MAIZE PRODUCTION INTENSIFICATION IN KENYA
By
John Otieno Olwande

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Community Sustainability – Doctor of Philosophy
2018

ABSTRACT
MAIZE PRODUCTION INTENSIFICATION IN KENYA
By
John Otieno Olwande
Soil infertility is one of the major problems contributing to low and stagnated agricultural
productivity in sub-Saharan Africa. In Kenya, this problem is manifested in maize where yields
have remained low and stagnated over time despite increased use of inorganic fertilizers and
improved seed varieties. More effective alternatives and/or complimentary actions to address this
problem thus remains germane. This dissertation contributes to that endeavor through two broad
objectives: to generate evidence that can support decisions to address the problem of low
agricultural productivity in general and of maize in particular in Kenya; and to contribute to the
body of knowledge about agricultural intensification in sub-Saharan Africa.
The first essay uses household panel survey data from rural Kenya covering a period of 13 years
(1997 – 2010) to examine trends and patterns in land and labor productivity of maize, measured
as net returns to land and to family labor. Results show declining landholdings and farm sizes but
maize occupied over one-half of cultivated land. Land productivity declined by 42% for
households with at least 10 acres and by 33% in the most important maize producing regions.
Labor productivity increased in areas with smaller landholdings and higher population density
because of increase in land productivity, and declined or only marginally increased in areas with
larger landholdings and lower population density because of a decline in land productivity. These
results demonstrate that increasing maize production and returns to family labor in Kenya will rely
on improving yields especially in the major maize growing areas where this has declined.

The second essay uses data on maize production in five major maize growing counties in Kenya
to compare maize farmers’ perceived soil fertility to measured soil fertility. It also investigates the
influence of farmers’ perceptions of soil fertility on their adoption (use) of soil fertility
management practices. Results show little agreement between farmers’ perceived and measured
soil fertility, and farmers mostly judge the fertility status of soil by crop performance. Farmers
apply management practices that may not match the fertility needs of soil on their plots,
exemplified by the persistent application of an acidifying fertilizer (diammonium phosphate
(DAP)) and low application of organic soil amendments even on plots with soils that are acidic
and deficient in organic carbon. Farmers on average are more likely to apply inorganic fertilizer
to plots they perceive to be infertile, and they treat manure or compost and inorganic fertilizers as
serving substitute roles in soil fertility. These results suggest policy and extension information
gaps regarding soil fertility management.
The third essay uses the same dataset as in the second essay together with rainfall data to estimate
technical efficiency of maize farmers and the effect of farmers’ soil fertility perception on technical
efficiency. It also demonstrates the importance of including environmental production conditions
and agronomic practices in agricultural productivity and efficiency analysis. Average technical
efficiency level is 0.75 and 0.70, respectively, with and without environmental variables and
agronomic practices in the model, indicating that scope for increasing maize yield through better
management of inputs exits and that omission of environmental variables and agronomic practices
underestimates technical efficiency. Farmers’ perception of soil fertility and the consistency of
their perception with measured soil fertility both have significant effects on technical efficiency,
underscoring the importance of information that can enhance farmers’ accurate understanding
about soil fertility conditions on their farms to help them make better production decisions.

Copyright by
JOHN OTIENO OLWANDE
2018

For my family
Salome, Chamola, Atara, Hawi
For my mother
Risper Olwande
In memory of my late father
Olwande Diang’a
For my step-brother
Eric Olwande

v

ACKNOWLEDGEMENTS

I express my sincere gratitude to Dr. John Kerr, my major advisor and dissertation committee
chair. The completion of this dissertation and my entire PhD program is because of his invaluable
guidance, mentorship and motivation. In addition to my major advisor, I also thank my advisory
and dissertation committee members, Dr. Steven Gray, Dr. Thomas Jayne and Dr. Robert Myers,
for their guidance in my research and writing process and during the entire program. Their
insightful suggestions and constructive criticisms greatly shaped my approach to research and
writing.
The completion of my PhD program would have been a dream had it not been for the sacrificial
support I received from Dr. John Kerr and Dr. Thomas Jayne. I particularly am deeply grateful to
Dr. Jayne for encouraging and supporting me to join the PhD program at Michigan State University
(MSU), to Dr. Kerr for accepting me to be his student and to both for generously funding my
studies. I also thank Dr. Melinda Smale, Dr. Milu Muyanga and Dr. Miltone Ayieko for their
motivation and encouragement before and after I joined the program.
My special gratitude goes to the Department of Community Sustainability (CSUS) for offering me
the George and Nancy Axinn International Scholarship award to support my studies. I also thank
the Food Security Group at the Agricultural, Food and Resource Economics (AFRE) department
and Tegemeo Institute of Egertion University, Kenya, for providing me the data for dissertation
research. I particularly thank Dr. Thomas Jayne and Dr. Milu Muyanga of AFRE and the Director
of Tegemeo, Dr. Miltone Ayieko, for facilitating my access to the data.

vi

My sincere thanks to fellow graduate students with whom we shared moments of joy and
frustrations and breakthroughs and dead ends during the program. I appreciate the support I
received from, among others, Socheat Keo, Mayuko Kondo, Awa Sanou, Aryal Giri, Nahid Sattar,
Yu Jina, Soo Jeong, KJ Lee, Obafemi Elegbede, Arfang Dabo, Godwin Debrah, Juma Mmongoyo
and Chewe Nkonde. My special thanks to Brendan O’Neill for helping me understand the different
soil quality parameters.
I extend thanks to the families of Dr. Miltone Ayieko and Dr. Milu Muyanga who welcomed me
to East Lansing and made me part of them throughout my program. I also express my special
thanks to the family of Drs. Rex and Vangie Alociljia and the entire International Life Group for
their emotional and spiritual support through the weekly bible study meetings and constant prayers.
My special and sincere thanks go to my mother, Risper Olwande and late father, Olwande Diang’a.
Through their relentless toil tilling the land, they provided the much they could for me and my
siblings. Although they did not have the means to provide decent education for me and my siblings,
their words of encouragement and messages of hope to us motivated me to seize available
opportunities to acquire education and always aim higher.
I am deeply grateful to my uncle Humphrey Omwomo and step-brother Eric Olwande for the
sacrifice they made to pay for my school fees. I particularly am indebted to Eric for his relentless
effort and sacrifice in paying for my schooling when I had lost hope in ever completing high
school. His sacrificial support to my education will remain a permanent mark in my professional
life. May God richly reward him! I also thank my brothers and sisters who always encouraged me
in many ways.

vii

My family has been instrumental to my successful completion of the PhD program. I am indebted
to my wife Salome Olwande and our son and daughters, Chamola Olwande, Atara Olwande and
Hawi Olwande. The sacrifice they made to allow me live and study thousands of miles away from
them is invaluable. The love, patience and emotional support they provided and continue to
provide me are simply overwhelming. May God bless them!
Finally, I thank the Almighty God for His favor throughout this journey. May all glory remain
with Him!

