Technical efficiency of rice seed production and their determinants in Chitwan, Nepal – A one-step scaling stochastic frontier approach

Abstract

The rice seed subsector plays a significant role in attaining self-sufficiency of rice. In the context of the huge demand-supply gap of rice seeds, it is imperative to increase productivity for assuring environmental sustainability and food security, by increasing the technical efficiency of rice seed production. The study used data from 223 rice seed growers in the Chitwan district of Nepal. A one-step scaling stochastic frontier production model was used to determine the technical efficiency of rice seed production and its determinants. The study revealed that the mean technical efficiency was higher (96.15%) in Bharatpur than in Madi (79.61%). The inefficiency of 3.85% for Bharatpur can be bridged by focusing and targeting education level, contact with extension agents, training and adoption of climate change adaptation strategies; (ii) the gap of 20.39% for Madi can be bridged by focusing and targeting experience, contact with extension agents and adoption of climate change adaptation strategies; (ii) this could further be supported by increasing the usage of inputs such as land, labor, urea and amount of herbicide, but this route might be more favorable in Bharatpur due to increasing return to scale (1.17) compared to Madi (0.94). Policymakers, and the local and provincial governments should focus on the significant socio-economic determinants and encourage the adoption of resistant varieties, improved water management, nutrient management, residue management and changing cropping time, as adoption of these strategies were found to increase technical efficiency by 256%.

Keywords:

• Climate change
• Cobb–Douglas
• return to scale
• stochastic frontier
• technical efficiency

Reviewing Editor:

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

Subjects:

• Economics
• Agriculture & Environmental Sciences
• Econometrics

1. Introduction

Rice (Oryza sativa L.) is the primary cereal crop grown in Nepal (Thapa & Bhusal, 2020). Rice production equals almost half of the total cereal grain production and more than half of the total calorie requirement of Nepalese (Simkhada & Thapa, 2022). The sub-sector contributed 13.60% to Nepal’s agricultural gross domestic product (AGDP) in 2022 (MoALD, 2023). The recent statistics of rice production show that rice is cultivated in 1.4 million hectare (ha) of cultivable land and 5.1 million metric tons (mt) of rice is obtained with a productivity of 3.47 mt/ha (MoALD, 2023).

Nepal’s food security is highly dependent on staple cereals, with rice holding a major position. However, the current status of rice production is not encouraging. Gairhe et al. (2021) revealed that, while output growth was just 2% each year, the growth rates of rice exports and imports were 25% and 38%, respectively. In this context, the seed sector can play a significant role in increasing rice crop production and productivity. Approximately 30–40% of the overall production can be attributed to high-quality seeds (Gauchan, 2017). However, the annual rice seed supply (19,304 mt) fails to meet the annual rice seed requirement (69,263 mt) in Nepal (MoALD, 2023). There is also a high yield gap of rice i.e., the difference between potential yield (5.4 mt/ha) and the national average yield of rice (3.47 mt/ha) (MoALD, 2023) across sites, seasons and management practices (Basukala & Rasche, 2022; Devkota et al., 2021). This gap could be attributed to inadequate seed production compared with demand, scarce resources and a lower rate of adoption of modern farming technologies.

Farmers have been facilitated to produce and sell rice seeds, but there is poor realization of benefits by rice producers under limited resources and inputs. Furthermore, the introduction of the Prime Minister Agriculture Modernization Project (PMAMP) by the Government of Nepal has not been able to achieve the national self-sufficiency goal through increased rice production. In addition, 45,285 tons of rice seeds were imported by Nepal in 2022 according to the Department of Customs, most of which were hybrid. Future projections by Prasad et al. (2011) showed a constant inability of domestic rice production in Nepal to shorten the demand-supply gap. Given the restricted amount of arable land, horizontal expansion by placing more land area under rice production is impossible (Choudhary et al., 2022).

The productivity of rice seeds can be improved through technological advancements, efficient technology, or both. In countries like Nepal, technological advancements in agriculture have not been able to completely enhance output (Takahashi et al., 2020). This is often attributed to the inability and poor willingness to adjust the input levels (Schultz, 1964), along with the presence of hurdles in institutional and sociocultural aspects (Suresh, 2015). The opportunity cost of efficiently using existing technology can be more than the introduction of new technologies aimed at enhancing agricultural productivity (Takahashi et al., 2020). Efficient and enhanced production of rice seed could provide a way to increase the availability of rice seeds in the country, thereby leading to increased production of rice. In addition, efficiency achievement of agricultural production can help to achieve the social, economic and environmental aspects of agricultural sustainability (Đokić et al., 2022). The rice production can be boosted by increasing the technical efficiency which ultimately assures food security of nation (Majumder et al., 2016).

The importance of rice seed has been recognized for its contribution to the national economy, but few studies have focused on the impact of climate change adaptation on technical efficiency of rice farming in Nepal. To date, few studies have explored the impact of such adaptation practices on technical efficiency (Ho & Shimada, 2019a, 2019b). If adaptation to climate change can be linked to technical efficiency, adaptation strategies would have a stronger practical significance. Adaptation strategies play a role in sustaining incomes and improving the livelihoods of farmers; thus, it is necessary to identify their impact on technical efficiency. The literature on technical efficiency are mostly found for developing countries and countries with similar economies, and a much smaller number relates to rice seed growers in developing countries, especially in countries like Nepal. Dhungana et al. (2004) used the Data Envelopment Analysis (DEA) approach and estimated the technical efficiency of rice farmers in Nawalparasi district of Nepal to be 87%. Unlike DEA approach, Khanal and Maharjan (2013) used a two-step stochastic frontier model and reported the mean technical efficiency of rice seed growers in Chitwan to be 81%. Unlike the two-step model, Subedi et al. (2020) used a one-step stochastic frontier approach and reported the average technical efficiency of the rice-growing farmers in Jhapa to be 92%. This study contributes to the literature on agriculture efficiency by using a one-step stochastic frontier approach along with a scaling property which is robust and better than models discussed above (Wang & Schmidt, 2002) along with incorporation of climate change adaptation strategy as a determinant of efficiency. The present article adds to the literature that links crop insurance, subsidy, adaptation of climate change adaptation strategies and other socio-economic variables with the technical efficiency. In this light, our objective to study on technical efficiency can be of significance in order to utilize the scarce available resources more efficiently and improve the current productivity of rice seeds, taking into consideration the determinants of efficiency in the face of climate change.

2. Research methods

2.1. Conceptual framework

The conceptual framework of our study is shown in Figure 1. The figure shows that output of rice seed is the function of the inputs and the technical efficiency of the rice seed production is affected by socio-economic, institutional and other factors. By identification of the significant determinants of the technical efficiency, the output of rice seed production can be increased. This ultimately leads to increased productivity, efficiency and improvement of the livelihood status of the rice seed growers as well as grain producers in long term.

Figure 1. Conceptual framework of the study.

2.2. Study site

The study was conducted in Bharatpur Metropolitan City and the Madi Municipality of Chitwan District, Nepal (Figure 2). This district was selected because it lies in the Terai region and has good potential for rice seed production. Furthermore, Bharatpur and Madi were chosen purposively for study purposes because the two local levels have higher rice seed production in the district. Although the city expansion rate is high in Bharatpur, 500% in the last 30 years (Rai et al., 2020) with population growth rate of 29.5% in 10 years (CBS Nepal, 2022), indicating declining fertile agricultural lands, but still 56.53% of the area¹ is cultivable (Devkota et al., 2023) and there are major pocket areas dedicated for rice seed production in the local level of the district (Regmi et al., 2022) like Patihani. Furthermore, the major contribution to the rice seed production in the district is from Bharatpur and the Prime Minister Agriculture Modernization Project (PMAMP) has established Rice Zone in the major pocket areas of Bharatpur for commercialization. On the other hand, Madi municipality has 85% of cultivable land (Adhikari et al., 2020) which is one of the remote part of the district. Despite the rate of variation in cultivable land and city expansion rate, the pocket areas of both the local levels have significant contribution to the rice seed production in the district.

Figure 2. Map of the study area. Source: ArcGIS.

Chitwan lies in the southwestern corner of the Bagmati Province, with an area of 2238 sq. km. The district has an altitude ranging from 144 to 180 m above sea level in both tropical and subtropical climates (Khanal & Kattel, 2017). The minimum temperature in the district is 7 °C, and the maximum is 42.5 °C. The average annual precipitation in the district is 1968 mm (Khanal & Kattel, 2017).

