FACTORS AFFECTING TECHNICAL EFFICIENCY SCORES ESTIMATED FOR THE COTTON SECTOR OF THE HARRAN PLAIN IN TURKIYE: A STOCHASTIC FRONTIER ANALYSIS

The current study deals with the technical efficiency of cotton farmers operating on the Harran Plain of Turkiye with an application to the two well-known stochastic approaches, i


I. INTRODUCTION
There are interesting concerns both in terms of poverty reduction and national economic aspects arising from the role of cotton production in national development in Turkiye.Cotton farming has traditionally been considered the main livelihood of the farm households operating in the major plains of Turkiye.The cotton sector on the Harran Plain, one of the largest plains of the Southeastern Anatolia region in Turkiye, is almost entirely characterized by middle-income cotton producers who were responsible for about 21 percent of the national cotton production.With cotton the most-planted field crop on the Harran Plain, it is commonly accepted among local farmers that cotton is the most profitable agricultural commodity.Between 1995 and 2019, the area under cotton cultivation in Turkiye increased more than twenty times and reached 477,868 hectares with a production amount reaching 2.2 million metric tons [1].
The cotton sector, loaded with a lot of roles in farmers' livelihoods as such, has been disrupted by several problems.First of all, inefficient production techniques lead to low levels of yield and quality factors.Based on a dataset compiled using information gathered from a sample of cotton farmers operating in the Harran Plain, Binici et al. (2006a) reported that most cotton farmers in the region are inefficient input users.In addition, excessive irrigation practices, which are widely applied in the Harran Plain, are the main drivers of increased soil salinity.This problem is due to the shallow groundwater table and can seriously disrupt cotton production [2]- [4].
In addition, the prevailing marketing system in the area is not sufficient to provide local cotton farmers with the possibility of supplying their products at reasonable prices.Factors like these have reducing effects on farmer incomes.As a result, poverty will continue to be a trap for most households.Therefore, improving production performance while ensuring sustainable use of resources is the main challenge for the growth of middle-income cotton farmers.However, the opportunity to improve farm production based on the expansion of cultivated land is limited to meeting the growing demand for cotton required for Turkiye's ever-increasing population.Therefore, advances in technology and productivity/efficiency are the only hope of production increase to meet the increasing demand for cotton.
While production functions of farmers operating at full efficiency level were assumed to be known, it was necessary to estimate these functions based on data using either parametric or non-parametric (also known as Stochastic Frontier Analysis and Data Envelopment Analysis, respectively) techniques as the parameters of such functions always remained unknown in practice.Starting from this point, literature on efficiency has evolved in two directions of which is to use parametric techniques [5]- [17] and the other one is to use non-parametric techniques [18], [19].
The bulk of the literature focusing on parametric techniques has developed in the area where technical efficiency and inefficiency factors are incorporated simultaneously within a stochastic model [7], [9], [15]- [17], [20]- [26].However, in some empirical papers by opponents of the above method, a two-step procedure was adopted, i.e. stochastic frontier production function parameters were estimated first, and then the estimated technical inefficiency effects were retracted on the various farmer-specific variables that are expected to be important in explaining the level of technical incompetence of the farmers sampled.This two-step approach contradicts standard assumptions that inefficiency effects are independently and identically distributed to estimate unknown values.However, using predicted technical inefficiency effects in a regression model that includes other explanatory variables is not consistent with the assumption of uniformly distributed technical inefficiency effects in the stochastic model [27].Despite this debate over whether or not either analysis of the impacts of farmspecific factors on productive efficiency should be handled within a simultaneous model, the two-step procedure is still quite popular in determining the linkage between productive efficiency and firmspecific factors.
In Turkish agriculture, it is important to measure efficiency and productivity for several reasons.Firstly, efficiency and productivity are the key indicators to evaluate farm households as they are the accepted performance measures and success parameters.Secondly, to hypothesize the determinants of inefficiency it is important to isolate the impacts of efficiency and productivity from the environmental impacts once they are estimated.Improving the performance of farm households is then closely related to policies that are formed by identifying sources of inefficiency.

