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Agriculture
, Volume 10 (4) – Apr 3, 2020

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agriculture Article DEA Performance Measurements in Cotton Production of Harran Plain, Turkey: A Single and Double Bootstrap Truncated Regression Approaches 1 , 1 2 3 Tamer Isgın ¸ *, Remziye Özel , Abdulbaki Bilgiç , Wojciech J. Florkowski and Mehmet Resit ¸ Sevinç Department of Agricultural Economics, Faculty of Agriculture, Harran University, 63050 Sanlıurfa, ¸ Turkey; rozel@harran.edu.tr Department of Agricultural Economics, Faculty of Agriculture, Atatürk University, 25240 Erzurum, Turkey; abilgic@atauni.edu.tr Department of Agricultural & Applied Economics, University of Georgia, Athens, GA 30602, USA; wojciech@uga.edu Department of Bozova Vocational School, Harran University, 63850 Sanlıurfa, ¸ Turkey; rsevinc@harran.edu.tr * Correspondence: tisgin@yahoo.com; Tel.: +90-414-3183718 Received: 9 February 2020; Accepted: 17 March 2020; Published: 3 April 2020 Abstract: A single and a double bootstrap of data envelopment analysis examines Harran Plain cotton farming in Turkey. The single bootstrap technique was employed to derive the bias-corrected eciency values under both constant returns to scale (CRS) and versus variable returns to scale (VRS) technologies while discriminating between the two technologies using a smoothed bootstrap test statistic. Results indicated that the farms operated under VRS technology. Given that VRS technology prevailed across Harran Plain cotton farmers sampled, we then determined factors aecting the bias-corrected technical eciencies using the double bootstrap technique. Another important ﬁnding in the single bootstrap analysis is that cotton farmers in the region have a U-shaped technical eciency based on the input and output scale. Thus, small-scale farmers tend to use their resources more eciently in cotton farming than that of both medium- and large-scale farmers. Interestingly, the medium-scale farmers with resource ineciency are at the forefront of the other two types of farmers (i.e., small-scale and large-scale) on the Harran Plain in Turkey. The results also showed that most of the farm and farmer speciﬁc as well as economic factors play a signiﬁcant role in explaining the technical eciency values. Keywords: cotton; data envelopment analysis; eciency measurement; single and double bootstrap; Turkey 1. Introduction Cotton has strategic importance in Turkish agriculture, industry, and trade. Turkey is one of the top cotton-producing countries and produced 2,450,000 MT in 2017 [1], while the textile industry represents one of the leading sectors in the Turkish economy and accounted for 16% of total export value in 2017. Exports of ready-to-wear cotton items were worth $17 billion and textiles were valued at $8 billion in 2017 [2]. Rapid economic development and a changing demographic structure in Turkey has led to a fast increase in domestic demand for textile products. Speciﬁcally, due to the speedy increase in the number of textile and clothing stores and shopping centers throughout the country, domestic textile sales have increased signiﬁcantly in recent years. Turkey’s growing young population, migration to urban areas, refugee inﬂux from Syria and other countries, and the increase in tourism have contributed Agriculture 2020, 10, 108; doi:10.3390/agriculture10040108 www.mdpi.com/journal/agriculture Agriculture 2020, 10, 108 2 of 17 to a substantial increase in the domestic consumption of cotton products. In 2017/2018, domestic consumption was expected to reach 1.57 MMT (7.2 million bales), a ﬁvefold increase in the annual cotton consumption since the 1980s [2,3]. Turkish total cotton imports reached 401,000 MTs in 2018, of which nearly 30% (118,000 MTs) were imported from the United States [2]. The growing domestic demand for cotton has turned the previously net exporting country into a net importer since 1992. Southeastern Anatolia, known as the Fertile Crescent or Upper Mesopotamia, covers 20% of all irrigable land in Turkey. The Southeastern Anatolian Project (SAP) has been a massive $32 billion public development project intended to improve farmer welfare in the region [2,4]. When all irrigation schemes under that project are completed, an additional 1.7 million ha will double the country’s irrigated farmland. The Southeastern Anatolia (SEA) region will cement its prominent position as a cotton supplier. The Harran Plain, one of the largest plains in the SEA region covers 225,109 ha, of which 140,000 ha are currently being irrigated [2]. Local farmers view cotton as the most proﬁtable crop. The cotton area increased more than ﬁvefold between 1995 and 2017, reaching 116,391 ha with a harvest of 546,917 MTs [1]. The Harran Plain alone accounts for about 22% of the country’s cotton production. However, both yield and quality are low due to ineciencies. The main reasons for the ineciency is excessive or inadequate use of inputs such as fertilizer, improved seeds, irrigation, and extension services, which helps explain the less than expected productivity of the cotton sector, as well as the internal ineciency in the use of available farm resources such as land, labor, and capital in the SEA region. For example, the use of excessive water has been cited as one of the main causes of soil salinity, which leads to reduced yields in cotton production in the region [4,5]. The Ministry of Agriculture and Forestry (MAF) has been providing technical and ﬁnancial assistance to farmers to build modern drip irrigation systems and prevent ecological problems by avoiding water wastage. The MAF eorts have focused on moving from open canal irrigation systems to closed systems to reduce water loss during transportation [2]. While cotton yield in the country (1683 kg/ha) ranks third after China (1751 kg/ha) and Brazil (1686 kg/ha) in general, in some years the yield in Turkey has been more than the other two countries [6]. The increased use of improved technologies and/or the eciency of farmer input use in cotton production on the Harran Plain oers potential to close the yield gap permanently. As stated in one of earlier studies [7], improvements in cotton productivity in the region may result from more ecient input use. In the near future, growth in the region’s cotton production, especially in the plain, can result from more ecient use of land, capital, labor, and other inputs, especially irrigation. Unfortunately, there are other external factors hindering the rational use of inputs by cotton producers in the country. For example, most of the inputs used in cotton farming are import-based, preventing the use of the desired inputs at full capacity as a result of swings in exchange rates. For example, when the January and year-end December periods are taken as a reference, the exchange rates of the USD ($) against the Turkish Lira (TL) in 2011, 2012, and 2013 were 19.63%, 3.25%, and 16.32%, respectively, exhibiting high volatility with non-stationary structure. Of course, fuel and fertilizer are among the most vulnerable inputs exposed to the exchange rate uncertainty. As such, at a time when the appreciated Turkish Lira lowers the production costs, it would be possible to increase the amount of energy inputs such as fuel, pesticides, and fertilizer, as well as overhead inputs such as labor and capital, including land, which appears to be quasi-ﬁxed in cotton production. Although cotton is the most frequently cultivated crop in the Harran plain, little is known concerning farmers’ eciency in the use of production inputs. In addition, all of the above-mentioned problems show that the input-oriented approach to solving problems in cotton production would be more rational and advantageous than alternative techniques. Additionally, as in other production sectors (industry and service sectors), the decision-making units (DMU) in the agricultural sector have more control over inputs than they have over outputs. An input-oriented approach was therefore used in our analysis of technical eciency. Meanwhile, the research on the technical eciency of cotton production and the determinants of the variability of eciency levels among farmers with advanced analysis techniques is almost non-existent in the region or in the country. Therefore, this study attempts Agriculture 2020, 10, 108 3 of 17 to analyze the technical eciency of cotton production on the Harran Plain using an up-to-date data enveloping analysis, DEA, (including the application of the double bootstrap technique) and seeks to close the current knowledge gap by providing empirical evidence on resource utilization eciency. In this context, the available double bootstrap DEA techniques developed by Simar and Wilson [8], hereafter SW, were applied to the data. SW have empirically shown that the traditional two-stage DEA method (TTS-DEA) involves severe limitations. First, the TTS-DEA method is incompatible with the underlying data generation