This chapter presents the descriptive results of socio-economic characteristics and farm specific factors of production of sample households. It also provides the empirical results of Tobit two-limit model for technical, allocative and economic efficiency of common bean production with detailed explanation of significance variables.
The results of descriptive analysis
Demographic, socio-economic and institutional characteristics of the sample households: For the descriptive statistics such as mean, percentage, standard deviation and frequency were used.
Age: Regarding to common bean production, age of the household head was believed to be a great source of experience in day-to-day activity of human being. So, elderly heads of household were expected to have more experience in common bean production. As a result in Table 6, the average age of the sample household heads was 45.4 years with maximum of 66 and minimum of 29 years. Of the total sample farmers, nearly 7.7% were younger than 35 years and only about 3.51% were older than 58 years and were above economically active range. The majority of the household heads (51.11%) were found in the age ranges of 36 and 46 years.
Family size (FAMSIZE): The family size of the respondents was categorized into four. As (Table 6) below reveals respondents with family size of the sample farmers ranged from one (1) to 13 with a mean of 10.25. The majority of the households (47.3%) had 11-15 family members whereas, 46% of sample households had 7-10 family members and 6.4% had 3-6 also 0.3% had 16 family members.
Educational level (EDUC): Education was a social capital which has a positive influence on household ability to understand to utilize new technological information and also to know their right and obligation. The survey result showed that from the sampled respondents of smallholder farmers, only 46.6% of the household heads were illiterate while the remaining 53.4% of the respondents were at least capable of reading and writing. As indicated in Table 6, out of the total sample household heads, 33.6% have attained formal education while 16.3% of them were able to read and write and 3.5% of the respondent attended the religious education.
Marital status of the sample household heads: Regarding the marital status of respondents as indicated in Table 6 below, 92% of the sample households were married households. The result also revealed that 1.6% of the sample households have never married and 6.4% were divorced and non-of them were widowed.
Religion of sample household heads: Religion of sample household heads about 55% of the sample farmers selected for this study were followers of Orthodox, 36.7% of the sample farmers were followers of Protestant and 8.3% were Muslim as shown in Table 6 below.
Land/farm size: This refers to the area of cultivated land (own, rented) for common bean by the household during 2020/21 production year. According to Andreu, larger farms are relatively better efficient than small size farms. Therefore, households with larger area of cultivated land had the capacity to use compatible technologies that could increase the efficiency of the household, enjoy economies of scale and relatively better efficient than small size farms. According to the survey result, the average land holding of the sample households was 1.54 hectare with a standard deviation of 1.09 and minimum of 0.25 hectare and maximum of 3.5 hectare.
Extension service: It is a dummy variable, in order to give effective extension service to the farmers, the district assigned professional development agents in each kebele. The development agents are graduates of different colleges specializing in three agricultural streams such as crop production, animal husbandry and natural resource management. In this study, 92.3 percent of the sample respondents reported that they have been receiving extension services and advice about common bean production. The extension workers also visit farmers on different intervals. Some farmers are being visited more frequently while others have no chance at all to be visited by extension workers. The survey result indicates that, about 59.4, 18.6, 11.8 and 2.5 percent of the sample households were received extension service more than four times (year), three times (year), two times (year) and one times (year) respectively.
Land preparation: The number of ploughing indicates an intensity of land preparation that helps for appropriate germination of the seed which is expected to have a direct impact on yield.
As indicated in Table 6 below, about 32.90% of the respondents ploughed their farm one times, 61.66% ploughed their farm two times and 5.44% of the farmers plough their land three times.
Distance to nearest market: This variable represents the distance between a household residence and the nearest market center measured in km. It was hypothesized that distance from market place is negatively related to efficiency. This was because those farmers far away from market are less accessible for farm inputs and market information and transportation become costly and difficult. Out of the total sample households surveyed, about 49.52% indicated that their common bean farm was inside the range of 2 km-4 km from the market and 36.42% were even inside the radius of 5 km-7 km where as 14.06% were far from the home above 8 km.
Table 6. Socio-economic and institutional characteristics of the households (categorical variable).
Sex: The sample composed of both male and female smallholder farmers. Of the total sampled smallholder farmers, 3.6% or 11 were female and 96.4% or 302 were male.
