Impact of Variety Type and Irrigation on Technical Eciency of Potato Farmers: The Case of Terai Region of Nepal

The national average potato productivity is far below as compared to other neighbouring countries due to several production constraints. Variety and irrigation are the important factors to increase production. The aim of this study is to nd the technical eciency of potato production and to estimate the impact of variety type and irrigation on technical eciency. A multistage random sampling procedure was employed to select 300 potato farmers from three districts of Nepal. The study used a stochastic frontier production function model to nd the production elasticity coecients of inputs, determinants of eciency, and technical eciency of potato farmers. Results showed that variety type and irrigation have a signicant positive impact on the technical eciency of potato production. Nepalese improved varieties adopter farmers were more ecient (73%) than Indian (66%) and local (59%) potato varieties. Likewise, Irrigated potato farming has higher eciency (71%) than rainfed potato (61%) farming. The mean technical eciency value of potato farmers was 69 per cent and farmers can increase it with better use of available resources. It is suggested that use of improved potato varieties and irrigation application along with proper amounts of inputs used help to improve technical eciency of potato farmers.


Introduction
Potato is a staple food of High hills whereas it is used as a major vegetable crop in the Terai and Mid hills of Nepal. Nepalese farmers have been cultivating potatoes for over 200 years and it is one of the important crops to address the problem of food insecurity because it has a great potential to grow yearround in the country. Potato production plays an important role in the economy of Nepal. It accounts for 42.46% in the total vegetable cropped area of Nepal providing economic bene ts as well as creating employment opportunities for the rural farmers. The area under this crop is 195173 ha with a production of 2881829 mt. The national average productivity of potato is 14.76 mt/ha (MoALD 2019).
The productivity of potato is far below as compared to neighbouring countries India and China 22.56 and 18.76 mt/ha respectively. In 2017, Nepal imported 290804 mtpotatoes with a value of $43063000. The import has been increased more than 6 times over 10 years of period (FAOSTAT 2018). Although the annual growth rate of potato productivity was 1.76 percent per annum in the last 17 years, the gap between potential yield and farm-level production is still very high (Timsina et al. 2019). The Lower level of production is associated with the poor adoption of agricultural technologies, ine cient use of resources such as land and fertilizer, and lack of research (Adhikari and Bjorndal 2012; Bhattarai et al. 2015). There are various technical, environmental, and socioeconomic factors contributing to low potato production in Nepal. To substitute the import of potato, it is necessary to increase production through improvements in potato production e ciency. To increase the e ciency of potato farmers, it is important to know the causes of the ine cient use of resources. Improving e ciency in production allows farmers to increase their output without additional inputs and changing production technologies resulting in increased productivity (Bravo-Uretra and Pinheiro 1997). In general, resources in the agricultural sector, especially in under-developed countries are being utilized ine ciently (Ahmad et al. 2006). Potato productivity and e ciency may be affected by various farm-speci c factors such as variety types, amount of fertilizer and seeds, labor use, irrigation condition, farm size, family size, credit accessibility to farmers, technical support, education level of household head, land type, land use pattern, etc. Technical e ciency is the capacity of a farm to produce an optimum quantity of output with the given level of inputs. The productivity of potatoes could be improved by increasing the production e ciency of smallholder farmers. To increase the productivity of smallholder farmers more e cient use of inputs is necessary.
Several studies have been conducted about potato productivity and technical ine ciency of potato production in developing countries. Amara et al. (1999) analyzed the technical e ciency among potato farmers and examined the farmers' attitude towards technological innovation. Wilson (1998)  reported that the mean technical e ciency of potato farmers was estimated at 65%. They found that technical e ciency was positively in uenced by the age of the farmer, education years, farming experience, frequency of extension services, and land size, whereas negatively in uenced by household size.
Study on technical e ciency of potato farmers in Nepal is very limited, whilst the majority of the research focused on adoption-related issues.A study conducted in Eastern Hill of Nepal revealed that the improved seed had a positive impact onvegetable production e ciency (Shrestha et al. 2015).Enhancing adoption of improved potato varieties could impact on farmer's income, household food, and nutritional security (Gairhe et al. 2017). Shrestha et al. (2015) found that farm-speci c factors such as seed types, credit access, and technical support signi cantly affected ine ciency in vegetable production. Furthermore, policies need to focus on innovating and adopting improved seed varieties, easy access to credit facilities, and technical support and backstopping to farmers. Improved variety is one of the important factors to increase the e ciency of potato farmers. In Nepal, farmers are cultivating Nepalese improved, Indian, and local potato varieties.Till date, Nepal Agricultural Research Council (NARC) has released eleven and registered ve potato varieties.These varieties have large yield potential and the adoption of these varieties can greatly enhance national potato production (Ka e and Shah 2012). Moreover, improved varieties have high yield potential and diffusion of these technologies can greatly enhance national potato production (Tufa et al. 2015). No studies have been conducted on the impact of Nepalese improved potato varieties on technical e ciency. Therefore, this study also helps to identify and compare the e ciency level of Nepalese improve and others (Indian and local) potato varieties.
Irrigation is one of the important factors to increase potato productivity. A regular water supply is necessary to gain a higher potato yield (Ierna et al. 2011;Levy et al. 2013). However, drought has an adverse effect on potato growth and productivity (Levy et al. 2013). Panta et al. (2019) in Dadeldhura district of Nepal found that only 13.3% of the potato land had irrigation facilities.. Likewise, a study conducted in the Terai region of Nepal found that lack of proper irrigation facilities was one of the important problems in potato farming ). In Nepal, technical e ciency of potato cultivation in irrigated and rainfed conditions is lacking. This study identi ed the e ciency level of both irrigated and rainfed potato farmers.
The primary objective of this study is to estimate the impact of Nepalese improved varieties and irrigation on the technical e ciency of potato production. Secondly, the paper also provides a detailed analysis of technical e ciency of potato production and yield gap due to technical ine ciency in Nepal.Thus, this study is important to policymakers as the information can be used to identify major interventions areas to improve productivity. Furthermore, identi cation and implementation of appropriate management practices to increase e ciency will result in increasing potato productivity among the potato farmers in Nepal.