II.1 DATA COLLECTED AND THE MATERIAL USED
The research project was started by the University of Harran and funded by the Scientific and Technological Research Council of Turkiye (TUBITAK) with reference number 110K374.Individual units and a subset of survey data were used in this analysis.
The information acquired using a data collecting method also known as the farmer registration information and financial incentive systems, applied to a random sample of cotton farmers working on the Harran Plain, constitutes the majority of the core materials utilized in this article.This method addresses the problem of survey respondents having trouble recalling their responses to questions about their agricultural practices.Farmers are frequently confronted with queries about their previous farming techniques.The study reported in this paper uses farmer diaries based on payments to motivate farmers to voluntarily participate in the survey and so limit the problems generated by the problem of misremembering the answers to comprehensive survey questions.
The implementation of a financial inducement system that allows for the financial and production record keeping with the least amount of information loss would ensure that participant farmers are provided an incentive to complete farmer diaries on a daily or at least weekly basis.As a result, a payment schedule was established, allowing our member farmers to get a one-time-only payment after finishing the diaries after the season.
We used a stratified random sample technique to choose several representative cotton farmers who would be given diaries to fill out beginning with the 2012 crop season.We then administered frequent visits (10 to 20 depending on the location) to these farmers throughout the season to control these diaries.Two steps were taken to carry out the sampling.First, we purposely identified 51 villages based on their representative properties.On the Harran Plain, 1,029 registered cotton farmers were actively farming the crop and these farmers are to be counted as the overall farmer population.In the second stage, a stratified random selection strategy with a 5% acceptable error margin was used to choose a total of 126 cotton farmers to furnish the farmer diaries.This procedure yields four size strata that represent the region's entire farmer population.There will be 49, 49, 21, and 7 cotton growers sampled in each of the four size strata, respectively.

II.2 ANALYTICAL FRAMEWORK
To estimate frontier production functions for efficiency assessments, stochastic frontier analysis (SFA) has been utilized extensively in the literature.The stochastic frontier analysis pays particular attention to how the composite error term takes the form, differentiating between measurement errors and other sources of statistical noise.This is in contrast to Data Envelopment Analysis (DEA), which makes no assumptions about the distributional form for inefficiency terms or the functional forms of production functions.Contrary to what DEA claims, not all deviations from the maximum production are considered to be the result of technological inefficiency from the SFA perspective.With Farrell (1957) [28] reporting that production functions of firms must be estimated using data on individual levels and functional forms, stochastic frontiers have since been developed further capitalizing on this notion [29].
The two major representations of the stochastic frontiers are the Cobb-Douglas model and the Transcendental logarithmic (hereafter, translog) model [30], [31].The Cobb-Douglas stochastic frontier model imposes several technological constraints, such as requiring constant elasticity of scale and unity elasticity of input substitution.However, the translog stochastic frontier model, which has a flexible functional form, does not impose any such limitations, and the range of the elasticity of substitution ranges from negative infinity to positive infinity.Hence the Cobb-Douglas model is nested in the Translog model.
We can specify these models as: Cobb-Douglas: (1) where Yi is the i-th firm's output, Xi is a K x 1 vector holding the input logarithms; β is a vector of unknown parameters; and εi is the composite error term, which is made up of two distinct error components from different sources, i.e.,   =   −   where vis are the error component resulting from measurement errors and other factors beyond the farmer's control and are assumed to follow a normal distribution N(0,   2 ).The uis, on the other hand, are nonnegative random variables linked to technological inefficiency and are supposed to come from a normal distribution with mean µ and variance   2 , which is truncated at zero from below, where µ is defined as and where Zis are farm and farmer-specific variables that are hypothesized to have an impact on technical inefficiency level.
Following the  parameterization of Battese & Cora [6]; The log-likelihood function for normal and truncated normal pairs may then be written as (1 ) ln 0.5ln 2 ln ln ln 0.5 (1 ) Where µi is specified as before, 2 , (. ) represents the cumulative distribution function of a standardized normal variable, and εi is the composite error term for each firm in question.The parameters, ,    2 , and  in the above likelihood function are the choice variables for which the values are to be estimated by maximizing the function using the FRONTIER 4.1 computer program developed by Coelli in 1996 [32].The ratio of the observed output to matching stochastic frontier output is the technical efficiency term for a single data point in SFA: However, the inefficiency term, ui is not observed while the composite error term is.Thus estimating technical efficiency scores requires taking the expected value of ui conditional on   =   −   [13]: where  Λ = √(1 − )  2 ;   = ln(  ) −   , and the cumulative distribution function of a standardized normal variable is again represented by (. ).

