soil conservation and small-scale food production in highland ethiopia: a stochastic metafrontier...

Soil Conservation and Small-scale Food Production in Highland Ethiopia: A Stochastic Metafrontier Approach

Haileselassie Medhin, University of Gothenburg

Gunnar Köhlin, University of Gothenburg

ABSTRACT

This study adopts the stochastic metafrontier approach to investigate the roleof soil conservation in small-scale highland agriculture in Ethiopia. Plot-levelstochastic frontiers and metafrontier technology-gap ratios were estimated forthree soil-conservation technology groups and a group of plots without soilconservation. Plots with soil conservation were found to be more technicallyefficient than plots without. The metafrontier estimates showed that soilconservation enhances the technological position of naturally disadvantagedplots. The potential advantage of efficiency measurement in the evaluation offarm technologies is also discussed.

UNIVERSITY OF GOTHENBURG

SCHOOL OF BUSINESS, ECONOMICS AND LAW

Soil Conservation and Small-scale Food Production in Highland Ethiopia: A Stochastic

Metafrontier Approach

Haileselassie MedhinUniversity of Gothenburg

Gunnar KöhlinUniversity of Gothenburg

September 2010



Introduction

‒ Ethiopian highland agriculture is characterized by Small-scale

subsistence farming, high rainfall dependency, backward

technology, high population pressure, severe land degradation,

etc…

‒ It has one of the lowest productivity levels in the world.

‒ Better land management visa Soil and Water Conservation (SWC)

technology is a often cited as the best solution.

‒ Many SWC technologies – we often don’t know what works where

in the real world.



The major issues in the economics of SWC

1) The determinants of successful SWC adoption:

‒ Risk behavior and time preference of peasants

‒ Off–farm activities and resource endowment

‒ Yield variability effect

2) Empirical analysis of the effect of SWC on productivity:

‒ Mixed results.

‒ The results are also case specific, both in type of SWC and in theagro-ecological characteristics of the study areas.

‒ There is no universally accepted methodological framework to assesthe role SWC on productivity.



Simple productivity decomposition

‒ Applying a simple concept of productivity decomposition, this study aims

to contribute to the ongoing quest for a better methodological framework

to asses the role of SWC in small-scale agriculture.

‒ An important relationship: change in technology can bring a change

in efficiency in either direction.

Change in Productivity

Advance in Technology Improvemnt in Efficiency+

=

Pushing the PPF outward

Producing as close as possible to the PPF



Efficiency

‒ Economic Efficiency = Technical Efficiency (TE) + Allocative Efficiency (AE)

‒ TE:- the ability of a firm to obtain maximum output from a given set of

inputs

‒ AE:- the ability of a firm to use the inputs in optimal proportions given

their prices and the production technology

‒ This study is mainly concerned with TE.



The net effect

‒ Therefore, the effect of a given SWC technology as observed in yield

change in the net effect of the two sources: the direct technology effect

and the indirect efficiency effect.

‒ Such a decomposition would have important policy implications if a given

SWC technology has in deed has an efficiency effect. For example:

‒ Yield effect without decomposition: negative or insignificant

‒ Yield effect with decomposition: positive technology effect and

negative efficiency effect

‒ Recommendation:- Examine the negative efficiency effect and design

strategies that can correct it.



Figure 1: Improvement in Technology and Technical Efficiency

T

Q

X

YQ

YT

Input

Output

FT

F

T

Let the output at the new technology is Y*.

If Y*=YT, TE

OLD=TE

New

If YQ<Y*<Y

T, TE

OLD>TE

New

If Y*=YQ, TE

OLD>TE

New, productivity remains constant.

If Y*<YQ, TE

OLD>TE

New, produvtivity declines.

Productivity increases.



Main objectives

‒ Assess the feasibility of efficiency measurement methods for

such decomposition

‒ Examine the relevance of such decomposition using

household data from Ethiopia

‒ Test if different SWC practices are indeed ‘technologies’

‒ And on the way,

‒ Explore links between SWC and efficiency

‒ Highlight some overlooked challenges of efficiency analysis in

agriculture (at the center of efficiency analysis are strong assumptions

regarding ‘technology’)



Measuring technical efficiency

‒ To measure TE, one needs to estimate the production function.

