Determinants of technical , allocative and economic efficiencies among onion producing farmers in irrigated agriculture : Empirical evidence from Kobo district , Amhara region , Ethiopia

This study investigated the determinants of technical, allocative and economic efficiencies among small-scale onion farmers in North Wollo zone of Amhara National Regional State, Ethiopia. Structured questionnaires were used to collect data from 200 respondents randomly selected from designated locations in the study area. A stochastic production frontier function was fitted to the sample households. The findings revealed that land related factors such as land distance, ownership, and fragmentation explained much of the technical inefficiencies in addition to other socio-economic characteristics of farm households (age, market access, training access, years of experience in onion production, farm income, responsibility and field visit) were found to be significant at different levels of significance for technical efficiency. The variables that explained allocative efficiency were plot distance, market access, sources of irrigation water, extension visit, farm income and field visit. Major determinants for economic efficiency were age of the household, plot distance, fertility, source of irrigation water, extension visit, experience in onion production, land fragmentation and farm income. It is therefore suggested that any development intervention program through irrigation should consider the aforementioned socioeconomic characteristics and determinants of efficiency for success. Tenure insecurity and land fragmentation also play significant role for farmers to adopt the available technologies and maximize production on irrigated farms. Likewise, it has shown positive effect on production inefficiency, calling for the need to think about policies targeting land consolidation at least with in farms, improving institutional services (extension, market, training, attitude change on credit utilization), soil management options and increased investment in irrigation services could jointly contribute to the improvement in efficiency of onion farmers in the study area.

farmers (MoA, 2010).Agriculture contributes about 41% of the country's GDP, employs 83% of total labour force and contributes 90% of exports (EEA, 2012).Ethiopian agricultural sector has always been an important component of the country's economy.A sectoral analysis in 2011 of the real GDP indicated that the agricultural sector contributed about 41.1% of the GDP, with crop, livestock, forestry and fishery accounting for 27.5, 10.6, 2.9, and 0.2% respectively (CSA, 2012).This implies that the crop sub-sector contributed 66.9% of agriculture GDP.
Though agriculture remains the most important sector of the Ethiopian economy, its performance has been disappointing and food production has been lagging behind population growth (Demeke, 2008).Kobo district is among the north eastern area endowed with ground and surface water sources and substantial quantities of vegetables are grown under irrigation during dry season (KGVDP, 2005).
Despite its potential, kobo district productivity increase is said to be declining (CSA, 2012).Similarly, productive efficiency for most crops still falls under 60% (Haji, 2008).These shortfalls are attributed to inefficiencies in production.Therefore, the need for the efficient allocation of productive resources cannot be overemphasized.Presently, there are very few firm-level studies of efficiency in the developing economies, particularly in Ethiopia.
As far as the researcher knows, no specific investigation into farm level productive efficiency involving onion production is carried out in the study area, as most of these studies focus on only the resource use efficiency (Belay et al., 2010).
The total irrigable land potential in Ethiopia is 5.3 million hectares assuming use of existing technologies, including 1.6 million hectares through Rain Water Harvesting (RWH) and ground water.There are 12 river basins that provide an estimated annual run-off of 125 billion m 3 per year, with total irrigating potential of 3,731,222 ha from surface water.
The potential available estimates for RWH range from 40,000 to 800,000 ha.The area under irrigation development to-date is estimated to be 640,000 ha for the entire country which is 5% of the potential irrigable (Awulachew et al., 2010).Irrigation benefits the poor through higher production, higher yields, lower risk of crop failure, and higher and year-round farm and nonfarm employment.Irrigation enables smallholders to adopt more diversified cropping patterns, and to switch from low value staple production to high-value marketoriented production.Increased production makes food available and affordable for the poor (Asayehegn et al., 2011).
In the light of the foregoing, this study examined farm household' technical, allocative and economic efficiencies of smallholder drip and furrow irrigated farm production in Kobo district of Amhara National Regional State Ethiopia.

