Assessment of the operational and environmental efficiency of agriculture in Latin America and the Caribbean

74 Original Paper Agric. Econ. – Czech, 64, 2018 (2): 74–88 doi: 10.17221/260/2016-AGRICECON The Intergovernmental Panel on Climate Change (IPCC 2014) reported that between 2000 and 2010 the annual greenhouse gas (GHG) emissions caused by human activity increased more than in any previous decade, in spite of regional efforts to reduce them. This increase was mainly due to energy supply (47%), industry (30%), transport (11%) and building (3%) sectors. In fact, GHG emissions have increased in all sectors, except in agriculture, forestry, and others which use soil. Notwithstanding, there is no doubt that agriculture is highly important with respect to GHG emissions (Kuo et al. 2014). Not all countries contribute to the same extent to GHG emissions. Thus, developed regions with 17% of the world’s population produce 43% of the total CO2 equivalent in metric tons, while developing regions, representing 83% of the world’s population, release 57% of these emissions in metric tons (PRB 2014; UNDP 2014). In 2012, the contribution of LAC to GHG emissions amounted to only 9.9% of global emissions. These GHG emissions come from energy use (40.4%), agriculture (19.8%), land-use change and forestry (31.5%), waste (5.3%) and industrial process (3.0%) activities (Sánchez and Reyes 2015). The growth of the economies of the LAC region experienced a slowdown in 2012, resulting in a 3% reduction in the gross domestic product (GDP) versus the prior year. Nevertheless, despite this decrease in GDP, the agricultural sector only accounted for 5% of LAC’s GDP in 2012, a relatively lower level than in previous years (World Bank 2016). The aforementioned takes into account the fact that the annual growth rate of the agricultural sector of the LAC in the last three years was 2.9% higher than the total growth (ECLAC et al. 2015). LAC faces a background of global economic decline, a loss of buoyancy as world trade contracts, an upswing in adverse climatic events and increased outbreaks of crop pests and diseases that are intensified by a greater variability in the climate. Climate change is now an issue of undoubted relevance and is considered one of the major costs that is affecting Assessment of the operational and environmental efficiency of agriculture in Latin America and the Caribbean Juan-Javier MORENO-MORENO*, Francisco VELASCO MORENTE, Maria Teresa SANZ DIAZ Universidad de Sevilla, Sevilla, Spain *Corresponding author: [email protected] Moreno-Moreno J.-J., Velasco Morente F., Sanz Diaz M.T. (2018): Assessment of the operational and environmental effi - ciency of agriculture in Latin America and the Caribbean. Agric. Econ. – Czech, 64: 74–88. Abstract: Governments in Latin America and the Caribbean (LAC) require information that can be used to strengthen environmental agricultural strategies. However, in LAC there is not enough comparative analysis regarding operational performance and environmental performance, which are particularly important for sustainable agriculture. Th e objective of this study is the measurement of operational, environmental and unifi ed (operational and environmental) effi ciency through data envelopment analysis (DEA) for an environmental assessment in the agricultural sectors of eighteen LAC countries. Th e DEA in this study evaluates each country based on six variables: capital stock, labour, land, consumption of fertilizers, value of the gross agricultural production and agricultural emissions (CO2eq). Th is empirical study fi nds that six LAC countries attained full effi ciency in terms of the three effi ciency measurements. Th ree countries exhibit the highest level of unifi ed effi ciency, but show some level of ineffi ciency in the other two measurements (operational and environmental effi ciency). In contrast, nine countries failed to achieve the maximum unifi ed effi ciency score. Keywords: agricultural performance, damages to scale, DEA, returns to scale, unifi ed effi ciency 75 Agric. Econ. – Czech, 64, 2018 (2): 74–88 Original Paper doi: 10.17221/260/2016-AGRICECON society today and will continue to have an impact in the future (Cihelková 2011). Thus, reconciling agricultural productivity and environmental performance will be key factors for LAC in tackling the economic slowdown (ECLAC et al. 2013; 2015). There have been a number of studies that have analysed agricultural productivity in LAC and they have shown different results. Notable among them is Pfeiffer (2003), who estimated a meta-production