Production efficiency of potato in South Gondar Zone, Ethiopia

Abstract

Potatoes are vital for food security and subsistence farming, especially in highland regions. Enhancing production could lift people out of poverty and boost income, while promoting better nutrition and sustainable yields for farmers. The objectives of the study were to analyze the technical, allocative and economic efficiencies of potato producers and to identify factors determining technical, allocative and economic efficiencies of the potato producers. This study took a sample of 390 households from North West part of Ethiopia in South Gondar zone by using multistage sampling to draw a representative sample. The data was collected through questioner, key informant interview, focus group discussion. The study was employing both descriptive and econometric methods of data analysis. Stochastic frontier analysis model was used for this study to know production efficiency of the sampled households and two limit tobit model used to estimate source of inefficiency among potato producers. The average technical, allocative and economic efficiency (EE) score were 61%, 93% and 57%, respectively. Potato production efficiency influenced significantly by sex of the house hold, membership in cooperative, access of training, availability of credit and extension service. Based on the findings government and non-government organizations should give attention in awareness of services of cooperative, facilitate training and access of credit in relation to potato production to increase productivity of farmers.

Keywords:

• Efficiency
• stochastic frontier
• Tobit
• potato

Reviewing Editor:

• M. Luisa Escudero-Gilete, Food Colour and Quality Laboratory, Dpt. Nutrition and Food Science, Universidad de Sevilla, Sevilla, Spain

Subjects:

• Agriculture & Environmental Sciences
• Food Additives & Ingredients
• Development Studies
• Economics and Development
• Sustainable Development

1. Introduction

At the beginning of the twenty-first century, a number of factors put more strain on the global food system, including rising income levels, urbanization, changing food consumption patterns brought about by globalization and an expanding population (Gastelo et al., 2014). Since agriculture constitutes a sizable portion of the economies of every African nation, it can be a sector that helps achieve a number of important continental priorities, including the eradication of hunger and poverty, promotion of intra-African trade and investment, rapid industrialization and diversification of the economy, sustainable management of the environment and natural resources, creation of jobs, human security and shared prosperity (Dumre et al., 2020).

The lion’s share of Ethiopia’s gross domestic product (GDP), employment, and foreign exchange earnings comes from the country’s dominant sector, agriculture, which is also expected to continue to play a significant role in promoting the nation’s overall economic development in the years to come (CSA, 2021). In Ethiopia, the GDP in 2020–2021 is derived from agriculture at a rate of 32.7%. Additionally, it accounts for 80% of jobs, 70% of industrial raw materials, 85% of the nation’s food supply and 81% of foreign earnings (FDRE, 2017).

Ethiopia’s pleasant climate, close proximity to markets in Europe and the Middle East and relatively inexpensive labor force provide it a competitive edge in growing a variety of horticulture commodities. On the other hand, vegetables make up about 2.08% (8.76 million quintals) of all crop production each season and occupy about 1.64% (238,564 hectares) of all crop-producing land nationwide. Small-scale producers are the primary producers of this type of production (CSA, 2020).

For most Ethiopian smallholder farmers, root crops are a reliable source of food, income and foreign exchange. Potatoes are a major root and tuber crops grown in Eastern and Central Africa for food and cash. They also help reduce poverty, generate income and create jobs in subsectors that handle production, processing and marketing (Degebasa, 2019; Campos & Ortiz, 2019).

Potatoes are a staple food consumed by almost two-thirds of the world’s population, and in 2020, 359.07 million tons were produced worldwide (Dongyu, 2022). Worldwide, potatoes are farmed, and in the last 15 years, their total production has more than doubled in some sub-Saharan African (SSA) nations (Nyawade et al., 2019).

Ethiopia has the highest potential for producing potatoes among African nations because of its highlands, which make up 70% of the nation and are home to a large percentage of the population (Tolessa, 2019; Kabeto, 2021). It also has a promising future in raising the standards of the country’s basic diet in both rural and urban areas. Potatoes account for 82.30% of the total area planted for root crops, and 91.26% of the total root crop productions in Ethiopia. They rank first in terms of volume production and consumption among root and tuber crops, followed by cassava, sweet potatoes and yams (CSA, 2021).

The Ethiopian government aims to increase the nation’s economic benefits and food security. Consequently, agricultural households may see an increase in income because of increased output and enhanced selling effectiveness (Tolno et al., 2016). Increased potato yield can help smallholder potato farmers support themselves as the population expands quickly and is necessary to meet rising demand (Gildemacher et al., 2009).

The effective utilization of resources is essential in numerous emerging nations, including Ethiopia (Tenaye, 2020), and Ethiopia’s potato-growing conditions are underutilized compared to other nations. The most significant issues with production and productivity are related to poor resource and crop management (Tolessa, 2019).

The goal of increasing farm profits and lowering production costs globally is to maximize resource usage efficiency through improved resource management in crop production (Tolessa, 2019). Therefore, it makes sense for nations such as Ethiopia to gain from higher productivity through more effective use of the resources at hand.

Approximately, 40% of potato growers are located in Ethiopia’s northwestern region, which is ideally positioned for potato production and the nation’s primary potato-growing region (Deressa et al., 2017). Because potato mature earlier than most other crops at times of urgent food need, he discovered that it is a key crop for food security and a hunger reliever in this and numerous other sections of the country. It is essential for its contribution to food security and is a source of cash income for a substantial number of rural households (Bazie & Adimassie, 2017). It also has huge potential to contribute to the national economy for smallholder farmers through its value-added goods (Tiruneh et al., 2017).

Favorable environmental conditions, Ethiopia’s average potato production is 13.27 tons per hectare (CSA, 2021), which is less than the global average yield of 20 tons per hectare. However, progressive farmers achieve yields of up to 35 t/ha under the same rain-fed conditions by utilizing high-quality seed potatoes of improved varieties, in conjunction with enhanced management techniques (Bymolt, 2014).

The efficiency analysis results for wheat production, according to Tiruneh and Geta (2016) indicate that technical efficiencies ranged from 23 to 99%, with a mean of 57%. This shows that given the current technologies and inputs accessible to smallholder wheat farmers, there is a significant potential to boost wheat productivity and that farmers are not operating at the frontier of possible production. Distance to all weather roads negatively affects efficiency, but factors, such as sex, age, education level of the family head, livestock holding, group participation, farm size, fragmentation, tenure status and investment in inorganic fertilizers positively affect efficiency.

