Increase economic productivity is a way to help smallholder farmers to become more resilient to the greater climate risks. In order to make smallholder farming profitable through an IMOD, it is important to examine the economy performance of these farmers.

1. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency of Producers’ in the Dryland
Areas of West Africa: a Multi-Output Stochastic
Metafrontier Approach
Alphonse Singbo
&
Pierre Sibiry
Bamako, Mali
May 29, 2015
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

2. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

3. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
2 Objective of the study
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

4. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
2 Objective of the study
3 Model Specification
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

5. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
2 Objective of the study
3 Model Specification
4 Data
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

6. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
2 Objective of the study
3 Model Specification
4 Data
5 Results
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

7. Objective Framework Modelling Data Summary results Conclusion
Contents
1 Motivation
2 Objective of the study
3 Model Specification
4 Data
5 Results
6 Conclusion
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

8. Objective Framework Modelling Data Summary results Conclusion
Agriculture value added
Agriculture value added and Population growth
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

9. Objective Framework Modelling Data Summary results Conclusion
Agriculture value added
Agriculture value added and Population growth
Country Agriculture Rate of pop.
(% of GDP) (1998 − 2015)
US 1.4 0.7
Brazil 5.3 0.9
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

10. Objective Framework Modelling Data Summary results Conclusion
Agriculture value added
Agriculture value added and Population growth
Country Agriculture Rate of pop.
(% of GDP) (1998 − 2015)
US 1.4 0.7
Brazil 5.3 0.9
Ghana 25.2 2.22
Niger 38.3 3.3
Nigeria 22.3 2.9
Mali 39.4 2.7
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

11. Objective Framework Modelling Data Summary results Conclusion
Motivation
Increase economic productivity is a way to help smallholder
farmers to become more resilient to the greater climate risks.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

12. Objective Framework Modelling Data Summary results Conclusion
Motivation
Increase economic productivity is a way to help smallholder
farmers to become more resilient to the greater climate risks.
In order to make smallholder farming profitable through an
IMOD, it is important to examine the economy performance
of these farmers.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

13. Objective Framework Modelling Data Summary results Conclusion
Motivation
Increase economic productivity is a way to help smallholder
farmers to become more resilient to the greater climate risks.
In order to make smallholder farming profitable through an
IMOD, it is important to examine the economy performance
of these farmers.
However, the study on inter-regional efficiency in Dryland
systems is rare.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

14. Objective Framework Modelling Data Summary results Conclusion
Motivation
Increase economic productivity is a way to help smallholder
farmers to become more resilient to the greater climate risks.
In order to make smallholder farming profitable through an
IMOD, it is important to examine the economy performance
of these farmers.
However, the study on inter-regional efficiency in Dryland
systems is rare.
Additionally, no study in WCA attempts to compare the
production possibilty in the region using on household level
data.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

15. Objective Framework Modelling Data Summary results Conclusion
Motivation
Increase economic productivity is a way to help smallholder
farmers to become more resilient to the greater climate risks.
In order to make smallholder farming profitable through an
IMOD, it is important to examine the economy performance
of these farmers.
However, the study on inter-regional efficiency in Dryland
systems is rare.
Additionally, no study in WCA attempts to compare the
production possibilty in the region using on household level
data.
Previous studies related to Africa have used aggregate country
level data.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

16. Objective Framework Modelling Data Summary results Conclusion
Objective
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

17. Objective Framework Modelling Data Summary results Conclusion
Objective
1 Measure and compare technical efficiency of producers in the
dryland systems.
From the modelling :
Estimate Technical Inefficiency in each country : Ghana,
Niger, Nigeria and Mali
Estimate the metatechnology ratio (technology gap) of each
country relative to the whole region
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

18. Objective Framework Modelling Data Summary results Conclusion
Objective
1 Measure and compare technical efficiency of producers in the
dryland systems.
From the modelling :
Estimate Technical Inefficiency in each country : Ghana,
Niger, Nigeria and Mali
Estimate the metatechnology ratio (technology gap) of each
country relative to the whole region
2 Identify the position of each country regarding the
metafrontier.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

19. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency, Metafrontier Efficiency and
Metatechnology Ratio (MTR)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

20. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency, Metafrontier Efficiency and
Metatechnology Ratio (MTR)
Definition
Technical Efficiency (TE) : the ability of a producer to obtain
the maximum output from a given input vector.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

21. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency, Metafrontier Efficiency and
Metatechnology Ratio (MTR)
Definition
Technical Efficiency (TE) : the ability of a producer to obtain
the maximum output from a given input vector.
Definition
Metafrontier Technical Efficiency (MTE) : the ability to obtain
the maximum output from a given input vector with respect to the
production frontier of the region (metafrontier).
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

22. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency, Metafrontier Efficiency and
Metatechnology Ratio (MTR)
Definition
Technical Efficiency (TE) : the ability of a producer to obtain
the maximum output from a given input vector.
Definition
Metafrontier Technical Efficiency (MTE) : the ability to obtain
the maximum output from a given input vector with respect to the
production frontier of the region (metafrontier).
Definition
Metatechnology Ratio (MTR) : the distance between the
frontier of a country relative to the metafrontier.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

23. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

24. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

25. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

26. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
O
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

27. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽
O
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

28. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽
A
B
O
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

29. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽
A
B
O
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

30. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽
A
B
O
𝑇𝐸 =
𝑂𝐴
𝑂𝐵
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

31. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency framework
Input x
Output y
a
b
c
d
e
f
g
i
h
j
Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽
A
B
O
𝑇𝐸 =
𝑂𝐴
𝑂𝐵
For example, 𝑇𝐸 = 0.6 indicates that the output vector, y, is
60% of the maximum output that could be produced by a
farm using the input vector, x.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

32. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

33. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
Input x
Output y
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

34. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
Input x
Output y
1
1 1
1
1
1
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

35. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
Input x
Output y
1
1 1
1
1
1
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

36. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
Input x
Output y
1
1 1
1
1
1
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
2
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

37. Objective Framework Modelling Data Summary results Conclusion
Metafrontier framework
Input x
Output y
1
1 1
1
1
1
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

38. Objective Framework Modelling Data Summary results Conclusion
Metatechnology ratio (MTR)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

39. Objective Framework Modelling Data Summary results Conclusion
Metatechnology ratio (MTR)
Input x
Output y
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

40. Objective Framework Modelling Data Summary results Conclusion
Metatechnology ratio (MTR)
Input x
Output y
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

41. Objective Framework Modelling Data Summary results Conclusion
Metatechnology ratio (MTR)
Input x
Output y
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

42. Objective Framework Modelling Data Summary results Conclusion
Metatechnology ratio (MTR)
Input x
Output y
Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1
0
C
D
E
 TE of A according to CF2: 𝑻𝑬 𝑨
𝑪𝑭 𝟐
=
𝟎𝑪
𝟎𝑫
 TE of A according to the Metafrontier: 𝑻𝑬 𝑨 =
𝟎𝑪
𝟎𝑬
 𝑴𝑻𝑹 𝑨
𝟐
=
𝑻𝑬 𝑨
𝑻𝑬 𝑨
𝑪𝑭 𝟐
=
𝟎𝑪 𝟎𝑬
𝟎𝑪 𝟎𝑫
=
𝟎𝑫
𝟎𝑬
𝑴𝑻𝑹 𝑨
𝟐
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

43. Objective Framework Modelling Data Summary results Conclusion
Empirical Modelling
First step : Stochastic distance function. For each country run
the Modified Translog function to estimate parameters and the TE
− ln yi
m = β0 + βdDi
k + βlFi
l + k βk ln(xi
k) + l βl ln(
yi
l
yi
m
)
+1
2 k j βkj ln(xi
k) ln(xi
j) + 1
2 l h βlh ln(
yi
l
yi
m
) ln(
yi
h
yi
m
)
+1
2 k l βkl ln(xi
k) ln(
yi
l
yi
m
) + vi − ln(TEi
)
where : vi ∼ iid N(0, σ2
v ) and vi and TEi
are distributed independently
and TEi
∈ (0, 1[
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

44. Objective Framework Modelling Data Summary results Conclusion
Empirical Modelling
Second step : Metafrontier programming. From the parameters
estimated in Step 1, we solve tle LP problems to ensure that the
metafrontier envelop the country frontiers (convexity)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

45. Objective Framework Modelling Data Summary results Conclusion
Empirical Modelling
Second step : Metafrontier programming. From the parameters
estimated in Step 1, we solve tle LP problems to ensure that the
metafrontier envelop the country frontiers (convexity)
The LP problem is :
minβ x · β
st : xi · β ≥ xi · βk
where : βk
is the estimated coefficient vector associated with the
country group stochactic frontier obtained in step 1.
x is the arithmetic average of the xi vectors over all farms.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

46. Objective Framework Modelling Data Summary results Conclusion
Empirical Modelling
Third step : Compute the Metatechnology ratio (MTR).
MTRi
k = exiβk
exiβ
Final step : Compute TE relative to the metafrontier.
TE
i
= TEk
i
× MTRk
i
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

47. Objective Framework Modelling Data Summary results Conclusion
Data
The baseline survey data collected within the CRP dryland
systems in 2012 were used in four countries : Ghana, Niger,
Nigeria and Mali
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

48. Objective Framework Modelling Data Summary results Conclusion
Data
The baseline survey data collected within the CRP dryland
systems in 2012 were used in four countries : Ghana, Niger,
Nigeria and Mali
Outputs are aggregated into two groups : Cereals and Other
crops (legumes and cotton)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

49. Objective Framework Modelling Data Summary results Conclusion
Data
The baseline survey data collected within the CRP dryland
systems in 2012 were used in four countries : Ghana, Niger,
Nigeria and Mali
Outputs are aggregated into two groups : Cereals and Other
crops (legumes and cotton)
Inputs are aggregated into five categories : capital, materials,
livestock, labor and land
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

