TECHNICAL EFFICIENCY ANALYSIS OF CITRUS FARMS IN BRAZIL Authors: Marcelo José Carrer, Hildo Meirelles de Souza Filho & Fabiana Ribeiro Rossi.

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1 TECHNICAL EFFICIENCY ANALYSIS OF CITRUS FARMS IN BRAZIL Authors: Marcelo José Carrer, Hildo Meirelles de Souza Filho & Fabiana Ribeiro Rossi Authors Marcelo José Carrer Department of Production Engineering Federal University of São Carlos, Brazil Hildo Meirelles de Souza Filho Department of Production Engineering Federal University of São Carlos, Brazil Fabiana Ribeiro Rossi Department of Production Engineering Federal University of São Carlos, Brazil The authors thank FAPESP (São Paulo Research Foundation) for the financial support of this research (regular Project 2013/ ). Selected Paper prepared for presentation at the International Food and Agribusiness Management Association s 2015 Annual Meeting - IFAMA 25th Annual World Forum and Symposium, Saint Paul, Minnesota, USA, June 14-17,

2 TECHNICAL EFFICIENCY ANALYSIS OF CITRUS FARMS IN BRAZIL Abstract: This study aims to investigate the impact of personal aspects as well as aspects of the decision-making process (Rougoor et al., 1998) on the technical efficiency of citrus farms in Brazil. Primary data for the crop year of 2013/14 (cross sectional data) was collected from a sample of 98 farms located in the State of São Paulo, one of the largest citrus regions in the world. The single stage model developed by Battese and Coelli (1995) was used in order to estimate the stochastic production frontier translog as well as the determinants of efficiency of farms. The results showed that the technical efficiency index across citrus farms ranges from 28% to 97%, with a mean of 75%. The expectation formation (personal aspect), the use of long-term contracts, and the adoption of Information Technology (IT) tools for production planning and control (aspects of decision-making processes) were significant determinants of the technical efficiency. This result confirms the hypotheses built around these variables. The adoption of management and commercialization tools by citrus farmers may considerably increase technical efficiency in Brazilian citrus production. Keywords: citrus farms, IT management tools, technical efficiency. 1. INTRODUCTION Rougoor et al. (1998) developed a theoretical model relating personal aspects and aspects of the decision-making process with efficiency in agriculture. Following the study of Rougoor et al. (1998), some empirical studies tested this relationship with regard to several farming activities (Wilson et al., 1998; Wilson et al., 2001; Trip et al., 2002; Solís et al., 2009; Cabrerra et al., 2010; Chang and Mishra, 2011). Most of them showed significant and positive effect of the adoption of management tools on the efficiency of farms. This article adopts the approach of Rougoor et al. (1998) in order to test hypotheses regarding the effects of personal aspects and aspects of the decision-making process on the technical efficiency of citrus farms in the State of São Paulo, Brazil. Brazil is the largest world producer of orange and exporter of orange juice, with million tons of oranges and million tons of orange juice exports in 2013 (IBGE, 2013; CitrusBR, 2013). However, Brazilian citrus production has been undergoing crisis since the late 2000s. According to Neves (2010), the number of independent citrus growers in the State of São Paulo, the country s largest orange producer, has gone from 15,000 in 2001 to 12,627 in Data from Conab (2013) 2

3 showed that in 2013/14 the number of growers fell yet again to 10,100. Within the same period, there was a 23.8% reduction in the production area, which decreased from 609,475 hectares (ha) in 2000 to 464,447 ha in 2013 (Conab, 2013). Some hypotheses have been raised in order to explain this crisis, such as the reduced growth in the demand for orange juice; the increasing backwards vertical integration of orange juice processors; and mainly the low production efficiency of several farms (Neves, 2010, Figueiredo et al., 2013). However, no empirical studies have attempted to measure the technical efficiency levels of citrus farms and identify the factors that explain the differences in efficiency among them. It is possible to raise the hypothesis that personal aspects of citrus farmers (expectations and abilities, e.g.) as well as aspects of the decision-making process (IT tools applied to the planning and controlling production, e.g.) are important to determine the efficiency differentials among farms. Furthermore, identifying the factors that explain such efficiency differentials is of essential importance for the elaboration of public policies and private strategies in an activity undergoing a moment of crisis. In this context, this paper has two complementary aims: (i) estimate a production frontier based on data from citrus farms in Brazil, thus making it possible to understand the characteristics of the production technology and calculate an efficiency index of the farms; and (ii) identify the effect of personal aspects of farmers as well as aspects of the decision-making process on the technical efficiency of the farms. In order to achieve these aims, primary data was collected from a representative random sample of 98 citrus farms in the State of São Paulo, Brazil. The data was collected in the context of a research project financed by the São Paulo Research Foundation (Fapesp-2013/ ) and refers to the crop year 2013/14 (cross-sectional data). A stochastic frontier model with a single estimation stage (Battese and Coelli, 1995) was adopted in order to estimate a production translog frontier and the effects of management variables on the technical efficiency/inefficiency of the farms. The study innovates by testing the relationship between personal aspects and aspects of the decisionmaking process in citrus farming, an activity of extreme importance for Brazilian agriculture. Additionally, a variable that measures the different aspects of the use of Information Technology (IT) tools for productions planning and control was created, which is another innovative aspect of this study. In addition to this introduction, this paper comprises five sections. The next section presents the theoretical framework necessary to the construction and analysis of production frontiers, as well as a literature review on the impact of the adoption of 3

