Technology Gap Efficiency of Small-Scale Rice Processors in Anambra State, Nigeria

Abstract

This paper aims to examine the technology gap efficiency of small-scale rice processors in Anambra State, Nigeria. The research was conducted through a survey of 100 small-scale rice processors in Anambra State. Data were collected with structured questionnaires and analyzed using descriptive, stochastic frontier analysis, stochastic meta-frontier model, and inferential statistical techniques. The study revealed that important variables to rice processing present in the state are paddy, firewood, water, and huller. Concerning the economic-specific factors, the cost of grading and other processing assets contributes to inefficiency. The results equally showed that the technology gap efficiency of small-scale rice processors in the industry is tied to or tangential to the frontier output, meaning that the processors in Anambra State are making use of the best technology available. The average efficiency index for the processors in the industry was 0.506, implying that their output is below potential by 49.4%. The results also revealed the technology gap efficiency for the participating and non-participating processors as 0.924 and 0.983, respectively, meaning that the participants need to close an 8.0% gap, and the non-participants need to close a 2.0% gap. These gaps are caused by the high cost of processing equipment, high cost of input, and inadequate infrastructure, among others contributing factors. The paper concluded that the average meta-technical efficiency (0.498) of small-scale rice processors in Anambra State is low and needs to be improved through the provision of adequate technology, training, and infrastructure to bring the current industrial production capacity to 100.0%.

1. Introduction

1.1. Background to the Study

Rice processing is an important part of Nigeria’s agricultural sector and has the potential to bring significant value to the country. Rice is a staple food in Nigeria and an important food and calorie source for the population. The majority of Nigerians, regardless of ethnic group, rely on rice for their daily diet [1]. Eating one cup of rice (65 g net weight) provides 53 g of carbohydrates. This corresponds to 23.6% of the daily carbohydrate requirement and 10.6% of the daily energy requirement of 2000 calories [2,3]. The reason is that processing promotes local production and consumption of rice. Processing rice can add value to the grain and reduce post-harvest losses. Danbaba identified this as the main cause of rice shortages in Nigeria [4]. Danbaba further clarified that in 2022, not all of the 8 million metric tons (MT) of milled rice, which was consumed at 34.5 kg per capita, was produced in Nigeria [4]. This supports Foyekus’ claim that 44.0% of the 7 million MT of milled rice demanded and supplied in Nigeria in 2018 were imported from other countries [5]. Rice processing or milling is a combination of operations that turn paddy into high-quality white rice and is highly dependent on processors’ management capabilities [6]. In their study, they found that small-scale rice processors were relatively young (36–45 years old), with 11–15 years of processing experience [6]. This level of experience is sufficient to make the farmers understand the basics of small-scale rice processing in the study area. They pointed out that a large household size of 6–10 people lowers the cost associated with wage labor. Ibitoye et al. outlined the steps involved in rice processing from the paddy stage as cleaning, hulling, milling, polishing, grading, sorting, and packing [6]; equally, the returns from small-scale rice processing in their study were affected by the education level and labor availability through a large household size.

The United States Agency for International Development (USAID) submitted that the majority of rice processing in Africa is carried out by small farm-level processors [7]. To date, much of the research has focused on smallholder rice production, with a few studies directed towards milled rice processing in Nigeria. Even the few experts on rice processing focus on profitability rather than looking at the efficiency of the rice industry, which can help policymakers to understand the level of loss in the sector. A study by Akolgoa and Asumboya reported that rice processing is highly profitable and education level has a significant impact on a processor’s profits [8]. Rice processing will help improve Nigeria’s economic stability and the livelihoods of those who depend on the business for survival. Rice processing also has the potential to create jobs within the country and generate additional income for farmers who are in the business of small-scale rice processing options. This will help to reduce poverty within the country and improve the overall standard of living. Rice processing can help reduce the cost of the crop, improve shelf-life, and make it more affordable to the general public [9]. In addition, processing rice can reduce the environmental impact of harvesting. A more efficient processing machine can reduce water and energy usage and reduce the amount of waste. This helps reduce the overall environmental impact of processing activities and ensures that rice remains a sustainable food source for people [10]. Some of the environmental impacts of rice processing include the burning of rice husks, greenhouse gas (GHG) emissions, and the burning of firewood that is unsafe for environmental sustainability [11].

For a technology gap to exist in the rice processing industry, two or more groups of small processors must operate in heterogeneous technological environments or have separate economic opportunities. Ng’ombe argued that differences in economic opportunities and environmental conditions (differences in regional resource endowments) may constrain groups from selecting the best technology from an array of potential technologies, which can result in differences of products obtainable [12]. Brown opined that the cost of digital capital, or the advancement of modern devices to increase production, can introduce technological factors into traditional Cobb–Douglas functions [13]. Scholars hypothesized that one group’s technology must be more advanced than the other to cause differences in production [14]. To fill this gap, representatives of this study included participants in agricultural interventions [Value Chain Development Programme (VCDP)] who received processing training and are exposed to capacity-building and subsidized equipment, and non-participants who have not benefited from the intervention.

The Federal Government of Nigeria was reimbursed by the International Fund for Agricultural Development (IFAD) for the cost of implementing a 6-year FGN/IFAD-supported Value Chain Development Programme [15], to address low productivity issues, insufficient access to means of production and production facilities, inadequate research and extension advisory, inadequate funding and credit, inadequate market and land infrastructure, and post-harvest processing of rice and cassava commodity [3]. Obianefo et al. showed that rice productivity improved by 52.1%, increasing from its baseline of 2.5 MT/ha in 2014 to 4.8 MT/ha in 2019 [3]. In addition, this work will help to confirm whether the improvement in rice production cuts across the processing sub-sector in the study area.

Moreover, several available studies on technology gap efficiency (TGE) are focused on rice production [12,16,17], with none addressing the TGE of rice processing. Determining the technology gap ratios (TGRs) for the rice processing industry will help policymakers understand the area that urgently needs to be addressed to improve rice processing efficiency and ensure the achievement of self-sufficiency in Nigeria.

1.2. Statement of the Problem

Demand for milled rice is rising in Nigeria as the population grows and access to higher-quality food is limited [3]. The current economic situation in Nigeria has made milled rice an option for many families. It is the main staple for most Nigerian diets and is therefore a highly sought-after commodity [18]. The popularity of milled rice, particularly amongst the lower-income population, has created a sharp increase in demand for this product.

Reiteratively, the demand for milled rice has increased significantly in recent years and is expected to increase further in the future. Danbaba [4] reported a milled rice demand of 8 million MT in 2022, compared to the 7 million MT demanded in the previous year. This has confirmed the reports that rice demand in Nigeria increased by 7.8% per annum, while the supply increased by 2.3% [19]. The current demand and supply situation of milled rice in Nigeria is alarming; given the current trends, it is clear that the demand for milled rice will continue to grow, which will continue to drive prices up, making it increasingly difficult for lower-income families to afford basic staples.

Nigeria’s main producers of milled rice, mostly in rural areas, are struggling to keep up with the public demands while facing challenges of expensive inputs and a lack of access to credit. It impedes the ability of small-scale processors to expand and continue to expand their activities [9]. Without access to credit and other financial resources, small-scale processors are left behind in terms of the adoption of modern production technologies, which remains the chief source of production gaps. This is of particular concern as such technology is essential for enhancing and improving the quality of milled rice.

Similarly, rising transportation costs and border closures by the Nigerian government have increased the cost of producing and distributing milled rice. Rising input costs, such as seeds, fertilizers and pesticides, were driven by inflationary pressure caused by the ongoing naira devaluation, which affected the price of paddy purchased by processors.

Again, there is a lack of reliable and accurate data on milled rice production in Nigeria. Without accurate information, it is hard to effectively address the production, and marketing challenges faced by the industry. Issues such as processor’s income levels cannot be accurately assessed, which will hamper the ability to develop effective policy interventions in the area of rice processing. Therefore, to address the challenges of milled rice production in Nigeria and Anambra State in particular, there is a need for the government to intervene in farming communities. This could include introducing subsidies to reduce processing costs, providing credit facilities, and better access to markets, and increasing support for research, data collection and policy interventions. Moreover, for an efficient distribution of milled rice, greater investments in technology and infrastructure are required to enable small-scale processors to adopt improved processing techniques, storage facilities and better transportation systems. For these policies to work effectively, they need to be understood in detail, including the profile of people involved in the enterprise, as this affects their technical expertise in operating the proposed modern equipment. A study by Bime et al. reported that a greater proportion (42%) of small-scale rice processors in Cameroon are between the ages of 31–40 years old, and 58.0% of them have low-level of education (primary school), with 64.0% reporting 0–5 years of processing experience [20]. In another study by Bolarin et al., they found that the average age, household size, and processing experience are 47.6, 5.9, and 15.8, respectively [21]. Again, more than half (56.7%) of the processors had primary education. Uchemba et al. suggested improving the educational qualifications of farmers [22]. This is because it has a significant impact on the performance and productivity of farmers.

To understand the impact of government interventions in the rice processing sector, the study found that it is necessary to examine the TGE among participants and non-participants of the Anambra State VCDP. This study is the first to use probabilistic meta-frontier techniques to determine the industrial efficiency of rice processors in Anambra’s agricultural intervention platform and to uncover invisible entrepreneurial heterogeneity between participants and non-participants. Using this method provides more credible results for policy intervention [23] in the rice industry. Therefore, it is hypothesized that TE differs between participants and non-participants in Anambra State VCDP due to differences in access to entrepreneurial opportunities and subsidies for modern processing equipment. The findings of this research will inform policymaking to maximize rice processing and supply to the economy. However, the main purpose of this paper is to understand the impact of participation in a government intervention program on rice processing efficiency. How will equipment subsidy intervention affect TE in the rice mill industry? This will be operationalized through specific objectives aimed at:

i.

Estimating the group-specific processing function for the participants and non-participants of the agricultural intervention program;

ii.

Estimating the economic-specific processing function for the rice industry;

iii.

Describing the TGR, TE and MTE of the small-scale rice processors in the study;

iv.

Identifying the challenges of small-scale rice processing in the study area.

2. Literature Review

2.1. Conceptual Review

2.1.1. Small-Scale Rice Processing

The classification of an enterprise based on size is a reflection of its production and sales turnover, number of employees, and amount of capital investment [24,25,26], among others. Small-scale operators have fewer than 250 employees on their payroll [27]. However, small-scale rice processing involves activities such as drying, cleaning, husking, grading, and polishing to convert a raw grain into a value-added product. This process increases the value of the rice by removing the inedible husk as well as any foreign material that may be present. Rice is a staple food for over 50.0% of the world’s population and is an important part of global nutrition projects [6,28]. Involvement in small-scale rice processing could benefit a rural farmer’s income. By converting raw grain into higher-value products, farmers can avoid the huge markups typically charged by millers, which leaves them with more money to support their families. Additionally, by having the option to process rice, farmers can determine the quality specifications to ensure their rice meets the standards of customers.

Despite the high-income opportunities, there are many obstacles to starting a small processing rice business. From a technical perspective, most small-scale operators lack the necessary technology and skills to process rice properly [29]. There is also a need to raise capital to pay for the necessary equipment to ensure operational efficiency. Additionally, the market needs to be developed for small millers to take advantage of the new value-added products. However, many governments and NGOs are working to support small-scale rice processing projects to empower local farmers, improve incomes and livelihoods, and increase food security [30]. With proper training, infrastructure, and access to finance, small-scale rice milling can be a viable business opportunity for rural farmers.

Furthermore, rice processing is typically carried out either manually or mechanically. Manual processing involves the use of traditional tools and techniques to hull, husk, polish, and mill the rice [31]. This process is labor-intensive and time-consuming and typically results in a low-quality product [9]. Mechanical processing, on the other hand, employs modern machinery and equipment to efficiently and quickly process the rice. This method of processing is much faster and results in superior-quality products.

Despite the obvious advantages of mechanical processing, most rice processing in Nigeria still relies on manual methods [32]. This is due to several factors including a lack of access to the latest technology, limited resources, and a lack of technical expertise. As a result, the TE of rice processing in Nigeria is much lower than it could be.

2.1.2. Technical Efficiency of Small-Scale Rice Processing

TE is an important factor in the success of small-scale rice processing in Nigeria. It is critical for achieving higher yields, improving product quality, and reducing production costs. Unfortunately, TE in the sector is low, with much of the existing equipment being outdated [33] and inefficient. This has resulted in reduced yields, higher production costs, and ultimately lower profits for small millers. Md. Abu et al. described TE as a firm’s capacity to attain maximal output from a fixed set of inputs [34]. Ehirim et al. preferred to view TE as the extent to which time, effort, or cost is well managed for an intended task or purpose [35]. The study by Diarra et al. reported that TE of small-scale rice processing ranges from 65–70% [36]. Similarly, Asmiya and Sivarajah reported a shrinking TE value of 60% among small-scale rice processors [37]. These statistics validate the need to promote government interventions in the agricultural sector.

Several steps can be taken to improve TE of small-scale rice processing in Nigeria; this is because improving efficiency is proportionate to an improved standard of living [38,39]. The first step is to invest in modern and efficient equipment. This includes replacing old and inefficient machines with modern versions that are designed to reduce energy consumption and increase throughput [33]. It also includes investing in appropriate tools, such as polishers and hullers, that can help to improve the quality of the final product. In the next step, it is important to ensure that small-scale processors have access to the necessary technical expertise. This includes training in the latest techniques and technologies, as well as support in troubleshooting and maintenance. This is particularly important in rural areas, where access to technical support is often limited.

Furthermore, it is important to ensure that small millers have access to the necessary resources. This includes access to credit and other financial support, as well as access to spare parts and other items that may be needed for repairs and maintenance. By providing these resources, small millers will be able to effectively access the capital and resources needed to improve their efficiency. In conclusion, improving TE in small-scale rice processing in Nigeria is essential for ensuring the sector’s long-term success. By investing in modern, efficient equipment, providing access to technical expertise and resources, and supporting small millers in their efforts to improve efficiency, the sector can be well on its way to achieving greater success. This assertion supports the statement by Diosdado and Biley that the level of technical know-how and technology adoption affects the efficiency of production [40]. Many works on TE were conducted in the field of rice production, though none has been established on small-scale rice processing in the study area. Ehirim et al. found the TE of rice farmers in their study to 0.47 [35]. Md. Abu et al. reported 0.80 for submerged rice production, 0.77 for drought, and 0.74 for saline rice production [34]. Mohammad et al. found a TE of 0.75 in their study for rice production [41].

