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Analysis of Factors Affecting the Allocative Efficiency of Maize Production: In Case of Nunu Kumba Woreda, East Wollega Zone

Allocative efficiency is one of the most important measures of firm profitability. Hence, this study was aimed to examine the efficient utilization of existing resources and identify the effect of socio-economic and institutional factors on the allocative efficiency of maize production. The multi-stage sampling procedure was applied to the population of maize farmers from the area under study and 330 respondents were proportionally selected from four kebeles of the study area. A Stochastic production frontier model was used to estimate economic and technical efficiency score which used to drive allocative efficiency score, while Tobit model was used to identify factors affecting allocative efficiency score. The result of the study shows that allocative efficiency score was 79.49 with a minimum of 47.23%, and a maximum of 94.4. The Tobit model estimation result revealed that Allocative efficiency was positively and significantly affected by education, farm size, livestock holding, and market distance, while negatively and significantly affected by sex, age, family size, off-farm income, and credit utilization. Accordingly, the study recommended the need to supply enough amounts of improved seed and fertilizer on time to increase maize productivity. It also suggested the need for policy to encourage farmers’ education, easily available and affordable credit services on time, increase the provision of extension service as well as give training for farmers on correct input application and improved farm technologies to improve the production efficiency of maize farms.


Methodology of the study 4.1 Description of the study area
The study was carried out in Nunu Kumba woreda of East wollega zone of Oromia regional state. Nunu Kumba is one of 180 woredas in the Oromia Region of Ethiopia, and Located at 232km, west of Addis Ababa. Part of the East wollega Zone, Nunu Kumba is bordered on the southwest by the Didessa River, which separates it from the Ilubabor Zone, on the northwest by Jimma Arjo, on the north by Guto Wayu, on the northeast by Wama Bonaya, and on the southeast by Wama which separates it from the Jimma Zone. The administrative center of this woreda is Nunu.
This woreda was selected by the Ministry of Agriculture and Rural Development in 2004 as one of several areas for voluntary resettlement for farmers from overpopulated areas in the East Wollega Zone. Together with Amuru Jarte, Bila Seyo, Gida Kiremu, Ibantu, Jimma Arjo and Limmu, Nunu Kumba became the new home for a total of 22,462 heads of households and 112,310 total family members (Resettlement, 2004).

Sample size and sampling technique
Nunu Kumba woreda is purposively selected for this research because of the prevalence of maize producers in the area. A multi-stage sampling procedure was applied to the population of maize farmers from the area under study. In the first stage, four kebeles of maize farming are purposively selected based on the intensity of maize production in the study area. In the second stage, a 330 sample size of maize farmers were selected from four kebeles based on the formula developed by Yamane (1967). After that, the number of respondents taken from each kebeles by proportionate stratification, and the sample size of each kebeles (stratum) is proportionate to the population size of the stratum.
For this study, primary data was used. The primary data on socio-economic variables such as demographic characteristics, extension services, credit access, amount and cost of labour, oxen power used, the amount and cost of inputs used such as seed, planting fertilizer (DAP), and top dressing fertilizer (UREA), as well as the number of outputs obtained, was collected using a structured questionnaire and interview.

Model Specification: Approaches to Efficiency Analysis
There are two approaches to efficiency analysis which is econometric (parametric) which was used by Battese (1989), and non-parametric approach, which used by Sengupta (1989). A non-parametric method like Data Envelopment Analysis (DEA) and a parametric method like Stochastic Frontier Analysis (SFA) are two common techniques used for estimating production efficiency or inefficiency. However, SFA is applied mostly in efficiency estimation in preference to DEA because of the former has the ability to deal with stochastic noise and amenable to statistical testing of hypotheses (Coelli et al., 2005). According to Coelli et al. (1998), the stochastic frontier is considered more appropriate than DEA in agricultural applications especially in developing countries where the data is likely to be influenced by measurement errors and the effects of shocks (weather conditions, diseases, etc).
Journal of Natural Sciences Research www.iiste.org ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online) Vol.9, No.23, 2019 As noted by Rathnayake and Amarathunge (nd) The stochastic frontier approach is one of the parametric approaches used to measure farm efficiency and enables to distinguish inefficiency from deviations that are caused by factors beyond the control of farmers (noise). But in DEA the method there is no functional form imposed on the production frontier and there are no assumptions made on the error term. It combines noise and inefficiency together and calls the combination inefficiency.
According to Catherine and Jeffrey (2013) stated, Cobb-Douglas function is preferable to trans log function. Cobb Douglas production has the advantage of being self-dual, a computational advantage in estimating efficiency scores and interpretation of elasticity of inputs as well as its less vulnerability to multicollinearity problem which included in trans log function. As a result, Cobb Douglas stochastic production function was applied in this study.

Model specification for Allocative Efficiency
In this study, Cobb-Douglas production function was used in measuring the allocative efficiency index of maize farmers. Maize production is a dependent variable which depends on the explanatory variables such as human labour, fertilizers applied (DAP and UREA), oxen power used, amount of seed planted and size of land allocated for maize production. Therefore, the allocative efficiency index was estimated following physical production relationships derived from the Cobb-Douglas production function. Thus, the specific model estimated is given by Where: Y is total quantity of maize produced per hectare (kg); X1 is the amount of seed planted (kg); X2 is the amount of DAP applied; X3 is amount of UREA applied in maize by a household; land allocated to maize production (ha) by a given household; X5 is human labour used by a given household in maize production (person days); is oxen power used for maize production; is constant and Ui is error term. In order to make this function suitable to estimate by using the Ordinary Least Squares method, the function was linearized using logarithm and gave the following regression specification: Where and βi are parameters to be estimated. According to Chukwuji (2006), allocative efficiency analysis is done by estimating a Cobb-Douglas production function using OLS. It is followed by computing the value of the marginal product (VMPi) for each factor of production, which then is compared with the marginal input cost (MICi). Results from equation (4)   y is the geometrical mean of maize output  xi is the geometrical mean of input i and  βi will be the OLS estimated coefficient of input i. Since geometric mean is used to multiply several quantities of input together to produce a product (combine data values with a product instead of a sum as arithmetic mean), it's preferred to arithmetic and harmonic mean. The value of marginal product of input I (VMPi) was obtained by multiplying marginal physical product (MPi ) by the price of output (Py). Thus, Finally, allocative efficiency was calculated as follow: Where: Pi = Marginal cost of the i th input (unit price of input).
According to Grazhdaninova and Lerman (2004), allocative efficiency is determined by comparing the value of marginal product of input I (VMPi) with the marginal factor cost (MFC ). Since farmers are price takers in the input market, the marginal cost of input i approximates the price of the factor i, Px . Chavas et al. (2005) stated that, ifVMPi > P 8 , the input is under used and farm profit can be raised by increasing the use of this input. Conversely, ifVMPi < P 8 , the input is overused and to raise farm profits its use should be reduced. The point of allocative efficiency (maximum profit) is reached when VMPi = P 8 .

Stochastic frontier model
In this study, Cobb-Douglas production stochastic frontier which independently proposed by Aigner et al. (1977) and Meeusen and Van den Broeck (1977) was assumed to be appropriate model for the analysis of technical Journal of Natural Sciences Research www.iiste.org ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online) Vol.9, No.23, 2019 efficiency of the maize farmers. The basic advantage of the model is that it enables us to simultaneously estimate the farmers' productivity and determinants of technical efficiency (Battese and Coelli, 1992). The stochastic production function is defined as: Y is maize output (kg/ha); X is Vector of input quantities; β is Vector of unknown parameters; and ε is stochastic disturbance/error term consists of U and V.
Based on the factors of production, the Cobb-Douglas stochastic production frontier was specified as follows: From this equation, the linear form of this production function was expressed as follow: Where: Y is total quantity of maize produced per hectare (kg); X1 is the amount of seed planted (kg); X2 is the amount of DAP applied; X3 is amount of UREA applied in maize by a household; land allocated to maize production (ha) by a given household; X5 is human labour used by a given household in maize production (person days); is oxen power used for maize production; is constant; and vi is the measurement errors in input use and/or yield. ui is also a non-negative truncated half normal, F(0, H I ) random variable associated with farmspecific factors, and technical inefficiency of the farm and ranges between zero and one. It measures the shortfall in output from its maximum value given by the stochastic frontier. A truncated distribution is a conditional distribution resulting when the domain of the parent distribution is restricted to a smaller region. As a result, truncated normal distribution was used in this study, due to the efficiency score is ranged between 0 and 1. Technical efficiency was estimated by maximum likelihood method and efficiency levels were predicted from the stochastic frontier production function estimation. Therefore, the log likelihood for the normal-truncated normal model was specified as follow: Economic efficiency was determined from the estimation of system equations composed of a production function and of the order conditions of the production cost minimization which developed by Schmidt and Lovell (1979). It was measured using Cobb-Douglas stochastic frontier cost function for maize production by using the maximum likelihood method. For a given level of production, the economic efficiency is measured by the ratio of minimum cost to the observed cost.
Its Cobb Douglas frontier dual cost function with double log form can be written as follow: Where: h is cost of production of the mn farm (ETB); Yi is output of the mn farm (kg); W1 is wage or price of the mn farm input per unit of measurement; and g = Constant.
Since economic efficiency is the product of allocative and technical efficiency, economic efficiency and technical efficiency is the basis for measuring farm specific allocative efficiency (i.e., AE=EE/TE). The allocative efficiency obtained was regressed on socio-economic and institutional factors by using Tobit model as specified below:

Result and Discussion Estimation of allocative efficiency
The farmers' allocative efficiency estimates of their production resources were presented in table 4.1 To enable this estimation, marginal physical product, value of marginal product, and marginal factor costs (unit price of input factors) were determined.
The results of allocative (resource use efficiency) are presented based on the following criteria; when AE =1, resources are optimally utilized, when AE < 1, resources are over utilized and when AE > 1, resources are underutilized.
The result presents that the efficiency indicator (AE=21.31) of seed took a positive sign which shows that planted seeds were being underutilized. To use seed efficiently, farmers need to increase the amount of seed which has high quality and disease resistance traits.
The efficiency indicator (AE=4.15) of planting fertilizer (DAP) took a positive sign which portrayed that planting fertilizer is underutilized. A farmers is said to be allocative efficient at the optimum, they need to increase the use of planting fertilizer from the current quantity they are using. That means when they increase the amount of planting fertilizer from the current level, they become efficient maize producer. This implies that planting fertilizer is very important and has a significant effect on maize output.
The efficiency indicator of land size allocated for maize production is less than one (AE=0.94), which suggests that lands were over utilized. The value of the marginal product of land was less than its costs. Accordingly, land was not optimally used and farmers should reduce the expenditure on rented land to obtain optimum utilization of land.
The efficiency indicator of top dressing fertilizer (TDF) is -2.84, which showed that maize farmers were not only grossly inefficient in the use of top dressing fertilizer but also the marginal value of overusing it was negative. This requires using the required amounts of top dressing fertilizer to become an efficient or optimal point of using it. This reduction should be done only up to the level where AE equals to one and positive. This implies that miss utilization of fertilizers affects productivity negatively.
The efficiency indicator for labour (AE=1.54), shows that maize farmers are underutilized the labour resource. To obtain the optimum value of labour use, it is required to increase the labour use per man-day. This finding also consistent with the findings of Nzomoi (2006) who identified that the amount of labour force employed by a producer significantly influences the amount of average output and profitability. Thus increased family labour to an optimal level of one man hour per day not only leads to improved maize output and profitability but also reduces the problem of marginal product of labour is less than the average value of goods and services consumed by the family member.
The result also showed that return to the scale of this production is 0.992 which shows maize production in the study area follows decreasing return to scale. It implies that output increases less than proportionately as all inputs increase proportionately. That means output was increased by less than increased (doubled) input, which arises from inefficiently allocating resource.

