Factors affecting the technical efficiency of potato production under the command area of the PMAMP project in Nepal: The case of Bajhang district

Abstract

With the trend of decreasing productivity in agriculture, the Government of Nepal endorsed a special project, the Prime Minister Agriculture Modernization Project (PMAMP), in 2015. The project selected Bajhang district as the potato zone to boost the production and productivity of potatoes. Against this background, we determined the technical efficiency of potato production and the socio-economic variables determining the frontier using six local levels of Bajhang. The study surveyed a total of 101 households, which were randomly selected following a purposive sampling. This study employed a one-step stochastic frontier method to determine the technical efficiency of potato production in the district. The results revealed that potato production in the district under the command area of the potato zone was technically efficient at 87.75%. The significant elements of the technical inefficiency were years of schooling, access to credit, extension agent visits and receiving training. Thus, the inefficiency of 12.25% can be bridged by focusing and targeting the significant socio-economic aspects. Furthermore, the inefficiency can be reduced by increasing the usage of inputs like fertilizers, labor, farm size, and seeds, which had positive coefficients while the model suggests decreasing the usage of bullocks in potato cultivation. The return to scale was 0.898, revealing the decreasing nature of returns to production. These findings can be used by policy makers, practitioners, PMAMP and concerned stakeholders to increase the efficiency of potato production.

Keywords:

• PMAMP
• potato
• return to scale
• stochastic
• technical efficiency

REVIEWING EDITOR:

• M. Luisa Escudero-Gilete, Universidad de Sevilla, Spain

SUBJECTS:

• Microeconomics
• Econometrics

1. Introduction

Potato, being a major cash crop in Nepal, is way behind (16.72 ton/ha) in productivity compared to the global average (20.95 ton/ha) (MoALD, 2019). It is used along with vegetables in the Terai region and as a staple food in the hilly regions of Nepal (Bajracharya & Sapkota, 2017). Potato ranks fourth in terms of area coverage of food crop in Nepal and second in production (Timsina et al., 2013). Usually, potatoes are contrasted with cereals in terms of their nutrition profile and edible mass because potato contains a diverse range of nutrients, and its edible mass amounts to around 85% compared to 50% in cereals (IYP, 2008).

Potato is a major stable food crop on every continent (Doboch et al., 2022). Potatoes exhibit significantly higher productivity than major cereal crops, thereby contributing to food security as well as nutritional security (Gairhe et al., 2023). More importantly, a developing nation can uplift the status of small-holder farmers, improve the country’s food security status, and garner wealth by investing in efficient potato farming (Tiruneh et al., 2017). Jessie (2017) appreciates the food security role of potatoes; they are both energy-rich and protein-rich. Oumer et al. (2014) assert that the net profit generated from the cultivation of potatoes can be ten times that obtained from the grains.

Being a daily household commodity, Nepal’s consumption of fresh and processed potatoes is increasing annually, reaching 80.56 kg/capita/year in 2013 (FAOSTAT, 2013). Population growth, urbanization, and increased consumption in industries are the reasons for increasing demands for fresh and processed potato items recently (Devaux et al., 2021). This has resulted in a heavy import of potatoes from neighboring countries. Nepal imported US$71,230,036 worth of potatoes in 2021 while only being able to export US$ 127,633 worth of potatoes in the same year (FAOSTAT, 2021).

The agricultural practices, especially in the hills of Nepal, involve mostly marginalized and smallholder farmers (Sapkota & Bajracharya, 2018; Shrestha et al., 2017). In addition, poor technical knowledge might be hindering the production and productivity of potato growers in the hills due to a poor understanding of efficiency (Sapkota & Bajracharya, 2018). Furthermore, the unavailability of quality seeds, fertilizer shortage at cultivation time, shortage of labor, poor market, lack of technical knowledge on pest management, and topographic barriers are the major challenges in potato production in Nepal (Bajracharya & Sapkota, 2017). Besides, the inability to maintain the food security status of the country due to insufficient production of potatoes has been reported by Sulaiman and Andini (2013). In this context, few studies have determined the technical efficiency of potato production in Nepal, viz. Adhikari et al. (2020) and Lamichhane et al. (2019). The studies reported efficiency gaps of 31% and 21%, respectively, for potato production in Nepal. Thus, it is inevitable and eminent to overcome the challenges of potato production by bridging the gap in technical efficiency in potato production.

Thus, with the aim of promoting the commercialization of different agricultural commodities, the Government of Nepal endorsed the Prime Minister Agriculture Modernization Project (PMAMP) in 2015 (Adhikari & Thapa, 2023; Thapa & Dhakal, 2024a). Accordingly, Bajhang district was selected as a potato zone under the PMAMP project, aiming to boost production, productivity, and the area under potato cultivation. Furthermore, the Sustainable Development Goals (SDGs) have put priority on agricultural productivity, which envisages additional research on efficiency in production in developing countries (UN, 2019). However, the growth rate of national production and productivity of potatoes is erratic (Figure 1). The decrease in area of production in the last decade, after 2014 AD, could be due to land fragmentation, emigration, or muscle drain, increasing dependency on remittances, internal migration to urban areas and so on (Rijal et al., 2021; Thapa et al., 2022a; 2022b). The variation in the area, production, and productivity of potatoes in Bajhang district has also been fluctuating over the years despite the increasing trend (Annex 1).

Figure 1. National production and productivity of potato in last two decades (2001-2021 AD).