function to analyse the change in agricultural productivity in the Andean community over the period 1972–2000. Bharati and Fulginiti (2007) also stand out. They used a translog frontier production function to estimate the agricultural productivity in the original Mercosur member countries and later associate members over the period 1972–2002. A feature of both studies is that they concluded that technical progress is the main contributor to agricultural productivity. Lending support to results obtained from previous studies, Ludena (2010) estimated the total factor productivity growth (TFP) in LAC between 1961 and 2007 using a Malmquist index. His study showed that agricultural productivity growth is due to technical change. In the last two decades of this period agricultural productivity grew at a faster rate as a result of changes in efficiency and mainly because of new technologies. Looking to provide information on agricultural productivity, Zúniga (2011) performed data envelopment analysis (DEA) to derive a Malmquist index over the period 1994–2010 in Central America. This study confirms that gains in agricultural productivity in the LAC countries in the last decades are associated with new technologies. In this context, this work also concluded that increases in agricultural productivity are due to technical changes and efficiency changes. A previous study by Solís et al. (2009), using an input-oriented stochastic distance frontier simultaneously with a technical efficiency effects model, concluded that improvements in technical efficiency are financially beneficial to farm households while also contributing to environmental sustainability. This study was performed with the aim of determining the extent to which technical efficiency is related to activities promoted by two natural resource management programs of 639 farms in El Salvador and Honduras. More recently, Martín-Retortillo et al. (2014) analysed the growth of agricultural production in LAC between 1950 and 2010. The study used Hayami and Ruttan’s (1985) induced development model to estimate the evolution of partial productivities of labour and land, and growth accounting methodology to measure the TFP. This work found that the efficiency gains made a modest contribution to the important increase in production, which was mainly caused by the use of capital, along with more moderate increases in the use of land and labour (Martín- Retortillo et al. 2014). Another study applied a growth accounting approach combined with DEA to measure TFP growth and to break down the contributions of technical change and changes in technical efficiency agricultural to growth in LAC over the period 1980–2012. This study by Nin-Pratt et al. (2015) showed that productivity increased faster in the countries that increased inputs per work than in countries with limited access to capital and land. Besides, it concluded that agricultural growth is mainly due to increases in the consumption of fertiliser, land productivity and the use of capital. Furthermore, these researchers point out that growth patterns have amplified differences in labour productivity among LCA countries. Focusing on South American countries, a translog production function and a Malmquist index applied by Trindade and Fulginiti (2015) showed that agricultural productivity growth accounted for half of the three-fold increase in agricultural output between 1969 and 2009 and that performance is sensitive to R&D investments in this sector. It also found that there was no evidence of a slowdown in agricultural productivity growth in this region between 2000 and 2009. However, although recognising the contributions of all of the above-mentioned studies to the assessment of agricultural productivity growth in specific LAC countries, it must be said that these previous studies did not report an environmental performance analysis in agriculture, with the exception of Nin-Pratt et al. (2015) who recently analysed the agro-ecological efficiency in their study of the productivity and performance of agriculture in LAC. Finally, it is important to point out the contribution of Ebata (2011), who estimated the TFP in the agricultural sector of Central America and the Caribbean over the period 1976–2006, using a translog production function and the Malmquist index approach. In contrast to other studies, this study found that TFP growth rates improved over this period when no externalities were taken into account. Nonetheless, a lower rate of growth was identified between 1992 and 2006 in most countries when CO2 emissions were included in the analysis. 76 Original Paper Agric. Econ. – Czech, 64, 2018 (2): 74–88 doi: 10.17221/260/2016-AGRICECON This study uses the nonparametric approach of DEA for environmental assessment to measure operational efficiency, environmental efficiency and unified efficiency, under both operational and environmental efficiency measurements in the agricultural sector of 18 LAC countries. This work also determines the types of returns to scale (RTS) and damages to scale (DTS) in each country in 2012 based on two outputs (value of the gross agricultural production and agricultural emissions (CO2eq)) and four inputs (fertilisers, capital stock, labour and land). The aim inn this investigation is to identify the most efficient countries and – with this empirical comparison – to provide relevant information to orient the inefficient countries so that they can work on strengthening environmental strategies to reduce their environmental carbon footprint in agriculture and create a sustainable agriculture. The DEA methodology is widely used and recognised way to measure production efficiency, but it has also been used to evaluate the environmental performance (Scheel 2001; Zhou et al. 2008). Färe et al. (1989, 1993, 1996) were among the earliest authors who used DEA in the context of weak disposability and who employed environmental DEA technology to analyse productivity when some outputs are bad. Since then, different methods have been proposed in order to process the bad outputs in a DEA (Scheel 2001). Although an environmental assessment model is called for, DEA does not only estimate environmental efficiency in the environmental assessment approach (Dios-Palomares et al. 2014). This approach includes environmental variables and the conventional production variables. That is, the distance that spans the efficient frontier includes operational efficiency, environmental efficiency and unified efficiency, which cannot be separated into an environmental analysis model of these features (Sueyoshi and Goto 2011a; Dios-Palomares et al. 2014). So, a country’s environmental performance cannot be determined without first estimating its operational performance. There has been very little DEA for the environmental assessment approach to measure the environmental efficiency of the agricultural sector in LAC (Dios- Palomares et al. 2014). Thus, this study uses the DEA model for the environmental assessment proposed by Sueyoshi and Goto (2011a; b) to analyse the agricultural sector in LAC. An important feature is the use of DEA-RAM (Range-Adjusted Measurement), first proposed by Cooper et al. (1999), because it can easily incorporate the good output and bad output into a unified treatment. Also, this approach allows the measuring of the type of RTS when handling the good outputs and DTS when handling the bad outputs for environmental assessment (Sueyoshi and Goto 2011a; 2013). MATERIALS AND METHODS In our evaluation of the agricultural sectors of LAC countries, it is assumed that there are n countries, (j= 1, …, n) and each country uses input levels xik > 0 (i = 1, …, m) to produce two kinds of outputs: good outputs grk > 0 (r = 1, …, s) and bad outputs bfk > 0 (f = 1, …, h). The agricultural sector performance of the kth country is presented as follows. Operational efficiency in good outputs This refers to an inefficient country reaching its operational efficiency by decreasing its directional vector of inputs in order to increase its directional vector of good outputs as much as possible. This study therefore evaluates the operational efficiency of the kth country by using a non-radial model as follows: ܯܽݔσܴ௜௫݀௜௫௠ ௜ୀଵ ൅σܴ௥ ௚݀௥ ௚ ௦ ௥ୀଵ ݏǤݐǤσݔ௜௝ɉ௝ ௡ ௝ୀଵ ൅݀௜௫ൌݔ௜௞ሺ݅ൌͳǡǥǡ݉ሻ σ݃௥௝ɉ௝ ௡ ௝ୀଵ െ݀௥ ௚ൌ݃௥௞ሺݎൌͳǡǥǡݏሻ σɉ௝ ௡ ௝ୀଵ ൌͳǡɉ ௝൒Ͳሺ݆ൌͳǡǥǡ݊ሻ ݀௜௫൒Ͳሺ݅ൌͳǡǥǡ݉ሻǡ݀௥ ௚൒Ͳሺݎൌͳǡǥǡݏሻ (1) where superscript (g) is used to specify the good outputs. Here, λ = (λ1, …, λn)T is the jth intensity variable. ݀௜௫ (i = 1, …, m) and ݀௥ ௚ (r = 1, …, s) are all slack variables related to the ith input and the good outputs, respectively. Furthermore, the upper and lower bounds of each good output are expressed by ᤻݃ൌ ݉ܽݔ௝൛݃௥௝ൟ and ᤻݃ൌ݉݅݊ ௝ ൛ ݃௥௝ ൟ  and the upper and lower bounds of each input are expressed by ݔ᤺ൌ݉ܽݔ ௝ ൛ ݔ௜௝ ൟ  and ݔ᤺ൌ݉݅݊ ௝൛ݔ௜௝ൟ , respectively. So ܴ௥ ௚ൌͳȀሾሺ݉൅ݏሻሺ᤻݃െ᤻݃ሻሿ for each r and ܴ ௜௫ൌͳȀሾሺ݉൅ݏሻሺݔ௜െݔ௜)ሿ for each i indicate the ranges for good outputs and inputs, respectively. An operational efficiency score of the specific kth country is measured by θ = 1 –൫σܴ௜௫݀௜௫כ௠ ௜ୀଵ ൅σܴ௥ ௚݀௥ ௚כ ௦ ௥ୀଵ ൯ where (*) indicates the optimal values in the model (1). The