viii

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................................... xi
LIST OF FIGURES ..................................................................................................................... xiv
INTRODUCTION .......................................................................................................................... 1
REFERENCES ............................................................................................................................... 9
CHAPTER 1: TRENDS AND PATTERNS IN LAND AND LABOUR PRODUCTIVITY OF
MAIZE IN KENYA ...................................................................................................................... 12
1.1 Introduction .................................................................................................................... 12
1.2 Conceptual framework ................................................................................................... 16
1.3 Data source and analysis ................................................................................................ 18
1.4 Results and discussion.................................................................................................... 21
1.4.1
Patterns and trends in landholding and land allocation to maize production ......... 21
1.4.2
Patterns and trends in land and labor productivity in maize production................. 28
1.5 Conclusions and implications for policy ........................................................................ 46
APPENDIX ................................................................................................................................... 50
REFERENCES ............................................................................................................................. 52
CHAPTER 2: FARMERS’ PERCEPTIONS OF SOIL FERTILITY AND ADOPTION OF SOIL
FERTILITY IMPROVEMENT PRACTICES ............................................................................. 56
2.1 Introduction and Study Objectives ................................................................................. 56
2.2 Methods and Data........................................................................................................... 61
2.2.1
Conceptual Framework ........................................................................................... 61
2.2.2
Analytical Strategy.................................................................................................. 66
2.2.2.1
Farmers’ perceived and measured soil fertility ............................................... 66
2.2.2.2
Adoption of soil fertility management practices ............................................. 69
2.2.3
Data sources and variables ...................................................................................... 70
2.2.3.1
Data sources ..................................................................................................... 70
2.2.3.2
Variables .......................................................................................................... 73
2.3 Results ............................................................................................................................ 79
2.3.1
Farmers’ perceived versus measured soil fertility .................................................. 79
2.3.2
Adoption of soil fertility management practices ..................................................... 95
2.4 Conclusion and Implications ........................................................................................ 101
REFERENCES ........................................................................................................................... 105
CHAPTER 3: TECHNICAL EFFICIENCY AND SOIL FERTILITY AND AGRONOMIC
PRACTICES IN MAIZE PRODUCTION IN KENYA ............................................................. 111
3.1 Introduction and Study Objectives ............................................................................... 111
3.3 Methods and Data......................................................................................................... 114
3.3.1
Conceptual Framework ......................................................................................... 114
3.3.2
Stochastic frontier analysis ................................................................................... 117
ix

3.3.3
Model choice and estimation strategy................................................................... 125
3.3.3.1
Model choice ................................................................................................. 125
3.3.3.2
Estimation strategy ........................................................................................ 127
3.3.4
Data sources and variables .................................................................................... 129
3.3.4.1
Data sources ................................................................................................... 129
3.3.4.2
Variables ........................................................................................................ 130
3.4 Results .......................................................................................................................... 139
3.4.1
Model diagnostic test results................................................................................. 139
3.4.1.1
Likelihood ratio test of presence of technical inefficiency............................ 139
3.4.1.2
Production frontier functional form test: translog vs Cobb-Douglas ............ 140
3.4.1.3
Stochastic frontier model test ........................................................................ 140
3.4.2
Stochastic production frontier estimation results .................................................. 141
3.4.3
Technical efficiency estimation results ................................................................. 146
3.4.3.1
Determinants of technical (in)efficiency ....................................................... 146
3.4.3.2
Technical efficiency estimates....................................................................... 149
3.5 Conclusion and implications ........................................................................................ 153
APPENDIX ................................................................................................................................. 156
REFERENCES ........................................................................................................................... 163

x

LIST OF TABLES

Table 1.1: Levels of and changes in mean landholding, total area planted, and area allocated to
plots with maize 1997-2010 .......................................................................................................... 23
Table 1.2: Mean landholding, total area planted and area allocated to plots with maize, by village
population density (pooled sample – 1997-2010) ......................................................................... 23
Table 1.3: Changes in mean landholding, total area planted and area allocated to plots with
maize, by population density, (1997-2010) .................................................................................. 24
Table 1.4: Levels of and changes in mean landholding, total area planted and area allocated to
plots with maize, by landholding categories, 1997-2010 ............................................................. 25
Table 1.5: Mean landholding, total area planted and area allocated to plots with maize, by zone
(pooled sample – 1997 - 2010) .................................................................................................. 27
Table 1.6: Changes in mean landholding, total area planted and area allocated to plots with
maize, by zone, 1997-2010 ........................................................................................................... 27
Table 1.7: Average share of monocropped and intercropped maize plots in total area planted and
in total area of plots with maize, 1997 - 2010............................................................................... 28
Table 1.8: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) over time (mean) ................................................................................................... 29
Table 1.9: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by landholding (mean)........................................................................................... 30
Table 1.10: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by population density (mean) ................................................................................ 31
Table 1.11: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by gender of household head (mean) .................................................................... 34
Table 1.12: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by distance to tarmac road (mean) (pooled sample – 2004 – 2007)...................... 34
Table 1.13: Land and labor productivity and family labor use rate on maize intercrop and
monocrop plot (mean) ................................................................................................................... 36
Table 1.14: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by agro-regional zone (mean)................................................................................ 38
1.15: Land and labor productivity and family labor use rate on maize plots (both monocrop and
intercrop) by hired labor use (mean) ............................................................................................. 41
xi

Table 1.16: Land and labor productivity and land-labor ratio on maize plots (both monocrop and
intercrop) by mechanized land preparation (mean) ...................................................................... 42
Table 1.17: Mean percentage change in labor productivity of maize (both monocrop and
intercrop) as the sum of percentage changes in land productivity and land-labor ratio, 2004-2010
....................................................................................................................................................... 43
Table 2.1: Dummy table of data measuring agreement between farmers’ perception and
measured soil fertility ................................................................................................................... 67
Table 2.2: Distribution of sample households across administrative units, 2014 ......................... 72
Table 2.3: Adoption rates of various soil fertility management practices (N=1268) ................... 77
Table 2.4: Summary statistics of explanatory variables in the adoption estimation (N=1268) .... 78
Table 2.5: Chi-square test of independence between farmer perceived and measured soil fertility
....................................................................................................................................................... 82
Table 2.6: Kappa statistic measuring degree of agreement between perceived and measured soil
fertility........................................................................................................................................... 83
Table 2.7: Mean comparison test of selected variables according to farmers’ perception about
soil fertility status .......................................................................................................................... 84
Table 2.8: Probit marginal effect estimates of the relationship between farmers’ perceived and
measured soil fertility ................................................................................................................... 87
Table 2.9: Probit marginal effect estimates of the relationship between farmers’ perception about
soil fertility and measured soil properties ..................................................................................... 92
Table 2.10: Farmers’ reported indicators of soil infertility........................................................... 94
Table 2.11: Correlation matrix for the regression equations ........................................................ 96
Table 2.12: Multivariate probit estimation results of factors affecting adoption of soil
management practices (N=1268) .................................................................................................. 98
Table 3.1: Variable description and summary statistics (N=1102) ............................................ 138
Table 3.2: Likelihood ratio test results of the Wang (2002) model against KGMHLBC, CFCFGH
and Stevenson models ................................................................................................................. 141
Table 3.3: Stochastic production frontier estimates .................................................................... 143
Table 3.4: Maize output elasticity with respect to inputs (mean) ............................................... 145
Table 3.5: Marginal effects of exogenous determinants of technical inefficiency (sample means)
..................................................................................................................................................... 147
xii

