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INTRODUCTION
Yam is a tropical plant of African and Asian origin, is monocotyledonous, is in the Dioscoreaceae family, and has a reserve organ that is a tuber. It has six genera, including Dioscorea, which is the most important with 600 identified species although only 12 species are edible (Coursey 1967, cited by Thurston, 1989). The characteristics change according to the variety. Those in the Dioscorea genus are generally dioecious (Santos and Macêdo, 2002). The plant appears as a vine, with aerial tubers called bulblets and underground tubers (Hata et al., 2003). The latter are the useful part and are used for consumption and propagation of new crops (Cabrera et al., 2008).
According to the FAO (2021), in 2018, the African continent was the largest producer worldwide, with close to 97% of production (70.9 million tons). In contrast, the Americas represented 2.0% of global production (1.4 million tons) (Vargas, 2019). Colombia, according to Agronet (2019), had an area of 27,099 ha in 2018, with a production of 315,434 t and an average yield of 9 t ha -1. The Caribbean region provided 96% of the yam cultivated area. According to Reina (2012), Colombia had the highest yield rate in the world for yam cultivation, as well as the production characteristics: seed quality, planting type, soil type, and varieties or clones but current statistics show low production.
According to Farrell (1957), agricultural success is achieved when maximum production is achieved through the best combination of inputs or elements. Technical efficiency is defined as a strategy that guarantees that an organization or productive unit obtains maximum levels of production by using fewer physical units of each input without compromising the quality of the product. In this case, it is proposed that yam production will be more efficient with greater amounts of yams in a productive unit, with a smaller number of inputs. Economic efficiency studies evaluate whether producers carry out activities in the best possible way, making the most of the resources available to them (De los Ríos, 2006).
The Cobb Douglas production function has been used in other studies to determine the technical efficiency of agricultural production (Martínez, 2002; Bakhsh et al., 2006; Erhabor and Emokaro, 2007). It shows the relationships of a product and the variations of the inputs, demonstrating the contribution of each input and was presented as statistical evidence by Charles Cobb and Paul Douglas in 1928. The empirical evidence of the theory of production through the Cobb Douglas function determines the contributions of each factor of production and approaching the production frontier, the economies of scale and efficiency understood as the result of the rational use of production factors.
For this reason, this paper aimed to analyze the efficiency of yam production in the Caribbean Region of Colombia, determine the elements that could increase it, and reveal whether yam production is technically efficient and which elements explain this situation.
The African continent leads yam production and the investigation of technical efficiency in yam, it should be noted that in Colombia the presence of these studies was not evidenced and that is why the works from Africa are taken as a reference for this work. For example, Orewa and Izekor (2012) analyzed the efficiency of yam production in the State of Edo in Nigeria and produced a model that can be replicated to evaluate different production systems. Aliyu and Shelleng (2019) also analyzed the technical efficiency and economic efficiency of yam producers. They used the Envelopment Analysis of DEA data results and showed that 57% of farmers had a technical efficiency of 0.81 and more, while 43% operated with an efficiency level lower than 0.81. The mean technical efficiency of the 100 farmers sampled in the study area was 0.78. The farmer with the best practices had an efficiency of 1.00, while 0.37 was the lowest. In terms of economic efficiency, the efficient producer saved about 5% of production costs.
This study aimed to demonstrate the empirical evidence of the theory of production with the Cobb Douglas function, which determines the contribution of each production factor and approaches the production frontier; the economies of scale and efficiency are understood as the result of the rational use of production factors.
Orewa and Izekor (2012) showed that the production inputs that could increase yam production include expansion of farmland, increased use of yams, fertilizers, and labor. The educational level of the respondents, the size of the household and the agricultural experience were the socioeconomic characteristics that had a significant and negative effect on the technical inefficiency of the farmers.
In the case of yams in the Caribbean Region, this evaluation looked at the extent using more land to expand production in fiscal units could lead to an efficient process, as well as some inputs such as fertilizer and labor. This study specifically sought to estimate the technical efficiency of yam producers in the producing areas of the Caribbean Region and the factors that determine the production efficiency levels.
This article introduces the topic highlighting statistical data on yam production in the world, in Latin America and in Colombia and then shows the theoretical model and the mathematical model of the Cobb Douglas function. The results of the estimates, the calculations of technical efficiency, and the ideas are presented as conclusions resulting from the discussion of the data and comparison with other studies carried out in other places in the yam production system for technical efficiency.