equation in the parentheses indicates the 77 Agric. Econ. – Czech, 64, 2018 (2): 74–88 Original Paper doi: 10.17221/260/2016-AGRICECON level of inefficiency. The operational efficiency is obtained by subtracting inefficiency from unity. ܯ݅݊σݒ௜ݔ௜௞ ௠ ௜ୀଵ െσݑ௥݃௥௞ ൅ɐ ௦ ௥ୀଵ  (2) ܯ݅݊σݒ௜ݔ௜௞ ௠ ௜ୀଵ െσݑ௥݃௥௞ ൅ɐ ௦ ௥ୀଵ  (j = 1, …, n) ݒ௜ ൒ܴ௜௫ሺ݅ൌͳǡǥǡ݉ሻ,ݑ௥൒ܴ௥ ௚ (r = 1, …, s), σ: URS Here, vi(i = 1, …, m), ur(r = 1, …, s) and σ are the dual variables corresponding to the first, second and third groups of constraints from the primal problem or model (1). Also, URS is unrestricted. Measurement of the RTS To explain the RTS measurement it is necessary to describe the economies of scale (SE), which is defined as the quantity of an increase in a good output resulting from a proportional increase in all inputs (Sueyoshi and Goto 2013). After calculating the SE, it is possible to determine the RTS. That is, the RTS measurement aims to make a projection onto the efficient frontier in which each inefficient country evaluated has to project its good outputs. Hence, to determine the type of RTS, the SE value must be expressed in terms of the efficiency and inefficiency of the kth country. That is, if a kth country is efficient, then the value of the SE is obtained as follows: ܵܧൌሺσ ݒ௜כሺݔ௜௞ െ݀௜௫כሻ ௠ ௜ୀଵ ሻ൫σݑ௥ כ൫݃௥௞ ൅݀௥ ௚כ൯ ௦ ௥ୀଵ ൯ Τ ൌ ൌ ͳ ቀͳ൅൫ɐȗσݒ௜כሺݔ௜௞ െ݀௜௫כሻ ௠ ௜ୀଵ Τ൯ቁൗ (3) On the contrary, if a kth country is inefficient, then its projected point on an efficient frontier is found in ൬ܺ௞െ ܩ௞൅݀௫כ ݀௚כቁ, an optimal solution (λ, dx*, dg*) of the model (1). That is to say: ܵܧൌሺσ ݒ௜כሺݔ௜௞ െ݀௜௫כሻ ௠ ௜ୀଵ ሻ൫σݑ௥ כ൫݃௥௞ ൅݀௥ ௚כ൯ ௦ ௥ୀଵ ൯ Τ (4) The equations (3) and (4) indicate that the sign of the dual variable (σ) determines the value of SE and the RTS in all efficient and inefficient countries in terms of operational efficiency. Then, assuming a single projection of an inefficient country onto an efficient frontier and a single set of references for the projected country, the model (5) calculates the upper bounds ʍത and the lower bounds ɐ as follows: Max/Min σ s.t. constraints in both (1) and (2) σܴ௜௫݀௜௫௠ ௜ୀଵ ൅σܴ௥ ௚݀௥ ௚ൌσݒ௜ݔ௜௞ ௠ ௜ୀଵ െσݑ௥݃௥௞ ൅ɐ ௦ ௥ୀଵ  ௦ ௥ୀଵ  (5) Consequently, the type of the RTS for the kth country can be obtained: (a)Increasing RTS ՞Ͳ൐ɐȗ൒ɐȗ (b)Constant RTS ՞ɐȗ൒Ͳ൒ɐ ȗ (c)Decreasing RTS ՞ɐȗ൒ɐȗ൐Ͳ For instance, suppose that a country exhibits increasing RTS in its operational performance. This means that a unit increase in inputs in the agricultural activity should produce good outputs more proportionally than the unit increase in inputs. Accordingly, a country ought to increase its current level of agricultural activity to achieve its operational efficiency in good outputs. Additionally, a decreasing RTS indicates that a unit increase in inputs produces good outputs, i.e., value of the gross agricultural production in our case, less proportionally than the increase in inputs. However, a constant RTS indicates that a unit increase in inputs increases agricultural production to the same proportion as the increase in inputs. Environmental efficiency in bad outputs In contrast, environmental efficiency refers to an inefficient country achieving its environmental efficiency by increasing the directional vector of inputs in order to decrease the directional vector of bad outputs as much as possible. Thus, this study evaluates the environmental efficiency of the kth country by using a non-radial model as follows: ܯܽݔσܴ௜௫݀௜௫௠ ௜ୀଵ ൅σܴ௙ ௕݀௙ ௕ ௛ ௙ୀଵ  ݏǤݐǤσݔ௜௝ߣ௝ ௡ ௝ୀଵ െ݀௜௫ൌݔ௜௞ሺ݅ൌͳǡǥǡ݉ሻ σܾ௙௝ߣ௝ ௡ ௝ୀଵ ൅݀௙ ௕ൌܾ௙௞ሺ݂ൌͳǡǥǡ݄ሻ σߣ௝ ௡ ௝ୀଵ ൌͳǡߣ ௝൒Ͳሺ݆ൌͳǡǥǡ݊ሻ ݀௜௫൒Ͳሺ݅ൌͳǡǥǡ݉ሻǡ݀௙ ௕൒Ͳሺ݂ൌͳǡǥǡ݄ሻ (6) where superscript (b) is used in order to specify the bad outputs. Here, ݀௙ ௕ሺ݂ൌͳǡǥǡ݄ሻ are all the slack variables related to the bad outputs. The ranges for the model (6) are calculated as follows: ܴ௙ ௕ൌͳȀ༰ሺ݉൅݄ሻሺ௙െ௙ሻ༱ for each f and ܴ ௜௫ൌͳȀ༰ሺ݉൅݄ሻሺݔప ഥെݔ௜ሻ༱ for each i. Furthermore, the upper and lower bounds of each bad output are 78 Original Paper Agric. Econ. – Czech, 64, 2018 (2): 74–88 doi: 10.17221/260/2016-AGRICECON expressed by ܾ௙ൌ݉ܽݔ௝൛ܾ௙௝ൟ and ܾ௙ൌ݉݅݊௝ ൛ ܾ௙௝ ൟ , respectively. Then, the environmental efficiency score (θ) of the kth country is measured by: Ʌൌͳെ൫σܴ௜௫݀௜௫כ௠ ௜ୀଵ ൅σܴ௙ ௕݀௙ ௕כ௛ ௙ୀଵ ൯ The model (6) has the following dual formulation: ܯ݅݊െσݒ௜ݔ௜௞ ௠ ௜ୀଵ ൅σݓ௙ܾ௙௞൅ɐ ௛ ௙ୀଵ  ݏǤݐǤെσݒ௜ݔ௜௝ ௠ ௜ୀଵ ൅σݓ௙ܾ௙௝ ൅ɐ ௛ ௙ୀଵ ൒Ͳ (7) ݒ௜൒ܴ௜௫ሺ݅ൌͳǡǥǡ݉ሻǡݓ௙൒ܴ௙ ௕ (f = 1, …, h), σ: URS Here, vi = (i = 1, …, m), wf = (f = 1, …, h) and σ are dual variables corresponding to the first, second and third groups of constraints from the primal problem or model (6). Also, URS is unrestricted. Measurement of the DTS