑑𝑁 (0, 𝜎𝑣2) (4)
and 𝑢𝑖 ~ 𝑖𝑖𝑑𝑁+ (0, 𝜎𝑢2) (5)
As mentioned before, (Aigner, Charles Albert Knox, & Schmidt, 1977) attempt to use the MLE
method for parameterization of the half-normal model. However, this estimation takes place in
terms of sigma square and lambda square
𝜎2 = 𝜎𝑣2 + 𝜎𝑢
2 and 𝜆2 = 𝜎𝑢
2
𝜎𝑣2 ≥ 0. (6)
A firm is said to be perfectly technically efficient if all the aberrations from the frontier are due to
noise vi and inefficiency term is irresponsible for these deviations. It can also be expressed as
𝜆 = 0. Both lambda and gamma parameterization methods can be used. Wan & Battesse (1992)
suggest the following procedures for the estimation of the parameter through maximum likelihood.
Finding density function for vi and ui; joint density function E = V-U; the conditional density function
for U given E = e; density function for the production value Yi, the logarithm of the likelihood
function for sample observation and finally taking first order conditions with respect to the
parameters to be estimated. (Wan & Battesse, 1992) can be referred for further detailed
explanations. After the estimation of parameters, it is easy to carry out the remaining calculations
in the analysis. Now it is possible to find the technical efficiency and the maximum probable
production of the fruit producers.
Field research design/ Methods of data gathering
Logar province is one of the thirty-four provinces of Afghanistan, located in the southern part of
the country. It has 4,568 square kilometer area which is 0.7 percent of the total Afghan territory.
Maidan Wardak and Ghazni provinces are to its west. Paktia province is to the south, Nangarhar
in the east and Kabul is to the north of the Logar province. Capital is Pole Alam which is located
sixty-five kilometers to the south of Kabul, the capital city of Afghanistan. Pashtun, Tajik, and
Hazara are the main tribes living in this region.
The following model shows the empirical and operational definition of the variables.
ln 𝑌𝑖 = 𝛽0 + 𝛽1 ln 𝐿𝑎𝑛𝑑𝑖 + 𝛽2 ln 𝑃𝑙𝑎𝑛𝑡𝑖 + 𝛽3 ln 𝑊𝑎𝑡𝑒𝑟𝑖 + 𝛽4 ln 𝐹𝑒𝑟𝑖 + 𝛽5 ln 𝑀𝑎𝑛𝑢𝑟𝑒𝑖
+𝛽6 ln 𝑙𝑎𝑏𝑜𝑢𝑟𝑖 + 𝛽7 ln 𝑃𝑒𝑠𝑖 + 𝛽8 ln 𝑂𝑡ℎ − 𝐼𝑛𝑠𝑖+𝛽9 ln 𝑇𝑟𝑒𝑒𝑖 + 𝑣𝑖 − 𝑢𝑖 (7)
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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Where i=1, 2, 3..., n. Ln is natural log. β is an unknown parameter to be estimated. Y or “Output”
is dependent variable and shows the total value of fruits in Afghani. “Land” is the area on which
the fruit trees are planted. “Plant” shows the money spent on purchasing new bushes in the last
year. “Water” refers to the total irrigation hours in one year. “Fer” is the quantity of fertilizers used
such as urea and Di-Ammonium Phosphate (DAP). “Manure” is a quantity of farm manure. “Labor”
is the sum of household members and waged labor days2 worked in fruit production. One working
day is considered to be equal to eight working hours. “Pes” shows the price of various types of
pesticides for trees. “Oth-ins” are all other inputs such as sand and materials. The “tree” is the
total number of trees in the garden.
𝑢 = 𝛿0 + 𝛿1𝐴𝑔𝑒 + 𝛿2𝐸𝑑𝑢𝑐 + 𝛿3𝐸𝑥𝑝𝑒𝑟 + 𝛿4𝐻𝐻𝑆 + 𝛿5𝐷𝑎𝑚𝑎𝑔𝑒 + 𝛿6𝑆𝑒𝑐
+𝛿7𝐴𝑖𝑑 𝑣𝑎𝑙𝑢𝑒 + 𝑤 (8)
“Age” shows the years of age of the primary decision maker or gardener. “Educ” represents the
years of schooling of the gardener. “Exper” is producer’s work expertise in fruit production. “HHS”
represents household size. “Damage” is the number of trees destroyed because of war or other
circumstances. “Sec” stands for the security of the area. “Aid values” are aid provided by the
government or other institutes. "𝛿" is unkown paratmeter to be predicted and “w“ is a random
variable which is defined by the truncation of normal distribution.
