Analysis of the technical efficiency of barley production in North Shewa Zone of Amhara regional state, Ethiopia

Abstract Inefficiency in barley production is among the challenges to agricultural transformation in Ethiopia. North Shewa zone of Amhara regional state is not exception in this regard. As such addressing inefficiency is among the crucial efforts for agricultural transformation. The objective of the current study was to analyze the technical efficiency of barley production in north Shewa zone of Amhara regional state, Ethiopia. For this purpose 385 farm households were randomly selected from four purposively selected districts in the zone. The one-step maximum likelihood estimation result of the Cobb-Douglas production function result reveals that seed application, DAP fertilizer application, UREA fertilizer application, land under barley production, labor and oxen ownership have a positive and significant effect on barley production. The predicted average technical efficiency score is found to be 85.06 percent implying that given existing input mix and technology it is possible to increase the production of barley on average by 14.94%. The study found that education, non/off farm income, access to market information, access to extension service and tropical livestock unit are found to have a positive and significant effect on the technical efficiency of barley production while distance from the market and marital status (divorced) have a negative significant effect on technical efficiency of barley production. The result suggests that the government should encourage farmers vocational trainings and participation in off/non-farm activities, improve access to market information, access to extension services, livestock ownership and access to market to improve barley production efficiency.


PUBLIC INTEREST STATEMENT
Agriculture is the backbone of the Ethiopian society and the national economy at large. The study analyzed the technical efficiency of Barley Production in North Shewa Zone of Amhara Regional State, Ethiopia, using a one-step maximum livelihood approach on a stochastic frontier model. The result revealed that education, non/off farm income, access to market information, access to extension service and tropical livestock unit have a positive and significant effect on the technical efficiency of barley production while distance from the market and marital status have a negative significant effect. Thus, stakeholders should take this into account in their effort to improve barley production.

Introduction
Evidences show that agricultural aector is the backbone of the Ethiopian society and the national economy at large. The sector accounts for almost 50% of the nation's GDP and over 80% of its total export earnings. The sector also generates over 80% of employment opportunities for country's productive work force and hence, it is a crucial sector for inclusive economic growth and development. It is also fundamental for addressing issues related to poverty and food insecurity (https://www.cultivaid.org/wpcontent/uploads/2020/08/North- Shewa-Development-program-delegation-booklet-.pdf, accessed 5/18/ 2021). As such agricultural transformation is central to ensure both the local and national development goal of the country.
Like other parts of the country, the vast majority of the population in North Shewa zone also engaged in agriculture as a major source of livelihood. Barley is among the top four cereal crops produced in Ethiopia and the country has a strong potential in terms of the production of this crop. For instance, the total barley production during the 2020 production year was 2.35 million metric ton. Barley production in Ethiopia have shown moderate improvement over the last ten production years despite a decreasing growth trend. For instance, the growth rate of barley is found to be 8.27%, 4.55% and 2.17% during the 2018, 2019 and 2020 production years respectively (https: // www.indexmundi.com/agriculture/?country=et&commodity=barley&graph=production, 5/18/2021).
Despite the huge potential the country has, Ethiopian barley cultivators achieve low yields. Amhara regional state in general and North Shewa zone are not exception in this regard. The production is also not sufficient to meet the rapidly increasing demand for this crop. The flourishing investment particularly in alcoholic beverage factories has contributed towards the rapid increase in demand for barley. To meet the increasing demand for this crop, barley production improvement through the introduction of technologies and improved varieties in high potential areas is quite crucial.
There have been efforts to improve the production and productivity of this crops in the zone through adoption of new agricultural technologies. However, the effort to advance barley production and productivity is not successful. This might be due to inefficient utilization of existing input and available technologies by barley producing farm households. It is believed that ensuring efficient utilization of existing resource is assumed to be cost effective than introducing new technologies. According to Asefa (2011) if existing inputs and technologies are not efficiently utilized, trying to introduce new technologies will not be cost-effective. As such, it very crucial to measure the technical efficiency and its determinants in the production of Barley in the study area.