50. Objective Framework Modelling Data Summary results Conclusion
Data
The baseline survey data collected within the CRP dryland
systems in 2012 were used in four countries : Ghana, Niger,
Nigeria and Mali
Outputs are aggregated into two groups : Cereals and Other
crops (legumes and cotton)
Inputs are aggregated into five categories : capital, materials,
livestock, labor and land
The multilateral Tornqvist price index is used to construct an
implicit quantity index for each output and input.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

51. Objective Framework Modelling Data Summary results Conclusion
Data
Data are in Purchasing Power parity ($)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

52. Objective Framework Modelling Data Summary results Conclusion
Data
Data are in Purchasing Power parity ($)
Two Outputs Ghana Niger Nigeria Mali
Cereal 53, 358.34 578.42 3, 151.67 2, 66.77
Other crops 52, 626.20 214.35 5, 996.91 323.10
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

53. Objective Framework Modelling Data Summary results Conclusion
Data
Data are in Purchasing Power parity ($)
Two Outputs Ghana Niger Nigeria Mali
Cereal 53, 358.34 578.42 3, 151.67 2, 66.77
Other crops 52, 626.20 214.35 5, 996.91 323.10
Five Inputs
Capital 52.86 36.00 99.33 85.93
Labor (man − hours) 5.42 7.35 7.34 11.75
Land (ha) 6.24 9.46 9.21 14.38
Materials 371.68 346.92 1, 551.89 930.30
Livestock (livestock units) 1.64 9.46 2.63 9.08
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

54. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

55. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
Estimated of the Distance Function Elasticities
Variables
ln OtherCrops
ln Capital
ln Labor
ln Land
ln Materials
ln Livestock
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

56. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
Estimated of the Distance Function Elasticities
Variables Ghana
ln OtherCrops −0.619∗∗∗
ln Capital 0.167
ln Labor 0.396
ln Land 0.063
ln Materials 0.121∗∗
ln Livestock −0.693∗∗∗
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

57. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
Estimated of the Distance Function Elasticities
Variables Ghana Niger
ln OtherCrops −0.619∗∗∗
−1.056∗∗∗
ln Capital 0.167 1.649∗∗
ln Labor 0.396 0.779
ln Land 0.063 4.798
ln Materials 0.121∗∗
−0.098
ln Livestock −0.693∗∗∗
−15.923∗∗∗
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

58. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
Estimated of the Distance Function Elasticities
Variables Ghana Niger Nigeria
ln OtherCrops −0.619∗∗∗
−1.056∗∗∗
−0.615∗∗∗
ln Capital 0.167 1.649∗∗
0.088∗
ln Labor 0.396 0.779 0.148
ln Land 0.063 4.798 −0.020
ln Materials 0.121∗∗
−0.098 0.048∗∗
ln Livestock −0.693∗∗∗
−15.923∗∗∗
−0.107
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

59. Objective Framework Modelling Data Summary results Conclusion
Estimated parameters
Estimated of the Distance Function Elasticities
Variables Ghana Niger Nigeria Mali
ln OtherCrops −0.619∗∗∗
−1.056∗∗∗
−0.615∗∗∗
−0.065∗∗∗
ln Capital 0.167 1.649∗∗
0.088∗
−0.160∗∗∗
ln Labor 0.396 0.779 0.148 1.227∗∗∗
ln Land 0.063 4.798 −0.020 −0.836∗∗∗
ln Materials 0.121∗∗
−0.098 0.048∗∗
0.090
ln Livestock −0.693∗∗∗
−15.923∗∗∗
−0.107 0.296∗∗∗
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

60. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency and Metatechnology ratio
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

61. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency and Metatechnology ratio
Estimates of technical efficiency (TE) and Metatechnology
ratio (MTR)
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

62. Objective Framework Modelling Data Summary results Conclusion
Technical Efficiency and Metatechnology ratio
Estimates of technical efficiency (TE) and Metatechnology
ratio (MTR)
Country TE country MTR
frontier
Ghana 0.996 0.164
Niger 0.996 0.063
Nigeria 0.452 0.053
Mali 0.989 0.109
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

63. Objective Framework Modelling Data Summary results Conclusion
Implications
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

64. Objective Framework Modelling Data Summary results Conclusion
Implications
Smallholder producers are operating at the high level of their
country frontier indicating that there are homogeneous
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

65. Objective Framework Modelling Data Summary results Conclusion
Implications
Smallholder producers are operating at the high level of their
country frontier indicating that there are homogeneous
Comparing to the metafrontier, Nigeria producers are
operating at the lowest level and Ghana producers are at the
highest level
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

66. Objective Framework Modelling Data Summary results Conclusion
Implications
Smallholder producers are operating at the high level of their
country frontier indicating that there are homogeneous
Comparing to the metafrontier, Nigeria producers are
operating at the lowest level and Ghana producers are at the
highest level
Along with the GPS mapping it is possible to map the
position of producers performance in the region.
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

67. Objective Framework Modelling Data Summary results Conclusion
Thanks
Comments and suggestions are most welcome !
A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA