Gadisa Girma¹*, Nigusu Abera ², Yimenu Kassa³, Zewditu Berhun⁴, Abi Tolosa5, Genet Shiferaw⁶ 

¹ Department of Agricultural Ecoomics, Salale University, Ethiopia (Email: gadisag2@gmail.com; Phone:  +251924031078) 

²Department of Agricultural Economics, Salale University, Ethiopia (Email: boonaaifaa@gmail.com), ³ Department of Agricultural Economics, Salale University, Ethiopia (Email: baymfbt@gmail.com) ⁴Department of Agribusiness and Value Chain Management, Salale University, Ethiopia (Email:  zewditube23@gmail.com) ⁵ Department of Animal Science, Salale University, Ethiopia (Email: abitolossa6@gmail.com)  ⁶ Department of Agricultural Economics, Salale University, Ethiopia (Email: iyaya2007@gmail.com)

ARTICLE INFORMATION	ABSTRACT
*Corresponding author:  Gadisa Girma  E-mail: gadisag2@gmail.com   Keywords:  Efficiency  Ethiopia  Milk  Stochastic Frontier  Two-limit Tobit	This study aimed to estimate economic efficiency levels and identify its  determinants for milk producers’ households in North Shewa Zone, Oromia Region, Ethiopia. Three stages random sampling technique was used to select  400 sample farmers. The data were analyzed using descriptive statistics and an econometrics model. The result of the stochastic frontier model showed significant and positive elasticity of lactation cow, green forage, and crop  residue. The estimated mean values of technical, allocative, and economic efficiency were 58%, 77.6%, and 44.7% respectively. The yield gap due to  technical inefficiency was 9.6 liters per cow per day. A two-limit Tobit model  result shows that education, amount of concentrate feed used, grazing land,  type of breed, and frequency of extension contact contributed significantly  and positively to technical efficiency. Moreover, total land, dairy farm experience, dairy membership, and type of breed affect allocative efficiency significantly and positively while the amount of concentrate feed used had a  significant and negative effect on allocative efficiency. Economic efficiency is  also affected significantly and positively by education level, total land, grazing land, type of breed, and frequency of extension contact. To improve the  efficiency level of farmers, due attention should be given to the use of  concentrate feed, improving feed availability, adequate and proper management of grazing land, and using of improved breed and dairy  cooperatives.

ARTICLE INFORMATION ABSTRACT 

Ethiopia has the tenth-largest livestock inventory in the  World. The country has the largest number of livestock,  more than any other country in Africa. Ethiopia leads with a staggering 60.39 million cattle, while Tanzania, in the  second position, has an estimated total of 33.9 million cattle (Africa Census, 2020). Though Ethiopia has a large  livestock inventory, the productivity of cattle remains  low.  

According to Central Statistical Agency (CSA) (2020),  there are around 7.56 million dairy cows in Ethiopia. Of these, 15.04 million are milking cows. On average, each  cow produces 1.48 liters of milk daily. Nathaniel et al.  (2014) indicated that dairy inputs and service provisions  are still at the infant stage and the development of  improved dairy cows is limited in the country.

The  increase in milk production may have come mostly from  the increased number of cows rather than increased  productivity. Nega and Simeon (2006) indicated the  inefficiency among smallholder dairy producers due to  the inefficient use of scarce resources. Understanding the  existence of inefficiency and different factors  contributing to the inefficiency by farmers and  policymakers helps to improve efficiency with a view to  bringing a desired change in the sector. However, most  efficiency studies in agricultural economics focus on  technical efficiency, which is just one component of  overall economic efficiency.

Focusing only on technical  efficiency (TE) understates the benefits that producers  could from improvements in overall performance. Unlike  technical efficiency, research done on economic  efficiency, especially in milk production is limited. In  addition, many empirical studies did not consider yield  gaps because of technical inefficiency among milk  producers.  

North Shewa Zone, Oromia Region in Ethiopia has milk  production potential, and the demand for milk and milk  products has been increasing while output is not able to  meet the higher demand. Moreover, there is an output  difference among dairy producers.

Dairy producers have  little knowledge of how to use minimum cost (cost  efficiency) in the study area. Therefore, knowledge about  the level of economic efficiency of smallholder milk  production and the underlying socio-economic and  institutional factors causing inefficiency may help to  assess the opportunities for increasing milk production.  Additionally, to the best of knowledge, no studies have  been conducted in the area of economic efficiency (EE) of  milk production, especially in the study area.

Hence,  there is a need to fill the existing knowledge gap by  addressing issues related to technical, allocative  efficiency (AE), and EE of smallholder milk production in  the study area by providing empirical evidence on  smallholder milk producers. Therefore, the objective of  this study was to estimate economic efficiency levels and  identify the determinants for milk producer households  in North Shewa Zone, Oromia Region, Ethiopia. 

METHOD AND MATERIALS 

Study Area 

This study was conducted in the North Shewa Zone of  Oromia Regional state, Ethiopia due to its high potential  

in milk production. It has a total of 13 districts and is  bordered on the South by Oromia Special Zone  Surrounding Addis Ababa, on the South West by West  Shewa, on the North by the Amhara Region, and on the  South East by East Shewa. 

Sampling Techniques and Sample Size  Determination 

Three stages of random sampling procedures were  employed to draw a representative sample. In the first  stage, four districts, Degem, Wuchale, Debra Libanos, and  Girar Jarso, out of 13 milk producing districts in the zone,  were purposively selected.