II.3 VARIABLES USED IN THE ANALYSIS
Participants in the survey were also interviewed to answer questions in two categories: (1) production characteristics, which included measures such as the size of operation, type of ownership, commodity yields, and land characteristics; and (2) farmer characteristics, which included gender, age, and education, among others.Table 1 describes the output and input variables that are used to estimate frontier production functions, while Table 2 summarizes the description of the dependent and explanatory (Z) variables that are used in our econometric analysis.These tables per se are self-explanatory and describe the variables used in the analyses quite comprehensively.Quantity of seeds used in cotton production (kilograms)

FERTILIZER (X2)
The variable denoted as FERTILIZER represents the net total amount of ammonium and phosphate contained in commercial brand fertilizers used in cotton production and is measured in kilograms.

LABOR (X3)
Working hours depleted (family as well as hired labor).

CAPITAL (X5)
Capital input includes the annualized flow of capital services required by cotton production and is measured in TL.

LAND (X6)
Land area input is considered as the land area under cotton cultivation and measured in hectares. 1Abbreviated for Turkish Liras Source: Authors, (2023).
Table 2: Z variables' definition for the stochastic frontier analysis (inefficiency determinants).

TEVRS
Technical efficiency is calculated using the assumption of variable returns to scale, with a value ranging from 0 to 1.

EXPERIENCE (Z1) Farmer experience (Years) EDUCATION (Z2)
If the farmer attended high school or high school and college, the dummy variable will have a value of 1, otherwise, it will have a value of 0.

HSIZE (Z3)
Household size; the number of people living in the household.OFF-FARM (Z4) The value of the dummy variable is 1 if the farmer works outside the farm and 0 otherwise.FMLYLBOR (Z5) Share of the family labor force in total labor input (%) LSEGMENT (Z6) Parcel segmentation on land is the number of parcels under the farmer's ownership or tenancy.LNDOWNR (Z7) If the farmer owns the land he farms, the dummy variable will have a value of 1; otherwise, it will have a value of 0.

LOCNHRRN (Z8)
Dummy variable that indicates the location of the agricultural activity has a value of 1 if it is situated in Sanliurfa's Harran district.

LOCNACKL (Z9)
Dummy variable that indicates the location of the agricultural activity and returns 1 if the land is in Sanliurfa's Akcakale district.