2.3. Sampling and sample design

We carried out purposive sampling for the interview schedule from Bharatpur Metropolitan City and Madi Municipality, as these local levels have high rice seed production in the district. Purposive sampling was performed in the respective municipalities to select the largest rice seed-producing ward, followed by simple random sampling of rice seed growers in each ward to prevent potential biasedness. The sampling frame was prepared from the roster obtained from PMAMP, Agriculture Knowledge Center (AKC), the Agriculture Section and seed companies at the local level. The sample size (n) was estimated using the Slovin formula (Equation (1)(1) $$n=\frac{N}{1+N\text{\hspace{0.17em}x\hspace{0.17em}}{e}^2}$$(1) ). (1) $$n=\frac{N}{1+N\text{\hspace{0.17em}x\hspace{0.17em}}{e}^2}$$(1) where N is the population size, n is the sample size to be estimated, and e is the margin of error (maintained at 5% in this study).

Thus, the sample size was calculated to be: n = $\frac{503}{{1+(503 \mathrm{x} 0.05}^2)}$ = 223.

After calculating the total sample size in the district, the sample size taken from Bharatpur and Madi was estimated using proportionate random sampling to prevent potential bias. Thus, the sample size to be taken from Bharatpur was calculated as $${\mathrm{n}}_1=\left(351/503\right)\text{x 223}=\text{156}$$

The sample size for the Madi was calculated as: $${\mathrm{n}}_2=\left(152/503\right)\text{x 223}=\text{67}$$

Primary data were collected in March 2023. Before commencement of the survey, a consent statement was read to the household to make them understand the purpose of the survey and get their written consent to go on with the administration of the questionnaire. The dignities and values of the respondents were safeguarded with confidentiality.

In order to ensure the data reliability, the enumerators were properly trained and the questionnaire was pretested. The necessary corrections were made after pretest and ultimately interview schedule was carried out. Focus Group Discussion (FGD) and Key Informant Interview (KII) were conducted with the AKC Chitwan, chairpersons of seed companies, CBSP and progressive farmers to gather collective information and verify the responses obtained from the respondents.

The ethics approval was not required for survey studies as the study included farmers within the the Bagmati Province, under the Directorate of Agriculture Development. However, the study was conducted according to the principles mentioned in World Medical Association - Declaration of Helsinki and made sure it adheres to research integrity and participant confidentiality.

2.4. Variables used for determination of technical efficiency of rice seed production

2.4.1. Variables for the efficiency measurement by the frontier model

To measure efficiency, five different inputs were used in the stochastic production frontier model: land size, labor (man-days), amount of urea, seed rate and amount of herbicide used, while the rice seed production per hectare was kept as the output variable (Table 1).

Table 1. List of variables for the efficiency measurement.

Variables	Description	Expected sign
Output
Ln (Output)	Total production of rice seed (kg) per ha
Inputs
Ln (Labor)	Total man-days (days)	±
Ln (Urea)	Total amount of urea used (kg/ha)	+
Ln (Seed)	Total amount of seeds required (kg/ha)	+
Ln (Herbicide)	Total herbicide used (liters/ha)	±
Ln (Land)	Total land under cultivation (ha)	+

Note: Ln refers to the natural logarithm of the respective variables.

To ensure the data reliability, the data was checked for significance of skewness (Appendix A) to assure the inefficiency is present in production, which is inevitable for studying technical inefficiency.

2.4.2. Variables for the inefficiency in the production function

The exogenous variables that were used to determine inefficiency are briefly described in Table 2. The variables in our study were chosen because they are found to affect technical efficiency of agricultural production in different studies. The compelling rationale for choice of the different variables along with their probable impact is explained briefly.

Table 2. List of exogenous variables for the inefficiency effect model.

Variables	Description
Family members in rice seed production	Number of family members involved in rice seed production
Education level of household head (HHH)	Number of years of formal schooling
Experience of HHH	Number of years of involvement in rice seed production
Contact with extension agent	1 denotes farm households having contact to agricultural extension agent and 0 = otherwise
Cooperative involvement	1 if member of cooperative and 0 = otherwise
Training related to rice seed production	1 if farmer received training related to rice seed production and 0 = otherwise
Adaptation to climate change	1 denotes farm household adopts a climate change adaptation strategy (Appendix D) and 0 = otherwise
Crop insurance	1 if farm has done crop insurance and 0 = otherwise
Received subsidy	1= received and 0 = did not receive

Family involvement in rice seed production is generally expected to have a negative relationship with inefficiency in rice seed production. The coordinated effort of family members in resource management contributes to increased technical efficiency and improves overall outcomes in rice seed cultivation (Biswas et al., 2021; Rahman et al., 2012). Furthermore, the education level of a household is generally expected to have a negative relationship with technical inefficiency (Mishra et al., 2018). This implies that farmers with more years of education are more efficient because of their enhanced access to information and contact with recent technologies. In contrast increased years of formal education may not directly address these resource constraints or provide practical solutions to the specific limitations faced by rice seed growers in their agricultural practices (Subedi et al., 2020). Similarly, experienced farmers may be more efficient because of better knowledge and farming practices learnt over time due to which they also use the resources efficiently (Azumah et al., 2019). In contrast, experienced farmers may be reluctant toward use of new technologies and hence lower technical efficiency (Biswas et al., 2021). When farmers visit extension agents or extension service-providing institutions, they are acquainted with diverse information on efficient technologies. Thus, they are expected to be better at gaining information and awareness and, therefore, increase their efficiency (Mengui et al., 2019; Siaw et al., 2021; Thomas et al., 2020). Similarly, farmers involved in cooperatives are expected to become frequently acquainted with recent technologies and farming practices which increase their technical efficiency. Furthermore, farmers who have received training are expected to gain more ideas on farming practices and the utilization of recent technologies which increase technical efficiency (Mengui et al., 2019). However, if training doesn’t match with local needs then this may decrease the efficiency of production of rice seed (Khanal & Maharjan, 2013).

This study aimed to determine whether adaptation strategies against climate change affect the technical efficiency of rice seed growers. Farmers who adopt climate-change strategies are expected to be more efficient because such strategies often involve adoption of innovative technologies and practices associated with overcoming of losses (Priyanto et al., 2022). We also incorporate a risk management variable, crop insurance, to explain farm inefficiency. This can be insightful for further research on the efficiency of risk management with the introduction of crop insurance by the National Insurance Authority. Farmers with crop insurance are expected to produce more efficiently (Roll, 2019). This insurance used by rice farmers would, in principle, reduce production risks and create incentives for their production (Castro et al., 2023). But, some studies suggest that insurance may not guarantee an increase in technical efficiency as adverse selection and moral hazard in crop insurance could lead rice farmers to change their incentive to produce efficiently (Fadhliani et al., 2019; Wu et al., 2020).

Similarly, the provision of subsidies by government institutions regarding rice seed production was assessed for its impact on the efficiency of rice seed production. The Seed Supply, Production and Management Directives, 2078 has provided subsidies for producers of source seed and improved seed, as well as subsidies to farmers on the price for the purchase of improved seeds. The income effect due to subsidy may have both positive and negative effects on efficiency and productivity (Latruffe et al., 2017). In the positive aspect, subsidies provide farmers with the necessary financial means to use recent technologies or to invest in efficiency-improving on-farm organization. In contrast, if farmers are less motivated to perform well with more income due to subsidies, the efficiency may decrease (Zhu & Lansink, 2010).

There can be other exogenous variables affecting the technical efficiency like distance to the main highway, labor availability, rate of urbanization, market access, etc. which have not been included in our study.

2.5. Analytical model

2.5.1. Determination of the frontier production function

For the purpose of estimating technical efficiency, two functions are generally popular: Cobb–Douglas (CD) and the trans-log production function. Both models have been widely used in empirical studies. For our analytical model, we employ the Cobb–Douglas stochastic frontier approach. The use of the CD model is advantageous because it provides a contrast between the data fit and computational likelihood (Tesema, 2022). The model provides convenience in the interpretation of production elasticity. In addition, the CD function is prudent owing to the degree of freedom and its self-dual nature, flexibility and reliability in interpreting the returns to scale obtained from the coefficients (Bravo-Ureta & Evenson, 1994). The CD model is a special case of a trans-log production function with unitary elasticity of substitution. Bezu et al. (2021) reported that the CD function adequately represents technology and has little impact on efficiency measurements (Coelli et al., 2005). The application of the CD model has recently been preferred in many types of studies dealing with efficiency (Barasa et al., 2019; Bezu et al., 2021; Tesema, 2022), owing to the adequate representation of agricultural production technology.