Access to credit: Common bean requires high costs for production. Respondents in the study area interviewed whether or not they need access for credit services. From the total respondents replied about 72.21 percent were not get credit service and 27.79 percent were got credit service in the institute as present in Table 7. Mostly smallholder farmers, get credit from creditors (private lenders), Omo-microfinace institute and bank. The study indicated that in the district 5.38 percent of credit had gain from private lenders with interest rate reached 50 up to 100 percent, 18.47 percent from Omo-microfinance with interest rate 300 ETB from 1000 ETB in a year and 3.93 from commercial bank of Ethiopia with interest rate of 100 ETB from 1000 in a month.
Extension service: In order to give effective extension service to the farmers, the district assigned professional development agents in each kebele. The development agents are graduates of different colleges specializing in three agricultural streams such as crop production, animal husbandry and natural resource management. In this study, 92.3 percent of the sample respondents reported that they have been receiving extension services and advice about common bean production. 7.7% of the respondent’s haven’t got extension service. The extension workers also visit farmers on different intervals. Some farmers are being visited more frequently while others have no chance at all to be visited by extension workers. The survey result indicates that, about 59.4, 18.6, 11.8 and 2.5 percent of the sample households were received extension service more than four times (year), three times (year), two times (year) and one times (year) respectively as show in Table 7.
Training: An appropriate training given to the farmers may improve productivity by enhancing their management capacity and their production performance. In this study area, farmers were getting training from surrounding agricultural office and other governmental and non-governmental organizations. Among the sample farmers, 93.7 percent of farmers were trained on different common bean related aspects and the rest 6.3 percent of the respondent had not received any training on the subject matter previously. This indicates that majority of the sample farmers were received training as shown in Table 7.
Crop pest: It was taken as dummy variable, which takes 1 if pest affect the product of common bean and 0 otherwise. In the study area common bean production is sensitive to crop pest. Crop pest has adverse effect on economic efficiency level of common bean producer. If the sample common bean producer is affected by crop pest, obviously there would be a loss in output of common bean production. Because of this, crop pest was expected to affect efficiency level of smallholder common bean production negatively. Among the sample farmers, 37.8 percent of farmers were exposed to common bean crop pest and the rest 62.2 percent of the respondent had not expose to common bean crop pest. This indicates that majority of the sample farmers common bean was not exposed to crop pest as shown in Table 7.
Off/non-farm income (OFARM): This was treated as a dummy variable and measured as 1 if the household is involved in off/non-farm activities and, 0 otherwise. Some farmers in the study area were engaged in various off/non-farm activities. The main activities were selling of firewood, being hired in other’s farm and selling local drink. The survey indicated that 11.11% of the respondents were engaged in off/non-farm activities. They also mentioned that availability of excess labor, attractive income and mainly shortage of land as the reasons for their engagement in off/non-farm activates.
Table 7. Socio-economic and institutional characteristics of the households (dummy variable).
Livestock holding: Livestock have diverse function and livestock plays crucial roles for the livelihood of the farmers in mixed farming system. They provide food in the form of meat, milk, and non-food items such as draft power and manure as inputs into crop production. As shown in Table 8, goat and sheep, hen, oxen, cows, calves and donkey are the livestock which the respondents have. On average, the sample household farmers owned 7.05, 6.3, 2, 1.75, 1.27, and 1.11 respectively. Donkey was use for transport of farm inputs and outputs. Moreover, the sample respondent owned 7.05 sheep and goats were keep as a source of income and hedging against risk during the crop failure. Moreover, the survey results showed that the average tropical livestock unit per sample household was 4.78 per household with the standard deviation of 2.75 TLU. On top of this, as it is indicated in Table 8, the average holding of oxen per household found to be 1.92 TLU which statically implies that 2 oxen per household sample respondent with a standard deviation of 0.92 TLU. The standard deviation here indicates that there is variability in livestock holding among the households.
Cropping system: The dominant farming system of the district is crop-livestock mixed. Crop production district is limited to autumn season and the major types of crop that are produced include common bean, teff, wheat, maize, barley, and sorghum. The district was experienced by producing twice a year. The first season was start from February up to the end of July and the second start from the mid of August up to the end of December. On the first season the most growing crops are teff, maize, wheat, barley, sorghum and common bean in small amount. On the second season most of the land i.e. on average almost half the total hectare will covered by common bean. Though modern input application, especially fertilizer is there, the performance of major crops in terms of yield is encouraging. The mean area coverage (hectare) of major crops in 2020/21 production year is presented in Table 8. The result indicated that on average sample farmers have of 0.25 with the minimum and maximum of 5.5 hectare. As shown in Table 8, in the district most farmers use their own land for the production of common bean on average 1.54 hectare of land with the standard deviation of 1.09 because the data was collected in second season Which implies that common bean is the most dominant legume crop in the district as compared to other cereals such as wheat, teff, maize, barley and sorghum.