‒ Many approaches to measure TE, each with their own merits and

deficiencies - the choice depends on the nature of the problem at

hand.

‒ Nonetheless, given the higher noise experienced in agricultural

data, stochastic frontier models fit agricultural analysis better

(Battese, 1992).



The key assumption

‒ An important assumption in TE measurement is that individual

firms (or farms) included in the frontier being estimated operate

at the same level of technology.

‒ Violation of this assumption biases TE estimates as output

differentials emanating from technology differentials could be

treated as TE differentials. Or, firms with higher technology

could appear more efficient they are.

‒ The Stochastic Metafrontier model, a recent variant of stochastic

frontier models, is developed to correct this bias.



The challenge as an opportunity

‒ In order to get unbiased TE estimates, we need to make sure that all

firms/farms in our sample operate at the same technology. How do we

do that?

‒ We identify possible technologies

‒ We classify our sample based on these possible technologies’

‒ We test if there is a significant difference between the

technologies in each sub-sample

‒ What if we use SWC as a possible technology?

‒ An opportunity to test if different SWC methods are indeed

technologies and evaluate how good of a technology they are

(measure Technology Gaps).



Figure 3: The Stochastic Metafrontier Curve

S. Frontier

for Group1

S. Frontier for Group 2

S. Frontier for

Group 4

The metafrontier Curve Output

Y

Inputs X

S. Frontier for

Group 3



Measuring TE using the stochastic Metafrontier approach

‒ The stochastic frontier function is defined as:

Where: Yi = output of the ith firm, Xi = vector of inputs, β = vector of parameters,

Vi = random error term and Ui = inefficiency term.

‒ In agricultural analysis the term Vi capture random factors such as measurement errors,

weather condition, drought strikes, luck, etc…

‒ Vi are assumed to be independently and identically distributed normal random variables with

constant variance, independent of Ui which are assumed to be non-negative exponential or

half-normal or truncated (at zero) variables of N(μi, σ2), where μi are defined by some

inefficiency model [ Coelli et al, 1998; Battese and Rao, 2002].

)( i );(Y ii UV

i eXf

, i = 1, 2,...., n (1)




‒ TE for firm i is defined as:

‒ Now assume that there are j groups of firms in an industry, classified

based on their technology. Suppose that for the stochastic frontier for a

sample data of nj firms the jth group is defined by:

iui eTE

)( ij );(Y ijij UV

ij eXf

(2)

(3), i = 1,2,....,nj




‒ Assuming the production function is of Cobb–Douglas, this can be re –written as:

‒ The ‘overall’ stochastic frontier of the firms in the industry without stratifying

them into technology groups is:

‒ Equation (5) is nothing but the Stochastic Metafrontier function. In simple

terms, the Stochastic Metafrontier function is the envelope of group stochastic

frontiers.

j

UVXUV

ij nieeXf ijijijijij ,....,2,1,);(Y)(

ij

jUVXUV

i nnwherenieeXf iiiii ,,....,2,1,*)(Y***)**(

; i

(4)

(5)




‒ Hence, we can have two different TE estimates of a firm, own with respect to the

frontier of its technology group and another with respect to the metafrontier. We

will call these estimates Group TE (TEi) and Meta TE (TE*i) respectively.

‒ The coefficients of each group’s stochastic frontier, the Group TEs for each firm,

and the coefficients for variables that determine TE can be estimated using

Maximum Likelihood Estimation (MLE).

iui eTE

*

iui eTE



Technology Gap Ratio (TGR)

‒ From the definition of the metafrontier, it is expected that the deterministic values

Xijβ and Xiβ* should satisfy the inequality Xijβ ≤ Xiβ*. According to Battese and Rao

(2002), this relationship can be written as:

‒ Equation (6) simply indicates that, if there is a difference between the estimated

parameters of a given group and the metafrontier, it should arise from a difference in

at least one of the three ratios, namely the technology gap ratio (TGR), the random

error ratio (RER), and the technical efficiency ratio (TER). That is,

(6)

(7)

***X

X

i

ij

1i

i

i

i

U

U

V

V

e

e

e

e

e

e

*,

*

*

*

)*(

*X

X

i

ij

i

i

U

UVV

V

V

iX

iTE

TE

e

eTERande

e

eRERe

e

eTGR

i

i

i

ii

i

i

i




‒ TGR estimates the proportion the technology differential of each firm in a group,

relative to the best technology in the industry. This assumes that all groups have

potential access to the best technology in the industry. TGR and TER can be

estimated for each firm.