This measurement changes the SE concept for a new concept, SD (scale damages). The SD corresponds to the SE in the bad outputs (Sueyoshi and Goto 2013). The DTS measurement aims to indicate a projection onto the efficient frontier in which each inefficient country evaluated has to project its bad outputs. To obtain the type of the DTS, the value of the SD must be expressed in terms of the efficiency and inefficiency of the kth country. Then, if the kth country is efficient the value of the SD is obtained as follows: ܵܦ ൌሺσ ݒ௜כሺݔ௜௞൅݀௜௫כሻ ௠ ௜ୀଵ ሻ൫σݓ௙ כ൫ܾ௙௞ െ݀௙ ௕כ൯ ௛ ௙ୀଵ ൯ ൗ ൌͳ൫ͳെሺɐכσݒ௜כሺݔ௜௞൅݀௜௫כሻ ௠ ௜ୀଵ Τሻ ൯ Τ (8) On the contrary, if a kth country is inefficient, then its projected point on an efficient frontier is found in ൬ܺ௞൅ ܤ௞െ݀௫כ ݀௕כቁ of an optimal solution (λ, dx*, db*) of the model (6). That is to say: ܵܦൌ൫σݒ௜כ௠ ௜ୀଵ ሺݔ௜௞൅݀௜௫כሻ൯ ቀ σݓ௙ כ ௛ ௙ୀଵ ൫ܾ௙௞െ݀௙ ௕כ൯ ቁ ൗ (9) Equations (8) and (9) indicate that the sign of a dual variable (σ) determines the value of the SD and the DTS in all efficient and inefficient countries in terms of environmental efficiency. Then, assuming a single projection of an inefficient country onto an efficient frontier and a single set of references for the country projected, the model (10) calculates the upper bounds ɐത and the lower bounds ɐ, as follows: Max/Min σ s.t. constraints in both (6) and (7) σܴ௜௫݀௜௫௠ ௜ୀଵ ൅σܴ௙ ௕݀௙ ௕ൌെσݒ௜ݔ௜௞ ௠ ௜ୀଵ ൅σݓ௙ܾ௙௞ ൅ɐ ௛ ௙ୀଵ  ௛ ௙ୀଵ (10) Consequently, the type of the DTS for the kth country can be obtained: (a) Increasing DTS ՞ɐȗ൒ɐȗ൐Ͳ (b) Constant DTS ՞ɐ ȗ ൒Ͳ൒ɐȗ (c) Decreasing DTS ՞Ͳ൐ɐכ൒ɐȗ DTS has an opposite managerial implication for the RTS. Suppose that a country belongs to those with increasing DTS. This means that a unit increase in inputs to agricultural activity produces bad outputs more proportionally than the unit increase in inputs. For this reason, a country should reduce the current size of its agricultural activity to attain its environmental efficiency in bad outputs. Yet this result indicates that this country ought to use technological innovations in agricultural activity in order to reduce its bad outputs – agricultural emissions (CO2eq) in our case. Additionally, a decreasing DTS means that a unit increase in inputs produces bad outputs less proportionally than the increase in inputs. Nevertheless, a constant DTS means that a unit increase in inputs produces agricultural emissions (CO2eq) in the same proportion as the increase in inputs. Unified efficiency measurement The operational and environmental efficiency approach is first presented in a separate treatment. Nonetheless, the main purpose of the DEA for the environmental assessment is to calculate both of the measures in a unified treatment because a production activity produces not only good outputs but also bad outputs. The resulting model (11) unifies model (1) and (6) in such a manner that the integration provides a single set of intensity variables to produce a unified (operational and environmental) efficiency, i.e., model (11) can express the two efficient frontiers in a single set of intensity variables. Also, the direction of the possible projection in model (11) includes both of the operational and environmental efforts of the adaptive strategy for environmental protection (Sueyoshi and Goto 2011b). Then, this study evaluates the unified efficiency of the kth country by using the model as follows: 79 Agric. Econ. – Czech, 64, 2018 (2): 74–88 Original Paper doi: 10.17221/260/2016-AGRICECON ܯܽݔσܴ௜௫ሺ݀௜௫ା൅݀௜௫ିሻ ௠ ௜ୀଵ ൅σܴ௥ ௚݀௥ ௚ ௦ ௥ୀଵ ൅σܴ௙ ௕݀௙ ௕௛ ௙ୀଵ ݏǤݐǤσݔ௜௝ɉ௝െ݀௜௫ା௡ ௝ୀଵ ൅݀௜௫ି ൌݔ௜௞ሺ݅ൌͳǡǥǡ݉ሻ σ݃௥௝ɉ௝ ௡ ௝ୀଵ െ݀௥ ௚ൌ݃௥௞ሺݎൌͳǡǥǡݏሻ σܾ௙௝ɉ௝ ௡ ௝ୀଵ ൅݀௙ ௕ൌܾ௙௞ሺ݂ൌͳǡǥǡ݄ሻ σɉ௝ ௡ ௝ୀଵ ൌͳǡɉ ௝൒Ͳሺ݆ൌͳǡǥǡ݊ሻ ݀௜௫ା൒Ͳሺ݅ൌͳǡǥǡ݉ሻǡ݀௜௫ି൒Ͳሺ݅ൌͳǡǥǡ݉ሻ ݀௥ ௚൒Ͳሺݎൌͳǡǥǡݏሻ݀௙ ௕൒Ͳሺ݂ൌͳǡǥǡ݄ሻ (11) where superscripts (g) and (b) are used in order to specify the good outputs and bad outputs, respectively. Here, ݀௜௫ related to the ith inputs is separated into its positive and negative part (݀௜௫ା and ݀௜௫ି). The input slacks in the first group of constraints in model (11) indicate ݀௜௫ା–݀௜௫ି = ݀௜௫ . The variable transformation of input slacks requires the nonlinear conditions: ݀௜௫ା–݀௜௫ି= 0 (i = 1, …, m), which indicate that the two slack variables are mutually exclusive. Then, a simultaneous occurrence of both ݀௜௫ା≥ 0 and ݀௜௫ି≥ 0 is excluded from the optimal solution of model (11). To satisfy the nonlinear condition in model (11), this study used the following two computational alternatives: First, solve the model (11) with ݀௜௫ା–݀௜௫ି= 0 (i= 1, …, m) as a nonlinear condition in a programming problem. Second, put ݀௜௫ା≤ ܯݖ௜ା, ݀௜௫ି≤ ܯݖ௜ି, ܯ ݖ௜ା+ ܯ ݖ௜ି≤ 