4 management tools on the efficiency of farms. The third section presents the sample of farms, the variables, and the econometric model of stochastic frontier used for data analysis. The fourth section undertakes an analysis of the main aspects of production technology by means of the estimated parameters of production frontier, especially the partial elasticities of the production factors and the elasticities of scale of the farms. The fifth section presents and discusses the technical efficiency index of the farms and the factors determining the efficiency differentials. Lastly, section six presents the implications of the results for public policies and private strategies, the limitations of the study, and some suggestions for future works. 2. THEORETICAL FRAMEWORK The theoretical framework of this article is divided into two subsections. In the first, the concepts of production frontier as well as of technical efficiency are formalized according to the theory of efficiency frontiers. In the second section, a literature review on management aspects and its relation with the efficiency of farms is performed TECHNICAL EFFICIENCY The neoclassical microeconomics presupposes that firms aim to maximize profit and/or minimize the production costs subject to technological restriction. One of the postulates of the theory is that firms operate in a technically efficient manner. It is assumed that firms choose efficient combinations of the production factors, given the production technology available. Thus, firms produce in a certain point of the production function. Inefficiencies are only admitted in the choice of production scale. However, in the real world, it is very plausible to expect that some firms may face restrictions even to operate on the production function. 1 The situation exposed in the above paragraph illustrates the possibility of the existence of technical inefficiency within firms. The task of economic theory is to incorporate such possibility into its models. Furthermore, once identified the inefficiencies of a set of firms in a same sector, it is important to investigate the causes of 1 A firm that does not operate on the production function also does not operate on an isoquant, that is, does not produce the maximum possible product with its factors endowment and the technology available. Such a firm would be operating at its production set, though it would not reach the frontier of this set (the frontier of maximum production allowed by the set), which in turn is determined by neoclassical microeconomic theory as a production function (Chambers, 1988). 4

5 such inefficiencies. In other words, it is crucial to comprehend the factors differentiating the firms that operate efficiently from those that do not. The theory of frontiers efficiency, developed from the seminal papers of Koopmans (1951), Debreu (1951) and Farrell (1957), is mainly concerned with the estimation of efficiency frontiers, from which inefficiency indexes of firms that do not operate on the frontiers are calculated. Production, costs, and profit frontiers are estimated and taken as benchmark with which technical and economic performances of different firms in a same industry are compared. Koopmans (1951) presented a formal and widely used definition of technical efficiency: a firm is considered technically efficient if an increase in a product that the firm produces requires a reduction in the production of another product or the increase in the use of at least one of the firm s production factors. Or yet, the reduction in the use of a production factor requires an increase in the use of at least one other production factor or a reduction in the production level of the technically efficient firm. Thus, according to Koopmans (1951), a technically inefficient firm may produce the same level of production by using less production factors or may utilize the same endowment of factors in order to produce a production level greater than the level it already produces. In turn, Debreu (1951) and Farrell (1957) developed a measure of technical efficiency. This measure takes into consideration the technology available, as well as all the production factors utilized and the product obtained by the firm. Assuming an orientation of reduction in the use of production factors, the measure is defined as: Technical Efficiency = 1 the maximum proportional reduction possible in the use of all production factors, given the technology available and a specific production level. If the firm is technically efficient, it will not be possible to reduce the use of production factors and continue producing the same amount of product, and thus the measure of efficiency will be equal to one. For inefficient firms, it is possible to reduce the use of production factors proportionally in order to obtain the same amount of product, and the measure of efficiency will be smaller than one. Assuming an orientation of increase in product, the Debreu-Farrell measure is defined as: Technical Efficiency = 1 the maximum possible proportional increase in product given the technology available and the production factors utilized. Technically efficient firms are not able to increase production level with the same endowment of factors and technology available, and thus the measure assumes value 5