Thus, in the proposed scaling property model, we employ the Cobb–Douglas functional form. The Cobb–Douglas form is, in fact, a special case of the trans-log production function where the interaction terms between inputs are not considered (Equation (2)(2) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\xi i\left(\mathit{\text{Vi}}-\mathit{\text{Ui}}\right)$$(2) ): $$\text{\hspace{0.17em}ln\hspace{0.17em}}{Y}_i=\text{\hspace{0.17em}ln\hspace{0.17em}}{Y}_i*-{\text{U}}_{\text{i}},\hspace{0.17em}{\text{U}}_{\text{i}}\ge \hspace{0.17em}0$$

(Battese, 1992) (2) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\xi i\left(\mathit{\text{Vi}}-\mathit{\text{Ui}}\right)$$(2)

Where,

Y_i is the output of the i^th farmer, ${Y_i}^{*}$ represents the maximum possible level of output, X_i is a vector of input variables, ξ_i is the error term equal to (V_i− U_i), ln is the natural logarithm, and i is the number of observations for n samples.

Y_i is the rice seed output (kg)

β₀ – β₅ are parameters to be estimated.

X includes the input variables (Table 1)

ξ_i is the composed error term, equal to (V_i− U_i).

V_i is a two-sided random error component beyond the control of the farmer

U_i is a one-sided inefficiency component.

The technical efficiency (TE_i) of rice seed production by the i^th farmer was determined using the expectation of U_i conditional on the random variable ξ_i (Equation (3)(3) $${\text{TE}}_i=\frac{Y_i}{Y_i\text{*}}=\frac{f\left(X_{i,}\beta \right)\text{\hspace{0.17em}exp\hspace{0.17em}}(V_i-U_i)}{f\left(X_{i,}\beta \right)\text{\hspace{0.17em}exp\hspace{0.17em}}(V_i)}=\text{\hspace{0.17em}exp}\left(-{\text{U}}_{\text{i}}\right)\hspace{0.17em}$$(3) ). It follows that: (3) $${\text{TE}}_i=\frac{Y_i}{Y_i\text{*}}=\frac{f\left(X_{i,}\beta \right)\text{\hspace{0.17em}exp\hspace{0.17em}}(V_i-U_i)}{f\left(X_{i,}\beta \right)\text{\hspace{0.17em}exp\hspace{0.17em}}(V_i)}=\text{\hspace{0.17em}exp}\left(-{\text{U}}_{\text{i}}\right)\hspace{0.17em}$$(3) so that 0 ≤ TE_i≤ 1

2.5.2. Stochastic frontier approach with scaling property in the inefficiency

We used a one-step model (Equation (2)(2) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\xi i\left(\mathit{\text{Vi}}-\mathit{\text{Ui}}\right)$$(2) ) because the two-step model (a stochastic frontier production function followed by Tobit regression) is biased in the first and second steps (Wang & Schmidt, 2002). This bias can take a severe form, which has been proven with Monte Carlo evidence by Wang and Schmidt (2002). The one-step estimators correctly specify the model as well as being asymptotically optimal if we further introduce the scaling property in the model proposed in (Equation 4(4) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\mathit{\text{Vi}}-\hspace{0.17em}u\left(\mathit{\text{Ci}}\prime ,\delta \right)$$(4) ) by letting the ‘pre-truncation variance be proportional to the square of the pre-truncation mean’ (Wang & Schmidt, 2002). This implies that U_i is distributed as h (C_i^′,δ) times N (µ, σ²)⁺. In terms of mathematical expression, U_i is distributed as $$\text{N\hspace{0.17em}}{\left[\mu \text{\hspace{0.17em}h\hspace{0.17em}}\left({\text{C}}_{\text{i}}{}^{\prime },\delta \right),\hspace{0.17em}{\sigma }^2\text{h\hspace{0.17em}}{\left({\text{C}}_{\text{i}}{}^{\prime }\text{,}\delta \right)}^2\right]}^{+}$$ where δ₀, … δ₁ are the parameters to be estimated; C_i^′ is a socio-economic characteristics of respondent household (Table 2), µ is mean of the distribution and σ² is the variance.

This assumption was made, as described by Simar et al. (1994). Using this assumption, we can test whether inefficiency is determined by C_i^′, not taking into account the assumption on the basic distribution (U_i*). We used this model (Equation 4(4) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\mathit{\text{Vi}}-\hspace{0.17em}u\left(\mathit{\text{Ci}}\prime ,\delta \right)$$(4) ) because of its three properties (Wang & Schmidt, 2002):

1. The scaling factor h(C_i^′,δ) adjusts (stretches or shrinks) the horizontal axis to adjust the scale of the U_i distribution without changing its shape.

2. The scaling property derives the effect of C_i^′ on inefficiency, irrespective of the distribution of U_i* and.

3. Ultimately, the parameterization of β and δ is made possible irrespective of the basic distribution.

Finally, the Cobb–Douglas frontier production (Equation (4)(4) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\mathit{\text{Vi}}-\hspace{0.17em}u\left(\mathit{\text{Ci}}\prime ,\delta \right)$$(4) ) along with the introduction of scaling properties gave the ‘one-step frontier production function with scaling property,’ which is thus specified below (Belotti et al., 2013; Wang & Schmidt, 2002). (4) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\mathit{\text{Vi}}-\hspace{0.17em}u\left(\mathit{\text{Ci}}\prime ,\delta \right)$$(4)

Such that, $${\mathrm{U}}_{\mathrm{i}}=\text{u}\left(C_i{}^{\prime },\mathrm{\delta }\right)\sim \text{h}\left({\mathrm{C}}_{\mathrm{i}}{}^{\prime },\mathrm{\delta }\right){\text{U}}_{\mathrm{i}}{}^{*}$$ where h (C_i^′,δ) ≥ 0, that is, a positive function of the determinants, and U_i* refers to a basic distribution. Thus, the scaling factor and scaling property implies that inefficiency distribution is the same for all firm as it is determined by U_i*, while the inefficiency distribution scale varies for individual firms determined by the vector C_i^′.

2.5.3. Histogram of the model

A histogram was obtained to plot the distribution of technical efficiency as a result of scaling the model (Equation (4)(4) $$\text{ln\hspace{0.17em}}{Y}_i={\beta }_o+{\displaystyle \sum }_{n=1}^N{\beta }_n\mathit{\text{ln}}{X}_{\mathit{\text{ni}}}+\mathit{\text{Vi}}-\hspace{0.17em}u\left(\mathit{\text{Ci}}\prime ,\delta \right)$$(4) ). This validates whether the error term for the inefficiency effects is distributed according to our assumption.

2.5.4. Maximum likelihood estimation

The maximum likelihood method was used to estimate the model parameters, the function of which was expressed using variance parameters. We determined the maximum likelihood estimates of the frontier and the determinants of inefficiency. The Likelihood Ratio (LR) test was used to check for inefficiency in the model (Equation (5)(5) $${\chi }^2=\hspace{0.17em}-2\left[L\left(H_0\right)-L\left(H_1\right)\right]\hspace{0.17em}$$(5) ). The LR test is shown below, as recommended by Huang and Lai (2017). (5) $${\chi }^2=\hspace{0.17em}-2\left[L\left(H_0\right)-L\left(H_1\right)\right]\hspace{0.17em}$$(5)

Where L(H₀) and L(H₁) are the log-likelihood values of the restricted model (ordinary least squares) and the frontier model (truncated normal stochastic frontier approach with scaling property), respectively. Critical values were used as a reference to test the hypotheses (Appendix B). This can be confirmed by testing the significance of skewness after executing the Cobb–Douglas production function, which depicts the presence of inefficiency. This can act as guidance on whether to run the more expensive maximum likelihood method.

2.6. Determination of level of productivity of the growers

To determine the productivity level, we used the concept of return to scale (RTS), which was obtained from the Cobb–Douglas stochastic frontier production function used in the model. The value of RTS can be defined as the summation of the output elasticities of the inputs used in production, that is, the summation of the coefficients (betas’). Thus, the RTS can be interpreted as: (6) $$\mathrm{\text{RTS}}=\sum _{i=1}^5{\beta }_i\dots$$(6)

The value of RTS can be interpreted based on the results obtained as shown in Table 3.

Table 3. Interpretation of the level of productivity (return to scale).

