Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency of Producers’ in the DrylandAreas 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

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

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

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

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

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

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

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 0.7Brazil 5.3 0.9

Ghana 25.2 2.22Niger 38.3 3.3Nigeria 22.3 2.9Mali 39.4 2.7

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

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 0.7Brazil 5.3 0.9

Ghana 25.2 2.22Niger 38.3 3.3Nigeria 22.3 2.9Mali 39.4 2.7

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

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 0.7Brazil 5.3 0.9

Ghana 25.2 2.22Niger 38.3 3.3Nigeria 22.3 2.9Mali 39.4 2.7

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

MotivationIncrease economic productivity is a way to help smallholderfarmers to become more resilient to the greater climate risks.

In order to make smallholder farming profitable through anIMOD, it is important to examine the economy performanceof these farmers.

However, the study on inter-regional efficiency in Drylandsystems is rare.

Additionally, no study in WCA attempts to compare theproduction possibilty in the region using on household leveldata.

Previous studies related to Africa have used aggregate countrylevel data.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

MotivationIncrease economic productivity is a way to help smallholderfarmers to become more resilient to the greater climate risks.

In order to make smallholder farming profitable through anIMOD, it is important to examine the economy performanceof these farmers.

However, the study on inter-regional efficiency in Drylandsystems is rare.

Additionally, no study in WCA attempts to compare theproduction possibilty in the region using on household leveldata.

Previous studies related to Africa have used aggregate countrylevel data.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

MotivationIncrease economic productivity is a way to help smallholderfarmers to become more resilient to the greater climate risks.

In order to make smallholder farming profitable through anIMOD, it is important to examine the economy performanceof these farmers.

However, the study on inter-regional efficiency in Drylandsystems is rare.

Additionally, no study in WCA attempts to compare theproduction possibilty in the region using on household leveldata.

Previous studies related to Africa have used aggregate countrylevel data.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

MotivationIncrease economic productivity is a way to help smallholderfarmers to become more resilient to the greater climate risks.

In order to make smallholder farming profitable through anIMOD, it is important to examine the economy performanceof these farmers.

However, the study on inter-regional efficiency in Drylandsystems is rare.

Additionally, no study in WCA attempts to compare theproduction possibilty in the region using on household leveldata.

Previous studies related to Africa have used aggregate countrylevel data.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

MotivationIncrease economic productivity is a way to help smallholderfarmers to become more resilient to the greater climate risks.

In order to make smallholder farming profitable through anIMOD, it is important to examine the economy performanceof these farmers.

However, the study on inter-regional efficiency in Drylandsystems is rare.

Additionally, no study in WCA attempts to compare theproduction possibilty in the region using on household leveldata.

Previous studies related to Africa have used aggregate countrylevel data.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Objective

1 Measure and compare technical efficiency of producers in thedryland systems.

From the modelling :

Estimate Technical Inefficiency in each country : Ghana,Niger, Nigeria and Mali

Estimate the metatechnology ratio (technology gap) of eachcountry relative to the whole region

2 Identify the position of each country regarding themetafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Objective

1 Measure and compare technical efficiency of producers in thedryland systems.

From the modelling :

Estimate Technical Inefficiency in each country : Ghana,Niger, Nigeria and Mali

Estimate the metatechnology ratio (technology gap) of eachcountry relative to the whole region

2 Identify the position of each country regarding themetafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Objective

1 Measure and compare technical efficiency of producers in thedryland systems.

From the modelling :

Estimate Technical Inefficiency in each country : Ghana,Niger, Nigeria and Mali

Estimate the metatechnology ratio (technology gap) of eachcountry relative to the whole region

2 Identify the position of each country regarding themetafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency, Metafrontier Efficiency andMetatechnology Ratio (MTR)

DefinitionTechnical Efficiency (TE) : the ability of a producer to obtainthe maximum output from a given input vector.

DefinitionMetafrontier Technical Efficiency (MTE) : the ability to obtainthe maximum output from a given input vector with respect to theproduction frontier of the region (metafrontier).

