Assessment of Profit Efficiency of Smallholder Maize Farmers in Limpopo Province, South Africa: A Stochastic Frontier Approach

The study was conducted in Limpopo (Fig. 1), one of South Africa’s provinces (Fig. 2), which has a population of 5,854,000 (1 million inhabitants) and is located in the northern part of the country bordered by Zimbabwe, Botswana, and Mozambique. It has an area of 125,754 km² and is divided into five districts: Capricorn, Vhembe, Sekhukhune, Mopani, and Waterberg.

The survey included all the districts. The area is famous for wildlife and Bushveld, and it includes a portion of the Kruger National Park. Polokwane, formerly known as Pietersburg, is the capital city of the Limpopo province.

The Department of Agriculture in Limpopo provided a database containing the details of the smallholder maize farmers in the specified area, as of November 2020. For this study, 307 smallholder maize growers were selected to take part, using a stratified random sampling method encompassing all five districts in the province. The sample size was determined by the Kreje and Morgan formula as follows:

The formula is constructed as follows: S=X2NP(1−P)d2(N−1)+X2P(1−P) S = \frac{{{X^2}NP\left( {1 - P} \right)}}{{{d^2}\left( {N - 1} \right) + {X^2}P\left( {1 - P} \right)}} Where:

S – required sample size

The sample size was then stratified according to the 5 districts/geographical with different numbers of farmers, hence the different sample sizes presented in Table 1. A simple random sampling was employed to select each district’s respective samples. The Department of Agriculture classifies all farmers as smallholder farmers, therefore, having some common characteristics.

Primary data was collected using a semi-structured questionnaire with questions aligned with the study’s objective. The questionnaire included both open-ended and closed questions. It was divided into four sections, namely, demographic and socio-economic characteristics, production, marketing, and challenges facing the farmers. The primary data utilised in the analysis was obtained through face-to-face interviews with 307 smallholder maize farmers in the research area. The interview tool was validated by two agricultural economists at the University of South Africa and piloted on 15 farmers not included in the main survey.

Primary data was collected from smallholder maize farmers, and it was carefully coded, processed, arranged, and analysed. STATA 17, a software for statistics and data, was used to conduct the data analysis.

The study utilised the stochastic profit frontier approach, as outlined by Ojo et al. (2009) and Oguniyi (2008), who employed the Battese and Coelli (1995) model to formulate a profit function that is presumed to conform to the stochastic frontier concept. The profit frontier model commences by examining a stochastic profit function with a multiplicative disturbance term as depicted in equation (1). (1) π=f(pi, Zikβi)e(Ei) \pi = f\left( {{\rm{pi}},{Z_{\rm{i}}}{\rm{k}}{{\rm{\beta }}_{\rm{i}}}} \right)e\left( {{E_{\rm{i}}}} \right)

The normalised profit, represented by π, is calculated by subtracting the variable cost from the gross revenue and then dividing the result by the price of the output. The normalised price of variable inputs used by the farm, denoted by pi, is obtained by dividing the cost of these inputs by the price of the output. The level of the kth fixed factor on the farm is denoted as Z_i. The vectors of parameters are represented by β_i. An error term, denoted by e_i, is utilised. Additionally, the stochastic disturbance term, E_i, consists of two independent elements, V, and U. (2) Ei=Vi+Ui {E_{\rm{i}}} = {V_{\rm{i}}} + {U_{\rm{i}}} where

Vi follows a NID(0, δ²) distribution, while U_i represents profit inefficiency in a one-sided disturbance form and is independent of V_i.

The stochastic profit function model is applicable for analysing cross-sectional data. It estimates both the individual profit efficiency of the respondents and the factors influencing the profit efficiency at the same time. By combining equations (1) and (2), as outlined in equation (3), the farm’s frontier is determined. (3) π=f(Pi,Zik,β)e(U+V) {\rm{\pi }} = {\rm{f}}\left( {P{\rm{i}},{Z_{\rm{i}}}{\rm{k}},{\rm{\beta }}} \right){{\rm{e}}^{\left( {{\rm{U}} + {\rm{V}}} \right)}}

The ratio of predicted actual profit to the predicted maximum profit for a maize farmer defines the profit efficiency of an individual farmer, as shown in equation (4).