process (DGP) to produce meaningful statistical properties (e.g., unbiasedness) to describe technical eciency scores. Additionally, SW have shown the correlation of environmental factors with error term since input and output variables interact with environmental factors. Secondly, the DEA eciency scores are serially correlated invalidating statistical inferences. To overcome the constraints, SW used a double bootstrap procedure with consistent inferences to explain and predict eciency scores with valid standard errors and conﬁdence intervals [9]. Another feature that distinguishes our study is that earlier studies have implemented a double bootstrap technique by choosing the technical eciency of the farmers (e.g., constant returns to scale, CRS, versus variable returns to scale, VRS) based on verbal assumption without empirically testing, whereas this study empirically presents the existence of the farm technical eciency by using a single bootstrap technique. After the return to scale parameters for the sampled farms, assuming either CRS or VRS are determined by conducting a statistical test based on a single bootstrap technique, a double bootstrap method was then applied to determine both the eciency amount and non-discretionary factors playing roles in the eciency of cotton production on the Harran Plain. Therefore, the current study is novel in this respect. Included in the subsequent sections is the outline of methods used in the analysis and data description. Model comparison together with a speciﬁcation test and discussion of the eects of variables on the DEA eciency scores are given in Section 3. The ﬁnal part presents conclusions along with some policy implications. 2. Materials and Methods 2.1. Survey Design and Variable Selection for the Empirical Speciﬁcation First, 51 villages inhabited by 1029 cotton farmers were purposely selected, thought to be representative of the study area. Next, a total of 126 cotton farmers were selected using a stratiﬁed random sampling design introduced by Yamane [10] with an allowable percentage error margin of 5%. To assure the representativeness of the cotton farmer population, the selected farmers were divided into four size segments leading to a stratiﬁed distribution yielding 49, 49, 21, and 7 cotton farmers in each stratum. Farmer participation was voluntary. Farmers were supplied with diaries at the beginning of the 2012 production season. For the production season of 2012, we made a comparison between the variations in cotton yields obtained from the participant and non-participant farmers and no signiﬁcant dierence existed, indicating the Hawthorne eect was not present in our data set. In addition, we ascertain that our data set would not run into the problem of self-selection bias reasoning that our participatory farmers were randomly selected and even if the eects of both the self-selection bias and the Hawthorn are possible these eects would be oset thanks to the bootstrap technique used in this analysis. Meanwhile, in a standard DEA context, homogeneity in DMU’s refers to the condition where all DMUs under investigation are subject to similar conditions in terms of the topography, climate, and commonly applied farming techniques. When we apply this perspective, the homogeneity requirement in DMU’s in our data set is attained because all our farmers operate in the same region (the Harran Plains), face the same climatic conditions, and, therefore, apply similar farming techniques. Additionally, our output and input sets are constructed by taking representative (identical) measures into consideration. For example, while the farmers had a choice of using dierent fertilizer types, we converted those usages into the net nitrogen and phosphorous amounts. Similarly, in the calculation of family and hired labor, we converted the total number of hours and used the net Agriculture 2020, 10, 108 4 of 17 man-hour equivalent instead. Thus, we met the homogeneity requirement across all DMUs for every input used and output produced by the cotton sector of the Harran Plain region. The recording of the information was controlled by 10–20 visits to farmers throughout the season depending on the village location. Such an approach built a trusted relationship between the survey workers and the farmers, which better motivated farmers, minimizing the risk of recording false entries. Farmers received payments for recording ﬁnancial and production information after harvest. Each farmer was also interviewed on matters related to (1) production characteristics, including measures such as size of the operation, ownership type, yields, and land characteristics; and (2) farmer characteristics such as gender, age, and education (Table 1). After deleting an outlier value in one of our inputs in DEA, the remaining 125 farms formed our working sample. Table 1 lists deﬁnitions of variables used in the empirical analyses including units of measurement. Five variables (e.g., seed (SEED), the amounts of nitrogen and phosphorus (FRTLZR), family and hired labor (LABOR), herbicide and insecticide value (PESTICIDE), and value of working capital (OTHRCAP) capture the inputs used in cotton production per decare (YIELD). Table 1. Descriptive statistics for variables used in econometric analysis. Variable Name Variable Description Mean Std. Dev Min. Max. VIF First Stage Variables (DEA Variables) YIELD Total cotton yield (kg/da) 461.498 111.555 120.000 965.500 N/A SEED Cotton seed quantity (kg/da) 2.502 0.963 1.030 6.667 N/A Net nitrogen and net phosphorus used in cotton FRTLZR 28.263 10.662 9.884 86.575 N/A production (kg/da) LABOR Working hours depleted (family as well as hired labor/da) 51.466 41.434 2.091 71.867 N/A PESTICIDE Herbicide and insecticide value (Turkish Liras/da) 27.264 14.543 2.091 71.867 N/A Value of working capital other than seeds, fertilizers, and OTHRCAP pesticides and ﬁxed capital, including depreciation, repair, 293.643 109.589 62.200 611.022 N/A and maintenance (Turkish Liras/da) LAND Cotton area (da) 107.905 111.397 6.500 800.000 N/A Second Stage Variables 1 if farming experience less than 10 years, 0 otherwise EXPERN1 0.192 0.395 0.000 1.000 N/A (reference group) EXPERN2 1 if farming experience between 10 and 20 years, 0 otherwise 0.424 0.496 0.000 1.000 2.303 EXPERN3 1 if farming experience between 20 and 30 years, 0 otherwise 0.232 0.424 0.000 1.000 2.027 EXPERN4 1 if farming experience greater than 30 years, 0 otherwise 0.152 0.360 0.000 1.000 2.240 1 if farmer attended an elementary school, 0 otherwise ESCHOOL 0.496 0.502 0.000 1.000 N/A (reference group) SSCHOOL 1 if farmer attended a secondary school, 0 otherwise 0.128 0.335 0.000 1.000 1.386 HSCHOOL 1 if farmer attended a high school, 0 otherwise 0.376 0.486 0.000 1.000 1.884 HSIZE1 1 if household size less than 6 members, 0 otherwise 0.224 0.419 0.000 1.000 N/A HSIZE2 1 if household size between 6 and 10 members, 0 otherwise 0.400 0.492 0.000 1.000 2.195 1 if household size greater than 10 members, 0 otherwise HSIZE3 0.376 0.486 0.000 1.000 2.605 (reference group) OFF-FARM 1 if farmer has an o-farm job, 0 otherwise 0.304 0.462 0.000 1.000 1.429 FSIZE1 1 if farm size under cotton less than 5 ha, 0 otherwise 0.328 0.471 0.000 1.000 N/A FSIZE2 1 if farm size under cotton between 5 and 10 ha, 0 otherwise 0.272 0.447 0.000 1.000 1.936 FSIZE3 1 if farm size under cotton between 10 and 20 ha, 0 otherwise 0.216 0.413 0.000 1.000 2.532 1 if farm size under cotton greater than 20 ha, 0 otherwise FSIZE4 0.184 0.389 0.000 1.000 5.499 (Reference group) LNDOWNR 1 if farmer owns the land he farms, 0 otherwise 0.824 0.382 0.000 1.000 1.218 1 if farm is located in the central district of Sanliurfa LOCNCNTR 0.496 0.502 0.000 1.000 N/A (reference group) LOCNACKL 1 if land is located in the Akcakale district of Sanliurfa 0.232 0.424 0.000 1.000 1.720 LOCNHRRN 1 if farm is located in the Harran district of Sanliurfa 0.272 0.447 0.000 1.000 1.579 HRDLBOR 1 if farm uses only family labor, 0 otherwise 0.112 0.317 0.000 1.000 1.713 FMLYLBRT Share of family labor in total labor (%) 0.317 0.315 0.000 1.000 1.561 TRACTDMY 1 if owns a tractor, 0 otherwise 0.720 0.451 0.000 1.000 2.228 TMACHNRY Number of total machines on the farm except tractors 6.760 5.583 0.000 22.000 3.372 PRCLNMBR Number owned or rented parcels 1.976 1.329 1.000 7.000 1.468 IRRGNMBR Number of times irrigation is applied to the land in operation 6.688 1.568 3.000 12.000 1.805 CAPLABRT Natural log of capital to labor ratio 2.484 0.988 0.711 4.301 2.029 LNDLABRT Natural log of land to labor ratio 5.821 1.024 7.532 3.847 1.039 Cotton support amount given based on production (Turkish SUBSIDY 2.572 2.658 0.158 18.480 4.470 Liras/10,000) Note: VIF stands for variance inﬂation factor while da refers to decare or hectare/10. The number of observations (N) is 125. LAND variable was not used in the DEA analysis. Agriculture 2020, 10, 108 5 of 17 Farm and farmer characteristics used as explanatory variables aecting DEA eciency scores