Results
The following table shows summary statistics (mean, median, minimum value, maximum value,
standard deviation) of the variables used in this study.
Table 1. Descriptive Statistics of Variables
Variables Units Mean Median Max Min Std. Dev Prob Obs
Output Afs 93546.72 67800 632500 0 105625.60 0.0000 196
Land Jirib 2.16 2 17 0.10 2.42 0.0000 196
Plant Number 32.85 20 315 1.00 48.57 0.0000 93
Water Hours 151.94 100 2200 5.00 227.82 0.0000 196
Fertilizer Kgr 182.81 104 1600 0 209.98 0.0000 196
Manure Afs 1723.68 1000 5500 500 1365.08 0.0002 19
Labor Days 53.97 40 500 2.00 60.93 0.0000 196
Pesticide Afs 1987.65 900 25220 0 3393.30 0.0000 196
Oth-Ins Afs 1662.25 0 60000 0 5095.46 0.0000 196
Tree Number 263.70 151 4100 20 428.92 0.0000 196
2 One labor day is equal to eight working hours.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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Age Years 38.33 35 80 17 14.77 0.0013 196
Educ Years 10.16 12 16 0 5.17 0.0000 196
Exper Years 12.80 10 50 0 11.06 0.0000 196
HHS Person 14.78 12 70 3.00 9.57 0.0000 196
Damage Number 7.77 0 81 0 13.04 0.0000 196
Sec 0-10 6.79 7 10 0 2.97 0.0000 196
Aid value Afs 4665.59 0 800000 0 57153.24 0.0000 196
Source: Own Computations.
Table 1 displays that on average every producer receives 93,546.72 Afghanis in one year as a
result of the fruit production. Land area for fruit production is in the range of 0.1-17 jirib with a
mean of 2.16 jirib3. In total, ninety-three gardeners planted new trees in last year. The minimum
usage of fertilizer and pesticide is zero, which means a number of producers do not use fertilizers
and/or chemical substance. Only nineteen observations used farm manure. Workday ranges
between 2-500 labor days and the average is fifty-four working days. Age of the primary decision
maker ranges between 17-80 years and the mean of age is thirty-eight years. The highest level
of education is a bachelor sixteen years. Illiterate gardeners are also present in the data. The
maximum number of household members is seventy and the minimum is three. The highest
number of damaged trees because of war or other circumstances is eighty-one and some
gardeners do not have damaged trees in their garden. Fruit gardens are located in various places
from the security point of view, such as very secure, least secure and in between. At least one
gardener received 800,000 Afghanis aids from the government.
Prior to parameter estimation, it is necessary to ensure homoscedasticity of the data. The Breusch
Pagan test is to ensure the existence or absence of heteroscedasticity in the data under study. In
this test, the error term is squared and divided by the mean error and the result gives 𝑉𝑖2. After
obtaining 𝑉𝑖2it is regressed against all the dependent variables of the model.
For a large sample, product of N or number of observations and R-square has a chi-square
distribution. To run the test, this formula is used (N-P) *R2~X2p ,where N is the sample size and P
is the number of dependent variable(s). The calculated X2 at five percent of significance level is
228.58 and computed critical value is 173.55. As a result, the computed chi-square is larger than
the critical value. The decision regarding H0= constant variance is to reject the null hypothesis.
This connotes, that the information is influenced by heteroscedasticity. This also means that the
assumption of homoscedasticity is violated in the data. Thus, it is important to take corrective
measures to reduce the effect of heteroscedasticity in the data.
3 One jirib is equal to 2000 square meters.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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A number of corrective measures such as taking natural logarithms, weighted least squares, and
others can be applied to data which solve the heteroscedasticity problem to a certain extent.
In this study, the variables are transformed to its natural log form. Taking logs might not solve the
problem perfectly, however, it will lessen the impact of heteroscedasticity to a tolerable extent.
Adjustments for heteroscedasticity increase the precision of slope coefficients estimations and
could be reflected more accurately. In addition, it also affects the technical efficiency of individual
firms.