1, ܯ ݖ௜ାand ܯ ݖ௜ି: binary (i = 1, …, m) into the model (11) and solve the model with the side constraints as a mixed integer programming problem. M stands for a very large number that need to determine before the computational operation. Thus, unified (operational and environmental) efficiency is measured by: Ʌൌͳെൣσܴ௜௫ሺ݀௜௫ାכ ൅݀௜௫ିכሻ ௠ ௜ୀଵ ൅σܴ௥ ௚݀௥ ௚כ ൅ ௦ ௥ୀଵ ൅σܴ௙ ௕݀௙ ௕כ௛ ௙ୀଵ ൧ Data This study includes eighteen LAC countries: Argentina, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru and Uruguay. The variables that are to be analysed were obtained from the Food and Agriculture Organization of the United Nations (FAOSTAT 2016) and Nin-Pratt et al. (2015) for the year 2012. They include four conventional input variables (capital stock, labour, land and consumption of fertilisers) and two outputs (value of the gross agricultural production and agricultural emissions (CO2eq)). The definitions of these variables are given below. Inputs Capital stock: The FAO statistics division has compiled an updated dataset of capital stock in agriculture from 1975 to 2007 using 2005 constant prices as the base year. The data for the year 2012 were obtained from the study of Nin-Pratt et al. (2015). They used figures of gross fixed capital stock formation. This measures the value of the existing fixed assets of farmers over a given period with each asset valued at new prices. Capital stock has two components: (1)crop capital covering land developments, plantation crops and machinery and equipment; (2) livestock including animal inventory and livestock fixed assets. Labour is the total economically active population in agriculture in thousands of peoples. The data refer to the 5th edition of the International Labour Organization, revised in 2009. Land includes arable land, permanent crops and permanent meadows and pastures, and it is expressed in thousands of hectares. Consumption of fertilisers refers to the quantity of nitrogen (N), phosphate (P2O5) and potash (K2O) and is expressed in tons. In this study, the consumption of fertilisers represents the increase of soil yield. The application of fertilisers is responsible for a portion of GHG emissions, yet the other inputs of this study are assumed to also affect the level of GHG emissions (IPCC 2006; Solazzo et al. 2016). Good output The value of gross agricultural production is expressed in millions of USD, based on the constant price of 2004–2006. It includes crop and livestock production. According to FAOSTAT (2016), the value of gross production is obtained by multiplying the gross production in physical terms by the output prices at the farm gate. As a result, it measures production in monetary terms at the farm gate level. Since the intermediate uses within the agricultural sector (seed and feed) were not subtracted from the production data, this value of the production aggregate refers to the notion of gross production. Bad output Agricultural emissions are expressed in gigagrams CO2 equivalent (CO2eq), and are those reported in 80 Original Paper Agric. Econ. – Czech, 64, 2018 (2): 74–88 doi: 10.17221/260/2016-AGRICECON the FAOSTAT domains of emissions from land use consistent with the IPCC. These are the bad output directional vectors of models 6 and 11. This variable includes crop and livestock production, forestry and associated land-use changes. According to the IPCC (2006), in agricultural emissions the key greenhouse gases of concern are CO2, N2O and CH4. Still, agricultural GHG emissions are dominated by non-CO2 gases, namely methane (CH4) and nitrous oxide (N2O), produced as a result of crop and livestock production and management activities. This variable comprises data on GHG emissions formed in the different agricultural sub-domains, giving a picture of the contribution to the total amount of GHG emissions from agriculture (FAO 2014). The IPCC guidelines for national GHG emissions for agriculture consider that emissions have a linear relationship with the size of the economic activity. That is, an increase in agricultural activity will produce a proportional surge in GHG emissions (Solazzo et al. 2016). In this respect, GHG emissions in LAC have historically been dominated by land use, land-use change and agriculture and forestry (IICA 2015). Enteric fermentation and manure emissions from livestock-rearing is the largest source of total agricultural emissions in LAC (FAO 2014). Livestock breeding results in the release of CH4 from enteric fermentation and N2O from the excreted nitrogen, as well as from nitrogenous chemical fertilisers (N) used to produce feed for