Application of Stochastic Frontier to Agriculture in Ethiopia

Figures & data

Figure 1. Conceptual framework.

Geographical information system output, 2021.

Figure 2. Map of the study area

Geographical information system output, 2021.

Table 1. Review on determinants of efficiency differential.

Efficiency determinants	Measurement unit	Expected sign	Authors
Age of household head	Years	Positive	Degefa 2017
Sex of household head (if male household head)	Dummy	Positive	Fantu et al. 2011
Education level of household head	Years of formal schooling	Positive	Mustefa et al. 2017
Total number of household members	Man equivalent	Positive	Sorsie et al. 2015
Total area of crop land held by household head	Hectares	Negative	Lemessa et al. 2017
Total livestock holding	TLU	Positive	Tsegaye and Ernst
Fertility status of maize plot	Dummy	Positive	Bati, Tilahun, and Kumar Parabathina 2017
Distance to nearest market	Kilometer	Negative	Tefaye and Beshir 2014
Uses of credit	Dummy	Positive	Meja, Alemu, and Shete 2021
Frequency of extension contacts	Numbers	Positive	Doo-Young et al. 2020
Off-/non-farm income	Dummy	Positive	Qamar et al. 2016

Review from literature (2021).

Table 2. Results of Cobb–Douglas stochastic frontier production function.

Ln of output	Coefficient	Std. Err.	z	P > z
Lan seed	0.218*	0.118	1.85	0.064
Lan land	0.342***	0.1064	3.21	0.001
Lan nitrogen phosphorous sulfur	0.073	0.079	0.93	0.354
Lan UREA	0.004	0.1005	0.04	0.965
Lan oxen	0.286***	0.1039	2.75	0.006
Lan labor	0.107	0.0839	1.28	0.201
Cons	1.419	0.489	2.90	0.004
Sigma square	0.499	0.070		0.362
Lambda	4.929	0.072		4.787

Note: *d *** refer to 10%, 5%, and 1% significance level, respectively.

Source: Stochastic frontier model result (2021).

Table 3. Technical, allocative, and economic efficiency score.

Variable	Observation	Mean	Std. Dev.	Min	Max
TE	154	0.638	0.19	0.04	0.944
AE	154	0.684	0.12	0.377	0.885
EE	154	0.436	0.14	0.0178	0.797

Source: Model result (2021).

Figure 3. Kernel density estimate for technical, allocative, and economic efficiency.

Figure 4. Distribution estimates of technical allocative and economic efficiency score.

Table 4. Determinants of technical efficiency and its marginal effects.

TE	Coefficients	Standard error	Marginal effects
			$\frac{\mathrm{\partial }E(y)}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }E(y^{\ast })}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }(\phi (Z_U-Z_L)}{\mathrm{\partial }{X}_j}$
Loss due to wild animals	0.011**	0.005	0.005	0.004	0.003
Educational levels	−0.012*	0.020	0.019	0.017	0.010
Family size	−0.007*	0.006	0.005	0.005	0.003
Farm experience	−0.0005	0.002	0.002	0.002	0.001
Sex of household	0.058	0.037	0.036	0.033	0.014
Farm size	0.004	0.014	0.014	0.012	0.007
Livestock holding	−0.0009	0.006	0.006	0.005	0.003
Slope of land	0.052***	0.018	0.017	0.015	0.010
Fertility status	0.039	0.030	0.029	0.025	0.017
Distance to plot	0.002	0.002	0.002	0.001	0.001
Land conservation	−0.013	0.030	0.028	0.025	0.015
Plowing frequency	0.00008	0.021	0.020	0.017	0.010
Distance to the markets	−0.0006	0.001	0.001	0.001	0.000
Extension contacts	0.002	0.003	0.003	0.003	0.002
Use of radio	−0.0089	0.031	0.030	0.026	0.015
Uses of mobile	0.0118	0.031	0.030	0.026	0.016
Credit uses	−0.024	0.030	0.029	0.025	0.015
Off-farm income	−0.094***	0.033	0.031	0.028	0.015
Constant	0.678***	0.117

Note: *, **, and *** significant at 10%, 5%, and 1% level significance, respectively.