include mutually exclusive multiple dummy variables representing farmer experience (Table 1), household size, education level, location, and farm size along with single dummy variables indicating o-farm work and land ownership. Other performance-related determinants that are discrete in nature include farmer age in years, the number of parcels owned or rented, and the irrigation frequency (the time irrigation recurs on the ﬁeld). The only performance-related determinant measured in continuous fashion is the percentage share of family labor input in the total labor force, ranging from zero to one. Location dummies indicate the municipal division of the Sanliurfa province and are used to identify the impact of location on the farm performance. It is hypothesized that farmers located in the central district are more ecient than those located in the Harran and Akcakale districts because farmers in the central district may have easier access to information. To avoid the dummy identiﬁcation problem, one of the location dummies is used as a reference variable. Similarly, land ownership could have an ambiguous impact on eciency. For example, land ownership could create an incentive to use soil-improving techniques in favor of eciency, while tenancy might encourage the tenant farmer to use inputs more eciently. Additionally, the impact of the share of family labor has an ambiguous eect (positive or negative): a larger share of hired labor may imply a more specialized, and thus more productive labor, but it might also be a source of moral hazard [11]. Farmer age could be expected to have a positive impact on eciency as older farmers are more experienced, but some authors discuss reasons for the opposite relationship [12], perhaps due to physical deﬁciencies as the farmer gets older (e.g., age impairment non-linearity). Similarly, higher eciency scores are expected for farms where full-time experienced farmers are more educated, household size is smaller, farmer operates on the land parcels close to each other, and irrigates the land. In small-scale families, there may be an inter-individual division of labor in which each member specializes in his/her task, and this attitude can be seen as a factor that increases technical eciency. On the other hand, technical eciency in scattered parcels can, of course, be disadvantageous compared to peers in parcels that are close to each other. 2.2. The Modeling Approach The DEA production frontier is constructed using linear programming techniques, which render a piece-wise linear frontier that envelops the observed input and output data. Technologies produced in this way possess the standard properties of convexity and strong disposability [13]. The DEA technique measures relative eciencies of a collection of farms in transforming inputs into outputs. Its origins date back to Charnes et al. [14], who introduced the CCR model based on the works of Farrell [15] and others. Later, Banker et al. [16] introduced the BCC model and accounted for variable returns to scale by adding a convexity constraint. The original DEA speciﬁcation has led to the multi-stage model development to cope with slacks and to meet criteria identifying the nearest ecient points [17] and making the model invariant to units of measurement. An input-oriented DEA model is given below for n decision-making units (farms), each producing Y outputs by using m dierent inputs. In this formulation X is the ith farm’s (mx1) input vector. For the whole sample, Y represents the (1xn) cotton yield vector and X denotes the (mxn) input per decare matrix. Focusing on the unit area limits variability by minimizing the eects on input and output values. Under the assumption of constant returns to scale (CRS), the eciency score is the set of solutions to the following linear programming problem: min sub ject to y + Y 0 (1) , x X 0 i i 0 Agriculture 2020, 10, 108 6 of 17 where is the technical eciency score for the ith farm; is an Nx1 vector of constants, where N is the number of farms in the sample; y shows the ith farm output per decare, while x denotes a vector of i i inputs per decare used in the production of y by the ith farm; Y and X denote a projected point due to radial contraction of the input vector x . The objective of the above linear programming is to ﬁnd the minimum so that the input vector x reduces to X , while holding the output level y i i constant. In this context, the value of will range between zero and one, with a score of near-zero implying ineciency, while a score of one implying a point on the frontier where the farm in the region is technically ecient. For a speciﬁcation under variable returns to scale (VRS), the additional convexity constraint 1 = 1 is added to the above linear programming, where 1 is a vector of ones [16]. The constraint guarantees that an inecient farm in the region is only benchmarked against units of a similar size. The scale eciency (SE) of an ith farm is obtained by dividing the technical eciency scores under CRS to the technical eciency scores under VRS and is at a (0, 1) interval. The approach allows the comparison of the technical eciency under the CRS and VRS technologies by using a smoothed single bootstrap technique [18]. The bias-corrected technical eciency values under both technologies were then derived. When the SE is 1, the farm has an ecient economy of scale, otherwise, inputs used in production are not ecient in scale [19]. To determine under what scale these technical eciencies are derived, the test is applied whether the scale eciency is 1 (CRS) or against the alternative hypothesis that the SE < 1 (VRS). The test statistic is: X X N N CRS VRS ˆ ˆ S = ( )/( ) (2) i i i=1 i=1 and the H is rejected if S is signiﬁcantly smaller than one. As such, a critical threshold value (C ) for statistic S is searched and if this critical value C is smaller than S, the H hypothesis is rejected. Unfortunately, the true distribution of S under H is unknown (the hypothesis of CRS) so C cannot be directly calculated, but Simar and Wilson [8,18] showed that one can bootstrap the distribution of S under H in their FEAR R package (FEAR R package, obtains bootstrapped CRS and VRS, respectively, as follows: Bc <boot.sw98(x,y,NREP = nrep, RTS = 3) and Bv <boot.sw98(x,y,NREP = nrep, RTS = 1, XREF = x, YREF = y, DREF = 1/e), where RTS = 3 and RTS = 1 for CRS and VRS, respectively; nrep is the number of bootstrap replications (e.g., here, 10,000), and DREF = 1/e, where 1/e is the eciency score under the CRS technology. The estimated value of S in R package can be called for S < colSums(1/Bc$boot)/colSums(1/Bv$boot), while in benchmark package in R, critValue(S,0.05) reports the C value for the test). The next step quantiﬁes the technical eciency scores by non-discretionary factors using a double bootstrap technique after empirically revealing the derived technical eciency values. The quantiﬁcation involves taking the inverse of the technical eciency values in Equation (1) and ˆ ˆ deﬁning it as = (1/ ). As a result, the variable dependent on the set of non-discretionary variables i i is transformed from the double boundary dimension to the single boundary dimension. In such a case, ˆ ˆ is conﬁned to the interval [1, 1) and the left-limit truncation regression is used to determine i i factors associated with the reciprocal of the technical eciency scores. The value of equals one indicates an ecient farm, while the larger value indicates an inecient operation. The relation between the dependent variable and non-discretionary variables can be shown as: ˆ ˆ = z + " , sub ject to : 1 (3) i i i where z is an (NxK) matrix of non-discretionary variables, is a vector of associated parameters to be estimated, and " is a continuous idd random error term. Given the necessity of 1 z , " is i i i distributed normally with left truncation at (1 z ) and standard deviation . Under this assumption, i Agriculture 2020, 10, 108 7 of 17 the parameters of the model in Equation (3) are obtained using the following left-truncated likelihood function: 0 1 " !# N 1 0 0 Y ˆ z 1 z B C 1 i B i C i B C L = ?B C 1 F (4) @ A " " " i=1 where ? and F are the univariate probability density and cumulative distribution functions for the standard normal, respectively. Fortunately, as long as the data generating process (DGP) is deﬁned, the double bootstrap technique can be used to empirically approximate the sampling distributions of and and construct the conﬁdence interval for proper inferences [20]. Detailed information about how the bootstrap works is included in the appendices provided at the end of this manuscript. 