Production factors, technical, and economic efficiency of soybean (Glycine max L. Merr.) farming in Indonesia

2.1 Production factors

The production factor analysis used the stochastic Frontier Cobb-Douglas production function model. The stochastic frontier model expands the original deterministic model to measure stochastic effects within the production limit [14]. The model of the stochastic frontier production function is as follows:

Coelli [15] briefly presented the stochastic frontier production function equation as follows:

where Y _it is the production of the ith farmers at the tth time; X _it are the variables of input used by the ith farmers at the tth time; β _i are the parameter variables to be estimated; v _it are the random variables related to external factors (climate, pests); the distribution is symmetrical and normal (v _it ∼ N(0,σ _v ²)); and u _it are the non-negative random variables, assumed to affect the level of technical inefficiency, related to internal factors, and the distribution is half-normal (u _it ∼ |N(0,σ _v ²|).

The model for estimating the production function in soybean farming is as follows:

where Y represents the production of soybean (kg), β ₀ represents the constant, X ₁ represents the land area (ha), X ₂ represents the seed use (kg), X ₃ represents the urea fertilizer (kg), X ₄ represents the NPK – nitrogen, phosphor, and potassium fertilizer (kg), X ₅ represents labor (days of work), v _i − u _i represents the error term ( u _i ), the effect of technical inefficiency of the model; β _i represents the coefficient of estimated parameters, where i = 1, 2, 3, … n.

Expected coefficient values were β ₁, β ₂, β ₃, β ₄, β ₅, > 0.

Meanwhile, the determinant of the parameter values for the distribution of production inefficiency effects in this research can be built using the following model:

where u _i represents the production inefficiency effect, δ ₀ represents the constant; Z ₁ represents the respondent’s age (years); Z ₂ represents the education level (years); Z ₃ represents the soybean farming experience (years); Z ₄ represents the number of household members (people); Z ₅ represents the dummy of seed certification (0: not certified, 1: certified); w _it represents the error term; and δ _i represents the coefficient of estimated parameters, where i = 1, 2, 3, … n.

Expected coefficient values were δ ₁, δ ₂, δ ₃, δ ₄, δ ₅ < 0.

2.2 TE

TE is the comparison between actual and potential production levels that can be achieved [16]. The TE rate can be measured using a variance ratio as follows [17]:

where

When γ is close to 1, σ _v ² is close to zero, and v _i is the predominant error, it implies technical inefficiency. The difference between the actual and potential productions indicates the inefficiency in production.

Meanwhile, based on Soekartawi [18], TE can be measured with the following equation:

where TE is the technical efficiency level, iY is the ith production (output), and iŶ is the estimated production in the ith observation obtained from the production function of Frontier Cobb-Douglas.

Measurement of TE from the production input side is the ratio of frontier input or costs to observation input or costs. The general equation of TE achieved by the ith observation at the tth time is defined as follows [19]:

where 0 < TE _i < 1.

2.3 Allocative efficiency (AE)

AE (price efficiency) shows the relationship between cost and output. AE can be achieved if a profit can be maximized by equating the marginal product of each production factor with its price [16]. According to Nicholson [20], price efficiency is achieved when the ratio between the marginal productivity value of each input (NPMx) and the input price (Px) or ki equals 1. This condition requires that NPMx equals Px or can be written as follows:

or

In fact, NPMx is not always the same as Px, but according to Sukartawi [16]:

a. (NPMx/Px) > 1 means that X input is inefficient; input X needs to be added to be efficient.

b. (NPMx/Px) < 1 means that input X is inefficient; input X needs to be reduced to be efficient.

c. NPMx/Px = 1 means that input X is efficient and maximum profit is obtained.

2.4 EE

EE is the multiplication of TE and AE (price efficiency). Therefore, EE can be written as follows:

where EE is the economic efficiency, TE is the technical efficiency, and AE is the allocative efficiency.