According to Dube et al. (2018), technical, allocative and economic efficiencies are estimated using a parametric stochastic frontier production (SFP) function (Cobb-Douglas), and the implications of inefficiency are examined in the second stage using a two-limit Tobit regression model. The results indicated a considerable degree of inefficiency in maize production, with mean technical, allocative and economic efficiency (EE) scores of 62.3, 57.1 and 39%, respectively. It was demonstrated that a variety of factors, including farm size, livestock holding, extension service participation, family size, educational attainment and the use of mobile devices, affected technical, allocative and EE.

Efficient use of resources is essential for improving the wellbeing of smallholder farmers and enhancing the yield of potatoes through efficiency. As a result, one of the prospective areas for potato production in Northwest Ethiopia is the South Gondar Zone, where this study aims to investigate the efficiency of potato production. Empirical evidence on the production efficiency of potato in the research area reveals little or almost non-existent information. As a result, production efficiency of potato in the south Gondar zone, Ethiopia was evaluated.

2. Literature review

2.1. Theoretical review

In microeconomics theory, a producer’s goal is to identify a way to produce maximum output using a given input with a minimum cost of production. This theory indicates producers within the framework of the free market rule and then allocates input and output efficiently to obtain the objective of maximum profit with minimum cost (Bahta et al., 2021). Productivity is defined as the ratio of production output to constraining resources or inputs (Waluse, 2006).

The foundation of microeconomic theory is the presumption that producers maximize behavior from both a technical and economic standpoint, whether from a producer or a consumer perspective. Producers optimize from two perspectives: economically, by finding solutions to price-related allocation problems, and technically, by avoiding wasting productive resources. Numerous writers have interchanged the terms productivity and efficiency and used them to describe a producer’s performance. However, these two concepts are not synonymous (Coelli et al., 2005).

Type and quality of inputs utilized in the production process (technical efficiency [TE]) and the degree to which these inputs are coupled with production technology in the production process are the two factors that determine agricultural output. Technological advancement can increase agricultural productivity by pushing the production frontier upwards. Alternatively, producers can become more efficient by improving their education, using inputs more wisely, and cropping and tillage techniques to make the most of the technology in place. Businesses that operate closer to the current frontier would exemplify this. Thus increasing efficiency or implementing new technologies can lead to higher productivity. Efficiency gains are frequently fully blamed for productivity increases, although this is frequently untrue because technical advancements may be the only factor that drives productivity. In economics, the term ‘efficiency’ is often used to describe the best possible utilization of resources during a productive process. Stated differently, a production process is deemed effective if it is structured such that, in light of the established production goals, no other method can yield a higher benefit when all expenses are considered (Shubik, 1978).

The history of microeconomics with efficiency measurements dates back to (Farrell, 1957), who established basic company efficiency metric. According to his proposal, a firm’s efficiency comprises its technical and allocative efficiency (AE). TE is defined as a firm’s capacity to produce on the iso-quant frontier, whereas AE is defined as a firm’s capacity to produce at a specific output level by employing input ratios that minimize costs. Therefore, a company’s ability to generate a specific product at the lowest possible cost for a particular degree of technology is known as EE. Productivity and efficiency are frequently used synonymously by academics, who view them as indicators of a firm’s performance. However, these two phenomena are not the same. Put simply, a farmer’s productivity is defined as the amount of output they produce for every unit of input. According to Coelli et al. (2005), productive efficiency is the ideal input mix for producing a given level of output, while minimizing production costs.

According to Malinga et al. (2015), TE can be defined as the best way for a farm’s inputs to be transformed into outputs that indicate production. TE evaluates whether converting inputs into outputs results in maximum productivity or output, without wasting resources. While AE measures a producer’s capacity to distribute inputs in the most efficient ways while considering market prices. According to Ojo (2006), EE can be defined as a farm’s ability to maximize output at the lowest possible cost while considering available technology to maximize profits.

2.2. Empirical review

Ethiopia is one of the top producers in Eastern Africa due to its appropriate agro-ecology and levels of domestic demand (FAO, 2019). CSA (2019) shows that potato production in Ethiopia was 1,044,436.359 tons and it covers 76,677.64 ha of land with a productivity of 13.62 tons/ha whereas CSA (2020) report displays a production of 924528.361 tons on 70362.22 hectors of land with a productivity of 13.13 tons/ha. And CSA (2021) report signified productivity of potato was 13.27 tons/ha and it is lower than world average which is 20.7 tons/ha (FAO, 2021) and very low as compared to an attainable level of 25 tons/ha on farmers field and about 35 tons/ha on research fields (Tiruneh et al., 2017).

The average technical, allocative, and economic efficiencies were 0.98, 0.77 and 0.75, respectively (Shahnavazi, 2018). The results showed that the consumption of seeds, manure, herbicides, fungicides, nitrogen, direct labor and water was greater than the optimal economic amount, while the use of pesticides and potash was lower than the optimal amount. This indicates that the production costs could have been reduced by 25%. The researcher discovered that resource allocation is the primary issue in potato production in Iran. Consequently, by optimizing the use of inputs, the profit margin could be increased and the maximum and minimum expected reductions in relation to the level of input consumption currently observed were associated with fungicide and seed, respectively. Water and seed inputs must be prioritized in terms of their values. It is anticipated that increasing EE will reduce Iran’s potato production costs.

According to Battese and Coelli (1995) constant term, age and schooling of farmers and year of observation are significant elements which have effects on technical inefficiency in the SFP function. The finding of Wang (2002) indicates that estimate each firm’s level of technical inefficiency and the way in which inefficiency depends on observable variables typically firm characteristics.

For rice production in Benin there are both technical inefficiencies and allocative inefficiencies. The sources of technical inefficiency were age, gender, education level and access to credit whereas allocation efficiency was influenced by age, gender, area planted, type of culture and access to credit (Houngue et al., 2020).

Tenaye (2020) noted that the following factors significantly impact TE: responsiveness to policy, household head’s education, family size, farm size, land fragmentation, land quality, usage of credit, extension services, off-farm work and crop share. The analyses also show which factors – labor, traction power, farm size, seeds and fertilizer – are responsive to changes in policy in the production function. The surveyed farmers’ mean household-level efficiency was 0.59, suggesting room for improvement in terms of TE. This suggests that if Ethiopian smallholder farms become technically effective, they can lower the amount of input required to produce an average yield of 41 percent.

3. Methodology

3.1. Description of the study area

The study was carried out in the South Gondar zone, which has the potential for potato production in north-west Ethiopia. Three districts, namely, Estie, Farta and Laygayent were selected as shown in Figure 1. The livelihood of the communities in this zone is mainly comprised a rain-fed mixed subsistence crop production-livestock farming system. The South Gondar Zone is located in the Amhara Regional state of Ethiopia. Debre Tabor is the capital city of this zone. South Gondar is bordered to the south by East Gojjam, to the southwest by West Gojjam and Bahir Dar, to the west by Lake Tana, to the north by Central Gondar, to the northeast by Wag Hemra, to the east by North Wollo, and to the southeast by South Wollo. It covers an area of 14,095 km² and sub-divided into 13 rural and 5 urban administrative areas.