Research Methodology
The data for this study was obtained from a survey of potato farmers from the Terai region of Nepal, which covered three districts: Jhapa from eastern, Bara from central, and Kailali from western Terai of the country. The Multistage random sampling procedure was employed for the selection of respondents. In the rst stage, three districts were selected based on the highest potato area from each three regions. After that, three pockets in each district were selected based on potato area and variety usedto capture the variations within the districts after the consultation withAgriculture Knowledge Centre and agricultural o cials of the local government. Lastly, 100 households from each district were selected using proportionate random sampling from each pocket. Therefore, a total of 300 households were selected for the study. A questionnaire was restructure according to the feedback from the pretesting. The households' survey was conducted from February to April 2018. The interview schedule questionnaire captured data on the amount of potato production and production-related socioeconomic variables. Information was collected on input-output variables such as labor hours, farm size, fertilizer dose, tillage hours, and seed quantity.Socio-demographic factors such as age, education, access to credit, training received, household size, migration status, variety types, and irrigation application. One focus group discussion was conducted in each pocket. The Collected information from three districts was entered in excel and data analysis was conducted by using software Stata (version 16.1). The research area is delineated in picture 1.

Descriptive statistics
Descriptive statistics was used to analyze the survey data using measures of dispersion such as percentage, frequency, and measures of central tendency such as mean, and standard deviation

Econometric model
The focus of this study was to nd out the impact of improved varieties on the technical e ciency of potato farmers across the Terai region of Nepal.There are two methods to determine technical e ciency as data envelopment analysis (DEA) and stochastic frontier method. The former is a nonparametric approachthat developed out of mathematical programming techniques while the later is a parametric approach that estimatestechnical e ciency within a stochastic production function model (Chakraborty et al. 2002;Coelli et al. 2005). The parametricapproach considersthe production functional form from a priori estimation of the data, while the non-parametric approach uses the data to determine the functional form. The major limitation of the non-parametric approach is that it assumes no sampling error and attributes all deviation from the production frontier to ine ciency (Diagne et al. 2013). In this study, thestochastic frontier analysis was used in preference to the DEA.

