Comparative Analysis of technical efficiency of wheat production in row planting and broadcasting methods: Empirical evidence from southern Ethiopia

A Cobb–Douglas stochastic production frontier was used to analyze the technical efficiency of wheat producers under row planting and broadcasting methods in Hadiya zone, southern Ethiopia. The estimated results of the Cobb–Douglas frontier model show that the mean technical efficiency was 83.4% and 57.8% under row planting and broadcasting, respectively. Approximately 646.882 kg/ha under row planting and 1393.038 kg/ha under broadcasting of wheat output were lost due to inefficiency. This reveals that under the existing practices there is a room to increase wheat yield more under broadcasting (42.2%) than row planting (16.6%) following the best-practice farms in the study area. The SPF model indicates that NPS, urea, labour and seed are significant determinants of wheat production level in both methods. The estimated SPF model together with the inefficiency parameters show that education, age, fertility status of the plot, family size, land fragmentation and extension contact were the main factors that had a significant influence on technical inefficiency of wheat farmers. Hence, emphasis should be given to improving the efficiency level of those less efficient farmers by adopting the practices of relatively efficient farmers in the area.


Introduction
Ethiopia the second most populous country in Africa and more than 70% of the population is still employed in the agricultural sector, but services have surpassed agriculture as the principal source of GDP. Currently, agriculture is contributes over 35.8% to the national GDP, almost 90% of export and 72.7% of employment (CIA 2018).
The agricultural sector is characterized by low productivity due to technical and socioeconomic factors. Generally, farmers with the same resources produce different per hectare outputs, because of management inefficiency inputs, limited use of modern agricultural technologies, obsolete farming techniques, poor complementary services such as extension, credit, marketing, and infrastructure, as well as poor and biased agricultural policies in developing countries like Ethiopia (FAO and WFP 2012).
Cereal production constitutes the largest sub-sector in the Ethiopian economy. It accounts for roughly 60% of rural employment, about 73% of the total cultivated land, and more than 60% of the total caloric intake of the country's population (Brasesco et al. 2019). Yield of cereals has been consistently well below world average, indicating poor productivity of the crops in the country. According to the latest World Development Indicators (World Bank Group 2020), the average cereal yield for the world was 3.574 t per hectare while, the average cereal yield in Ethiopia was limited to 2.538 t per hectare in 2017.
In sub-Saharan Africa, next to South Africa, Ethiopia stands in second in terms of total wheat area coverage and the amount produced (Hei, Shimelis, and Laing 2017). The highlands of the country, mainly Oromia, Amhara, Southern Nations Nationalities and Peoples' Region (SNNPR) and Tigray regions are the main wheat growing areas. Except for a few governments owned large-scale (state) farms and commercial farms of the country, nearly all small-scale farmers practise rain-fed cultivation to produce wheat (Demeke and Di Marcantonio 2013). Wheat is one of the main cereals cultivated in Ethiopia as it provides 14% of the total caloric intake, ranking as the second most important food behind maize (Brasesco et al. 2019). It is also a valuable food security crop in various parts of Ethiopia, and many farmers in the wheat belt use the crop as a source of family income (Kalsa 2019).
Wheat, teff, maize, sorghum and barely are the major cereals that occupied almost 81.46% of the total grain crop area in 2019/2020 cropping year. In the same production year, 1.79 million hectares of land were covered by wheat with a yield of 2.97 t/ha (CSA 2020). In SNNP Region, the total area covered by wheat was 0.13 million hectare by 0.62 million private peasant holders; and the total production in tonnes in the same year was 3.29 million, and its average productivity was 2.58 t/ha (CSA 2018). The total production of wheat in Hadiya zone for the year 2016/2017 was 0.11 million tonnes produced by 0.12 million private peasant holders who were engaged in wheat cultivation on 0.36 hectare. The average productivity was registered as 2.87 t/ha (CSA 2017).