In the second stage, two  kebeles from each district, with a total of eight kebeles  from four sampled districts, were selected purposively  due to their high dairy production potential. In the third  stage, 400 sample farmers were selected using a simple  random sampling technique based on probability  proportional to the size of milk producers in each of the  eight selected kebeles. The sample size was determined  by using the formula provided by Yamane (1967). 

Accordingly, the sample size for the study is determined  based on the following formula: 

Where, n = sample size (including the non-response rate  of 1%), N = Total milk producers in the study area, and e  = Level of precision considered. 

Table 1: Sample size distribution 

No .	Name of  sampled  district	Total  household  milk  producers	Sampled  househol d	Proporti on (%)
1	Degem	5570	60	15.00
2	Wuchale	13880	149	37.25
3	Debralibanos	4273	46	11.50
4	Girarjarso	13520	145	36.25
Total		37243	400	100

Source: North Shewa Livestock and Fishery Development Office  (2020) 

Types, Sources, and Methods of Data Collection 

The research is accomplished using primary and  secondary data sources, which are qualitative and  quantitative in nature. The primary data necessary to  achieve the designed objectives were obtained from  sample households through a structured questionnaire  for sampled households and a checklist for focus group  discussion and key informants interviews. Secondary data was collected from relevant sources such as articles,  proceedings, journals, CSA, and district annual reports  which were vital to the study. 

Data measurement 

i. Output variable: It is defined as the actual quantity of  milk produced and measured in liters (L) during the 2020  production year by sample households. This is a  dependent variable of the production function taken as a  continuous variable. 

ii. Input variables: Defined as the total inputs used by  sample household in the production of milk namely:  lactation cow (number), labor (Man-day), Green forage  (beli), and crop residue (beli) in the 2020 production year  (1beli=1kg).  

iii. Dependent variables: The dependent variables for this  study are; TE, AE, and EE scores of milk production  obtained from the stochastic frontier function.

iv. Inefficiency variables 

1. Sex: This is a dummy variable that was measured as 1  if the household head is male and 0, otherwise. 

2. Education: It is a continuous variable that is defined as  the education level of the sample household head. This  variable was measured in terms of years of schooling.

3. Concentrate: the total amount of concentrate used by  sampled households to produce milk in quintals (Qt). 

4. Total land: refers to the total area cultivated (owned,  shared, or rented in) land that the sample household  managed during the 2020 production year measured by a  hectare (ha).  

5. Extension: The frequency of extension agents contacting farmers and vice versa, measured by the  number of contact per production year.  

6. Grazing land: it refers to the total grazing land area  allotted by the sample household for cow milk production  during 2020 that was measured in ha.  

7. Type of breed: It is a categorical variable that takes a  value of 1 if the farmers use local breed, 2 if the farmers  use both local breed and cross-breed, and 3 if the farmers  use cross-breeding cows. 

8. Dairy experience: It is a continuous variable and refers  to the total years that the household participated in milk  production, which is measured in years.  

9. Distance: It is defined as the distance of the nearest market from the house of the household head in walking  minutes.  

10. Membership: It is the dummy variable that takes a  value of 1 if the sampled farmer is in a dairy cooperative  member and 0 otherwise.  

11. Feeding method: It is a dummy variable equal to 1 for  the farm that uses the total mixed ratio (TMR) and 0 if the  farm uses the pasture feeding method.  

12. Housing System: It is a dummy variable that takes 1  for farms that use free stall housing and 0 otherwise. 

Method of Data Analysis Descriptive statistics 

Descriptive statistics such as mean, minimum, maximum,  percentages, frequencies, and standard deviation or  standard error were applied to describe demographic,  socio-economic, farm characteristics, institutional  characteristics, and distribution of efficiency levels of milk producers in the study area. After coding and feeding the  collected data into the computer, STATA version 15 was  used for the analysis. 

Econometric analysis 

Specification of an econometric model 

Coelli et al. (1998) recommended that the Stochastic  Frontier Production Function (SFPF) is more appropriate  than DEA and deterministic models in agricultural  applications, especially in developing countries, where  measurement errors generally influence the data are  generally influenced by measurement errors and the  effect of weather, disease, and pests play a significant  role.

Some researcher argues that Cobb-Douglas  functional form has advantages over the other functional  forms in that it provides a comparison between the  adequate fit of the data and computational feasibility. It  is also convenient in interpreting the elasticity of  production and it is very parsimonious with respect to  degrees of freedom and it is convenient in interpreting  elasticity of production. 

In addition, the Cobb-Douglas production function is  attractive due to its simplicity and because of the  logarithmic nature of the production function that makes  econometric estimation of the parameters a simple  matter.

The translog production function is more  complicated to estimate the parameters having serious  estimation problems. One of the estimation problems is as the number of variable inputs increases, the number of parameters to be estimated increases rapidly. Another problem is the additional terms require cross-products of  input variables, thus making a serious multicollinearity  problem (Coelli, 1995). Therefore, this study used  stochastic production frontier to estimate the TE, AE, and  EE levels of smallholdermilk-producing farmers in the  study area. 

Following Aigner et al. (1977) and Meeusen and Van den  Broeck (1977), the general functional form of the  stochastic frontier model for this study is specified as  follows: 

Where z = 1, 2, 3… n; Yz represent the observed milk  output level of the zth sample farmer; f (Xz; βz) is the  convenient frontier production function (e.g. Cobb 

Douglas or Trans log); Xz denotes the actual input vector  by the zth farmer; βz stands for the vector of unknown  

parameters to be estimated; ɛz is a composed disturbance term made up of two error elements (Vz and  Uz) and n represents the number of farmers who will  involve in the survey. 