Table 8. Socio-economic characteristics of the sample households (continuous variable).
Inputs and input costs: Table 9 presents the description of inputs, their mean, min, max and associated costs. The total amounts of DAP fertilizer measured in Kg while its costs were expressed in Ethiopian Birr (ETB). On average, 239.13 kg of DAP was used while the average cost of these inputs was 5021.73 ETB.
The size of land used for common bean in study area by each farmer was measured in hectare. On average, the rental value of good quality of land 4424 ETB per hectare for one production year was used to estimate cost of land. Accordingly, on average, a given household allocate a total of 1.54 hectare of land for common bean production and its average cost was computed as 6812.96 ETB. On average, about 2.96 liter of chemicals was used during the production of the common bean and its average associated cost was 296.16 ETB.
The total amount of seeds used was computed as the sum of the seed. The corresponding seed costs were computed as the product of the total amount of seed used and market prices of a unit kg of seed. On average, the amounts of seed were 63.37 kg of common bean per household head of the respondent. The associated average costs of common bean seed 1550.26.
Labor was aggregated for each farmer in single unit man/days. The cost of hired labor was estimated based on the daily average wage rate (80 ETB per day) of the nearly village. As a result, total cost of labor input was the sum of cost of hired labor and opportunity cost of family labor. In aggregate, the average use of labor in man/days equivalent was about 105 which statically imply that 105 labor and labor costs has an average of 8436 ETB.
Table 9. Input uses and outputs for common bean production in district with its costs.
Table 9 result represents the main inputs uses for the production of common bean. The responses of household respondents show cost of land, chemical and fertilizer (DAP) were widely used for common bean production. From the Table 9, from the respondent, 24 households (7.66%) were rented the land for common bean production, also 309 households (98.72%), farmers were use chemical and 310 households (99.04) farmers were used fertilizer (DAP) and the source of the inputs are agricultural office, cooperative and trader. As shown in Table 10 the response of household shows all most all farmers use fertilizer (DAP). Field chemicals include pesticides and insecticides.
Table 10. Proportion of input user households in 2020/21 production year.
Production constraints: Crop pest was a serious problem that farmers were facing in the study area. About 38.0% of respondents reported that they were facing crop pest whereas 29.4% believes crop disease was the problem that they were facing. In addition to this, there was also a wide range of weed infestation in the study area which accounts 26.2%. Farmers also reported that there was labor shortage during peak agricultural production seasons (Table 11).
Table 11. Agricultural production constraints.
Descriptive statistics of variables used in the model: This section present summary statistics results of production variables used for analysis in the stochastic production frontier model, cost frontier and in Tobit model.
Descriptive s tatistics of production function variables: On average, sample farmers obtained 23.2 quintal of common bean. The average land area allocated to common bean production (owned shared and rented land) by household was 1.54 ha and ranged from 0.25 ha to 5.5 ha. The amount of seed that sampled households used were 63.75 kg on average. Like other inputs, human labor and oxen power inputs were also important, given a traditional farming system in the study area. Sampled households on average used 105 man equivalent labor and 14.3 oxen days for the production of common bean during 2020/21 production of second season. Sample farmer households also on average used 239.13 kg of DA (Table 12).
Table 12. Summary of input-output variables used to estimate the production function.
Descriptive statistics of variables used to estimate the cost function: As presented in Table 13 the mean and standard deviation of each variable used in the cost function along with their involvement to the total cost of cultivation are discussed as follows. On average total cost of Birr 25377.67 was required to produce 23.2 quintal of common bean. Among the various factors of production, the cost of labor, land and DAP accounted for the highest share 8436, 6812.96 and 5021.73 respectively. From the following the cost of oxen, cost of seed, and cost of chemicals takes, 3260.56, 1550.26, and 296.16 respectively out of total cost of cultivation.
Table 13. Descriptive statistics of variables used to estimate the cost function.