Study area
The study was carried out in Kobo district.It is located in the North Eastern part of Amhara National Regional State, North Wollo zone, Ethiopia, lying between 11° 54 ' 04" and 12° 20 ' 56" N latitude and  between 39° 25 ' 56" and 39° 49 ' 04" E longitude (Figure 1).The district has an altitude that ranges from 1400 to 3100 m above sea level.The district capital town, Kobo is about 570 km away from Addis Ababa on the way to Mekele (CSA, 2011;WOA, 2010).
According to the North Wollo Zone Agricultural Office (2010), Kobo district shares 43.74% of the total 47,292.7 ha of irrigable land of North Wollo, which is equivalent to 5.5% of the total irrigable land of the region (BoWME, 2005).Kobo district has total human population of 239,504 of which 120,383 (50.26%) are male and 119,121 (49.74%) are female.Out of the total population, 20.15% are urban dwellers.Kobo has a population density of 119.7 people per square kilometer, which is less than the zonal average of 132.3 per km 2 .The district has a total area of 2001.57km 2 .With regard to land use pattern of the district, cultivable land comprises the highest (29%) followed by degraded land (26.5%) (CSA, 2011).
According to WOA report, ( 2009), the agro climatic feature of the district is tropical as 7.9, 37.2 and 54.9% are Dega, Weyina dega and Kola respectively.As described by the report of WOA, 65% is plain while the rest 20, 6, 5 and 4% are mountainous, rugged, gorges and swampy.Kobo is characterized by low and erratic rainfall with mean annual rainfall of 670 mm that ranges from 500 mm to 850 mm.The temperature varies from a minimum of 19°C to a maximum of 33°C annually.Compared to other districts of the zone, Kobo district has relatively hot climate and it has mean annual temperature of 23.1°C.
The total land area under cultivation in the Kobo District is 58,045 ha, of which 90% is rain fed.Average land holding in the District is 0.75 ha, whereas average holding under irrigation is 0.15 ha.Main types of crops grown during rainy season are Teff, Sorghum, Maize and Chickpea in their order of area coverage.In the district, production of vegetables and root crops under rain fed condition is virtually impossible unless the seasonal rainfall is supplemented with irrigation water.Thus their production is limited to those households who have access to irrigation water.
In most irrigable lands of kobo, horticultural crops in general and onion in particular, play an important role in contributing to the household food security.Some of the vegetables and root crops produced using irrigation includes onion, tomato and pepper.Among the vegetables and root crops, onion takes the highest share.
Due to this, more than 75% of irrigated area, which is 4000 ha, was allocated for production of onion in the district that could generate income for the poor households (WOA, 2010).

Sampling procedure and sample size
The target population for this study was onion farmers in the study area.Since onion is produced in virtually all the areas of the district and in order to have a representative sample in achieving the stated objectives, the sampling procedure covered all the areas equally.Accordingly, a two-stage sampling procedure was employed in selecting the sample for this study.The first stage involved the random selection of six villages in different irrigation scheme.The second stage was the random selection of 100 farming households in each of the already selected group of scheme based on proportionate probabilistic sampling techniques.Accordingly, a sample of two hundred farming households was collected and subsequently analyzed for the study.The sampling distribution of the respondents is shown in Table 1.