MATERIALS AND METHODS
The study area was in the Caribbean region in the Sabanas microregions, the coastal zone of Cordoba, and Montes de Maria (Colombia). The Colombian Caribbean is located between 12º60' and 7º80' N and 75º and 71º W. It has an area of 536,574 km2. The average temperature is close to 25ºC. Throughout the different months of the year, with a maximum of 30°C in summer and a minimum of 22 or 23°C in winter. The climate is quite humid, with relative humidity that fluctuates between 77 and 82.5%. Rains in the Departments of Cordoba, Bolivar, and Sucre, in northern Antioquia, and in the Sierra Nevada de Santa Marta continue to be frequent and abundant, on average above 1,380 mm/year (IDEAM, 2021).
This article analyzed the technical efficiency of yam cultivation in the producing regions of the region such as: The Savannah Region of Cordoba, Sucre and Bolivar, the Coastal Region of Cordoba, and the Montes de Maria. The data were obtained with a survey applied to 98 farmers and were used to formulate a stochastic frontier econometric model with an estimation using the Cobb Douglas ordinary least squares method.
The distribution of the municipalities was done taking into account the main producing areas of the crop in the different departments of the Caribbean region (DANE, 2018), such as: Cordoba (Chinu, Cienaga de Oro, Lorica, Los Cordobas, Moñitos, Planeta Rica, Pueblo Nuevo, Puerto Escondido and Sahagun), Sucre (Chalan, Sam After, San Onofre and Toluviejo), Bolivar (Carmen de Bolivar, Maria La Baja, San Jacinto and San Juan de Nepomuceno) and Antioquia (Necocli, San Juan de Uraba and Turbo), for a total of 98 producers.
To determine the sample size, simple random sampling was used for small samples according to Rodríguez (2005). It was based on a universe of 15,398 yam farmers throughout the Caribbean Region, as reported in the official statistics of agricultural evaluations and Agronet (2018). The size of the productive unit was used as a sampling variable, and it was determined that 60% of the producers cultivate less than 2 ha and that 40% cultivate more than 2 ha. The simple random sampling equation for small samples was applied (1):
where, Z was the confidence level chosen in this case, 95%; p was the proportion of the population that contained the sample variable of farmers with more than 2 ha: 60%; q was the difference between the total population and the proportion of the population that did not meet the characteristic (in this case yams destined for the market) farmers with areas greater than 2 ha, and e was the maximum error allowed in the case of 10% n population size.
For this case, the variables in the equation were: N, total population, in this case 15,398 yam-producing farmers in the four departments; Z, the chosen level of confidence, 95% (1.96); p, proportion of farmers with units larger than 2 ha, 60%, 6,159 in total; and q, difference between the total population and the number of farmers with productive units less than 2 ha, 9,239 in total.
92 randomly distributed surveys were used in the area where yams are grown in the four departments of the study area, as shown in table 1.
Table 1. Survey distribution by proportional allocation of the yam Caribbean Region, 2019.
| Departament | Productive units | Percentage | Surveys |
|---|---|---|---|
| Bolivar | 5.558 | 36 | 33 |
| Cordoba | 7.164 | 47 | 43 |
| Sucre | 1.579 | 10 | 10 |
| Antioquia | 1.097 | 7 | 6 |
| Total | 15.398 | 100 | 92 |
Source: Calculations with statistical base, Secretariats of Economic Development The Caribbean Region, 2019.
The data on the number of productive units were obtained from the statistics of the agricultural sector available in the secretariat of economic and agro-industrial development in the yam producing departments, which were related to the data from the DANE (2018).
The information and field data were obtained from a structured survey applied to 98 farmers, composed of 40 variables and 70 questions made up of two blocks of questions. One block was a socioeconomic component (land tenure, experience as a producer, road infrastructure, land topography, family composition, educational level, family sources of income, economic), and the other was for technical activity (planting times, seeds, soil management, water management, pests, diseases, weeds, harvest management, postharvest and sale of the product), The data files were elaborated to feed the model that measured the technical efficiency of the yam production. For the analysis of the survey, descriptive statistics such as frequency distribution were used, in addition to the formulation of the econometric model to estimate the parameters and determine the production gaps.
It should be clarified that the analysis of the technical efficiency of a production system can be done in two ways: one, with the use of DEA (Data Envelopment Analysis) through linear programming techniques, or two, using the stochastic frontier with econometric techniques. Empirical studies, such as that of Rodríguez et al. (2017), have shown that there are no reasons to use one or the other method, and this choice is left to the discretion of the researcher. Here, the stochastic frontier was used with estimates using the Ordinary Least Squares method, which is widely known in empirical research with econometric models such as the one used in this study with the Cobb Douglas function.