Summary of descriptive statistics of efficiency model variables: As presented in Table 14 the mean and standard deviation of each variable used in efficiency model. On average the age composition of the household was 45.4 with standard deviation of 6.55 and the family size was 10.29 with standard deviation of 2.19. The education also takes 3.5 mean grade of the household with the standard deviation of 1.27. The land size which common bean produced was counts of 1.54 mean of hectare with the standard deviation of 1.09 and land preparation also 2.09 of mean value with standard deviation of 1.83. Among the various factors of production, the distance from the market counts 4.94 km from farm land with standard deviation of 2.39. The total livestock unit also takes the value of 4.78 of mean and standard deviation of 3.11.
Sampled households, on average, 96.4% of them were males household and rests were females. Out of the total respondents, 27.79% of them reported that they had an access to credit for common bean production during the survey period. From the sampled households, on average 92.3 get the extension contact by different frequency and the rest 7.7% wouldn’t get. Out of the sampled households, 37.8% were affected by the crop pest and 62.2% of them were able to control it. Only about 11.11% of the sampled farmers reported to earn off/non-farm income (Table 15).
Table 14. Descriptive statistics of categorical and continuous variables used to estimate efficiency of common bean.
Table 15. Descriptive statistics of dummy variables used to estimate efficiency of common bean.
Econometric results
This section presents the econometric model outputs of the production function; efficiency scores and factor that affect technical, allocative and economic efficiency of smallholder farmers in common bean production in the study area.
Hypothesis testing/estimation of product frontier: Before running the econometric model, first check the multicollinearity test in between continuous and dummy variables by using Variance Inflation Factor (VIF) and contingency coefficient. Second Cobb-Douglas versus Tran slog production function was check by using the decision to select functional form depends on the calculated (generalized) likelihood ration. The Third OLS versus Maximum Likelihood Estimation (MLE) or Stochastic Frontier Model (SFM) was checked by log likelihood ration. The test of each variables and models are shown below one by one.
The first conducted was the existence of multicollinearity problem between continuous and dummy variables. According to Gujarati, the value of VIF more than 10 is usually considered as an indicator of serious multicollinearity, and should be excluded from the model. On the other hand, variables having VIF of less than 10 are believed to have no serious multicollinearity problem and able to include as explanatory variables in the model. According to Gujarati, VIF is defined as:
VIF (Xi)=(1/(1-R2)) (29)
Where, xi=the ith explanatory variable regressed on the other explanatory variables.
R2=adjusted R-square; the coefficient of the determination in the (auxiliary) regression of Xi on the remaining repressors
As shown in Appendix Table 1-3 VIF means the farm specific variables, VIF of the explanatory cost of variables and VIF for the continuous socio-economic variables was 3.1, 5.93, and 1.34 respectively. This implies that there is no multicollinearity problem among the variables because of the number or the value of VIF is less than 10.
The contingency coefficients are calculated for each pair of discrete variables using contingency coefficient test.
C=√χ2/n+χ2 (30)
Where, C=contingency coefficients; n=total sample size; χ2=Chi-square test
As shown in the appendix Table 4 results of the contingency coefficient test such as, the categorical or dummy variables, contingency coefficient, which is a chi-square based measure of association, was employed to check for the presence of multicollinearity. According to Gujarati, a contingency coefficient value of 0.75 and above (i.e. ≥ 0.75) indicates the existence of strong relationship between the variables. By looking the contents of the table, it can be concluded that there is no problem of association among the variables as the respective coefficients are very low. Consequently, all the discrete variables were included in the estimation of the specific multiple linear regression models.
The second hypothesis tested was whether the problem technology of the sample household is better represent by the Cobb-Douglas function or Translog production function. To select the appropriate specification, both Cobb-Douglas and Translog function forms were estimated at shown on Appendix Table 5. The null hypothesis is the coefficient of interaction and square terms of Translog production function are zero. Based on equation 23 the result shown in Table 5 indicates that the calculated Likelihood Ration value (LR) equal to 28.14 that means LR=-2(lnH0)-ln(H1)=-2(-34.7-(-20.64)=-2*(-14.7)=28.14 while the critical likelihood ratio value at 21 degree of freedom equal to 32.67 (tabulated) or the critical value at (5%,1) is 32.67. since the calculated LR value is less than the critical value of Chi-square at 21 degree of freedom, the null hypothesis is accepted at 1% level of significance implying that Cobb-Douglas function form adequately represents the input output data of common bean production.