IRRGFREQ (Z10)
Frequency of irrigation applied to the land under cultivation.
Table 3 shows descriptive statistics for the input variables used to estimate production frontiers, whereas Table 4 shows descriptive statistics for farm and farmer characteristics (Z variables) utilized as explanatory factors for examining the drivers of technical efficiency scores.
The variable designated "OUTPUT" is the quantity of cotton produced in total kilograms.Six inputs capturing all the production factors that are used in cotton production (SEED, FERTILIZER, LABOR, PESTICIDE, CAPITAL, and LAND) are considered.Some of these input variables are measured in mass units (i.e., kilograms), while others are expressed in Turkish Liras (TL).The labor input (LABOR) is measured in working hours depleted by the farmer and considers paid and unpaid labor.The variable denoted as CAPITAL quantifies the annualized flow of capital services required by cotton production and is estimated by summing up all the expenses on fixed and variable inputs other than seed, fertilizer, labor, and pesticides.These expenses typically include yearly depreciation, rental costs for the land and/or machinery used in production plus other expenses on fuels and repair and maintenance services for the farm machinery.The variable designated "FERTILIZER" is the net amount of nitrogen plus phosphorus contained in commercial fertilizers applied and measured in kilograms.The variable "SEED" represents the amount of cotton seeds used to sow the field and is measured in kilograms as well.The variable designated "PESTICIDE" consists of such variable expenditures including those for both herbicidal and insecticidal chemicals and is measured in TL.Using Coelli's FRONTIER 4.1 software developed in 1996 and SFA methodologies separately applied to each frontier production function under the assumptions of variable returns to scale, technical efficiency ratings utilized as the dependent variable in our econometric studies are estimated [32].Some of the farm and farmer characteristics anticipated to influence technical efficiency scores include single dummy variables quantifying off-farm work status (OFF-FARM), land ownership status (LNDOWNR), and education level (EDUCATION), as well as a mutually exclusive multiple dummy variable representing farm location (LOCNCNTR, LOCNHRRN, and LOCNACKL).Other determinants affecting farmer performances are farming experience in years (EXPERIENCE), household size (HSIZE), number of parcels under the farmer's ownership or tenancy (LSEGMENT), and number of irrigation applied (IRRGFREQ).To quantify the effects of the proportion of family labor input in the entire labor force (measured in continuous percentages), we lastly incorporate the variable FMLYLBOR.The location dummies are used to identify the impacts of farmer locality on their performance measures.Due to improved access to knowledge, it is speculated that farmers in the central area are technically more efficient than those working in the Harran and Akcakale districts.Dropping one of the dummy variables from the analysis and using it as a reference variable instead would help avoid dummy trap problems and thus we followed this rule for all the dummy variables in our econometric analysis to keep the consistency throughout.The variable designated LNDOWNR quantifies the effects of land ownership status and could have an ambiguous impact on efficiency.Efficiency might be enhanced by applying soil-improving techniques, an incentive created by land ownership status.However, the tenant farmer may be encouraged to use inputs more effectively by his or her status as a land renter.
A bigger percentage of hired labor may indicate a more specialized, and hence productive, labor input, but it may also be a source of moral hazard.The influence of the amount of family labor might go either way (positive or negative) [33].Experienced farmers tend to operate more professionally; therefore, it would stand to reason that experience would increase efficiency.However, other writers explore reasons for the reverse connection [34], maybe because farming becomes more physically demanding as the farmer ages (e.g., age impairments-non linearity).Similarly, we hypothetically attach higher efficiency scores to those full-time experienced farmers who are more educated with smaller household sizes, operate on a smaller land tract divided by a smaller number of parcels, and finally irrigate the land more sensibly.

III. RESULTS AND DISCUSSION
In Table 5, the maximum likelihood estimates of the coefficients for the translog stochastic frontier model and the Cobb-Douglas model are shown.All the β coefficients from the Cobb-Douglas frontier model have expected signs and three of these coefficients turn out to be considered significant demonstrating the robustness of the model.In the translog frontier model, nine out of the twenty-seven coefficients are significant at the %1 level, four are significant at the %5 levels, and just one is significant at the %10 levels.Thus the translog frontier model is robust as well.
We check to see if the technical efficiency estimates produced from the two models have different means and variances.Even though the generalized likelihood ratio (LR) test indicates that the translog stochastic frontier model is an appropriate representation, we additionally investigate the sensitivity of technical efficiency levels to the functional form choice. Table 6 shows the production elasticities of individual inputs along with scale parameters.Both models yield production elasticities with all their signs (positive) in the direction expected.The land has the highest production elasticity indicating that it is the most prevalent factor of production.This finding is consistent when we particularly consider how scarce the land is to the farm households in Turkiye.This implies that farm households may be encouraged to continue cultivating their current land parcels.
The factors designated CAPITAL and PESTICIDE appear to be the second and third important factors of production, respectively, for the Cobb-Douglas frontier model while FERTILIZER and SEED inputs for the translog frontier model.These inputs (SEED, PESTICIDE, and FERTILIZER) are landenforcing factors of production tending to increase the productivity of existing land tracts and thereby promoting yields per hectare.In Turkiye, land degradation brought by elevated soil salinity and wind erosion is the number one constraint on the production and it is possible to state that efficient utilization of fertilizer, seed, and pesticides as well as a suitable combination of the three can mitigate the effects of this constraint.The scale elasticities for the Cobb-Douglas and translog frontier models are 0.96639 and 0.95124, respectively, implying slightly diminishing returns to scale.This means that the farmers are not the best operators in terms of production size.

