Soil Conservation Boosts Food Production in Ethiopia

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 role
of soil conservation in small-scale highland agriculture in Ethiopia. Plot-level
stochastic frontiers and metafrontier technology-gap ratios were estimated for
three soil-conservation technology groups and a group of plots without soil
conservation. Plots with soil conservation were found to be more technically
efficient than plots without. The metafrontier estimates showed that soil
conservation enhances the technological position of naturally disadvantaged
plots. The potential advantage of efficiency measurement in the evaluation of
farm 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 Medhin
University of Gothenburg
Gunnar Köhlin
University 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 the
agro-ecological characteristics of the study areas.
‒ There is no universally accepted methodological framework to asses
the 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*=Y
T
, TE
OLD
=TE
New
If Y
Q
<Y*<Y
T
, TE
OLD
>TE
New
If Y*=Y
Q
, TE
OLD
>TE
New
, productivity remains
constant.
If Y*<Y
Q
, 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 CurveOutput
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:
iu
i 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 
 

 
j
UVXUV
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).
iu
i eTE 
*
iu
i 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
1
i
i
i
i
U
U
V
V
e
e
e
e
e
e


 

*
, *
*
*
)*(
*X
X
i
ij
i
i
U
U
VV
V
V
i
X
i
TE
TE
e
e
TERande
e
e
RERe
e
e
TGR
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
TERTGR
e
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.
ii TGRTETEi
*
(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’β
Subject 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 Boosts Food Production in Ethiopia

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