Analytical techniques
Descriptive statistics and Cobb-Douglas stochastic production frontier approach was used to estimate the production function and the determinants of technical, allocative and economic efficiencies among onion farmers in the area.The stochastic function assumes the presence of technical inefficiency of production.
The specification involves a function specified for cross-sectional data, which has an error term, with two components, one to account for technical inefficiency.Hence, the function is defined by: Where: Y is the monetary value of onion crop per farm X is a kx1 vector of (transformations of the) input quantities of the ith firm; Β is a vector of unknown parameters to be estimated; Vi are random variables, two-sided (-∞<vi<∞) normally distributed random error.
N~(0,δv 2 ), which are assumed to be independent of the Ui that captures the stochastic effects outside the farmer's control (for example, weather, natural disasters, and luck ,measurement errors in production, and other statistical noise).The two components v and u are also assumed to be independent of each other.Thus, to estimate Cobb-Douglas production function, we must log all the input and output data before the data is analyzed (Coelli, 1995).The estimating equation for the stochastic function is given as: lnY=B0 +B1lnX1+B2lnX2 +B3lnX3+B4lnX4 +B5lnX5+ BlnX+V-U (2) In the area farming, land, labour, seeds, fertilizers, agro-chemical and irrigation water are generally regarded as inputs.On the basis of this, land (X1) in hectare, labour (X2) in person day, planting materials or seeds (X3) in kg, fertilizer in kg (X4), agro-chemical in liters (X5), irrigation frequency in days (X6) and irrigation methods (X7) dummy D=1 when drip and 0 otherwise were included in the stochastic frontier models.Technical efficiency of an individual firm is defined in terms of the ratio of the observed output (Y) to the corresponding frontier output (Y*), given the available technology, conditional on the levels of input used by the firm.
That is technical efficiency which is obtainable by the use of Frontier 4.1 (Coelli, 1996).Based on the individual farm's technical efficiency, the mean technical efficiency for the sample is obtained (Rahji, 2005).
Assuming that the production function in Equation ( 1) is self-dual (e.g., Cobb-Douglas), the dual cost frontier is derived algebraically and written in the following form: ) *, , ( Where Ci is the minimum cost of the i th farm associated with the adjusted yield of output Yi* and α is a vector of parameters to be estimated.The economically efficient input vector of the i th farm, Xie is derived by applying Shepard's Lemma and substituting the firm's input prices and adjusted yield of output level into the resulting system of input demand equations ) *, , ( / Where k represents the total number of inputs used.The observed, technically and economically efficient costs of production of the i th farm are then equal to Wi′ Xi, Wi′ Xit and Wi′Xie, respectively.According to Sharma et al. (1999) these cost measures are used to compute technical efficiency (TE), Following Farrel (1957) allocative efficiency (AE) can be derived from equation ( 6) and (7) as, indices of the i th farm.The production frontier was estimated using frontier model whereas the cost frontier is derived analytically from production assuming self-dual.The determinants of technical, allocative and economic inefficiencies are explained by: U i =δo+δ 1 Z 1 i +δ 2 Z 2 i +δ 3 Z 3 i +δ 4 Z 4 i +δ 5 Z 5 i +δ 6 Z 6 i +δ 7 Z 7 i + …+ Haile 2183 Where: for farm i, z is a vector of observable explanatory variables and δ is a vector of unknown parameters.Thus, the parameters of the frontier production function are simultaneously estimated with those of an inefficiency model, in which the inefficiency effects are specified as a function of other variables.U represents inefficiency effects; δo represents the intercept.After a thorough review of previous studies and the prevailing situation in the study area, socio economic and institutional factors (Zi's) that would affect efficiency were hypothesized as follows: Age of the household head (Agehh): The age of the household head is hypothesized to reflect the experience of the farmer.
Education level of the household head (Edeuclvl): Farmers are expected to acquire the ability of better management through education and can be used as a proxy variable for managerial ability.

Family size (Famsize):
Family is an important source of labour supply in rural areas.It is expected that households with many family members have better advantage of being able to use labor resources at the right time, particularly during peak cultivation periods.

Total cultivated land (Totcultlnd):
This refers to the size of (own, shared or rented in) all land the household managed during 2012 production season.

Land fragmentation (Fragment):
This is defined as the total number of plots that the farmer has managed during the 2012 production season.Plots in the area are highly fragmented and scattered over many places that would make difficult to perform farming activities on time and effectively.Increased land fragmentation leads to inefficiency by creating shortage of family labour, costing time and other resources that should have been available at the same time.

Number of livestock (Livstock):
This is the total number of livestock in terms of Tropical Livestock Unit (TLU).

