4.1. Study I: Evaluation of Technical, Scale, Economic and Allocative Efficiency of
4.2.2. Technical Efficiency of Edible Canna Farms and Determinants
0 1
2 ln[L(H )] ln[L(H )]
LR (31)
where H0 was assumed by the value of log likelihood for Cobb–Douglas and H1 represented the alternative hypothesis and was assumed by the value of log likelihood for the translog model (Coelli et al., 2005).
From Equation (31), the result of likelihood ratio test was calculated as LR
= −2 [−213.727 − (−202.009)] = 23.436. This value exceeded the critical value of Chi-squared distribution for the degree of freedom of 10, 18.307, at significance level of 5% level. Therefore, the null hypothesis was rejected. It means that the translog frontier production function was approved to be an appropriate model for the data collected in this study as compared with the Cobb–Douglas production function, which is usually adopted in the literature.
Furthermore, the present study used the results of maximum likelihood estimation (MLE) of regression to explain the data because the γ value was close to unity. As mentioned in the studies of Bezat (2011), Kea et al. (2016), and Taraka et al. (2012), if γ = 0, the technical inefficiency was not present, suggesting that OLS was adequately representative of the data.
Table 4.9 shows the estimation results of translog production function by using MLE; the value of γ was 0.8376, indicating that 83.76% of the variation of output quantity resulted from the technical inefficiency of farms. In addition, the results of the inefficiency effects model revealed that out of eight exogenous variables used, only education had a significant negative impact on the
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technical inefficiency of edible canna farms at the 10% significant level. The negative coefficient of education indicated that farmers with more years of schooling tended to achieve higher technical efficiency, which might be attributed to better ability in managing, allocating capital sources, as well as applying science and technology in production. This finding is consistent with statements of Bozoğlu and Ceyhan (2007), Khairo and Battese (2005), and Yami et al. (2013). This result also indicated that agricultural policies focusing on technical training courses should be initiated to help farmers in improving the efficiency of edible canna production.
The estimated coefficients in the translog production function were further used to compute the output elasticity of four inputs addressed in this study. The results of the calculated output elasticities with respect to individual input factors were presented in Table 4.10. On average, the output elasticities of all inputs were positive. Given the estimated output elasticity of seed and labor cost were the highest (0.425 and 0.194, respectively), implying that if the seed and labor cost increase individually by 1%, the yield of canna will also grow by 0.425% and 0.194%, respectively.
The output elasticity with respect to the nitrogen and phosphorus fertilizer were estimated to be 0.048 and 0.078 respectively, demonstrating that if nitrogen and phosphorus fertilizer individually increase by 1%, the yield will increase by 0.048% and 0.078%, respectively. In edible canna production, labor was required heavily during the harvest season, which usually lasts for a month.
Consequently, the labor cost would have a direct as well as significant impact on the efficiency of edible canna production in Backan province.
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Table 4.9. Maximum likelihood estimates for parameter of translog production function
Variables Coefficients Std. Err. t-Ratio
Constant (β0) −2.1912 3.3104 −0.6619
LnX1 (β1) 0.9092 0.5914 1.5373
LnX2 (β2) 1.5709 * 0.9537 1.6472
LnZ1 (β3) 0.0305 0.3260 0.0937
LnZ2 (β4) 0.2340 0.4610 0.5016
(LnX1)2/2 (β11) −0.2080 * 0.1142 −1.8202
(LnX2)2/2 (β22) −0.1976 0.1554 −1.2711
(LnZ1)2/2 (β33) 0.0033 0.0410 0.0818
(LnZ2)2/2 (β44) −0.0366 0.0643 −0.5695
LnX1 LnX2 (β12) 0.0399 0.0991 0.4022
LnX1 LnZ1 (β13) −0.0605 0.0543 −1.1131
LnX1 LnZ2 (β14) 0.1010 0.0737 1.3691
LnX2 LnZ1 (β23) 0.0362 0.0520 0.6952
LnX2 LnZ2 (β24) −0.0707 0.0810 −0.8732
LnZ1 LnZ2 (β34) −0.0048 0.0032 −0.1516
Inefficiency effects model
Constant 1.3916 * 0.7270 1.9141
Age (Years) −0.0070 0.0094 −0.7374
Education (Years) −0.0796 * 0.0467 −1.7045
Experience (Years) -0.1185 0.0917 −1.2927
Distance from farm to local market
(Kilometers) −0.0237 0.0267 −0.8870
Type of household (1 = Poor, 0 =
Otherwise) 0.2890 0.1841 1.5696
Credit access (1 = Yes, 0 = No) −0.0014 0.1574 −0.0088
Family size (Number) −0.0346 0.0666 −0.5188
Extension contact (1 = Yes, 0 = No) −1.2854 0.8738 −1.4711
σ2 0.5060 ** 0.2105 2.4034
γ 0.8376 *** 0.0647 12.936
Log Likelihood −174.4469
Note: *,**,*** indicates the significant at 10%, 5%, and 1%, respectively.
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Table 4.10. The output elasticity with respect to input variables
Variables Mean Maximum Minimum Std. Dev.
Seed 0.425 0.888 -0.218 0.131
Labor cost 0.194 0.700 -0.204 0.138
Nitrogen 0.048 0.146 -0.087 0.029
Phosphorus 0.078 0.346 -0.139 0.061
In short, the results revealed that it is recommended for the edible canna farms in Backan province as a whole to increase labor and seed quantities to boost the yield. In other words, the results suggested that the individual edible canna farmers should adjust and allocate input factors such as seed, labor, and fertilizer appropriately from overuses to improve efficiency in edible canna production, and in turn, farmers’ incomes would increase; this could further contribute to reducing the poverty rate in Backan province because the local livelihood relies heavily on edible canna production.
By using the translog production function, the results of the technical efficiency of edible canna farms in Backan province are exhibited in Table 4.11. The findings revealed that the average technical efficiency of edible canna farms was low with 0.74 and 0.72 in Nari district and Babe district, respectively. In other words, canna farms in Nari district and Babe district could expand their output by 26% and 28%, respectively, without changing the current input levels.
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Table 4.11. The distribution of technical efficiency (TE) levels of edible canna farms in Backan province
TE Levels
Nari District (n = 223) Babe District (n = 123) Number of
Farms
Percentage (%)
Number of Farms
Percentage (%)
<0.40 13 5.58 7 5.69
0.41–0.50 12 5.15 8 6.50
0.51–0.60 12 5.15 11 8.94
0.61–0.70 25 10.73 24 19.51
0.71–0.80 43 18.45 23 18.70
0.81–0.90 102 43.78 40 32.52
>0.90 16 6.87 10 8.13
Mean 0.74 0.72
Min 0.20 0.24
Max 0.94 0.95
Std. Dev. 0.17 0.16