The stochastic frontier functional approach requires a  priori specification of the production function to estimate  the level of efficiency. Among the possible algebraic  forms, Cobb-Douglas and trans-log functions were the  most popularly used models in the most empirical studies  of agricultural production analysis. Therefore, the Cobb Douglas production function was adopted for this study.  Thus, the Cobb-Douglas frontier function was specified as  follows: 

The linear form of Cobb-Douglas production functions for  this study was defined as: 

Where, ln denotes the natural logarithm (i.e., base e); j  represents the number of inputs used; z represents the  zth farm in the sample; Yz represents the observed milk  output of the zth sample farmer; Xjz denotes zth farm  input variables used in milk production of the zth farmer;  β_0 represent intercept; β_1-β_4 stands for the vector of  unknown parameters to be estimated and represent  elasticity of milk production; Ɛz is a composed  disturbance term made up of two error elements (Vz and  Uz); the symmetric component (Vz) is assumed to be  independently and identically distributed as random  errors with zero mean and variance N (0, σ2v), which  captures inefficiency as a result of factors beyond the  control of farmers and Uz proposed to capture  inefficiency effects in the production of milk. 

Assuming that the production function in equation (4) is  self-dual. Cobb Douglas), the dual cost function of the  Cobb-Douglas production function can be specified as:

Where z refers to the zth sample farm; j is the number of  inputs; Cz is the minimum cost of production; Wjz denotes input prices of z th farm; Y* refers to milk output  in litre; α’s are parameters estimated; Vz denotes random  variables assumed to be independent and identically  distributed random errors with zero mean and variance  and Uz denotes non-negative random variables which are  assumed to account for cost inefficiency and assumed to  be independent and identically distributed random errors  with zero mean and variance. 

Sharma et al. (1999) suggest that the corresponding dual  cost frontier of the Cobb-Douglas production functional  form in equation (5) can be rewritten as: 

The economically efficient input vector of the zth farm  Xze is derived by applying Arega and Rashid (2005) and  substituting the firms input prices and adjusted output  level, a system of minimum cost input demand equation  can be expressed as: 

We can define the farm-specific TE in terms of observed  milk output (Yz) to the corresponding frontier milk output  (Y*) using the existing technology. 

The cost efficiency of an individual farm is defined in  terms of the ratio of the observed cost (C) to the corresponding minimum cost(C*) given the available technology. That is, cost efficiency (CE): 

Where the observed cost (C) represents the actual  production cost whereas the minimum (efficient) cost  (C^* ) represents the frontier total production cost or the  least total production cost level. 

The farm-specific AE is defined as the ratio of minimum  total production cost (C*) to the actual observed total  production cost (C). Following Ali et al. (2012), the EE index was derived from  equations (8) and (9) as follows: 

Determinants of inefficiencies 

Where: , a latent variable representing the efficiency scores of farm z (TE, AE and EE); intercept;  β_kunknown parameter; Xkz are demographic,  institutional, socio-economic and farm-related variables  which are expected to affect TE, AE and EE; k is a number  of explanatory variables that affect TE, AE and EE and Uz are an error term that is independently and normally  distributed with mean zero and variance σ².

 

Likelihood ratio statistic 

Aigner et al. (1977) proposed the log likelihood function  for the model in equation (3) assuming normal  distribution for the technical inefficiency effects (Uz).  They expressed the likelihood function using λ  parameterization, where λ is the ratio of the standard  errors of the non-symmetric to symmetric error term (i.e.  λ= σ U/ σ v). According to Bravo and Pinheiro (1997)  gamma (γ) can beformulated as: 

In this study, the likelihood ratio test was conducted to  select the appropriate functional form that best fits the  data. The value of the generalized likelihood ratio (LR)  statistic to test the hypotheses that all interaction terms,  including the square specification, is equal to zero (H0:  βjz=0) was calculated as follows. 

Following Greene (2003) the hypothesis tests were  conducted using the log-likelihood ratio (LR) statistics, λ  which is defined in equation (14): 

Where: LR= Generalized log-likelihood ratio L (H_o) = Denotes the likelihood function value under the  null (Ho) L (H₁) = Denotes the likelihood function value under the  alternative hypothesis (H₁) 

This value was compared with the upper 5% point for the  χ^2distribution and the decision was made based up on  the model result. If the calculated χ^2 value is less than  the tabulated upper 5 percent point of the critical value,  we accept the specified null hypothesisis at a 5 percent  level of significance. 

Milk yield gap 

Yield gap is the difference between yield potential and  actual farmers’ yields over a given spatial or temporal  scale (Ittersum et al. 2013). The study measured the milk  yield gap to determine how much milk output is lost  because of inefficiency variation among milk-producing  farmers in the study area. From the stochastic model  defined in equation (15), TE of the zth farmer was  estimated as follows. 

Then solving for , Yz the potential milk output  (liter/cow/day) of each sample household is represented as: 

TEz= technical efficiency of the zth sample household in  milk production the frontier or potential output of the z^th sample household in milk production in liter/cow Yz=the actual or observed output of the z^th sample  household farmer in milk production in liter. Hence, milk  yield gap (liter/cow/day) =potential yield (liter/cow/day)- actual yield (liter/cow/day). 