Table 3.6: Technical efficiency estimates (mean) ...................................................................... 150
Table 3.7: Actual, frontier and foregone output (mean) ............................................................. 151
Table 3.8: Marginal product of inputs ........................................................................................ 153

xiii

LIST OF FIGURES

Figure 1.1: Aggregate maize yield and production in Kenya over time, 1990-2016.................... 14
Figure 1.2: Locally weighted scatterplot smoother (lowess) of maize yield over time ................ 15
Figure 1.3: Locally weighted scatterplot smoother (lowess) of land productivity of maize and
village population density ............................................................................................................. 32
Figure 1.4: Locally weighted scatterplot smoother (lowess) of labor productivity of maize and
village population density ............................................................................................................. 33
Figure 1.5: Locally weighted scatterplot smoother (lowess) of land productivity and distance to
tarmac road.................................................................................................................................... 35
Figure 1.6: Locally weighted scatterplot smoother (lowess) of labor productivity and distance to
tarmac road.................................................................................................................................... 35
Figure A1.1: Relationship between youth outmigration rate and village population density
(lowess regression using pooled sample – 2000-2010) ................................................................ 51
Figure 2.1: Conceptual framework for understanding farmers’ perceptions about soil fertility and
its influence on fertility management practices (Adapted from Halbrendt et al. (2014)) ............. 62
Figure 2.2: Percentages of farmer-perceived fertile and infertile plots across regions................. 80
Figure 2.3: Percentages of measured fertile and infertile plots across regions ............................. 80
Figure 2.4: Frequency distribution of DAP and manure use on plots with low soil pH (<5.5)
(39% of plots) ............................................................................................................................... 90
Figure 2.5: Frequency distribution of DAP and manure use on plots with low organic carbon
(<2.7%) (75% of plots) ................................................................................................................. 91
Figure 2.6: Frequency distribution of DAP and manure use on plots with both low organic
carbon (<2.7%) and low soil pH (30% of plots) ........................................................................... 91
Figure 3.1: Input-oriented technical efficiency illustration (Coelli et al 2005) .......................... 115
Figure 3.2: Output-oriented technical efficiency with one input and one output (Coelli et al 2005)
..................................................................................................................................................... 116
Figure 3.3: Output-oriented technical efficiency with two outputs and one input (Coelli et al
2005) ........................................................................................................................................... 116
Figure 3.4: Kernel density of technical efficiency estimates ...................................................... 150
xiv

Table A3.1: OLS regression results ............................................................................................ 157
Table A3.2: Maximum likelihood results of stochastic frontier model with Cobb-Douglas
specification ................................................................................................................................ 158
Table A3.3: Maximum likelihood results of stochastic frontier model of KMHLBC................ 160
Table A3.4: Maximum likelihood results of various stochastic frontier model of CFCFGH .... 161
Table A3.5: Maximum likelihood results of various stochastic frontier model of Stevenson
(1980) .......................................................................................................................................... 162

xv

INTRODUCTION
Agriculture remains the major livelihood source for the majority of the population in sub-Saharan
Africa and is essential for food security, poverty reduction and economic growth (The World Bank,
2007). Despite this fundamental role, agricultural productivity in sub-Saharan Africa is generally
low and its growth has stagnated (Haggblade & Hazell 2010; Otsuka & Larson, 2013). Among the
factors responsible for the poor performance of Africa’s agriculture are land degradation, small
and declining farm sizes because of population growth, reliance on rain-fed farming, low use of
external inputs in production and poor market infrastructure (Barbier & Hochard, 2014; The
Montpellier Panel, 2013; Haggblade & Hazell, 2010; Otsuka & Larson, 2013). Improving food
security, reducing poverty and realizing faster economic growth in this part of the world requires
accelerated and sustainable agricultural productivity growth (The World Bank, 2007; Diao et al,
2007).
The concern about low and stagnated agricultural productivity in sub-Saharan Africa applies to
Kenya as well. This is most evident in maize, the most important staple grain and which is widely
grown, where aggregate yield has exhibited a declining trend over the past quarter century.
Surprisingly, the declining trend in yield has occurred despite impressive growth in inorganic
fertilizer and improved seed use and remarkable public investments in rural infrastructure over the
years (Ariga & Jayne, 2009; Chamberlin, 2013; Smale & Olwande, 2014). Maize consumption
demand, on the other hand, has been on an upward trend due to sustained population growth,
resulting in a widening gap between consumption demand and production and increasing import
bill (Kirimi et al., 2011).

1

Because of its crucial role as the main staple food for a large section of the population, investment
in achieving sustainable productivity growth in maize remains a key goal in the government’s
policy and development strategies (Government of Kenya, 2010a, Government of Kenya, 2010b)
and development organizations’ support agendas. The government, international development
agencies and non-governmental organizations (NGOs) have continued to implement a range of
interventions, spanning the farm and input and output markets in efforts to boost maize production.
Notable among the interventions are the state’s fertilizer subsidy programs and producer price
support, alongside a strong establishment for seed research and development and investments in
rural infrastructure.
Clearly, we can expect these efforts to have enhanced maize production through faster growth in
yield in Kenya. The lack of yield growth in maize despite the largest price support, input subsidies,
and seed research efforts is puzzling. The scenario indicates existence of factors beyond what the
current efforts are delivering that may be playing a significant role in stymied maize yield, and
demonstrates the need for more effective alternatives and/or complimentary actions that can
nurture investments in greater production intensification in a sustainable way.
Smale & Olwande (2014) note that several explanations for the dismal performance in maize yield
have been advanced, including degraded soils associated with land pressures arising from
population density, reduced fallows and nutrient mining, resulting in poor crop response to
fertilizer use. Some of the explanations, however, have not been corroborated by evidence from
rigorous empirical investigation to understand the nature of the effects of these factors on maize
yield and the extent to which they may be contributing to the observed low and stagnated
productivity. Therefore, the search for strategies to address the problem of low and stagnated
agricultural productivity in Kenya remains germane.
2