Review of related literature
Efficiency is a relative concept. It is measured by comparing the actual ratio of output to inputs with the optimal ratio of output and inputs (Fried et al., 2008). The overall efficiency/economic efficiency is classified into technical efficiency and allocative efficiency. Allocative efficiency/price efficiency is the measure of the success in the selection of the input set among the optimal input set (Tutulmaz, 2014). It is the ability to choose cost minimizing mix of inputs at a given relative input price and available technology (Onour & Abdalla, 2011). On the other hand, a production is defined as technical efficient if a producer have to decrease one of the output or increase one of the inputs in order to increase output or if producers have to increase the inputs or decrease one of the outputs in order to decrease its input (Tutulmaz, 2014).
The two broad approaches to measure the technical efficiency of decision making units (DMUs) are the parametric and the non-parametric methods (Andor & Hesse, 2011). The non-parametric methods include the data envelopment analysis (DEA) and the free disposal hull (FDH). These methods are used to measure technical (technological) efficiency of a DUMs. The technical efficiency of a DUMs looks at the relationship between resource inputs or outputs. On the other hand, the parametric methods of efficiency measurement include the stochastic frontier approach (SFA), thick frontier approach (TFA) and distribution free approach (DFA). Description of these two approaches is presented here under.
The parametric method deals with both an optimal choice of the level and structure of inputs and outputs so as to minimize cost or maximize profit (Vincova, 2005). The main advantage of the parametric method is it allows a test of hypothesis concerning the goodness of fit of the model. However, the method requires the specification of a particular functional form and as such it maybe restrictive in most cases. On the other hand, the non-parametric is advantageous in that it does not require the specification of a particular functional form of the technology (Ajibefun, 2008). In this method is it is not possible to estimate parameters for the model. As a result, it is impossible to test hypothesis concerning the performance of the model (Ajibefun, 2008). The common parametric approach is the SFA while that of non-parametric is the DEA (Jarzebowski, 2013).
DEA is a linear programming method of measuring the efficiency of DMUs. The method was first introduced by Charnes, Cooper and Rhodes (CCR; Ray, 2004). The major problem with the CCR model of DEA is it assumes a constant returns to scale (CRS) of production which is less realistic. On the other hand since CCR assumes CRS it is impossible to determine technical efficiency score devoid of scale efficiency/inefficiency. To address this problem of the Charnes, Cooper and Rhodes (CCR), Banker, Charnes, Cooper (1984) and Ray (2004), extended the CCR model to BCC model to account for variables returns to scale (VRS; Andor & Hesse, 2011). BCC model can separately estimate pure technical efficiency and scale efficiency on the assumption that a VRS in production technology exist.
The SFA was first introduced by, Aigner et al. (1977), and Meeusen and van Den Broeck (1977) followed by Coelli et al. (2005). In this approach efficiency is predicted from a production function. It is measured as the difference between the predicted output and observed output (Erkoc, 2012). The SFA considers the production frontier as a random shock. It allows for deviation from the frontier to represent both inefficiency and an inevitable statistical noise. That is, it recognizes that random shocks beyond the control of a producer may affect the production of output (Constantin et al., 2009). Thus, the error term in the SFA has two components and both error terms are assumed to be independently and identically distributed with mean zero and constant variance (Erkoc, 2012).
The main benefits of DEA is, it does not require any assumption concerning the shape of the frontier and it allows for multiple inputs and outputs (De Witte & Marques, 2010). Nonetheless, it is sensitive to outliers and data uncertainty, although some authors have proposed improvements to tackle this issue (De Witte & Marques, 2010). On the other hand, the SFA, although it can model multiple output technologies, doing so is complicated, requires stochastic multiple output distance functions, and raises problems for outputs that take zero values. A potential advantage of the SFA over DEA is that random variations in catch can be accommodated, so that the measure is more consistent with the potential harvest under "normal" working conditions (Morrison et al., 2000). The SFA has advantages that it can consider statistical noises and outliers compared with the DEA (Honma & Hu, 2018).
Empirical studies have been conducted to measure the technical efficiency of barley production and determine the constraints to barley production efficiency across boundaries using the above discussed approaches. Studies undertaken to address the subject under consideration include (Agegnehu et al., 2006;Bati & Haji, 2014;Cholo et al., 2020;Shahraki & Aliahmadi, 2021;Shate et al., 2021;Tirfe & Kim, 2016;Tiruneh & Geta, 2016;Wollie, 2018;Wollie et al., 2018;Yadeta & Guta, (2019). The aforementioned studies on this subject revealed that barley producing farm households across boundaries are not efficient. For instance, Wollie, (2018) estimated a mean technical efficiency score of 70.9% for barley producing households in Meket District, Ethiopia, Yadeta and Guta (2019) predicted a mean technical efficiency score of 71% for barley producing households in in Tiyo district (Ethiopia), Cholo et al. (2020) estimated a technical efficiency score of 72% for barley producing households in Gamo Highlands of Ethiopia, and Shahraki & Aliahmadi, (2021) assessed the efficiency of barley producing farm households in Iran.
The limited studies undertaken on the subject (Agegnehu et al., 2006;Cholo et al., 2020;Jia et al., 2017;Tiruneh & Geta, 2016;Wollie, 2018;Yadeta & Guta, (2019) also tried to examine the factors affecting technical efficiency score of barley producing households across boundaries. Despite the effort to generate evidence on the factors affecting the technical of barley production across boundaries, the aforementioned studies produced inconsistent results. For instance, Wollie (2018) have found a negative effect of seed on barley production efficiency while Cholo et al. (2020) have found a positive effect of seed on barley production efficiency. On the other hand, (Cholo et al., 2020) have found a negative and statistically significant effect of literacy on barley production efficiency while Tiruneh & Geta, (2016) and (Yadeta & Guta, ((2019) have found a positive and statistically significant effect of education of technical efficiency of barley production.
The inconsistency in previous studies might be due to a different covariates considered in the stochastic frontier model and the inefficiency model, the different measurement techniques employed to measure the covariates included in the two models and variation in estimation approaches (the one-step and two-step estimation of stochastic frontier models). Some of previous literature on the subject employed a two-step estimation approach (Yadeta & Guta, (2019) whereby in the first step they estimated a stochastic frontier model to predict technical efficiency score and in the second step they estimated the inefficiency model. It is evident that estimation results from the two-step procedures are biased, and there is strong evidence showing that the bias can be very severe (Wang & Schmidt, 2002). The one-step estimation of stochastic frontier models argued to appropriate and is claimed to produce a less biased estimation output.
As such the findings of those studies are not generalizable and it is difficult to replicate the findings to the case of barley producing households in North Shewa zone of Amhara regional state, Ethiopia Using the findings from the existing literature to guide policy decision is misleading given the inconsistency in previous literature. This necessitates further investigation on the subject in the study area. That is, analyzing the technical efficiency of barley production in North Shewa zone of Amhara regional state, Ethiopia is crucial to guide policy decisions. The objective of the current study is to analyze the technical efficiency of barley producing households in North Shewa zone of Amhara regional state, Ethiopia. Specifically the current study tried to predict the technical efficiency of barley producing households and examine the determinant of technical efficiency using a single step procedure estimation technique. For this purpose a stochastic frontier model is employed.