many animals. The utilisation of manure and nitrogen fertilisers on agricultural land increases N2O emissions. Moreover, N2O and CO2 are released during the production of chemical nitrogen fertilisers (UNEP 2012). For the reader who is interested in the mathematical details of these models, several files have been created using the Wolfram Mathematica programme. These are available upon request. RESULTS AND DISCUSSION The efficiency measurements of the agricultural sector in 18 LAC countries are presented in Table2. The second column shows the operational efficiency and the third column shows the environmental efficiency, which have been calculated using models (1) and (6), respectively. Also, the fourth and fifth columns present the unified (operational and environmental) efficiency that was obtained using model (11). Figure 1 shows that Argentina, Belize, Bolivia, Brazil, Costa Rica, the Dominican Republic, Ecuador, Guatemala, Honduras, Mexico, Panama and Uruguay attained the maximum operational efficiency score (1.0000) in 2012. These countries exhibited the highest agricultural production with the lowest consumption Table 1. Variables of the agricultural sector during 2012 for 18 LAC countries Country Fertilizers Capital stock Labor Land Agricultural production Agricultural Emissions (CO2eq) Argentina 1 403 678 70 471 1 388 149 254 39 609 904 105 825 Belize 10 689 227 32 160 185 608 319 Bolivia 35 294 10 805 2 056 37 596 3 732 400 23 342 Brazil 13 195 074 233 127 10 478 275 607 145 545 149 444 704 Chile 527 415 22 692 957 15 755 8 583 679 11 518 Colombia 1 178 948 112 632 3 484 42 618 14 014 336 52 263 Costa Rica 172 725 2 365 317 1 812 3 061 382 3 394 Dominican Republic 59 571 11 024 438 2 352 2 824 180 7 692 Ecuador 291 420 21 182 1 219 7 507 7 335 057 13 734 El Salvador 121 630 2 454 577 1 572 1 196 889 2 826 Guatemala 266 966 10 679 2 148 3 809 4 744 677 8 387 Honduras 84 806 4 536 662 3 235 2 191 396 5 851 Mexico 1 814 509 126 536 7 708 106 705 38 098 572 82 661 Nicaragua 76 914 6 316 343 5 103 1 609 347 7 759 Panama 23 424 3 927 244 2 257 990 944 3 489 Paraguay 367 780 10 207 851 21 500 4 282 544 25 127 Peru 432 667 24 533 3 728 24 332 9 613 351 23 450 Uruguay 338 213 23 312 184 14 230 4 391 247 23 848 Source: According to the FAOSTAT and Nin-Pratt et al. (2015) 81 Agric. Econ. – Czech, 64, 2018 (2): 74–88 Original Paper doi: 10.17221/260/2016-AGRICECON of inputs, thus improving their agricultural competitiveness. They are followed by Nicaragua, El Salvador and Chile, with relatively small performances in terms of their operational efficiency, with efficiency levels of 0.9908, 0.9888 and 0.9882, respectively. This indicates that these countries made progress in improving their operational efficiencies by attaining a high operational efficiency of agricultural production. These three countries are followed by Paraguay with an efficiency score of 0.9726. Finally, Peru and Colombia had a lower operational efficiency, with efficiency levels of 0.9351 and 0.8604, respectively. Figure 2 shows the environmental efficiency of the evaluated countries in relation to their performance in reducing agricultural emissions of CO2 eq, which is measured using model (6). The results indicate that 11countries, including Argentina, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, El Salvador, Guatemala, Mexico and Peru attained the maximum efficiency level (1.0000), i.e., these countries have per- Table 2. Efficiency measurements of the agricultural sector for 18 LAC countries in 2012 Country Operational effi - ciency Environmental effi - ciency Unifi ed effi ciency as nonlinear programming Unifi ed effi ciency as mixed integer programming Best effi ciency levels in all the effi ciency measurements: Argentina 1.0000 1.0000 1.0000 1.0000 Belize 1.0000 1.0000 1.0000 1.0000 Bolivia 1.0000 1.0000 1.0000 1.0000 Brazil 1.0000 1.0000 1.0000 1.0000 Costa Rica 1.0000 1.0000 1.0000 1.0000 Mexico 1.0000 1.0000 1.0000 1.0000 Highest level of unifi ed effi ciency, but showing some ineffi ciency level in the other two measurements: Chile 0.9882 1.0000 1.0000 1.0000 Dominican Republic 1.0000 0.9716 1.0000 1.0000 Ecuador 1.0000 0.9740 1.0000 1.0000 Ineffi ciency scores under the unifi ed effi ciency measurement: Panama 1.0000 0.9883 0.9985 0.9985 El Salvador 0.9888 1.0000 0.9904 0.9904 Honduras 1.0000 0.9819 0.9877 0.9877 Nicaragua 0.9908 0.9673 0.9849 0.9849 Guatemala 1.0000 1.0000 0.9660 0.9660 Paraguay 0.9726 0.9206 0.9390 0.9390 Peru 0.9351 1.0000 0.9388 0.9388 Uruguay 1.0000 0.9186 0.9358 0.9358 Colombia 0.8604 1.0000 0.8784 0.8784 Average 