This dissertation contributes to addressing the aforementioned need. It pursues two overarching
objectives. The first is to generate empirical evidence to support decisions that can address the
problem of low agricultural productivity generally and of maize in particular in Kenya. The second
is to contribute to the body of knowledge about agricultural intensification in sub-Saharan Africa,
given the increasingly recognized fact by African governments that sustainable farm productivity
growth is key to achieving sustainable economic growth and improving the livelihoods of hundreds
of millions of their constituents. These overarching objectives are pursued through three separate
but linked essays.
The first essay (Chapter 1) is entitled “Trends and Patterns in Land and Labor Productivity in
Kenya”. In addition to low and stagnating productivity, farm sizes in Kenya have been shrinking
over time with rising rural population densities and sub-division. Moreover, the long-term low and
stagnated agricultural productivity growth may have depressed the generation of dynamic farmnonfarm growth multipliers and shifts in the composition of the labor force that have been the
foundation of economic transformation in other regions of the world (Mellor, 1976; Johnston &
Mellor, 1961; Lipton, 2005). This essay seeks to determine whether Kenya’s agricultural sector is
changing in ways that are promoting or retarding farm labor productivity, and to understand the
association between farm labor productivity and population density, land scarcity and market
access. Farm labor productivity is defined in terms of net returns to family labor, a measure that is
deemed most appropriate for profitability of farming for agricultural households.
The essay is focused on maize production and uses a nationwide five-wave (1997, 2000, 2004,
2007 and 2010) panel survey dataset on a sample of about 1500 agricultural households in Kenya.
Descriptive and bivariate analyses are conducted to examine trends and patterns in the size of

3

landholding, area planted and land allocation to maize using data for all the survey years, and in
land and labor productivity using data for 2004, 2007 and 2010 for which labor data was available.
Six key results emerge. First, average landholding declined by over 12% while average area
planted declined by 11%. Maize occupied over 50% of total area planted. The average area of plots
with maize for a household declined by 11% over time. Second, long-term labor productivity
(returns to family labor) increased by 38% overall, contributed by positive changes in land-labor
ratio of 16% and land productivity of 21%. The increase in land-labor ratio was because of a
decrease in family labor use rate on maize plots. Third, there was an inverse relationship between
landholding and land productivity and landholding and family labor use rate. Average labor
productivity increased for all households. However, the increase in labor productivity for those
with 10 or above acres was entirely because of positive change in land-labor ratio rather than in
land productivity, which declined by 42%. Fourth, average land productivity and family labor use
rate had direct relationships with population density while labor productivity was inversely related
with population density. Fifth, most remote households compared to their least remote counterparts
had lower land productivity, higher family labor use rate and lower labor productivity, on average.
Lastly, there was a remarkably small increase in labor productivity (0.7%) in the High Potential
Maize zone (HPMZ), Kenya’s most important maize producing region, because of a 33% decline
in land productivity. These results demonstrate that increasing maize production through land
expansion is infeasible. Increasing production and labor productivity will have to rely on yield
(land productivity) growth. This is especially urgent for the major maize growing areas where
yield has declined yet they are the main suppliers of maize in the domestic market.
The second essay (Chapter 2) is entitled “Farmers’ Perceptions and Adoption of Soil Fertility
Improvement Practices”. The evidence of increased adoption of fertilizer and improved maize seed
4

over time without significant growth in maize yield implies that continued use of fertilizers and
improved maize varieties on their own cannot achieve the needed growth in yield. There is need
for sustainable management practices that add organic matter and ameliorate soil acidity to restore
fertility and subsequently increase crop response to external inputs (Lal, 2006; Chivenge et al.,
2011; Kunhikrishnan et al., 2016; McCauley et al., 2017). We can expect that farmers’ perceptions
about the fertility conditions of their soils bear on their decisions about adoption of technologies
and agronomic practices to improve soil fertility. Few quantitative studies exist about the
correspondence of farmers’ perceptions about the fertility conditions of their soils and measured
soil fertility, and how those perceptions influence adoption (or use) of soil fertility management
technologies and agronomic practices. This essay compares maize farmers’ perceptions about the
fertility of their soils to soil fertility as measured by results from scientific test of soil chemical
properties. It also investigates farmers’ adoption (use) of soil fertility management practices, with
a focus on the influence of farmers’ perception about soil fertility. The essay makes a major
contribution of incorporating farmers’ perception as a factor in quantitative assessment of their
soil fertility management decisions.
The essay uses two cross-sectional household- and plot-level survey data on maize production
spanning five counties located in the major maize growing areas of Kenya. The first survey was
conducted in 2014 from a sample of 650 farm households spread in five counties, while the second
survey was conducted in 2016 on the same households as in the first survey, but the number
reduced to 623 due to attrition. The maize plots that were cultivated in the 2014 survey were not
necessarily targeted in the 2016 survey hence the non-panel nature of the plot-level data. Plot-level
data include laboratory-tested soil physical and chemical properties.

5

The relationship between farmers’ perceived and measured soil fertility and adoption of soil
fertility management practices are analyzed using three approaches. First, a chi-square test is used
to examine statistical independence between farmers’ perceived and measured soil fertility.
Second, interrater agreement technique (Fleiss et al. 2003) is used to estimate the degree of
agreement between farmers’ perception of soil fertility and measured soil fertility. Third, a probit
model is estimated to examine the relationship between farmers’ perceived and measured soil
fertility in the presence of other relevant factors. Lastly, a multivariate probit model is estimated
to identify the effect of farmers’ perception about soil fertility on their adoption of soil fertility
management practices.
Results show that there is little correspondence between farmers’ perceived and measured soil
fertility, and farmers mostly rely on crop performance to judge the fertility status of their soil. Soil
testing to understand the fertility condition of soil was a rare practice. These results imply that
farmers’ management practices may not be compatible with the fertility needs of their soils, as
exemplified by the persistent application of an acidifying fertilizer (DAP) and low application of
organic soil amendments such as manure and compost even on soils that are acidic and low in
organic carbon, potentially worsening the problem. Farmers’ soil fertility perception has a strong
relationship with the decision to apply inorganic fertilizer, but not other soil fertility management
practices such as applying manure or compost; the likelihood of applying inorganic fertilizer to a
plot increases when a farmer perceives a plot to be infertile. Farmers also appear to treat
manure/compost and inorganic fertilizers as substitutes. These results reflect gaps in policy and
extension, exemplified by the state’s aggressive promotion of use of inorganic fertilizers,
especially DAP, without accompanying concerted efforts to promote use of organic soil
amendments.
6

The third essay (Chapter 3) is entitled “Technical Efficiency and Soil Fertility and Agronomic
Practices in Maize Production in Kenya”. Lack of land for agricultural expansion in Kenya, and
indeed Africa (Chamberlin, Jayne, & Headey, 2014), implies that increasing agricultural
productivity is the feasible option that can spur broad-based economic growth, help reduce poverty
and enhance food security. Increasing agricultural productivity can be achieved through
technological change, increased efficiency in use of existing technology and productive resources
or both. This essay estimates technical efficiency level of maize farmers to determine potential
productivity gains possible through better management of production resources. It identifies
factors that affect variations in technical efficiency across farms, with a focus on the effect of
farmers’ soil fertility perception, and demonstrates the importance of including environmental
production conditions and agronomic practices in agricultural productivity and efficiency analysis.
Much of the literature on agricultural productivity and efficiency analysis have often ignored
farmers’ perceptions of soil fertility, environmental production conditions and agronomic
practices, in part due to data limitations, yet these factors can be expected to condition input choice
and use decisions and subsequently productivity and efficiency.
The data used in this essay is the same as in essay 2. In addition, the essay uses rainfall data
extracted from the Climate Hazards group Infrared Precipitation with Stations (CHIRPS) dataset
(Funk et al., 2015). The stochastic production frontier (SF) approach due to Meeusen & van Den
Broeck (1977) and Aigner et al (1977) is used to estimate technical efficiency of maize farmers,
with and without controlling for environmental conditions (soil fertility conditions and rainfall)
and agronomic practices, and identify factors responsible for variation in technical efficiency
across farms.