Methodology
The objective of the current study were to analyze the technical efficiency of barley production in North Shewa zone of Amhara regional state, Ethiopia, during the 2020 production year. The section that follows presented discussion on the research methodology employed to achieve the aforementioned objective.

Description of the study area
Ethiopia is administratively divided into regional states and chartered cities. The regional states are again divided into zones which are divided into Woreda (districts) and these are divided into kebele (wards). North Shewa is one of the 10 Zones in the Amhara Regional state. The Zone of North Shewa in Amhara regional state is bordered on the south and the west by the Oromia regional state, on the north by South Wollo zone and on the east by the Afar Regional state. The population of the zone is now estimated to reach 3,500,000; along with the entire population of Ethiopia it has more than doubled since 1994.

Data type and source
Primary data on socio-economic, institutional, demographic and production information is collected from 385 sample respondents belonging to four purposively selected districts of North Shewa zone of Amhara regional state, Ethiopia. Originally 400 questionnaire were distributed to sample farm households. However, from the total 396 questionnaire collected 385 is found to be valid for analysis. The demographic variables, socio-economic variables and production variables are collected for the 2020 production year.

Sample size and sampling technique
As it is indicated in the introduction section, the objective of the current study were to analyze to technical efficiency of barley production in North Shewa zone of Amhara regional state, Ethiopia. To select appropriate sample for this study a multistage sampling technique were employed. In the first stage four districts (Minjar Shenkor, Angolela Tera, Moretna Jiru and Menz Gera) in the zone were purposively selected taking into consideration their barley production potential. In the second stage 30 Kebeles were randomly selected and in the last stage followingVogel (1986) and Malhotra (2012) 400 households were selected from the 30 Kebeles. From the total 400 questionnaire distributed to farm households 385 questionnaire were found to be valid for analysis.