Profit efficiency (Eπ) (4) ππ max = exp exp [π(p,z) exp (1nV) exp ( ln μ)θ exp [π(p,z0] exp (1nV)θ \frac{{\rm{\pi }}}{{{{\rm{\pi }}^{{\rm{max}}}}}} = {\rm{exp}}\frac{{{\rm{exp}}[{\rm{\pi }}\left( {{\rm{p}},{\rm{z}}} \right){\rm{exp}}\left( {{\rm{1nV}}} \right){\rm{exp}}\left( {{\rm{ln\mu }}} \right){\rm{\theta }}}}{{{\rm{exp}}[{\rm{\pi }}\left( {{\rm{p}},{\rm{z}}0} \right]{\rm{exp}}\left( {{\rm{1nV}}} \right){\rm{\theta }}}}

Where π = predicted actual profit and π^max =predicted maximum profit

The frontier profit function can be estimated using the maximum likelihood technique, considering the density function of U_i and V_i. The expected value of π falls within the range of 0 to 1. When U_i equals 0, indicating that it lies on the frontier, the farmer can achieve the maximum potential profit based on the price and fixed factors. However, if U_i is greater than 0, the farm operates inefficiently, leading to reduced profit. To estimate all parameters simultaneously, the stochastic frontier function with behavioural inefficiency components, as described by Coelli et al. (2005) and Ojo et al. (209), was utilised in a one-step maximum likelihood estimation procedure. The specific Cobb-Douglas functional form for the maize producers in the study area was explicitly specified in equation (5). (5) InY=Inβ0+β1InX1+β2InX2+β3InX3++β4InX4+β5InX5+β6InX6+βnInXn+εi \begin{array}{*{20}{c}} {InY = In{{\rm{\beta }}_0} + {{\rm{\beta }}_1}In{X_1} + {{\rm{\beta }}_2}In{X_2} + {{\rm{\beta }}_3}In{X_3} + }\\ { + {{\rm{\beta }}_4}In{X_4} + {{\rm{\beta }}_5}In{X_5} + {{\rm{\beta }}_6}In{X_6} + {{\rm{\beta }}_{\rm{n}}}In{X_{\rm{n}}} + {{\rm{\varepsilon }}_{\rm{i}}}} \end{array} where:

ln – logarithm to base

The model considered various factors assumed to impact farmers’ efficiency in order to determine profit efficiency. The factors influencing profit inefficiency (U_i) were modelled in the following manner: (6) Ui=β0+β1X1+β2X2+β3X3+β4X4+β5X5++β6X6+β7X7+β8X8+ε \begin{array}{*{20}{c}} {{U_i} = {{\rm{\beta }}_0} + {{\rm{\beta }}_1}{X_1} + {{\rm{\beta }}_2}{X_2}{\rm{ + }}{{\rm{\beta }}_3}{X_3}{\rm{ + }}{{\rm{\beta }}_4}{X_4} + {{\rm{\beta }}_5}{X_5} + }\\ { + \,{{\rm{\beta }}_6}{X_6} + {{\rm{\beta }}_7}{X_7} + {{\rm{\beta }}_8}{X_8} + {\rm{\varepsilon }}} \end{array}

The explanatory variables considered are:

X₁ – age (in years)

A check for multicollinearity was conducted to ensure that there is no multicollinearity among the variables chosen in the model. The suitability of variables for econometric analysis was assessed for multicollinearity using the variance inflation factor (VIF). The VIF values for the selected variables related to profit efficiency/inefficiency can be found in Table 2. For the test, the total gross profit was used as the dependent variable, while the other variables were used as independent variables. As per the findings, the index variables for both efficiency and inefficiency had an average VIF of 1.846 and 1.304, respectively. This suggests that multicollinearity was not present.