DefinitionMetatechnology Ratio (MTR) : the distance between thefrontier of a country relative to the metafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency, Metafrontier Efficiency andMetatechnology Ratio (MTR)

DefinitionTechnical Efficiency (TE) : the ability of a producer to obtainthe maximum output from a given input vector.

DefinitionMetafrontier Technical Efficiency (MTE) : the ability to obtainthe maximum output from a given input vector with respect to theproduction frontier of the region (metafrontier).

DefinitionMetatechnology Ratio (MTR) : the distance between thefrontier of a country relative to the metafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency, Metafrontier Efficiency andMetatechnology Ratio (MTR)

DefinitionTechnical Efficiency (TE) : the ability of a producer to obtainthe maximum output from a given input vector.

DefinitionMetafrontier Technical Efficiency (MTE) : the ability to obtainthe maximum output from a given input vector with respect to theproduction frontier of the region (metafrontier).

DefinitionMetatechnology Ratio (MTR) : the distance between thefrontier of a country relative to the metafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency, Metafrontier Efficiency andMetatechnology Ratio (MTR)

DefinitionTechnical Efficiency (TE) : the ability of a producer to obtainthe maximum output from a given input vector.

DefinitionMetafrontier Technical Efficiency (MTE) : the ability to obtainthe maximum output from a given input vector with respect to theproduction frontier of the region (metafrontier).

DefinitionMetatechnology Ratio (MTR) : the distance between thefrontier of a country relative to the metafrontier.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x

Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x

Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O

Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O

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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O

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

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency framework

Input x Input x

Output y

Input x

Output y

a

b

c

d

e

f

g i

h

j

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O Input x

Output y

a

b

c

d

e

f

g i

h

j

Production Frontier ≡ 𝑃𝐹 𝑥; 𝛽

A

B

O 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

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metafrontier framework

Input x

Output y

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

1

1 1

1

1

1

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

2

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

Objective Framework Modelling Data Summary results Conclusion

Metatechnology ratio (MTR)

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

0

C

D

E

TE of A according to CF2: 𝑻𝑬𝑨𝑪𝑭𝟐 =

𝟎𝑪

𝟎𝑫

TE of A according to the Metafrontier: 𝑻𝑬𝑨 =𝟎𝑪

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐 =

𝑻𝑬𝑨

𝑻𝑬𝑨𝑪𝑭𝟐

=𝟎𝑪 𝟎𝑬

𝟎𝑪 𝟎𝑫 =

𝟎𝑫

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Metatechnology ratio (MTR)

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

0

C

D

E

TE of A according to CF2: 𝑻𝑬𝑨𝑪𝑭𝟐 =

𝟎𝑪

𝟎𝑫

TE of A according to the Metafrontier: 𝑻𝑬𝑨 =𝟎𝑪

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐 =

𝑻𝑬𝑨

𝑻𝑬𝑨𝑪𝑭𝟐

=𝟎𝑪 𝟎𝑬

𝟎𝑪 𝟎𝑫 =

𝟎𝑫

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Metatechnology ratio (MTR)

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

0

C

D

E

TE of A according to CF2: 𝑻𝑬𝑨𝑪𝑭𝟐 =

𝟎𝑪

𝟎𝑫

TE of A according to the Metafrontier: 𝑻𝑬𝑨 =𝟎𝑪

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐 =

𝑻𝑬𝑨

𝑻𝑬𝑨𝑪𝑭𝟐

=𝟎𝑪 𝟎𝑬

𝟎𝑪 𝟎𝑫 =

𝟎𝑫

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Metatechnology ratio (MTR)

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

0

C

D

E

TE of A according to CF2: 𝑻𝑬𝑨𝑪𝑭𝟐 =

𝟎𝑪

𝟎𝑫

TE of A according to the Metafrontier: 𝑻𝑬𝑨 =𝟎𝑪

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐 =

𝑻𝑬𝑨

𝑻𝑬𝑨𝑪𝑭𝟐

=𝟎𝑪 𝟎𝑬

𝟎𝑪 𝟎𝑫 =

𝟎𝑫

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Metatechnology ratio (MTR)