Production of wheat has significantly increased over the past years. However, previous studies show that wheat farmers in Ethiopia produce on average 2.5 t/ha, which is well below the experimental yield of above 5 t/ ha (MOA 2010, 2011, 2012cited in Gebreselassie, Haile, and Kalkuhl 2017. As a result of this, the country remains a net importer of wheat and experienced a huge gap between production (4.5 million tonnes) and has resulted in import dependence. For instance, in 2016, the Ethiopian Grain Trade Enterprise imported 750 thousand tonnes from Russia and Argentina and 300 thousand tonnes through food aid, resulting in 1.05 million tonnes of imported wheat (Brasesco et al. 2019).
Agricultural productivity can be improved through research and by applying improved agricultural technologies. One of the technologies in crop production introduced in the recent years is row sowing. Compared to broadcasting, it gives better yields as it allows better weeding and for better branching out and nutrient uptake of the plants and diminishes competition between seedlings (Amare 2018). The selection of a suitable sowing method plays an important role in the placement of seed at proper depth, which ensures better emergence and subsequent crop growth. The most common wheat sowing methods in Ethiopia is broadcasting (a simple throwing of seeds across the ground) or sowing seeds without any distinct arrangement with a high seed rate and uneven distribution. According to the Ethiopian Ministry of Agriculture, farm level productivity is 2.1 t/ha using traditional broadcasting while potential yield stands at 2.45 t/ha (MoA 2012).
Ethiopia has ample potential for wheat production; however, this potential has not been fully tapped yet. For example, studies by Tesfaye et al. (2018), Asfaw, Geta, and Mitiku (2019) and Abate (2018) indicated that shortage of improved varieties, producers' dependence on local seeds, high fertilizer and seed costs, poor agronomic practices, weeds, pests and diseases, and little research support to increase yields and climatic change are among major constraints hindering wheat production in Ethiopia. Empirical studies show that yields are very responsive to row planting for wheat production. Tolesa et al. (2014) reported average yield of 2.80t/ha (19.7%) in the highland areas using row planting which is above national average yield of 2.45t/ha in the country. The research systems together with other stakeholders have played a major role in delivering improved technologies for increasing productivity in the country (Biftu et al. 2016). In spite of these efforts, productivity is below the estimated potential. One major factor contributing to low productivity in the country is the low adoption rate of improved technologies (Beshir et al. 2012;Ahmed, Lemma, and Endrias 2014). Among these is the low adoption of row planting despite its ability to contribute to high yields (Vandercasteelen et al. 2013).
Agricultural extension activities have been concerned with the promotion, adoption and scaling up of wheat row planting practices; and adoption of the practice is seen as the factor for wheat yield enhancement in the country. As a result, manual planting of wheat in row has become one of the agronomic practices of smallholder farmers in the country. The conventional planting method, that is broadcasting seed by hand at high seed rates, reduce yield because uneven distribution of the seeds makes hand weeding and hoeing difficult, and plant competition with weeds lowers wheat growth and tillering. This causes wheat yield reduction. However, row planting with proper distance between rows and plant density allows for sufficient aeration, moisture, sunlight and nutrient availability leading to proper root system development Tolesa et al. (2014).
For most developing countries, enhancing the total production and productivity is not an option; rather it is a necessity and the first concern in their policies. The measurement of efficiency has remained an area of important research, especially in developing countries, where resources are scanty and opportunities for developing by inventing or adopting better technologies are dwindling (Wassie 2014). There have been various empirical studies conducted to measure technical efficiency of wheat producers in Ethiopia. But, none of them conducted their study on technical efficiency of wheat production under row planting and broadcasting methods. To the best of the author's knowledge and belief, there no similar studies have been undertaken in the study area. Moreover, the question of how technically efficient Hadiya zone wheat producers are under broadcasting and row planting methods, what factors can significantly affect their efficiency, and the yield gap due to inefficiency in the study area have not yet been answered. This study therefore measures and compares farm level efficiency of wheat production using row planting and broadcasting methods, yield gap due inefficiency and respective factors affecting their efficiency in order to enable farmers to apply more efficient sowing methods for wheat production.