Return to scale (RTS)	Explanation
<1	Decreasing return to scale
=1	Constant return to scale
>1	Increasing return to scale

Ultimately, the value of return to scale provides the region/zone of production in which individual farms are operating. In addition, the output elasticities ${\beta }_i$ of the individual inputs provide the percentage increase/decrease in the output per unit percentage increment in the level of that particular input used in production.

2.7. Index of severity/importance for rice seed production

We used the forced ranking technique to rank the reasons for rice seed production and the major problems in the study area after FGD and KII. The purpose of this indexing technique is to place different options in ascending or descending order of severity. This method is mostly used to rank problems and opportunities. The mathematical approach for using this index is: $$\mathrm{I}=\sum _{i=1}^n\frac{S_i{f}_i}{n}$$

(Adhikari & Thapa, 2023)

Where,

I = priority index such that 0 ≤ I ≤ 1

S_i = scale value at i^th priority

(S_i = 0.2, 0.4, 0.6, 0.8 and 1, respectively, for problem/importance ranks 1 to 5).

f_i = frequency of i^th priority

n = total numbers of observations.

2.8. Data analysis technique

Data entry was performed using MS Excel, and data analysis was performed using STATA Version 16. The one-step stochastic production frontier with scaling properties is estimated using the maximum likelihood method. The index of importance and severity was used to rank the major reasons for rice seed production and the major problems in rice seed production.

3. Results

3.1. Summary of the socioeconomic and demographic characters of rice seed growers

The socioeconomic and demographic characteristics of rice seed growers in Bharatpur Metropolitan City and Madi Municipality are presented in Figure 3. The average age of the respondents was 56 and 57 years in Bharatpur and Madi, respectively. The average number of years of schooling of the respondents were 9.35 years in Bharatpur and 10.12 years in Madi. Furthermore, the average family size was six at both local levels. At both local levels, the average number of members in the economically active age group is nearly four.

Figure 3. Socio-demographic characteristics of the respondent in Chitwan.

The other socio-demographic and institutional characteristics of rice seed growers are presented in Figure 4. The involvement of family members in rice seed production was significantly higher in Bharatpur (p < .05) than in Madi. The average land size, on the other hand, was not statistically different for either of the local levels. Rice seed growers from Madi had significantly more experience than those from Bharatpur (p < .10). Similarly, rice seed growers in Madi received significantly more training than those in Bharatpur (p < .001). The rice seed growers of Madi visited the extension agent more frequently than those of Bharatpur, which was statistically significant (p < .10).

Figure 4. Socio-economic characteristics of the respondent in Chitwan.

Besides the socio-economic characteristics, the descriptive statistics of the important variables like labor availability, machinery availability and market access in the two study sites have been shown in Table 4. From the table, it can be observed that Bharatpur had better access to labor, machineries as well as the national market while Madi had better access to the local market.

Table 4. Labor, machinery and market availability in the study area.

Variables	Bharatpur	Madi
Labor availability (% respondents)	87.18	74.63
Machineries availability (% respondents)	94.87	64.2
Local market access (% respondents)	8.33	14.93
National market access (% respondents)	91.67	85.07

3.2. Association among different socio-economic and demographic characteristics

3.2.1. Association of socio-economic and demographic characteristics with the local levels

The different socioeconomic variables and their associations with local levels are shown in Table 5. From the table, it can be observed that 82% of the respondents were male and almost 78% of the respondents had agriculture as their major occupation. The primary occupation of the respondents was significantly associated (p < .05) with location, that is, the two local levels.

Table 5. Association among the socio-economic variables with the local levels in Chitwan.

Variable	Overall	Bharatpur	Madi	χ^2 value	p Value
Gender
Male	183 (82.06)	129 (57.85)	54 (24.22)	0.139	.708
Female	40 (17.94)	27 (12.11)	13 (5.83)
Occupation
Agriculture	174 (78.03)	116 (52.02)	58 (26.01)	4.07**	.044
Other	49 (21.97)	40 (17.94)	9 (4.04)
Total	223 (100)	156 (69.96)	67 (30.04)

Notes: ** represents significance at the 5% level. The figures in parentheses indicate relative percentages.

3.2.2. Association of institutional involvement with two local levels

The involvement of different institutions and their associations with local levels are shown in Table 6. From the table, 47% of the respondents were observed to be members of cooperatives, 44% of the respondents had received training related to rice seed production and 66% of the respondents visited the extension agent.

Table 6. Association among the institutional involvement with the local levels of Chitwan.

Variables	Overall	Bharatpur	Madi	χ^2 value	p Value
Cooperative involvement
Yes	105(47.09)	77(34.53)	28 (12.56)	1.077	.299
No	118(52.91)	79(35.43)	39 (17.49)
Training
Received	99 (44.39)	72 (32.29)	27 (12.11)	0.65	.42
Not received	124(55.61)	84 (37.67)	40 (17.94)
Contact extension agent
Contact	148 (66.37)	116(52.02)	32 (14.35)	14.85***	.00
No contact	75 (33.63)	40 (17.94)	35 (15.70)
Total	223 (100)	156 (69.96)	67 (30.04)

Notes: *** represents significance at the 1% level. The figures in parentheses represent relative percentages.

The involvement of rice seed growers in cooperatives and participation in training were not significantly associated with each other. Contact with the extension agent was significantly associated with location (p < .001).

3.2.3. Association of the adoption of crop insurance, climate change adaptation strategies and availability of subsidy with the local levels

The adoption of crop insurance, availability of subsidies, adoption of climate change adaptation strategies and their association with location are presented in Table 7. Overall, 29% of the respondents adopted crop insurance. In the case of incentives, 66% of the respondents had received subsidies in one or both forms, while 67% had adopted a climate change adaptation strategy.

Table 7. Association of the adoption of crop insurance, climate change adaptation strategies and receipt of subsidy with the local levels of Chitwan.

Variable	Overall	Bharatpur	Madi	χ^2 value	p Value
Crop insurance
Adopted	65 (29.15)	34 (15.25)	31 (13.9)	13.59***	.001
Not adopted	158 (70.85)	122 (54.71)	36 (16.14)
Subsidy
Received	147 (65.92)	118 (53)	29 (13)	21.84***	.001
Did not receive	76 (34.08)	38 (17)	38 (17)
Adaptation strategies
Adopted	149 (66.82)	114 (51.12)	35 (15.70)	9.18***	.00
Not-adopted	74 (33.18)	42 (18.83)	32 (14.35)
Total	223 (100)	156 (69.96)	67 (30.04)

Notes: *** represents significance at the 1% level. The figures in parentheses represent relative percentages.

3.3. Genotype preference for rice seed production in Chitwan

The genotype of rice seeds grown by the rice seed growers in Bharatpur and Madi are shown in Figure 5. In Bharatpur and Madi, Sabitri was grown by the majority of farmers (55.13% and 92.53% of seed growers, respectively). The majority of growers preferring Sabitri to others could be attributed to its huge market demand in the district and the better straw quality of the genotype.

Figure 5. Genotype of rice seed grown by the rice seed growers in Chitwan.

3.4. Determinants of the technical efficiency of rice seed production

The estimates obtained from the scaled frontier model for Bharatpur and Madi are shown in Table 8 and Table 9, respectively. The model was estimated for 156 and 67 observations from Bharatpur and Madi, respectively, with Prob > χ² = 0.001, indicating the significance of the estimated parameters. Furthermore, the significance of sigma squared validates that the assumption of a truncated normal distribution for the error term (u_i) was appropriate for both local levels, as it signifies a robust model.

Table 8. Maximum likelihood estimates for Bharatpur from the truncated normal scaling property model.