3. Results and Discussion Table 2 shows computed eciency scores under the assumptions of CRS and VRS. Using the original DEA technique, the uncorrected average eciency scores are 71.20 and 83.50 (Table 2) for CRS and VRS, respectively. Table 2. Descriptive statistics of technical eciency scores. Variables Mean Std. Dev. Min. Max. Lower 95% CI Upper 95% CI CRS b b Uncorrected TEx100 71.20 19.10 26.10 100 67.84 74.57 % of TE = 1 12.80 % of TE 0.90 18.40 % of TE 0.50 84.00 a a Bias-corrected TEx100 64.11 16.20 23.70 90.50 59.20 70.10 b b 61.25 66.98 % of TE 0.90 0.80 % of TE 0.50 79.20 VRS b b Uncorrected TEx100 83.50 13.90 39.70 100 81.05 85.95 % of TE = 1 21.60 % of TE 0.90 37.60 % of TE 0.50 99.20 a a Bias-corrected TEx100 76.75 11.60 36.50 93.80 70.70 82.90 b b 74.70 78.80 % of TE 0.90 7.20 % of TE 0.50 99.20 a b The mean value of conﬁdence interval of the bootstrap. The constructed conﬁdence level of the interval around the mean value. The results indicate that an average cotton farmer that performs as eciently as its benchmark can achieve the same level of output using 28.8% and 16.5% fewer inputs, on average, under CRS and VRS, respectively. The original DEA eciency scores range from 26.10 to 100 for CRS and from 39.70 to 100 for VRS. The farms with the worst performance could save approximately 74% of their inputs by shifting to the eciency frontier. The production under VRS technology is more ecient than that of CRS technology (Figure 1). The eciency scores obtained from the VRS technology for 109 out of 125 farms (87.3%) are greater than the eciency scores obtained from the CRS technology, providing sucient evidence that there is room to improve cotton production eciency by modifying input use. Only 16 of 125 farms and 32 of 125 farms for CRS and VRS technologies, respectively, were found to be fully ecient. Interestingly, the VRS technology yields twice as many fully ecient farms than the CRS technology. Additionally, VRS values performed above 40% when the eciency value was below 40% in CRS (Figure 1). (The higher eciency of the VRS technology relative to that of the CRS technology is Agriculture 2020, 10, x FOR PEER REVIEW 8 of 17 VRS, respectively. The original DEA efficiency scores range from 26.10 to 100 for CRS and from 39.70 to 100 for VRS. The farms with the worst performance could save approximately 74% of their inputs by shifting to the efficiency frontier. The production under VRS technology is more efficient than that of CRS technology (Figure 1). The efficiency scores obtained from the VRS technology for 109 out of 125 farms (87.3%) are greater than the efficiency scores obtained from the CRS technology, providing sufficient evidence that there is room to improve cotton production efficiency by modifying input use. Only 16 of 125 farms and 32 Agriculture 2020, 10, x FOR PEER REVIEW 8 of 17 of 125 farms for CRS and VRS technologies, respectively, were found to be fully efficient. VRS, Interestingly, respectively. the V Th RS etec orih gno inal logy DEA yiel ef dficiency s twice as score man s y rafnge ully from efficie 26 nt .10 farm to 10 s th 0 for an th CRS e CRS and tec fro hn m ology. 39.70 to 100 for VRS. The farms with the worst performance could save approximately 74% of their inputs Additionally, VRS values performed above 40% when the efficiency value was below 40% in CRS by shi (Figure fting 1). to (The the ef higher ficien ef cy ficiency frontier. of the VRS technology relative to that of the CRS technology is The production under VRS technology is more efficient than that of CRS technology (Figure 1). shown in Figure 1). The percentage of cotton farmers who use inputs at a 90% efficiency or above is Th 18.40% e efficienc (appr y oximatel scores ob y ta23 ined far from ms) th and e VRS 37.6% tec hno (app logy roximate for 109 ly ou 47 t of far 125 ms) far un msder (87.3%) CRS ar an e g d rea VRS ter than the efficiency scores obtained from the CRS technology, providing sufficient evidence that there technologies, respectively, showing the potential for a 10% reduction in input use without a decrease is in cott room on yie to im ld. pro ve cotton production efficiency by modifying input use. Only 16 of 125 farms and 32 of 125 farms for CRS and VRS technologies, respectively, were found to be fully efficient. Table 2 compares the original DEA efficiency scores with those of the bias-corrected bootstrap Int efficienc erestingly, y esti mato the Vrs RS und tecer hno CRS logy and yiel Vd R sS tw tec ice hno as logi man es. y Th fully e bo ef ot fistrap cient farm technique s than sp thecified e CRS tec here hn , ology. which Agriculture 2020, 10, 108 8 of 17 Additionally, VRS values performed above 40% when the efficiency value was below 40% in CRS is the focus of the discussion hereafter, includes the analysis of the first appendix (Appendix A) in (Figure 1). (The higher efficiency of the VRS technology relative to that of the CRS technology is the appendices. The signs of bias are negative for all input-oriented cotton production. All original shown in Figure 1). The percentage of cotton farmers who use inputs at a 90% eciency or above is shown in Figure 1). The percentage of cotton farmers who use inputs at a 90% efficiency or above is efficiency scores under both technologies are greater than the bias-corrected results (Figure 2). At a 18.40% (approximately 23 farms) and 37.6% (approximately 47 farms) under CRS and VRS technologies, 18.40% (approximately 23 farms) and 37.6% (approximately 47 farms) under CRS and VRS performance below 60% in CRS, VRS is more likely to exceed this value in DMU. A similar situation respectively, showing the potential for a 10% reduction in input use without a decrease in cotton yield. technologies, respectively, showing the potential for a 10% reduction in input use without a decrease can be extended to other technology levels. in cotton yield. Table 2 compares the original DEA efficiency scores with those of the bias-corrected bootstrap efficiency estimators under CRS and VRS technologies. The bootstrap technique specified here, which is the focus of the discussion hereafter, includes the analysis of the first appendix (Appendix A) in the appendices. The signs of bias are negative for all input-oriented cotton production. All original efficiency scores under both technologies are greater than the bias-corrected results (Figure 2). At a performance below 60% in CRS, VRS is more likely to exceed this value in DMU. A similar situation can be extended to other technology levels. Figure 1. Technical efficiencies at CRS versus at VRS. Figure 1. Technical eciencies at CRS versus at VRS. Table 2 compares the original DEA eciency scores with those of the bias-corrected bootstrap eciency estimators under CRS and VRS technologies. The bootstrap technique speciﬁed here, which is the focus of the discussion hereafter, includes the analysis of the ﬁrst appendix (Appendix A) in the appendices. The signs of bias are negative for all input-oriented cotton production. All original eciency scores under both technologies are greater than the bias-corrected results (Figure 2). At a performance below 60% in CRS, VRS is more likely to exceed this value in DMU. A similar situation can be extended to other technology levels. Figure 1. Technical efficiencies at CRS versus at VRS. Figure 2. Biased corrected technical efficiencies at CRS versus at VRS. The average efficiency scores for CRS and VRS are 64.11% and 76.75%, respectively, indicating the opportunity for use from 35.89% to 23.25% for the same level of cotton yield (Table 2). For example, under the bias-corrected DEA, the efficiency of VRS technology outweighs the efficiency of Figure 2. Biased corrected technical eciencies at CRS versus at VRS. Figure 2. Biased corrected technical efficiencies at CRS versus at VRS. The average eciency scores for CRS and VRS are 64.11% and 76.75%, respectively, indicating the The average efficiency scores for CRS and VRS are 64.11% and 76.75%, respectively, indicating opportunity for use from 35.89% to 23.25% for the same level of cotton yield (Table 2). For example, the opportunity for use from 35.89% to 23.25% for the same level of cotton yield (Table 2). For under the bias-corrected DEA, the eciency of VRS technology outweighs the eciency of CRS example, under the bias-corrected DEA, the efficiency of VRS technology outweighs the efficiency of technology in yield of cotton production by about 12 points. Under the assumption of CRS technology with the bias-corrected DEA estimators, the share of farmers who use inputs eciently at 50% or above and 90% or above is 79.20 and 0.80 percent points, respectively. The corresponding shares under VRS technology are 99.2% and 7.2%, respectively. Under the VRS, the share of farmers who use 10% or fewer inputs ineciently is 0.8% under the biased-corrected DEA, but it increases to 37.6% under the corresponding uncorrected DEA. Therefore, eciency scores derived from the uncorrected (CRS or VRS) technologies tend to be upward biased. The uncorrected DEA bias was alleviated by the bootstrap technique (Figure 3). Under the CRS and VRS technologies, respectively, 20.8% and 0.8% of the farms in the region have an eciency score of less than 50%. Agriculture 2020, 10, x FOR PEER REVIEW 10 of 17 generally use resource allocation efficiently, rewarding themselves