III.1 EFFECTS OF TECHNICAL INEFFICIENCY
The two key metrics used to assess the overall consequences of technical inefficiency are σ 2 and γ.Both the Cobb-Douglas and the Translog frontier models' predicted values of σ 2 and γ are statistically significant to differing degrees (5% in the Cobb-Douglas model and 1% in the Translog model).This result agrees with previous findings.The Cobb-Douglas and Translog frontier models' estimated values are very substantially different from zero, indicating that the random component of the inefficiency effects considerably affects the level and variability of production for these sampled farmers.This finding is consistent with those found by Wadud (2003) [30], Sharma et al. (1999) [24], and Coelli and Battese (1996) [35].The Cobb-Douglas and Translog frontier models' respective generalized LR tests, designated as test number 1 in Table 7, lead us to strongly reject the null hypothesis that there is no technological inefficiency at the 5% level.This reveals the randomness of technical inefficiency effects in both models for the farm households operating on the Harran Plain of Turkiye.As a result, their standard response functions are insufficient representations of cotton output.
The generalized LR test presented in Table 7 further illustrates that the stochastic frontier model's explanatory factors, which are unique to the farm setting, have collectively influenced the level of technical inefficiency at the 5 percent level for both frontier models.Given that these factors are likely to have an impact on the productivity of local cotton farmers, it is crucial to look at the signs of the predicted coefficients for δi parameters linked to the various explanatory variables in both stochastic frontier models.
In all models, the signs of the estimates for the coefficients of farming experience are positive, showing that experienced farmers are technically less efficient than rookie farmers.While this compares to previous results obtained by several researchers [9], [30], [36], it contradicts the finding obtained by Sesabo and Tol (2007) [25].This could be attributable to easier credit availability for younger farmers.The coefficients of education in the two models as measured by a dummy variable (taking on values of 1 if the farmer has a high school or college degree) have positive signs indicating that higher education causes inefficiency which is not in the direction expected (significant at 10% and 5% significance levels, respectively).This conforms to the results found elsewhere [24], [35].The coefficients of the variables designated HSIZE and OFF-FARM are estimated to be negative, implying that household size and off-farm employment availability have a beneficial influence on efficiency, albeit these coefficients are only significant in the translog frontier model.This is not consistent with the findings by Sesabo and Tol (2007) [25].The estimates for the coefficients of the share of the family labor force in total labor input and the number of irrigation applied to turn out to be positive showing evidence of lowered efficiency levels as they tend to increase.However, the coefficients of the share of family labor input are not significant in both models while the coefficient of irrigation frequency is only significant at the 5% level in the translog stochastic frontier model.Although these findings about family labor input and irrigation frequency satisfy our initial expectations there are no similar results in the literature to which we can compare our findings.
The signs of the estimates for the coefficients of land disintegration as measured by the number of parcels under ownership or tenancy are estimated to be positive which translates into a negative impact on efficiency, i.e., the greater the plot size the lower the efficiency.This finding runs along similar lines to the results obtained by Coelli and Battese (1996) and Wadud (2003) [30], [35].The estimates for the coefficients of the dummy variable capturing the land ownership status have negative signs indicating that land owners are associated with higher efficiency levels than tenants (only significant in the Cobb-Douglas stochastic frontier model).This is perhaps because landowners would feel more responsible for tracts they operate on resulting in greater engagement of infrastructural investments and that would in turn result in greater efficiency levels.Last but not least, the outcomes of the two models show that the efficiency is negatively impacted by the location dummies for the districts of Harran and Akcakale.This indicates that farmers in the province of Sanliurfa's core area are associated with higher efficiency levels.This conclusion may be explained by the fact that farmers in the central district have easier access to financial instruments such as credits, derivative products, etc.
Results indicate that farm households have technical efficiency scores which substantially differ across the sample.Technical efficiency scores for the Cobb-Douglas frontier model range from 0.30 to 0.98, with a mean of 0.87 and a standard deviation of 0.12, while technical efficiency scores for the translog stochastic frontier model are predicted to range from 0.28 to 0.97, with a mean of 0.88 and a standard deviation of 0.11.The technical efficiency scores' frequency distributions are shown in Table 8 along with their summary statistics.The table shows that it is possible to enhance farm income and thereby welfare by improving efficiency.Production costs could be reduced by 12 percent if full technical efficiency levels were attained by farmer operations.