7

Three key results have emerged. First, average level of technical efficiency is 0.75 and 0.70,
respectively, with and without controlling for environmental variables and agronomic practices.
Inefficiency-induced foregone maize yield is 0.34 tonnes/acre when environmental variables and
agronomic practices are controlled for and 0.45 tonnes/acre without controlling for them. The
forgone output is substantial considering that the reported yield is only about 1.3 tonnes/acre.
Secondly, omission of environmental production conditions and agronomic practices from the
stochastic frontier model results in understated technical efficiency levels. Lastly, farmers that
view their plots as fertile have, on average, 19% lower technical inefficiency than those who view
their plots as infertile. In addition, those whose perceptions about the fertility status of their plots
are consistent with measured soil fertility have 2.9% lower technical inefficiency than those whose
perception is inconsistent with measured soil fertility, on average. These results indicate that scope
for increasing maize yield through better management of inputs exists and underscore the necessity
for farmers’ accurate understanding about soil fertility conditions on their farms to help them make
better production decisions. Failure to account for environmental production conditions and
agronomic practices in productivity and efficiency analysis may yield inaccurate results.

8

REFERENCES

9

REFERENCES

Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic
frontier production function models. Journal of Econometrics, 6, 21–37.
Ariga, J., & Jayne, T. S. (2009). Private Sector Responses to Public Investments and Policy
Reforms The Case of Fertilizer and Maize Market Development in Kenya (IFPRI Discussion
Paper No. 921).
Barbier, E. B., & Hochard, J. P. (2014). Land degradation, less favoured lands and the rural
poor: A spatial and economic analysis.
Chamberlin, J. (2013). Market access and smallholder development in Kenya and Zambia.
Michigan State University.
Chamberlin, J., Jayne, T. S., & Headey, D. (2014). Scarcity amidst abundance? Reassessing the
potential for cropland expansion in Africa. Food Policy, 48(2014), 51–65.
https://doi.org/10.1016/j.foodpol.2014.05.002
Chivenge, P., Vanlauwe, B., & Six, J. (2011). Does the combined application of organic and
mineral nutrient sources influence maize productivity ? A meta-analysis. Plant Soil, 342, 1–
30.
Diao, X., Hazell, P., Resnick, D., & Thurlow, J. (2007). The Role of agriculture in development:
Implications for sub-Saharan Africa. Washington, D.C., USA. https://doi.org/153
Fleiss, J. L., Levine, B., & Paik, M. C. (2003). Statistical Methods for Rates and Proportions.
John Wiley & Sons, Inc.
Funk, C., Peterson, P., Landsfeld, M., Pedreros, D., Verdin, J., Shukla, S., … Michaelsen, J.
(2015). Climate Harzads Group. https://doi.org/10.1038/sdata.2015.66
Haggblade, S., & Hazell, P. B. R. (Eds.). (2010). Successes in African agriculture: Lessons for
the future. Baltimore: The Johns Hopkins University Press.
Johnston, B. F., & Mellor, J. W. (1961). The role of agriculture in economic development. The
American Economic Review, 51(4), 566–593.
Kirimi, L., Sitko, N., Jayne, T. S., Karin, F., Muyanga, M., Sheahan, M., … Bor, G. (2011). A
farm gate-to-consumer value chain analysis of Kenya’s maize marketing system (Working
Paper No. 44). Nairobi.
Kunhikrishnan, A., Thangarajan, R., Bolan, N. S., Xu, Y., Mandal, S., Gleeson, D. B., … Naidu,
R. (2016). Functional Relationships of Soil Acidification, Liming, and Greenhouse Gas
Flux. Advances in Agronomy, 139, 1–71. https://doi.org/10.1016/bs.agron.2016.05.001
10

Lal, R. (2006). Enhancing crop yields in the developing countries through restoration of the soil
organic carbon pool in agricultural lands. Land Degradation & Development, 209(August
2005), 197–209.
Lipton, M. (2005). The family farm in a globalizing world: The role of crop science in
alleviating poverty (2020 Discussion Paper No. 40). Washington, DC.
McCauley, A., Jones, C., & Olson-Rutz, K. (2017). Soil pH and organic matter. Nutrient
Management, (8), 1–16.
Meeusen, W., & van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas
production functions with composed error, 18(2), 435–444.
Otsuka, K., & Larson, D. F. (Eds.). (2013). An African Green Revolution: Finding ways to boost
productivity on small farms. Dordrecht Heidelberg New York London: Springer.
https://doi.org/10.1007/978-94-007-5760-8
Smale, M., & Olwande, J. (2014). Demand for maize hybrids and hybrid change on smallholder
farms in Kenya. Agricultural Economics (United Kingdom), 45(4).
The Montpellier Panel. (2013). Sustainable intensification: A new paradigm for African
agriculture. London.
The World Bank. (2007). World development report 2008: Agriculture for development.
Washington, DC: The World Bank.

11

CHAPTER 1: TRENDS AND PATTERNS IN LAND AND LABOUR
PRODUCTIVITY OF MAIZE IN KENYA

1.1

Introduction

Despite recent trends showing a shift in the labor force out of farming, the agricultural sector
remains the single most important source of livelihoods for most people in Sub-Saharan Africa
(Yeboah & Jayne, 2016). However, agricultural performance has been largely disappointing
(Haggblade & Hazell, 2010). Land and labor productivity levels have remained low and stagnated
and per capita food production has been declining (Otsuka & Larson, 2013). African agriculture is
characterized by continued reliance on rain-fed and mostly low-input production; farms that are
small and declining in size over time due to population growth; a trend toward increased land
degradation (Barbier & Hochard, 2014; The Montpellier Panel, 2013); and marketing
infrastructure that, while improving, remains underdeveloped and imposes high costs on
participants in the agri-food system (Haggblade & Hazell, 2010; Otsuka & Larson, 2013).
The underperformance of African agriculture and the recognition of the central role of agricultural
productivity growth in development in the region has triggered a renewed interest in agriculture
by African governments and in international development circles (Otsuka & Larson, 2013; The
World Bank, 2008). While there is a broad consensus that an agricultural productivity revolution
is necessary to foster economic growth in sub-Saharan Africa, Otsuka & Larson (2013) note that
there is no consensus on how to realize that revolution. The authors suggest that debate on
strategies to adopt to promote general agricultural growth revolves around whether to focus on
small or large farms, to prioritize food staples or high value products, to promote production