The third hypothesis tested was whether Stochastic Frontier Models (SFM) adequately represents the input output data of common bean production or not. In other word, whether technical, allocative, and economic inefficiency is present in common bean production or not was tested. The test was conducted based on the statistical significance of standard deviation of technical inefficiency. The result of the test helps to identify whether common bean producer farmers are technically efficient or not. This is made in order to decide whether the traditional average production function (OLS) best fits the data set as compared to Stochastic Frontier Model (SFM) selected for this study. That mean if the null hypothesis H0:γ=0 is accepted against alternative hypothesis H1: γ ≠ 0, then the Stochastic Frontier Models (SFM) is identical to OLS specific indicating that there is no inefficiency problem within the common bean producer sample households. The result based on the equation 23 (Table 15) below indicates that calculated likelihood ratio value LR equals to 85.82 while the critical chi-square value at 5% level of significance equals to 3.84. Since the calculated likelihood ratio value LR is greater than the critical value of chi-square (χ2) at 1 degree of freedom, the null hypothesis is not accepted at 5% level of significance implying that stochastic production frontier model is appropriate than OLS or there is significant technical inefficiency variation among sample household farmers.
The fourth hypothesis tested was whether the explanatory variables/socio-economic variables in technical inefficiency effect model are simultaneously equal to zero or not. By using equation 23 (LR) the result shows below in table 24 indicates that the calculated value of LR equals to 85.82 while the critical chi-square (χ2) at 13 degree of freedom at 5% level of significance equals to 22.36. Since the calculated Likelihood Ratio value (LR) is greater than the critical chi-square (χ2) value the null hypothesis that explanatory variables in the technical inefficiency effect model are simultaneously equal to zero was not accepted at 5% level of significance. Hence, the explanatory variables associated with technical inefficiency effect model are jointly different from zero or jointly explain technical efficiency differences among sample common bean producer farmers (Table 16).
Table 16. Likelihood ratio tests for the model and parameters of the stochastic frontier analysis.
Production and cost efficiencies of farm specific variables: The Maximum-Likelihood (ML) estimates of the parameters of the stochastic production frontier were obtained using the program FRONTIER 4.1 software. These results were present in Table 17, which also presents the OLS results of the average production function for comparison. The sign of the slope coefficients both OLS and ML estimates are positive. The estimate of variance parameter gamma is also significantly different from zero, which implies that the inefficiency effects are significant in determining the level of common bean production and output of the sampled household farmers. The estimated production function given as follow.
Yi=3.45+0.33lnlabor+0.12lnox+0.73lnDAP+0.06lnseed+1.57lnland+0.15lnchem
Where,
Yi=common bean output per hectare in kg. Lnlabor=the number of inputted family and hired labor per hectare. Lnox =the amount of paired oxen for plough land for common bean. LnDAP=the quantity of DAP used per hectare for the production of common bean in kg. Lnseed=the amount of seed used per hectare in kg. Lnland=the amount of cultivated land that are used for common bean production per hectare. Lnchem=the quantity of chemicals used per hectare in liter.
Table 17. Ordinary Least Square (OLS) estimates the average production function and ML estimates of the stochastic production frontier for the sample common bean producer farmers.
As presented in Table 17 all variables are statistically significant. From these labor, land and DAP are significant at 1 percent probability level. And the rest oxen, seed and chemical are significant at 5 percent probability level. This informs that they were significantly different from zero and hence these variables were important in explaining common bean production in the study area. The coefficients of production function variables were positive. The positive production elasticity with respect to all variables implies that as each variables increase, common bean output will increase. On average, as the farmer increases area allocated for common bean, the amount of labor, oxen, DAP, seed, land and chemical for the production of common bean by 1 percent of each, the farmer can increase the level of common bean output by 0.33, 0.12, 0.73, 0.06, 1.57, 0.15 percent respectively.
To put in another words, understanding the determination of elasticity is necessary for the estimation of responsiveness of the output to inputs. All of the inputs on the stochastic frontier were statistically significant and had the expected signs. Gamma (γ) was also statistically significant. This is evidence of the fact that there were measurable and technical inefficiencies in common bean production probably caused by difference in socio-economic characteristics of household and their farm management practices. The result stochastic frontier of cost function estimates for common bean as shown above on Table 18.