Thus, Milk Yield gap = – Yz…………………………………………………………………………(16) 

RESULTS AND DISCUSSIONS 

Descriptive Statistical Results 

Table 2 below shows that about 10.75% of the sample  households were female-headed and the remaining  89.25% were male-headed. It was understood that  female-headed households in rural areas in Ethiopia face  more challenges in dairy production and marketing  compared with their male-headed counterparts.

This is  partly due to cultural barriers and their busy schedules as  they are engaged in domestic, reproductive, and  community roles. Moreover, from the total sampled  household, 2.5%, 50%, and 47.5% are using local, both  local and cross breed and cross breed milking cows in the  study area respectively. This indicates that the majority  of the sampled household use both crossbreed and local  as well as crossbreed only.

Table 2 also illustrates that  69.5% of the sampled household use free stalling while  30.5% do not use free stalling. The result shows that most  of the sampled farmers use free stalling in which cows are “free” to move around to eat, drink and rest wherever  they like. These barns provide easy access to feed and  clean water, as well as shade and protection from  inclement weather which in turn increase the  productivity of the milking cow.

The feeding method is  important to improve the productivity of the milking  cows there by the associated efficiency would increase  than pasture feeding method. The study shows that from  the sampled household, 76% use total mixed ratio while  the rest 24% not use. The finding implies that most of the  sampled milk producers use total mixed ratio in the study  area. Related with dairy membership, around 75.25% of  the sampled households are not participating in dairy member while 24.75% are participating in dairy  cooperative member.

This indicates that the majority of  the sampled household in the study area are not  participate in dairy membership. Farmer who participates  in dairy cooperative can get different information,  training, market access and etc. this leads them to  become more efficient than who do not participate in  dairy cooperative member. 

Table 2: Descriptive statistics of dummy variables 

Variables	Description	Frequency	Percen t
Sex	Male	357	89.25
	Female	43	10.75
Type of breed	Local	10	2.5
	Both	200	50
	Cross	190	47.5
Housing system	Not	122	30.5
	Free stall	278	69.5
Feeding method	Not	96	24
	Total mixed  ratio	304	76
Dairy membership	Not member	301	75.25
	Member	99	24.75

Source: Own computation (2020) 

In Table 3 below the descriptive statistics of total land,  grazing land, amount of concentrate feed used,  frequency of extension contact, distance of the from  home to the nearest market and Total livestock owned  were discussed. 

Land is the main resource needed by the milk producers  to earn their livelihoods. Farmers use most of their land  for crop production. The average total land of the  sampled milk producers’ was about 2.24 ha (Table 3). The  result implies that households in the study area have  relatively larger land size compared to that of the national  average of farmers in Ethiopia which is 1.2 ha. If total land  increases, dairy cows gets more outputs from crop  production (stover of sorghum, teff, wheat, fababean,  and etc) to feed their cows. 

Grazing land is the main resource needed by the farmers  to feed their livestock (like milking cow) which is the main  source of feed by providing different fodder, grasses and  etc. The average total grazing land of the sampled milk  producers was about 0.48 ha with a minimum of 0 ha and  3ha (Table 3). Farmer who has large grazing land has the  opportunity to get high yield of milk than the others in  the study area since grazing land provides feed for  lactation cows. 

Concentrate is one of the types of feed used in most of  milk producers in the study area which is used to increase  the production and productivity of lactation cow. The study indicates that, on average, the sampled farmers use  20.58qt of concentrate feed for cows per lactation period  with a minimum of 0 (not used) and maximum of 1300qt  (Table 3). This implies that most dairy farmers in the study  area use concentrate feed for their milking cows as feed  to get more milk productivity per day and per lactation  period. 

Extension work in the study area focuses on the provision  of general advisory services on major dairy production  practices (such as proper feeding system, housing system,  veterinary services on timely and how farmers manage  their milking cows day to day), and also give how the  farmers become dairy cooperative member to get  different information especially on the price of milk. 

Development agents have been giving extension services  in their respective field of specializations. They are  required to advice and follow up their farmer’s dairy  farm. The survey result also indicated that frequency of  extension contact in 2019/20 production year(lactation  period) was on average about 4.34 with the maximum  contact of like 24 times and minimum 0 times (no  contact) times per lactation period (Table 3). 

Distance is the time span required to reach the nearest  market from homestead of the milk producers farmers  and is essential variable in explaining the capacity of the  farmers’ performance. And it refers to how long time it  takes (in walking minutes) for a dairy farmers to sell their  milk and buy different inputs such as concentrate feed. It  is an important variable due to the fact that as the  farmers’ home located far from nearest market, there  would be limited access to get inputs easily and on timely  which is very important in dairy production.

Moreover  farmers whose house is near to the market can easily get  information on price of milk and provide also their  product to the market in a short period of time. The study  illustrate that distance from home to the nearest market  in man walking minute was on average 45.84 with the  maximum 180 minutes and minimum 1 minutes in the  study area (Table 3). 

Given a mixed farming system in the study area, livestock  has imperative contribution for household income and  food security. This income is very important especially to  buy feeds for milking cows. The type of livestock kept by  sampled farmers includes cow, oxen, bull, horse, mule,  donkey, calf, goat, and heifer.

Among others, oxen power  is the major input in crop production process serving as a  source of draft power which at the end produce different  crop by products that is used as fodder for milking cows.  On average, the livestock holding of the sampled farmers  in the study area was 4.69TLU per household with a minimum of 0 (no livestock other than milking cows) and  a maximum of 17.77 in TLU (Table 3). 