Figure 1. Location map of the study area (South Gondar). Source: Computed based on Ethio-GIS database.

3.2. Research design and data source

A cross-sectional research design was employed in this study to analyze the production efficiency of potato producers in South Gondar Zone, Ethiopia. Secondary and primary data were also used. Secondary data were sourced from published sources and primary data were collected from smallholder farmers who produce potato.

3.3. Sampling technique and sample size

This study used multistage sampling to obtain a representative sample. In the first stage, three districts were selected randomly from a list of potential potato production districts in the South Gondar Zone. In the second stage, three kebeles were selected from each district using simple random sampling from the list of district kebeles. The last stage sample producers were randomly selected from each selected kebele proportionally. The total number of potato producers on the selected kebeles was 13,489.

Using (Muganda and Muganda, 2003) table, the sample size was determined by considering the confidence level, degree of variability, and precision level. Consequently, n was calculated as follows: $$n=Z2(1-p)/\mathrm{e}2=\left(1.96\right)2\left(0.5\right)\left(0.5\right)/\left(0.05\right)2=385$$ where n is the required sample size when the population is large, Z is the normal standard deviation (1.96) corresponding to the 95% confidence level, p is the predicted target population characteristic assumed to be equal to 0.5, where the occurrence level is not known, and e is the desired level precision (0.05). Based on this, the sample size from the selected kebeles was 385. The study considered a 5% contingency for precision therefore, the total sample size was 404, and was taken proportionally from selected kebeles.

3.4. Methods of data collection

A semi-structured interview schedule consisting of both open-ended and closed-ended questions was prepared and administered to the sample potato producers. It was pre-tested using farmers who were not part of the sample, and the interview schedule was updated by incorporating the defects observed in the content.

3.5. Method of data analysis

This study employs both descriptive and econometric methods. Descriptive analysis was used to summarize important characteristics of the sample households, such as means, percentages and standard deviations. The econometric model is used to measure the level of technical, allocative and EE, and the source of inefficiency.

The drawback of the non-stochastic model is that it considers random elements (such as measurement errors and unfavorable weather) to be a part of inefficiency. Therefore, in comparison to other models that account for random errors, the inefficiency estimates are inflated when there is a high level of random error in the data or when there are few outliers. According to Coelli (1995), one of the critiques of the deterministic/non-stochastic approach is that it fails to consider the potential effects of measurement errors and other noise on the estimated frontier shape and placement.

Meeusen and Van Den Broeck (1977) and Aigner et al. (1977) independently devised a SFP function. Compared with other commonly used efficiency analysis approaches, the proposed methodology has some logical advantages. First, they are simple to apply and understand. Above all, the model makes it possible to distinguish between the impact of statistical noise and the systematic causes of inefficiency. Following Aigner et al. (1977) and Meeusen and Vanden Broeck (1977) we define the SFP model in Equation (1)(1) $$\mathit{\text{ln}}{y}_i={\beta }_0+{\displaystyle \sum }_{j=1}^5\hspace{0.17em}{\beta }_j\mathit{\text{ln}}{X}_{\mathit{\text{ij}}}+{\epsilon }_i$$(1) : (1) $$\mathit{\text{ln}}{y}_i={\beta }_0+{\displaystyle \sum }_{j=1}^5\hspace{0.17em}{\beta }_j\mathit{\text{ln}}{X}_{\mathit{\text{ij}}}+{\epsilon }_i$$(1) $${\epsilon }_i={\mathit{\nu }}_i+u_i$$

Here, ln denotes the natural logarithm, j represents the number of inputs used, i represents the ith farm in the sample, Yi represents the observed potato production of the ith farmer, X_ij denotes the jth farm input variables used in potato production of the ith farmer, ß stands for the vector of unknown parameters to be estimated, ɛ_i is a disturbance term composed of two elements (v_i and u_i). Random error (v_i) accounts for the stochastic effects beyond the farmer’s control, measurement errors, and other statistical noises and u_i captures technical inefficiency.

Aigner et al. (1977) proposed the log-likelihood function for the model in Equation (1)(1) $$\mathit{\text{ln}}{y}_i={\beta }_0+{\displaystyle \sum }_{j=1}^5\hspace{0.17em}{\beta }_j\mathit{\text{ln}}{X}_{\mathit{\text{ij}}}+{\epsilon }_i$$(1) , assuming a half-normal distribution for the technical inefficiency effects (u_i). They expressed the likelihood function using λ parameterization, where λ is the ratio of the standard errors of the non-symmetric to symmetric error term (i.e. λ = σu/σv). However, Battese and Corra (1977) proposed that the λ parameterization, where; was used instead of λ. The reason is that λ could be any non-negative value while γ ranges from zero to one and better measures the distance between the frontier output and the observed level of output resulting from technical inefficiency. $$\gamma ={\sigma }_u^2/\left(\sigma {\hspace{0.17em}}_{\nu }^2+{\sigma }_u^2\right)$$ $${\sigma }^2={\sigma }_{\nu }^2+{\sigma }_u^2$$ $$\gamma ={\sigma }_u^2/{\sigma }^2$$

TE is predicted by computing the ratio of the observed production values to the corresponding estimated frontier values. (2) $$\mathit{\text{TE}}={\beta }_0{\displaystyle \sum }_{j=1}^5{\beta }_{j\hspace{0.17em}}\mathit{\text{ln}}{X}_{\mathit{\text{ij}}}+(v_i-u_{i)}/{\beta }_0{\displaystyle \sum }_{j=1}^5{\beta }_{j\hspace{0.17em}}\mathit{\text{ln}}{X}_{\mathit{\text{ij}}}+v_i$$(2)

The dual cost function of the Cobb-Douglas production function can be specified as: (3) $$\text{ln}{c}_i={\alpha }_0+{\displaystyle \sum }_{j=1}^5{\alpha }_j\text{ln}{Z}_{\mathit{\text{ij}}}+{\alpha }_6{\text{lny}}_i*+{\epsilon }_i$$(3) $${\epsilon }_i={\nu }_i+u_i$$ where i refers to the ith sample farm, j is the number of inputs, C_i is the minimum cost of production, Z_i denotes input prices, Y* refers to farm output adjusted for noise v_i, u_i is allocative inefficiency and α is parameters to be estimated.