Determinants of Allocative Efficiency
The mean of allocative efficiency score was 79.49% which indicated that on average maize producer farmers in the study area used resource 79.49% efficiently and 20.51% of inputs were used below the optimal allocative efficiency level. There is a chance to increase the efficiency of maize producers by reallocating resources in cost minimizing way. The result suggests that the farmer with an average of allocative efficiency would enjoy a cost saving of 15.71% (i.e. 1-0.7949/0.943) to attain the level of the most allocatively efficient household. The most allocatively inefficient farmer would have an efficiency gain of 49.95% (i.e. 1-(.0.472/0.943)) to attain the level of the most efficient farmer. Table 4.2 presents the results of censored Tobit model regression of selected socio-economic and institutional support factors against farm allocative efficiency scores. Among the selected variables, experience, livestock holding, and extension visit was not significant, while the others were significant determinants of allocative efficiency.
Journal of Natural Sciences Research www.iiste.org ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online) Vol.9, No.23, 2019 As the result presented that allocative efficiency was positively and significantly influenced by education at 5% level. It indicates that allocative efficiency requires better knowledge and skills, which shows an educated farmer have better capacity in the optimal allocation of inputs than uneducated farmer. That means skilled farmers to have better skills of managing farm operations and understand new technologies that increase their production. This result is in line with the finding of Musa (2015), Kebede (2001), Saulos (2015 and Amaza and Olayemi (2000), stated education is an important factor in enhancing efficiencies of maize producer in the study; since educated farmers are access with improved and new technology which enhances productivity.
The result showed that farms size positively and significantly affect allocative efficiency at 5% level. It indicates that an increase in the farm size by a unit would increase the farm allocative efficiency by 2.8%. The result is consistent with the finding of Musa (2015) and Saulos (2015), found that a unit change in farm size would result a positive change in the probability of a farmer being allocatively efficient. As well as Bravo-Ureta and Pinheiro (1997) of Dominican Republic and Wadud (2003) of Bangladesh found that larger farmers tend to be more efficient in allocating inputs than small.
The result presented that age of the household have negative coefficient, and significantly affected allocative efficiency at 10% level. The result showing that one year increase in the farmer's age reduce the level of allocative efficiency by 1.4%. As the age of farmer's become increase and older, their ability to allocate resource appropriately would decrease. But it doesn't mean as the age of farmers in working age group increase, it reduces their ability of allocating resource efficiently. Because as their age was increased their ability of allocating farm input also increase until they become out of working age group and tired, and then decrease. Sex of household head was also found to have a negative and significant effect on allocative efficiency at 10%. It implies that maleheaded household less allocatively efficient than a female-headed household.
The experience of a household was affected allocative efficiency positively but not significant. It implies that a one year increase in the farmer's experience would increase allocative efficiency by 1.5%. That means more experienced farmers are appropriately allocated resource than less or inexperienced farmers. This result was in line with the finding of Nwachukwu and Onyenweaku (2009). Arrow (1972) stated in the literature of "economic implication of learning by doing" that management experience can guide to gain efficiency through better organization and knowledge of the results of experimenting with alternative production techniques.
The coefficient of livestock holding was positive and affected allocative efficiency positively. It indicates that a farmer who has livestock more allocative efficient by 2.9% than who doesn't have a livestock. Livestock has many contributions to farm activity because by selling them, farmers could purchase enough farm inputs. It's in line with the finding of Musa (2015), Kifle (2017) andSaulos, (2015), were found that livestock holding positively affect the allocative efficiency of farmers'. However, it is inconsistent with the finding of Bealu (2013).
Participation of households in off-farm income negatively and significantly affected allocative efficiency at 10% level. This indicates that a farmer who participates in off-farm income at farm season less allocatively efficient than who doesn't participate. The participations of households in non-farm activity was reallocate time away from farm and so less attend allocative efficiency enhanced activities which were given by agricultural development agency. The result is consistent with the finding of Bealu (2013), Musa (2015), and Kibaara (2005). But inconsistent with the finding of Kifle (2017) stated that off farm income help to improve allocative efficiency of farmers by overcoming financial constraint. However, off-farm income affects negatively allocative efficiency since they drop farm activity and go to do none farm activity. As a result, it is better if they participate in off-farm income generating activity at none farm seasons than at regular farm season. That means farmers doing none farm income generating activity by the opportunity cost of farm season which in turn harm efficiency of farmers.
According to the result presented, household size has negative coefficient and significantly affected allocative efficiency at 5% level. This implies that large households reduce the level of allocative efficiency of farmers by reducing farm income by putting extra pressure on farm income for food, clothing and education. The result is consistent with the finding of Nwachukwu, and Onyenweaku (2009) found that larger family size endangers reduction in the magnitude of allocative efficiency.
The result also showed that distance to the market positively affected allocative efficiency and significant at 5% level. This implies that when market distance increase by 1km the allocative efficiency of farmers could increase by 0.9%. Since long market distance by itself restricted the frequency and interest of farmers went to the market in a week, they didn't went many times in a week than once a week or by a two week, and enforce as they expended more time and put their full attention on farm activity than try to do other activity besides at farm season which harms allocative efficiency (i.e. off-farm income). But those found nearest to the market went many times in a week and also do off-farm activity as well as share their time and attention between off farm income and farm activity. As a result, they couldn't be allocatively efficient as those found far away from the market, but the supply of input (input market) is mandatory to found nearest to farmers than other markets. Because the opportunity cost of found nearest to the market is off-farm income which negatively affect allocative efficiency of the farmer.
According to the result revealed, coefficient of credit utilization was negative and significant at 5% level. It might be due to the amount of available credit doesn't cover the cost of input; consequently, farmers bought little Journal of Natural Sciences Research www.iiste.org ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online) Vol.9, No.23, 2019 33 inputs and inefficiently allocate it. The result is consistent with the finding of Nwachukwu and Onyenweaku (2009) have observed a significant negative relationship between the access of credit and allocative efficiency. Their argument was that inaccessibility of credit acts as a constraint in timely purchases of inputs and engagement of farm resources and thus puts an obstacle in improving the allocative efficiency in agriculture. Note: *, **, and *** represents the significant at 10%, 5% and 1% level.

Conclusion and Recommendation
The study concluded that maize farmers in the study area were not fully allocatively efficient in their production activities that need to increase this productivity of maize significantly. Allocative efficiency was significantly affected by education, farm size, livestock holding, and market distance, off farm income, and credit utilization. Based on the finding f the study, it is recommended that extension service experts should focus on training of the farmers on improved production management to enable as they use the existing resources efficiently and increase the productivity of maize. The Government should give due attention for farmers training through strengthening farmers' education and farmer training centers to make farmers more efficient producers and profitable by integrating local and traditional knowledge of farmers with formal knowledge. Farmers should be advised as they didn't work off-farm income generating activity at farm season. If they face a financial constraint, they should have to use credit and credit provider should give enough credit on time. Otherwise, the government should supply fertilizer and improved seed on credit.