The food production mechanism in Bajhang is highly ineffective as well as unorganized. Traditional farming has brought inefficient practices of using land, labor, and capital (Bibi et al., 2021). Efficiency in input allocation and combination can make a huge difference in the economics of farmers. However, there have been very few attempts to study the technical efficiency of potatoes in Bajhang through the one-step stochastic approach, as recent relevant literature like Lamichhane et al. (2019) have reported the mean technical efficiency of potato growers in different districts of Nepal to be 79% using the conventional two-step stochastic frontier approach. Very few studies have included the use of the one-step stochastic production frontier approach. Adhikari et al. (2020), in their study on the technical efficiency of potato growers in the Mid-Western Terai region of Nepal, reported the mean technical efficiency to be 69% through a one-step stochastic frontier approach. Thus, the application of a one-step stochastic production frontier approach to study the technical efficiency of potato production in the hills of Nepal could provide an addition to the existing few studies which make the use of such models (Thapa & Dhakal, 2024b).

There is very little information on the PMAMP potato zone and the project’s contribution to agricultural productivity, especially in Bajhang, a remote district of the Sudurpaschim Province of Nepal (H. Joshi, personal communication, February 7th, 2021). It is clear that the production system in Bajhang is inefficient, but knowledge and data regarding the precise degree of inefficiency and factors contributing to it are hazy. Furthermore, details about the hurdles in reaching efficient farming practices in the context of potato production in Bajhang are unclear. To be able to solve the problems of inefficient management and allocation of inputs and technology, it is obligatory to assess the magnitude of the inefficiency. Against this background, this study aims to make an important contribution to policy by addressing the key points that can be specified so as to enhance the yield of potatoes under the PMAMP zone command area through efficient potato production. In this light, our study has three specific objectives: determination of the level of technical efficiency of potato production in Bajhang district; determination of the significant determinants of technical efficiency and determination of the level of productivity of potato growers in the command area of the PMAMP Potato Zone, Bajhang district, Nepal.

2. Technical efficiency

Technical efficiency is the ability of a farmer to optimize outputs under the constraints of inputs and available technologies. The degree of technical inefficiency represents an individual farmer’s failure to obtain the greatest feasible output level given the combination of inputs and technologies employed. Farrell (1957) described technical efficiency as a measurement of any firm’s capacity to utilize given inputs in the most effective way. This means that a firm can either produce the optimal output from a given input (as output-orientation) or produce a fixed output utilizing a minimal level of inputs (input-orientation). The optimal level of output under resource constraints (inputs and technology) is depicted by the production frontier. Figure 2 shows the frontier where the magnitude of the technical efficiency is constrained by the inputs and technology used (adapted from Battese (1992)). The figure includes two axes: output (Y) on the y-axis and inputs (X) on the horizontal axis. The example below would imply that the level of production below the frontier would be deemed inefficient.

Figure 2. Technical efficiency of firms in input-output space.

There has been an increasing literature on measuring the technical efficiency of crop production in developing countries. However, very limited studies have made use of the one-step stochastic frontier approach under the command area of the PMAMP project in Nepal (Thapa & Dhakal, 2024b). Reviewing different literature, various works have assessed the magnitude of efficiency under different programs of the government, contracts, etc. in the context of smallholder farmers (Abate et al., 2019; Mango et al., 2015; Mengui et al., 2019; Missiame et al., 2021; Muzeza et al., 2023; Tesfaw et al., 2021). These studies revealed that the technical efficiency of smallholder farmers in developing countries lies between 0.30 and 0.95. Furthermore, these studies also reported that the efficiency of production among smallholder farmers is significantly affected by different socio-economic and institutional factors like years of schooling, contact with extension agents, training, access to credit, age of household, etc. This depicts a varying magnitude of technical efficiency among smallholder farmers in developing countries, which is in fact associated with different socio-economic, institutional and technical factors. In the case of Nepal, Adhikari et al. (2020) and Lamichhane et al. (2019) have reported the mean technical efficiency of potato growers in different districts of Nepal to be 79% and 69%, respectively. They also reported that the education level of the household head and the number of visits to the extension agents were significantly associated with the magnitude of the technical inefficiency of potato growers.

3. Research methods

3.1. Study area

The study was carried out in the six local levels¹ of Bajhang district (Figure 3), where potato is the major staple crop (GRAPE, 2022). Bajhang is a mountainous district of Sudurpashchim Province, Nepal. Its altitude ranges from 900 meters above sea level (masl) to 7,035 masl. It has an area of 3,422 km² and a population of 195,159. The six municipalities, as shown in Figure 3, are enlisted under the jurisdiction of the Project Implementation Unit of Potato Zone under the PMAMP project of Bajhang in the fiscal year 2019/20. The altitude of the study area varied from 1200 masl to 3000 masl.

Figure 3. Map of the study area (Source: ArcGIS).

3.2. Sampling procedure and determination of sample size

The intended population of the study were potato growers under the PMAMP command area of the Potato Zone in Bajhang. For the computation of the sample size (n), the formula given by Cochran (1963) was used: (1) $$n=\frac{Z^2\mathit{\text{pq}}}{e^2}$$(1)

Where n refers to the sample size, Z denotes the intended z-value producing the desired level of confidence, p denotes the estimated population percentage, and e is the error permitted in estimating the parameter. The formula was used because the population of potato growers is homogenous, i.e., mostly smallholder potato growers.