The technical efficiency of yam producers in the study area was analyzed with the Cobb-Douglas functional form production function.
The general form of this function was (2):
where, y was total yam production expressed in physical units; k was capital factor1; L was work; α was change in Y when capital factor changes; and β was change in Y when the labor factor changes.
In other words, the change that occurs in production when the units of capital and labor change or the response of production to changes in the use of the factor’s capital and labor. This is a general way of presenting the function in the model they disaggregate the factors of production.
The proposed model of the production function to measure the technical efficiency of yams was:
The general form of the Cobb Douglas function was (3):
where, Y was total production; K was units of capital factor, and L was units of work factor.
The form of the production function model with the factors in natural logarithm was (4):
where, ln was natural logarithm; Y was total yam production expressed in physical units (kg); X 1 was yield kg ha -1; X 2 was labor wages/ha; X 3 was seed amount of seed used/ha; X 4 was fertilizer kg ha-1; b 0 - b 4 were parameters to be estimated (regression coefficients); ε i was compound error term defined as V i - U i, and V i = Random variables were assumed independent of U i, identical and normally distributed with zero mean and constant variance N (0, Sv2).
In the case of inefficiency, factors that negatively affect the efficiency of yam production and have more to do with socioeconomic characteristics such as age, schooling, and experience were considered, according to Orewa and Izekor (2012) (5).
where, y was technical inefficiency; α 1 was age (years); α 2 was educational level (years); α 3 was agricultural experience (years); α 4 was area cultivated in yams in hectares; ε i = error term, and α 0 - α 3 were parameters to be estimated.
The estimation was made with the ordinary least squares method in Eviews v. 8. The original data from the field surveys of expert farmers in yam cultivation in the Caribbean producing regions of Colombia were organized in flat files of Excel for the calculations, graphical analysis and other tools that allow the analysis. They were then transformed into logarithms to measure the elasticity of production in relation to each of the independent variables or to the increase in production factors and the response in yam production, the model was run, inference tests statistics and information analysis.
The technical efficiency was calculated by relating the real yam production obtained in each of the productive units with the potential production, that is, the production frontier (6).
In this case, the natural logarithm of the economies of scale was used, calculated by multiplying the averages of each variable with the standard deviation, arriving at the economies of scale. For potential production, the initial Eq. (6) was replaced with the estimated parameters of each variable, giving the production frontier.
RESULTS AND DISCUSSION
Socioeconomic characteristics of the respondents
Table 2 presents some of the socioeconomic characteristics of the farmers according to the survey applied in the yam-producing areas of the Caribbean region.
Table 2. Socioeconomic characteristics of farmers who grow yams in the Caribbean Region.
| Characteristics | Frequencies |
|---|---|
| Gender | |
| Male | 93 |
| Female | 4 |
| Education | |
| None | 6 |
| Primary | 21 |
| High school | 42 |
| Technical | 15 |
| Professional | 8 |
| Postgraduate | 1 |
| Services | |
| Water | 6 |
| Electricity | 8 |
| Water, electricity, sewage and propane gas | 35 |
| Water, electricity, mobile phone | 30 |
| Mobile phone, water, propane gas | 18 |
| Age | |
| Minimum = 27 years | 1 |
| Maximum = 81 years Average = 57 years | 53 |
| Standard deviation = 13 | 46 |
| Experiences | |
| Mínimun >1 year | 2 |
| Maximun = 70 years | 50 |
| Average = 25 years Standard deviation = 15.2 | 45 |
Source: Surveys to 97 producers, Agrosavia 2019.
According to table 2, yam production in the Caribbean region is carried out in a greater proportion by men who make the decisions to cultivate and the techniques used. Something similar was found in a study by Ekunwe and Orewa (2007), who found that 98.6% of yam producers in Kogi were men. This author and the production of yam in Africa were taken as a reference for finding similar conditions in terms of the organization of production and producer type because Colombia yam species do not have studies on the technical efficiency.
For services, water and electricity predominated in the entire sample; however, more than 90% of those surveyed had cell phones.
It was observed that the yam producers had an advanced age with few young people, with an average age of 57 years, which indicated that the future will see less yam production. This implies that the farmers in the study area were aging. Similar results were found in the study by Orewa and Izekor (2012), where the majority (55.0%) of the respondents were within the age group of 50 to 59 years. The ages of the sampled farmers ranged from 35 to 65 years, with an average age of 51 years.
The predominant type of tenure was ownership in 40% of the sample; the average area devoted to this crop was 1.3 ha, and the mode was 1.0 ha.