IV. CONCLUSIONS
The Cobb-Douglas and translog stochastic frontier models are used in this study to examine the potential for finding technical inefficiency in terms of its patterns and sources for the case of local cotton growers working on Turkiye's Harran Plain.A specialized maximum likelihood estimation model is applied to estimate these efficiency scores along with their determinants simultaneously with the incorporation of stochastic frontiers and inefficiency effects into a single equation system.The inefficiency effects include such factors, namely education, farm experience, household size, off-farm job availability, the share of the family labor force, land fragmentation, land ownership status, irrigation frequency, and location of the farm relative to the central district of Sanliurfa.The system generates parameters of output elasticities calculated from both the stochastic frontier models, with their signs pointing in the desired directions.The study's findings demonstrate that the sampled local farm households exhibit slightly declining returns to scale in cotton production.The two well-known stochastic models, namely the Cobb-Douglas and the translog frontiers, generate wide ranges of technical efficiency scores that vary from 30% to 98% with a mean of 87% and 28% to 97% with a mean of 88%, respectively.It was detected that full technical efficiency levels attained by farmers ensure a reduction in production cost by 12%.
The findings of the study show that technical efficiency is significantly impacted by farm-specific explanatory factors included in the technical inefficiency effects model.Ironically the older, experienced farm Households with greater education tend to operate farming activities inefficiently.Technically speaking, the farm households operating in Sanliurfa's central region are more productive than those in Akcakale and Harran districts.Moreover, farm households that operate on larger, more fragmented land holdings are inherently less efficient.The well-being of farm households should be improved by robust agricultural policies targeting to reduce land fragmentation and increase technical efficiency and thereby improving farm income.

VI. ACKNOWLEDGMENTS
The Scientific and Technological Research Council of Turkiye (TUBITAK), which supported our study with reference number 110K374, has our sincere gratitude.Without their significant contributions, this study would not have been possible.
The writers' results, interpretations, and conclusions are their own, and they do not necessarily reflect the opinions of TUBITAK.

Table 1 :
Definition of the variables used to estimate frontier production functions.

Table 3 :
The input variables' descriptive statistics for estimating stochastic frontiers.

Table 4 :
Explanatory variables' descriptive statistics used to assess the inefficiency effects model.

Table 5 :
Estimates of the stochastic frontier models using the maximum likelihood technique.

Table 6 :
Output elasticities of inputs used in cotton production.

Table 7 :
Hypothesis tests for the stochastic frontier and inefficiency effects models.

Table 8 :
Frequency distribution of farm-specific technical efficiency.