In our study, the p-value was set to 0.07, as nearly 93 percent of smallholder farmers produced potatoes in the study area. The level of confidence was set to 95% (Z = 1.96 for a two tailed test), which implies that the error permitted was 0.05. The sample was computed as shown below: $$n=\frac{{1.96}^2\mathrm{*}0.93\mathrm{*}0.07}{{\left(0.05\right)}^2}=101$$

In the first stage, Bajhang district and the six municipalities (Figure 3) (sectors listed under the jurisdiction of the Potato Zone) were chosen purposively, representing the Potato zone. The second stage involved the identification of major potato producing municipalities, followed by a random sampling among five communities from each municipality. At last, the random selection of potato-producing households from each community was done. The pre-testing of the interview schedule was done among 5% of the total sample, and the necessary changes were made to the questionnaire. The interview schedule was carried out from February to March, 2021.

3.3. Conceptual framework

The conceptual framework of the interaction among the key variables associated with technical efficiency is shown in Figure 4 below. The provision of agricultural inputs to farmers is inevitable for increasing agricultural productivity and uplifting rural livelihoods to an optimal level (Kumar et al., 2015). We consider the major inputs like land, seed, fertilizer, labor, and bullock for the production process. Besides the agricultural inputs, the role of technical, institutional and socio-economic attributes cannot be kept clandestine. Farm managerial practices together with the role of technical, institutional and socio-economic attributes, determine the magnitude of the technical efficiency of potato growers (Abate et al., 2019; Wassihun et al., 2019). Thus, the magnitude of efficiency is affected by the interaction of technical, institutional and socio-economic determinants, either directly or in an indirect way. Figure 4 thus shows the interaction of possible variables obtained from Focus Group Discussion (FGD) that have an impact on technical efficiency among smallholder potato farms.

Figure 4. Conceptual framework of the study.

The overall outcome of the conceptual framework presents the net effect resulting from the interaction of technical, institutional and socio-economic factors. The nature of the variables and their existence at the individual level determine the type of effect on technical efficiency (positive or negative). In our study, we envisage a positive outcome, assuming that these determinants provide a suitable environment for smallholder potato growers in the PMAMP potato zone of the Bajhang district.

3.4. Data analysis

The data were carefully collected, entered to the MS Excel sheet, and further subjected to analysis using descriptive and relevant statistical tools using STATA Version 16. The descriptive statistics was obtained from the collected data. Furthermore, a one-step stochastic frontier approach was employed for the determination of the efficiency of individual farms.

3.5. Specification of the empirical model

For the purpose of estimating technical efficiency, generally two functional forms are popular: Cobb-Douglas (CD) production function and the trans-log production function. Both of these models have been popularly used in most empirical studies. For our empirical analysis, we employed the Cobb-Douglas production function to address the stochastic frontier approach. The CD model has advantages over other functional forms: it provides a comparison between the adequate fit of the data and computational feasibility (Tesema, 2022). The model provides convenience in interpreting the elasticity of production. Besides, the CD function is parsimonious with respect to the degrees of freedom (dof), and it has a self-dual nature, flexibility, and reliability in interpreting the returns to scale obtained from the coefficients (Bravo-Ureta & Evenson, 1994). The CD model also assumes unitary elasticity of substitution, constant production elasticity, and constant factor demand. If the interest is to analyze the efficiency measurement without analyzing the general structure of the production function, the CD function provides an adequate representation of technology and has an insignificant impact on the measurement of efficiency (Bezu et al., 2021). Furthermore, when farmers operate on small farms, the technology is unlikely to be substantially affected by the variable returns to scale. The application of the CD model has been preferred recently in many types of research dealing with efficiency, like Adhikari et al. (2020), Barasa et al. (2019), Bezu et al. (2021), Tesema (2022), and Thapa and Dhakal (2024b), owing to the adequate representation of agriculture production technology.

The empirical model of Cobb-Douglas frontier function for potato production is expressed as (Praveen et al., 2019): (2) $$\mu =\frac{\text{ln\hspace{0.17em}}\left(\raisebox{1ex}{$X_2$}\!\left/ \!\raisebox{-1ex}{$X_1$}\right.\right)}{t_2-t_1}$$(2)

Where Y_i is the potato output and X_i is the vector of the input variables (Figure 2), including the total potato cultivated area, quantity of fertilizers, quantity of seeds used, human labor and bullock used. Similarly, β_i denotes an unknown parameter to be estimated as a vector of linear terms, V_i refers to the random error with an assumption of a normal distribution N (0, σ²), and u_i refers to the inefficiency term distributed irrespective of v_i.

The technical efficiency is explained in terms of the ratio of observed output to the corresponding frontier output, given the levels of input used by the individual firm (Figure 2). The technical efficiency of i^th firm can thus be represented as: (3) $${\mathit{\text{TE}}}_i=\frac{Y_i}{Y^{\mathrm{*}}}=\frac{f\left(X_i,\beta \right)+\mathrm{\text{exp}}(v_i-u_i)}{f\left(X_i,\beta \right)+\mathrm{\text{exp}}\left(v_i\right)}=\mathrm{\text{exp}}(-u_i)$$(3)

The magnitude of the technical efficiency of the i^th potato growers’ firm, is now defined as TE_i = exp(-u_i), which has a technical inefficiency (u_i) that cannot be observed.

3.6. Estimation of the factors affecting technical efficiency

The one-step model has been used in our study, similar to the approach of Muzeza et al. (2023). In the model explained above, we assume a truncated normal distribution for measuring the mean level of technical efficiency (Baten et al., 2009), which is further a function of socio-economic determinants.

We used the single-stage estimation compared to the two-stage approach for the identification of the inefficiency determinants. In the two-stage approach, two steps are taken: (1) the inefficiency scores are obtained from the stochastic frontier model; (2) the inefficiency variables are regressed on the measures of the inefficiency scores. Unlike the two-stage model, the single-stage approach used involves a simultaneous estimation of the parameters, where inefficiency effects are presented as an explicit function of independent variables (Liu et al., 2020). The conventional two-stage model is seriously biased downward, as justified by the Monte-Carlo simulation (Wang & Schmidt, 2002). Furthermore, Wang and Schmidt (2002) validate the biasedness with two conclusions after confirming the biasedness:

1. The first step of the two-stage model is biased for the regression parameters if inefficiency determinants and the input variables are correlated.

2. Even if the inefficiency determinants and input variables are independent, the estimated inefficiencies are under-dispersed when we ignore the effect of determinants on inefficiency.

Thus, the second conclusion of their study provides evidence that the second-step estimate of the two-stage model for the effect of the determinants on the technical inefficiency is biased downwards (towards zero) irrespective of the correlation between the input variables and the socio-economic determinants. Also, from an econometric point of view, the problem is that inefficiency is measured with an error correlated with determinants, the regressor in the second-step regression of two-stage model. The one-step model is thus based on a correctly specified model and is asymptotically optimal (Wang & Schmidt, 2002).

The equation for the socio-economic factors affecting the technical inefficiency is expressed as below: (4) $$u_i={\propto }_o+\sum _{i=1}^5{{\propto }_{i}Z}_i$$(4)

Where α_o… α_i are the parameters that will be estimated and Z_i is the vector of farmers’ socio-economic characteristics affecting the technical inefficiency of the farms, viz., the age of respondent, years of schooling, access to credit, extension contact, and training, respectively, which are described in Table 1 below.

Table 1. Description of the variables used in the one-step model.

Variable	Name of the variable	Category of variable	Expected sign (+/-)	Details of the variable
Yi	Output	Continuous		Total amount of potato harvest (kg)
X1	Fertilizer	Continuous	+	Total quantity of fertilizers per hectare (kg)
X2	Seed	Continuous	+	Total amount of seed requirement (kg)
X3	Labor	Continuous	+/-	Total labor (Family and hired) in man-days (one man-day = 8 hours)
X4	Bullock	Continuous	+/-	Sum of domesticated and hired animal draft power (here bullock) in man-days (one man-day = 8 hours)
X5	Farm size	Continuous	–	Area for potato production (hectare) in a year
Socio-economic factors
Z1	Age	Continuous	+/-	Age of household head in years
Z2	Education level	Continuous	–	Number of years of formal education
Z3	Credit access	Dummy	–	1 if access to credit and 0 is otherwise
Z4	Visit by extension worker/services	Dummy	–	1 if service/extension receival and 0 is otherwise
Z5	Training	Dummy	–	1 if agriculture training receival and 0 is otherwise

The Likelihood Ratio (LR) test was used to confirm the presence of inefficiency in the model and also to confirm that the Maximum Likelihood Estimation (MLE) is better suited for the given data compared to the Ordinary Least Squares (OLS). The LR test is shown below, as recommended by Huang and Lai (2017): $${\chi }^2=-2\left[L\left(H_0\right)-L\left(H_1\right)\right]$$

Where L(H₀) and L(H₁) represent the log-likelihood values computed from the restricted ordinary least square (OLS) model and the unrestricted frontier model (one-step stochastic frontier approach), respectively. Critical values for the mixed chi-square distribution are obtained from Kodde and Palm (1986).

In this study, we chose five variables for the inefficiency measurement, which is due to the small sample size. Including more variables for a small sample size can lead to a weaker estimation of the coefficients concerning our study, which is a basic principle (Knofczynski & Mundfrom, 2007). These variables have been considered highly important due to their impact on technical inefficiency (Abate et al., 2019; Wassihun et al., 2019). Furthermore, our study area is in one of the nine most-rural districts declared by the Government of Nepal (Thapa, 2022), thus creating a high importance of the variables chosen to be included in the inefficiency effects model, particularly in the case of potato farming in rural areas. Furthermore, a meta-analysis by Thiam et al. (2001) reported that the ‘number of variables in the model’ and ‘sample size’ do not seem to significantly affect the estimates of the technical efficiency across different studies, including that in Asia.

3.7. Estimation of the level of productivity

The coefficients (estimated parameters) of a Cobb-Douglas stochastic frontier production function, β’s, refer to the output elasticities corresponding to the inputs used in the production. These coefficients can be deduced as elasticities of output with respect to the inputs used in the model (Pavelescu, 2014). Thus, with the help of the output elasticities of farms, we can determine the level of productivity or the nature of the farm. In other words, these output elasticities determine the nature of returns to scale, i.e., either constant return to scale (RTS), increasing RTS, or decreasing RTS, and also determine the implications for the respective farms. The total of the elasticities thus provides the RTS of the farms, as expressed below: (5) $$\mathit{\text{RTS}}=\sum _{i=1}^5{\beta }_i$$(5)

Where β₁, β₂…β₅ are the respective output elasticities when we use the inputs X₁, X₂…X₅, and these output elasticities can be, respectively, obtained from the model represented in Equation (2)(2) $$\mu =\frac{\text{ln\hspace{0.17em}}\left(\raisebox{1ex}{$X_2$}\!\left/ \!\raisebox{-1ex}{$X_1$}\right.\right)}{t_2-t_1}$$(2) above.

