ahsanullah mohsen · ahsanullah mohsen keywords: technical efficiency, fruit production, stochastic...

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


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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.


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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.


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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


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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.


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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)


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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.


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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.


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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


10

(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


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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


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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


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.


14

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ahsanullah mohsen · ahsanullah mohsen keywords: technical efficiency, fruit production, stochastic...

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