Stochastic production frontier model
The stochastic frontier regression model is a parametric analysis that has been commonly used to estimate technical ine ciency. The stochastic production function frontier shows the most e cient use of inputs to produce the maximum output. This study uses the method of estimating a stochastic frontier production function proposed by Aigner et al. (1977), and Meeusen and Van Den Broeck (1977). Kumbhakar et al. (1991) extended the stochastic frontier methodology by openly introducing the determinants of technical e ciency into the model. The stochastic frontier production function differs from the traditional production function in that it consists of two error terms. The rst error term accounts for technical e ciency and the second for factors such as measurement error in the output variable, the weather, and the combined effects of unobserved inputs. It is a homogeneous function that provides a scale factor enabling one to measure the return to scale and to interpret the elasticity coe cients with relative ease. It is also relatively easy to estimate because in the logarithmic form; it is linear and parsimonious (Beattie and Taylor 1985).

One-step Stochastic Production Frontier
In previous,two-step procedure was commonly used in the estimation of the stochastic production frontier. This approach estimates the observation-speci c ine ciency measure in the rst step, and then estimates the effect of the explanatory variables on the ine ciency measures in the second step. The two-step estimation procedure recognized as biased because the model estimated in the rst step is misspeci ed (Battese and Coelli 1995). Furthermore,Wang and Schmidt (2002) explained that if X (Input variables) and Z (Ine ciency variables) are correlated then the rst step of the two-step procedure is biassed. Even they are uncorrelated, ignoring the dependence of the ine ciency on Z will cause the rststep technical e ciency index to be undispersed, so that the results of second step estimations are likely to be biased downward.Due to the unsatisfactory statistical properties of the two-step estimation, the better approach of incorporating exogenous in uence on e ciency is the one-step procedure. Kumbhakar et al. (1991) and Reifschneider and Stevenson (1991) proposed one-step stochastic frontier in which the ine ciency effects (ui)expressed as an explicit function of the vector of rm-speci c variables and a random error.Therefore, in this study, allthe parameters of the stochastic frontier modeland ine ciency function were estimated together with a singlemaximum likelihood estimation (MLE) procedure.

Functional forms determination
Several functional forms have been developed to measure the relationship between input and output. The most common functional forms are Cobb-Douglas andtranscendental logarithmic (translog) function.The Cobb-Douglas has been widely used in many empirical studies particularly thoserelated to developing countries for farm e ciency analysis (Bravo-Ureta and Pinheiro 1997). Cobb-Douglas speci cation provides an adequate representation of agricultural production technology. In this study, we use an empirical Cobb-Douglas frontier production function model with double log form can be expressed as: Ln (yield) = ß 0 + ß 1 ln(Total labour in hours)+ ß 2 ln(Inorganic fertilizer)+ß 3 ln(Ploughing hours)+ ß 4 ln(Total Where, Ln is the natural logarithm, the dependent variable yield is the potato production per hectare (Kg/ha), ß 0 -ß 5 arethe parameters to be estimated. The inputs variable are totallabour hours required per hectare, inorganic fertilizer is the amount of Nitrogenous, Phosphatic, Potassic and other micronutrients per hectare (Kg/ha), ploughing constitutes total tillage hours required for one hectare of land, total seed is the potato seed rate per hectare (kg/ha), area cultivation is the area under potato cultivation (ha), Єi is the error term, equal to (V i -U i ), V i is a two-sided random error component beyond the control of the farmer and U i is a one-sided ine ciency component. In this study, the half-normal distribution is assumed for the asymmetric technical ine ciency parameter.

Estimation of technical e ciency
The farm speci c technical e ciency (TE i ) of the ith sample farmer was estimated by using the expectation of U i conditional on the random variable Єi

Summary statistics
The variables used in this study are presented in Table 1. For the stochastic production function variables, the average total potato output was 12.75 metric tons per hectare while the lowest was 1.2 metric tons per ha. The highest total potato production was 30 metric tons per ha. The productivity is lower than the national average productivity which was 14