4. Results and discussion

4.1. Summary statistics

A summary of the demographics and socio-economic characteristics of the potato growers in the PMAMP command area, Potato Zone, of Bajhang district is presented in Table 2 below. On average, most of the respondents (39%) were in the age group of 30–40 years, and the average age of the respondents was 40 years. A total of 51% of the respondents had a family size of 6–10, and the average household size was 8 members. The results of the survey revealed that 94% of the respondents were male. In terms of education level, 46.53% of respondents had completed the higher secondary level of education. The socio-economic status revealed that nearly 53% of respondents had access to training, while 78.22% of respondents had access to credit. The respondents were categorized on the basis of their yield category and the majority of respondents (38.61%) produced potatoes in their field with productivity ranging within 5–10 mt/ha. In terms of land holding, most of the respondents (71%) had land sizes smaller than 1 ha, while the potato -cultivated land (ha) was less than 1 ha in 99% of respondents, revealing the fact that the potato growers of the districts are smallholder farmers.

Table 2. Summary of descriptive statistics.

Variables	Class		Frequency	Percentage
Age	Less than 30		16	16
	30–40		39	39
	40–50		27	27
	above 50		19	19
Total			101	100
Family size	<6		24	24
	6 to 10		52	51
	10 to 14		20	20
	>14		5	5
Total			101	100
Gender	Male		95	94.05
	Female		6	5.94
Total			101	100
Education level	None		12	11.88
	Primary		28	27.72
	Secondary		14	13.86
	Higher secondary		47	46.53
Total			101	100
Access to training	Yes		53	52.47
	No		48	47.53
Total			101	100
Access to credit	Yes		79	78.22
	No		22	21.78
Total			101	100
Yield category	<1 ton/ha		2	1.98
	1–5 ton/ha		30	29.70
	5–10 ton/ha		39	38.61
	10–15 ton/ha		12	11.88
	>15 ton/ha		18	17.83
Total			101	100
Total Land size (ha)	<1 ha		72	71
	1 to 2 ha		18	18
	>2 ha		11	11
Total			101	100
Land under potato cultivation (hectare)	<1 ha		100	99
	1 to 2 ha		1	1
	>2 ha		0	0
Total			101	100
		Average	Min	Max
Age		40	20	70
Household size		8	3	23

Besides the socio-economic characteristics, the respondents in the study area grow rice, wheat, finger millet, and barley, along with potatoes, which were found to vary among the potato growers, particularly with altitude. The farmers of higher altitudes (above 1500 masl) preferably grew finger millets, wheat, and potatoes, while those in lower altitudes (near 1000 masl) grew rice, potatoes, and barley. Concurrently, almost all of the potato growers were found to practice the furrow method of irrigation for potato cultivation in the study area. In terms of seed tuber quality, the farmers were found to keep self-grown seed tubers in rustic storage and purchase the insufficient seed tubers from the cold stores of Dadeldhura district.

4.2. Level of technical efficiency for Bajhang potato growers

The efficiency score of the potato growers of PMAMP command area potato zone farmers is shown below in Table 3.

Table 3. Efficiency scores of potato growers of PMAMP Potato Zone command area.

Efficiency score (%)	Bajhang district
	Frequency	Percentage
30<	0	0.00
30–40	1	0.99
40–50	1	0.99
50–60	4	3.96
60–70	6	5.94
70–80	10	9.90
80–90	3	2.97
91–100	76	75.25
Total	101	100%
Mean TE (%)	87.75
Min TE (%)	36.6
Max TE (%)	99.80
Std. Dev.	23.33

From the perusal of Table 3, the majority of the farmers fall under the efficiency score of 91–100%, as 75.25% of total farmers fall under this category. However, the second-largest group of farmers (9.90%) fell under the category of 70%–80%. Overall, majority of the farmers (>98%) had an efficiency score greater than 50%. The minimum level of efficiency score was observed to be 36.6%. As a whole, since the mean technical efficiency is below 100%, i.e., 87.75%, the sampled potato growers had a level of production below the frontier. This variation in the magnitude of the technical efficiency (36.6% to 99.8%) could be explained by the varying combinations of inputs used by the farmers, thus yielding a varied level of output, ceteris paribus. Furthermore, it could also be attributed to the different altitudes of potato production in the study area, variability in irrigation, crop rotation, seed tuber quality, and other practices. The mean TE of 87.75% indicates that the potato growers could shorten the disparity between the observed and frontier levels of output by 12.25%.

4.3. Determinants of the level of technical efficiency

The estimates obtained from the one-step stochastic frontier model in the case of the potato growers in Bajhang district are presented in Table 4 below. The model was used based on the estimation of 101 observations, and with the value of Prob > Chi² = 0.00, it was confirmed that the estimated parameters were statistically significant for the determination of the magnitude of the technical efficiency. The variance observed from the model (the values of sigma squared (σ²) and lambda (λ)) in Table 4 are statistically significant, thus conforming to the assumption that the truncated normal distribution in our study is a proper choice, leading to a robust model.

Table 4. Maximum Likelihood Estimates obtained from stochastic production function.