The output was negative and significant. Hence, if the output increases by one percent it could decrease the total cost by 0.92 percent. In the case of labor, oxen, DAP, land and chemical if it increase by one percent it could increase the total cost by 1.02, 0.78, 1.09, 2.05 and 1.03 percent respectively.
This implies that the output remain an important contributor the cost efficiency in agricultural practice for common bean production. The estimated sigma square (σ2) was 6.008 and significant at 1 percent level indicates that goodness of fit. The gamma value of the MLEs the frontier cost function was 0.940. This value is statically not significant implying that 99.99 percent of variability of cost efficiency from agricultural production is attributed to output. And the rest 0.01 percent is due to random noises.
Moreover, the presence of technical inefficiency was tested by Likelihood Ratio (LR) which was -129.58 and lesser than the critical chi-square was 17.755 given by Kodde and Palm. Therefore, the nullhypothesis of cost inefficiency was rejected.
Table 18. ML estimate of the parameters of the Cobb-Douglas stochastic cost frontier function for common bean producers.
Technical, allocative and economic efficiency score class of technical efficiency: One of the objectives of this study was to estimate the technical efficiency levels of common bean producer farmers in Burji district. The estimation result showed that the mean efficiency level of common bean producer farmers were 63.7 percent with the minimum and maximum efficiency level of about 21.3 and 94.5 percent respectively appendix (Table 6). This shows that there is a wide disparity among common bean producer farmers in their level of technical efficiency, which may in turn indicate that, there exists a room for improving the existing level of common bean production through enhancing the level of farmers technical efficiency. To put in another words, on average sample common bean producer farmers in the study area incur a 36.3 percent loss in output due to technical inefficiency. The mean level of technical efficiency further tells us that the level of common bean output of the common bean producer farmers can increased on average by about 36.3 percent if appropriate measures were taken to improve the level of efficiency of common bean growing farmers. In other words, there is a possibility to increase yield of common bean about 36.3 percent using the resources at their disposable in an efficient manner without introducing any other improved external inputs and practices. It also indicated that small farmers in study area, on average, could gain higher output growth at least by 33 percent (1-63.7/94.5) through the improvements in the technical efficiency. Moreover, from the total sample households, more than 154 farmers technical efficiency was found to have 61 percent and above.
For more understanding of the distribution of the technical efficiencies, a percentage distribution of the predicted technical efficiencies was presented in Figure 6 below. The figure indicates that the frequency and the percentage of the occurrence of the predicted technical efficiencies in the range of 20 clustering. The technical efficiencies in the gap between 0.61-0.99 efficiencies range represents about 49.12% of the respondents. This implies that half of the farmers were moderately efficient in allocating resources and the farmers are moderately efficient in producing common bean at the given level of input.
Figure 6. Frequency and percentage distribution technical efficiency class of allocative efficiency.
As presented in Appendix Table 6, the mean allocative efficiency of the sample was 0.772 with a minimum of 0.222 and a maximum of 0.965. This mean in the short run there are opportunities for reducing common bean production by 0.228 (1-0.772) by performing the practice of technical efficient farmers in locality. The higher distributions of allocative efficiency level is between 0.81 to 0.99 with representing 144 sample of common bean producer farmers of which is 46 percent of the total sample of common bean producer farmers. This implies that almost of the farmers in the district have more 61 percent allocatively efficient around 283 and about 90.4 percent.
For detail explanation the distribution of the allocative efficiencies, frequency and percentage distribution of the predicted allocative efficiencies was show in Figure 7. The figure describes that the frequency and percentage occurrence of the allocative efficiencies in the gap between 20 individuals that clustering of allocative efficiencies.
Figure 7. Frequency and percentage distribution allocative efficiency.
Class of economic efficiency: As show in the Table 6, the highest distribution of economic efficiency level classes/ranges were 0.41-0.6 and 0.61-0.8 with each category representing 47.25 and 28.75 percent of the total sample of common bean producer farmers respectively. The average economic efficiency level for the sample farmers was 0.50, with the minimum of 0.107 and maximum of 0.879. This shows that there is a need to improve their level of economic efficiency. The result implies that if the farmers with an average level of economic efficiency were to reach the level of the most economically efficient household, then the farmers could experience a cost saving of 43 percent derived from (1-(0.500/0.879))*100. Similarly, the most economically inefficient farmer would save cost of 87.9 percent derived from (1-(0.107/0.879))*100 to attain the level of most/maximum economic efficiency farmer.