Log likelihood = 83.13 LR test (χ^2 = 49.99***, p < .001)			Number of observations = 156
			Wald χ^2 (5) = 2595.82
			Prob > χ^2 = 0.001
Ln (prod)	Coef	Std. err	z	p>|z|	[95% conf. interval]
Frontier
Ln_Land	0.067	0.026	2.60***	.009	0.017	−0.12
Ln_Labor	0.629	0.070	8.87***	.001	0.49	0.77
Ln_Urea	0.140	0.045	3.11***	.002	0.05	0.23
Ln_Herbicide	0.320	0.068	4.78***	.001	0.19	0.46
Ln_Seed	0.012	0.032	0.37	.712	−0.05	0.08
_const	0.390	0.380	1.01	.311	−0.36	1.13
Hscale
Member_riceseed	−0.795	0.423	−1.88*	.060	−1.62	−0.033
Subsidy_seed	0.457	0.485	0.94	.345	−0.49	1.40
Crop insurance	0.767	1.085	0.71	.480	−1.36	2.89
Adop_Climate	−2.56	1.484	−1.72*	.085	−5.46	0.35
Education	0.123	0.065	1.89*	.059	−0.004	0.25
Experience	0.149	0.071	2.09**	.037	0.009	0.28
Cooperative	0.045	0.349	0.13	.897	−0.639	0.73
Extworker_visit	−2.18	0.813	−2.68***	.007	−3.77	−0.58
Training	−1.05	0.621	−1.69*	.090	−2.26	0.16
Tau
_cons	0.089	0.098	0.91	.362	−0.103	0.28
Cu
_cons	−6.22	2.41	−2.58**	.010	−10.96	−1.49
Vsigmas
_cons	−4.014	0.121	−33.12***	.001	−4.25	−3.77
Variable	Coef.	Std. err	t	p>|t|	[95% conf. interval]
Sigma_v_sqr	0.018	0.002	8.25***	.000	0.014	0.023

Notes: *, ** and *** represent significant at 10%, 5% and 1% levels, respectively. The transformation cannot be done for sigma_u_sqr in the scaling-property model since it is a function of variables. The transformation is done only if the sigma_u_sqr is constant.

Table 9. Maximum likelihood estimates for Madi from the truncated normal scaling property model.

Log likelihood = 125.47 LR test (χ^2 = 62.21***, p < .001)		Number of observations = 67 Wald χ^2 (5) = 1075.25 Prob > χ^2 = 0.001
lnp	Coef	Std. err	z	p>|z|	[95% conf. interval]
Frontier
Ln_Land	0.03	0.03	1.03	.302	−0.03	0.09
Ln_Labor	0.69	0.05	15.15***	.001	0.60	0.78
Ln_Urea	0.14	0.03	4.80***	.001	0.08	0.19
Ln_Herbicide	0.06	0.02	2.52**	.012	0.01	0.10
Ln_Seed	0.02	0.03	0.85	.401	−0.03	0.08
_cons	−0.94	0.43	−2.17	.031	−1.79	−0.09
hscale
Experience	−0.06	0.02	−2.69***	.007	−0.10	−0.02
Extworker_visit	−0.19	0.09	−2.12**	.034	−0.37	−0.01
Adopt_Climate	−0.42	0.25	−1.66*	.096	−0.92	0.08
Crop insurance	0.22	0.18	1.21	.225	−0.14	0.58
Training	−0.16	0.15	−1.07	.284	−0.44	0.13
Subsidy_seed	0.14	0.15	0.95	.341	−0.15	0.44
Tau
_cons	0.44	0.09	4.98***	.001	0.27	0.61
Cu
_cons	−8.54	9.05	−0.94	.352	−26.27	9.19
Vsigmas
_cons	−6.63	0.45	−14.7***	.001	−7.51	−5.75
Variable	Coef.	Std. err.	t	p > t	[95% conf. interval]
Sigma_v_sqr	0.0013	0.00059	2.22**	.026	0.000	0.0032

Notes: *, ** and *** represent significant at 10%, 5% and 1% levels, respectively. The transformation cannot be done for sigma_u_sqr in the scaling-property model since it is a function of variables. The transformation is done only if the sigma_u_sqr is constant.

Furthermore, the skewness test for the Cobb-Douglas production was statistically significant (p < .01 and p < .05 for Bharatpur and Madi, respectively), which depicted the presence of inefficiency (Appendix A). This was further validated by the Likelihood Ratio (LR) test, which was statistically significant for the maximum likelihood estimates for both Bharatpur and Madi.

3.4.1. Maximum likelihood estimates

From Table 8, the Maximum Likelihood (ML) estimates of the production function for rice seed production in Bharatpur indicated that all parameters had a positive relationship. The parameters, viz., land size, labor, urea and amount of herbicide, were statistically significant, implying their positive influence on rice seed production.

Similarly, from Table 9, the likelihood estimates of the production function for Madi indicate a positive relationship between the three input variables and output. The parameters of labor, urea and amount of herbicide were statistically significant.

3.4.1.1. Labor

Labor (man days) was found to be significant at the 1% level of significance, with a p value of .001 for either of the local levels in the production frontier model. The positive sign of the coefficient indicates a positive association between labor and rice seed production. The results for Bharatpur reveal that a 1% increase in labor (man-days), ceteris paribus, led to a 0.63% increase in rice seed production, compared to 0.69% in the case of Madi.

3.4.1.2. Urea

The amount of urea fertilizer applied by the rice seed growers in Bharatpur and Madi was found to be significant at the 1% level of significance (p < .001) (Table 7). It can be deduced from these estimates that a 1% increase in the amount of urea leads to a 0.14% increase in rice seed production at the local level.

3.4.1.3. Land size

The land size for rice seed production of the rice seed growers in Bharatpur was significant at the 1% level (p < .001). This implies that a 1% increase in land size leads to a 0.067% increase in seed production, thereby exhibiting a positive relationship.

3.4.1.4. Amount of herbicide

Table 8 and Table 9 show that the amount of herbicide used by the rice seed growers in Bharatpur and Madi was significant (p < .001). A positive value indicates that the increased use of herbicides led to increased rice seed production. In Bharatpur, it can be implied that a 1% increment of herbicides (liters/ha) leads to a 0.32% increase in rice seed production. Similarly, for Madi, it can be implied that a 1% increase in the amount of herbicide leads to a 0.06% increase in rice seed production. It is not surprising that using plant protection chemicals can support the yield-attributing characteristics of rice, especially at the critical growth stages.

3.4.2. Determinants of technical efficiency

The h-scale (inefficiency) parameters shown in Table 8 and Table 9 relate to the farm-specific and socioeconomic positions of the rice seed growers in Bharatpur and Madi, respectively.

The parameters for Bharatpur included the number of members involved in rice seed production, the education level, experience in rice seed production, cooperative involvement, contact with extension agents, receipt of training, adoption of climate change adaptation strategies, adoption of crop insurance and receipt of subsidies. Among the eight variables estimated, six were found to be statistically significant for Bharatpur excluding adoption of crop insurance and receipt of subsidies.

In the case of Madi, six parameters–experience, contact with extension agents, adoption of climate change adaptation strategies, adoption of crop insurance, receipt of training and receipt of subsidy–were chosen as the determinants of technical efficiency. Of the six variables estimated, only three were found to be statistically significant: experience, contact with extension agents and the adoption of climate change adaptation strategies.

3.4.2.1. Members involved in rice seed production

The number of members involved in rice seed production was statistically significant (p = .06) in Bharatpur (Table 8). The negative sign of the coefficient implies that family member involvement in rice seed production decreased technical inefficiency. The participation of an extra family member leads to a 79.5% decrease in technical inefficiency.

3.4.2.2. Access to training

Participation in training was found to be a significant determinant of inefficiency in Bharatpur (Table 8) at the 10% level of significance, with a p value of .090. The negative value of the coefficient (−1.05) implies that the receipt of training leads to a decrease in technical efficiency. This can be interpreted as moving from farmers who did not receive training to those who had received training, leading to a 105% decrease in technical inefficiency.

3.4.2.3. Contact with extension agent

The contact of rice seed growers with the extension agent was statistically significant at the 1% level of significance for Bharatpur (Table 8) and at the 5% level of significance for rice seed growers in Madi (Table 9).

In the case of rice seed growers in Bharatpur, the negative value of the coefficient (−2.18) implies that contact with extension agents leads to a decrease in technical inefficiency. It can be interpreted that moving from farmers with no contact with extension agents to farmers who contact extension agents decreased technical inefficiency by 218%.

Similarly, for rice seed growers in Madi, the negative value of the coefficient (−0.19) implies that contact with an extension agent leads to a decrease in technical inefficiency. It can be interpreted that when moving from farmers with no contact with the extension agents to farmers who contact the extension agents, technical inefficiency decreased by 19%.

3.4.2.4. Adoption of climate change adaptation strategies

The adoption of climate change adaptation strategies by rice seed producers was statistically significant at the 10% level for both Bharatpur (Table 8) and Madi (Table 9). The negative values of the coefficients (−2.56 and −0.42, respectively) imply that the adoption of climate change adaptation strategies has a negative relationship with technical inefficiency. This can be interpreted as moving from a non-adopter to an adopter category; technical inefficiency decreased by 256% and 42% for rice seed production in Bharatpur and Madi, respectively.