2.1.3. Technological Gap Ratio (TGR) in Small-Scale Rice Processing

Small-scale rice processing in Nigeria is becoming increasingly efficient as the country looks to capitalize on the growing demand for locally-produced rice. In recent years, there has been a focus on improving the TE of small-scale rice processing to ensure that more value is added to the product, thereby increasing the profitability of production. The TGR in small-scale rice processing in Nigeria is a major cause for concern. TGR measures the ratio of the output for the frontier production function in a group relative to the potential output which is defined by the meta-frontier function of observed inputs [42,43].

In Nigeria, it is estimated that 85% of rice is produced by smallholder farmers; however, these farmers are operating with outdated technology and are unable to meet the demands of an ever-growing urban population [44]. This is resulting in a significant gap between the productivity of smallholder rice farmers, processors, and their urban counterparts. The TGR in small-scale rice processing in Nigeria is attributed to several factors, including a lack of access to modern technology, inadequate extension services, and limited access to credit and other inputs. Recently, some scholars defined TGR as the gap between the production technology adopted by rice farmers and the technology available [16] in the rice industry. They assumed that a TGR of one implied that the farmers adopted the most advanced technology available, whereas Ng’ombe [12] and Korotoumou et al. [45] submitted in their study that a ratio of less than one means that the farmers failed to adopt the most advanced technology. Small-scale processors are often unable to invest in better-quality equipment and there is a lack of knowledge regarding modern techniques. This leads to a lower production output and a higher rate of wastage. Furthermore, the lack of access to credit and other inputs has created a situation where small-scale processors are unable to take advantage of the opportunities presented by the market. Additionally, the lack of access to modern technology has led to an increase in the cost of production, which, in turn, has decreased the competitiveness of small-scale processors. The gap in small-scale rice processing in Nigeria needs to be addressed to ensure that processors can compete in the market and increase their productivity. To this end, the government must provide support to small-scale rice processors in the form of access to modern technology, training, access to credit, and other inputs as part of the objectives of VCDP.

The technological gap in small-scale rice processing in Nigeria is a major cause for concern and requires urgent attention from the government and other stakeholders. If the gap is not addressed, it will continue to affect the productivity of small-scale processors and the competitiveness of the rice market in Nigeria.

2.1.4. Meta-Technical Efficiency (MTE) of Small-Scale Rice Processing

Small-scale rice processing in Nigeria is becoming increasingly popular as a way to reduce post-harvest losses, improve farm incomes and increase food security. The ability to process, store and transport rice more efficiently is a key factor in improving the overall efficiency of small millers. MTE is an important component of small-scale rice processing, which is defined as an effective use of technology and other resources to facilitate the production process. Kanis et al. [46] noted that MTE is used to assess how efficient different firms in Bangladesh are in their operation or processing activities. MTE is a key component to reduce post-harvest losses and increase productivity, as it allows for better utilization of resources and improved quality control among different groups involved in rice processing. MTE can be improved through the use of modern processing and storage technologies, such as automated rice mills and grain silos. Automated rice mills can reduce post-harvest losses by 17–30% [4], while grain silos can provide a safe and efficient means of storing rice for a long period. Additionally, the use of modern processing technologies can reduce labor costs, improve product quality and reduce waste. Being that this is the first time the meta-stochastic approach is used to assess small-scale rice processing actors in Anambra State VCDP, the authors likened this research to the work by Xiangfei et al. [47], who viewed MTE as a structural change analysis.

In addition to the use of modern technology, other measures can be taken to improve MTE in small-scale rice processing. These include the adoption of good agricultural practices (GAPs), the establishment of quality assurance systems, and the implementation of effective monitoring and evaluation mechanisms. GAPs can help to ensure that the process is conducted safely and efficiently, while quality assurance systems can ensure that the products meet the required standards. Finally, monitoring and evaluation mechanisms can help to identify areas for improvement. MTE is, therefore, an important factor in improving the overall efficiency of rice processing in Nigeria. The above statement pointed to the assertion by Nan and Basil [48], who noted that MTE is a procedure developed to determine whether technology adoption differs among firms.

2.1.5. Challenges of Rice Production and Processing in Nigeria

One of the main challenges of rice processing value chain is inadequate infrastructure. Many African countries lack the basic infrastructure needed to transport and store the harvested rice, meaning that most of the rice is left to rot in the field or sold to traders at a low price. This is compounded by the lack of resources within the industry, with many small rice millers not having the funds to purchase the necessary equipment for processing [49].

Again, access to market is a major issue for the rice processing value chain in Africa. Limited access to market particularly in rural areas, means that farmers are unable to sell their rice at a fair price. This in turn leads to selling the rice to traders at much lower prices than they would have if small millers were able to access larger markets. Ampadu-Ameyaw et al. [50] believe that participants in the rice value chain need training.

The study by Sennuga et al. [33] further itemized some factors that militate small-scale rice processing as:

• Lack of infrastructure: inadequate roads, rail, or water infrastructure to facilitate the transportation of paddy and milled rice to and from production sites makes it difficult to efficiently source and distribute rice.
• Poor milling capacity: there are inadequate modern rice mills in Nigeria and the existing ones are using outdated, inefficient technology, which makes the milling process slow and costly.
• Inadequate storage and preservation facilities: poor storage and preservation infrastructure prevent the effective use of modern storage technologies, leading to a significant loss of paddy and milled rice due to deterioration and spoilage.
• Low yield and productivity of farms: Nigerian farmers continue to use traditional methods of cultivation and low-yielding varieties of rice, which reduces potential yields.
• Lack of access to finance: small-scale rice processors often lack access to the credit and capital needed to purchase the necessary processing equipment to improve their operations.
• Environmental degradation: unsustainable methods of rice farming have led to serious soil and water degradation in many areas, leading to reduced productivity.
• Increasing competition from other countries and imports: rice importation increased since the 1990s, causing the local industry to suffer. With these challenges, the rice industry is growing, with many public and private initiatives being put in place to improve yields and processing. Similarly, with the right investment and innovation, the industry has the potential to substantially increase its production to remain competitive in regional markets.
• Skills and technical know-how: even with the help of the government, which provided few processing machines at a subsidized price, the processors still need training on how to operate the machines.
• Limited access to information and innovation: the inability to get timely information about innovation by the rice processors is also a constraint to the processing of rice because processors are not up to date about the newest and latest method of processing; this could be attributed to the inability of the extension advisors to quickly locate smallholder farmers and small millers with information on current events in the industry.

2.2. Empirical Review of Related Studies

This review focuses on the available evidence that provides an overview of the current state of knowledge on the topic. The empirical review helps to identify gaps in the literature and inform future studies in the field. Nakanoa and Muniz [51] noted that an empirical review can provide insight into the research methods and results that are already available and can help researchers to develop new research questions and hypotheses. Being that no study ever existed in this study’s area of interest, there is a scarcity of evidence to review. The few available studies are found in the meta-frontier of rice production.

The study by Obianefo, Ng’ombe et al. [16] on TE and TGR of rice production in Anambra State, Nigeria, used a stochastic meta-frontier approach to establish the TE and MTE of upland and lowland rice farmers. Their study later reported the TGR of rice farmers. Their data came from a cross-section of 100 (70 upland and 30 lowlands) rice farmers randomly selected. Descriptively, the average age of farmers for the pooled data was 42.6, farming experience was 12.3, and the number of household sizes was 8.8, and the average number of years of formal study was 11.4. Later on, experience was found to positively increase the production efficiency of upland rice farmers. The value of TE for the rice production sector was 0.875 (87.5%), the MTE was 0.955 (95.5%), and the TGR was 0.882 (88.2%). From this evidence, one can observe that farmers have not adopted the most advanced technology available to them.

Majiwa and Mugodo’s study [52] on TE and TGR among rice farmers in Kenya surveyed 773 farmers in Mwea, West Kano, Ahero, and Bunyala rice growing regions. A stochastic meta-frontier analytical tool was used to estimate TE, MTE, and TGR. They found that Mwea, West Kano, Ahero, and Bunyala had TE values of 0.556, 0.475, 0.402, and 0.45, respectively. The MTE was recorded for Mwea, WestKano, Ahero, and Bunyala as 0.557, 0.784, 0.833, and 0.937, respectively. Furthermore, the TGR values were 0.998, 0.605, 0.482, and 0.48 for Mwea, West Kano, Ahero, and Bunyala, respectively. They used fractional regression models to reveal the determinants of efficiency, which are age, farmer’s gender, humidity, rainfall, temperature, and adopting technologies.

In the study by conducted Olasehinde et al. on the performance of Nigerian rice farms from 2010 to 2019, a stochastic meta-frontier approach was used to trace the events in the rice production economy [53]. They discovered a huge gap between domestic rice production and consumption patterns. The approach revealed heterogeneity in production technology across farms located in different regions. Both regions have low TE. However, rice farmers in the southern region of Nigeria are ranked better in production because of their managerial skills rather than technological gaps.

Okunola et al. examined the factors affecting the processing and quality of rice in Ekiti State, Nigeria. They selected nine towns from six local government areas where rice production is dominant in the state [32]. A questionnaire was used to randomly sample 300 rice processors. The study found that 47.0% of the processors are males and 53.0% are females; 66.7% of the processors have family sizes ranging from 4 to 7 persons, 63.8% of them have only primary education and 22.7% have no formal education; 70.0% of rice is gotten from middlemen and 80.0% of the processors used their savings as capitals. A total of 70.0% of the milling machines used are obsolete and characterized with high broken grains. In total, 90.0% of the processors depend on diesel engines to power the mills, while 7.0% had access to good storage facilities. None of the processors had access to a rice de-stoner.

2.3. Analytical Framework

2.3.1. Stochastic Frontier Model

The stochastic frontier model (SFM) was initially developed by Aigner et al. [54], and has been applied to firms’ managerial performance ever since [55,56,57]. SFM is an economic tool used to assess the efficiency of an organization based on the production function. It can measure the level of efficiency of a firm or an organization based on the outputs it has produced compared to its inputs. The SFM also explains production inefficiencies, which can be useful for determining trends in different industries or organizations. SFM is used to analyze the production strategy of an organization to identify potential sources of improvements in efficiency [58]. The model is based on the assumption that a certain level of production is achievable by any organization regardless of the level of inputs used. This means that organizations should strive to use the most efficient methods possible to maximize their outputs.

SMF is an econometric model that is primarily used to study economic efficiency and productivity. The model is employed to explore production efficiency and productivity within a range of organizations or firms. Forsund et al. noted that the measurement of firm-specific efficiency through frontier techniques has been intensively studied [59]. It is a regression model that incorporates random noise (V_i) in the production process and is often used to illustrate the TE of economic agents within a certain market. The SFM is usually implemented within a production function framework. The model assumes that production activities are stochastically distributed and that the expected level of production output is estimated by the maximum likelihood estimation method. This method is then applied to the production function, which has a parameter that governs the randomness of any production activity. These relationships are then modelled from the equations derived from the production function and projected onto a parameterized curve. This curve is used to measure the degree of inefficiencies that may either occur due to the production process or inefficiencies that occur when resources are used to produce different levels of output [59]. Though some firms can produce below the framework of frontier point, there cannot be any point above the production frontier given the available technology [58,60].

The SFM also helps identify the sources of possible inefficiencies in a production process. This is typically done by including a parameter in the production process that measures the inefficiency which may arise from differences in input utilization, labor practices, and other or unknown factors. This parameter will generally explain any observed discrepancy between expected and actual levels of output [61]. Aigner et al. [54] also noted that the specification of the stochastic frontier production function allows for the decomposition of the error term into a nonnegative random variable (U_i), associated with the technical inefficiency of the ith farm or firm, as well as the Gaussian error term (V_i), which represents random variation in output due to factors beyond farmers’ control. The SFM is not a substitute for traditional data-based analysis of production activity, but it does provide a useful tool for evaluating efficiency metrics. By helping to produce a better understanding of the production process, it can make decisions and policies more beneficial to economic productivity. Its application can also lead to a better understanding of economic factors and their impact on the production process. As such, the SFM may be used to determine the impact of policy measures on production processes, measure the effects of technological change on production processes, and so forth. The SFM may also be used to compare the efficiency of different markets or organizations, explore the impact of public policies on production, or evaluate the performance of different industries [19].

2.3.2. Stochastic Meta-Frontier Model

A stochastic meta-frontier model (SMF) is a new approach to estimating the production efficiency of ith firms. It is based on a rigorous statistical process that allows economists to assess how output and input are related, determining whether or not there are opportunities for improvements in production efficiency. Unlike traditional methods of evaluating production efficiency, the SMF model does not rely on averages to measure efficiency. Thus, the method adopted in this study is the Huang et al. [62] SMF model applied by Mariko et al. [17], which estimates the optimal output potentials of firms. The advantage of the SMF model is that it can be used to determine production frontier efficiency from a non-parametric perspective. This approach provides economists with an effective way to measure and compare firms’ relative production performance. Using this model, economists can observe the behaviors and patterns among productive units, and build a model which can reflect the efficiency of firms that would otherwise be overlooked by traditional approaches. This model goes beyond just looking at a firm’s output by also considering its characteristics and productivity curve.

The model works by estimating a particular firm’s production frontier using a probabilistic approach. To accomplish this, economists will calculate a measure of efficiency and performance such as the average production, and then compare it with the average performance of the entire industry by pooling the data. Then, the model will utilize a series of probability distributions and maximum likelihood estimations to determine which parameters are most likely to be at the “frontier” of the productivity of a particular firm. By observing how production departs from the regional norms, economists can determine how close an organization is to peak efficiency, or how much it can improve before they reach the maximum production that they are capable of achieving. Huang et al. [62] submitted that what differentiates SMF from the classical approach proposed by Battese et al. [63], and O’Donnell et al. [64] is its two-step approach. The first step estimates the firms’ specific frontiers, while the second step involves estimating the SMF function with external impacting variables in the industry [12,62].

The SMF model is ideal for organizations looking to make data-driven decisions about their operations. With this tool, companies can determine their production efficiency to maximize profits. This model can be applied to a variety of industries and sectors, making it an excellent choice for firms of all sizes. Furthermore, by using stochastic models, economists can better deal with dynamic changes within their industry to better estimate future production trends. Reiteratively, the SMF model is an innovative approach to improving production efficiency that can help firms make informed, data-driven decisions [12]. By implementing this model, firms can evaluate their performance relative to the industry and measure the returns they receive from investing in different production techniques and strategies, thus making the SMF model a powerful tool for economists and businesses alike.

If the small-scale rice processing industry has j production groups, the stochastic frontier model used for decision-making units is defined by:

$$\begin{gathered} Y_{ji}=f^j\left(X_{1i},X_{2i},\dots X_{mi};{\beta }^j\right)e^{V_{ji}-U_{ji}} \\ j=1,2,...,J;i=1,2,...,m \end{gathered}$$

(1)

where Y_ji is the observed output (milled rice) of the ith processors in the jth group, Xmi is the mth input quantity used, and β^j represents the vector of input parameters for the jth group. The production function (f^j) superscripted at j indicates that the processor’s specific frontier can vary across groups. The group in this regard refers to the participants and non-participants considered in the study. Based on the SMF model, the Vji is the random error term, denoting statistical noise, and Uji represents technical inefficiency. Vji is independent and identical to statistical distribution as N(0, ${\sigma }_{V^{J2}}$); U_ji represents $U_{ji}~N^{+}{(}^{vj}\left(Z_{ji}\right),{\sigma }^{j2})$, where Z_ji implies inefficiency components [65]. Taking the log of both sides in Equation (1), the maximum likelihood estimation (MLE) can be used to estimate the transformed regression model. From the SMF model, a firm’s TE is defined as:

$$T{E}_i^j=\frac{Y_{ji}}{f^j\left(X_{ji}\right)e^{Vji}}=e^{-Uji}$$

(2)

where X_ji is the vector of input of ith processors in the jth group and other variables remain as previously defined. Based on previous literature, it is assumed that Uji followed a half-Gaussian distribution. On this note, Assa et al. [66] suggested that the firm’s specific efficiency is given as 1 − TE.

Huang et al. [62] opined that the meta-frontier production function takes into consideration all groups in period t, which is defined as:

$$f^m\left(X_{ji}\right),j=1,2,\dots , J$$

(3)

The meta-frontier $f^m\left(X_{ji}\right)$ is surrounded by the individual group frontier $f^j\left(X_{ji}\right)$. Thus, the relationship between the individual group frontier and meta-frontier is defined as:

$$f^j\left(X_{ji}\right)=f^m\left(X_{ji}\right)e^{-U_{ji}^m,\forall j,i}$$

(4)

where $U_{ji}^m\ge 0$ implies that f^m > f^j. Furthermore, as found in Obianefo, Ng’ombe et al. [16], Huang et al. [62] argued that TGR is the ratio of jth firm’s production frontier to the meta-frontier as defined by:

$$TG{R}_i^j=\frac{f^j\left(X_{ji}\right)}{f^m\left(X_{ji}\right)}=e^{-U_{ji}^m}\le 1$$

(5)

where $TG{R}_i^j$ is the gap between the technology adopted and the technology available in the industry. A higher TGR means that the gap is closing.

3. Materials and Methods

3.1. Data

The present study was based on a field survey of participants and non-participants of an agricultural intervention programme in Anambra State. The design of the study drew from a combination of quantitative and qualitative methodologies, including variables, indicators, and items derived from available literature, such as the Value Chain Development programme, and other publications.

3.1.1. Area of the Study

The study was carried out in Anambra State. Anambra State is situated in the South-eastern region of Nigeria, comprising twenty-one local government areas (LGAs) and four agricultural zones. It is bordered by Delta State to the west, Imo State and Rivers State to the south, Enugu State to the east, and Kogi State to the north. The main indigenous ethnic group of the state is Igbo, making up 98% of the population, with the remaining 2% being Igala, mainly found in the north-western part of the state. Anambra State is located between latitude 5°32′ and 6°45′ N and longitude 6°43′ and 7°22′ E, and spans an area of 4865 sqkm [67].

In this study, smallholder farmers who are members of the Value Chain Development Programme (VCDP) rice processing cooperatives were included as participants of the agricultural intervention program. The VCDP works to create sustainable agricultural practices and improve the incomes of farmers through access to new technologies and farming methods. Furthermore, the VCDP aids in the formation of cooperatives and other farmer-based organizations to ensure that farmers have access to markets and other resources. Through the VCDP, smallholder farmers have seen an increase in access to markets, improved income levels, and a decrease in poverty [3].

Similarly, the VCDP has helped to improve the quality of agricultural products, enabling farmers to obtain better prices from buyers. The program is being implemented in eight LGAs (Anambra East, Anambra West, Ayamelum, Orumba North, Orumba South, Ihiala, Ogbaru, and Awka North) under two commodities (rice and cassava). The Anambra State VCDP submitted that the LGAs were selected based on comparative advantage in rice and cassava production [19]. Rice processors in this program are trained in the use of modern processing equipment to improve their productivity or efficiency. They are exposed to entrepreneurship training and subsidized modern parboiling (false bottom technology) and milling equipment.

3.1.2. Sampling Techniques and Sample Size

The researcher(s) utilized a multi-stage sampling process to create a representative sample size of 100 small-scale processors in Anambra State. The first stage involved purposefully selecting five local government areas (LGAs)—Anambra East, Anambra West, Ayamelum, Orumba North, and Awka North as these areas had a longer history of involvement in the program. At the second stage, 5 rice clusters were randomly chosen from each LGA, making a total of 25 clusters. The third stage involved randomly selecting 10 program rice processors and 10 non-program processors to complete the sample size. In addition, two extension personnel from the Anambra State Agricultural Development Programme (ADP) were employed and given instructions on the variables in the questionnaire. The data collection took place over the span of two weeks (2 to 16 November 2022).

3.1.3. Data Analysis

Data analysis is the process of extracting meaningful insights from raw data to answer research questions. Data analysis can be used to profile and better understand a population, identify trends and patterns, and make predictions. This study utilized a combination of analytical tools such as descriptive statistics, stochastic frontier analysis, stochastic meta-frontier analysis, and other inferential statistics. Objective 1 was achieved with one stage stochastic frontier model; this one-stage approach incorporated the inefficiency or group-specific components of the variables. Objective 2 was achieved with one stage stochastic meta-frontier model; the approach incorporated the external variables causing the gap in the industrial efficiency of the model or meta-frontier function. Objective 3 was predicted from the result of the stochastic and meta-stochastic frontier models. Furthermore, objective 4 was achieved with descriptive statistics. The heterogenous hypothetical assumption of the model was checked with the likelihood ratio (LR) text adopted from Kumbhakar et al.’s work [68].

3.1.4. Model Specification

The model specification in research refers to the process of selecting, defining, and parameterizing a particular model that is used to analyze a particular research question. In general, this includes specifying the mathematical form of the model, along with the associated parameters. Below are the models used to achieve the stated objectives.

(A). Cobb–Douglas Function

A more restrictive Cobb–Douglas function was used for the stochastic frontier and stochastic meta-frontier estimation. In the case of smaller sample sizes like in this study, Cobb–Douglass is used for all the estimations as the bravest option to retain the degree of freedom [16]. The Cobb–Douglas production function is used to describe the technological relationship between the amounts of two (or more) inputs and the amount of output. It was developed by Charles Cobb and Paul Douglas in 1928. However, Lee and Tyler [69] noted that the work by Aigner et al. [54] is founded on the stochastic frontier model which remains the best for efficiency analysis. The model definition is:

$$Ln{Y}_i={{\displaystyle \sum }}_{j=1}^6{\beta }_{j}Ln{X}_{ji}+\left(V_i-U_i\right)$$

(6)

where Ln is the natural log, Y_i is milled rice produced (kg), X₁ is the paddy rice (kg), X₂ is the amount spent on firewood (₦), X₃ is water for parboiling (litre), X₄ is the cost of labor (₦), X₅ is diesel (litre), and X₆ is the depreciation on huller (₦). V_i is the random noise, $U_i~N^{+}\left(v_j\left(Z_j\right)\right)$ are the individual/group-specific variables, which are age, years of formal education, processing experience, and household size. The economic-specific variables for the meta-analysis are the economic cost of grading and sorting, depreciation on false bottom technology, depreciation on other assets, and technological prowess.

(B). Descriptive statistics

It is a branch of statistics that deals with the analysis of data to summarize and present it in a meaningful way. A descriptive statistic is used to describe the dataset by providing an overview of the data, including measures of central tendency such as the mean and median, measures of dispersion such as the range and standard deviation, and measures of shape and symmetry such as the skewness and kurtosis. It also includes graphical representations of the data such as histograms, boxplots, and scatterplots. Descriptive statistics can be calculated as:

$$\overline{X}={{\displaystyle \sum }}^{ }\frac{F{X}_i}{n}$$

(7)

where $\overline{X}$= mean, X_i = variable outcome, n = sample size, and F = frequency.

3.1.5. Test of Hypotheses

Test of hypothesis is a statistical test that is used to determine if there is enough evidence in a sample of data to infer a certain conclusion about a population parameter. The process of hypothesis testing consists of four steps: stating the null and alternative hypotheses, selecting a significance level, computing a test statistic, and making a decision. As stochastic meta-frontier can only be applied when the test confirms heterogenous technology adoption among different groups [62,64] in the industry. The first step to check for the difference in technology adoption was to conduct a maximum likelihood estimation (MLE) of the pooled dataset; the next is to sum the values of the log-likelihood function from each group’s stochastic frontier estimation using the LR test defined by Kumbhakar et al. [68,70] as:

$$\lambda =-2[Ln\left(L\left(H_0\right)\right)-\left(Ln\left(L\left(H_1\right)\right)\right]$$

(8)

where Ln(L(H₀)) is the value of the log-likelihood function for stochastic frontiers estimated by pooling the data, and Ln(L(H₁)) is the sum of the log-likelihood values for the two groups’ (participants and non-participants) stochastic frontiers estimation. The degree of freedom for the meta-frontier test is six, calculated as K − 1 (K is the parameter of estimation with constant). The degree of freedom for the other parts of the test (inefficiency and external component) is the difference between the K for the frontier function without the inefficiency variables (H₀) and those with the inefficiency variables (H₁). The underlying rule of this supposition is that when the null hypothesis for homogenous technologies across groups is rejected, the researcher can proceed with a meta-frontier approach [62,71].

Table 1. Hypothetical text of stochastic frontier assumptions.

Assumptions	Ho	H1	LR-cal.	LR-tab.	DF	Decision
Existence of Homogenous technology	−163.894	−137.169	53.356	16.812	6	Rejected
No presence of an inefficiency component
Participants	−35.396	−30.422	9.948	9.210	2	Rejected
Non-participants	−39.960	−29.172	21.576		2	Rejected
No presence of external component	−102.764	−96.187	13.154	9.210	2	Rejected

Source: field survey, 2022.

shows the result of all the assumptions tested at 0.01 level of probability.

3.2. Summary of Data

Table 2. Summary of variables used to operationalize the research objectives.

	Participants					Non-Participants
	SI Unit	Mean	Std, Dev.	Min	Max	Mean	Std, Dev.	Min	Max
Output	Kg	388,354.0	826,664.2	2000.0	4,000,000.0	363,524.1	864,968.2	2000.0	4,000,000.0
Rice paddy	Kg	517,805.3	1,102,218.9	2666.7	5,333,333.3	484,698.9	1,153,291.0	2666.7	5,333,333.3
Firewood	₦	30,022.4	25,159.8	6822.0	90,291.0	42,570.1	27,070.5	5982.0	95,066.0
Water	Liter	61,926.0	56,558.5	12,500.0	187,500.0	31,304.6	37,273.6	12,500.0	187,500.0
Labor wage	₦	155,780.9	111,557.5	48,592.0	420,000.0	221,361.3	93,180.4	51,000.0	420,000.0
Diesel	Liter	52.7	27.3	25.0	100.0	63.4	22.1	25.0	100.0
Dep. Huller	₦	20,548.9	10,892.1	3662.3	37,500.0	58,190.0	60,608.4	4029.8	200,000.0
Cost of sorting grading and packing	₦	27,251.5	14,814.6	5000.0	49,500.0	27,656.6	14,144.8	5000.0	49,500.0
Dep. false bottom	₦	9834.0	11,560.1	0.0	35,000.0	9971.5	12,854.0	0.0	40,000.0
Dep. of other assets	₦	127,533.3	66,892.7	16,310.0	277,886.0	116,116.3	62,865.6	16,310.0	251,217.0
Technology prowess	%	65.3	9.3	47.5	85	64.7	8.9	46.3	85
Sex	Dummy	0.5	0.5	0	1	0.7	0.5	0	1
Age	Years	44.6	11.2	26	62	46.0	9.8	25	65
Marital status	Dummy	1.5	0.5	1	2	1.5	0.5	1	2
Years of formal education	Year	11.6	5.0	4	20	10.6	4.9	4	20
Processing experience	Year	10.7	6.0	5	25	9.5	2.6	5	20
Household size	No	8.2	2.8	4	12	7.2	2.2	4	12

Source: field survey, 2022.

below is the summary of all the variables used to operationalize the study objectives. The summary table revealed that the average paddy supplied to the milling machine by the participants was 517,805.3 kg and that supplied to the non-participants was 484,698.9 kg, after milling that helped to convert the grain to milled rice; the participants recorded an average output of 388,354.0 kg, which was 363,524.1 kg for non-participants. This indicates that 25.0% of the initial paddy weight was lost in the rice value chain. These values confirmed the assertion of Sadiya and Hassan [72] that 21.0% of rice is lost at the processing stage. The participants spent an average of NGN 30,022.4 on firewood, and NGN 42,570.1 was spent by non-participants. This amount represents part of the cost incurred in the parboiling of paddy to prepare for a quality milling experience. An average of 61,926.0 liters (participants) and 31,304.6 liters (non-participants) of water were used for the parboiling business. The non-participants used less water than the participants, possibly because they lacked the funds to purchase enough for their processing activities and the environment. On the other hand, the average wages paid to the hired labor force were NGN 155,780.9 for participants and NGN 221,361.3 for non-participants, suggesting that rice processing was more labor-intensive for non-participants as they did not have subsidized equipment to boost their processing capacity. Bolarin et al. and Okunola et al. found that the agricultural intervention participants had a clear advantage over non-participants [21,32] when it came to diesel consumption (52.7 liters for participants and 63.4 liters for non-participants) and processing quality. The VCDP subsidizes the cost of processing equipment by 70%, which results in smaller depreciation values for participants. In addition, the introduction of the false bottom parboiling method has been a technological advancement for the participants, leading to higher-quality rice grains.

The research findings showed that the participants had a technology proficiency (prowess) of 65.3%, whereas the non-participants had a slightly lower proficiency of 64.7%. Shah et al. [73] compared technology proficiency to revolutionary technology when they defined it as the capability to employ technology successfully and efficiently in order to reach the desired results. The mean age of 44.6 (participants) and 46.0 (non-participants) as indicated by the group-specific variables demonstrates that the small-scale rice processors included in the analysis are relatively young and in their productive production stage. This value corresponds with the study of Ibitoye et al., who mentioned that processors involved in their study are between 36 and 45 years [6]. Furthermore, they assumed that age has an impact on the managerial capability of the respondents as age is the primary cause of risk avoidance. On average, participants and non-participants spent 11.6 and 10.6 years in formal learning institutions, respectively, indicating that most processors did not finish their secondary education. This is consistent with the results of Bime et al., who found that 58.0% of processors in their study had primary education [20]. Participants and non-participants had an average processing experience of 10.7 and 9.5 years, respectively, showing that they spent considerable time at the enterprise to gain insight into rice processing. Additionally, the average household size was 8.2 and 7.2 for participants and non-participants, respectively, confirming Ibitoye et al.’s claim that respondents’ households ranged from 6 to 10 people [6]. This household size is large enough to provide inexpensive family labor.

4. Results and Discussions

4.1. Parameter Estimates for Group-Specific Stochastic Frontiers

Table 3. Parameter estimates for group-specific stochastic frontiers.

Participants (n = 50)				Non-Participants (n = 50)
Variable Names	Estimates	Std. Err.	Z	Estimates	Std. Err.	Z
Log-Paddy-input (kg)	1.003	0.108	9.26 ***	−0.086	0.126	−0.68
Log-Cost of Firewood (N)	0.118	0.036	3.28 ***	0.144	0.111	1.30
Log water (Liter)	−0.680	0.147	−4.61 ***	0.124	0.399	0.31
Log-Cost of labor (N)	−0.199	0.281	−0.71	0.455	0.422	1.08
Log-Diesel (Liter)	0.002	0.003	0.76	0.000	0.005	−0.04
Depreciation on Huller (N)	−0.060	0.096	−0.63	0.196	0.172	1.14
Constant	9.307	1.514	6.15 ***	7.586	2.755	2.75 **
Group-specific variables
Age (year)	0.063	0.050	1.27	−0.023	0.045	−0.5
Years of formal education	0.191	0.114	1.68 *	0.020	0.090	0.22
Processing experience (years)	−0.105	0.138	−0.76	0.003	0.171	0.02
Household size (No)	−0.292	0.226	−1.29	0.599	0.255	2.35 ***
Constant	−3.667	3.240	−1.13	−4.327	3.109	−1.39
Model statistics
Log-likelihood	−29.462			−99.227
Gamma	0.641			0.410

Source: field survey, 2022. Note. * p < 0.1, ** p < 0.05, *** p < 0.01.

shows the parameter estimates of the small-scale rice processors’ stochastic frontier model (SFM) for the two groups (participants and non-participants). Below Table 3 is the model diagnostic tools which reported a gamma value of 0.641 and 0.410 for the participants and non-participants, respectively. This implied a 64.1% and 41.0% deviation from frontier output emanated from the group-specific variables, while the remaining 35.9% and 59.0% hailed from the random noise or disturbances, respectively. The gamma is a parameter in stochastic frontier analysis (SFA) that measures the inefficiency of production. Huang et al. suggested that gamma is used to measure how far output falls short of the achievable maximum [62]. However, a gamma value greater than zero indicates inefficiency. It has been shown that participants with a higher gamma value are more efficient in delivering a quality output using the subsidized equipment. Equally, the cause of their inefficiency is attributed to their managerial characteristics, not the machine becoming obsolete.

Among the participants, the result shows that paddy, firewood, and water are the most important inputs in rice processing in the study area. The coefficient of the log of paddy is positively significant at a 1% level of probability; this implies that a unit increase in the quantity of paddy processed is associated with a 1.003 kg increase in milled rice output. The paddy goes through five stages in processes such as soaking and parboiling to soften the outer husk and facilitate removal during milling, drying to reduce moisture content, milling to remove the husk, polishing to give it a shiny and attractive appearance, grading to sort the milled rice by size, shape, and colour, and sorting (de-stoning) the rice by hand or machine to remove discoloured grains and foreign matter. Another important variable is firewood, whose coefficient is positively significant at a 1% level of probability. This implies that a 1% increase in the amount spent on firewood for rice parboiling will lead to an 11.8% increase in milled rice output. The study equally revealed that the coefficient of water was negative and significant at a 1% level of probability; this implies that a 1% increase in the volume of water used for parboiling will reduce milled rice output by 68.0%. With a recent technique of rice processing known as false bottom technology, rice parboiling is carried out by steam. Paddies do not need to come in contact with water during parboiling. Parboiling with false bottom technology is a method of parboiling rice that utilizes an inverted bowl-shaped vessel with a false bottom. The false bottom creates a barrier between the water and the grain, allowing the grain to be cooked in steam instead of boiling water. This method is beneficial for parboiling rice because it preserves the nutrition, flavor, and texture of the grain without overcooking it. It also reduces cooking time and energy consumption [21].

The group-specific variables are reported at the bottom of Table 3. Note that in a one-stage SFA, the variable with a positive coefficient has a negative effect on TE, while those with negative coefficients have a positive effect on TE [16]. From the result of the participating small-scale processors, it can be observed that years of formal learning negatively affect TE at a 10% level of probability. Experience and household size have the expected negative sign, which means a positive effect on TE. This positive effect on TE by household size was confirmed among the non-participating processors at a 5% level of probability.

4.2. Estimation of Parameters of the Stochastic Meta-Frontier (SMF)

The result for the SMF is presented in

Table 4. Stochastic meta-frontier parameter.

Anambra State, Nigeria
Variable Names	Estimates	Std. Err.	z
Log-Paddy-input (kg)	0.520	0.171	3.05 ***
Log-Cost of Firewood (N)	0.135	0.052	2.58 **
Log-water (Liter)	−0.725	0.182	−3.98 ***
Log-Cost of labor (N)	0.383	0.308	1.24
Log-Diesel (Liter)	0.001	0.004	0.32
Depreciation on Huller (N)	0.196	0.119	1.65 *
Constant	6.398	1.744	3.67 ***
Economic-specific variables
Economic cost of grading and sorting	1.960	1.129	1.74 *
Depreciation on False bottom technology	−0.044	0.151	−0.29
Depreciation of other assets	2.219	1.305	1.70 *
Technology prowess	0.003	0.030	0.11
Constant	−20.075	8.841	−2.27 **
Model statistics
Log-likelihood	−160.000
Gamma	0.557

Source: field survey, 2022. * p < 0.1, ** p < 0.05, *** p < 0.01.

; the research showed that paddy, the cost of firewood, water, and depreciation on huller are highly significant when it comes to the output of milled rice, emphasizing their value in the industry. The coefficient of paddy was positive and significant at a 1% level of probability; this implies that if all things are equal, a 1% increase in the quantity of paddy processed is associated with a 52.0% increase in milled rice output in Anambra State. Again, the cost of firewood is positively significant at a 5% level of probability; this means that a 5% increase in the amount earmarked for firewood used in parboiling of paddy is only associated with a 13.5% increase in milled rice production in the study area. Just as expected, the coefficient of water was negative and significant at a 1% level of probability. This implies that a 1% increase in the quantity of water used in parboiling activity is associated with a 72.5% reduction in output. As pointed out earlier, the recent method of rice parboiling requires less water since the false bottom technology uses a steam parboiler method. Furthermore, the coefficient of depreciation on huller is positive and statistically significant at a 10% level of probability; this implies that a 10% increase in mechanical milling operation (the use of a machine) will increase milled rice output by 19.6%. If all things are equal and processing inputs are held constant, milled rice will increase by 6.398 kg in Anambra State.

The study further revealed a diagnostic gamma value of 0.557, meaning that the meta-frontier function experienced a 55.7% deviation from the maximum or expected optimal. This deviation from optimum output is associated with economic-specific variables. As submitted earlier, the inefficiency components with negative coefficients have a positive effect on the MTE [12,16]. Only the false bottom has the expected negative sign, though it was not significant at any level of probability. Furthermore, the economic cost of grading and sorting, and depreciation on other assets were positive and significant at a 10% level of probability, meaning that the said economic-specific variables are contributing to inefficiency in small-scale rice processing in Anambra State. The inefficiency observed in small-scale rice processing in the state which can be attributed to economic-specific variables suggests that the general equipment should be upgraded to be similar to what the VCDP beneficiaries have. However, Schlickmann et al. allude that machines are sustainably considered obsolete due to their inadequate environmental and social performance [74].

4.3. Estimation of the Technical Efficiency and Technological Gap Ratio

Table 5. Technical efficiency scores and technology gap ratios.

		Mean	Std. Dev.	Min	Max
Rice industry	TE	0.506	0.196	0.001	0.844
	MTE	0.498	0.200	0.002	0.843
	TGR	1.000	0.199	0.318	1.678
Participants	TE	0.700	0.217	0.145	0.929
	MTE	0.751	0.196	0.167	0.949
	TGR	0.924	0.140	0.557	1.153
Non-participants	TE	0.544	0.214	0.009	0.845
	MTE	0.566	0.229	0.008	0.868
	TGR	0.983	0.322	0.408	1.870

Source: field survey, 2022.

presents the results of the estimated group and regional TE, MTE, and TGR. The study found that the mean TE scores for agricultural intervention for participants and non-participants are 0.700 and 0.544, respectively; the implication is that small-scale rice processors participating in the intervention program are operating at 30.0% below optimal capacity, while the non-participants are operating at 45.6% below their full capacity; the result for the non-participant is consistent with 0.556 recorded by Mwea district in Kenya [52], whereas the 70.0% is in agreement with Diarra et al. [36] who reported that TE of small-scale rice processing ranges from 65–70%. For processors in the two groups to attain 100% frontier output, they would have to bridge the gap between their current output and the maximum achievable output. It will be needed that processors in the industry engage in activities such as entrepreneurship training, and participation in agricultural intervention program to improve their managerial skills. In terms of MTE, the mean value for the participants and non-participants is 0.751 and 0.566, respectively. Thus, on average, participating small-scale processors are closer to the industrial potential than their non-participating counterparts. Furthermore, non-participating processors would need to increase their production levels to match the participants’ level of output; this finding on participant’s MTE agrees with 0.784 reported by Majiwa and Mugodo in West Kano [52], while the non-participant MTE is in agreement with 0.557 recorded in Mwea District. In addition, the average TGR for participants and non-participants is 0.924 and 0.983, respectively. This implies that the participants and the non-participants have to, respectively, close 8.0% and 2.0% gaps to be technically efficient. This assertion is in agreement with Ng’ombe [12] and Obianefo, Ng’ombe et al. [16], who stated that a TGR of less than 1 indicates that the respondents have not adopted the most advanced technology. On the other hand, the output of the non-participants is closer to being tangential to the meta-frontier output compared to the participants. This does not imply that the non-participants are more productive, but that the capacity of their outdated processing equipment or scale efficiency is lower. It could also mean that the participants have not been able to come to terms with the type of technologies administered to them. Furthermore, the rice industry’s TE and TGR are 0.506 and 0.498, respectively. This indicates that the rice industry is operating 49.4% below the optimal capacity and needs to close a 50.2% gap to be technically efficient before their average optimal rice output is equivalent to the expected optimal production levels. There is so much inefficiency among small-scale rice processors in Anambra State. It could be as a result of their inability to purchase modern milling equipment or some environmental-specific factors. This study has proven why demand has not been able to equal supply since processors are not maximizing their scale efficiency. This TGR results have a large effect on how efficient and profitable the rice industry is. The research revealed that there is a disparity in productivity levels. The MTE of 0.566 for non-participants demonstrates that some processors are not taking full advantage of the available technology, leading to lower productivity and increased production expenses.

4.4. Challenges of Small-Scale Rice Processing

The challenges encountered by small-scale rice processors in Anambra State are shown in Figure 1. These challenges are the factors that contributed to the high level of inefficiency of small-scale rice processing in the study area. Most of these factors remain the reason demand has not equaled supply in Nigeria. Evidently from the figure, 46.9% of agricultural intervention participants are challenged by poor market information, while their non-participating counterparts reported 67.9% to the challenge; issues with a high level of competition were also reported by 34.0% of the participants, and 50.6% of the non-participants; these findings are in agreement with the report of Ampadu-Ameyaw et al. [50]. Another challenge encountered is the issue of a bad road network with a percentage value of 76.2% for participants and 69.8% for non-participants. Lack of technical know-how was reported by participants at 30.7%, while the non-participants reported it at 45.4%. These challenges are in agreement with the issues raised by Sennuga et al. [33]. Rice processors in developing countries lack access to reliable market information; additionally, poor road network makes it difficult for processors to transport their product to access wider market option. The issue relating to technical know-how is a serious one because small-scale processors often lack the needed knowledge and skills necessary to maximize their production process.

Additionally, processors participating in the VCDP recorded issues with inadequate market infrastructure at 56.9%, and the non-participants reported at 65.3%; poor storage facility was reported at 49.8% by the participants, while the non-participants reported it at 58.8%. Again, the participants are challenged by inadequate finance at 60.4%, with this being reported at 87.1% by the non-participants. These findings are consistent with the study by Akinnira and Faleye [49]. Most rural communities in Nigeria lack access to established markets, which makes it difficult to connect buyers and sellers; another concern is that poor access to a storage facility leads to spoilage and pest infestations. It also contributes to price volatility in the agricultural sector. It is also important to note that inadequate finance will limit processors’ ability to take advantage of new market opportunities.

The problems found in this study are especially acute in developing countries because poverty is pervasive in such areas. Governments, international organizations, and other stakeholders must take action to address them; without such action, the global food supply will remain at risk.

5. Conclusions and Recommendations

The research on the technology gap efficiency of small-scale rice processors in Anambra State, Nigeria, has highlighted the need for the government to invest in the local agricultural sector to ensure the success of small-scale rice processing. The findings have demonstrated that the existing technology gap has an adverse effect on the productivity of processors. The fact that participants of agricultural intervention recorded 70.0% TE against the 54.4% reported by the non-participants could explain the low industrial efficiency value of 50.6% TE. The use of obsolete equipment by the non-participants can act as a limiting force to achieving higher efficiency value. The result of the participants has confirmed the empirical findings of other scholars, who reported 30.0% postharvest loss in rice sub-sector. However, the only way to improve agricultural productivity is through rural intervention.

Certain measures should be taken to reduce the technological gap, such as providing access to training, technology, and capital. This is because the technology gap is an important factor in determining efficiency among small-scale rice processors. By addressing the issue of access to modern technologies and equipment, small rice millers in the area would be able to increase the efficiency of their operations and ultimately increase their profits. With adequate funding and collaboration between local and international organizations, including governments and NGOs, this sector could achieve considerable success in the near future.

Furthermore, the findings also demonstrate that the TGE of small-scale rice processors is far from optimal. The lack of access to modern technology and the lack of technical expertise amongst the processors are primary factors contributing to the low TGE. The implementation of appropriate public policies, the promotion of technology transfer, and the available technical assistance are all essential for improving the TGE. Ultimately, this will result in higher efficiency and productivity for the processing sector as a whole, leading to greater economic gains for the region.

Despite the importance of this study, several challenges were encountered during the research. They include non-availability of data, scarcity of funding to increase the scope of the study, and non-willingness of the respondents to release important information. Above all, we recorded many successes that can influence policy implementation.