with higher efficiency scores. On the other hand, when we look at the relationship between biased-corrected efficiency scores and capital input (Figure 4), it seems that the efficiency scores of the farmers who are poor in capital are higher than the farms with medium and high levels of capital. Therefore, the input losses of capital- intensive farms will be higher than the farms in other groups. This is most likely due to idle capital accumulation in farms (e.g., more than one tractor), and excess capital needs to be redirected towards the production of other products or combinations of production process. Table 3. Relationships between inputs used in the production of cotton and bias-corrected efficiency of VRS technology. Bias-Corrected Efficiency × Ln-Capital Ln-Labor Ln-Land Ln-Yield Variable 100 Farm Classifications Mean (Std. Mean (Std. Mean (Std. Mean (Std. Number Mean (Std. Dev.) Dev.) Dev.) Dev.) Dev.) Ln-Capital Classifications <8 7.819 (0.010) 6.862 (6.862) −0.327 (0.147) 6.240 (0.053) 76.424 (14.205) 2 8 ≤ Ln-Capital < 9 8.584 (0.345) 6.935 (0.763) 0.610 (0.318) 5.993 (0.299) 83.437 (6.320) 9 9 ≤ Ln-Capital < 10 9.579 (0.313) 7.370 (0.864) 1.283 (0.417) 6.116 (0.307) 75.659 (11.012) 36 10 ≤ Ln-Capital < 11 10.391 (0.241) 7.704 (0.988) 2.086 (0.361) 6.138 (0.232) 78.043 (11.873) 46 ≥11 11.510 (0.402) 8.633 (0.865) 3.112 (0.462) 6.059 (0.254) 74.257 (12.476) 32 Ln-Labor Classifications <6 9.297 (0.647) 5.771 (0.313) 1.044 (0.616) 6.145 (0.098) 86.058 (0.810) 6 6 ≤ Ln-Labor < 7 9.818 (0.845) 6.565 (0.238) 1.738 (0.827) 6.022 (0.378) 85.875 (5.651) 26 7 ≤ Ln-Labor < 8 10.016 (1.003) 7.588 (0.260) 1.635 (0.942) 6.113 (0.268) 75.774 (11.782) 41 8 ≤ Ln-Labor < 9 10.588 (0.746) 8.463 (0.264) 2.242 (0.756) 6.105 (0.213) 70.453 (11.921) 35 ≥9 11.266 (0.448) 9.431 (0.283) 2.892 (0.481) 6.182 (0.150) 74.826 (8.995) 17 Ln-Land Classifications <0 7.819 (0.010) 6.862 (0.091) −0.327 (0.147) 6.240 (0.053) 76.424 (14.205) 2 0 ≤ Ln-Land < 1 8.940 (0.476) 7.079 (0.695) 0.648 (0.227) 6.183 (0.267) 79.398 (11.057) 16 1 ≤ Ln-Land < 2 9.862 (0.413) 7.642 (0.873) 1.529 (0.307) 6.064 (0.298) 75.305 (11.682) 49 Agriculture 2020, 10, 108 9 of 17 2 ≤ Ln-Land < 3 10.763 (0.469) 7.842 (1.183) 2.475 (0.281) 6.161 (0.239) 77.380 (11.792) 39 ≥3 11.643 (0.412) 8.651 (0.853) 3.380 (0.342) 6.002 (0.192) 76.987 (11.913) 19 Figure 3. The relationship between VRS biased-corrected technical eciency scores and natural Figure 3. The relationship between VRS biased-corrected technical efficiency scores and natural logarithm of yield per decare. logarithm of yield per decare. The conﬁdence interval for the mean value of the biased-corrected DEA eciency scores can be calculated in two dierent ways. The conﬁdence interval can be obtained by taking the averages of the conﬁdence intervals calculated for the individual eciency scores using the bootstrap estimators. The other, more robust method is the same as applied in calculating the conﬁdence interval for the mean of the uncorrected DEA eciency scores using the classical method. The choice of either method is unclear in the literature [9,21–23]. As can be seen in Table 2, the conﬁdence intervals obtained from the average of the individual conﬁdence intervals of the bootstrap technique are much larger than those obtained by the classical method. While the conﬁdence intervals obtained from the mean of the individual conﬁdence intervals of the bootstrap estimators indicate that the eciency scores vary widely, the conﬁdence intervals obtained by the classical method show that this variability is limited for both technologies. The uncorrected and bias-corrected DEA eciency scores for both CRS and VRS technologies have similar conﬁdence interval widths, while the unadjusted DEA scores for both technologies have a higher conﬁdence interval. For example, the conﬁdence interval obtained by the classical method for VRS technology implies that the farmers could reduce their inputs in cotton production by 14.05%–18.95% while maintaining the same level of yield. To ﬁnd out which operating technology is prevalent on the Harran Plain, one can test returns to scale parameters by using the DEA eciency scores and bootstrapping procedure [8,18,24]. The null hypothesis of the prevalence of the CRS technology can be rejected if the estimated statistic is less than the critical value obtained by the bootstrapping estimators. The computed test statistic is S = 0.8527 and the bootstrapping analysis computed the critical value of 0.9360 at 5% signiﬁcance level, resulting in the rejection of CRS technology in favor of VRS technology. Such an outcome supported expectations based on the comparison between CRS and VRS technologies, making the VRS technology the dominant cotton production technology among the Harran Plain farmers. The level of association between inputs, outputs, and biased-corrected eciency levels was examined once the appropriate cotton production technology was identiﬁed. Table 3 classiﬁes the inputs used in cotton production, using the logarithmic scale. The results indicate that farmers cluster in the third and fourth groups. In each input group, the bias-corrected technical eciency variable showed a dierent structure and high variability in cotton production. Especially in the second, third, and fourth groups, the value of bias-corrected technical eciency decreased sharply as the use of resources increased to achieve higher cotton output. However, in the fourth group, the average eciency values recovered slightly more than the values in the other groups. Nevertheless, the value is still below the average value of the ﬁrst group in the classiﬁcation of all inputs used in cotton production. When farms expanded their inputs, up to 35% of input was wasted until the fourth group. Therefore, the diseconomies of scale in cotton production prevail, a cost disadvantage, leading to increase per unit-cost cotton production. Agriculture 2020, 10, 108 10 of 17 Table 3. Relationships between inputs used in the production of cotton and bias-corrected eciency of VRS technology. Bias-Corrected Ln-Capital Ln-Labor Ln-Land Ln-Yield Variable Farm Eciency 100 Classiﬁcations Number Mean (Std. Mean (Std. Mean (Std. Mean (Std. Mean (Std. Dev.) Dev.) Dev.) Dev.) Dev.) Ln-Capital Classiﬁcations <8 7.819 (0.010) 6.862 (6.862) 0.327 (0.147) 6.240 (0.053) 76.424 (14.205) 2 8 Ln-Capital < 9 8.584 (0.345) 6.935 (0.763) 0.610 (0.318) 5.993 (0.299) 83.437 (6.320) 9 9 Ln-Capital < 10 9.579 (0.313) 7.370 (0.864) 1.283 (0.417) 6.116 (0.307) 75.659 (11.012) 36 10 Ln-Capital < 11 10.391 (0.241) 7.704 (0.988) 2.086 (0.361) 6.138 (0.232) 78.043 (11.873) 46 11 11.510 (0.402) 8.633 (0.865) 3.112 (0.462) 6.059 (0.254) 74.257 (12.476) 32 Ln-Labor Classiﬁcations <6 9.297 (0.647) 5.771 (0.313) 1.044 (0.616) 6.145 (0.098) 86.058 (0.810) 6 6 Ln-Labor < 7 9.818 (0.845) 6.565 (0.238) 1.738 (0.827) 6.022 (0.378) 85.875 (5.651) 26 7 Ln-Labor < 8 10.016 (1.003) 7.588 (0.260) 1.635 (0.942) 6.113 (0.268) 75.774 (11.782) 41 8 Ln-Labor < 9 10.588 (0.746) 8.463 (0.264) 2.242 (0.756) 6.105 (0.213) 70.453 (11.921) 35 9 11.266 (0.448) 9.431 (0.283) 2.892 (0.481) 6.182 (0.150) 74.826 (8.995) 17 Ln-Land Classiﬁcations <0 7.819 (0.010) 6.862 (0.091) 0.327 (0.147) 6.240 (0.053) 76.424 (14.205) 2 0 Ln-Land < 1 8.940 (0.476) 7.079 (0.695) 0.648 (0.227) 6.183 (0.267) 79.398 (11.057) 16 1 Ln-Land < 2 9.862 (0.413) 7.642 (0.873) 1.529 (0.307) 6.064 (0.298) 75.305 (11.682) 49 2 Ln-Land < 3 10.763 (0.469) 7.842 (1.183) 2.475 (0.281) 6.161 (0.239) 77.380 (11.792) 39 3 11.643 (0.412) 8.651 (0.853) 3.380 (0.342) 6.002 (0.192) 76.987 (11.913) 19 The relationship between the usage levels of aggregated inputs (e.g., capital, labor, and land), the cotton yield and corresponding biased-corrected eciency scores are depicted in Figures 4–6. For example, when the cotton yield and eciency performance of farmers are evaluated, an outward-looking U-shaped curve emerges (Figure 3). In cotton yield, it is observed that medium-sized farm enterprises are inecient compared to small and large-scale farm enterprises. Agricultural enterprises with average cotton yield per decare have higher input losses compared to low and high yield enterprises in terms of yield production. These businesses can reach the same eciency level by using less input on their cotton production. Business farms that plan high yields per decare generally use resource allocation eciently, rewarding themselves with higher eciency scores. On the other hand, when we look at the relationship between biased-corrected eciency scores and capital input (Figure 4), it seems that the eciency scores of the farmers who are poor in capital are higher than the farms with medium and high levels of capital. Therefore, the input losses of capital-intensive farms will be higher than the farms in other groups. This is most likely due to idle capital accumulation in farms (e.g., more than one tractor), and excess capital needs to be redirected towards the production of other products or