Research methodology
Description of the study area Hadiya zone is one of the administrative zones found in Southern Nations Nationalities and Peoples Regional State of Ethiopia. The administrative centre of Hadiya zone is Hosanna town, which is located 232 km southwest of Addis Ababa. The zone is bordered on the south by Kembata Tembaro, on the southwest by the Dawro zone, on the west by the Omo River which separates it from Oromia Region and the Yem special woreda, on the north by Gurage, on the northeast by Silte, and on the east by the Alaba zone. The altitude of the zone ranges from 501 to 3000 m.a.s.l with the mean annual temperature ranging from 10.54°C to 22.54°C. Agroecology of the zone is classified as lowland 3.1%, midhighland 65.3%, and highland 31.6% with an average annual rain fall ranging from 801 to 1400 mm. The zone has about 1.66 million total populations, of whom 49.7% are male and 50.3% are female. It has a total area of 3,469,58.5 hectares (HZoANRs 2017). Both crop and livestock production are the dominant farming systems and play a central role in the livelihood of the population in the study area. Major cereal crops cultivated include wheat, barley, sorghum, and maize. Among cereal crop produced, the study area is well known for wheat production ( Figure 1).

Sampling method and sample size determination
Multi-stage sampling technique was employed for this study. In the first stage, the Hadiya zone was purposively selected based on the extent of wheat production. In the second stage, wheat producing districts in the zone were identified based on the extent of wheat production and two wheat producing districts namely Soro and Duna were selected randomly. In the third stage, three wheat producing kebeles 1 from each of the two districts were selected randomly and fourthly, the households were stratified and listed in to two groups (households sowing wheat using row planting and broadcasting methods) in collaboration with each kebeles Development Agents (DA). Finally, 203 sample farm households, 94 from row planting and 109 from broadcasting methods were selected by simple random sampling technique based on Probability Proportional following formula given by Yamane (1967).
where, n is sample size, N is number of wheat producing households using both methods within selected two districts which is 43,873 and e is the desired level of precision which was taken to be 7%.

Sources of data and method of data collection
In this study both primary and secondary data were used.
The data set contained detailed information on households' socioeconomic and demographic characteristics, farm characteristics, input utilization, output produced and institutional related variables. The primary data were collected from randomly selected sample respondents using a structured questionnaire. The comprehensive data were collected from February 2017 to March 2017 through trained enumerators who were capable of speaking the local language as well as English and supervisors using semi-structured questionnaire. Collected data were coded and entered in SPSS statistical packages. After entry, the data were cleaned for potential outliers before subjecting them to thorough statistical analysis.
The data cleaning process involved conducting preliminary descriptive analysis to identify irregularities and inconsistencies in data entry, which were correcting by crosschecking on the questionnaires. Besides to primary data, this study used secondary data collected from different journals, internet, and bureau of agriculture of the zone and districts.

Methods of data analysis
Descriptive and econometric analytical methods were used to analyze the data collected from smallholder farmers.

Descriptive analysis
This method was used to summarize and analyze the sample households input use, output levels and their socio-economic, demographic and institutional characteristics, used in the frontier production and in the inefficiency model, respectively. Descriptive statistical analysis was employed to analyze the survey data using measures of dispersion such as percentage, frequency and measures of central tendency such as mean and standard deviation.

Analytical framework
There are two distinct approaches for estimating efficiency in production: An econometric or stochastic frontier and data envelopment analysis (DEA), which uses mathematical programming method (Greene 2008). The stochastic frontier approach was proposed by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977), later modified by Jandrow et al. (1982). The potential for the misspecification of functional form resulting in biased estimates of technical inefficiency is considered to be a weakness of the stochastic frontier approach relative to nonparametric approaches such as DEA. Another disadvantage of stochastic frontier is that the selection of a distributional form for the inefficiency effects may be arbitrary (Coelli 1995). However, the main criticism of DEA is that it assumes all deviations from the frontier are due to inefficiency and because of this, non-parametric frontier methodology may overstate inefficiencies and hence outliers may have profound effect on the magnitude of inefficiency (Llewelyn and Williams 1996). In addition, in DEA no account is taken of the possible influence of measurement errors and other noise upon the frontier. For a number of reasons, production efficiency studies in the developing countries agriculture like Ethiopia are treated by using stochastic frontier model. This might be due to data are likely to be influenced by the measurement errors and the effects of random shocks such as weather, pest infection, drought, diseases, fires, etc (Coelli and Battese 1996). Due to these errors and random shocks stochastic frontiers take into account stochastic error by decomposing the error term into stochastic and inefficiency components. Therefore, the random effect outside of the control of the decision maker including the statistical noise will be captured by stochastic component and the one-sided component captures deviations from the frontier due to inefficiency.
Specification of stochastic frontier model Following Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977), the stochastic frontier model can be specified as follows: The production frontier can be represented by different production functional forms. Cobb-Douglas and Translog production function are most commonly used in the empirical estimation of frontier models, each having their merits and demerits. In literatures, both models dominate in stochastic frontier and econometric inefficiency estimation (Coelli et al. 2005). However, the work by Kopp and Smith (1980) suggests that functional specification has only a small impact on measured efficiency. For this study Cobb-Douglas was selected using log likelihood test.