6 equal to one. Technically inefficient firms, in turn, could better utilize the production factors and available technology to increase production level. Figure 1 illustrates the measures of technical efficiency oriented towards maximum level of production and minimum use of production factors. In this case, producer A is located below the production frontier, that is, he/she is not operating in a technically efficient manner. The technical inefficiency of this producer is measured horizontally, assuming minimum use of factors orientation, or vertically, assuming maximum product orientation. Producer A, who utilizes the vector of production factors x A and produces the product y A, would be technically efficient if he/she increases the production level with the same endowment of factors (shifting to the y A, x A point); or if he/she reduces the use of factors while obtaining the same level of production (shifting to the point y A, x A ). In both cases, this producer would be operating on the production frontier T, which shows the maximum production level, y, for each factors endowment and for the production technology available. It is noteworthy that this production frontier may present growing, decreasing, or constant returns to scale depending on the method adopted to estimate it, on the assumptions related to the function representing the production technology and the production data available. 2 Figure 1. Technical Efficiency. Source: Fried; Lovell e Schmidt (2008) MANAGEMENT AND EFFICIENCY 2 A technology with decreasing returns to scale implies that when the firm increases the use of factors in a proportion t, product grows in a proportion lower than t. In the case of constant returns, the increase in factors in a proportion equal to t generates an increase in product in the same proportion. For increasing returns, in turn, an increase in the use of factors by proportion t results in an increase in product in a proportion greater than t. 6

7 The theoretical model developed by Rougoor et al. (1998) shows that the use of technology applied to the making of management decisions, the way in which decisions are made, and the human capital of farmers are of fundamental importance to determine technical and economic efficiencies of farms. The model assumes that aspects of the decision-making process (e.g., the use of IT tools to production and commercialization management) as well as personal aspects (e.g., motivations, management aims, and abilities of the farmer) directly affect the process of decision-making and the production processes, thus influencing the technical and economic efficiencies of farms. The author also found, through literature review, that few empirical studies tested the effect of aspects of the decision-making process and of personal aspects on the performance of farms. In this context, some more recent empirical studies have tested the influence of management factors on the differentials of technical and economic efficiencies of rural properties (Wilson et al., 1998; Wilson et al., 2001; Trip et al., 2002; Solís et al., 2009; Cabrera et al., 2010; Chang and Mishra, 2011). Wilson et al. (1998) employed the practice of product stocking as a proxy to measure the level of production planning of potato farmers in the United Kingdom (UK). The authors found a positive and statistically significant connection between this variable with the technical efficiency of farms, thus confirming the hypothesis that management planning positively affects the efficiency of the production process. Wilson et al. (2001) adopted the theoretical model of Rougoor et al. (1998) and tested the effect of personal aspect variables (experience, schooling and management aims) as well as aspects of the decision-making process (number of sources of information that farmers utilize) on the technical efficiency of wheat farms in England. The authors showed that the objectives of maximizing annual profits and protecting the environment are positively related with the technical efficiency of farms. Moreover, the farmers who seek information and have more years of managerial experience are also associated with higher levels of technical efficiency. The study of Wilson et al. (2001) reinforces the suggestion made by Rougoor et al. (1998) that further studies should include more information on aspects of the managerial decision-making process (adoption of management technologies, e.g.). Following the theoretical model of Rougoor et al. (1998), Trip et al. (2002) created four management variables related to: (i) the quality of the establishing of aims (goals and policy), (ii) the quality of production planning (planning), (iii) the quality of the collecting and monitoring of operational results (data recording and monitoring), and (iv) the quality of the evolution of the firm s performance (evaluation). Based on data from 7

8 flower producers in the Netherlands, the authors showed evidence that producers who present higher quality in the collecting and monitoring of data and in the evolution of the operational performance of their firms operate with higher levels of technical efficiency. The authors concluded that decision-making variables are of fundamental importance to explain efficiency differentials of farms. In an analysis of the technical efficiency of peasant farmers in Central America, Solís et al. (2009) found that education and extension services present positive and significant effects on household efficiency. For the authors, these results support the premise that an increase in human capital enables rural households to improve the use of resources, thus achieving higher productivity. Cabrera et al. (2010) showed that the managerial strategy of intensification of dairy production (feed/cow) and the adoption of automated systems for production control have positive effect on technical efficiency indexes of dairy farms of Wisconsin, USA. Chang and Mishra (2011) found that US dairy farmers who adopted automated milking systems, kept production records, and made use of regularly scheduled veterinary services achieve higher levels of technical efficiency. The studies of Rougoor et al. (1998) and Wilson et al. (1998, 2001) suggested the analysis of the effect of IT tools for farm management on the efficiency. It is supposed that the IT tools have great potential to help farmers in their decision-making process. For example, when farmers follow the market via internet they obtain, at a low cost, real-time information on prices of production factors, products, and available technologies. Perfect knowledge of the prices and production technologies, and its changes over time, is important to the production planning and the choice of the optimal demand of factors and optimal production level, in accordance with what is assumed by microeconomic theory. In turn, managerial systems of cost and productivity control are also fundamental for farmers to monitor and optimize the use and allocation of the production resources, resulting in higher operational efficiency. IT tools for planning and control of agricultural production allow for better coordination and monitoring of productive processes, reducing internal transaction costs and increasing the factors productivity. 3 Furthermore, such tools are important in order to increase coordination, reduce the asymmetry of information and, consequently, the 3 Costs of internal coordination, of obtaining information, and of monitoring production activities of a firm are examples of transaction costs within the firm. 8