Hypothesis testing
Before proceeding to the empirical analyses of technical e ciency and its determinants, a generalized likelihood ratio (LR) test was employed to determine which model is better. We used a LR test based on log-likelihood values of restricted and the unrestricted model. In this study, the LR test was performed to test three null hypotheses ( Table 2).The rst null hypothesis tested was the test for the existence of the ine ciency component of the composed error term. The null hypothesis was no ine ciency problem exists in potato farmers. This null hypothesis was rejected at one degree of freedom and 1% level of signi cance because LR-value (124.72) is greater than the critical value (5.41) (Annex 3).
The second null hypothesis tested was a test for appropriate functional form; Cobb-Douglas versus Translog production functional form. The calculated LR test value is equal to -100.09 and the critical value of chi2 at 15 degrees of freedom at 5% level of signi cance is 29.92, which is higher than the critical value (Annex 4). This implies that the Cobb-Douglas functional form was preferred to estimate the technical e ciency of the potato farmers.The third null hypothesis evaluated between half-normal and truncated normal distribution (Annex 4). The null hypothesis is accepted, therefore, we used half-normal distribution in the stochastic production frontier model.

Empirical results
Before the estimation of stochastic frontier production function model, explanatory variables and ine ciency variables selected for estimation were checked for the multicollinearity problem using variance In ation factor (VIF) (Annex 1&2). The value of VIF above 10 is considered as serious multicollinearity (Gujarati 2006), but in our result none of the variables VIF value exceed 2;average VIF value foundin case of explanatory variableswere 1.08 and 1.07 for ine ciency variables(Appendix 1 and 2). Note: *P < 0.1, **P < 0.05, ***P < 0.01 A Cobb-Douglas production function was estimated using half normal stochastic production methods. All input variables and dependent variables are log-transformed, the coe cient represents elasticity. The value of gamma was 0.79, which is the ratio of the variance of the ine ciency component to the total error term. It indicates that about 79% variation in the output of potato farmers was due to technical e ciencies. Additionally, the value sum of the estimated parameters associated with all the inputs is 0.82 which indicates decreasing return to scale. This implies that a 1% increase in these all production input variables leads to 0.81% increase in potato production.
We found that potato area; seed quantity and labour use are signi cant and have a positive and signi cant effect on potato production. The coe cient of potato farm size is signi cant and positive at the 1% level of signi cance. The result implies that a 1% increase in potato area increases the value of potato output by 0.13%.Seed quantity is signi cant at 1% level of signi cance. The ndings indicate that 1% increase in seed quantity increases the potato production by 0.52%. Similarly, labour quantity is positive and signi cant at the 10% level of signi cance, indicating that a 1% increase in the labour quantity increases the potato output by 0.17%.
The ine ciency factors presented in Table 3 relate to the farmers' socio-economic characters. The variables include seed source, training received related to potato farming, migration, education of household head, use of Nepalese improved potato varieties and availability of irrigation.The dummy variable use of Nepalese improved potato varieties had a negative effect on technical ine ciency and signi cant at 1% level of signi cance. Likewise, the coe cient of irrigation availability had a negativeand signi cant at 1% level of signi cance. This means that when other factors are held constant, farmers who irrigated at least one time to potato farming are more technically e cient than others who didn't apply irrigation. Table 4 shows the summary and distribution of technical e ciency of potato farmers in the Terai region of Nepal. We found a mean technical e ciency score of about 0.69 with a standard deviation of 0.16. The TE scores for potato farmers in the sample ranged from 0.11 to 0.93. The average technical e ciency for surveyed farmers was 69%. A higher percentage of farmers (57%) have a TE value of more than 70%. Nearly, about a quarter of the farmers hada TE value of less than 60%.  Table 5 shows the distribution of technical e ciency of potato farmers by variety types and irrigation conditions. Farmers were cultivating three types of varieties i.e. Nepalese improved (NARC released and registered), Indian and local. The result indicates that Nepalese improved varieties adopter farmers are more e cient (73%) than Indian (66%) and local (59%) potato varieties. Likewise, in terms of irrigation condition, the technical e ciency of irrigated potato farmers was 71 per cent while in rainfed conditionswas 61 percent. 4.5 Estimates of potato yield gap due to ine ciency Yield gap is de ned as the difference between technically full e cient production and actual production in farmers' elds. Therefore, the yield gap is the amount which represents a lower yield due to technical ine ciency. From the stochastic model, TE of the ith household is estimated to be:

Level of Technical E ciency of Potato Farmers
WhereTE i is the technical e ciency of the ith sample household in potato production; Y i = Actual/observed yield of the ith sample household in potato production Y i * = Frontier/ potential output of the ith sample household in potato production Based on the above equation, we estimated the potential yield of potato for each sample household in potato production. The result is presented in Table 6. The computed mean potential yield was17755 kg/ha. It was noticed that the mean yield gap was 5,002 kg/ha at 69% mean technical e ciency with actual average output and the potential outputs were 12,753 kg/ha and 17,755 kg/ha respectively.This indicates that surveyed households were producing 5,002 kg/ha lower potato production than their potential yield.