Table 5. Tobit model estimates for a determinant of allocative efficiency and its marginal effects.

Allocative efficiency	Coefficients	Standard error	Marginal effects
			$\frac{\mathrm{\partial }E(y)}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }E(y^{\ast })}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }(\phi (Z_U-Z_L)}{\mathrm{\partial }{X}_j}$
Loss due to wild animals	0.0013	0.001	0.003	0.003	0.002
Educational levels	−0.00183	−0.002	0.013	0.011	0.007
Family size	−0.0008	−0.001	0.004	0.003	0.002
Farm experience	0.0005	0.001	0.001	0.001	0.001
Sex of household	0.028	0.028	0.025	0.021	0.008
Farm size	−0.020	−0.020	0.010	0.008	0.006
Livestock holding	0.006*	0.006	0.004	0.003	0.002
Slope of land	0.003	0.004	0.012	0.010	0.006
Fertility status	0.009	0.010	0.020	0.017	0.011
Distance to plot	−0.002	−0.002	0.001	0.001	0.001
Land conservation	0.022	0.022	0.020	0.016	0.010
Plowing frequency	0.012	0.013	0.014	0.011	0.007
Distance to the markets	−0.0002	0.0001	0.0001	0.0001	0.0001
Extension contacts	−0.0028	−0.003	0.002	0.002	0.001
Use of radio	−0.0266	−0.027	0.021	0.017	0.012
Uses of mobile	0.038**	0.038	0.021	0.017	0.013
Credit uses	0.0044	0.004	0.020	0.017	0.011
Off-farm income	−0.0340*	−0.034	0.022	0.018	0.010
Constant	0.606***	0.606

Note: *, **, and *** significant at 10%, 5%, and 1% level significance, respectively.

Table 6. Tobit model estimates for the determinant of economic efficiency and its marginal effects.

Economic efficiency	Coefficients	Standard error	Marginal effects
			$\frac{\mathrm{\partial }E(y)}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }E(y^{\ast })}{\mathrm{\partial }{X}_j}$	$\frac{\mathrm{\partial }(\phi (Z_U-Z_L)}{\mathrm{\partial }{X}_j}$
Loose due to wild animals	0.0064**	−0.006	0.004	0.003	0.00019
Educational levels	−0.013*	−0.014	0.015	0.015	0.0006
Family size	−0.005*	−0.005	0.004	0.004	0.00018
Farm experience	−0.0002	0.000	0.001	0.001	0.00005
Sex of household	0.054**	0.054	0.028	0.027	0.00102
Farm size	−0.0109*	−0.011	0.011	0.010	0.00044
Livestock holding	0.004*	0.005	0.005	0.004	0.00019
Slope of land	0.038***	0.039	0.014	0.013	0.00095
Fertility status	0.023	0.023	0.022	0.022	0.00115
Distance to plot	−0.00008	0.000	0.001	0.001	0.00004
Land conservation	0.0014	0.001	0.022	0.022	0.00077
Plowing frequency	0.0098	0.010	0.015	0.015	0.00058
Distance to the markets	−0.0002	0.000	0.001	0.0001	0.00002
Extension contacts	−0.0016	−0.002	0.002	0.002	0.00009
Use of radio	−0.018	−0.019	0.023	0.022	0.00093
Uses of mobile	0.016*	0.016	0.023	0.023	0.00094
Credit uses	−0.017	−0.017	0.022	0.022	0.00083
Off-farm income	−0.068***	−0.068	0.024	0.024	0.0013
Constant	0.417***	0.417

Note: *, **, and *** significant at 10%, 5%, and 1% level significance, respectively.

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