Variables	Parameter	Maximum likelihood estimates		p>|Z|
		Coefficients	Standard Error
Efficiency
Constant	β0	0.905	0.557	0.052
ln (Fertilizer)	β1	0.272	0.075	0.000***
ln (Seed)	β2	0.327	0.068	0.000***
ln (Labor)	β3	0.053	0.122	0.33
ln (Bullock)	β4	−0.234	0.107	0.015**
ln (Farm size)	β5	0.480	0.100	0.000***
Inefficiency
Constant	α0	−0.238	0.465	0.305
Age	α 1	0.125	0.009	0.10
Years of schooling	α 2	−0.026	0.020	0.098*
Access to credit	α 3	−0.000	0.000	0.088*
Extension contact	α 4	−1.065	0.533	0.0227**
Training	α 5	−0.335	0.276	0.097*
Diagnostics
Wald chi-square		221.89
Prob > Chi^2		0.000***
Total Variance	σ^2(=σ^2u+σ^2v)	0.307
Sigma_u	σu	0.549
Sigma_v	σv	0.073
Gamma	γ (σ^2u / σ^2)	0.98
Lambda	λ	0.13
Log Likelihood		−80.26
Mean level of technical efficiency = 87.75%

*, **, and *** means significant at 10%, 5% and 1% level of significance, respectively.

4.4. Estimates from maximum likelihood

At first, the LR test was performed to confirm whether to run the more expensive MLE. The LR test was found to be significant at the 1% level of significance, thereby confirming the presence of inefficiency in the model as well as confirming that MLE is better suited than the restricted model of OLS. The LR statistic for testing the absence of technical inefficiency at the frontier was calculated to be: $$\text{LR}=-2*\left(-86.229+80.2678\right)=11.92$$

This value exceeds the critical χ² (1%, 1 degree of freedom) value of 6.63 (obtained from mixed table of Kodde and Palm (1986)) at the 1% level of significance, thus proving the presence of inefficiency as well as confirming that the stochastic frontier approach best fits our data.

The Maximum Likelihood (ML) estimates obtained from the stochastic production function is shown in Table 4, which revealed a positive relationship for all parameters except for the bullock (man days), which imposed a negative relation with the yield. The parameters, viz., fertilizer, seed, labor, and farm size, have positive signs. Fertilizers, seeds and farm size are highly significant at 1% level of significance, while bullock (man days) is statistically significant at the 5% level of significance.

4.5. Fertilizer

From Table 4, the amount of fertilizer (kg) applied by potato growers in Bajhang is significant at the 1% level of significance (p < 0.01). The positive sign of the coefficient indicates that increasing the use of fertilizers leads to enhanced yield. In econometric terms, a 1% increase in fertilizer use leads to an increase in potato yield of 0.27%. This finding is consistent with what was expected and concurs with the results reported by Martey et al. (2019), Thomas et al. (2020), Bordoloi and Lama (2022), and Ermias (2020). The positive relation hereby is not surprising, as use of fertilizers (NPK) promote growth and development of the potato tubers.

4.6. Seed

Similarly, from Table 4, the quantity of seed tubers (kg) used by the potato growers is significant at the 1% level of significance (p < 0.0001). The positive value of the coefficient indicates that increasing the amount of seed tubers leads to enhanced yield. In econometric terms, a 1% increase in the use of the seed tubers leads to an increase in the yield of potatoes by 0.33%. These findings concur with the findings of Barasa et al. (2019), who reported a 0.37% increase in potato yield due to a 1% increment in quantity of seed tubers. Martey et al. (2019) and Thomas et al. (2020) also reported similar results in their studies. The positive relation hereby represents that more seed tubers per unit area leads to an increased yield of potatoes.

4.7. Bullock

The use of Bullock (man days) by potato growers is significant at the 5% level of significance (p < 0.05). The negative value of the coefficient depicts that increasing the use of bullock for labor purposes leads to a reduced yield (Table 4). In econometric terms, a 1% increase in the use of the bullock as labor leads to the decrease in the yield of potatoes by 0.23%. The negative relation hereby indicates that the use of bullocks is not economic for potato production. Similar findings were reported by Verma (2021), who reported the negative effect of using bullock labor on the productivity of crops. However, Wassihun et al. (2019), in their study, reported an increase in potato yield when bullock labor was used in potato cultivation, which contradicts with our findings.

4.8. Farm size

The farm size (ha), i.e., area under potato cultivation, of the potato growers in Bajhang is significant at the 1% level of significance (p < 0.0001) for the output. The positive coefficient depicts that increasing the farm size leads to a better yield. In econometric terms, a 1% increases in the size of the farm increases the yield of potatoes by 0.48%. The positive relation here is as expected, and our study concurs with the findings of Miebi (2019).

4.9. Determinants of the level of technical inefficiency

The factors affecting the inefficiency among the respective farms are shown in Table 4. These factors and determinants are represented by the socio-economic and farm-specific characteristics of the potato growers in the PMAMP potato zone, Bajhang district. The socio-economic and farm-specific characteristics include age, years of schooling, access to credit, contact with an extension agent and training received. Except for the age of the household head, the rest of the variables are statistically significant.