Distance of household's residence (Distress):
Distance between farmer's residence and onion plot is assumed to have negative impact on efficiency.

Farm income (Totfincom):
This includes all income from on farm and off farm activities of the household.It is a continuous variable measured in the amount of income (birr) the household head and/or other members get per year.

Land ownership (Lndowner):
This is a dummy variable measured as 1 if the farm for production of onion is on sharecropping basis and 0 otherwise.and techniques given by the extension agent during the production season and was defined using a dummy variable 1 for service user 0 for nonuser.

Access to market (Accmkt):
It is dummy 1 for those who have access to market otherwise 0.

Field visit (Fieldvis):
In the study area, field visit program is adjusted for farmers at their locality and nearby districts in the region.It is dummy 1 for those who have access to field visit otherwise 0.

Access to training (Acctrain):
Training is an important tool in building the managerial capacity of the farmer.It is dummy 1 for those who have access to training otherwise 0.

Responsibility (Responsi):
Responsibility in different social and committee leadership give the farmers opportunity of sharing information on improved production techniques by interacting with other farmers and experts thereby improve efficiency.It is dummy variable taking the value of 1 if the household has different responsibility in the kebele and 0 otherwise.

RESULTS AND DISCUSSION
The mean age of the respondents is 46.59 years and the modal age is 41 to 50 years, which constituted about one-third of the total respondents (Table 2).The age of the farmer according to Adewumi and Omotesho (2002) is expected to affect his labor productivity and output.This agrees with findings of former studies Tsoho (2004).
The study revealed that more than 90% of the respondents were married, while the remaining were either single or widow(ers), respectively.The mean family size was 6.02 persons per respondent and it ranged from 1 to 12.The study also revealed that 57% have attained between primary and tertiary education.More than two-third of the respondents have had religious education.The farmer's years of experience ranged from 5 to 45 with an average of 23.21 years.Farmers experience is expected to have a considerable effect on farmer's productive efficiency.Almost all the respondents have inherited farming as an occupation, while the others were introduced to farming by either friends or relatives.About 90% of the respondents have farming as their main occupation and only 10% adopts farming as their secondary occupation.

Efficiency analysis
The expected parameters and the related statistical test results obtained from the analysis of the maximum likelihood estimates (MLE) of the Cobb-Douglas based stochastic frontier production function parameters for irrigated season vegetable farmers are presented in Tables 3 and 4.
The variance parameters of the production function represented by Sigma-squared (σ 2 ) and Gamma (γ) are all significant even at 1%.The Lambda is greater than one (λ = 8.41).The statistical significance of Lambda showed that there exits sufficient evidence to suggest that technical inefficiencies are present in the data.Theoretically, this implies a good fit for the estimated model and correctness of the distributional assumptions for the Ui and Vi.The statistical significance of the sigmasquared also indicated a good fit for the model.The estimated gamma (0.89) shows the amount of the variation in onion outputs which results from technical efficiency of the sampled farmers (Berhan et al., 2014).
The results of the estimated parameters revealed that all the coefficients of the physical variables except quantity of seeds used, conform to a priori expectation of a positive signs.The positive coefficient of land, labour, fertilizer, agro-chemical and irrigation implies that as each of these variables is increased, ceteris paribus, vegetable output increased.The negative sign of the seeds suggest a situation of excessive (and, hence, inefficient) use of planting material in the production of vegetable in the area.
The coefficient of the variable associated with land although positive, is statistically not significant even at 10% level of significance.The coefficients of the three physical variables: labor, fertilizer and irrigation water are all significant even at 1% level of significance.Therefore,  and Onyenweaku and Effiong (2005).

The returns to scale (RTS)
The return to scale (RTS) analysis, which serves as a measure of total resource productivity, is given in Table 5.The maximum likelihood estimates (MLE) of the Cobb-Douglas based stochastic production function parameter of 0.464 is obtained from the summation of the coefficients of the estimated inputs (elasticties).It indicates that onion production in study area was in the stage II of the production surface which is decreasing positions of return to scale where resources and production were believed to be efficient.

Multiple regression analysis (OLS)
Based on the literature on previous studies; nine characteristics are chosen as indicators of the farmer's socio-economic environment and are subsequently used as explanatory variables in the analysis of productive efficiency for onion production under irrigation in the study area.The Technical, allocative and economic efficiency estimates derived from SFA will be regressed, using a censored Tobit model on the following farmspecific explanatory variables that might explain variations in production efficiencies across farms.Estimation with OLS regression of the efficiency scores would lead to biased parameter estimates since OLS assumes normal and homoscedastic distribution of the disturbance and the dependent variable (Greene, 2003).As the distribution of the estimated efficiencies are censored from above at the value one, Tobit regression (Tobin, 1958) is specified as Where E i is an efficiency score, and V~N (0, σ 2 ) and β j are the parameters of interest.
The results of the analysis of the relationship between the farmer's characteristics and efficiency indices are presented in Table 6.
The results indicated that, overall, the explanatory ability of the variables included in the analysis is limited (R 2 values are generally low) and not all regressions or parameters are significant.This result agrees with the findings of several researchers who have generally obtained an R 2 value of less than 0.5 in their secondary analysis similar to this study.For example, Xu and Jeffrey (1997) obtained an R 2 value of 0.21, 0.31 and 0.19, respectively.
The variables fragment, ownership, total farm income, training and participation in field day visit affect efficiency positively while responsibility and age of the household head affect technical efficiency negatively.Households who have got the chance to participate in field visit and field days are more efficient than their counter parts.Because it improves the technical knowhow and skill of the farmers thereby exchange of experience will improve the efficiency.The result shows that access to field visit is found to have positive and significant effect (at 5% level of significance) on farmers' technical efficiency in production.
The result shows that households having better farm income would devote their time and effort in day to day farming activities and able to use improved technologies thereby production efficiency improved.Thus the result is found to have positive and significant effect on farmers' technical efficiency in production.
Experience in onion production is a proxy measure of managerial and technical knowhow.The result shows that experience is found to have positive and significant effect on farmers' technical efficiency in production.This result is in conformity with the finding of Abdukadir (2010).
Extension contact and training has a positive sign and is statistically significant in technical efficiency and negative sign in allocative efficiency indices.The positive and statistically robust relationship between extension and efficiency supports the notion, which implies that farmers who had more extension visits/teachings are likely to be more successful in gathering information and understanding new practices and the use of modern inputs which in turn will improve their EE through higher levels of TE and AE respectively.These results are consistent with the findings of Onyenweaku and Nwaru (2004) and Rahji (2005).Contrarily, the study disagreed with findings of those of Parikh et al. (1995) that have found extension to be negatively and statistically related to efficiency indices.
Source of irrigation water has positive and statistically significant coefficients for AE and EE.But, the opposite is true for the TE as its relationship is negative and nonsignificant.The positive coefficient suggests that farmers who use underground water to irrigate their onion are allocatively and economically more efficient than those who use surface water.Interestingly, these same categories of farmers are however, technically less efficient.This finding is consistent with Baba and Wando (1998) that the there is a positive and significant relationship between the source of water and the efficiency of the farmers.
The coefficients of family size, farm size, education status, off farm income, credit use, TLU, and land ownership systems are not important in explaining the variation in TE, AE and EE of farmers in the study area.