Experience was important, which on average was 25 years, guaranteeing security in production and confidence in the information provided in the survey. In the Caribbean Region, experience was greater than in the findings of Orewa and Izekor (2012), where 31% of the respondents had an agricultural experience of 5 to 10 years, and 28.89% had between 11 and 15 years of experience. Similarly, a study by Oluwatusin (2011) reported 14-year experience in the cultivation of yams in the State of Osun in Nigeria.
The results of the regression with the least squares method and the estimation of parameters can be seen in table 3.
Table 3. Results of the regression model Cobb Douglas yam Caribbean Region, 2020.
| Variable | Coefficient | Standard error | Statistical t | Probability, P value |
|---|---|---|---|---|
| C | -24.66196 | 1.217744 | -20.25217 | 0.0000 |
| Yield | 0.0335867 | 0.061149 | 0.586550 | 0.5590 |
| Labor | -0.85319 | 0.080946 | -10.07237 | 0.0000 |
| Seed | 0.033881 | 0.090412 | 0.374736 | 0.7087 |
| Fertilization | -0195797 | 0.077759 | -2.518011 | 0.0135 |
| Cost | 1.846620 | 0.086735 | 21.29035 | 0.0000 |
Source: Calculations based on Agrosavia 2019 fieldwork.
The results of the least squares estimation of the production function in table 3 are interpreted as follows: the value of the intercept, -24.66196, indicates that, with this yam production per hectare with the inputs used, there was inefficiency, and the α value of the function and the estimated parameters were the β values, there will be as many values as explanatory variables and this value indicates that keeping the other variables constant and varying one in particular, the quantity produced changes. However, an increase of one factor does not always cause increases in production in the same proportion, so the sum of the coefficients βs generated a result less than 1, which indicated decreasing returns to scale.
Yam production is determined by the yield expressed in kilograms per hectare, and the higher the yield, the higher production is expected to be. The positive coefficient of 0.0335867 meant that an increase in 1% of the yield saw production increased by 3%. Labor, with a coefficient of -0.85319, meant that labor was underutilized; 78 wages are excessive to cultivate 1 ha of yams. The seed, with a coefficient of 0.033881, indicated that it is a necessary factor, and that, if its use is improved, more quantities of yams could be produced. Fertilization, with a coefficient of -0.195797, meant that fertilizer is being used in an irrational way, so the reaction is opposite, one could think about doing soil analysis and supplying according to the requirements of the crop and the edaphic demand. Finally, the cost of inputs such as herbicides and other production elements, with a coefficient of 1.846620, indicated that elements must be incurred that would generate an additional cost, such as soil analysis, but that would increase production. Under production conditions, maximum efficiency was not reached, with underutilization of some factors such as labor and fertilization.
When comparing the results found in the Caribbean Region of Colombia, there was some coincidence with those of Shehu et al. (2010) in the case of yam production in the State of Benue Nigeria, where the seed was a basic factor that determined the increase in yam production and was closely related to the study by Orewa and Izekor (2012) on the variables labor and fertilizer.
The results for the measurement of the technical efficiency of yams in the Caribbean Region differ to some extent from those of Orewa and Izekor (2012), who worked in the State of Edo in Nigeria for farm size, with a coefficient of 0.495, the yield had 0.540, the fertilizer had 0.040, and the labor had 0.367, which was positive and statistically significant. The cultivated area should be increased with an expected increase in fertilizer and labor, so productivity can be increased.
The results showed that the technical efficiency was 0.77, which indicates that production was inefficient because, for there to be no technological gap, this value must be equal to 1. Also, according to the sum of the elasticities of the variables in relation to production, there were decreasing returns to scale with a value of 0.90. This means that, although there was productivity in the cultivation of yams, the inputs were not used properly, as in the case of labor and fertilizers. On the other hand, efforts should be made to improve the seed component, which is the basis of the entire production process. These results compared with what was found by Orewa and Izekor (2012) with a technical efficiency of 0.69, however for this study with the average yields only a technical efficiency of 0.31 is reached, with a margin of 0.69 for improvement.
In the yam production system in the Caribbean Region and in view of the scope of this work, despite its degree of adaptation, the yields were low, on average 7.8 t ha-1, with a minimum of 2 t ha-1. This was due in part to poor management practices such as seed treatment, which, despite the existence of technologies, had very low adoption. The same happens with varieties that are grown and new varieties with resistance to diseases, but many producers do not use them. Obtaining production with higher yields would have repercussions on food security as this product is consumed daily by the population of the Caribbean Region, as evidenced in the present investigation.
Determinants of technical inefficiency
The inefficiency was studied considering the socioeconomic characteristics of the farmers that were described at the beginning of the results. The results of the estimation with the Ordinary Least Squares are presented in table 4.