Empirical model specification
The analysis of technical efficiency in this study has two components. The first is the estimation of a stochastic production frontier that serves as a benchmark against which to estimate the technical efficiency of wheat producers while the second component identifies exogenous factor that are associated with producer's performance in the production of wheat. Following from the aforementioned discussion the empirical model of the Cobb-Douglas frontier function is specified as follows: where Ln is the natural logarithm; output is the total output of wheat produced in kg/ha; seed is the total quantity of wheat seed used in kg/ha; NPS/Urea is the total amount of Nitrogen, Phosphorous and Sulphur (NPS) /urea fertilizer in kg/ha; area is the area covered by wheat in hectares; labour is family and hired labour measured in man-days; oxen is used in oxen day and herbicide is the total cost of herbicide for wheat production and measured in Ethiopian Birr; v iis a symmetric component and permits a random variation in output due to factors beyond the control of the decision making unit such as weather, omitted variables and other exogenous shocks., independently and identically distributed as N (0, σ v 2 ); and µ iis a non-negative random variable, independently and identically distributed as N (µ, σ µ 2 ) intended to capture technical inefficiency effects in the production of wheat measured as the ratio of observed output to maximum feasible output of the ith household.
In this study, the estimates for all parameters of the stochastic frontier and inefficiency effect model were estimated in a single stage using the maximum likelihood (ML) method. In single stage approach, inefficiency effects are expressed as an explicit function of a vector of various independent variables. In two-stage estimation procedure in which first the stochastic production function is estimated, from which efficiency scores are derived, then in the second stage the derived efficiency scores are regressed on explanatory variables. If the variables used in the single stage are highly correlated which leads to biased results due to multicollinearity (Coelli, Rao, and Battese 1998).
The µ i was obtained by half-normal distribution with mean µ i and, σ 2 , such that: where Educ represents the education level of the household farmer measured in continuous years of formal schooling; Sex is the sex of households which takes a value of 1 if the household head is male and zero, otherwise; Age represents the age of the household head in number of years; Fert represents the fertility status of the wheat plot, which would take a value 1 if the land is perceived fertile and 0, otherwise; Slop represents the slope of the wheat plot takes 1 if the land is perceived plain and 0 otherwise; Lives is the total number of livestock in terms of Tropical Livestock Unit (TLU); Fams represents the number of household size; Totcultlnd represents the total land size operated by the farmer during the production year including his owned land, sharecropped lands and rented lands; Frag represents the number of plots of all annual crops the farmer managed during the production year including his own, hired and sharecropped; Ownl represents land owned by household, which would take a value of 1 if the land is his/her own or rented and 0 if the land is sharecropped; Credit represents access to credit for wheat production 1 if the household received credit, 0 otherwise; Exten represents frequency of extension contact, measured by the number of extension visits by extension agents in production season. The variance parameters for maximum likelihood estimates are expressed in terms of the parameterization using the FRONTIER 4.1 (Coelli 1996) computer program as follows: where s 2 is the total variance of the model and the term represents the ratio of the variance of inefficiency's error term to the total variance of the two error terms defined above. In the prediction of firm level technical efficiencies, Battese and Coelli (1995) pointed out that the best predictor of exp(−µ i ) is obtained by: where is the density function of a standard normal random variables. The farm-specific technical efficiency is defined in terms of observed output (Y i ) to the corresponding frontier output (Y i ) using the available technology derived from the result of the Equation (7) above as: TE takes value on the interval (0, 1), where 1 indicates a fully efficient farm.