Analytical framework
The two most important approaches to estimate efficiency/inefficiency level are the stochastic frontier production function (parametric) and the Data Envelopment Analysis (DEA) or nonparametric approach. DEA has the power of accommodating multiple outputs and inputs in technical efficiency analysis. Nonetheless, DEA fails to take into consideration the possible impact of random shock like measurement error and other noise in the data Tim J Coelli (1995). On the other hand, the stochastic frontier does not accommodate multiple inputs and outputs and is more likely to be influenced by misspecification issues. However, the fact that the latter incorporates stochastic component into a model increased its applicability in the analysis of technical efficiency of agricultural productions. Thus, for this study the stochastic frontier production function was employed and was adapted from (Addai & Owusu, 2014;Salau et al., 2012).

The empirical stochastic frontier production function model
The empirical stochastic frontier model used the Cobb-Douglas specification for the analysis of the technical efficiency of barley farms in North Shewa zone of Amhara regional state. The Cobb-Douglas functional form was frequently employed in related efficiency studies (Danso-Abbeam et al., 2012;Mohammed, 2012). In the current study a log linear Cobb-Douglas production function were specified as given by equation (1):

Cobb-Douglas production functions specification
Where; β 0 , β 1 , β 2 , β 3 , β 4 , β 5 , and β 6 are parameter estimates, V is the disturbance term and assumed to be independently and identically distributed as N 0; σ v ð Þ and is intended to capture events beyond the control of farmers. On the other hand, U is a non-negative random variable, independently and identically distributed as N 0; σ u ð Þ intended to capture the technical inefficiency effects in the production of barley. Table 1 presented description of the variables in the log-linear Cobb-Douglas production function.
The household level efficiency score is measured as the ratio of observed output to potential output (Timothy J T. J. Coelli et al., 2005). That is; In equation (2), TE i stands for the technical efficiency score of the i th household, Y i stands for the actual level of output and F X i ; β ð Þexp stands for the potential level of output. The value of TE i is limited within the range 0 to 1(T. Tim J Coelli, 1995; Timothy J T. J. Coelli et al., 2005), with 1 showing full technical efficiency or production along the frontier and 0 showing full technical inefficiency.

Factors affecting technical efficiency
To examine the factors affecting the household level inefficiency score, the following model is established.
Where U i refers to the technical inefficiency of households, δ i`s is the parameter to be estimated, W i`s refers to socio-economic characteristics that affect technical inefficiency which include Sex, Age, Education, Marital status, Dependency ratio, Family size, Off/non-farm income, Farm experience, Membership to Cooperative, Extension service, Total Land size, improved seed, access to market information, distance from the market, access to extension service, access to credit and livestock holding and is the random/error term. Table 2 description of the variables incorporated in the inefficiency model.

Result and discussion
The objective of the current study is to analyze the technical efficiency of barley production in North Shewa zone of Amhara regional state. For this purpose a stochastic frontier model is applied on a data collected from 385 sample households in four selected districts of the zone. The section that follows illustrates discussion of the results from the one-step maximum likelihood estimation. The discussion of the result starts with the eta Endogeneity Test followed by the inefficiency model estimation (estimation of the Cobb-Douglas production function and the determinants of efficiency) and predicted technical efficiency scores.

Endogeneity test (eta Endogeneity test)
The current study employed stochastic frontier model with a one-step maximum likelihood estimation technique. It is claimed that the consistency of the estimation result depends on exogeneity of the explanatory variables (Amsler et al., 2016). For this reason addressing the endogeneity problem if any is very crucial. To check for the possible endogeneity problem the sfkk command which provide post estimation routines, such as predicting the efficiency, testing the endogeneity, and documenting the results is used (Karakaplan, 2017). In the current study endogeneity is examined for the variables DAP fertilizer and UREA fertilizer. The result presented in Table 3Table 4 revealed that the eta endogeneity test result fail to reject the null hypothesis, which means that a correction for endogeneity in the model is not necessary.