3.4.2.5. Education level of respondents

The educational level of the respondent households was statistically significant (p = .059) (Table 8). A positive coefficient sign (0.12) indicates that an additional year of formal education leads to an increase in inefficiency. An increase in the education level by an additional year led to a technical inefficiency increment of 12%.

3.4.2.6. Experience in rice seed production

The farming experience of the respondents was statistically significant at the 5% level (p = .037) in Bharatpur (Table 8). The positive coefficient sign indicates that increasing experience by an additional year leads to an increased technical inefficiency of 15%.

Unlike Bharatpur, the rice seed growers in Madi had years of experience that was statistically significant at the 1% level of significance (Table 9). The negative coefficient sign (−0.06) indicates that an additional year of experience leads to a decrease in technical inefficiency. The results indicate that an additional year of experience leads to a 6% decrease in the technical inefficiency.

3.5. Technical efficiency (TE) for rice seed production in Bharatpur and Madi

The technical efficiency distribution of rice seed production in Bharatpur and Madi is shown in Appendix C, which shows a histogram of the truncated normal distribution.

From Table 10, The largest group of rice seed growers (86.54%) in Bharatpur fell under the category of 91–100% technical efficiency (86.54%). The second largest group (7.05%) of rice seed growers ranged from 81 to 90%. The results revealed that most growers had more than 80% technical efficiency in rice seed production. Although a few farmers struggled to attain technical efficiency, the minimum level of technical efficiency was 55.99% and the highest was 99.99%. The mean technical efficiency is 96.15%.

Table 10. Technical efficiency (TE) scores of rice seed production in Chitwan.

	Location
Efficiency scores	Bharatpur		Madi
	Frequency	Percentage	Frequency	Percentage
<50%	0	0	0	0
51–60%	4	2.56	0	0
61–70%	0	0	3	4.48
71–80%	6	3.85	34	50.75
81–90%	11	7.05	23	34.33
91–100%	135	86.54	7	10.45
Total	156	100	67	100
Mean TE (%)	96.15		79.61
Min TE (%)	55.99		67.55
Max TE (%)	99.99		92.35
Std. dev	0.07		0.072

In the case of Madi (Table 10), most of the farmers (50.75%) were 71–80% efficient. The second-largest group (34.33%) falls within the range of 81–90% efficiency, followed by 91–100% efficiency (10.45% of farmers). A minority of farmers (4.48%) fell within the efficiency range of 61–70%. For Madi, the lowest level of technical efficiency was 67.55%, whereas the maximum value was 92.35%. The mean technical efficiency of rice seed production in Madi was determined to be 79.61%. Few growers (2.56%) in Bharatpur had 51–60% technical efficiency of rice seed production which is an outlier (Appendix C) in the efficiency score.

3.6. Relative technical efficiency between the adopter/non-adopters of climate change adaptation strategies

A significant and positive relationship was found between the adoption of climate change adaptation strategies and the technical efficiency of rice seed production at both local levels. To further gauge climate change and substantiate the previous finding, the mean technical efficiency was compared between the rice seed growers who had adopted a climate change adaptation strategy and those who did not adopt any strategy. The results obtained from the independent sample t-test between adopters and non-adopters are presented in Table 11. The contrast in efficiency between the categories of adopters was statistically significant at the 1% level of significance. Rice seed growers who adopted climate change adaptation strategies were statistically more efficient (p < .002) than those who did not adapt to the changing climate.

Table 11. Independent sample t-test for comparison of the mean technical efficiency between the adopters and non-adopters of climate change adaptation strategy in Chitwan.

Groups	Obs	Mean	Std. err	Std. dev	95% C.I		t-value	p Value
Adopters	149	0.953	0.010	0.080	0.931	0.975
Non-adopters	74	0.909	0.009	0.118	0.891	0.928
Combined	223	0.921	0.007	0.111	0.906	0.935
Difference		0.043	0.014		0.015	0.072	3.054***	.002

Note: *** represent significant at 1% level.

The statistically higher mean technical efficiency of the adopters of climate change adaptation strategies further underscores the clear linkage between the adoption of climate change adaptation strategies and improved technical efficiency in rice seed production. Thus, the positive association suggests that embracing these strategies can lead to more effective and efficient agricultural practices, which are crucial for sustaining rice seed production in the face of evolving climate challenges.

3.7. Estimating the level of productivity

Table 12 shows the productivity levels of rice seed production in Bharatpur and Madi. Inelasticity can be confirmed if a 1% increment in inputs leads to a less than 1% increment in output.

Table 12. Return to scale for rice seed production in Bharatpur Metropolitan City and Madi Municipality.

	Elasticity
Input variables	Bharatpur	Madi
Land	0.067	0.03
Labor	0.629	0.69
Urea	0.14	0.14
Seed	0.012	0.02
Herbicide	0.32	0.06
Return to scale	1.17	0.94

The increase in usage of the inputs for Bharatpur increased the output in higher proportion for a given proportion of input use: a 1% increase in man-days of labor increased output by 0.63%, while a 1% increase in the amount of herbicides, amount of urea, land size and seed rate increased output by 0.32%, 0.14%, 0.067% and 0.012%, respectively. In the case of Madi Municipality, the increase in input use increased the output, but less in proportion to the amount of input used: a 1% increase in man-days of labor increased the output by 0.69%, while a 1% increase in the amount of urea, herbicide, land size and seed rate increased the output by 0.14%, 0.06%, 0.03% and 0.02%, respectively.

In terms of returns to scale, the production function of rice seed growers in the Bharatpur metropolitan area exhibited an increasing return to scale (1.17). This implies that a 1% increment in all inputs for rice seed growers increased the output by 1.17%, ceteris paribus, with a mean technical efficiency of 96.15%. Unlike in Bharatpur, rice seed production in Madi exhibited a decreasing return to scale (0.94). This implies that a 1% increment in all inputs for rice seed growers increased the output by 0.94%, ceteris paribus, with a mean technical efficiency of 79.61%. To improve the scale of production efficiently, the following inputs may be targeted at either of the local levels: land size, labor, seed rate, amount of urea and herbicides. However, this route might not be preferable in Madi because of decreasing returns to scale.

3.8. Index of importance for rice seed production

The use of a forced ranking scale to determine the factors responsible for choosing rice seed production by farmers at both local levels is shown in Figure 6. From the figure, it can be observed that most of the respondents chose to produce rice seeds because of good returns, followed by a better market demand for rice seeds. This is further followed by awareness of the import of hybrid seeds from foreign countries and neighbor influence, while agro-climatic suitability was considered the least important reason behind the respondents’ choice of rice seed production.

Figure 6. Rank of important factors for rice seed production.

3.9. Index of severity of the problems faced by rice seed growers

The use of a forced ranking scale to determine the major problems in rice seed production at both local levels is illustrated in Figure 7. From the figure, it can be observed that most of the respondents faced the problem of input unavailability followed by adverse climate change, such as heavy rainfall and high temperatures. This was further followed by lack of irrigation and technical knowledge, while insect pest problems were considered the least problematic by the respondents.

Figure 7. Rank of major problems in rice seed production.

4. Discussion

4.1. Maximum likelihood estimates from stochastic production function

In the stochastic model, a positive relationship was observed between the labor (man-days) and production. Rice seed production, especially rouging activities, is labor-intensive, and an increase in labor will positively enhance several labor-based rice seed production activities, such as land preparation, transplanting, weeding, rouging, fertilizer application and harvesting. Similar results were reported by Muzeza et al. (2023) in their study on technical efficiency of maize production in Zimbabwe, where labor had a positive relationship with maize output. Similarly, Obianefo et al. (2021) and Biswas et al. (2021) in their study on technical efficiency of rice production in Nigeria and Bangladesh, respectively, reported that increased labor leads to increased production. In contrast with our findings, Chandio et al. (2019) and Mazhar et al. (2022), in their study on technical efficiency of rice production in Pakistan reported a negative relationship between labor and the production of rice, for which they claimed that smallholder rice growers used excess labor and non-improved varieties.

A positive relationship was observed between the amount of urea and its production in the stochastic frontier model. Urea contains 46% nitrogen and its increased usage leads to better growth and development of rice plants. Furthermore, the application of urea at critical growth stages can improve the yield-related characteristics of rice plants. Similar results were reported by Muzeza et al. (2023) and Obianefo et al. (2021), who also reported that increased use of fertilizer leads to increased rice production in both lowland and upland conditions of Zimbabwe. Chandio et al. (2019), Biswas et al. (2021) and Mazhar et al. (2022) also reported that fertilizer application in appropriate dose had a positive relationship with production in the stochastic frontier model.