Results and discussion
Descriptive statistics results Descriptive analysis results indicated that, average age of sample household heads was 46.28 years with a range of 26-67 years. This implies that most of the household heads were within their productive age. With regards to the sex of respondents, about 86.2% of the sample households were male headed. Education enhances the acquisition and utilization of information on improved technologies by farmers as well as their innovativeness. The educational level of the household head, on average, was 3.63 years with the minimum of zero and maximum of 12. Family labour plays an important part in the success of a smallholder farming practices in that the farmer does not need to spend too much money on labour costs. The average family size of the sampled household heads was 5.6 with a minimum of 2 and a maximum of 8. From the total of about 146.5 hectares of land cropped during 2016/2017 cropping season by sample farmers, most of the sample household (69.2%) operated on their own land. Other than own land in the study area, farmers have other sources of land mainly through two informal arrangements, sharecropping and renting. Annual crops are sown in different plots and are fragmented and scattered over different places. A farmer on average has 2.27 plots with the number of plots varying from one to five. About 48.75% of the sample household heads perceived their wheat cultivated land as fertile.
In the study area, livestock has considerable role for household income and food security. The livestock holding was measures in terms of TLU. Sample farmers on average own livestock of 5.24 TLU and it ranges from 1.3-20.12 TLU. The survey result indicated that the average frequency of extension contacts during the production season in relation with wheat production was about 3.66 times with standard deviation of 1.96. In the production year, about 56.2% of the sample households used credit from different sources.
As indicated in Table 1, the average wheat output in row planting (3250 kg/ha) was 1360 kg/ha higher than in broadcasting (1890 kg/ha). The average land allocated for wheat row planted was 0.67 ha and the average wheat broadcasted land was 0.74 ha. The result indicated that, on average, row planting increases human labour and oxen power requirement by 18.14% and 12.14%/ha, respectively, over broadcasting. Regarding fertilizer type, the most commonly and intensively used chemical fertilizer for the production of major cereal crops are NPS and Urea. The survey results revealed that wheat row planting minimizes the average NPS and Urea requirement by 31.33% and 29.02%/ha, respectively, over broadcasting. The other very important variables are seed and herbicide. The result also indicated that, on average row, planting decreases the amount of seed and herbicide requirement by 23.59% and 12.97%/ha, respectively, over broadcasting.

Hypotheses testing
It is possible to test various hypotheses using maximum likelihood ratio test in stochastic production function method, which were not possible in non-parametric models. Therefore, before going on to the estimation of the parameters of the model from which individual level efficiencies are estimated, it is essential to examine various assumptions related to the model specification. Tests of hypothesis for the parameters of the frontier model are conducted using the generalized likelihood ratio statistics, λ, defined as: where, L(Ho) and L(H 1 ) are the values of the log-likelihood function under the null and alternative hypotheses, Ho and H 1 , respectively. Tests of hypotheses for the parameters of the frontier model were conducted using the generalized likelihood ratio statistics, λ, defined by Equation (9). In this study, following three hypotheses were tested.
The first test was carried out by estimating the stochastic frontier production function and conducting a likelihood ratio test assuming the null hypothesis of no technical inefficiency (Ho: γ = 0). The calculated likelihood ratio value, λ = 48.55 for row planting and 53.34 for broadcasting, presented in Table 2 are found to be greater than the critical value of 6.63. Since the calculated likelihood ratio value is greater than the critical value, the null hypothesis is rejected at 1% level of significance implying that stochastic frontier production is more appropriate than average response function. Consequently, the null hypothesis that wheat farmers in both methods in the area are fully efficient is rejected.
Similarly, the second test was estimated for the selection of the appropriate functional form (Cobb-Douglas versus Translog production function). The test result show that the calculated value of λ = 38.46 for row planting and 40.88 for broadcasting methods are less than the critical value of 48.27, thus the null hypothesis is not rejected at 1% level of significance implying that Cobb-Douglas functional form best fit the data set.
The last test is that the whether all coefficients of the inefficiency effect model are simultaneously equal to zero, (H 0 : U i = δ 0 = δ 1 = δ 2 … δ 12 = 0). The calculated value of λ = 67.74 and 59.58 for row planting and broadcasting, respectively, are greater than the critical value of 26.21, showing that the null hypothesis (H 0 ) that explanatory variables are simultaneously equal to zero is rejected at 1% significance level. This confirms that there is a room to improve wheat output by identifying inefficiency factors.