9 transaction costs between firms of a same agri-food production chain (Kuhlmann and Brodersen, 2001). In manufacture and services sectors, the diffusion of IT tools to assist technical processes (material processing technology) and managerial processes (information processing technology) is very high. Empirical studies showed positive and statistically significant impact of the use of such tools on technical and economic efficiency indexes of firms (Brynjolfsson and Hitt, 2000; Shao and Lin, 2002; Becker et al., 2003). Frequently, the use of these tools also generates positive externalities, such as firm organizational innovations that are complementary to IT (Brynjolfsson and Hitt, 2000). 4 Despite their very low diffusion in Brazilian agriculture, there are several IT tools for agricultural production planning and control. Among these tools are simple electronic spreadsheets for costs control and production records, as well as more integrated management systems and precision agriculture technologies (Zijp, 1994; Kuhlmann and Brodersen, 2001). Kulhmann and Brodersen (2001) present the characteristics and potentialities of an integrated management systems applied to agriculture. Using production, prices and other market data, these systems assist farmers in their decisionmaking, which may improve efficiency. The authors also showed that these kind of systems present low diffusion in farm management. In turn, precision agriculture consists in the georeferencing of farms so that soil characteristics, production, and yields of each plot of land can be known. Thus, input quantities are established in accordance with the demands of each plot and the monitoring of production becomes very detailed. The adoption of these techniques demands, jointly, the adoption of very advanced information systems. The main benefits are reduction in the use of inputs, better control of production and, consequently, gains in technical and economic efficiency (Lowenberg-DeBoer, 1996). In general, it is assumed that the adoption of these management tools results in improvements in the process of making managerial decisions and, consequently, in gains in efficiency. It is important to also stress that the potential positive results owing to the use of IT tools are conditioned to the characteristics of human capital (farmers and their employees), as well as to the manner in which they use the technologies in order to 4 The home-office organizational arrangement, adopted by several firms as a work organization tool, is a good example of organizational innovation complementary to the development and adoption of IT tools. This arrangement is only viable due to the reduction in costs of information and monitoring obtained through the development of IT tools. 9

10 organize the information and make the decisions, according to the theoretical model of Rougoor et al. (1998). Therefore, it is necessary that the effects of the use of IT tools for management (aspect of the decision-making process) are jointly measured, vis-à-vis characteristics of the decision-making process (receiving of services and technical assistance, e.g.) and of human capital (schooling of farmers, e.g.). 3. METHOD 3.1. Data and Variables Brazilian citrus production is concentrated in the State of São Paulo, which had a share of 74% participation in the total production of 17,549,536 tons of orange produced in Brazil in 2013 (IBGE, 2013). Orange production in the State of São Paulo has two main destinations: industrial processing (orange juice) and fresh fruit market. In 2013, 83% of production was destined to the processing industry (IEA, 2013). All farms of the sample of this study are in this State of São Paulo due to its great share in Brazilian citrus production. The Central, South, and North regions of the state were established as the target of the sampling process. According to the data from LUPA (2008), these regions comprised 9,370 farms with citrus production (50% of the state s total). A random selection was undertaken, resulting in 98 farms, with a sample error of 10% and a confidence level of 95%. 5 The data collection was carried out from March to September 2014, referring to the crop year 2013/14 (cross-sectional data). Interviewers applied a structured questionnaire themselves, which was divided into three blocks: (a) personal aspects of citrus farmers; (b) structural aspects of production (use of production factors, production, and technology) and (c) aspects of the decision-making process. Table 1 presents the description of production factors (land, work, capital, fertilizers and pesticides) used to estimate the production frontier, as well as personal aspects and aspects of the decision-making process (managerial variables) tested as determinants of efficiency of the farms. Among the personal aspects variables, it was considered that the expectation formation is related to the drives and motivations of the farmer, while schooling and the technical and managerial assistance are related to 5 A The formula used to calculate the sample s minimum size was: n = Z 2.p.q.N E 2.(N 1)+Z 2.p.q, in which n is the size of the sample; Z is the abciss of the normal distribution, fixated in the confidence; N is the size of the population; E is the admitted sample error; and p is the true value of the proportion of one of the chosen variables (a value 0,5 was adopted for p, given that this information was not available and that q = 1- p). 10