For extra implication of the distribution of the economic efficiencies, a percentage distribution of the predicted economic efficiencies was presented in Figure 8. The frequencies occurrence of the predicted economic efficiencies in range 0.41-0.6 indicates that the highest number of farmers, which are 148 respondents and about 47.25% of the respondents. While 28.75% of the respondents have more than 0.61 economic efficiency, which implies that farmers are highly efficient in producing a given amount of common bean at the minimum cost for a given level of technology.
Figure 8. Frequency and percentage distribution allocative efficiency.
Potential, yield and actual level of output
Reckoning the individual farmer’s technical efficiency and actual output in common bean production enables to determine the potential level of common bean output and output gap of the individual common bean producer farmers through efficient use of existing inputs and technology. The potential common bean output was estimated based on equation Yi*=Yi/TEi* where Yi*=the potential level of output for individual sample of common bean producer farmers, Yi is the actual output for individual sample of common bean producer farmers and TEi* is technical efficiency of individual sample of common bean producer farmers. Whereas the output gap maybe defined as the difference between technically full efficient output or potential level of output and observed output/the actual/of individual sample common bean producer farmers in the district. Therefore, yield/output gap is the amount, which represents less output due to technical inefficiency. As shown in Table 19 below, summarizes the results of actual, yield/output gap and potential level of common bean output among sample common bean producer farmers. The average amount of actual, output gap and potential common bean output during 2020/21 production year was, 23.185 kg/m2, 13.212 kg/m2 and 36.397 kg/m2 with the standard deviation of 0.667, 4.261 and 3.894 respectively. This shows that mean technical inefficiency was 33 percent which is caused by 13.212 kg/m2 gap output of common bean on the average with mean actual value 23.185 kg/m2 and the potential output value of 36.397 kg/m2. This implies that sample households common bean producer in the study area were producing on average 13.212 kg/m2 lower common bean output than their potential output.
Table 19. Actual, potential and output gap due to technical inefficiency.
Factors affecting technical, allocative and economic efficiency of smallholder common bean producers
The discussion about each significant variable are presented as follows:
Age: The estimated coefficients of age for technical efficiency was positive signs and significant at 5 percent. The coefficient of 0.032 for age (technical efficiency) shows that, for sample period, an increase in age by one year led, on average, to an increase in technical efficiency by 0.032%. The result is similar with the findings of Abdulai, which may be because of the accumulated experiences that have been gathered over time. They become skillful as they get older and may have an interest in the use of new methods of production.
Family size: The coefficient of family size for technical efficiency and economic efficiency is positive and statistically significant at 10 percent significance level. The coefficient of 0.056 and 0.047 for technical efficiency and economic efficiency respectively shows that, an increase in family size by one member, on average, the technical and economic efficiency increase by 0.056% and 0.047% respectively. The result is similar to the previous expectation that farmers those having large family size are more efficient than farmers having small family size, because; family labor is the main input in crop production as the farmer has large family size he would manage crop plots on time and may able to use appropriate input combinations. This is in line with the findings of Mohammed. In similar manner, the coefficient of family size for economic efficiency is also positive and statistically significant at 1 percent. This might be because farmers with large family size had better capacity for optimal allocation of resources. This result is in line with the results of Okoruwa.
Education: The coefficient of education is positive estimated coefficients for all efficiencies and significant at 1 percent. Positive and significant impact of education on all types of efficiencies confirms the importance of education in increasing the efficiency of common bean production. It is a variable that is expected to increase managerial ability and led to good decisions in farming. Because of their better skills, access to information and good farm planning, better to manage their farm resources and agricultural activities than illiterate one. In other word, if the sampled household was literate through different way, the technical, allocative and economic efficiency was increase by 0.078, 0.056 and 0.072% respectively. This is in line with earlier studies by Jema and Andersson.
Land size: Land cultivated for common bean was found to have significant and positive impact on TE and EE with the significant level of 1 and 10% respectively. In other word, if one hectare of land for common bean increase, the technical and economic efficiency increased by 0.127 and 0.052% respectively. This is in line with the hypothesis made. This might be because of Farmers with larger area of cultivated land have the capacity to use compatible technologies that could increase the efficiency of the farmer, enjoy economies of scale. This result is in line with the argument of Andreu. Therefore, larger farms are relatively better efficient than small size farms.