AE is predicted by computing the ratio of the estimated value to the observed cost values. (4) $$\begin{array}{c}\mathit{\text{AE}}={\alpha }_0{\displaystyle \sum }_{j=1}^5{\alpha }_0\mathit{\text{ln}}{Z}_{\mathit{\text{ij}}}{\alpha }_6\mathit{\text{ln}}{y}_i{}^{\text{*}}+(v_i+u_i)/\\ {\alpha }_0{\displaystyle \sum }_{j=1}^5{\alpha }_0\mathit{\text{ln}}{Z}_{\mathit{\text{ij}}}+{\alpha }_6\mathit{\text{ln}}{y}_i{}^{\text{*}}+v_i\end{array}$$(4)

EE is multiplication of the predicted value of TE and AE.

3.6. Definition of variables and hypotheses

3.6.1. Inputs

Land (land): This is the entire size of the plot(s) used by each sample farmer to produce potatoes during the production year. Farmers may own the land or may have acquired it through sharing cropping agreements, hiring or renting. Therefore, hectares of the plot allotted for potato production during the production season of 2022–2023 were considered for this study.

Human labor (labor): During the 2022–2023 crop season, this input records the labor used for various agronomic procedures related to potato production. However, age and sex disparities among the labor force were predicted. Therefore, by using the standard individual work was converted to Man Days (MDs) in order to create a homogenous group of labor to be added. As a result, the total number of MDs used for land preparation, planting, input application, culture and harvesting were used to indicate human labor input.

Oxen (oxen): Oxen labor is one of the main inputs of production in the study area because of small-scale farmers and less-mechanized farming practices. Oxen were used for plowing the study area. Therefore, the total number of oxen days allotted to potato-producing activities throughout the 2022–2023 production season was used to calculate the amount of oxen labor.

Seed (seed): This speaks of the total kilogram of potato seed utilized by every farmer in the sample throughout the year 2022–2023.

Fertilizer (ferti): This refers to the amount of chemical fertilizer used by sample households for potato production and is measured in kg.

Input prices: Costs of input gathered using primary and secondary data to estimate the cost function. The average local rental land value in the area, expressed in Birr/ha, was used to estimate the unit price or cost of land. Because the area’s wage rate fluctuates greatly between the slowest and busiest times of the year, the average wage rate for the period when various agronomic practices are implemented to determine the labor cost in Birr/MD. The average daily rental value of a pair of oxens was calculated for ox work and the market price for fertilizer and seed.

3.6.2. Dependent variables

1. Output (yield): this is the dependent variable in the SFP function model. It is the amount of potato that is attained from the given factor of production and technology in the cropping season by the sampled potato producers through rain-fed farming and is measured in kilograms.

2. Total cost: This is another dependent variable, which is the stochastic frontier cost function or dual cost function.

3.6.3. Independent variables

These variables affect efficiency. As shown in Table 1 after a thorough review of previous studies and the prevailing situation in the study area, different factors (demographic, socio-economic and institutional) that affect efficiency are hypothesized as follows:

Table 1. Definition and hypothesized effects of variables.

No	Variable code	Variable description	Unit of measurement	Expected sign for efficiency
1	sex	Sex of the household head	Dummy; 1 = male, 0 = female	+
2	age	Age of household head	Years	±
3	edu	Education level of household head	Categorical; 1 = illiterate, 2 = read and write, 3 = primary school, 4 = secondary school and 5= certificate and above	+
4	famsize	Size of family	Adult equivalent	+
5	farsize	Land-holding size	Hectare	+
6	livstock	Total number of livestock in terms of TLU	TLU	+
7	extpvfr	Contacts of farmers with extension workers	Dummy; 1 = yes, 0 = otherwise	+
8	cred	Access of credit	Dummy; 1 = yes, 0 = otherwise	+
9	train	Training about potato production	Dummy; 1 = yes, 0 = otherwise	+
10	offfi	Activities of non/off farm	Dummy; 1 = yes, 0 = otherwise	±
11	coop	Farm household membership in cooperative	Dummy; 1 = yes, 0 = otherwise	+
12	mob	Ownership of mobile	Dummy; 1 = yes, 0 = otherwise	+

Sex (sex): The gender of the household head is captured as a dummy variable indicating whether the household is headed by a male or a female. The findings of Tiruneh and Geta (2016), and Dominic Midawa Gulak (2021) show that male-headed households positively influence production efficiency. In this regard, the gender of the household head is hypothesized to positively influence the efficiency potato production.

Age (age): This refers to the age of the household head, measured in years. It is a significant variable that positively affects production efficiency positively (Dube et al., 2018; Jote et al., 2018; Tiruneh & Geta, 2016). Farmers with more years of experience are expected to be more efficient. However, older farmers are relatively unlikely to change their long life farming exercise, which is usually traditional and less efficient. Moreover, labor productivity decreases with age younger farmers tend to be relatively more productive because of the difficult nature of farm operations (Ike and Inoni, 2006). Therefore, this study hypothesized an indeterminate relationship between age and potato production efficiency.

Education (edu): This variable is the education level of the household head and measured as a categorical 1 for illtreat, 2 for read and write, and 3 for primary school, 4 secondary school, 5 certificates and above. This variable can be used as a proxy for managerial abilities. The education level of the household head has a significant positive value on efficiency, as shown by various researchers on different crops (Tiruneh et al., 2017; Dube et al., 2018; Tenaye, 2020), and farmers with more years of schooling tend to be more efficient, presumably due to their enhanced ability to acquire technical knowledge, which makes them closer to the frontier.

Farm Size (land): measured in terms of landholding size in hectares, which refers to the area of cultivation (own, shared or rented in). This variable positively determines the efficiency of farmers positively (Dube et al., 2018; Tenaye, 2020). As farmers holding large farms have the capacity to use compatible technologies that could increase their efficiency, farmers holding large farms are more efficient.

Number of livestock (tlu): The total number of livestock in the tropical livestock unit (tlu). Livestock support crop production in many ways; it can be a source of cash, draft power and manure that is used to maintain soil fertility, and it also serves as a shock absorber to unexpected hazards in crop failure and is the main source of animal labor in crop production (Solomon, 2012; Tiruneh & Geta, 2016). Therefore, in this study, the effect of livestock on efficiency was hypothesized to be positive.

Extension service (extpvfr): This is a continuous variable that is the number of contacts of farmers with extension workers in the production year. The extension agent provides agricultural extension services and practices in agronomy, crop protection, input use, soil conservation, and other activities Tenaye (2020) which access to extension services serves as a bridge for the diffusion of new technologies to improve the level of efficiency. Farmers who accessed extension services had a higher level of efficiency than those who failed to access them services (Tesema, 2021). The greater the linkage between farmers and development agents’ knowledge transfer from the extension worker to the farmer and the agricultural productivity problem from farmers to extension workers and production of marketable surplus (Ngwako et al., 2021; Dube and Burhan, 2022). Therefore, access to extension services in this study had a positive effect on the efficiency of potato production in the study area.

Credit (cred): This is a dummy variable that represents access to credit for farm-related purposes by the smallholder farmers. If the farmer has taken credit, the variable takes a value of one, and zero otherwise. Hence, access to credit is an essential source for improving the agricultural activities of smallholder farmers, and this is supported by empirical studies conducted by Tenaye (2020). This study hypothesizes that access to credit positively influences farmers’ production efficiency.

Training (train): Training is an important tool in building the managerial capacity of farmers, and farmers receiving vocational training have the ability to produce more output because training will increase their understanding (Abdullah et al., 2019; Meskel et al., 2020). In this study, training is defined as a dummy variable whose value of one indicates that the farmer received training on any of the potato production and market activities, and zero otherwise. This study hypothesizes that training has a positive impact on farmers’ levels of efficiency.

Non/off-farm occupation (offi): This is a dummy variable that has a value of one if the farmer or his economically active family members are engaged in any non/off-farm employment and, zero otherwise. Off-farm activities supplement agricultural activities in terms of providing cash income by purchasing the necessary inputs in a timely (Tesema, 2021). However, Asfaw (2021) argued that farmers who participate in off-farm work are likely to be less efficient in farming as they share their time between farming and other income-generating activities. The effect of this variable can be positive or negative.

Cooperative membership (coop): This variable indicates farm household membership in cooperative and is considered a dummy variable that takes a value of one if the farm household head is a member and zero otherwise. Being a member of a cooperative helps farmers adopt improved technologies that are related to access to inputs and information (Dominic Midawa Gulak, 2021; Dube et al., 2018; Nwaru et al., 2011). This study hypothesizes a positive relationship between cooperative membership and the efficiency of potato production.

Potato farming experience (exper): This is a continuous independent variable indicating the potato production experience of the household head in years. Farmers with more experience in potato production are expected to be in a better position to know how to produce the crop and about the potential benefits than farmers with less experience in potato production activities (Dominic Midawa Gulak, 2021; Mengui et al., 2019). In this study, this variable was hypothesized to positively determine the potato production efficiency.

Mobile ownership (mob): The dummy variable for mobile ownership is assigned a value of one if the respondent has mobile ownership and zero otherwise. Mobile ownership can be considered as a proxy for information. It is expected that mobile farmers have more access to information about technologies, such as the use of fertilizer, improved seed, and best practices (Ahmed et al., 2018). Hence, in this study, we hypothesize that mobile ownership has a positive effect on the efficiency of potato producers.

3.7. Ethical statement

Ethical approval was obtained from the ethical review committees of the College of Agriculture and Environmental Science the behalf of the University of Gondar. Written informed consent for participation in the study was obtained.

4. Result and discussion

This section presents the findings of the study and discusses the results. This chapter is organized into two parts. The first part presents a descriptive analysis that deals with the demographic and socio-economic characteristics of sample households and their input utilization. The second part includes econometric analysis, which deals with the estimation of the potato production function, potato cost function, and source of inefficiency.

4.1. Descriptive statistics

4.1.1. Demographic and socioeconomic characteristics of sample households

In this study, the total number of sampled households was 390. The average age of the sampled households was 48.8 with a minimum of 30 years and a maximum of 71. This indicates the average productive age of the sampled households. For the adult equivalent, the mean was 4.03, whereas the minimum and maximum adult equivalents of the sampled households were 1.6 and 9.5, respectively.

Livestock holding was one of the variables that affected potato production among farmers. In this study, the variable was measured in a tlu and converted to a standardized unit based on Storck et al.’s conversion factor. As shown in Table 2, the average number of TLU was 5.23 with a minimum of 0 and maximum of 19.82. The results show that there was a significant difference in the ownership of livestock. In the study area, farmers walk an average of 4.23 km to reach the nearest market, with a minimum of 1 km and a maximum of 8 km. This indicates that some potato producers walk more time to reach the nearest market than others do.

Table 2. Descriptive statistics of continuous variable.

Variables	Total (N = 390)
	Mean	St. De	Minimum	Maximum
Age	48.8	8.8	30	71
Adult equivalent	4.03	1.57	1.6	9.5
Market distance	4.23	1.59	1	8
Livestock (TLU)	5.23	3.17	0	19.82
Potato produced kg	2521.4	1788.081	300	11,600
Landholding size	1.53	0.76	0.25	5

Source: Computed from own survey data.

According to the study, the mean of the total land holding size of the sample house hold was 1.53 ha with a minimum of 0.25 ha and maximum of 5 ha. Furthermore, the average potato production was 2521.4 kg with a minimum of 300 kg and a maximum of 11,600 kg.

4.1.2. Input utilization and cost of potato production

The production function for this study was estimated using five input variables, and the output was the dependent variable of the function. As shown in Table 3 the mean output was 2521.41 kg with a minimum value of 300 kg and a maximum of 11,600 kg. With regard to plot of size to potato production the maximum was 3 ha whereas the minimum was 0.06 ha with a mean of 0.37 ha. The study shows a great difference between potato output and plot size for potato production among the sampled households.

Table 3. Input utilization in potato production.

Variables	Mean	Std.De	Min	Max
Output (k.g)	2521.41	1788.081	300	11,600
Land (ha)	0.37	0.326	0.06	3
Labor (man day)	85.72	46.85	11.43	425.7
Oxen (oxen days)	6.14	3.492	1	18
Seed (k.g)	668.94	549.21	25	2550
Fertilizer (k.g)	84.02	104.17	10	750
Total cost (birr)	43,140.36	32,801.36	3920	163,610
Cost of land (birr)	6608.27	6951.56	158	57,010
Cost of labor (birr)	15,521.84	13,062.42	1310	85,150
Cost of oxen (birr)	3367.7	2607.04	250	14,450
Cost of seed (birr)	14,098.59	11,996.35	590	57,250
Cost of fertilizer (birr)	3442.28	4085.93	115	23,010

Source: Computed from own survey data.

Furthermore, these data indicate that there was a large difference between the maximum and minimum labor used as one of the inputs. The mean number of labor was 85.72 man-days with a minimum of 11.43 and a maximum of 425.7 man-days. The other input was oxen, measured as oxen days that took a mean of 6.14 oxen days with a maximum of 18 oxen days and a minimum of 1 oxen day in the study area. This shows that some potato producers used more oxen days but the others used few numbers of oxen days. With regard to seed, the mean was 668.94 kg with a great difference between the maximum and minimum of 25 kg and 2550 kg, respectively. The final input used by the potato producer was fertilizer. In the study area, the average fertilizer kg used was 84.02 with a maximum of 750 kg and a minimum of 10 kg, which indicates a large difference in the application of fertilizer technology.

In addition to the amount of inputs used, the study examined the total cost of inputs and individual input costs as follows. According to these findings, the average total cost of potato production was 43,140.36 birr. The maximum total cost was 163,610 birr whereas the minimum cost was 3920 birr. With regard to individual input costs, the first was land. The average cost of land in the study area was 6608.27 birr which encounter a maximum of 57,010 birr and a minimum of 158 birr. The other input cost was labor cost, which average 15,521.84 birr at a maximum of 85,150 birr and a minimum of 1310 birr. In the study area, the farming system is traditional. Therefore, there was an oxen cost for potato production. The mean oxen cost was 3367.7 birr with a maximum of 14,450 birr and a minimum of 250 birr. The other major input cost was seed cost, which took an average of 14,098.59 birr with a maximum of 57,250 birr and a minimum of 590 birr. The average cost of fertilizer was 3442.28 birr whereas the maximum and minimum costs were 23,010 birr and 115 birr, respectively.

4.2. Econometric results

4.2.1. Estimation of production efficiency

This section presents TE, AE and EE of potato producers as well as the determinants of efficiency were estimated and discussed. A two-step analysis was performed for the efficiency estimation procedure. First, the technical, allocative and economic efficiencies of potato producer farmers were estimated from the Cobb-Douglas stochastic frontier model and its dual cost function. Second, the factors influencing the efficiency of potato producers were identified using the two-limit Tobit model.

Before interpreting the econometric analysis, the data were tested for multicollinearity using the variance inflation factor (VIF). For categorical variables, the contingency coefficient was calculated to test for multicollinearity. Tests for multicollinearity using both VIF and contingency coefficients confirmed that there was no serious linear relationship among the explanatory variables.

In Table 4, the inefficiency term (u) is significant at the 1% level, which indicates that there was technical inefficiency in potato production in the study area. The value of Lambda (λ) was greater than zero, which also ensured inefficiency in the data. When λ is equal to 0, there are no technical inefficiency effects, and all deviations from the frontier are due to noise (Aigner et al., 1977).

Table 4. Estimation of stochastic frontier production function.

Variable	Coefficient	Stan. Error
Lnland	0.229***	0.072
Lnlabour	0.26***	0.053
Lnoxen	0.198***	0.066
Lnseed	0.25	0.05
Lnfertilizer	0.07	0.037
Intercept	7.26	0.536
Sigma u	0.49***	–
Sigma v	0.421***	–
Lambda (λ)	1.163***	–
Number of observations	390	–
Log likelihood	−317.90	–
Prob > chi^2	0.000	–
Sigma squared (σ^2)	0.417	–
Gamma ($\gamma$)	0.58***	–

Source: Computed from own survey data.

***represents 1% level of significance.

The other variable gamma (γ) has a value of 0.58, which shows that out of the total variation in potato production, 58% was due to technical inefficiency, while the remaining 42% was due to noise (vi), which is expected, especially in the case of agriculture where uncertainty is greater.

The model interpretation of the coefficients of the inputs is presented through the partial elasticities of outputs, which indicates the relative change in potato output from a percentage change in inputs. Among the five input variables in the production function, land, labor and oxen have a significant effect in explaining the variation in potato production among farmers.

The coefficient of labor was 0.6, significant at less than one percent and had a greater coefficient among the inputs in potato production in the study area. This indicates that potato production requires more activities covered by labor. As labor increase by 1% the output increased by 60% for citrus paribus. The coefficient of land was significant at less than 1% significance level, and it has the second elasticity of production, implying that more potato output could be obtained by using more land for potatoes. The value of the coefficient of land shows that keeping other quantities of inputs the same, a one percent increase in potato land would increase the output by 22%, while keeping other input variables constant.

The oxen power is also the other significant input in the potato production at a less than one percent significance level. When the oxen power was increase by one percent the output increased by 19%. This means that as the farmers used more oxen power, potato production also improved. The fourth variable was seed, but it was insignificant in potato production because the farmers in the study area used old improved seeds, which had more years in their hybrid in the research center. In group discussions, farmers explained that they lack new improved potato varieties, which negatively affects their potato production. The coefficient of fertilizer was also insignificant. This could be because producers did not apply fertilizer technology appropriately and did not use it in a timely manner. The sum of the estimated coefficients of inputs was the elasticity of production and was found to be 1.007.

As Table 5 shows in the Stochastic cost function analysis, five input costs were used for potato production in the study area. Among these, labor costs cover the higher cost of potato production, which has a coefficient of 0.38, and it is significant at the 1%. The seed cost covers the second stage of total cost. As the seed cost increase by one percent total cost increases by 29% at less than one significance level. The other input cost was land cost, which has a coefficient of 0.14 and is significant at less than one significance level. The fourth factor is the cost of the fertilizer. When the cost of fertilizer increase by 1% the total cost increased by 11%. Oxen power cost is also one of the costs, as the cost of oxen increases by 1%, the total cost increases by 9% and is significant at less than 1%.

Table 5. Estimation of stochastic frontier cost function.

Variable	Coefficient	Stan. Error
lnoutput	−0.003	0.002
Lnland cost	0.136***	0.008
Lnlabour cost	0.377***	0.0078
Lnoxen cost	0.086***	0.007
Lnseed cost	0.293***	0.011
Lnfertilizer cost	0.105***	0.006
Intercept	1.516***	0.027
Sigma_u	0.068***	–
Sigma_v	0.006***	–
Lambda (λ)	10.87***	–
Number of observations	390	–
Log likelihood	621.73	–
Prob > chi^2	0.000	–
Sigma squared (σ^2)	0.0046	–
Gamma (ᵞ)	0.98***	–

Source: Computed from own survey data.*** represents 1%  level of significance

4.2.2. Scores of technical, allocative and economic efficiencies

The statistics for the estimated efficiency scores of the technical, allocative and EE indices are presented in Table 6. The mean TE of the sample potato-producing households was found to be 0.61 with a minimum of 0.23 and a maximum of 0.89. The results indicate that there was a wide range of TE between potato producers, and there was a possibility for an average farmer to increase the level of output by 39% farmers to produce at a fully efficient level with the given level of inputs and technology. On the other hand, if the average farmer of the sample could achieve the TE level of their most efficient counterpart, then they could increase their output by 32% that was (1–0.61/0.89) × 100. Hence, there is considerable room to increase output, where farmers cultivate potato without additional inputs, given the existing technology in the area studied. The mean allocative was 0.93 with a minimum of 0.71 and a maximum of 0.98. EE was also estimated to be an average of 0.51, a minimum of 0.22 and a maximum of 0.85. This shows that average farmers would be able to reduce their actual costs of potato production by 49% by operating at full technical and AE levels to produce the existing level of output. In general, the results show that there is great potential for increasing potato output and decreasing costs of production with the existing resource base for producers.

Table 6. Summary statistics of efficiency indices.

Type of efficiency	Mean	Std. dev	Min	Max
Technical efficiency	0.61	0.127	0.23	0.89
Allocative efficiency	0.93	0.064	0.71	0.98
Economic efficiency	0.57	0.128	0.22	0.85

Source: Computed from own survey data.

The distribution of efficiency indices indicated in Figure 2 shows that approximately 21% of potato producers had TE scores below 0.50, and approximately 97% of the farmers had TE scores lower than 0.8, which also revealed the existence of more prospects for producers in increasing production by improving TE in potato production in the study area. Approximately, 30% of potato producers had EE scores below 0.50, and 99% had EE scores below 0.8, indicating that there is a large possibility of improving the EE of potato producers in the study area.

Figure 2. Frequency distribution of efficiency scores. Source: computed from own survey data.

The efficiency score distribution shows that no potato producer had full TE, AE or EE score in these estimates. Based on these results, a wider variation in efficiency scores indicates farmers’ inefficiency in utilizing their resources, which further implies the existence of a wider scope for improvement in potato production in the study area.

4.2.3. Sources of inefficiency in potato production

In the efficiency score analysis, the results showed that there were differences among farmers in their technical, allocative and EE as shown in Table 7. Based on this estimation, the source of inefficiency was estimated. For the estimation of inefficiency scores used as dependent variables, which were obtained by deducting the results of technical, allocative and economic efficiencies from 1.00, inefficiency scores of sample households were regressed against socio-economic, demographic and institutional factors that are expected to affect inefficiency levels using the two-limit Tobit model. This method was selected because the inefficiency indices estimated from the stochastic frontier model and dual cost function were limited to between zero and one, which could possibly be censored.

Table 7. Estimates of Tobit regressions on TI, AI and EI.

Variables	Technical inefficiency		Allocative inefficiency		Economic inefficiency
	Coefficient (std. error)	Marginal effect	Coefficient (std. error)	Marginal effect	Coefficient (std. error)	Marginal effect
Sex	0.04*	0.042	−0.015	−0.015	0.032	0.032
	(0.023)	0.041	(0.01)	−0.01	(0.023)	0.001
		0.001		−0.046		0.0002
Cooperative membership	−0.05**	−0.047	−0.003	−0.002	−0.045**	−0.045
	(0.019)	−0.046	(0.007)	−0.002	(0.019)	−0.044
		−0.001		−0.011		−0.0003
Training	−0.03*	−0.035	−0.007	−0.008	−0.08**	−0.038
	(0.019)	−0.034	(0.008)	−0.005	(0.019)	−0.038
		−0.0007		−0.028		−0.0002
Credit	−0.01	−0.01	−0.014**	−0.014	−0.021	−0.21
	(0.014)	−0.01	(0.006)	−0.009	(0.013)	−0.21
		−0.0002		−0.051		−0.0001
TLU	−0.003	−0.003	−0.004***	−0.003	−0.005**	−0.005
	(0.002)	−0.003	(0.001)	−0.002	(0.002)	−0.005
		−0.0001		−0.013		−0.00003
Mobile	0.02	0.018	−0.036***	−0.035	−0.003	−0.003
	(0.017)	0.018	(0.007)	−0.023	(0.016)	−0.003
		0.0003		−0.155		−0.00001
Primary	−0.02	−0.026	0.064**	0.063	0.009	0.009
	(0.06)	−0.026	(0.026)	0.049	(0.059)	0.009
		−0.001		0.16		0.00004
Secondary	−0.03	−0.031	−0.04*	0.04	−0.008	−0.008
	(0.06)	−0.031	(0.025)	0.03	(0.058)	−0.008
		−0.001		0.161		−0.00004
Month	−0.05	−0.053	−0.045***	−0.045	−0.075***	−0.075
	(0.02)	−0.052	(0.009)	−0.032	(0.019)	−0.074
		−0.001		−0.157		−0.0004
Constant	0.42***		0.1***		0.479***
	(0.073)		(0.031)		(0.071)

Source: Computed from own survey data.

***,** & * represents 1%, 5% & 10% level of significance, respectively.

Among the 12 independent variables hypothesized to create a difference in the level of efficiency score among farmers nine of them are significant. The sex of the household head showed a positive effect on the technical inefficiency of the potato farms, which was significant at the 10% significance level. Female-headed households would have better opportunities to carry out frequent follow up and supervision of farm activities on their plots. Cooperative membership negatively influences technical and economic inefficiency at the 5% significance level. As farmers become members of the cooperative, the inefficiency level decreases. Training also has a negative influence on technical and economic inefficiency at the 10% and 5% significance levels, respectively. Access to credit has a negative impact on allocative inefficiency at the 5% significance level. Livestock ownership and inefficiency also have a negative relationship. This negatively influences allocative inefficiency and economic inefficiency at the 1% and 5% levels, respectively. Mobile ownership was another variable that decreased allocative inefficiency at the 1% significance level.

The marginal effect was estimated for the significant variables in technical inefficiency, allocative inefficiency and economic inefficiency. Sex of the household head positively affects technical inefficiencies, indicating that male-headed households are inefficient compared to female-headed households. From the marginal effect analysis, the coefficients of this variable indicate that, as the household tends to be led by males, the overall probability and level of technical inefficiency would increase by 4.2%. In addition when the household head became male, the expected value of technical inefficiency increased by 4.1%. This shows that females pay more attention to potato production than males do. Male house heads could participate more in other crops. This result is similar to Mengui et al. (2019). Hence, women have accumulated more experience in cultivating potato production than their male counterparts.

Cooperative Membership of the household head to farmer cooperatives has a negative and statistically significant effect on technical inefficiency and economic inefficiency at the 5% level of significance. Farmers who are members of farmer cooperatives receive more information on production technologies and easily access inputs through the organization than farmers who are not members of the cooperatives. As a result, they adopt and apply new production technologies, and hence are more efficient in potato production. As the farmers were members of the cooperative, the marginal effect of the variable had an overall probability and level of technical inefficiency, and economic inefficiency decreased by 4.7% and 4.5%, respectively. Additionally, when the household head became a member, the expected values of technical inefficiency and economic inefficiency decreased by 4.6% and 4.4%, respectively. The result is similar to (Tiruneh & Geta, 2016; Wudineh & Endrias, 2016; Ahmed et al., 2018; Sisay et al., 2015; Dominic Midawa Gulak, 2021).