Table 3: Descriptive statistics of continuous variables 

Variable description	Mean	Std.  Dev.	Minim um	Maxim um
Family size(AE)	3.86	1.63	1	9.05
Education (year of  schooling)	3.69	3.84	0	15
Dairy farm  experience(years)	14.96	10.73	1	60
Total land(ha)	2.24	1.72	0.125	10
Grazing land(ha)	0.48	0.46	0	3
Amount of  concentrate feed  used(qt)	20.58	77.68	0	1300
Frequency of  Extension(number)	4.34	14.29	0	24
Distance from home  to market(minute)	45.84	31.75	1	180
Total livestock  owned (TLU)	4.69	2.67	0	17.77

Source: Own computation (2020) 

Inputs used for milk production and cost function 

The production function for this study was estimated  using four input variables. On average, sample  households produced 4989.03 lit of milk per lactation  period, which is the dependent variable in the production  function. The number of lactation cows, by sample  households during the study, ranged from 1 to 9 with an  average number of 2.94.

On average, the amount of  human labour, green forage, and crop residue used by the  sampled milk producers was 717.45 man day (MD), 202.3  qt, and 38.2 qt respectively(qt=quintals). Among the  various cost factors of production, the cost of lactation  cow accounted for the highest share (56112.5 birr). 

Following the cost of lactation cow, the cost of labor takes  a major share out of the total cost of production which is  21523 birr. Besides, the cost of crop residue takes the  smallest share (3152.56 birr) out of the total cost of milk  production (Table 4). 

Econometric Results 

Hypothesis Testing 

The first null hypothesis tested was test for the selection  of the appropriate functional form for the data; Cobb Douglas versus Translog production function. The  functional form that can best fit the data was selected by  testing the null hypothesis. The result indicated that the  null hypothesis was accepted and Cobb-Douglas functional form best fits the data. The second null  hypothesis tested was the test for the existence of the  inefficiency component of the composed error term of  the Stochastic Frontier Model (SFM).

This is made in order  to decide whether the traditional average production  function (OLS) best fits the data set as compared to the  stochastic frontier model selected for this study. The  result showed that the SFPF was an adequate  representation of the data.

The third null hypothesis is  explored that farm-level technical inefficiencies are not  affected by the farm and farmer-specific variables,  and/or socio-economic variables included in the  inefficiency model. The result indicated that the null  hypothesis is rejected in favor of the alternative  hypothesis that explanatory variables associated with the  inefficiency effect model are simultaneously not equal to  zero. Hence, these variables simultaneously explain the  difference in efficiency among sampled farmers (Table 5). 

Table 4: Summary statistics of variables used to estimate  milk production and cost function 

Variable	Unit	Mean	Std.  Dev.	Mini mum	Maximu m
Milk  output  per  lactation	Liter	4989. 03	5161. 66	300	48000
Lactation  cow	Numb er	2.94	2.03	1	9
Labor	(MD)	717.4 5	410.7 6	54	3078
Green  forage	Beli	202.3 0	1243. 97	2	24300
Crop  residue	Beli	38.20	59.74	1	560
Cost of  lactation  cow	Birr	5611 2.5	6339 4.22	8000	320000
Cost of  labor	Birr	2152 3	1232 2.82	1620	92340
Cost of  green  forage	Birr	1867 6.63	1064 05.1	160	2065500
Cost of  crop  residue	Birr	3152. 56	3775. 36	97.5	42000

Source: Own computation (2020) 

Parameter estimates of the SFPF model and cost  function 

The maximum likelihood estimate of the parameters of  the SFPF for milk producers in the North Shewa Zone was  presented in Table 6. The results of the model showed the  input elasticity for each input in the SFPF. Among four input variables analyzed in the stochastic frontier model,  the parameter for lactation cow and crop residue were  found to be significant at 10%, as hypothesized as well as  green forage was found to be significant at 5%. The  parameter estimate for labor turned out to be  insignificant. The insignificance of the estimated  coefficients for labor implies that the use of this input has  no significant effect on milk production in the study area. 

Table 5: Generalized likelihood ratio tests of hypothesis  for the parameters of the SFPF 

Null  hypothesis	Df	LR	χ2 value at  5%	Decision
H0 = βzj = 0	10	15.46	18.31	Accept H0
H0 = γ = 0	1	10.04	3.84	Reject H0
H0 : δ0 = δ1=δ2=. . δ12 = 0	12	149.3 8	21.03	Reject H0

Source: Own computation (2020) 

Table 6: MLE for the parameters of the SFPF 

Variables	Parameter	Coef.	Std. Err.
Intercept	β0	7.645	0.527
Ln lactation cow	β1	0.109*	0.062
Ln labor	β2	0.101	0.074
Ln green forage	β3	0.062**	0.084
Ln crop residue	β4	0.074*	0.039
Variance parameter:
λ = σu/σv		1.33	0.173
Gamma (γ)		0.64

Note: ** and * refers to 5% and 10% significance level,  respectively. 

Source: Model output (2020) 

The SFPF model results reveal that the estimated positive  and coefficient of lactation cow (0.109), green forage  (0.062), and crop residue (0.074) were found to be  significant and positive at 5% (green forage) and10%  (lactation cow and crop residue) probability level. This  indicated that lactation cows, green forage, and crop  residue were the most important determinant inputs of  milk production in the study area.

This suggests that a one  percent increase in lactation cow for milk production, all  things being equal, would lead to an increase of 0.109%  in the output of milk production. In the same way, on  average a one percent increase in the quantity of green  forage and crop residue, milk output would increase by  0.062% and 0.074% respectively. 

The diagnostic statistics of the inefficiency component  reveal that sigma squared (σ²) was statistically significant  at 5% which indicates the goodness of fit, and the  correctness of the distributional form assumed for the  

composite error term. The ratio of the standard error of  U (σ_u) to the standard error of V (σ_v), known as lambda  (λ), is 1.33. Based on λ, gamma (γ) which measures the  effect of technical inefficiency in the variation of  observed output can be derived (i.e.γ = λ²/([1+λ²])) (Bravo  and Pinheiro, 1997). The estimated value of gamma (γ)  was 0.64 which indicates that 64% of the total variation  in milk output from the frontier is due to technical  inefficiency among sample farmers in the study area and  36% of the variation in output from the frontier is due to  random noise or random error (beyond the control of the  farmers). 

The dual frontier cost function derived analytically from  the stochastic production frontier shown in Table 6 is  given by: 

Efficiency scores and their distribution 

The MLE results of the stochastic frontier production  functions are estimated for the individual farm level TE,  AE, and EE independently for sample smallholder  farmers. The model output presented in Table 7 indicates  that the mean TE of sample farmers was about 0.580 with  a minimum level of 0.156 and the maximum level of  0.842.

This means that if the average farmer in the  sample was to achieve the technical efficiency level of its  most efficient counterpart, then the average farmer  could realize 31.12% derived from (1-0.580/0.842)*100  increased milk output by improving TE with existing  inputs and technology, using the resource at their  disposal in an efficient manner without introducing other  improved or external inputs and practice. 

In addition, Table 7 shows that the average AE of the  sample farmers was about 0.776 with a minimum of  0.299 and a maximum of 0.979. This shows that farmers  are not allocatively efficient in producing milk. Hence, a  farmer with an average level of AE would enjoy a cost  saving of about 20.74% derived from (1 – 0.776/0.979)*100 to attain the level of the most efficient  farmer.

Similarly, the mean EE of the sample farmers was  0.447 implying that there was a significant level of  inefficiency in the production process. That is the  producer with an average EE level could reduce the  current average cost of production by 44.81% which is  derived from (1-0.447/0.810)*100 to achieve the  potential minimum cost level without reducing output  levels. It can be inferred that if farmers in the study area  were to achieve 100% EE, they would experience  substantial production cost savings of 44.81%. This low average level of EE was the total effect of both technical  and allocative inefficiencies. 

Table 7: Estimated TE, AE and EE scores 

Types of  efficiency	Mean	Std.  Dev.	Min	Max
TE	0.580	0.141	0.156	0.842
AE	0.776	0.148	0.299	0.979
EE	0.447	0.133	0.102	0.810

Source: Model output (2020) 

The distribution of the TE scores showed that about 47%  of the sample households had TE scores of 0.6 to 0.799.  11% of the households’ TE scores fell in the range of 0.2- 0.399. On average, households in this cluster have room  to enhance their milk production at least by 42%. Out of  the sample households, only 2% had a TE score of greater  than 0.8.

This implies that about 98% of the households  can increase their production at least by 20%. The AE  distribution scores indicated that about 59.25% of milk  producers operated above 0.8 efficiency level. The  distribution of EE scores also implies that 51.75% of the  household heads have an EE score of 0.4-0.599. This also  indicates the existence of substantial economic  inefficiency than technical and allocative inefficiency in  the production of milk during the study period in the  study area (Table 8). 

Table 8: Distribution of TE, AE, and EE 

Efficiency  range	TE		AE		EE
	Frequency %		Frequency %		Frequency %
<0.2	3	0.75	0	0	15	3.75
0.2-0.399	44	11	1	0.25	124	31
0.4-0.599	157	39.25	77	19.25	207	51.75
0.6-0.799	188	47	85	21.25	53	13.25
0.8-0.999	8	2	237	59.25	1	0.25

Source: Model output (2020) 

Yield gap due to technical inefficiency 

Yield gap analysis is an essential tool to measure to what  extent the production could be increased if all factors are  controlled. Using the actual output values of the  predicted TE indices, the potential output was estimated  for each household in milk production per cow per day.  Hence, the mean level of the actual and potential milk  yield per cow per day was 10.1 liter /cow/day and 19.7  liter /cow/day, respectively. Using the t-test method, the  mean difference of the actual and the potential yield was  found to be statistically significant at a 1% level of  significance. Therefore, the average milk yield gap that is  lost due to technical inefficiency, which was the mean  

difference between the actual (10.1 liter/cow/day) and  the potential output (19.7lit/cow/day) was,  9.6lt/cow/day (Figure 1). This indicates that there is room  to boost milk production on average by 9.6 liter/cow/day  with the existing level of input use. On average, the  money value of milk output that was lost due to technical  inefficiency (yield gap) was 153.6birr/cow/day, since the  value of 1lt of milk is 16 Ethiopian birr. 

Figure 1: Distribution of actual and potential level of  milk output 

Source: Own computation (2020) 

Determinants of inefficiencies 

The result of two- limit Tobit model (Table 9) for each  significant variable and its marginal effects of change in  explanatory variables (Table 10) on TE, AE, and EE were  discussed as follows. 

Educational 

The findings of the study show that education affected TE  and EE of milk producers significantly and positively at 1%  significance level. The positive sign implies that more  educated farmers tend to be more efficient in milk  production than the less educated in the study area.

This  is due to the fact thatbetter-educatedd household heads  can use dairy technology easily and are able to apply  technical skills imparted to them. Aone-yearr increase in  the educational level of the household head increases the  probability of a farmer being technically efficient and  economically efficient by 0.34% and 0.01%, and the mean  values of technical and economic efficiencies by about  0.92% and 0.97% with an overall increase in the  probability and levels of technical and economic  efficiencies by 1%, and 0.98%, respectively. The result  agreed with the finding of Al-Sharafat (2013). 

Total land 

The result indicated that total land was a positive and  significant effect on AE and EE at a 1% level of significance  as expected. This implies that, total land is an important  factor in influencing the level of AE and EE in the  production of milk or positively contributes to AE and EE of milk production in the study area.

This implies that  households who have more land were relatively better in  AE and EE. A unit increase in total land (ha) would  increase the probability of the farmer being AE and EE by  about 1.09% and 0.01% and the expected values of AE  and EE by about 0.94% and 0.86% with an overall increase  in the probability and levels of AE and EE by 1.13% and  0.87%, respectively. 

Dairy experience 

Experience significantly and positively affected AE of  sampled households at 10% level of significance, which is  in line with the hypothesis made. The possible reason is  that having more experience and knowledge of on dairy  production methods, would increase the probability of  the farmers to participating in dairy production. The more  dairy production experience, the higher the likelihood of  accumulating physical and social capital.

The  accumulation of physical and social capital can offer  farmers’ better exposure and capacity to produce more  dairy production. The study result revealed that, a one year increase of experience in dairy farming would  increase the mean values of AE by about 0.04% with an  overall increase in the probability and the level of AE by  about 0.04%. The finding of this study agrees with the  earlier research finding of Al-Sharafat (2013). 

Dairy membership 

It was found to have a significant and positive effect on  AE 10% significance level. The result indicates that the  sample farmers who participated in dairy members were  more efficient than others. This is because farmers who  participate in dairy cooperatives can get different  knowledge, information, training, and market access.  Moreover, the computed marginal effect result also  shows that, a change in the dummy variable, dairy  member from (0 to 1), would increase the probability of  the farmer being allocatively efficient by about 4.35% and  the expected values AE by about 3.22% with an overall  increase in the probability and levels of AE by 3.92%. 

Amount of concentrate used 

The result revealed that, the amount of concentrate feed  used by sampled households affected TE positively and  significantly at 1% and affect AE negatively and  significantly at 5%. This may be due to the fact that  concentrated feed provide different nutrients for milking  cows which increase the productivity of lactation cow.  But the price of this feed is become increasing due to this,  farmers may fail to allocate (minimize) the cost of this  feed. Furthermore, the computed marginal effect result  shows that, a unit increase in concentrate (qt) would  increase the probability of TE and decrease the  

probability of AE by 0.01% and 0.01% and increase mean  values of TE and decrease the mean values of AE by 0.02%  and 0.01% with an overall increase in the probability and  the level of TE and decrease an overall AE by about 0.02%  and 0.02% respectively. This is in line with the research  results of Amlaku et al. (2013). 

Grazing land 

Grazing land significantly and positively affected both TE  and EE of the sampled households’ at1% level of  significance, which is in line with the hypothesis made.  The possible reason is that having more grazing land  provides more feed for the milking cows which results  increase in milk output. It is the main resource needed by  the farmers to feed their livestock which is the main  source of feed by providing different fodder and grasses.  A unit increase of grazing land would increase the  probability of a farmer being both technically and  economically efficient by 1.97 % and 0.04% and the mean  values of TE and EE by about 5.58% and 3.92% with an  overall increase in the probability and the level of TE and  EE by about 5.85% and 3.96% respectively. 

Type of breed 

The result indicated that type of breed was a positive and  significant effect on TE at 5% and AE and EE at 1% level of  significance respectively as expected. This implies that,  cross breed is an important factor in influencing the level  of TE, AE and EE in the production of milk or positively  contributes to TE, AE and EE of milk production in the  study area. Breeds are believed to be genetically  improved which makes them more efficient than local  breeds.

A change from local to cross breed milking cows  increases the probability of a farmer being TE, AE, and EE  by 0.85%, 8.69% and 0.07% and the mean values of  technical, allocative and economic efficiencies by about  2.33% ,7.54% and 7.61% with an overall increase in the  probability and levels of technical, allocative and  economic efficiencies by 7.53% , 9.02%, and 7.69 %,  respectively. The result is in line with previous studies by  Mekdes (2017). 

Frequency of extension contact 

The result showed that the variable had positive sign and  significant effect on TE and EE at 1% level as expected.  The reason is that farmers who had more frequency of  extension; could lead them to improvements in resource  allocation, facilitates practical use of modern techniques  and use inputs in appropriate way during dairy  production.

A one times increase in frequency of  extension of household head increases the probability of  a farmer being technically efficient by 0.17% and the mean values of technical and economic efficiencies by  about 0.46% and 0.42% with an overall increase in the  probability and levels of technical and economic efficiencies by 0.5% and 0.42%, respectively. The finding  is in line with the study of Fita et al. (2013). 