combinations of production process. Agriculture 2020, 10, x FOR PEER REVIEW 11 of 17 Figure 4. The relationship between VRS bias-corrected technical eciency scores and natural logarithm Figure 4. The relationship between VRS bias-corrected technical efficiency scores and natural of farm capital. logarithm of farm capital. Figure 5. The relationship between VRS bias-corrected technical efficiency scores and natural logarithm of farm labor. Figure 6. The relationship between VRS bias-corrected technical efficiency scores and natural logarithm of farm land (da). There is a similar U-shaped relationship between efficiency values and farmers’ labor input use levels (Table 5). Those who use medium-scale labor-intensive resources in cotton production will have higher input losses than the other two types of farm enterprises on the Harran Plain. Considering that such cotton farm enterprises are in sharecropper (tenant) types, it is possible for them to reach the cotton yield level of small and high-scale enterprises by making more savings in the amount of labor. The relationship between the land amount and efficiency scores is similar to the Agriculture 2020, 10, x FOR PEER REVIEW 11 of 17 Agriculture 2020, 10, x FOR PEER REVIEW 11 of 17 Figure 4. The relationship between VRS bias-corrected technical efficiency scores and natural Figure 4. The relationship between VRS bias-corrected technical efficiency scores and natural Agriculture 2020, 10, 108 11 of 17 logarithm of farm capital. logarithm of farm capital. Figure 5. The relationship between VRS bias-corrected technical efficiency scores and natural Figure 5. The relationship between VRS bias-corrected technical eciency scores and natural logarithm Figure 5. The relationship between VRS bias-corrected technical efficiency scores and natural logarithm of farm labor. of farm labor. logarithm of farm labor. Figure 6. The relationship between VRS bias-corrected technical eciency scores and natural logarithm Figure 6. The relationship between VRS bias-corrected technical efficiency scores and natural Figure 6. The relationship between VRS bias-corrected technical efficiency scores and natural of farm land (da). logarithm of farm land (da). logarithm of farm land (da). There is a similar U-shaped relationship between eciency values and farmers’ labor input use There is a similar U-shaped relationship between efficiency values and farmers’ labor input use There is a similar U-shaped relationship between efficiency values and farmers’ labor input use levels (Table 3). Those who use medium-scale labor-intensive resources in cotton production will have levels (Table 5). Those who use medium-scale labor-intensive resources in cotton production will levels (Table 5). Those who use medium-scale labor-intensive resources in cotton production will higher input losses than the other two types of farm enterprises on the Harran Plain. Considering that have higher input losses than the other two types of farm enterprises on the Harran Plain. have higher input losses than the other two types of farm enterprises on the Harran Plain. such cotton farm enterprises are in sharecropper (tenant) types, it is possible for them to reach the Considering that such cotton farm enterprises are in sharecropper (tenant) types, it is possible for Considering that such cotton farm enterprises are in sharecropper (tenant) types, it is possible for cotton yield level of small and high-scale enterprises by making more savings in the amount of labor. them to reach the cotton yield level of small and high-scale enterprises by making more savings in them to reach the cotton yield level of small and high-scale enterprises by making more savings in The relationship between the land amount and eciency scores is similar to the relationship between the amount of labor. The relationship between the land amount and efficiency scores is similar to the the amount of labor. The relationship between the land amount and efficiency scores is similar to the capital and activity. It seems the presence of distant fragmented land will decrease the eciency in cotton production. The level of relationship between the land amount and eciency scores is similar to the level of the relationship between capital and activity. It seems that the amount of land will become more dicult as the cotton production plan becomes dicult, or perhaps the presence of distant fragmented land will decrease the eciency in cotton production. Overall, the bias-corrected technical eciency values in the region resemble a U-shaped curve, i.e., the most ecient cotton farms were the smallest and the largest. However, the results from the smallest cotton farms require attention because of the large farm number in the sample yet few of them in each input group (Table 3). Lerman [25] and Latrue et al. [26] indicated low technical eciency among the mid-scale farms. The region may develop remediation programs for farmers who waste resources in cotton production. Table 4 shows the parameters of the bias-corrected eciency values along with their conﬁdence interval values derived from the double bootstrap technique for the truncated regression model (see Appendix B). The subsequent discussion is based on the bias-corrected technical eciency scores and covers only statistically signiﬁcant variables. Since the dependent variable is the reciprocal of Agriculture 2020, 10, 108 12 of 17 bias-corrected technical eciency in the double bootstrap analysis, the technical eciency decreases with positively signed parameters and increases with negatively signed parameters. Table 4. Estimates of non-discretionary variables from the double bootstrap analysis. 90% Conﬁdence 95% Conﬁdence 99% Conﬁdence Bias-Corrected Variables Interval Interval Interval Estimates Lower CI Upper CI Lower CI Upper CI Lower CI Upper CI INTERCEPT 8.3126 *** 11.3140 6.7506 11.6417 6.2699 12.4395 5.1379 EXPERN2 0.1077 0.2451 0.0156 0.2673 0.0410 0.3196 0.0886 EXPERN3 0.0870 0.2309 0.0492 0.2593 0.0779 0.3048 0.1308 EXPERN4 0.0019 0.1574 0.1685 0.1837 0.1980 0.2580 0.2558 SSCHOOL 0.0657 0.2064 0.0816 0.2363 0.1129 0.2821 0.1811 HCSCHOOL 0.0083 0.1110 0.1300 0.1333 0.1553 0.1813 0.2076 HSIZE2 0.1992 *** 0.0772 0.3431 0.0459 0.3702 0.0138 0.4082 HSIZE3 0.2937 *** 0.1653 0.4603 0.1297 0.4850 0.0711 0.5237 OFF-FARM 0.0709 0.1844 0.0391 0.2086 0.0619 0.2491 0.1028 FSIZE2 0.0575 0.1786 0.0601 0.2033 0.0851 0.2455 0.1359 FSIZE3 0.1539 * 0.3166 -0.0135 0.3463 0.0114 0.4049 0.0759 FSIZE4 0.2068 0.4394 0.0162 0.4813 0.0656 0.5663 0.1647 LNDOWNR 0.1459 ** 0.0123 0.3076 0.0147 0.3277 0.0817 0.3906 LOCNACKL 0.0339 0.1691 0.0960 0.1914 0.1234 0.2425 0.1760 LOCNHRRN 0.0139 0.1031 0.1296 0.1249 0.1534 0.1670 0.2010 HRDLBOR 0.1873 * 0.0303 0.3879 0.0065 0.4209 0.0851 0.5002 FMLYLBRT 0.2804 ** 0.1025 0.5133 0.0640 0.5586 0.0278 0.6218 TRACTDMY 0.0122 0.1252 0.1468 0.1482 0.1746 0.2040 0.2192 TMACHNRY 0.0046 0.0088 0.0181 0.0115 0.0212 0.0170 0.0257 PRCLNMBR 0.0753 *** 0.0458 0.1188 0.0386 0.1250 0.0253 0.1380 IRRGNMBR 0.0259 0.0612 0.0084 0.0685 0.0156 0.0850 0.0301 CAPLABRT 1.0188 *** 0.8338 1.3413 0.7790 1.3848 0.6580 1.4729 LNDLABRT 1.1403 *** 1.4835 -0.9559 1.5246 0.9043 1.6105 0.7841 SUBSIDY 0.0243 0.0028 0.0538 0.0085 0.0607 0.0184 0.0727 SIGMA 0.2202 *** 0.2198 0.2805 0.2126 0.2860 0.1982 0.2968 Note: *, **, *** show statistically signiﬁcance levels at 10%, 5%, and 1%, respectively. The covariate that signiﬁcantly and negatively impacts the bias-corrected eciency scores is the household size. Thus, the bias-corrected technical eciency scores under the assumed VRS technology increase as the household size increases. This ﬁnding is consistent with research reported elsewhere [27]. The increase in household size can pose a challenge, especially if children are present because the adults may not allocate time to cotton production when needed. This ﬁnding coincides with that reported by Coelli et al. [19]. Having an o-farm job negatively impacts farm technical eciency. While this is a weak trend and the ﬁnding is not consistent with a previous study [12], it is in keeping with all ﬁndings reported earlier [19,22]. Farmers with non-agricultural income may have to concentrate resources on non-agricultural businesses which may lead to less eciency on farms. Cotton yield eciency decreases gradually in the region as the size of agricultural farms increases compared to small-scale enterprises (less than 5 ha) and the results coincide with the ﬁndings of the international literature [7,26,28–32], while they contradict ﬁndings reported by Wadud and White [33], Latrufe et al. [9], and Balcombe et al. [22]. While cotton farmers in Akçakale are less ecient than farmers in the central district, farmers in the Harran district are more ecient than those in the central district, but the dierences are statistically insigniﬁcant. It might be due to easier access to information and the proximity of the relevant private and public institutions to farmers in the central district. Technical