After the heteroscedasticity adjustments, the final MLEs for equation 9 and 10, are presented in
table 2.
ln 𝑌 = 𝛽0 + 𝛽1 ln 𝐿𝑎𝑛𝑑 + 𝛽2 ln 𝑃𝑙𝑎𝑛𝑡 + 𝛽3 ln 𝑊𝑎𝑡𝑒𝑟 + 𝛽4 ln 𝐹𝑒𝑟 + 𝛽5 ln 𝑀𝑎𝑛𝑢𝑟𝑒
+𝛽6 ln 𝑙𝑎𝑏𝑜𝑢𝑟 + 𝛽7 ln 𝑃𝑒𝑠 + 𝛽8 ln 𝑂𝑡ℎ − 𝐼𝑛𝑠+𝛽9 ln 𝑇𝑟𝑒𝑒 + 𝑣 (9)
𝑢 = 𝛿0 + 𝛿1𝐴𝑔𝑒 + 𝛿2𝐸𝑑𝑢𝑐 + 𝛿3𝐸𝑥𝑝𝑒𝑟 + 𝛿4𝐻𝐻𝑆 + 𝛿5𝐷𝑎𝑚𝑎𝑔𝑒 + 𝛿6𝑆𝑒𝑐
+𝛿7𝐴𝑖𝑑 𝑣𝑎𝑙𝑢𝑒 + 𝑤 (10)
Table 2. Estimated Coefficients
Variables Parameters Cobb-Douglas
Stochastic Frontier
Constant β0 7.63*** (0.703)
Ln Land β1 -0.212 (0.173)
Ln Plant β2 0.014* (0.008)
Ln Water β3 0.398*** (0.078)
Fer β4 0.044 (0.029)
Ln Manure β5 -0.004 (0.012)
Ln Labor β6 0.043 (0.074)
Ln Pes β7 -0.020 (0.013)
Ln Oth-ins β8 0.006 (0.009)
Ln Trees β9 0.497*** (0.124)
Inefficiency Model
Constant 𝛿0 -23.242***
(4.919)
Age 𝛿1 0.037
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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(0.135)
Educ 𝛿2 -0.550
(0.205)
Exper 𝛿3 -0.550***
(0.239)
HHS 𝛿4 -0.584***
(0.118)
Damage 𝛿5 0.184***
(0.073)
Sec 𝛿6 -1.901***
(0.663)
Aid value 𝛿7 0.0000387***
(0.000019)
Sigma squared 98.972***
Gamma 0.999***
Log-likelihood function = -347.43699
Mean technical efficiency TE 43.42%
Source: Own Computations. ***, **, * significance level at 1%, 5%, and 10% respectively.
The coefficient of land is negative but insignificant. Additionally, the output decreases due to the
fact that materials considered for a certain area will be shared with the expanded land region and
it results in declining production.
The coefficient for new plants is positive and significant at ten percent significance levels.
However, the expected sign for plants is negative. The positive sign of them may be because the
extra care given for new plant affects the old one resulting in higher fruit production. A one percent
increase in new plants increases fruit output by 0.014 percent. Positive signs significantly affect
production. The coefficient of water shows that watering is not at an optimum level and with an
increase of one percent in watering, production rises by 0.39 percent. Afghanistan is periodically
hit by drought. Deficiency of water is one of the major problems of Afghan farmers. The slope
coefficient for labor is 0.043 and insignificant in this study. A study by Tadesse, Bedassa, &
Krishnamoorthy (1997) also confirms that the coefficient of labor which is 0.162 does not have a
significant impact on the production. However, in a study conducted by Battesse & Coelli (1993),
labor has a large impact on production. The number of trees also has a positive effect on the
production of fruits. Adding one percent of trees contributes to an increment of 0.5 percent on
average to total output. The reason for the high impact of trees is that adding trees require minimal
material compared to its yields.
The coefficients of experience, household size, damaged trees, security, and aid value in the
inefficiency model are significantly different from zero. Experience has a negative sign which
means higher experience leads to less inefficiency and in turn it leads to higher output. Household
size also has a negative sign. It depicts that a family with more members is likely to have higher
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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production and higher efficiency compared to those households having fewer members. The
cause is that in Afghanistan every household member who can work - even if they are not adults
- work in the garden. The additional work of household members results in the higher output. The
sign of damaged trees is positive showing that with a higher number of damaged trees, the
inefficiency of the farmer will also increase. Security has a negative sign indicating that fruit
production in safer areas has a higher efficiency rate compared to a less safe area. Aid value
unexpectedly has a positive sign, which means aid value increases inefficiency. However, the
coefficient is near to zero and hence it is can be said the effect of aid value on inefficiency is
unimportant.
Finally, two parameters in the final part of Table 2 are related to the two random variables in the
model namely, vi, and ui. The value of gamma is an indicator of the extent to which the firm is
influenced by the inefficiency term. Therefore, the estimated high value of gamma shows that the
evidence of inefficiency is strong in this model. If gamma is equal to zero, then the model is
reduced to the production function where inefficiency variables are also fitted in the first equation
and the second model is eliminated.