11 capability. The expectation variable seeks to measure the impact that the crisis in citrus production and the buyers concentration (few orange juice processing firms) have had upon the incentives for better allocation of resources in citrus production. 6 On the one hand, it is expected that the farmers who formed unfavorable expectation in relation to the future of citrus activity will be unmotivated and with low incentives to make a good management of production, which tends to affect technical efficiency in a negative way. On the other hand, it is expected that a higher schooling level of farmers and greater use of technical assistance have positive effect in the efficiency of the farms, as show in most of the reviewed studies (Wilson et al., 2002; Solís et al. 2009; Chang and Mishra, 2011). The variable adoption of long run contracts to commercialize production, aspect of the decision-making process, was used as proxy to assess whether the farmer plans or not to improve commercialization. It is expected that those who adopt long-term contracts (for more than one crop year) have a more efficient commercialization planning and, thus, operate with higher levels of technical efficiency than those who commercialize production in the spot market or by means of short-term contracts (for a single crop year). The index of IT management tools is another variable for the testing of the effect of aspects of the decision-making process. This is a proxy variable to assess the intensity of the use of a set of planning tools (e.g., following the market via internet) and production control (e.g., cost control management systems and precision agriculture technologies). This is a variable of great interest in this study. It is expected a positive effect of the use of IT management tools on the technical efficiency of farms. Table 1. Description of the variables used in the analysis. Variable Production (y) Area (x1) Labor (x2) Capital (x3) Description Number of orange boxes produced in the crop year 2013/14. Area with orange trees in production in the crop year 2013/14 (in hectares). Hours of labor employed in orange production in the crop year 2013/14. Annual service flow of tractors and main agricultural implements used in orange 6 Brazil has the largest orange juice processing company in the world, called Cutrale. Cutrale and two other companies (Citrovita/Citrosuco and Dreyffuss) process approximately 80% of Brazilian orange production (Neves, 2010; Figueiredo et al., 2013). Complaints coming from citrus farmers and their representative associations about the market power of the oligopsony have increased in recent years. 11

12 Fertilizers (x4) Pesticides (x5) Undergraduate (z1) Expectations (z2) Technical and managerial assistance (z3) Adoption of long run contracts (z4) Index of IT management tools (z5) production in the crop year 2013/14 (in machine hours). Amount of NPK fertilizers used in orange production in the crop year 2013/14 (in kg). Total expenditure with pesticides (acaricides, herbicides and insecticides) in the crop year 2013/14. * Dummy variable with value equal to 1 if the producer has undergraduate education, and equal to 0 if not. Variable with value from 1 to 5 (1 = complete disagreement and 5 = complete agreement) obtained from the following statement: The environment of commercial disputes and anticompetitive practices of orange juice processing companies has negatively affected my investments in citrus production in recent years and continues to affect my expectation in relation to the future of the activity. Dummy variable of value equal to 1 if the farmer has received technical and/or managerial assistance for the production of orange, and equal to 0 if not. Dummy variable of value equal to 1 if the producer adopted long-term contracts in order to sell orange, and equal to 0 if not. Proxy variable for commercialization planning. Index of value ranging from 0 to 7 that measures the use of seven IT tools for production planning and control: i) electronic spreadsheets of cost control; ii) electronic records of input stock; iii) electronic records of production, productivity and incidence of pests per plot of land; (iv) use of integrated managerial software systems; v) use of internet to access market information; vi) adoption of precision agriculture techniques; vii) quality certifications. * Since several pesticides with different measures (liters and kg) are used, it was necessary to create the total expenditure with pesticides instead of a physical amount. This strategy was also used by Picazo-Tadeo and Reig-Martinez (2006) in their analysis on the efficiency of citrus properties in Spain. Descriptive statistics of the variables used in the analysis are presented in Table 2. As can be seen, the sample comprises small, medium and large size farms, with high variation of orange production and production factors endowment. This sample characteristic is interesting for the investigation of returns of scale, as well as for the 12

13 analysis of the effect of personal aspects and aspects of the decision-making process on technical efficiency. The level of schooling of the farmers in the sample is relatively high, with 51% of producers having undergraduate education. The expectation formation index presented an average of , which indicates that most citrus farmers formed unfavorable expectations of the future of citrus farming due to the commercial conflicts and the lowprice crises occurring in the last three years. Among the 98 producers, 50 received technical and/or managerial assistance frequently during the crop year 2013/14. The use of long-term contracts as a structure of governance in the transactions of orange was adopted by 37.7% of the sample. In turn, the index of IT tools applied to the management of farms presented an average of This shows that, among the seven tools investigated, on average, citrus farmers adopted 3.18 for the production management in the crop year 2013/14. Table 2. Descriptive statistics of the variables used in the analysis. Variable Mean Standard Deviation Minimum Maximum Production (y) 59, , , Area (x1) Labor (x2) 8, , , Capital (x3) 2, , , Fertilizers (x4) 60, , , Pesticides (x5) 110, , , ,038, Under graduation (z1) Expectations (z2) Technical assistance (z3) Long run contracts (z4) Index of management (z5) Stochastic Frontier and Inefficiency Effects Model The data was analysed by means of an econometric model of stochastic frontier of production, as proposed by Aigner et al. (1977), and Meeusen and van den Broeck (1977). A translog functional form was applied to represent the technology/production function, while the single stage model proposed by Battese and Coelli (1995) was applied to identify the factors determining the differences in efficiency among the farms within the sample. The proposed econometric model can be described by the following general form: 13