Land size and productivity of rice seeds were found to have a positive relationship in our study. A similar study was conducted by Biswas et al. (2021) in Bangladesh and Tesema (2022) in Ethiopia. Land is an important factor of production and production of rice seed is not possible without land. Jin et al. (2015) in their study on productivity in China showed that agricultural productivity can be increased through optimal land use and management.

In our study, a positive relationship was observed between the amount of herbicide used and the output of rice seeds. This may be due to better plant health because the application of herbicides in rice can prevent the loss of rice seed yield, as well as enhance the yield-attributing characteristics of the rice. Similar results were reported by Obianefo et al. (2021) in Nigeria, who concluded that the use of herbicides for plant protection leads to increased rice production in both lowland and upland areas. Tesema (2022) also reported that greater use of herbicides and pesticides had a positive relationship with rice production in Ethiopia. Ho and Shimada (2019a) also reported that plant protection costs have a significant and positive relationship with rice output in the Vietnamese Mekong Delta. In contrast to our findings, Biswas et al. (2021) and Mazhar et al. (2022) reported a negative relationship between plant protection chemicals and rice production, which they justified by stating that their study was within an organic farming zone and that chemicals were applied only when needed.

The interaction effect of the input variables on production is not provided in this study which is a limitation of our study. A further empirical investigation is important to identify interaction effect of the input variables.

4.2. Determinants of the technical inefficiency

Our study reveals that household members’ involvement in rice seed production leads to greater technical efficiency. The involvement of members in rice seed production leads to more efficient production due to reduced labor costs, as well as increased farming time and attention to rice seed production activities. Furthermore, with more family members, there is an opportunity for better resource allocation and utilization. For instance, family members can coordinate irrigation schedules, optimize fertilizer use and ensure timely seed selection and storage. This coordinated effort in resource management contributes to increased technical efficiency and improved overall outcomes in rice seed cultivation. Similar findings were reported by Biswas et al. (2021) and Rahman et al. (2012) in their studies on technical efficiency of rice production in Bangladesh. In contrast with our findings, Khanal and Maharjan (2013) and Subedi et al. (2020), in their studies on the technical efficiency of rice seed growers and rice growers in the Terai region of Nepal, respectively, reported that family labor and the increasing number of family members had a negative relationship with technical efficiency.

In Bharatpur, the receipt of training had a significant and positive relationship with technical efficiency. Our findings are in line with those of Mengui et al. (2019), who concluded that to reduce technical inefficiency of growers in Cameroon, training should be provided to enhance their knowledge. Training in new technologies and practices can help farmers use their resources efficiently. In contrast, Khanal and Maharjan (2013) reported that training did not have a significant impact on the technical efficiency of rice seed growers in the Terai region of Nepal. They reported that the mismatch of training compared to local needs could be the reason for these findings.

In our study, in both local levels, contact with the extension agent was associated with a decrease in technical inefficiency. Similar results were reported by Abate et al. (2019) in their study on technical efficiency of crops in Ethiopia, who insisted that frequent contact with extension agents led to better knowledge and information, thus leading to the proper use of available inputs in crop production. Contact with extension agents might increase seed growers’ knowledge of how to use available resources more efficiently, thus decreasing inefficiency. Furthermore, increased awareness of contact with extension agents leads to greater demand for agricultural inputs as concluded by Dawit (2012) in their study on efficiency of wheat production in Ethiopia. Our findings are similar to those of Ho and Shimada (2019a) in their study on technical efficiency of rice production in Vietnam, Mengui et al. (2019) in Cameroon, Siaw et al. (2021) in their study on technical efficiency of maize production in Ghana and Thomas et al. (2020) in their technical efficiency study of tomato production in Ghana.

The adoption of climate change measures, such as alternate wetting and drying, irrigation management and resistant varieties, leads to a better yield than farmers unable to cope with climate change. Climate change measures often encourage adoption of innovative technologies and practices. By leveraging these technologies, rice seed growers can enhance monitoring, optimize resource allocation and make informed decisions, ultimately leading to increased technical efficiency. The implementation of different adaptation strategies against climate change can overcome losses in production, thus signifying maximum output and enabling efficient farming (Priyanto et al., 2022). Ho and Shimada (2019a) in their study on technical efficiency of rice production in Vietnam reported that adaptation strategies improved the technical efficiency by 13%–14%. They also reported that farmers adopting climate change measures manage their inputs efficiently, and hence, improve the economic production of rice. Furthermore, Priyanto et al. (2022) also reported that the adoption of climate change adaptation strategies increased technical efficiency of rice production in Indonesia by 0.06%.

Although it is not as expected, positive sign of education could be attributed to very few years of formal education on average (nine years), because the additional years of education might not have had an impact on increasing technical efficiency. Increased years of formal education may not directly address these resource constraints or provide practical solutions to the specific limitations faced by rice seed growers in their agricultural practices. Furthermore, an additional year of schooling does not guarantee hands-on experience in developing specific skills related to rice-seed production. Piya et al. (2012) reported that education level had a negative relationship with technical efficiency in Chitwan district, which concurs with our study. Similarly, Subedi et al. (2020), in their study of the technical efficiency of rice growers in the Terai region of Nepal, reported a significantly negative relationship between years of education and technical efficiency. Biswas et al. (2021) and Rahman et al. (2012), in their study in Bangladesh, reported similar results, where the education level of respondents had a negative relationship with technical efficiency in rice production. Priyanto et al. (2022) also reported a negative relationship between education and technical efficiency among rice growers in Indonesia, although the relationship was not significant.

In our study, the MLE estimates for technical efficiency of rice seed growers in Bharatpur revealed that years of experience had a negative relationship with technical efficiency. Although not as expected, the difference in years of experience for the two local levels was statistically significant at the 10% level of significance (Figure 4), and rice seed growers in Madi had more years of experience in rice seed production, which might be one of the reasons why experience had a negative relationship with efficiency in Bharatpur and a positive relationship with efficiency in Madi.

The negative relation of efficiency and years of experience could be attributed to the fact that the farmers who did not have agriculture as primary occupation had more years of experience (8.68 ± 0.741 years) compared to farmers with primary occupation as other than agriculture (7.86 ± 0.28 years). This implies that by the time farmers gain more years of experience in farming, they might become interested in other business- or service-related activities. In addition, in the case of farmers with primary occupations such as agriculture, greater experience can sometimes lead to cognitive biases such as confirmation bias or the tendency to rely on familiar patterns and assumptions. Additionally, with increased experience, individuals may become set in their ways and resistant to adopting new technologies, methods, or approaches. They may be reluctant to embrace innovation or unfamiliar techniques that can hinder their technical efficiency. Similar results were reported by Biswas et al. (2021) in their study in Bangladesh, although the rice growers had an average of 25 years of experience.

In the case of Madi, the farmers had more years of experience (Figure 4). With increased experience, farmers allocate resources wisely and utilize these technologies efficiently. Furthermore, they are acquainted with better practices, knowledge and methods for rice seed production. Khanal and Maharjan (2013), in their study on the technical efficiency of rice seed growers in the Terai region of Nepal, reported that experience has a significant positive impact on technical efficiency. Subedi et al. (2020) also reported that farming experience had a positive relationship with technical efficiency of rice production. Choudhary et al. (2022) also reported that experienced farmers are technically more efficient in their study on rice sub-sector.

The availability of subsidy and adoption of crop insurance were not found to be a significant determinant of the technical efficiency in our study. Generally, subsidy for rice seed growers in Nepal and in Chitwan, is provided for purchase of improved seeds, farm machineries and fertilizers (Panta, 2019). The null effect of provision of subsidy on technical efficiency of rice seed production in this study might be due to lack of a clear regulation and evaluation mechanism (Gautam et al., 2022). Despite the provision of subsidies farmers may be less motivated to perform well due to increased incomes (Latruffe et al., 2017; Minviel & Latruffe, 2017). The actual impact of subsidy on performance of farmers and production is not provided in this study and hence needs a further empirical investigation. In case of crop insurance, this paper cannot provide evidence as to why insurance is not associated with technical efficiency, but one possible explanation can be that the insurance is subsidized in Nepal and this may lead the farmers to work less efficiently, purchase lower quality seeds and other moral hazards (Castro et al., 2023; Zhu & Lansink, 2010).