‒ Note that it should be the case TEi ≤ TEi*. Therefore TER is expected to be greater

than or equal to unity. RER is not observable because it is based on the non-

observable disturbance term Vi. Hence, as far as the estimation is concerned,

equation (6) can be re-written as:

(8)iiU

U

TERTGRe

e

e

e

i

i

**X

X

i

ij

1




‒ Combining (7) and (8) gives

‒ This is a very important identity in the sense that it enables us to estimate

to what extent the TE (hence productivity) of a given firm or group of firms

could be increased if it adopted the best available technology in the

industry.

‒ This also indicates that TGR is less than or equal to unity. If a given firm

has a TGR of 1, it simply means that the firm uses the best technology

available in the industry.

‒ In our case, individual plots are the firms and they are grouped into

different technology groups according to the type of their SWC technology.

iiTGRTETE

i* (9)



Estimating the Envelope

‒ In reality, all production points of the group stochastic frontiers may not lie on or below

the metafrontier. There could be outlier points to group stochastic frontiers (that is why

they are stochastic!) which could also be outliers to the metafrontier. This indicates that

estimating the metafrontier demands the very definition of the metafrontier as an

assumption: all production points of all groups are enveloped by the metafrontier curve.

Hence, the metafrontier curve can be estimated using a simple optimization problem,

expressed as:

‒ X’ is the row vector of means of all inputs for each technology group; β is the vector

group coefficients and β* is the vector of meta coefficients we are looking for. This is a

simple linear programming problem. Each plot’s production point will be an equation

line in a sequence of simultaneous equations with an unknown right hand side variable.

Minimize X’βSubject to Xiβ ≤ Xiβ*

(10)



Data and Empirical Specification

‒ Data from the Ethiopian Environmental Survey (by EDRI, UoG and World

Bank) that covers about 1760 households 14 kebeles in the Ethiopian

highlands.

‒ Teff and wheat plots (total of 1228 plots)

‒ Emphasis on three SWC technologies (stone bunds, soil bunds and bench

terraces) and a group of plots with no SWC.

‒ But the estimation of the metafrontier requires all SWC technologies.

Hence the remaining SWC technologies are also included in the estimation

even though excluded in the analysis.



SWC Groups

Mean Value

Variable None Soil bunds Stone bunds Bench terraces Pooled

Yield(kg/ha) 1035.87 815.32 955.76 943.79 1076.02

Labor(days) 38.61 39.80 48.97 47.96 43.42

Traction(days) 5.74 5.23 4.79 6.99 6.15

Fertilizer(ETB) 24.99 14.16 20.66 28.74 30.57

Manure(kg) 41.79 37.26 58.03 64.96 57.70

Note that plots without SWC have higher yield. Can we conclude SWC has negative effect?



Estimation Procedure

‒ Estimate stochastic frontiers for each SWC technology group and for the

pooled data

‒ Test for technological variance using the Likelihood Ratio Test (LRT)

‒ The LRT compares the values of the likelihood functions of the sum of the

separate group estimations and the pooled data. In a simple expression, the

value of the LRT statistic (λ) equals -2{ln[L(H0)] - ln[L(H1)]}; where ln[L(H0)] is the

value of the log likelihood function for the stochastic frontier estimated by

pooling the data for all groups and ln[L(H1)] is the sum of the values of the log

likelihood functions of the separate groups.

‒ If the LRT test rejects the pooled presentation (or in other words, if it signals

that there is technological variance among plots cultivated under different

SWC technologies), the stochastic metafrontier will be estimated.



The Empirical Model

- Each stochastic frontier will have two components:

The production function:

The technical effects function:

- Both parts are estmated simultanously using FRONTIER 4.1

LnOutputij = β0j + β1jLnlandij + β2jLnlaborij + β3jLntractionij +β4jLnseedij + β5jLnfertij + β6jLnManij +

β7jFertDij + β8jManDij + exp(Vij –Uij)

μij= δ0j+ δ1jmalehhij + δ2jagehhij + δ3jeduchhij + δ4jhhsizeij + δ5jmainactDij+ δ6joffarmij +δ7jliv_valueij +

δ8jfarmsizeij + δ9jdistownij + δ10jdeboDij + δ11jtrustij + δ12jassi-outDij + δ13jassi-inDij + δ14jplotageij +

δ15jsharecDij + δ16jrentDij + δ17jirrigDij + δ18jlemDij + δ19jdagetDij + δ20jgedelDij +δ21jhillyDij +δ22jhiredDi

j+δ23jplotdishomeij+wij



Table 2: Definition of Variables

Part One: Production

Function

Part Two: Technical Effects Function

Plot Output and Inputs Plot Characteristics Household Characteristics Social Capital

LnOutput: Natural Logarithm of Kg output LnLand: Natural Logarithm of hectare plot area LnLabor: Natural Logarithm of labor(Person days) LnTraction: Natural Logarithm of animal traction(Oxen days) LnSeed: Natural Logarithm kg seed LnFert: Natural Logarithm of fertilizer applied (BIRR) LnMan: Natural logarithm of manure (kg) fertD: Dummy for Fertilizer Use( 1 if used, 0 otherwise) ManD: Dummy for Manure Use( 1 if used, 0 otherwise)

plotage : Plot Age ( Years that the household cultivated the plot) plotdishome: Distance from home (Minutes of Walking) hireD: Hired Labor use Dummy (1 if used, 0 otherwise) Plot Slope, Meda as a Base case:

dagetD: Dummy for Daget (1 if daget, 0 otherwise) hillyD: Dummy for Hilly (1 if Hilly, 0 otherwise) gedelD: Dummy for Gedel (1 if Gedel, 0 otherwise) LemD: Dummy for Soil Quality (1 if Lem, 0 otherwise) Cultivation Arrangement, Own Cultivation as a Base Case:

sharecD: Dummy for Share Cropping (1 if share cropped, 0 otherwise) rentD: Dummy for Rented Plot (1 if rented, 0 otherwise) irrigD: Irrigation Dummy (1 if irrigated, 0 otherwise)

Malehh: Dummy for sex of household head (1 if male, 0 if female) Agehh: Age of household head in years Educhh: Years of schooling attended by household head Hhsize: Total family size of the household mainacthh: Dummy for main activity of the household head (1 if farming, 0 otherwise) Offarm: Total income earned off farm throughout the year Liv_value: Total value of livestock owned by the household Farmsize: Total farm size cultivated by the household in hectares Distowm: Distance to the nearest town in walking minutes

deboD: Dummy for Debo participation (1 if yes, 0 if No) trust : Number of people the household trusts assi-inD: Dummy for any assistance received from neighbors (1 if Yes, 0 if No) assi-outD: Dummy for any assistance forwarded to neighbors (1 if Yes, 0 if No)



Results

Technical Efficiency and SWC: Group Stochastic Frontiers

Table 3: Coefficients of the Production Function (βs).

Variable

Coefficient

(t-ratio)

None Soil

Bunds

Stone

Bunds

Bench

Terraces

Pooled

β0

Land

Labor

Traction

Seed

Fertilizer

Manure

Fertilizer Use

Dummy

Manure Use Dummy

4.2487**

(20.4663)

0.3496**

(8.0103)

0.2794**

(5.9290)

0.2081**

(5.3726)

0.2502**

(10.3058)

-0.0878

(-1.5757)

0.0613

(1.1711)

0.4230

(1.6245)

-0.2959

(-1.1053)

4.3130**

(4.7752)

0.3436*

(1.6600)

0.2992

(1.6263)

-0.1521

(-1.1041)

0.2678**

(2.8847)

-0.1332

(-0.6145)

0.1215

(0.6437)

0.5533

(0.5705)

-0.3893

(-0.3986)

4.5430**

(14.7057)

0.2377**

(4.3778)

0.1408**

(2.5056)

0.3395**

(6.0643)

0.1193**

(3.1099)

-0.0248

(-0.1993)

0.1541**

(2.3833)

0.0575

(0.0973)

-0.6386*

(-1.8279)

5.8685**

(6.3162)

0.7310**

(3.8998)

0.0082

(0.04735)