4.10. Years of schooling

From Table 4, the years of schooling are significant at the 10% level of significance (p < 0.10). The negative coefficient implies that with an additional year of schooling, the level of technical inefficiency decreases. Interpreting the coefficient, an increase in the level of education by an additional year leads to a 0.026 unit decrease in technical inefficiency, ceteris paribus. This is due to the higher education affecting respondents’ attitudes and ideas, making them more receptive, thoughtful, and capable of evaluating the advantages of the new technology. The household heads’ educational backgrounds are thought to be a significant factor in determining how open-minded they are to new concepts and technologies. Farmers with more education are anticipated to use new technology to boost their labor and land production (Abate et al., 2019). Similar results were reported by Abate et al. (2019) and Tesfaw et al. (2021). Lamichhane et al. (2019) also reported education (years of schooling) to increase technical efficiency of potato growers in mid-western Terai region of Nepal.

4.11. Access to credit

The access of credit for farmers is significant at the 10% level of significance (p < 0.10). The negative coefficient sign indicates that the availability of credit to farmers decreases technical inefficiency. Interpreting the coefficient, moving from no-credit access to having a credit access leads to a 0.0000006 unit decrease in technical inefficiency, ceteris paribus. Potato growers with access to credit are expected to be more efficient than those without credit access because credit can help farmers overcome financial restrictions and it also influences their capacity to obtain and use inputs and implement farm management decisions on time (Abate et al., 2019). Thus, the availability of credit alleviates financial restraints and facilitates the timely procurement and utilization of inputs, as well as the opportunity to acquire new technical packages like high-yielding seeds, resulting in increased efficiency (Bekele, 2013). Similar results were also reported by Abate et al. (2019), Mengui et al. (2019), and Missiame et al. (2021).

4.12. Contact with extension agent

The contact with extension agents is significant at the 5% level of significance (p < 0.05). The negative coefficient implies that contact with an extension agent is associated with decreased technical inefficiency. Interpreting the coefficient, moving from no contact to contact with an extension agent leads to a 1.06 unit decrease in technical inefficiency, ceteris paribus. Abate et al. (2019) insisted that frequent contact with extension agents leads to better knowledge and information, thus leading to the proper use of available inputs in crop production. The contact with an extension agent might increase the knowledge of potato growers on the use of available resources more efficiently, thus decreasing the inefficiency. Furthermore, increased awareness upon contact with extension agents leads to a greater demand for agricultural inputs (Dawit, 2012). Our findings are similar to the results reported by Mengui et al. (2019), Thomas et al. (2020), and Siaw et al. (2021). Similarly, in the case of mid-western Terai region of Nepal, Lamichhane et al. (2019) reported that contact with extension agent increased the technical efficiency of potato growers.

4.13. Training received

The receiving of training is significant at the 10% level of significance (p < 0.10). The negative coefficient sign indicates that participation in training is associated with increased technical efficiency, ceteris paribus. Interpreting the coefficient, moving from farmers with non-receival of training to participation in training leads to a 0.33 unit increase in the technical efficiency of potato growers, ceteris paribus. Our findings are in line with the findings of Mengui et al. (2019), who concluded that to reduce technical inefficiency of potato growers, training shall be provided to enhance their knowledge of potato production. Training on new technologies and practices can help farmers use the resources efficiently.

4.14. Estimating the productivity level

The production elasticities and RTS determine the yield of the potato in potato farms under the PMAMP Potato Zone of Bajhang district. Table 5 below shows the productivity levels of the farmers in the district.

Table 5. Return to scale and elasticity of production.

Variables	Elasticity
Ln (Fertilizer)	0.2722928
Ln (Seed)	0.3273613
Ln (Labor)	0.0532266
Ln (Bullock)	−0.2343749
Ln (Farm size)	0.4800098
Return to scale	0.8985156
(Nature)	(Decreasing return to scale)

The elasticity of an input (e) can be defined as the percent increment in yield due to a unit percentage increase in inputs. From our observation, all inputs are inelastic (e < 1). The farm size has the largest value of the elasticity coefficient, followed by seed cost, amount of fertilizer, labor, and bullock, respectively. Unlike other inputs, the negative elasticity coefficient of bullock implies that increase in bullock (man days) by 1% leads to a decrease in output by 0.23%. The other inputs having an elasticity coefficient less than 1 but a positive value mean that, upon greater usage of these inputs, there won’t be a significant rise in output, ceteris paribus. In other words, upon interpreting the elasticity coefficient for farm size, a 1% increase in farm size (ha) leads to 0.48% increment in output of potatoes. Similarly, a 1% increase in the amount of seed tubers (kg) and quantity of fertilizer (kg) leads to a 0.33% and 0.27% increment in output of potatoes, respectively. At last, a 1% increment in labor usage (man days) leads to 0.053% increment in potato output.

The Return to Scale (RTS) is defined (for a Cobb-Douglas production function) as the sum of the coefficients of the production function model (Equation (5)(5) $$\mathit{\text{RTS}}=\sum _{i=1}^5{\beta }_i$$(5) ). RTS provides information about the zone in which the farms are operating. The production function of the farmers in the Bajhang district under PMAMP potato zone exhibited a decreasing RTS (0.898), which implies that a proportionate increment of all inputs by 1% enhances the output by 0.898%, ceteris paribus, at a mean technical efficiency of 87.75%. Similar findings were reported by Muzeza et al. (2023) and Ermias (2020). Thus, to enhance their scale of production in an efficient way, farm size, fertilizer, seed, labor, and bullock use can be targeted.

5. Conclusion

From the results revealed by the analysis, we can draw two major conclusions. At first, the mean level of the technical efficiency of the potato production was higher (87.75%). Although, the efficiency score was higher, the potato growers produced below the level of frontier, accompanied by a wide range of variation in the efficiency scores. This suggests that a varied combination of different inputs by the farmers led to different output, which is due to the varied socio-economic characteristics.