Our study didn’t include other variables, for instance – distance to market, due to multi-collinearity problems and failure to achieve concavity with those variables. Further study is required to explore the impacts of other possible variables on the technical efficiency—for instance, the amount of subsidy received, the amount of insurance premium can be kept as determinants.

4.3. Level of technical efficiency

The findings suggest that all farmers produce below the level of the optimum frontier. The different levels of efficiency could be attributed to the mixed usage of inputs by the growers, thereby leading to varied output levels. The overall results imply that rice seed growers could shorten the gap between their observed output and frontier optima by 4% in Bharatpur, while rice seed growers in Madi have to bridge a gap of 21% to achieve an optimal level of technical efficiency. The difference in technical efficiency could be attributed to the combination of the use of the input for production, as well as the different socio-economic determinants of the two locations.

Similar results with rice seed growers in Bharatpur were reported by Chandio et al. (2019) in their study in Sindh, Pakistan, where they reported 97% technical efficiency and Subedi et al. (2020), who reported a technical efficiency of 91.7% in Terai region of Nepal. Similarly, the results for Madi (79.61% technical efficiency) concur with the findings reported by Khanal and Maharjan (2013) in their study on the technical efficiency of rice seed growers in the Terai region of Nepal, where they reported a mean technical efficiency of 81% with a wide range of variation in efficiency scores. Piya et al. (2012) also reported the technical efficiency of rice seed growers in Chitwan district to be 74%, which is similar to our findings with respect to Madi Municipality. Similarly, Choudhary et al. (2022) reported a 75.2% technical efficiency of the rice sub-sector in the Chitwan district of Nepal.

The better technical efficiency observed in the case of rice seed growers in Bharatpur could be attributed to the positive role of different socio-economic variables viz family members involvement in rice seed production, adoption of climate change adaptation strategies, visit to extension workers and participation in training, as well as the efficient use of inputs land, labor, urea and herbicides. Furthermore, Bharatpur is an urban area, and farmers have easy access to labor, machineries, markets and infrastructure, which may have played a positive role in increasing their technical efficiency (Table 4). Bharatpur has easy availability of Indian labor for most of their field activities. However, we observed an outlier in case of Bharatpur as 2.56% of farms were relatively low in technical efficiency. This could be attributed to the input unavailability in proper time and consequences of adverse climate (Figure 7) in those farms. Despite the best practices and rational use of input, unavailability of inputs like fertilizers and seed in time can affect the production. The impact of adverse climate can be diverse in some farms who are not able to cope with the impacts. This finding provides a research gap to study the vulnerability impact assessment of climate change among rice seed growers in the study area so as to prioritize the more vulnerable groups and strengthen their coping ability against severe impact of climate change.

In case of Madi, there was poor availability of labor due to outmigration. Bharatpur is an urban area and thus it has better access to the machineries unlike Madi. Although machinery was available in some places of Madi, majority of the land there is lowland making it difficult to use machines. In case of market access, Bharatpur had better access to the national market while Madi had better access to the local market. This could also be attributed to better market infrastructures and development activities in Bharatpur (Rai et al., 2020).

The study doesn’t take into account the marginal and highly commercial rice seed producers. Thus, the findings cannot be generalized for all type of rice seed growers. The study is mostly applicable for the smallholding rice seed growers of Chitwan district of Nepal. Further study is necessary to study the technical efficiency for commercial rice seed production.

4.4. Policy implications

It can be suggested to the rice seed growers to focus on increasing the usage of inputs such as land, labor, urea and herbicides in Chitwan, but this route might be more preferable in Bharatpur due to increasing returns to scale. Furthermore, the government, policy makers and practitioners should work on providing formal education, making extension services more accessible, providing training to seed growers, creating programs to involve youth in rice seed production and encouraging rice seed production through awareness. Ultimately, local and provincial-level institutions should include climate change adaptation strategies in their annual programs to encourage the adoption of such strategies. This can have a two-fold effect: increased technical efficiency and adaptation against threats in the face of climate change.

5. Conclusion

From the study, we can draw two major conclusions. First, the mean level of technical efficiency of the rice seed growers was higher (96.15%) in Bharatpur than in Madi (79.61%). Although the efficiency score was higher for both, the rice seed growers produced below the frontier level, accompanied by a wide range of variation in the efficiency scores. This suggests that a varied combination of different inputs by farmers leads to different outputs. The second understanding from the study is associated with bridging the disparity between observed and actual frontier outputs. For this purpose, we can make three major suggestions: (i) the inefficiency of 3.85% for Bharatpur can be bridged by focusing and targeting the socioeconomic aspects, viz., education level, contact with extension agents, training and adoption of climate change adaptation strategies; (ii) the gap of 20.39% for Madi can be bridged by focusing and targeting the socioeconomic aspects, such as experience, contact with extension agents and adoption of climate change adaptation strategies; (iii) this could further be supported by increasing the usage of inputs such as land, labor, urea and amount of herbicide. Thus, adaptation to climate change increased the technical efficiency of rice seed growers.

Further studies on the resource use efficiency analysis of inputs, interaction effect of input variables and impact of other determinants, viz., market access, amount of subsidy, and amount of insurance premium can be suggested.

Ethical approval

We would like to note that according to Directorate of Agriculture Development, Government of the Bagmati Province, ethics approval is not required for survey studies including farmers in the province. Therefore, this study was conducted according to the principles mentioned in World Medical Association – Declaration of Helsinki and adheres to research integrity and participant confidentiality.

Consent form

Before commencement of the survey, a consent statement was read to the household to make them understand the purpose of the survey and get their written consent to go on with the administration of the questionnaire. The dignities and values of the respondents were safeguarded with confidentiality.

Author contributions

Rabin Thapa: Conception and design of the research, analysis and interpretation of data, drafting of the paper and the final approval of the version to be published.

Shiva Chandra Dhakal: Conception and design of the research, drafting of the paper, revising it carefully and the final approval of the version to be published.

All the authors agree to be accountable for all aspects of the work.

Disclosure statement

No potential 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 research was funded by the Government of Bagmati Province, Ministry of Agriculture and Livestock Development, Nepal.

Notes on contributors

Rabin Thapa

Rabin Thapa The author currently works as Agriculture Extension Officer at Ministry of Agriculture and Livestock Development, Nepal. He has done his Masters in Agricultural Economics. His area of interests includes agricultural production economics, applied econometrics and climate change.

Shiva Chandra Dhakal

Dr. Shiva Chandra Dhakal The author currently works as the Director of the Directorate of Planning at Agriculture and Forestry University, Nepal. He is also an Associate Professor of the Department of Agricultural Economics and Agribusiness Management, Faculty of Agriculture in the same university. His area of interests includes climate change, production and marketing economics and agribusiness.

Notes

1 LAND COVER MAP - BHARATPUR SUB-METROPOLITAN CITY, CHITWAN |Resources (nepalindata.com).

Appendices

Appendix A

Table A1. Skewness test for confirmation of the presence of inefficiency.

Skewness/kurtosis tests for normality						Decision for inefficiency
Variable	n	Pr (skewness)	Pr (kurtosis)	------ Joint ------
				Χ^2 (2)	Prob > chi^2
Efficiency (Bharatpur)	156	0.0005	0.0217	17.38***	0.0002	Presence
Efficiency (Madi)	67	0.0449	0.0920	6.86**	0.0324	Presence

Note: ‘**’ and ‘***’ represent significance at 5% and 1% levels, respectively.

Appendix B

Table B1. Critical values for the mixed chi-square distribution.

Significance Level
dof	0.25	0.1	0.05	0.025	0.01	0.005	0.001
2	2.090	3.808	5.138	6.483	8.273	9.634	12.810

Source: Kodde and Palm (1986).

Appendix C

Figure C1. Distribution of technical efficiency for Bharatpur and Madi, respectively.

Appendix D

Table D1. Prioritization of the major climate change adaptation strategies in the study area.

Options Criteria	Varietal selection	Residue management	Water management	Planting time	Nutrient management
Effectiveness	5	5	4	5	4
External effects	5	4	5	4	3
Availability	4	5	3	4	4
Accessibility	5	4	4	2	4
Affordability	4	3	3	5	3
Profitability	5	5	5	5	5
Total mark	28	26	24	25	23
Rank	I	II	IV	III	V

Notes: Where, the scale of 0–5 represents; 0 = no significance 1= low significance 2 = low significance 3 = moderate significance 4 = high significance and 5 = strong significance.