Training contributes negatively and significantly to decreasing technical inefficiency and economic inefficiency at the 10% and 5% probability levels, respectively. Farmers who received training in potato production and marketing the marginal effect of the variable had an overall probability and level of 3.5% and 3.8%, respectively, which would decrease technical inefficiency and economic inefficiency by these percentages, respectively. Furthermore, the expected values of technical inefficiency and economic inefficiency decreased by 3.4% and 3.8%, respectively. Training is an important tool for building the managerial capacity of household heads. Household heads who received training in potato production and marketing increased their technical and EE. Similar results were reported by (Menelek Asfaw, 2021; Ahmed et al., 2013).

Credit has a negative effect on allocative inefficiency at the 5% significance level. The results indicate that credit availability enables farmers to make timely purchases of inputs that they cannot otherwise provide from their own budget by overcoming liquidity constraints, which may affect their ability to apply inputs and implement farm management decisions on time. Farmers got credit, the marginal effect of the variable had an overall probability level of 1.4%, which would decrease allocative inefficiency, and the expected value of allocative inefficiency would decrease by 0.9%. This result is consistent with (Obare et al., 2010; Alemu et al., 2022; Nwaru et al., 2011).

Education has a significant negative impact on allocative inefficiency at the 10% level. The negative and significant impact of education on allocative inefficiency shows the importance of education in decreasing potato production inefficiency. This indicates that educated farmers are more efficient than are illiterate farmers. In other words, educated farmers have a relatively better capacity for optimal allocation of inputs. The marginal effect of the variable has an overall probability level of 4%, which would decrease allocative inefficiency, and the expected value of allocative inefficiency would decrease by 3%. The findings of this study are similar to (Tesema, 2021; Ahmed et al., 2018; Sisay et al., 2015).

The number of livestock owned, measured in tlus and a proxy for estimating a farmer’s wealth status, has a negative and significant effect on allocative inefficiency and economic inefficiency in potato production at the 1% and 5% levels of significance, respectively. Farmers who owned a greater number of livestock were more allocatively and economically efficient than those who owned a smaller number of livestock in the study area in potato production. This is because livestock provides working power (oxen for draught power), manure fertilizer, and is a source of income that can be used to purchase the necessary agricultural inputs. As the number of livestock increases, the marginal effect of the variable has an overall probability level of 0.3% and 0.5%, which decreases allocative inefficiency and economic inefficiency by these percentages, respectively. The expected values of allocative inefficiency and economic inefficiency decreased by 0.2% and 0.5%, respectively. These results are consistent with those of (Ahmed et al., 2018; Alemu et al., 2022; Sisay et al., 2015).

Mobile phones are also variables that influences allocative inefficiency. This was significant at the 1% level and had a negative impact on allocative inefficiency. Farmers who have mobile phones with an overall probability level of 3.5% decrease allocative inefficiency. The expected value of the allocative inefficiency decreased by 3.2%. Mobile phone ownership is related to information access and helps producers obtain up-to-date market information, which enables better resource utilization. This means that a farmer who owns a mobile phone has better market information access, and hence is less likely to be inefficient in potato production than farmers who do not own mobile phones (Ahmed et al., 2018; Sisay et al., 2015).

Extension visits had a negative effect on technical inefficiency, allocative inefficiency and economic inefficiency of potato farms at the 1% significance level. The overall probability levels decrease technical, allocative, and economic inefficiency by 5.3%, 4.5% and 7.5%, respectively. The expected values of technical inefficiency, allocative inefficiency and economic inefficiency decreased by 5.2%, 3.2% and 7.4%, respectively. Farmers who were visited more frequentlcy by extension agents responded quickly to new technologies and appreciated correct management practices such as timely planting and weeding, the correct amount of fertilizer to be applied, correct seed rate and general management of the farm. Therefore, households that receive more extension visits from extension workers appear to be more technically, allocatively and economically efficient than their counterparts. This result is consistent with (Mengui et al., 2019; Dube et al., 2018; Menelek Asfaw, 2021; Tesema, 2021; Obare et al., 2010; Tenaye, 2020).

5. Conclusion and recommendation

The results of the study indicate that the average age of sampled households was the productive age. Among the sampled potato producers, there were differences in livestock holdings and land holdings. The results of the production function showed that land, labor and oxen days were the inputs that significantly and positively affected potato production. The production efficiency of potato signifies inefficiency in terms of technical, allocative and EE. The average technical, allocative and EE scores are 61%, 93% and 57%, respectively. This indicates that producers have room to improve their efficiency using existing inputs. The study found efficiency differences between potato producers and estimated sources of inefficiency, which were brought about by demographic, socio-economic and institutional variables.

The sex of the household head had a positive effect on the technical inefficiency of the potato farms, whereas cooperative membership negatively influenced technical inefficiency and economic inefficiency. Training also has a negative influence on technical and economic inefficiencies. Access to credit has a negative effect on allocative inefficiency. Livestock ownership and inefficiency also have negative relationships that negatively influence allocative and economic inefficiency. Similarly, mobile ownership decreases allocative inefficiency because producers find information through their mobile devices.

Based on the findings, the study suggests that local and federal governments pay attention to cooperative organizations and create awareness among farmers about the importance of membership in cooperatives. Training also has an impact on the efficiency of potato producers; hence, government and non-government organizations should provide training regarding potato production. Similarly, visiting a potato farm with an extension agent positively affects efficiency. Extension workers should visit and provide training to farmers. The last and not the least significant variable was access to credit. Therefore, credit access must be established and facilitated through rural finance institutions to improve potato productivity.

Acknowledgments

We express our gratitude to the South Gondar Zone Agricultural Office and the District Agricultural Office for their facilitation of data collection.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Upon reasonable request, the corresponding author will make the data analyzed for this study available.

Additional information

Funding

University of Gondar was the budget source of this study.

Notes on contributors

Zework Aklilu

Zework Aklilu: contributes in the conception and design, analysis and interpretation of the data, drafting of the article and final approval.

Tefera Berihun

Tefera Berihun: contributes in the conception and design, analysis and interpretation of the data, revising critically and final approval.

Solomon Zena

Solomon Zena: contributes in the conception and design, revising critically and final approval.

Asmamaw Alemu

Asmamaw Alemu: contributes in the conception and design, revising critically and final approval.