0.9853 0.9846 0.9789 0.9789 0.80 0.85 0.90 0.95 1.00 Argentina Belize Bolivia Brazil Costa Rica Dominican Rep. Ecuador Guatemala Honduras Mexico Panama Uruguay Nicaragua El Salvador Chile Paraguay Peru Colombia Figure 1. Operational efficiency 0.80 0.85 0.90 0.95 1.00 Argentina Belize Bolivia Brazil Chile Colombia Costa Rica El Salvador Guatemala Mexico Peru Panama Honduras Ecuador Dominican Rep. Nicaragua Paraguay Uruguay Figure 2. Environmental efficiency 82 Original Paper Agric. Econ. – Czech, 64, 2018 (2): 74–88 doi: 10.17221/260/2016-AGRICECON formed well in environmental efficiency compared to the other countries that were evaluated in this study. They are followed by Panama and Honduras, with efficiency levels of 0.9883 and 0.9819, respectively. Thus, the performance of these countries in reducing agricultural emissions of CO2 eq. is comparatively high. These countries are followed by Ecuador, the Dominican Republic and Nicaragua, with efficiency levels of between 0.96 and 0.77. Paraguay and Uruguay had the lowest environmental efficiencies: 0.9206 and 0.9186, respectively. In the preliminary results, operational and environmental efficiencies were treated separately. Still, the main objective of this study was to measure the unified efficiency because a production activity produces not only good outputs but also bad outputs. The unified efficiency is the integration of both the operational and environmental efficiency and provides a comprehensive evaluation of the performance of the agricultural sector by taking into account the efforts towards achieving specific agricultural production goals as well as, in an appropriate form, the environmental regulation targets that aim to reduce the agricultural emissions of CO2 eq. Figure 3 shows that Argentina, Belize, Bolivia, Brazil, Chile, Costa Rica, the Dominican Republic, Ecuador and Mexico attained the highest unified (operational and environmental) efficiency level (1.000), i.e., to improve their efficiency in agricultural activity and to satisfy the environmental targets, these countries pay attention not only to obtaining the highest agricultural production, but also to reducing the agricultural emissions of CO2 eq. They are followed by Panama, El Salvador, Honduras and Nicaragua, with 0.9985, 0.9904, 0.9877 and 0.9849, respectively. The results show that these countries made progress in improving their agricultural goals by attaining a comparatively high unified (operational and environmental) efficiency. They are followed by Guatemala, with an efficiency score of 0.9660. Paraguay, Peru, Uruguay and Colombia had the lowest unified efficiencies, which ranged between 0.87 and 0.93. Table 2 indicates that in 2012, the averages of the operational efficiency (0.9853) and environmental efficiency (0.9846) were relatively high when measured separately. However, the unified efficiency (0.9789) is still of a lower magnitude than the operational efficiency and environmental efficiency. In any case, it can be seen in Figure 4 that the operational efficiency became more balanced than the environmental and unified efficiency among the 18 LAC countries. This finding indicates that the 18 LAC countries have been primarily oriented towards satisfying their agricultural production goals and, secondly, their agriculturalenvironmental targets. The radar chart (Figure 4) and Table 2 show three groups of countries. The first includes Argentina, Belize, Bolivia, Brazil, Costa Rica and Mexico. The second group is made up of Chile, the Dominican Republic and Ecuador. The last group includes Panama, El Salvador, Honduras, Nicaragua, Guatemala, Paraguay, Peru, Uruguay and Colombia. The first group exhibits the best status, its countries having attained the maximum efficiency under the three models when compared to the other countries analysed. Nevertheless, achieving the maximum efficiency does not mean that they have reached the maximum efficiency in a real situation of agricultural productivity and environmental performance and, 0.80 0.85 0.90 0.95 1.00 Argentina Belize Bolivia Brazil Chile Costa Rica Dominican Rep. Ecuador Mexico Panama El Salvador Honduras Nicaragua Guatemala Paraguay Peru Uruguay Colombia 0.75 0.80 0.85 0.90 0.95 1.00 Argentina Belize Bolivia Brazil Costa Rica Mexico Chile Dominican… Ecuador Panama El Salvador Honduras Nicaragua Guatemala Paraguay Peru Uruguay Colombia Operational efficiency Environmental efficiency Unified efficiency Figure 3. Unified (operational and environmental) efficiency Figure 4. Comparison of the efficiency measurements for 18 LAC countries