Estimation of production function parameters
The production function parameters were specified and estimated using the maximum likelihood estimation (MLE) method to analyze the technical efficiency of sample households in the production of wheat in row planting and broadcasting methods in Hadiya zone. The model comprises of twenty-one parameters, seven of them were the explanatory variables of the stochastic frontier function while twelve of which were the explanatory variables that are hypothesized to influence the technical efficiency scores and the remaining two being the parameters associated with the distribution of ν i and µ i .
The value of sigma-squared (σ 2 ) for frontier of wheat output was statistically significant at 1% level which indicates the goodness of fit of the specified assumption of the composite error terms distribution. The Gamma (γ) value which measures the ratio of the variance of the inefficiency component to the total error term was 54% under row planting and 78% under broadcasting. This suggests that technical inefficiency effect makes significant contribution to variation of wheat production in study area. As the Table 3 depicts that the result of stochastic frontier model for NPS, urea, human labour and seed are all positive and significant, indicating these inputs significantly increase wheat output in both row planting and broadcasting methods. Accordingly, a percentage increase in NPS, Urea, human labour and seed increases the output of wheat by 0.15%, 0.13%, 0.17% and 0.41%, respectively under row planting and 0.12%, 0.14%, 0.11% and 0.33%, respectively under broadcasting method.

Yield gap due to inefficiency and technical efficiency scores
The model output in (Table 4) indicated that, there was a variation in technical efficiency (TE) among sample households. The mean TE was 83.4% and 57.8% under row planting and broadcasting, respectively; confirmed that, the average technical efficiency of Hadiya zone wheat producers is higher in row planting than broadcasting. This implies that on average wheat output can be increased by 16.6% under row planting and 42.2% under broadcasting while utilizing existing resources and technology if inefficiency factors are fully addressed properly. In other words, on average the sample households decrease their inputs by 16.6% under row planting and 42.2% under broadcasting method to get the output they are currently getting.  The distribution of the TE scores as shown in the Figure 2, revealed that majority (80.85%) of the sample farmers have TE score greater than or equal to 50% under row planting and about (56.88%) of the sample farmers have TE score greater than or equal to 50% under broadcasting. That is why the distribution of the TE scores is skewed to the right for row planting and slightly normal distribution for broadcasting. Moreover, the frequencies of occurrences of the predicted technical efficiencies in range indicate that the highest number of households have technical efficiencies between 0.80 and 1 under row planting and no farmer have technical score of more than 0.90 under broadcasting. All this again showed that wheat producers are more technically efficient when using row planting than broadcasting in the study area.

Yield gap due to technical inefficiency
Yield gap may be defined as the difference between technically full efficient yield and observed yield. Therefore, yield gap is the amount which represents fewer yields due to technical inefficiency. Based on Equation 3 above the potential wheat output was estimated for sample wheat producer farmers by dividing the actual individual level of wheat output by the predicted technical efficiency scores from stochastic frontier model. After calculating potential wheat output, the yield gap of wheat was estimated. Yield gap is estimated by the difference between technically full efficient yield and observed yield. The mean result is presented in Table 4. It was observed that mean technical inefficiency was 16.6% under row planting and 42.2% broadcasting which caused 646.882 and 1393.038 kg/ha yield gap of wheat  on average, respectively. This shows that sample households in study area were producing on average 646.882 and 1393.038 kg/ha lowers wheat output than their potential yield under row planting and broadcasting methods, respectively. This shows that under the existing practices there is a room to increase wheat yield more under broadcasting than row planting following the best-practice farms in the study area.