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

Input x

Output y

Country 1 frontier ≡ 𝐶𝐹1 𝑥; 𝛽 1

0

C

D

E

TE of A according to CF2: 𝑻𝑬𝑨𝑪𝑭𝟐 =

𝟎𝑪

𝟎𝑫

TE of A according to the Metafrontier: 𝑻𝑬𝑨 =𝟎𝑪

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐 =

𝑻𝑬𝑨

𝑻𝑬𝑨𝑪𝑭𝟐

=𝟎𝑪 𝟎𝑬

𝟎𝑪 𝟎𝑫 =

𝟎𝑫

𝟎𝑬

𝑴𝑻𝑹𝑨𝟐

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Empirical Modelling

First step : Stochastic distance function. For each country runthe Modified Translog function to estimate parameters and the TE

− ln yim = β0 + βdDik + βlFi

l +∑

k βk ln(xik) +

∑l βl ln( y i

ly i

m)

+ 12

∑k

∑j βkj ln(xi

k) ln(xij) +

12

∑l∑

h βlh ln( yil

yim) ln( yi

hyi

m)

+ 12

∑k

∑l βkl ln(xi

k) ln(yi

lyi

m) + vi − ln(TEi)

where : vi ∼ iid N(0, σ2v ) and vi and TEi are distributed independently

and TEi ∈ (0, 1[

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Empirical Modelling

Second step : Metafrontier programming. From the parametersestimated in Step 1, we solve tle LP problems to ensure that themetafrontier envelop the country frontiers (convexity)

The LP problem is :

minβ x · βst : xi · β ≥ xi · β̂k

where : β̂k is the estimated coefficient vector associated with thecountry 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

Objective Framework Modelling Data Summary results Conclusion

Empirical Modelling

Second step : Metafrontier programming. From the parametersestimated in Step 1, we solve tle LP problems to ensure that themetafrontier envelop the country frontiers (convexity)

The LP problem is :

minβ x · βst : xi · β ≥ xi · β̂k

where : β̂k is the estimated coefficient vector associated with thecountry 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

Objective Framework Modelling Data Summary results Conclusion

Empirical Modelling

Third step : Compute the Metatechnology ratio (MTR).

MTR ik = exiβ

k

exiβ

Final step : Compute TE relative to the metafrontier.

T̂Ei= T̂Ek

i× M̂TRk

i

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

The baseline survey data collected within the CRP drylandsystems in 2012 were used in four countries : Ghana, Niger,Nigeria and Mali

Outputs are aggregated into two groups : Cereals and Othercrops (legumes and cotton)

Inputs are aggregated into five categories : capital, materials,livestock, labor and land

The multilateral Tornqvist price index is used to construct animplicit quantity index for each output and input.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

The baseline survey data collected within the CRP drylandsystems in 2012 were used in four countries : Ghana, Niger,Nigeria and Mali

Outputs are aggregated into two groups : Cereals and Othercrops (legumes and cotton)

Inputs are aggregated into five categories : capital, materials,livestock, labor and land

The multilateral Tornqvist price index is used to construct animplicit quantity index for each output and input.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

The baseline survey data collected within the CRP drylandsystems in 2012 were used in four countries : Ghana, Niger,Nigeria and Mali

Outputs are aggregated into two groups : Cereals and Othercrops (legumes and cotton)

Inputs are aggregated into five categories : capital, materials,livestock, labor and land

The multilateral Tornqvist price index is used to construct animplicit quantity index for each output and input.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

The baseline survey data collected within the CRP drylandsystems in 2012 were used in four countries : Ghana, Niger,Nigeria and Mali

Outputs are aggregated into two groups : Cereals and Othercrops (legumes and cotton)

Inputs are aggregated into five categories : capital, materials,livestock, labor and land

The multilateral Tornqvist price index is used to construct animplicit quantity index for each output and input.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

Data are in Purchasing Power parity ($)