0.3116**

(2.4046)

0.0866

(1.2983)

0.0381

(0.3887)

-0.1461

(-1.0644)

-0.0605

(-0.1352)

1.1504

(1.4711)

4.3618**

(35.4124)

0.3149**

(12.0299)

0.2290**

(8.4113)

0.2071**

(8.2998)

0.2337**

(15.5857)

-0.0038

(0.1303)

0.0235

(0.8208)

0.0410

(0.2832)

0.0116

(0.0758)

**Significant at α=0.05; *Significant at α=0.10



Results – SWC and TE

‒ Plots cultivated under all SWC technologies experience a considerable level of technical

inefficiency.

‒ The No SWC group is the least-efficient group. SWC seems to be positively correlated

with efficiency, controlling for farmer characteristics. The land cost of SWC is not

accounted, which means the positive effect is be higher than estimates in our model.

‒ In most cases, negative relationships between various and household attributes and TE

disappear or are reversed in the presence of one of the soil conservation technologies.

‒ The LRT test statistic is calculated to be 371.24, which is extremely significant.

There is in deed a technological variance between plots cultivated under different

SWC practices.

‒ The TE estimates of the pooled specification are not valid ( most efficiency studies

in the literature use the pooled specification!!!)



Results – TE and Technology Gaps

Technology Group Variable Mean

None

TGRa

Meta TE

Group TE

0.9494

0.62061

0.65497

Stone bunds

TGR

Meta TE

Group TE

0.9539

0.64607

0.67614

Soil bunds

TGR

Meta TE

Group TE

0.7806

0.60600

0.77970

Bench terraces

TGR

Meta TE

Group TE

0.9629

0.65748

0.68733

a TGR=technology gap

ratio



Results – TE and Technology Gaps

‒ The Meta TE of a plot quantifies by how much the output of a given plot could be

increased if it had the best technology available in the area.

‒ Plots with soil bunds have the lowest mean TGR, 0.7806. This simply means, even if

all soil bund plots attain the maximum technology available for the group, they will

still be about 21.9% away from the output that they could produce if they use the

maximum technology available in the whole sample.



Back to the big question - Is SWC a good technology?

‒ We identify the best practice plots that define the metafronntier ( plots TGR

equal to 1).

‒ And then we look for the role of SWC

SWC and frontier plots

Type of SWC technology

Total number of plots cultivated under this SWC

technology

% share

Total number of frontier plots

cultivated under this SWC

technology

% share

None 667 54.3 75 51.2

Stone Bunds 357 29.1 56 38.1



SWC is a Good technology

The percentage share of plots with SWC is significantly higher in the best

technology group compared to the percentage share in the over all

sample, especially for stone bunds.

The share of steep plots in the best-practice group increases with SWC

technology.

Better soil quality plots have a higher share in the best-practice group

compared to poorer soil quality plots .

Better quality plots, with or without SWC, define the best technology in

the survey area. SWC helps in providing this chance to poor quality plots.

Therefore, SWC is a good technology.



Concluding Remarks

‒ Plots cultivated under SWC technology proved to be more efficient. Investigating

the origins of the efficiency differential with an approach that internalizes

adoption issues could have important policy values.

‒ SWC has a dual effect on productivity – via efficiency and technology. Studying the

specific channels in which a given SWC technology affects efficiency could shed

some light on why labaratory-effective technologies perform poorly in the real

world.

‒ SWC helps poor quality plots to get the privilege of being best technology plots.



Concluding Remarks (Cont’d)

‒ SWC is part of a plot’s composite technology. Therefore, its effect should

be assessed controlling for other factors that define the plot’s technology,

some related to SWC adoption. The metafrontier approach seems

promising to perform such task.

‒ In general, the stochastic metafrontier approach could help in the impact

assessment of new technologies and policy interventions in industries

with heterogeneous firms and strategies .

‒ Example: The ‘matching problem’:- ‘Which SWC technology to which agro-

economic environment?’ One can approach this problem by performing a

stochastic metafrontier analysis on clearly defined agro-economic groups.

soil conservation and small-scale food production in highland ethiopia: a stochastic metafrontier...

Technology

economics of swc

law soil conservation

role of soil conservation

role swc

role of swc

effect of swc

production technology

swc technologies