Table 9: A two-limit Tobit regression results of determinants of TE, AE and EE 

Variables	Parameters	TE		AE		EE
		Coef.	Std. Err.	Coef.	Std. Err.	Coef.	Std. Err.
Const	δ0	0.4261***	0.0479	0.4517***	0.0430	0.4517***	0.0430
Sex	δ1	0.0272	0.0203	0.0029	0.0215	0.0221	0.0178
Education	δ2	0.0102***	0.0017	0.0026	0.0018	0.0098***	0.0015
Total land	δ3	0.0008	0.0038	0.0120***	0.0040	0.0087***	0.0033
Experience	δ4	-0.0003	0.0006	0.0012*	0.0006	0.0004	0.0005
Membership	δ5	-0.0246	0.0150	0.0422*	0.0159	0.0061	0.0131
Concentrate	δ6	0.0002***	0.0001	-0.0002**	0.0001	0.0001	0.0001
Grazing land	δ7	0.0595***	0.0139	-0.0129	0.0147	0.0397***	0.0122
Type of breed	δ8	0.0257**	0.0118	0.0960***	0.0125	0.0770***	0.0103
House system	δ9	-0.0051	0.0091	0.0094	0.0096	0.0010	0.0080
Type of feeding	δ10	-0.0052	0.0153	0.0248	0.0162	0.0130	0.0134
Extension	δ11	0.0051***	0.0080	0.0005	0.0017	0.0042***	0.0014
Distance	δ12	-0.0002	0.0031	0.0000	0.0022	-0.0002	0.0002

Note: ***, ** and *sign represents significance at 1%, 5%, and 10% levels, respectively. 

Source: Model output (2020) 

Table 10: Marginal effects of change in explanatory variables 

Variables	Marginal effect of			Marginal effect of			Marginal effect of
	TE			AE			EE
	∂E(y)	∂E(y ∗ )	∂[φ(ZU) − φ(ZL)]	∂E(y)	∂E(y ∗ )	∂[φ(ZU) − φ(ZL)]	∂E(y))	∂E(y ∗ )	∂[φ(ZU) − φ(ZL)]
Sex	0.0268	0.0249	0.0074	0.0027	0.0022	0.0025	0.0220	0.0218	0.0004
Education	0.0100	0.0092	0.0034	0.0025	0.0021	0.0024	0.0098	0.0097	0.0001
Total land	0.0007	0.0007	0.0002	0.0113	0.0094	0.0109	0.0087	0.0086	0.0001
Experience	-0.0003	-0.0002	-0.0001	0.0011	0.0009	0.0011	0.0004	0.0004	0.0000
Membership	-0.0242	-0.0224	-0.0073	0.0392	0.0322	0.0435	0.0061	0.0060	0.0000
Concentrate	0.0002	0.0002	0.0001	-0.0002	-0.0001	-0.0002	0.0001	0.0001	0.0000
Grazing land	0.0585	0.0538	0.0197	-0.0121	-0.0101	-0.0117	0.0396	0.0392	0.0004
Type of  breed	0.0253	0.0233	0.0085	0.0902	0.0754	0.0869	0.0769	0.0761	0.0007
House  system	-0.0050	-0.0046	-0.0017	0.0089	0.0074	0.0085	0.0010	0.0010	0.0000
Type of feed	-0.0051	-0.0046	-0.0017	0.0234	0.0197	0.0208	0.0130	0.0129	0.0002
Extension	0.0050	0.0046	0.0017	0.0005	0.0004	0.0005	0.0042	0.0042	0.0000
Distance	-0.0002	-0.0002	-0.0001	0.0001	0.0001	0.0001	-0.0002	-0.0002	-0.0000

Note: ∂E(y)/(∂X j ) (total change), ∂E(y^* )/(∂X j )(expected change) and (∂[φ(Z U )-φ(Z L)])/(∂X j ) (change in probability). Source: Model result (2020). 

CONCLUSION AND RECOMMENDATION Conclusion 

The study estimated efficiencies using the stochastic production frontier model. The findings indicated that number of lactation cows, green forage and  crop residue were significant determinants of  production level. The study also found that farmers  can increase milk production by 42% without  increasing inputs if they were technically efficient,  reduce current cost of inputs by 22.4% with cost minimization way and improve EE by 55.3% when  resources are used efficiently.

The positive and  significant variables namely; education, total land,  dairy experience, dairy membership, amount of  concentrate feed, type of breed and frequency of  extension in the present study imply that they play  great role in enhancing efficiency and productivity of  milking cow.

An important conclusion coming from  the analysis is that, milk producers in the study area  are not operating at full TE, AE and EE level which  implies that there is an opportunity for milk  producers to increase output at existing levels of  inputs and minimize cost without compromising  yield with present technologies. 

Recommendations  

The result of the study provides information and got  some policy recommendations to policymakers and  extension workers as follows: 

Regional government should have a responsibility to keep on the provision of education, and adequate  extension services in this area so that farmers can  use the available inputs more efficiently under the  existing technology. 

• Livestock office should give great attention to a  cross variety of cows by using artificial insemination in the study area. 
• Dairy cooperative should be encouraged by the  concerned body like woreda, zonal and regional  government. 
• The study revealed that the number of lactating  cows, green forage and crop residue were found to  be highly significant hinting that these are the most  critical input to increase milk production and  productivity. So that producers and policy makers  should use this opportunity to alleviate the existing  level of food deficiency & poverty that is to say in  designing development policy specifically for  improving milk production. 
• Adequate and proper management of grazing land  should be done by the farmers and concerned  bodies. 

Conflict of interest 

All authors declare that there is no any conflict of interest  regarding publication of this manuscript.  

Acknowledgment 

First and foremost, we would like to thank the Almighty  God who gave us the courage through his endless love  and blessings that helped us in finalizing the research. We  also express our heartfelt appreciation to Salale  University for funding this research. 

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