Two Outputs Ghana Niger Nigeria MaliCereal 53, 358.34 578.42 3, 151.67 2, 66.77Other crops 52, 626.20 214.35 5, 996.91 323.10Five InputsCapital 52.86 36.00 99.33 85.93Labor (man− hours) 5.42 7.35 7.34 11.75Land (ha) 6.24 9.46 9.21 14.38Materials 371.68 346.92 1, 551.89 930.30Livestock (livestock units) 1.64 9.46 2.63 9.08

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

Data are in Purchasing Power parity ($)

Two Outputs Ghana Niger Nigeria MaliCereal 53, 358.34 578.42 3, 151.67 2, 66.77Other crops 52, 626.20 214.35 5, 996.91 323.10

Five InputsCapital 52.86 36.00 99.33 85.93Labor (man− hours) 5.42 7.35 7.34 11.75Land (ha) 6.24 9.46 9.21 14.38Materials 371.68 346.92 1, 551.89 930.30Livestock (livestock units) 1.64 9.46 2.63 9.08

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Data

Data are in Purchasing Power parity ($)

Two Outputs Ghana Niger Nigeria MaliCereal 53, 358.34 578.42 3, 151.67 2, 66.77Other crops 52, 626.20 214.35 5, 996.91 323.10Five InputsCapital 52.86 36.00 99.33 85.93Labor (man− hours) 5.42 7.35 7.34 11.75Land (ha) 6.24 9.46 9.21 14.38Materials 371.68 346.92 1, 551.89 930.30Livestock (livestock units) 1.64 9.46 2.63 9.08

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Estimated parameters

Estimated of the Distance Function Elasticities

Variables Ghana Niger Nigeria Maliln 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∗∗ 0.090ln Livestock −0.693∗∗∗ −15.923∗∗∗ −0.107 0.296∗∗∗

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

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

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

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

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

Objective Framework Modelling Data Summary results Conclusion

Estimated parameters

Estimated of the Distance Function Elasticities

Variables Ghana Niger Nigeria Maliln 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∗∗ 0.090ln Livestock −0.693∗∗∗ −15.923∗∗∗ −0.107 0.296∗∗∗

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency and Metatechnology ratio

Estimates of technical efficiency (TE) and Metatechnologyratio (MTR)

Country TE country MTRfrontier

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency and Metatechnology ratioEstimates of technical efficiency (TE) and Metatechnologyratio (MTR)

Country TE country MTRfrontier

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

Objective Framework Modelling Data Summary results Conclusion

Technical Efficiency and Metatechnology ratioEstimates of technical efficiency (TE) and Metatechnologyratio (MTR)

Country TE country MTRfrontier

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

Objective Framework Modelling Data Summary results Conclusion

Implications

I Smallholder producers are operating at the high level of theircountry frontier indicating that there are homogeneous

I Comparing to the metafrontier, Nigeria producers areoperating at the lowest level and Ghana producers are at thehighest level

I Along with the GPS mapping it is possible to map theposition of producers performance in the region.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Implications

I Smallholder producers are operating at the high level of theircountry frontier indicating that there are homogeneous

I Comparing to the metafrontier, Nigeria producers areoperating at the lowest level and Ghana producers are at thehighest level

I Along with the GPS mapping it is possible to map theposition of producers performance in the region.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Implications

I Smallholder producers are operating at the high level of theircountry frontier indicating that there are homogeneous

I Comparing to the metafrontier, Nigeria producers areoperating at the lowest level and Ghana producers are at thehighest level

I Along with the GPS mapping it is possible to map theposition of producers performance in the region.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

Objective Framework Modelling Data Summary results Conclusion

Implications

I Smallholder producers are operating at the high level of theircountry frontier indicating that there are homogeneous

I Comparing to the metafrontier, Nigeria producers areoperating at the lowest level and Ghana producers are at thehighest level

I Along with the GPS mapping it is possible to map theposition of producers performance in the region.

A. Singbo & P. Sibiry Metatechnology frontier in the Dryland Areas of WA

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