14 ln(y i ) = f(x i ; β) + v i u i i = 1, 2,, N (1) in which yi denotes the production of the i-th firm; f is the production function; xi is a vector of logarithms of physical quantities of inputs used by the farm (land, labor, capital, fertilizers and pesticides); is a vector of the parameters of the production function to be estimated; vi is a random error term, independent and identically distributed (i.d.d.); ui is an asymmetric non-negative random error associated with the technical inefficiency of the i-th farm, and i denotes the i-th of 98 farms in the sample. Maximum likelihood is usually used to estimate the values of the unknown parameters, after making assumptions regarding the functional form of technology and distributions of ui and vi. In the case of the Battese and Coelli (1995) model, the inefficiency term u follows a positive truncated normal distribution with constant scale parameter u 2 and a location parameter that depends on additional explanatory variables: u ~ N + (μ, σ u 2 ) with μ = δz (2) in which is an additional parameter vector to be estimated, and z is a vector of explanatory (managerial) variables that affect the efficiency/inefficiency of the farms. We specify the stochastic frontier production function as a translog function with the following specific form: lny i = β 0 + β 1 lnx 1i + β 2 lnx 2i + β 3 lnx 3i + β 4 lnx 4i + β 5 lnx 5i + β 11 ( 1 2 ln2 x 1i ) + β 12 lnx 1i lnx 2i + β 13 lnx 1i lnx 3i + β 14 lnx 1i lnx 4i + β 15 lnx 1i lnx 5i + β 22 ( 1 2 ln2 x 2i ) + β 23 lnx 2i lnx 3i + β 24 lnx 2i lnx 4i + β 25 lnx 2i lnx 5i + β 33 ( 1 2 ln2 x 3i ) + β 34 lnx 3i lnx 4i + β 35 lnx 3i lnx 5i + β 44 ( 1 2 ln2 x 4i ) + β 45 lnx 4i lnx 5i + β 55 ( 1 2 ln2 x 5i ) + v i u i (3) μ i = δ 1 z 1i + δ 2 z 2i + δ 3 z 3i + δ 4 z 4i + δ 5 z 5i (4) The unknown parameters of equations (3) and (4) are estimated simultaneously by maximum-likelihood using the package frontier (Coelli and Henningsen, 2010) in the statistical environment R. 4. ANALYSIS OF PRODUCTION FRONTIER: ASPECTS OF TECHNOLOGY The results of the parameters estimated for the translog production frontier with inefficiency effects (equations (3) and (4)) may be observed in Table 3. 14

15 Table 3. Maximum-likelihood estimates for the parameters of the translog production frontier and inefficiency effects model. Variable Parameter Coefficient Standard Error z-value Constant *** lnx1 (hectares) *** lnx2 (labor hours) lnx3 (machine hours) *** lnx4 (kg NPK) *** lnx5 (pesticides expenditures) lnx1 x lnx lnx1 x lnx lnx1 x lnx lnx1 x lnx lnx1 x lnx * lnx2 x lnx lnx2 x lnx lnx2 x lnx lnx2 x lnx lnx3 x lnx *** lnx3 x lnx lnx3 x lnx lnx4 x lnx lnx4 x lnx lnx5 x lnx Inefficiency model z1 (under graduation) z2 (expectations) *** z3 (technical assistance) z4 (long run contracts) * z5 (index of management tools) *** Variance Parameters s *** *** Log-Likelihood Chi-squared *** - Efficiency mean N = 98 *** Significant at 1%, ** significant at 5%, * significant at 10%. The variance parameter presented a value approximate to 1 (0.8053) and a statistical significance at the 1% level, which, in turn, means that the inefficiency term (ui) is important to explain the deviation of the firms in relation to the production frontiers. Furthermore, the likelihood-ratio test was carried out in order to test the null hypotheses 15

16 that there is no technical inefficiency in orange production within the farms analyzed. 7 The calculated chi-squared exceeded the tabled chi-squared at the 1% level of statistical significance. 8 Thus, it is possible to conclude that the stochastic model with the inclusion of the inefficiency term is more adequate than the traditional production models (without the inefficiency term) to explain the production of orange by the firms of the sample. The mean scaled variables for the product (y) and production factors (xn) were used in the estimation of the translog function, which is usually done in empirical analyses (Alvarez and Arias, 2004; Rahman and Rahman, 2008; Olsen and Henningsen, 2011; Manjunatha et al., 2013). 9 Among the first-order parameters of the five production factors, three present statistical significance at 1% level: land, capital, and fertilizers. The first-order parameters associated to the labor factors and pesticides did not present a statistical significance at 10% level. By using mean-scaled variables, it is possible to interpret the first-order coefficients of the translog function as the partial elasticities of production for the sample mean. 10 Thus, a 1% increase in the area in production results in an increase of % in the production of the farm that represents the mean of the sample (factors and production), if other production factors are kept constant. The interpretation for the other production factors is analogous. The elasticity of scale (sum of partial elasticities) at mean values was , which indicates constant returns to scale, considering the inputs and output at the sample mean. This result is very interesting and shows that, considering the sample mean for the quantities of inputs and output, the firms are operating in the optimal scale region. Next, we calculate and discuss the elasticity of scale for each farm within the sample, in order to show the differences of returns to scale among farms. Since all partial elasticities of the factors presented a positive value, it can be noted that the estimated translog production frontier respects the condition of monotonicity for the mean of the sample. The condition of convexity was tested by calculating the second- 7 In case the null hypotheses is accepted, = 0 and, therefore, the model is reduced to a traditional production model estimated by Ordinary Least Square method. 8 The calculated chi-squared presented a value of The tabled chi-squared with 1% statistical significance is of In the case of functional forms which are not sensitive to the measure units (for instance, Cobb-Douglas and translog), working with the variables divided by their respective means (x i x) does not affect the results of the economic measures related to the production technology (scale elasticity, substitution elasticity, etc.), since the values of the second-order coefficients are not changed. The technical efficiency indexes of the firms do not change. 10 Since the logarithms of the variable means divided by their mean values are equal to zero, the first-order coefficients of the translog function may be directly interpreted as the partial elasticities of production for the sample s mean (for a firm which represents the sample s mean). 16

17 order matrix (Hessian), which must be negative definite (Chambers, 1988). This condition was also respected for the sample mean. One of the main characteristics of the translog function is the possibility to calculate the scale index elasticities (sum of the partial elasticities) for each of the sample s farms. This characteristic allows for verifying which farms are operating with increasing, constant or decreasing returns to scale, as well as to find the optimum operation scale of farms for the available production technology. Farms which operate with constant returns (elasticity of scale index = 1) are at the optimum production scale (scale efficiency). In turn, farms that operate with decreasing or increasing returns may increase factors yields by changing the scale of production. Table 4 classifies the 98 farms in the sample, according to their elasticity of scale indexes (ESI). Table 4. Elasticities of scale of farms calculated from the translog production frontier. Group Elasticity of scale intervals Number of farms % I < % II 0.95 a % III 1 a % IV 1.05 a % V a % VI > % Groups I and II comprise farms that operate with decreasing returns of scale (ESI<1). It was found that 33 rural properties (33.7% of the sample) were operating with decreasing returns of scale. These farms could increase factor yields means by reducing the scale of production. The farms of group I are, mainly, of large size, with orange production above 100,000 boxes in 2013/14. It is important to mention that the firms of group II (elasticities of scale between 0.95 and 0.99) are operating very close to the scale of optimum production (region of constant returns of scale). Firms from group III (elasticity of scale between 1 and 1.049) are also operating close to the region of constant returns of scale, however with slight increasing returns. Therefore, considering the production technology represented by the translog frontier, 17 firms (17.3% of the sample) operate in the optimum scale region (or very close to it). In turn, the 57 firms in groups IV, V and VI (58.2% of the sample) may benefit from gains in scale by increasing the use of all production factors and, consequently, producing larger volumes of orange with greater factor yields. In the group VI are 28 farms with the greatest inefficiency of 17

18 Elasticity of scale scale. They could obtain significant gains in factors yields if they increase the scale of operations (for every 1% in the use of all factors, these farms would obtain gains in orange production of, at least, 1.21%). All of these firms are of small size, with production scale bellow 20,000 boxes during the crop year 2013/14. By relating the elasticity of scale indexes with production of the farms, it is possible to infer the optimum production scale for the production technology available. The optimum production scale (production for ESI=1) is within the interval from 55,000-85,000 boxes of orange per crop year (Figure 1). In fact, as previously presented, when calculated the elasticity of scale for the sample mean (production of 59,281 orange boxes), an index of was verified, which indicates constant returns of scale for this level of production. 1,8 1,6 1,4 1,2 1 0,8 0,6 0,4 0, Production (thousand boxes) Figure 2. Relationship between elasticity of scale indexes and orange production. 5. TECHNICAL EFFICIENCY ANALYSIS From the econometric estimates of production frontier, it is possible to obtain the efficiency index of the firms. Battese and Coelli (1993) demonstrated that the technical efficiency of the i-ith firm can be obtained from the following equation: TE i = E[exp( u i ) E i = e i )] = exp( μ σ 2 ) ( Φ[(μ σ ) σ ] Φ( μ σ ) ) (5) where μ = (1 γ)z i δ γe i, σ 2 = γ(1 γ)σ s 2, e i = v i u i, and Φ represents the distribution function of the standard normal random variable. 18

19 Table 5 summarizes the results of the technical efficiency indexes calculated for each farm in the sample, according to the equation (5). Five groups of farms were created according to their technical efficiency indexes. Table 5. Efficiency index of rural properties Technical efficiency score Number of farms <50% % 24 70,01-80% 13 80,01-90% 25 >90,01% 25 Average efficiency 0,7524 Standard deviation 0,1767 Maximum 0,9702 Minimum 0,2831 The technical efficiency indexes of the farms were between the minimum of 28.3% and maximum of 97%, with a mean of 75.2% and standard deviation of 17.7%. It is possible to notice that, in average, the farms produced approximately 75.2% of the maximum that they could produce with the same physical quantities of factors, considering the production technology. The mean technical efficiency index of 75.2% is in line with the efficiency index of 78% encountered by Bravo-Ureta et al. (2007) for agricultural activities in Latin America in their meta-regression analysis of TE agriculture. It is important to note that there is a high variability among the efficiency index of the farms, with 25 farms operating very close to the frontier (efficiency score > 0,9) vis-à-vis 35 operating more distant (efficiency score < 0,7). In this sense, it is fundamental to investigate factors determining technical efficiency differentials among the farms, which is the aspect of main interest of the present paper. Among the five management variables used to explain the technical efficiency differential, three presented statistical significance and an expected effect: expectations, use of long run contracts, and the index of IT management tools. It is important to stress that the estimated parameters for the managerial variables show the effect of these variables upon the inefficiency of firms. Therefore, z variables with a negative sign in Table 3 exert a negative effect upon inefficiency (and positive upon efficiency). Furthermore, the value of the estimated parameters only shows the direction of the relationship between the variable and the inefficiency of the farms. In order to calculate 19

20 the marginal effect of each variable upon the technical efficiency of the farms, it is necessary to calculate the partial derivative of technical efficiency in relation the variable: TE z = (1 γ)(φ( μ σ σ )e μ 1 + 2σ2 Φ( σ Φ( μ σ ) 1 + σ )e μ 2σ2 σ (Φ( μ Φ( σ ))2 μ σ σ )φ( μ μ σ σ )e μ 1 + 2σ2 Φ( μ σ ) ) μ z (6) in which φ (. ) denotes the probability density function of the standard normal distribution, and μ z equation (4). 11 is the marginal effect of a z-variable on the term as defined in The index of management tools variable presented a negative effect upon the inefficiency of firms and statistical significance at 1% level. The marginal effect of the variable, calculated for the sample mean, indicates that each additional management tool used by a farmer increases the technical efficiency index of farm by 1.88%, ceteris paribus. Considering this marginal effect, it can be observed that, in average, a farmer who uses the seven management tools investigated operates on an efficiency index 13.16% superior to that of a farmer who does not use any management tool, ceteris paribus. This result confirms the hypothesis that IT tools applied to planning and control of production optimize the decision-making process and, consequently, increase the technical efficiency of rural properties. These tools assist farmers in planning, coordination and monitoring of productive activities in their rural properties, resulting in greater efficiency in the use of production factors. This result is in accordance with the studies of Rougoor et al. (1998), Wilson et al. (2002) and Trip et al. (2002). The main practical implication of the result is the need of a greater diffusion of IT tools for planning and control of the production in Brazilian citrus farming. Farmers who wish to operate more efficiently must be concerned with the adoption of planning tools (integrated management systems, e.g.) and control (cost and yields control spreadsheets, e.g.) to improve the decision-making process and technical efficiency. Public policies should be concerned with training and incentives to speed up the diffusion of management tools. The expectations variable also presented the expected sign and a statistical significance at 1% level. This result confirms the hypothesis that the citrus farmers who formed unfavorable expectation in relation to citrus activity operate with lower technical 11 Equation (6) can be used to calculate the marginal effects of each of the variables z upon the technical efficiency index of each of the firms in the sample. It is common to present the results of the marginal effect of each variable for the sample mean. 20

21 efficiency than those whose expectations are either positive or neutral. The main deteriorative effect of the expectations is the reduction in the farmer s motivation and, consequently, in the incentives for allocation and optimal use of production factors. This result confirms the effect of personal aspects (motivations) on technical efficiency, in accordance with the theoretical model of Rougoor et al. (1998). The result associated to the expectations variable has an important implication for public policies, mainly for the anti-trust enforcement agency, as the unfavorable expectations is related to the oligopsony market strategies. Reversing the farmers unfavorable expectations would motivate them towards better allocation and optimal use of production factors, thus improving technical efficiency of farms. The use of long run contracts for commercialization of orange production present a negative effect on inefficiency at a statistical significance of 10% level. The marginal effect of the variable indicates that, in average, the use of long run contracts increases technical efficiency of farms in 2.33%, ceteris paribus. Long run contracts can be considered a commercialization-planning tool that affects also production planning. Farmers who adopt contracts may carry out their production plans based on an amount of product already negotiated in advance. Additional managerial efforts are made due to risk reduction and the commitments assumed. Frequently, contracts specify additional quality and standardization clauses for the product and pay higher prices for such, which incentives farmers to improve monitoring of production. Additionally, the long run contract is also a tool for managing price risk, increasing the predictability of the revenue. This result shows that the adoption of efficient governance to trade has positive effects on the production process. It is also important to note that the under graduation and the technical assistance variables did not present statistical significance at 10% level. The schooling variable was the single one with a sign opposite of that which was expected. In fact the level of schooling of the farmers was found relatively high (average of 13 years of study), so most of them have at least the minimum necessary schooling to undertake the available technologies and management tools. This explains why those variables are not able to explain technical efficiency differentials in this study. 6. CONCLUDING REMARKS The main objective of this paper was to show an estimation of a production frontier for citrus farms in Brazil, so that it would be possible to investigate the role played 21

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