EE is defined as the ratio of the total minimum production costs (C*) observed to the actual total production costs (C) [21].

where 0 < EE < 1.

3.1 Factors affecting soybean production

The results of stochastic frontier model estimation described the best performance of farmers as respondents at the level of existing technology. Estimation was carried out using the maximum-likelihood estimate (MLE) method. Variables significantly influencing soybean production were land area and the use of urea fertilizer at α-level of 1%, NPK fertilizer at α-level of 5%, and seeds at α-level of 10%. The use of labor had no significant effect on soybean production (Table 1).

Land area and use of urea fertilizer had positive signs and significant effects on soybean production at a 99% confidence level (α-level of 1%) (Table 1). A coefficient value of 0.83 indicated that an additional 1% of land area for soybean farming (where other inputs remain the same) could increase soybean production by an additional 0.83%. It implies that if farmers want to increase soybean production, the land area cultivated by farmers must be extended. This finding follows previous research stating that increasing the land area would positively affect soybean productivity and production [22–27]. Furthermore, a study in China showed that the land area per capita parameter positively affected TE [28].

A coefficient value of urea fertilizer of 0.02 indicated that an additional 1% of urea fertilizer (where other inputs remain the same) could increase soybean production by an additional 0.02%. It implied that urea fertilizer should be increased to enhance soybean production. This result concurs with the previous studies in Ghana and China [25,28]. Moreover, previous studies [29,30] found that using fertilizer positively affected the EE of soybean farming in Nigeria and Myanmar.

The use of NPK fertilizer significantly affected soybean production at a 95% confidence level (α-level of 5%) and had a positive sign. A coefficient value of 0.01 indicated that an additional 1% NPK fertilizer could increase soybean production by 0.01%. The implication is that NPK fertilizer should be increased to enhance soybean production. NPK fertilizer contains nitrogen, phosphate, and potassium. Phosphate is important for strengthening plant tissue, especially stems, to prevent plants from falling and speeding up the process of seeds ripening [5], while potassium is important for plant growth and development [31] and produces higher seed quality [32].

Using soybean seeds significantly affected soybean production at a 90% confidence level (α-level of 10%). The positive sign with a coefficient value of 0.11 implied that every 1% additional seed could increase soybean production by an additional 0.11%. Previous studies [22,28,30,33–35] found that an increase in the number of seeds significantly and positively affected productivity and soybean production. Therefore, if farmers want to increase soybean production, the input of soybean seeds must be increased according to the needs of the soybean planting area.

3.2 Soybean production inefficiency

A variable that at a 90% confidence level had a significant effect and positive sign on the soybean production inefficiency was the soybean farming experience. The farmer’s age, educational level, number of household members, and dummy types of seeds did not significantly affect the inefficiency of soybean production. This finding contrasts with the previous study [36], which stated that the older the farmer and the higher the educational level, the soybean production tends to become more inefficient. Furthermore, Asodina et al. [22] found that the high involvement of young people in soybean production could affect the sustainability of soybean cultivation. The number of household members and dummy types of seed variables with negative signs indicated a tendency that the greater number of household members and the use of certified seed types, the more efficient the soybean production. The average efficiency result was 77.05% (Table 2). The value was categorized as efficient because it was greater than 0.70, the limit of efficiency [15].

The experience in soybean farming had a positive coefficient value of 0.022, meaning that the more experienced farmers in soybean farming, the more production inefficiency increased. It is presumably because the longer farmers experience soybean farming, the more difficult it is for them to accept new technology. It could be because farmers feel that they are already experts in soybean farming and more comfortable with the existing farming system that has been implemented [33]. This finding is in contrast with the previous studies [22,33,37,38], which found that the experience of farmers in soybean production greatly influences production efficiency, and conversely, the low experience of farmers can be a challenge in soybean production. The study by Mariyono [5] stated that increasing farmers’ capacity has enhanced soybean production. Therefore, social interaction and providing information when promoting technology are indispensable [39]. The other study revealed that the role of extension in disseminating varieties and technology positively impacts technology adoption at the farm level [37] and further influences the TE of soybean farming [40].

3.3 TE of soybean farming

The more experienced a farmer in soybean farming, the less efficient the soybean production was (Table 2). Farmers with 1–5 years of experience in soybean farming had the highest average TE score of 99.07%, while soybean farmers with experience of 6–10 years and 11–15 years, respectively, had an average TE score of 77.38% and 72.25% (Table 3). However, because the value was greater than 0.70 as the limit of efficiency [15], it can be said that soybean farming in the Tabanan Regency of Bali Province was categorized as technically efficient. This finding aligns with the previous studies [24,41], which revealed that the average TE of soybean farming in Indonesia was 81 and 76.7%, respectively, and in Ethiopia was 72.81% [42].

3.4 AE and EE of soybean farming

AE and EE were obtained by calculating the ratio of input prices to output prices. Soybean farming with farmer experience of 1–5 years resulted in an average value of AE of 0.659. It indicated the inefficient AE of soybean farming. The complete distribution of TE, AE, and EE of soybean farming among farmers with 1–5 years of farming experience is shown in Table 4.

The combined effect of TE and AE efficiencies showed that the average EE of soybean farming in a group of farmers with 1–5 years of experience was 0.654. It indicated that soybean farming was not yet economically efficient. The previous study by Setiawan [43] showed an AE of 1.73% and an EE of 1.66%. The cause of low EE was the low AE, even though the TE was relatively high. According to Henderson [44], TE or AE differences significantly affected all productivity indicators. The low AE, which caused low EE, indicated that soybean farming in a group of farmers with 1–5 years of experience has been unable to produce the maximum profit. It was likely the cause of farmers’ decreased interest in cultivating soybean.

The distribution of AE and EE among a group of farmers with soybean farming experience of 6–10 years was less than 0.50. It showed that allocative and economically, soybean farming carried out by farmers with experience in soybean farming for 6–10 years was inefficient because it could not provide the maximum profit, even though technically, most of the farmers were at a high level of efficiency (Table 5). The combined effect of TE and AE showed that the average EE of soybean farming in a group of farmers with 6–10 years of experience was 0.194, much lower than that of farmers with 1–5 years of experience. It meant that soybean farming with 6–10 years of farmers’ experience was not economically efficient and could not provide the maximum profit.

The distribution of AE and EE among a group of farmers with 11–15 years of experience in soybean farming was less than 0.50 (Table 6). It meant that allocative and economically, soybean farming of all farmers with 11–15 years was inefficient because they were unable to produce the maximum profit.

The combined effect of TE and AE showed that the average EE of soybean farming in the group of farmers with 11–15 years of experience was 0.133, much lower than the groups of farmers with 1–5 years and 6–10 years of experience. It implied that soybean farming was not economically efficient. As in the case of other farming experience groups, the cause of low EE was the low AE, which indicated that soybean farming could not provide the maximum profit. It could be said that the longer the soybean farming experience of farmers in the Tabanan Regency of Bali Province, the lower the level of TE, AE, and EE. This finding contrasted with several previous studies in Nigeria and Ethiopia, which found that farming experience had a significant positive effect on EE [29] and AE [45], as well as being a social variable that had a significant effect in reducing economic inefficiency among soybean farmers [42].

The low EE in soybean farming in Tabanan Regency, Bali Province, Indonesia, based on the group of farmers’ experiences, showed that soybean farming was not economically efficient. A solution to reduce production costs can be implemented to achieve better efficiency value. Another study conducted in Nganjuk Regency, East Java Province, Indonesia, showed that for soybean farmers who were still unable to achieve EE, the opportunity for saving production costs to achieve EE was high [46]. Effectively using inputs was important in increasing farmers’ income and reducing soybean production costs [47].