Discussion
The result found production variables such as farm size, the seed used and labour used contributed positively towards technical e ciency, whereas in the e ciency model, variety type and irrigation are major factors that determine technical e ciency.
The stochastic frontier model estimated potato land area has a higher e ciency level implies that potato productivity could be increased by further expanding the cultivated area or shifting other lands for potato farming. Larger farmers have much greater access to public services, credit and other inputs (Sharif and Dar 1996) wheareas, farmers with small land size cultivating more intensively and inadequate allocation of inputs (Khanal et al. 2018). Prasanna and Lakmali (2016) and Tiruneh et. al. (2017) also found a positive association between potato farm size and technical e ciency. Another signi cant variable is seed rate that farmers are using less seed rate than recommended. The higher rate of seed quantity increases the plant population and increases yield (Ahmad et. al. 2006). A study conducted by Bajracharya & Sapkota (2017) also reported that farmers were unaware of the recommended rate of seed rate and using a lower rate of seed in Baglung district of Nepal. However, the result is contradicted with Wassihun et al. (2019), they mentioned that seed rate with higher than recommended may result in low potato production due to high competition of nutrients. Likewise, Potato farming is the labour-intensive and farmers rely heavily on manual labour. The higher number of labour is required for better weeding, fertilizer and pesticide application. Similarly, more labouris also required for land preparation, planting, and harvesting processes. Therefore, the higher number of labour used households not only performed their cultural activities very well but also increased their level of technical e ciency. The result is consistent with Dubeet. al. (2018) in Ethiopia found that amount of seed, area of the plot and labour were positive and signi cant input variables in potato production.
Farmers who adopted NARC released and registered potato varieties were more e cient than farmers who adopted Indian and local potato varieties. Moreover, the way potato farmers increase their productivity depends on the type of varieties they used for potato cultivation. In Nepal, lack of improved quality seed was the most important problem in potato production (

Conclusion
This paper estimates the impact of variety type and irrigation on the e ciency of potato production.
Moreover, it also determines the technical e ciency level of potato farmers and its determinants in Nepal. The empirical analysis was carried out by employing half normal stochastic frontier analysis. Results showed that among the ve main factors of production (land, labour, fertilizer, tillage hours and seeds) used, potato area, labour and seed were the major factors associated with potato production. The signi cant determinants of technical ine ciency variables include the use of Nepalese improved varieties and irrigation availability. Use of NARC released improved varietieswas also positively signi cant to the technical e ciency of potato farmers. Farmers who adopted NARC released potato varieties (Janakdev, Cardinal, Khumal Red, etc.) havea higher level of technical e ciency than those farmers who adopted Indian (Arun Gold, Kanpure, C-40) and local varieties (Tharualu). Farmers who applied irrigation in potato farming were more technically e cient than others. The nding also indicates that Nepalese improved varieties adopted farms are more technically e cient than Indian and local varieties user farms.
The technical e ciency of potato farmers could be increased by 31% onaverage through better use of labour, seed and land. For better improvement of e ciency factors, farmers should use Nepalese improved varieties instead of Indian and local potato varieties and there should be an expansion of irrigation facilities for better potato production in the Terai region of Nepal.

Declarations
Ethics approval and consent to participate The study obtained permission from participants to involve in the study and received an ethical clearance

Consent for publication
It is not applicable for this article Authors' contribution SPA designed and collected the data and drafted paper. YNG, KPT and SG edited and provided feedback to improve the paper. All authors read and approved the nal manuscript.

Funding
The research was unded by Nepal Agricultural Research Council.

Availability of data and materials
The datasets used in this article are available from the corresponding author on request.