Barley production efficiency and its determinants
As it is clearly indicated in the introduction section of this article barley production has a very significant socio-economic benefit for the locality under study and the country at large in terms of ensuring inclusive economic growth, reduced poverty and food insecurity. Measuring the technical efficiency of barley production and examining the determinants of its production efficiency is quite crucial in the effort towards improving the above-mentioned socio economic benefits of this crop. The technical efficiency and determinants of technical efficiency of barley production is evaluated using a single step maximum likelihood estimation technique.
The one-step maximum likelihood estimation result from the Cobb-Douglas production function reveals that the variables seed application, land size under cultivation, fertilizer application, labor and oxen power ownership in the production process have a positive and significant effect on barley yield. All the factors included in the Cobb-Douglas production function are found to significant at one percent level of significance. The implication of this finding is that those list of factors are which are seed application, land size under cultivation, fertilizer application, labor and Where 0 = Perfect production inefficiency and 1 = Perfect production efficiency. Source: Authors computation based on survey data, 2020. oxen power ownership very critical in the efforts to improve barley production in the North Shewa zone of Amhara regional state, Ethiopia.
The results from the inefficiency model indicate that household head level of education have a positive and statistically significant effect on barley production efficiency at one percent level of significance. That is, farm households with educated household head tend to increase their resources use efficiency compared those with illiterate household head. This is consistent with the claim that education opens the mind of the farmer to new knowledge and information regarding better methods of farming. Educated farmers are also believed to be less resistant to new production technologies and techniques. The finding is consistent with (Tiruneh & Geta, 2016;Wollie, 2018;Yadeta & Guta, (2019). Non/off farm income is also found to have a positive and statistically significant effect on the technical efficiency of barley production at five percent level of significance. This might be due to the fact that non/off farm income improves farm households' capacity to access farm technologies and improved varieties.
Likewise, access to market information and access to extension service are also found to have a positive and statistically significant effect on technical efficiency of barley production in the study area. It is expected that extension agents provides farmers with new production, new ideas developed by agricultural research experts, improved crop varieties, better livestock control, improved water management, and the control of weeds, pests or plant diseases. Farm households with better access to these service are expected to improve the level of technical efficiency in barley production. The result is consistent with the findings of (Tiruneh & Geta, 2016) and (Yadeta & Guta, (2019). The finding on the variable access to market information might be due to the fact that the market information can help farmers identify lower input costs and optimized agricultural technologies use. It is believed that better access farm market information help the farm households benefit from opportunities in the supply chain relationships.
The result show that tropical livestock unit have a positive and statistically significant effect on technical efficiency of barley production in the study area. This implies that farm household with better livestock possession are efficient compared with those with limited livestock possession. Such a result might be due to the fact that farm households with better livestock possession have better relative capability to access farm technologies. On the other hand, distance from the market and marital status (divorced) have a negative and significant effect on technical efficiency of barley production. Longer distance from the market makes it relatively difficult for the farmers to production inputs and technologies. The above finding on distance from a market is consistent with (Cholo et al., 2020).  Figure 1 and Table 5 presented the frequency distribution of barley producing farm households considered in this study. From the figure and

Conclusion and policy implications
Evidences shows that Inefficiency of resource allocation is among the critical constraint in the effort to achieve the maximum possible barley production. As such efforts to ensure agricultural transformation in general and improved barley production and productivity in particular should aim at addressing the inefficiency of resource allocation in the locality under study. For this purpose it is crucial to analyze the technical efficiency of barley production. Studies have been undertaken to analyze the technical efficiency of farm households producing the aforementioned agricultural product (Bati & Haji, 2014;Cholo et al., 2020;Jia et al., 2017;Tiruneh & Geta, 2016;Wollie, 2018;Wollie et al., 2018;Yadeta & Guta, (2019).The aforementioned studies on the subject produced inconsistent result mainly due to a different covariates included in the models and the difference in the measurement techniques of the variables of interest. These proves the need for further investigation on the subject in North Shewa zone of Amhara regional state, Ethiopia. The current study aimed at analyzing the technical efficiency of barley production in North Shewa zone of Amhara regional state, Ethiopia using a one-step procedure maximum likelihood estimation approach on a data collected from 385 sample households.
The study result revealed that land size under cultivation, seed application, fertilizer application, labor and oxen employed have a positive and significant effect on barley yield. The study also found that education, non/off farm income, access to market information, access to extension service and tropical livestock unit are found to have a positive and significant effect on the technical efficiency of barley production while distance from the market and marital status (divorced) have a negative significant effect on technical efficiency of barley production. Therefore in the effort to improve the technical efficiency of barley production the government should encourage farmers vocational trainings and adult education and improve farm households participation in off/non-farm economic activities, improve access to market information using alternative local medias conferences and campaigns, ensuring better access to extension services, improving livestock ownership by linking farmers with local credit institutions and providing market through introducing local/village level to improve barley production efficiency.

Funding
This work was supported by the Debre Berhan University;

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

correction
This article has been republished with minor changes. These changes do not impact the academic content of the article.