Determinants of technical inefficiency of wheat producers
After the technical efficiency level at which wheat is produced was calculated, finding out factors that affect inefficiency levels among the sampled farmers was the next most important step of this study. Table 5 shows factors that affect inefficiency in wheat production. Out of the twelve variables used, six variables (education, age, fertility status of the plot, family size, land fragmentation and extension contact) were found to affect significantly the efficiency of wheat farmers. Education status of household head as shown in Table  5 influenced inefficiency negatively. This could be because of educated farmers have the ability to get information from various sources and can apply the new information on their farm that would increase outputs of wheat. Besides to this, it will help them to adopt modern agricultural technologies and be able to produce higher output using the existing recourses more efficiently. This result is in line with the findings of Debebe et al. (2015), Musa, Lemma, and Endrias (2015), and Asfaw, Geta, and Mitiku (2019).
Age of household head (which is a proxy variable for farming experience) had a statistically significant and negative relationship with technical inefficiency of wheat production under broadcasting method. This indicates that as the age of farmers increases their inefficiency reduces which leads to improvement in the level of technical efficiency. This may be because farmers become more expert in different agronomic practices as they become experienced. The result is in conformity with the results of Alemu, Tegegne, and Beshir (2018) and Ayele, Haj, and Tegegne (2019).
The estimation result indicates that planting wheat on fertile soils was found to significantly reduce technical inefficiency of wheat producers. This may be associated with those fertile lands require less commercial fertilizer application which leads to reduction in cost. This result is similar with the studies by Mamo et al. (2017) and Asfaw, Geta, and Mitiku (2019).
The negative coefficient of family size implies that an in increase in this variable would lead to decrease in the level of technical inefficiency wheat producers under broadcasting method. The reason for this was probably because broadcasting method demands more human labour than row planting. Since family labour is the main input in crop production as the farmer has large family size would manage crop plots on time and may able to use appropriate input combinations by using their own labour. This result is similar with the findings of Deme (2014) and Edosa, Kebede, and Shumeta (2019).
The positive and significant value of the coefficient of fragmentation in Table 5 indicates that fragmented land causes time loss in travel and inconvenience in agricultural management. This means that fragmented land leads to reduce efficiency by creating lack of family labour, wastage of time and other resources that would have been available at the same time. This finding is in line with empirical findings of Asfaw, Geta, and Mitiku (2019) and Ayele, Haj, and Tegegne (2019).
Finally, as shown in Table 5, the study result also confirmed that the presence of more contact between extension agents and farmers made farmers more technically efficient. Extension services are assumed to help in dissemination and adoption of new technologies. In addition, this extension services offer guidance to the farmers related to the use of various resources and provide consultancy services in managing their scarce resources more efficiently. The findings are consistent with earlier results of Debebe et al. (2015) and Edosa, Kebede, and Shumeta (2019).

Conclusion and recommendations
The difference between actual agricultural production and potential for increasing its productivity still persists in Ethiopia. To address this, it needs boosting of agricultural productivity and improves living standard of farmers either through use of modern inputs technology or decreasing the present level of inefficiency. Thus, it is possible raise productivity through improving efficiency by using existing resource base and available technology. Therefore, this study was conducted to estimate technical efficiency of wheat producer farmers under row planting and broadcasting methods in Hadiya zone, Southern Ethiopia. The findings of this study, confirmed that there is a room to enhance production and productivity by improving the technical efficiency of wheat production more under broadcasting method than row planting, given same level of input and current technology. The estimated stochastic frontier Cobb-Douglas production function indicates that the amount of NPS, Urea fertilizers, human labour and seed had a positive and significant effect on the level of wheat production under both methods. The positive coefficient of these parameters indicated that increased use of these inputs up to the recommended level increases the production level. The results also confirmed that, the estimated SPF model together with the inefficiency parameters shows that education status, age, fertility status of the plot, family size, and frequency extension contact were found to significantly and negatively affect the level of technical inefficiency of wheat producer farmers while land fragmentation was found to significantly and positively affect the level of technical inefficiency of wheat producer farmers in both methods.
Therefore, government and other concerned bodies need to strengthen farmers' access to education that could be implemented through expansion of farmers training centre or expansion of formal and non-formal education in the area. The local government and any concerned bodies should also arrange on-farm demonstration and trials, give continuous trainings on the agricultural production and management for younger producers. It also is important to improve soil fertility by applying organic manures and practicing different soil conservation techniques. Lastly, hence farmers that operate a larger number of plots are less efficient than others, land consolidation strategy is needed. Note 1. Kebele is the smallest administrative hierarchy in Ethiopia.