Conclusion
The study aimed at finding out the determinants of technical, allocative and economic efficiency levels of onion farmers at the Kobo Girana Valley Development Irrigation Project in the Eastern Amhara Region of Ethiopia.
In terms of methodology, the Cobb-Douglas specification of the model performed better than the translog specification.Therefore, the Cobb-Douglas stochastic frontier production was estimated, from which TE and EE extracted.The study indicated that 82.6 and 76.8% were the mean levels of TE, under drip and furrow irrigated, respectively.This in turn implies that farmers can increase their farm production on average by 17.4 and 23.2% respectively when they were technically efficient.Similarly, the EE of drip and furrow were 51.49 and 44% respectively.In the second step of the analysis, relationships between efficiency indices (TE, AE and EE) and variables expected to have effect on farm efficiency were examined.This was relied on maximum likelihood estimation of frontier model of inefficiency effect, where inefficiency, expressed as functions of 19 independent variables.Among them, age, plot distance, fragment, source of water, experience in onion production, farm income, fertility status and extension visit were found to be statistically significant to affect the level of production efficiency.
The inputs that were important in determining output were fertilizer, labour, oxen power and seed cost were statistically significant as well as most of them maintaining their expected signs.The results indicated that the extension contact, source of water, and crop diversification exhibited higher levels of positive significant impact on TE and EE, the location of the farm exerts a negative significant impact on TE.In addition, farm location has a statistically positive association with AE.In all, extension contact exerts a uniform impact on all the efficiency indices.Thus, the results of the study give information to policy makers and extension workers on how to better aim efforts to improve farm efficiency as the level and specific determinant for production efficiency.These findings stresses the need for appropriate policy formulation and implementation to enable farmers reduce their inefficiency in production as this is expected to have multiplier effects ranging from farm productivity growth to economic growth and poverty reduction at macro level.
In the study area, field visit promotes technical efficiency of irrigated onion production.This indicates that the existing training and field visit experience sharing services should be continued and promoted in improving the technical efficiency and thereby the performance of farmers.Therefore, it is recommend that government should have a prime responsibility to improve the performance of farmers training center much more in these areas and others so that farmers can use the available inputs more efficiently under the existing technology.Therefore extension services has to keep on aiming to provide information and practical farming knowledge for all farmers particularly those involving in irrigation to improve resource utilization and reduce cost of production in irrigated agriculture.The analysis also indicated that participation in collective action like crop protection is vital in improving the efficiency.
The result also revealed that land related factors such as land size, land ownership, and land fragmentation explain much of the technical inefficiencies in addition to other socio-economic characteristics of farm households.Total land size is inversely related to the technical efficiency.We also observed that land size has negative effect on onion yield, which signifies the theory of inverse relationship between farm size and productivity in onion production.All these imply that labor market is still imperfect that causes households' to relay on family labor.Farmers are more efficient on owned plots than leased in (in the form of sharecropping and fixed rent) plots.Tenure insecurity play significant role for farmers to adopt the available technologies and maximize production on irrigated farms.Likewise, land fragmentation has showed positive effect on technical inefficiency, calling for the need to think about land consolidation at least within farms.Hence, it can be concluded that onion production can further be increased by introducing improved water application technologies like drip and sprinkler suitable for small farmers with appropriate policies aimed at creating tenure security, perfecting labor market and consolidating fragmented plots.

Figure 1 .
Figure 1.Location of the study area
Experience in onion production (Experio): the number of years of experience is directly related to the farmers know how on onion production.Off-farm/non-farm income (Offincome): Dummy variable having a value of 1 if the farmer is involved in off-farm/non-farm activities, 0 otherwise.Access to credit (Acscdt): is a dummy variable which indicates accessibility of credit which is 1 if the farmer can access credit, 0 otherwise.Extension service use (Extserv):Extension service given to farmers was measured as how much farmers implement the advice and *** significant at 10, 5 and 1% significance level, respectively.Source: Author computation (2013).theseare the major factors explaining onion production under irrigation condition in the area.The finding agrees with those ofTsoho et al. (2013) Ajibefun et al. (2002)

Table 1 .
Sampling distribution in the study area.

Table 2 .
Socio-economic characteristics of the households' heads in the study area.

Table 3 .
Estimated stochastic production frontier function.

Table 4 .
Estimated stochastic cost frontier function.

Table 5 .
Elasticities and returns to scale of the parameters of stochastic frontier production function.

Table 6 .
Relationship between transformed efficiency indices and farm-farmer characteristics.