Table 4 Regression results for measuring the inefficiency of the yam production system Caribbean Region, 2020.
| Variable | Coefficient | Standard error | Statistical t | Probability, P value |
|---|---|---|---|---|
| C | 3.200428 | 1.677.481 | 1.907883 | 0.0595 |
| Age | -0.741254 | 0.447519 | -1.656362 | 0.1011 |
| Education | -0.352789 | 0.268630 | -1.313293 | 0.1924 |
| Experience | 0.566239 | 0.142375 | 3.977104 | 0.0001 |
| Area in yam | 0.961213 | 0.133686 | 7.190101 | 0.0000 |
Source: Calculations based on Agrosavia 2019 fieldwork.
Table 4 presents the relative efficiency levels, showing which variables caused inefficiency under these conditions. The negative sign of the parameter indicates that the variable positively influenced the efficiency of production; under these conditions, the age coefficient (-0.741254) indicated that the older the farmers are, the more knowledgeable about the crop they have, and they can achieve better results in production than young farmers.
Similarly for education (-0.3352789), farmers with more years of education tend to be more technically efficient in yam production, perhaps because they are less reluctant to change and to accept new knowledge; in this case, less years of study meant less efficiency in cultivation.
These results coincide with similar reports by Pius and Odjuvwuederhie (2006), Ekunwe et al. (2008), Ojo et al. (2009), Shehu et al. (2010) and Oluwatusin (2011), where more years of education increased the probability of adopting efficient technologies that tended to increase; the same conclusion was reached by Martínez and Gómez (2012) in a study on the adoption of soil technologies for cotton in the Upper Magdalena Warm Valley.
Experience in cultivation had a parameter value of 0.566239 with respect to efficiency; it can be inferred that more years cultivating yams meant lower efficiency, perhaps because they are reluctant to change and have difficulty modifying the use of inputs. Contrary results were found in the works of Orewa and Izekor (2012), who showed that the more they experiment, the less inefficiency yam cultivation has in Edo Nigeria. Other results, such as that of Oluwatusin (2011), for yam producers in the State of Osun in Nigeria indicated that, with more years of experience, producers become more specialized.
The area dedicated to the cultivation of yams with a parameter value of 0.961213 indicated that it is not necessarily possible to increase efficiency with greater cultivated area. Here, this applies the principle of productivity to produce more using the same quantities of the factor or to produce the same units of product but spending less. With the same surface, it is possible to obtain greater kilos of yams per hectare.
When interrelating the socioeconomic variables with the techniques for understanding the efficiency of yam cultivation in the Caribbean Region of Colombia, it was observed that there was underutilization of some resources, such as labor, that uses the greatest amount of wages for the nine months of productive cycle. This could be improved if periodic weed controls are carried out in the early phenological stages of the crop. On the other hand, fertilization had effects contrary to what was expected, as explained by the lack of soil analysis and the lack of knowledge of the nutritional requirements of the crop.
The empirical result of the model estimated with ordinary least squares showed that production was inefficient and that there were technological gaps. In the first place, the presence of decreasing returns to scale was evidenced, expressed in the summary of the value of the regression coefficients with a value of 0.9 = β and α values of 0.1; for increasing returns, they must be greater than 1. 1-α represents the inefficiency of production, which is only overcome with yields of 25 t ha-1. It is noted that these results are the product of field work with uncontrolled research, so the results are not conclusive but can be used as a reference for production decisions.
CONCLUSIONS
Even though farmers present some rationality in the allocation of resources, technical efficiency was not fully achieved (0.77), as evidenced in the underutilization of some production factors such as labor and fertilizers. The number of wages was excessive, and the fertilization was carried out without technical criteria that lead to inefficiency in the production process.
The technical inefficiency in yam production with wide production gaps was demonstrated with an average yield of 10 t ha-1, a production gap of 0.60, and a technical efficiency of 0.396, far from optimal production, calculated as 25 t ha-1. Even though the return indicators with current production showed positive net income, the underutilization of resources and the presence of production gaps were evident.
In yam production, the seed is an important input as the basis of all activity. It could be seen that rational management is carried out because it contributes positively to production; however, this participation in efficiency can be increased when new seed production and storage techniques are incorporated.
Within the socioeconomic characteristics of the producers, schooling and experience in cultivation stood out. These two elements are key to fighting inefficiency since it was intended to prove and identify, in this direction the experience of farmers should be taken advantage of and combined with the level of education inasmuch as greater receptivity would be achieved, higher levels of adoption and therefore technical efficiency would increase.