12

practices that rely on fertilizers and modern seed varieties, and the extent that governments should
get involved in markets. In their efforts to promote agricultural productivity, over the last decade
many African governments have revived input subsidy programs to encourage the use of chemical
fertilizers and modern seed varieties on food staples, and/or operated directly in food markets to
raise producer prices for farmers (Jayne & Rashid, 2013).
This description of the region’s general trends in agricultural productivity applies in most respects
to Kenya. Agricultural productivity is low and has generally stagnated over the long term.
Specifically, yield of maize, the most important staple grain which is grown by virtually every
agricultural household in the country, has shown a declining trend in the long term (Figure 1.1).
The long-term picture is a result of sustained decline in yield witnessed in the period 1990-2003,
which has not been offset by the slow rate of increase in yield observed between 2004 and 2015,
and levels of which have remained lower than in early 1990s (Figure 1.2). The yield increase
observed after 2004 is attributable to a range of efforts at revitalization of agriculture as part of the
strategy to revive Kenya’s economy after decades of persistent decline. The efforts focused mainly
on reviving collapsed and dysfunctional agricultural institutions that offer services to farmers,
policy and regulatory reforms and investments that facilitate farmers’ access to input and output
markets (Government of Kenya 2010).
In addition to low and stagnated productivity, farm sizes have been shrinking over time with rural
population densities and sub-division, with most affected areas being those with high agroecological potential and where population densities are highest (Muyanga & Jayne, 2014). The
pressure on farm land because of population increase is one of the factors responsible for soil
degradation from nutrient mining, which is one of the main reasons for low and stagnated
agricultural yields (Government of Kenya, 2014; Tittonell et al., 2008; Marenya & Barrett, 2007).
13

Rapidly rising population combined with stagnant agricultural productivity growth and limited
potential for cropland expansion is making Kenya increasingly dependent on food imports for its
national food security (FAOSTAT, 2014). Moreover, the country’s record of relatively low
agricultural productivity growth over the past several decades has depressed the generation of
dynamic farm-nonfarm growth multipliers and shifts in the composition of the labor force that
have been the foundation of economic transformation in other regions of the world (Mellor, 1976;
Johnston & Mellor, 1961; Lipton, 2005).

4000

2.20

3500

2.00

3000

1.80

2500

1.60
y = -0.0013x + 1.6361

2000

1.40

1500

1.20

1000

Yield (mt/ha)

Production ('000 mt)

Figure 1.1: Aggregate maize yield and production in Kenya over time, 1990-2016

1.00
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Year
Production ('000 mt)

Yield (t/ha)

Linear (Yield (t/ha))

Source: Author’s compilation using data from the Ministry of Agriculture, Livestock and Fisheries (MoALF)
Note: Yield is computed from production and area estimates by the MoALF. Area data includes those of monocropped and inter-cropped maize plots. So, yield includes all plots with maize on them.

14

1.70
1.65
1.60
1.50

1.55

Yield (mt/ha)

1.75

1.80

Figure 1.2: Locally weighted scatterplot smoother (lowess) of maize yield over time

1990

1995

2000

2005

2010

2015

Year

Source: Author’s computation using data from Ministry of Agriculture, Livestock and Fisheries (MoALF)

The broad objectives of this study are to: (1) determine whether Kenya’s agricultural sector is
changing in ways that are promoting or retarding farm labor productivity; and (2) understand the
association between farm labor productivity and population density, land scarcity and market
access. We define farm labor productivity in terms of net returns to family labor, a measure that
we deem most appropriate for profitability of farming for agricultural households. We attempt to
address the following questions in pursuit of these objectives:


How has land area planted to maize changed over time?



How has labor productivity of maize changed over time? What is the pattern in labor
productivity across different segments of population density, market access and
landholding?

15



How are increased population density, smaller farm sizes and market access associated
with labor productivity of maize? What does this mean for agricultural intensification in
Kenya?

1.2

Conceptual framework

Boserup (1965) posited that rising population density exerts pressure on access to land, inducing
farmers to adopt more intensive systems of land use. Farmers move away from extensive to
permanent cultivation systems through a gradual transition from long fallow periods, involving
shifting cultivation, to multiple cropping of land, where multiple successive crops are planted on
the same area of land every cropping year. This change in land use system is accompanied by more
intensive use of inputs, such as labor, compost, manure, improved seeds, inorganic fertilizers and
irrigation, to increase production.
The link between population density and labor productivity, defined as net returns to family labor,
can be summarized through the following identity:

𝑦=

(1.1),

≡ ×

where 𝑌is net revenue from output from a plot, 𝐿 is family labour days used in production on the
plot, and 𝐴 is the area of the plot. The ratio
land productivity (yield),

is labour productivity. It is identically a product of

, and land-labour ratio, , which can be considered as efficiency of

family labour (Auer, 1966). Logarithmic transformation of (1.1) and differencing results in (1.2),
which shows that family labor productivity growth is the sum of growth in yield and in land-family
labor ratio:

16

∆ ln 𝑦 = ∆ ln

≡ ∆ ln

(1.2).

+ ∆ ln

Alternatively, we can express the identity in (1.2) as in (1.3):

∆ ln 𝑦 = ∆ ln

≡ ∆ ln

+ ∆ ln(𝐴) − ∆ ln(𝐿)

(1.3).

It is straightforward from (1.2) that when land expansion is infeasible, faster growth in land
productivity is imperative to improving labor productivity. If population is rising and land sizes
are shrinking, and if labor use is increasing in a manner that makes the land-labor ratio to decline
faster than growth in land productivity, we would expect labour productivity to decline. This would
result in undesirable effects on the economic welfare of agricultural households and can lead to
loss of incentives for households to produce maize. However, increase in population might not
necessarily translate to increase in family labor use on maize. Households may allocate more of
their labor to other farm and non-farm enterprises while maintaining labor use on maize at the
same level or even reducing it altogether. If labor use in maize declines more than area under maize
declines, then the land-labor ratio will increase. If the increase in land-labor ratio were sufficiently
large to offset any decline in land productivity, then we would expect to see a rise in labor
productivity.
Therefore, on one hand we would expect a positive association between population density and
labor productivity, driven by increased land productivity because of increased input use. On the
other hand, an inverse relationship between population density and labor productivity would be
possible and would mean that the increase in land productivity that would be expected from
increased labor supply and capital inputs is not sufficiently large to compensate for the cost of