The variance parameters for the frontier profit function show statistical significance at a 1% level (p < 0.001), indicating a strong fit and confirming the accuracy of the specified error term’s distributional assumptions.

The stochastic profit frontier model estimated fourteen parameters, including ten from the Cobb-Douglas frontier model and four explanatory variables believed to impact profit efficiency scores. The cost of fertiliser had a negative impact, indicating that a 1% increase in fertiliser cost would decrease profit efficiency, which is consistent with Mujuru et al. (2022) study. Labour and herbicide costs were not significant, suggesting no direct relationship with farmer profitability. However, the negative coefficient for labour cost implies that reducing hired labour expenses would improve farmer profit efficiency, in line with Jonah et al. (2020) findings. Oyewole and Oyewole (2023) also found a positive relationship between labour cost and profit efficiency. The remaining two parameters were associated with the distribution of μi and vi. Among the ten variables modelled for profit efficiency, four were statistically significant. Water, tractor, and maize processing costs were significant at the 1% level (p < 0.001), while transport cost was significant at the 10% level (p < 0.10). These findings align with Anang and Shafiwu (2022) results, indicating that tractor costs negatively impact profit efficiency among smallholder maize farmers. The coefficients of all statistically significant variables were negative, suggesting that reducing the cost of these variables would improve profit efficiency. The results indicate that a 1% increase in water, transport, and maize processing costs would lead to respective decreases in profit efficiency of 0.160, 0.126, and 3.893. It is worth noting that these factors impact in isolation on the performance of farmers, as they access them differently. For instance, some farmers do not have access to water at all, while some do have access. Moreover, in terms of the transportation to the informal market where they sell, some farmers struggle with transportation because it is expensive, while others have their own transportation.

The inefficiency model results indicated that the respondents’ farming experience and level of education had negative coefficients and were statistically significant. Farming experience was significant at a 5% level (p < 0.05), while education was significant at a 10% level (p < 0.10). In a study by Dabessa et al. (2021), it was found that educational level positively impacts farmers’ profitability. Conversely, a study by Amesimeku and Anang (2021) revealed that years of farming experience have a positive correlation with farmers’ profit efficiency, supporting the current study’s findings. These results align with Okorie et al. (2021) findings, which highlighted that educational level and years of farming experience positively influence profit efficiency to a significant degree. Therefore, it can be concluded that as these variables decrease, maize farmers’ profit inefficiency increases. Thus, maize farming experience and higher levels of education are crucial for profitability. Farmers with higher educational levels and more maize farming experience registered lower profit losses compared to those with lower education levels and less maize farming experience. Age and household size were found to be statistically insignificant, indicating that these factors did not affect farmers’ profit inefficiency. This contrasts with Ngeno’s (2024) study, where household size was negatively and statistically significant, suggesting that larger households may have more labour resources and be more motivated to work, ultimately improving profit efficiency. Adnan et al. (2021) noted that age is a factor affecting profit efficiency among maize farmers, differing from the current study’s findings.

Table 3 presents the profit efficiency distribution of smallholder maize farmers. The findings reveal that profit efficiency varied from 0 to 0.90, with an average of 0.612. This suggests that the average maize farmer could potentially increase their profit by 38.8%, by enhancing technical and allocative efficiencies. It indicates that there are opportunities for farmers to boost their farm incomes, ultimately contributing to alleviating poverty. This could represent a significant achievement for many farmers, given that maize farming is their primary source of income. To achieve this, government intervention is needed to assist farmers. The government can help by educating farmers about external factors like market access and climate change issues. The government can also provide training to farmers on proper maize production practices, which include the use of better fertilisers and seeds, as well as the use of agrochemicals, which will improve their output. These can significantly reduce inefficiencies in maize production and improve profitability.