In research, it is important to ensure that the model used in the study is better than other
alternative representations. Numerous models have to be tested with a specific statistical test and
choose the best fitting model for the analysis. According to Battesse & Coelli (1995), these
attempts can be conducted using likelihood ratio testing methods.
In likelihood ratio tests, null hypothesis tests are conducted by using log-likelihood functions. If
the likelihood function of restricted and unrestricted models are divergent, it shows that the
unrestricted model with more variables is better. However, it does not say if it is significantly better.
Hence, the difference between likelihood ratios is tested to make sure that this alteration is
statistically significant. If the difference is significant, a hypothesis which is in favor of the
unrestricted model is accepted and the opposite is rejected. The formula for the likelihood ratio
test is available as equation 11.
𝜆 = −2[log(𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 (𝐻0)) − log(𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 (𝐻1))] (11)
Since it is assumed the data has a chi-square distribution, it is easy to find the critical value of five
or one percent of the upper tail of the X2-table with corresponding degrees of freedom (dfH0-dfH1).
The result of lambda or log-likelihood is compared with the critical value of a chi-square table.
Similar to other evaluations, in the likelihood ratio test null hypothesis is rejected when test value
is larger than the critical value.
Table 3. Hypotheses Tests of Stochastic Production Function Parameters
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
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Hypotheses Log (likelihood) Critical value df Decision
H0:
β1=β2=β4=β5=β6=β7=β8=δ1=δ2=0
-166.96 21.666 9 Reject H0
H0: γ=δ0=δ1=…= δ7=0 -179.08 23.209 10 Reject H0
H0: δ0= 0 -203.42 33.409 17 Reject H0
Source: Own Computations
At first, individually insignificant parameters are tested jointly. A number of betas and deltas in the
first null hypothesis are individually insignificant. Hence, this test shows if these parameters are
jointly and significantly equal to zero. The first null hypothesis is rejected with one percent level
of significance. Rejection of first null hypothesis means that even though the parameters are
individually insignificant, the pattern, including these restrictions is a better fit of data estimation.
The second null hypothesis is tested to make sure the producers are affected by the technical
inefficiency. If the null hypothesis is accepted, the model will be reduced to classical Cobb-
Douglas having all the variable in a single equation production function and so the inefficiency
model will be eliminated. The second null hypothesis is rejected at one percent level of
significance. It can, therefore, be concluded that stochastic production function with inefficiency
effect is the suitable representation for the analysis and estimations.
The third null hypothesis is to provide evidence that the intercept of inefficiency model is unequal
to zero. The null hypothesis, showing the technical inefficiency intercept equal to zero is rejected
at one percent significance level. The decision is, the intercept is significantly different from zero.
Discussion & Conclusion
The aim of this paper was to find the factors affecting the technical efficiency of fruit producers in
Logar province. To achieve the aims and objectives of the paper, the Stochastic Frontier
Production Model was used. The data was collected from the gardeners in Logar province of
Afghanistan. Application of the suggestions and bringing further development in the
corresponding aspects will help interviewed fruit producers in Logar province to have a higher
technical efficiency and reasonable quantities of output.
The mean technical efficiency was found to be very low, namely 43.42% on average for the
participants. This equally means that orchard owners are not operating in a technically efficient
manner. From the parameters estimated, it can be concluded that water and the number of fruit
trees play a major role in increasing fruit production. Moreover, experience, household size, the
number of damaged trees, and security are important determinants of technical efficiency of
producers. From the hypothesis tests, it is concluded that all input variables - which are presented
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
13
in the stochastic frontier model as an independent variable - are affecting the output either
positively or negatively corresponding to the signs they have. To this end, every demographic and
socioeconomic variable in the inefficiency model influences the technical efficiency of participants.
This also means that all the variables in both models are accountable for the final production and
technical efficiency of participating gardeners in the Logar province.
For this paper, 196 gardeners were interviewed. The results and observations cover only the
specific group of orchard owners. Hence, the outcomes obtained could not be generalized to the
Logar province or Afghanistan. Therefore, a comprehensive research is needed to encompass
large data. The future studies should be in a position to have the features and the ability to draw
the conclusions, which could represent all the horticulturists. Moreover, the future research with
the said characteristics could give recommendations for all gardeners of Afghanistan and the
authorities could take corrective measures accordingly.
The technical efficiency of fruit production in Afghanistan - A case study of Logar province
14
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