17

increased use of labor and the capital inputs. This would suggest an economically unsustainable
path for agricultural intensification.
We would expect a positive association between labor productivity and improved access to
markets. Input and output market access influences output supply and input demand (Pingali et al,
1987) and availability of relevant market information and transaction costs are key determinants
of market access. High population density facilitates the flow of such information and reduces
transaction costs (Chamberlin, 2013; Ricker-Gilbert et al, 2014). Thus, market access has a direct
relationship with labor productivity.
The relationship between population density and farm sizes is well grounded on the Boserup
(1965) hypothesis. We would expect area planted to maize to decline over time as population
increases. Similarly, we would expect the share of area planted to maize in total area planted to
decline over time, as households are likely to gradually diversify or shift to farm enterprises with
higher value, such as horticulture and dairy, in efforts to maximize output per unit of land.
However, given the importance of maize in household food supply, we would not expect the share
of maize area in total area planted to decline significantly. We would expect these changes to be
larger in the least densely populated villages than in the most densely populated villages because
in the most densely populated villages scope for further reduction of plot sizes and diversification
may be reaching a limit since landholdings have already become very small on average.
1.3

Data source and analysis

We use a nationwide five-wave panel survey dataset covering 13 years on a sample of 1500
agricultural households in Kenya, collected by Egerton University’s Tegemeo Institute of
Agricultural Policy and Development. The data pertains to the 1996/97, 1999/00, 2003/04,
18

2006/07 and 2009/10 cropping years, hereafter referred to as 1997, 2000, 2004, 2007 and 2010,
the years in which the data were collected. While not considered nationally representative, the
sample covers all eight of Kenya’s important agro ecological zones (AEZ) spread over 24 districts
as defined in 1997. Argwings-Kodhek et al (1999) explain the sampling process in detail. The data
contains a range of information about household farm and non-farm activities, including detailed
information on cropping, livestock keeping and off-farm earning activities.
First, we examine trends and patterns in the size of landholding, area planted and land allocation
to maize using data for all the survey years (1997-2010). The pooled sample has 6,977
observations, distributed across the years as shown in the second column of Table 1a. Because the
sample contains only farm households, there are no landless households included in the sample.
Landholding is self-reported household owned total land area. Total area planted by a household
is calculated as the sum of area of individual plots planted in the main season. The short season is
not included to avoid double counting, since plots planted in the main season are often the very
ones planted in the short season in two-season areas. Likewise, only main season production is
counted as output. Area under maize is measured as the sum of the size of each plot that contains
maize. Most plots containing maize in Kenya are inter-cropped, and hence we should interpret the
area measure as the size of the plots on which maize was planted.
We conduct a descriptive analysis of trends and patterns in labor productivity on plots with maize
on them, as well as decomposed components and change over time. This analysis uses data for
the 2004, 2007 and 2010 survey years, which contain detailed information on production, input
use, and hired and family labor used on households’ largest maize plot in the main season. On
average, the share of the largest maize plot in households’ total planted maize area in the main
season was 89% over the three years, and increased from 86% in 2004 to 91% in 2010. Therefore,
19

we are confident that this analysis captures the vast majority of maize produced by this nationwide
sample of farm households.
There are 3977 largest maize plots (observations) in the dataset. We exclude from the analysis the
following: observations that do not have family labor use on the largest maize plot, because our
interest is in returns to family labor; observations that had less than 20% share of maize in the total
value of crops produced on the largest plot with maize; observations with reported area of less than
0.2 acres for the largest plot with maize, because of concerns about potentially large measurement
error in computing productivity; and observations that had negative net value of crop production.
The final number of observations used in the analysis is 3256, distributed as follows: 1153 in 2004;
1098 in 2007; and 1005 in 2010.
We measure labor productivity in terms of net returns to family labor-day, where a day is in terms
of 6-hour farm-work day1. Because intercropping of maize with other crops is a common practice
(2910 of the largest maize plots had more than one crop, with 66% of these having one or two
other crops besides maize), we include the value of these crops in computing productivity. Net
returns are computed as total gross value of all crops produced on the largest plot with maize net
of the cost of variable inputs (land preparation, seeds, fertilizers, and hired labor) used on the plot.
District median crop prices are used to value the crops. The cost of fertilizer is similarly computed
for fertilizer applied on the largest plot with maize. For land preparation, seeds and hired labor,
the actual expenditure incurred on these inputs on the largest plot with maize are used. Because
more than one year of data is used, net returns are adjusted for inflation using the well-known

1

6 hours is the average of the number of hours of farm work in a day reported in the data.

20

Fisher’s ideal price index, with 2004 quantities and district median prices for the crops (maize and
those intercropped with it) used as the base.
Throughout, we disaggregate the analysis by quintiles of village population density, quintiles of
distance to tarmac (paved) road (an indicator of market access), landholding categories and agroecological zone. Village population density, an indicator of land pressure, is measured as village
landholding, in square kilometers, per capita. It is computed as the ratio of the total number of
residents to the sum of landholdings of the sample households in a village. For trends and patterns
in labor productivity, we also separate between monocrop versus intercrop maize cropping
systems, gender of household head, use of mechanized land preparation and use of hired labor in
maize production.
1.4

Results and discussion

We first present trends and patterns in household landholdings, planted land size and land
allocation to plots with maize. Trends and patterns in labor productivity and its components are
discussed next. Change in labor productivity over time is decomposed into its components and
results discussed.
1.4.1

Patterns and trends in landholding and land allocation to maize production

Trends in mean landholding, area planted, and planted area allocated to plots with maize is reported
in Table 1.1. Over time, household average landholding reduced by 0.8 acres, representing a
decline by over 12% in 13 years. The effect of reduced average landholding is reflected in the
reduction in area planted by 11%, from an average of 3.5 acres in 1997 to 3.1 acres in 2010.

21

Smallholder farmers in Kenya are highly diversified in their production. The crops produced
include cereals such as maize, sorghum, millet, beans; roots and tubers such as potatoes and
cassava; industrial crops such as tea, coffee and sugarcane; and a range of fruits and vegetables.
Mixed farming involving crops and livestock is also a common practice. Although agro-ecological
conditions determine the specific crops and livestock species that can be profitably produced in
each locality, maize production is supported to various extents in virtually all agro-ecological
zones of Kenya. Maize is the single most important crop in terms of planted area allocation, with
plots with maize occupying over 50% of the total area planted, on average (Table 1.1). Over time,
the average area of plots with maize for a household declined by 11%, commensurate with the
decline in average total area planted by a household.
The trends and patterns in Table 1.1 have two important implications. First, the shrinking
landholdings and the subsequent decline in area planted among smallholder farmers support
evidence presented in Jayne et al (2014) that most farms in Kenya, and indeed the region, are
declining in size as rural populations continue to rise with little or no potential for land expansion
for agriculture. Therefore, this puts the onus on strategies to achieve agricultural growth through
agricultural intensification and productivity growth on existing farmland.