Distance from market: Distance from home to the nearest market was also significant at 10 percent level of significance in determining technical efficiency. The negative coefficient implies that farmers far from markets are less technically efficient compared to their counterparts who reside nearby markets. This means as 1 km increase of home from the market, the technical efficiency would decrease by 0.071%. This might be due to the fact that as farmers are located far from market, there would be limited access to input and output markets and market information. Moreover, higher distance to market leads to higher transaction cost that reduces the benefits that accrue to the farmer. More importantly, longer distance from market discourages farmers from participating in market-oriented production. Similar result was found in the work of Alemu.
Livestock (TLU): The coefficient of livestock ownership for technical efficiency is positive and statistically significant at 1 percent. It was also positive and statically significant for allocative and economic efficiency at 5 percent significance level. Positive and significant impact of livestock ownership on technical efficiency may due to the importance of livestock in the crop production system (as source of draft power, income and manure) that may help to maintain soil fertility and result in maximization of output. This means, as one unit increase in livestock unit, the technical, allocative and economic efficiency increased by 0.082, 0.041 and 0.062% respectively. It’s also in line with the result of Wondimu, in the case of confirms the considerable contribution of livestock in reducing the current cost of inputs in common bean production.
Sex: Sex of household head was found to have positive and significant impact on TE, AE and EE at 5, 10 and 5 percent respectively, which is in line with the hypothesis made. Furthermore, as expected, male households were more efficient than female households. The possible explanation is that male households might have better practical experiences in farming. Also, one might argue that female households are too much occupied with domestic activities and had little time for the management of their common bean plots that led to low technical efficiency levels. The result is in line with the finding of Aynalem.
Access to credit: The results also indicated that access to credit had a positive and statistically significant effect on both allocative and economic efficiency at 10 percent significant level, which indicates that farmers with access to credit tend to exhibit higher levels of efficiency. Credit availability shifts the cash constraint outwards and enables farmers to make timely purchases of those inputs that they cannot provide from their own sources. This means if the household get credit access, the allocative and economic efficiency would increase by 0.032 and 0.023% respectively. This result is in line with the arguments of Amadou.
Extension contact: The coefficient for the access to extension has statistically significant positive relationship with technical and economic efficiency at 1 percent. Similar results were obtained by Binam. The positive estimated coefficient for contact with extension workers implies that efficiency increases with the number of visits made to the farm household by extension workers. Moreover, during the survey, most farmers contact extension agent four times per year.
Training: Training is an important tool in building the managerial capacity of the farmers. Farmers who received training was hypothesized to be more efficient than those who did not received training. The coefficient for dummy variable, training indicates that if a farmer was access to training, the technical, allocative and economic efficiency score would increase by 0.029, 0.021 and 0.016% respectively. The coefficient of training is positive for technical, allocative and economic efficiencies and statistically significant at 1, 10 and 1 percent significance level respectively. This may be because training enables them to use inputs in cost minimizing input ratio. This result is in line with the finding of Nejuma.
Crop pest: The coefficient for crop pest was negatively significant at 1 percent level for all efficiency. This means if the household’s common bean was exposed to crop pest the technical, allocative and economic efficiency would be decreased by 0.41, 0.075 and 0.092 percent respectively.
Off/non-farm income: The coefficient of off/non-farm activity with respect to technical efficiency is statistically significant at 5 percent and for allocative and economic efficiency at 1 percent level. The result is in line with the findings of Hasen, and Abebayehu. Off/non-farm occupation may affect the technical efficiency positively for the reason that the income obtained from such activities could be used for the purchase of agricultural inputs and augments financing of household expenditures which would entirely dependent on agriculture. It is also positive and significant at 1 percent for allocative and economic efficiency. This may be because; the availability of off/non-farm income shifts the cash constraint outwards and enables farmers to make timely purchases of those inputs which they cannot provide from on farm income. So, if the farmer was engaged in off/no-farm income, the technical, allocative and economic efficiency of the farmer would increase by 0.092, 0.052 and 0.056% respectively of the common bean production. Therefore, it enables farmers in maximizing its output at efficient cost of production (Table 20).
Table 20. Tobit two-limit regression estimates of technical, allocative and economic efficiency.