The second understanding from the analysis is associated with bridging the disparity between the observed and the actual frontier output. For this purpose, we can make two major suggestions: (i) the inefficiency of 12.25% can be bridged by focusing and targeting the socio-economic aspects, viz., years of schooling, access to credit, contact with an extension agent, and receiving of training; (ii) this could further be supported by increasing the usage of inputs like fertilizer, labor, farm size and seed while decreasing the usage of bullock so as to enhance the output, but this route might not be that preferable owing to the decreasing RTS (0.898).

5.1. Policy recommendations

The following two recommendations can be derived based on the findings of our study:

1. Foremost, our study empathically encourages for a purposeful pursuit of rectifying the socio-economic determinants that have an impact on technical efficiency, viz., years of schooling, access to credit, contact with an extension agent, and training received. Thus, to address these issues, it is vital to implement a multifaceted approach. Commencing with educational empowerment, the schemes of tailored informal education for less-educated farmers stands as a beacon of potential. By augmenting their knowledge and skills, a substantial reduction in technical inefficiency could be realized, thus culminating in a marked surge in agricultural output. Concurrently, the pressing financial constraints faced by farmers can be decisively mitigated through a strategic enhancement of credit accessibility. This could be achieved by relaxing credit limits, particularly during the pivotal planting season, facilitating the timely acquisition of essential inputs. To this end, forging a symbiotic alliance between the government and financial institutions like banks and microfinance organizations is not only advisable but essential. Moreover, leveraging informal credit channels could offer an additional reservoir of support to farmers in need. The transformative influence of extension agents cannot be underestimated. Establishing a robust network of interaction between farmers and extension agents, spanning local to provincial levels, is a linchpin in fortifying the technical efficiency of potato production. This connection can enable farmers to harness inputs with heightened efficiency, subsequently bolstering the overall quality and quantity of potato production. Strategic training initiatives, meticulously tailored to the nuances of potato cultivation, have the potential to exert a catalytic impact on reducing technical inefficiency. These training interventions, precisely targeted at the potato growers within the project’s sphere of influence hold the promise of refining techniques, streamlining processes, and harmonizing efforts.

2. Furthermore, to fortify the robustness of the proposed policy measures, a concerted emphasis on the augmentation of input utilization warrants unwavering attention. In particular, a heightened adoption of pivotal inputs such as fertilizers and high-quality seeds stands as an imperative stride towards bolstering technical efficiency. These inputs, underscored by their positive impact on productivity, possess the potential to propel agricultural outputs. Simultaneously, a judicious reevaluation of farm size holds intrinsic value in this transformative pursuit. Historical data attesting to the statistically significant correlation between increased farm size and heightened technical efficiency demands a nuanced approach to land allocation and utilization. Optimizing the spatial distribution of cultivation activities in line with this correlation could yield substantial dividends in terms of enhanced potato production. However, a departure from conventional practices is warranted in the domain of draught animal usage. Substantiated by empirical evidence, the curtailment of bullock employment emerges as a prudent directive. By deviating from this approach and adopting contemporary, mechanized alternatives, a resounding uptick in potato yield becomes an attainable reality. In summation, the synthesis of enlightened input utilization, prudent farm size management, and the strategic reduction of bullock involvement encapsulates a formidable strategy that augments and amplifies the efficacy of the recommended policies. The convergence of these initiatives propels the agricultural landscape towards an era of unparalleled productivity, securing a robust and flourishing potato sector for years to come.

5.1.1. Ethical approval

Ethical approval was not required as this study involved beneficiaries within the Potato Zone of the project. The ethical guidelines were followed in accordance with the World Medical Association’s Declaration of Helsinki to ensure research integrity and participant confidentiality.

5.1.2. Consent form

The participants in our study were well informed about the study objectives, and informed consent was obtained from all the participants in written form prior to the study.

Authors’ contributions

Shikshit Parajuli: conception and design of the research, data collection, analysis and interpretation of the data, drafting of the paper and final approval of the version to be published. Rabin Thapa: design of the research, data collection, analysis, and interpretation of data, drafting of the paper, revising it carefully and final approval of the version to be published.

Disclosure statement

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

Data availability statement

The data that support the findings of this study are available from the corresponding author, Rabin Thapa, upon reasonable request.

Additional information

Funding

The study did not receive any funding from any organization(s) or institution(s).

Notes on contributors

Shikshit Parajuli

Shikshit Parajuli worked as agriculture officer at Myagdi Rural Municipality, Nepal. He holds a Masters degree in Agricultural Extension from Agriculture and Forestry University, Chitwan, Nepal. His area of interest includes agricultural extension and agricultural economics.

Rabin Thapa

Rabin Thapa is a government officer and an econometrics enthusiast. He is an Agriculture Extension Officer in Agriculture Information and Training Center (AITC), Ministry of Agriculture and Livestock Development, Nepal. His area of research includes agricultural economics, climate change and time-series econometrics. He holds a Masters degree in Agricultural Economics from Agriculture and Forestry University, Chitwan, Nepal.

Notes

1 The local level of Nepal refers to either Metropolitan cities, Municipalities, or Rural Municipalities.

Annex

Annex 1. Trend of area, production and productivity of potato in Bajhang district, Nepal.

Source: Statistical Information on Nepalese Agriculture (MoALD).