eciency declines for farms dependent entirely on hired labor. Such farms are deprived of control over the business, while the work division might not have been fully rationalized among employees. In contrast with this ﬁnding, Latrue et al. [26] and Olson and Vu [23] found that hired labor increased the technical eciency of farms. Technical eciency increases with the ratio of Agriculture 2020, 10, 108 13 of 17 family to total labor. This ﬁnding supports the previous result which showed the positive eect of family workforce on eciency scores. Although the results were found to be statistically insigniﬁcant, the more tractors, machinery, and equipment farmers own, the more ecient cotton production in the region becomes. The results support the notion that the tractor can maintain the largest share in tool and machinery capital, while in general, it might be a proxy variable for high-income or large-scale farm enterprises. Since the tractor can be simultaneously used in more than one production pattern, input usage time or harvest time may sometimes overlap in dierent ﬁelds or dierent crops. Therefore, overlapping time can, of course, pose a reduction in technical eciency. Additionally, surprisingly the average technical eciency of a cotton farm increases as the number of operated parcels, owned or rented, increases, as long as these parcels are close together, giving farmers the chance to manage their products simultaneously. Technical eciency increases with an increase in the ratio of capital to labor, while it decreases with an increase in the ratio of land to labor. Such ﬁndings correspond to earlier reports [9,26] and indicate planned and rational distribution of resource use by some over-capital farms in cotton production process, whilst they are compatible with the eects of tractor and machine variables on eciency on the Harran Plain. A conﬁrmed negative relation between technical eciency and land to labor ratio indicates that the amount of land per-hourly unit of labor decreases the technical eciency of cotton farming, contradicting earlier results of Olson and Vu [23]. The eciency values increase as the amount of support given to cotton by the government increases, although its impact was not statistically signiﬁcant. Cash supports may be more eective when given during the production process. 4. Conclusions The current inquiry’s focus is twofold. First, the study investigated the relative performance measurements of farms using a random sample of 125 cotton farmers operating on the Harran Plain, Turkey, and applying the single bootstrap approach (Appendix A). Results revealed that the bias-corrected technical eciency scores under the assumptions of CRS and VRS technologies averaged 71.20% and 83.50%, respectively, implying that sampled cotton farmers wasted 28.8%–16.5%, respectively, of inputs. Concerning the average eciencies, poor input use has contributed to declining technical eciency. Meanwhile, overuse of input ranging from around 17% to 29% poses a major threat to the environment on the Harran Plain, while it is also economically indispensable. The biased and bias-corrected technical eciency values under the assumption of VRS were found higher than those computed under CRS technology. The ﬁnding has been further conﬁrmed by a statistical test to generate its critical value using a bootstrap technique. Another important result in the single bootstrap analysis is that the cotton farms are characterized by a U-shaped technical eciency based on the input and yield scale. Thus, small- and large-scale farms use inputs more rationally than medium-size farms, wasting relatively less input to produce the same cotton output per decare. Additionally, medium-size farms need to balance capital, labor, and land against input applications. The timing and frequency of irrigation to reach the same cotton production per decare may be another input that requires attention and could prevent not only excessive water use but long-term consequences associated with salinity. This paper also applied a double bootstrapped truncated regression (DBTRM) to quantify the relation between non-discretionary and bias-corrected technical eciency (Appendix B). The analysis takes place in a unique loop shown in the model section. The analysis of the marginal eects indicates that farmers engaged in agricultural work are likely to be technically more ecient. Although non-agricultural work oers informal education opportunities broadening knowledge, teaching new skills, and enriching experience, which might improve the ability to manage input use, it has not been found, unfortunately, to transfer this accumulated knowledge to agriculture. The understanding that technical eciency increases with household size could provide an opportunity for the family workforce to increase cotton production. The result that coincides with an increase in technical eciency was the land area decrease, supporting the notion that the household labor endowment Agriculture 2020, 10, 108 14 of 17 does match the operated land area. Further investigation of the issue is warranted because the age structure of all household members and gender composition of the farm was not considered. Since the expansion of land operated by a farm is possible only by renting or buying land from another farmer in the region, creating job opportunities outside agriculture is a broader challenge faced by provincial and national governments. The increase in technical eciency in households having a tractor, but the same eect of other machinery likely reﬂects the use of a tractor for multiple purposes, not limited to ﬁeldwork. It appears that only if other equipment is owned by a farm will technical eciency increase. Future studies may collect more detailed data on tractors and other equipment to establish a more accurate link to technical eciency. The decreasing technical eciency on farms using only hired labor indicates that the landowner allocates a limited amount of time to manage the farm. Possibly, the oered remuneration provides little incentive or the quality of hired labor is low. If the reason for using only hired labor results from the landowner having a job outside agriculture, the phenomenon may open a chance for the development of professional farm managers, who could improve cotton production, especially given the prevailing waste of inputs. Consistent with these results, technical eciency increases as the ratio of family to total workforce increases, indicating that through a planned division of labor, the family can achieve a desired production yield in the region. Factors that have a consistently positive impact on eciency measures include the ratio of capital to labor and increased land fragmentation. The latter eect on eciency scores is consistent with the generally accepted idea that farmers operating a large number of parcels tend to be more ecient. Addressing land fragmentation through policy is dicult because the reasons behind land fragmentation are often rooted in culture; encouraging land consolidation through targeted grants may be a more viable approach. One possible limitation of this study is the lack of knowledge of the seed types and the kind of technology that farmers use. For example, if a distinction between conventional and organic cotton production could have been made, meta frontier analysis would have provided more robust results than the bootstrapped DEA analysis. A future study can investigate the impacts of farm and farmer characteristics on technical eciency using the stochastic frontier approach. In that case, technical eciency measures take into account dierences in the sources from which errors originate. That perspective can attempt to distinguish between errors arising from farmer discretion and errors arising from systematic factors. Author Contributions: Conceptualization, T.I. and A.B.; methodology, T.I.; software, T.I., A.B. and W.J.F.; validation, T.I., A.B., W.J.F., R.Ö. and M.R.S.; formal analysis, T.I., A.B. and W.J.F.; investigation, T.I. and M.R.S.; resources, M.R.S. and R.Ö.; data curation, T.I., R.Ö., A.B. and W.J.F.; writing—original draft preparation, T.I., M.R.S., and R.Ö.; writing—review and editing, T.I. and M.R.S.; visualization, M.R.S. and R.Ö.; supervision, T.I. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Scientiﬁc and Technological Research Council of Turkey (TUBITAK), grant number 110K374. Acknowledgments: We are highly grateful to the Scientiﬁc and Technological Research Council of Turkey (TUBITAK) for supporting our project numbered as 110K374. Without their valuable contributions, this research could never have been completed. The ﬁndings, interpretations, and conclusions expressed in this article are solely those of the authors and do not necessarily represent the view of TUBITAK. Conﬂicts of Interest: The authors declare no conﬂict of interest. Appendix A. Simar and Wilson’s Algorithm # 1 The application of the single bootstrapping procedure follows four steps: (1) the calculation of the original technical eciency values for all farms in the sample (i = 1, ::: , N) using Equation (1) and denotes them as . Next, a random sample of the original sample size N is drawn from this smooth estimate and is denoted , i = 1,::: , N; i Agriculture 2020, 10, 108 15 of 17 ˆ ˆ (2) a new pseudo data is constructed for x and y , where x = ( / )x and y = y for i = 1, ::: , i i i i i i i i N, with y and x the original output and input vectors of the ith farm, respectively; i i (3) new DEA eciency score is obtained for each farm in the region by taking the previous pseudo data as a reference for each CRS and VRS conditions; , CRS (4) steps (1) to (3) are repeated B times to yield a set of B new DEA either eciency scores , VRS or eciency scores . Here, B is set as 10,000 in each CRS and VRS application. Appendix B. Simar and Wilson’s Algorithm # 2 Following Simar and Wilson’s [24] Algorithm 2, the procedure is as follows: Step 1 obtains the DEA technical eciency scores ( ) under determined scale using Equation (1). ˆ ˆ ˆ Now, take the reciprocal of the technical eciency score by letting = (1/ ) where bounds from i i i one to inﬁnity for i = 1, ::: , N and it becomes compatible with the left-truncation regression, mostly used in output-oriented approach; Step 2 uses the method of maximum likelihood for the left-limit truncation regression to estimate ˆ ˆ of and ˆ of in the left-limit truncation regression of on non-discretionary variable Z, where > 0; Step 3 implies a loop for each i = 1, ::: , N following four steps (i)–(iv) B times to obtain N set of bootstrap estimatesf g : i,b b=1 (i) draw " from N(0, ˆ ) distribution with left-truncation at (1 z ); i " (ii) Compute = z + " ; i i ˆ ˆ (iii) construct a pseudo data set x , y where x = ( / )x and y , y . Note that we can also i i i i i i i i construct the pseudo x from the original DEA eciency scores as ˆ ˆ ˆ ˆ ˆ ˆ x = [(1/ )/(1/ )]x = ( / )x , where = z + " ; i i i i i i i i i i (iv) using the above pseudo data set and the DEA in Equation (1) under the determined scale ˆ ˆ calculate pseudo ecient estimates = 1/ for i = 1, ::: , N; i i ˆ ˆ ˆ ˆ ˆ ˆ Step 4 computes bias-corrected estimates where bias = , where = ((1/B ) ) ; i i 1 i i i b=1 i,b ˆ 0 ˆ ˆ ˆ ˆ Step 5 regresses on z to estimate and ˆ using the maximum likelihood for the left-truncation; Step 6 is a loop over the next three steps (i)–(iii) B times to generate a set of bootstrap estimates ˆ ˆ f( , ˆ ) g b=1 ˆ ˆ (i) for each i = 1, ::: , N draw " from N(0, ˆ ) distribution with left-truncation at (1 z ); i " (ii) compute = z + " ; i i (iii) use the maximum likelihood method to estimate the truncated regression of on z to yield i i ˆ ˆ estimates and ; ˆ ˆ ˆ ˆ ˆ ˆ Step 7 uses the bootstrap estimates ( and ˆ ) from Step 6 and the estimates ( and ˆ ) generated in Step 5 to construct (1) conﬁdence intervals for original and . The (1) conﬁdence interval of ˆ ˆ ˆ ˆ the jth element of the vector as the Pr(b a ) 1 such that the estimated conﬁdence /2 /2 j j ˆ ˆ ˆ ˆ interval is [ + a , + b ]. j j /2 /2 References 1. TUIK. Crop Production Statistics. Available online: http://www.turkstat.gov.tr/PreTablo.do?alt_id=1001 (accessed on 12 May 2018). 2. Sirtioglu, I. Turkey Cotton and Products. Available online: https://apps.fas.usda.gov/newgainapi/api/report/ downloadreportbyﬁlename?ﬁlename=Cotton%20and%20Products%20Annual_Ankara_Turkey_3-23-2018. pdf (accessed on 12 May 2019). 3. Pınar, M.; Akyıl, N.; Er, S.; Ertürk, Y.E. Cotton Production Status and Projection Report: 1997–1998, 2nd ed.; Agricultural Economics and Policy Development Institute (TEPGE): Ankara, Turkey, 1998. (In Turkish) Agriculture 2020, 10, 108 16 of 17 4. Basal, H.; Sezener, V. Turkey Cotton Report. In Proceedings of the 11th Regional Meeting of the International Cotton Advisory Committee, Antalya, Turkey, 5–7 November 2012; pp. 5–7. 5. Cullu, M.A.; Aydemir, M.; Qadir, M.; Almaca, A.; Ozturkmen, A.R.; Bilgic, A.; Agca, N. Implication of groundwater ﬂuctuation on the seasonal salt dynamic in the Harran Plain, south-eastern Turkey. Irrig. Drain. 2010, 59, 465–476. [CrossRef] 6. Agricultural Production Statistics by Country. Available online: https://www.indexmundi.com/agriculture/ (accessed on 4 August 2019). 7. Binici, T.; Demircan, V.; Zulauf, C.R. Assessing production eciency of dairy farms in Burdur province, Turkey. J. Agric. Rural Dev. Trop. Subtrop. 2006, 107, 1–10. 8. Simar, L.; Wilson, P.W. Statistical inference in nonparametric frontier models: The State of the Art. J. Prod. Anal. 2000, 13, 49–78. [CrossRef] 9. Latrue, L.; Balcombe, K.; Davidova, S.; Zawalinska, K. Technical and scale eciency of crop and livestock farms in Poland: Does specialization matter? Agric. Econ. 2005, 32, 281–296. [CrossRef] 10. Yamane, T. Statistics An Introductory Analysis, 2nd ed.; Harper and Row: New York, NY, USA, 1967. 11. Bojnec, Š.; Latrue, L. Determinants of technical eciency of Slovenian farms. Post Commun. Econ. 2009, 21, 117–124. [CrossRef] 12. Larsén, K. Eects of machinery-sharing arrangements on farm eciency: Evidence from Sweden. Agric. Econ. 2010, 41, 497–506. [CrossRef] 13. Färe, R.; Grosskopf, S.; Norris, M.; Zhang, Z. Productivity Growth, Technical Progress, and Eciency Change in Industrialized Countries. Am. Econ. Rev. 1994, 84, 66–83. 14. Charnes, A.; Cooper, W.W.; Rhodes, E. Measuring the eciency of decision making units. Eur. J. Oper. Res. 1978, 2, 429–444. [CrossRef] 15. Farrell, M.J. The Measurement of Productive Eciency. J. Royal Stat. Soc. Ser. A 1957, 120, 253–281. [CrossRef] 16. Banker, R.D.; Charnes, A.; Cooper, W.W. Some Models for Estimating Technical and Scale Ineciencies in Data Envelopment Analysis. Manag. Sci. 1984, 30, 1078–1092. [CrossRef] 17. Koopmans, T. Activity Analysis of Production and Allocation, 1st ed.; John Wiley & Sons: New York, NY, USA, 1951. 18. Simar, L.; Wilson, P.W. Sensitivity Analysis of Eciency Scores: How to Bootstrap in Nonparametric Frontier Models. Manag. Sci. 1998, 44, 49–61. [CrossRef] 19. Coelli, T.; Rahman, S.; Thirtle, C. Technical, allocative, cost and scale eciencies in Bangladesh rice cultivation: A non-parametric approach. J. Agric. Econ. 2002, 53, 607–626. [CrossRef] 20. Monchuk, D.C.; Chen, Z.; Bonaparte, Y. Explaining production ineciency in China’s agriculture using data envelopment analysis and semi-parametric bootstrapping. China Econ. Rev. 2010, 21, 346–354. [CrossRef] 21. Brümmer, B. Estimating conﬁdence intervals for technical eciency: The case of private farms in Slovenia. Eur. Rev. Agric. Econ. 2001, 28, 285–306. [CrossRef] 22. Balcombe, K.; Fraser, I.; Latrue, L.; Rahman, M.; Smith, L. An application of the DEA double bootstrap to examine sources of eciency in Bangladesh rice farming. Appl. Econ. 2008, 40, 1919–1925. [CrossRef] 23. Olson, K.; Vu, L. Economic eciency in farm households: Trends, explanatory factors, and estimation methods. Agric. Econ. 2009, 40, 587–599. [CrossRef] 24. Simar, L.; Wilson, P.W. Estimation and inference in two-stage, semi-parametric models of production processes. J. Econ. 2007, 136, 31–64. [CrossRef] 25. Lerman, Z. Productivity and Eciency of Individual farms in Poland: A Case for Land Consolidation. Available online: https://ageconsearch.umn.edu/record/19835 (accessed on 8 February 2020). 26. Latrue, L.; Davidova, S.; Balcombe, K. Application of a double bootstrap to investigation of determinants of technical eciency of farms in Central Europe. J. Prod. Anal. 2008, 29, 183–191. [CrossRef] 27. Aravindakshan, S.; Rossi, F.; Amjath-Babu, T.S.; Veettil, P.C. Application of a bias-corrected meta-frontier approach and an endogenous switching regression to analyze the technical eciency of conservation tillage for wheat in South Asia. J. Prod. Anal. 2018, 49, 153–171. [CrossRef] 28. Berry, R.A.; Cline, W.R. Agrarian Structure and Productivity in Developing Countries: A Study Prepared for the International Labour Oce Within the Framework of the World Employment Programme; John Hopkins University Press: Baltimore, MD, USA, 1979; ISBN 978-0-8018-2190-5. 29. Ramalho, E.A.; Ramalho, J.J.S.; Henriques, P.D. Fractional regression models for second stage DEA eciency analyses. J. Prod. Anal. 2010, 34, 239–255. [CrossRef] Agriculture 2020, 10, 108 17 of 17 30. Grabowski, R.; Kraft, S.; Pasurka, C.; Aly, H.Y. A ray-homothetic production frontier and eciency: Grain farms in Southern Illinois. Eur. Rev. Agric. Econ. 1990, 17, 435–448. [CrossRef] 31. Barrett, C.B. On price risk and the inverse farm size-productivity relationship. J. Dev. Econ. 1996, 51, 193–215. [CrossRef] 32. Helfand, S.M.; Levine, E.S. Farm size and the determinants of productive eciency in the Brazilian Center-West. Agric. Econ. 2004, 31, 241–249. [CrossRef] 33. Wadud, A.; White, B. Farm household eciency in Bangladesh: A comparison of stochastic frontier and DEA methods. Appl. Econ. 2000, 32, 1665–1673. [CrossRef] © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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