Secondly, maize

remains fundamental to Kenyan agriculture. Even with a small decline in the proportion of total
planted area under maize, still over 50% of planted land in Kenya is devoted to maize and hence
one of the most effective entry points for accelerating agricultural productivity growth in Kenya is
to raise the yields and profitability of maize.
The declining landholding and farm sizes is largely a result of increasing population. We would
expect decline in landholding and farm sizes to be larger in least densely populated villages than
in most densely populated villages because in most densely populated villages landholdings and
22

farm sizes may have already become so small that land cannot be feasibly subdivided; in such
areas, we would expect high rates of migration of youth out of the area and/or shifts in the local
labor force from farm to non-farm activities. Indeed, our data shows that outmigration rate of youth
is positively correlated with population density (see Figure A1.1 in the Appendix). The analysis in
Table 1.2 shows that overall, average landholdings and area planted, both total and allocated to
plots with maize were significantly larger in the least densely populated villages than in the most
densely populated villages. The proportion of area of plots with maize to total area planted was
also significantly larger in the least densely populated villages.
Table 1.1: Levels of and changes in mean landholding, total area planted, and area allocated to
plots with maize 1997-2010
Year

N

1997
1499
2000
1441
2004
1396
2007
1335
2010
1306
Total
6977
Change (1997-2010)
% change
* p<0.10, ** p<0.05, *** p<0.01

Total
landholding
(acres)

Total area
planted (acres)

6.1
6.0
6.3
6.1
5.3
5.9
-0.8**
-12.53

3.5
4.1
3.9
3.6
3.1
3.7
-0.4*
-11.11

Area planted
with maize
(acres)
1.8
2.1
1.9
1.9
1.6
1.9
-0.2*
-11.25

Proportion
of maize
area in total
area planted
0.59
0.57
0.54
0.54
0.54
0.56
-0.05***

Table 1.2: Mean landholding, total area planted and area allocated to plots with maize, by village
population density (pooled sample – 1997-2010)
Quintile of village
population density

N

1st (lowest)
1426
2
1394
3
1400
4
1418
5th (highest)
1339
Difference in mean
(5th - 1st)
* p<0.10, ** p<0.05, *** p<0.01

Total
landholding
(acres)
14.5
5.67
4.0
3.2
2.2

Total area
planted in main
season (acres)
7.3
3.6
2.9
2.5
1.9

-12.3***

-5.4***

23

Area planted
(acres)
3.9
1.7
1.4
1.2
1.0

Maize
Proportion of
total area planted
0.64
0.53
0.53
0.52
0.56

-2.9***

-0.07***

As hypothesized, average landholding declined over the 13-year period by a higher percentage in
the least than in the most densely populated villages (Table 1.3). This, however, was not the case
for total area planted and area of plots with maize.
Table 1.3: Changes in mean landholding, total area planted and area allocated to plots with
maize, by population density, (1997-2010)
Quintile of village
population density

Total landholding
(acres)

1st (lowest)
2
3
4
5th (highest)

-2.5
-1.0
-0.1
0.0
-0.2

1st (lowest)
2
3
4
5th (highest)

-16.6
-16.3
-3.2
-1.1
-8.2

Maize
Total area
planted in main
Area planted Proportion of total
season (acres)
(acres)
area planted
Absolute change (1997-2010)
-1.0
-0.5
-0.02
-0.5
0.1
0.07
0.0
-0.4
-0.16
-0.3
-0.1
-0.04
-0.2
-0.2
-0.08
% change
-13.6
-11.9
-14.2
9.6
0.8
-24.6
-10.9
-12.9
-13.5
-17.3

In Table 1.4, we categorize farm households into three groups according to landholding; less than
5 acres, 5-10 acres, and above 10 acres, and examine trends and changes in mean landholding,
total area planted and area allocated to plots with maize. The average landholding in the <5 acres
category increased by 12% overall, although between 2000 and 2010 average landholding
consistently declined. Total area planted for this category also increased overall, but a consistent
decline is observed between 2000 and 2010. Both average area of plots with maize and its share
in total area planted declined over time. For the >10 acres category of landholding, total planted
area and area of plots with maize increased marginally (by 7% and 9%, respectively). These results
indicate that increasing maize production can only be through increased productivity even in areas
where average landholding may be larger; there is little scope for area expansion for maize
production.

24

Table 1.4: Levels of and changes in mean landholding, total area planted and area allocated to plots with maize, by landholding
categories, 1997-2010
Year

N

<5 acres

1997
2000
2004
2007
2010
Pooled
Change (1997-2010)
% change

968
931
868
878
915
4,560

2.0
2.4
2.3
2.3
2.2
2.2
0.2
12.4

Total area
planted in
main season
(acres)
2.0
2.4
2.1
1.9
1.8
2.0
0.1
3.4

5-10 acres

1997
2000
2004
2007
2010
Pooled
Change (1997-2010)
% change

330
319
359
286
263
1,557

6.8
6.8
7.0
6.9
6.7
6.8
0.0
-0.6

>10 acres

1997
2000
2004
2007
2010
Pooled
Change (1997-2010)
% change

201
191
169
171
128
860

24.4
22.3
25.2
24.0
24.1
24.0
-0.3
-1.2

Landholding

Total landholding
(acres)

25

Maize
Area planted
(acres)

Proportion of total
area planted

1.1
1.3
1.0
1.0
0.9
1.1
0.0
-0.5

0.60
0.56
0.54
0.54
0.53
0.56
-0.05

4.0
4.5
5.0
4.4
4.0
4.4
0.1
1.9

2.0
2.4
2.5
2.3
2.1
2.3
0.1
4.8

0.56
0.55
0.52
0.55
0.57
0.55
0.01

10.4
11.6
10.7
11.2
11.1
11.0
0.7
6.6

5.0
5.9
5.0
5.9
5.4
5.4
0.4
8.6

0.55
0.59
0.55
0.57
0.55
0.57
0.01

A wide variation obtained in the land variables across agro-ecological zones (Table 1.5). Overall,
average landholding was largest in the High potential maize (HPM) zone and smallest in the
Western Highlands (WH) and Central Highlands (CH), the most densely populated of the zones.
This pattern is also reflected in total area planted. It is worth noting that despite having the lowest
yield levels of maize (shown later) among the agro-ecological zones, the Lowlands had among the
highest average share of area of plots with maize in total area planted.
Over time, average landholding declined in all the zones except in WH, while average total area
planted declined in most of the zones (Table 1.6). Average area of plots with maize also declined
in all the zones except in the CL. Positive but small changes in the average share of plots with
maize in total area planted were registered only in the HPM, CL and Western Transitional (WT)
zones.
The patterns and trends in the land variables across agro-ecological zones provide an important
insight to agricultural intensification. Because most rural households attempt to meet their own
staple maize consumption needs through own production, maize production remains important to
most smallholder farmers even in agro-ecological settings where maize productivity is relatively
low. With declining farm sizes even in these agro-ecologies, it remains a question of whether
efforts should be directed at increasing maize yield, or whether it would be more worthwhile to
encourage higher value enterprises such as horticulture in such areas.

26

Table 1.5: Mean landholding, total area planted and area allocated to plots with maize, by zone
(pooled sample – 1997 - 2010)
Zone
Coastal Lowlands
Eastern Lowlands
Western Lowlands
Western Transitional
High Potential Maize Zone
Western Highlands
Central Highlands
Marginal Rain Shadow
Overall

N

Total
landholding
(acres)

Total area
planted in main
season (acres)

379
780
850
792
1,905
742
1,273
256
6,977

5.5
5.8
3.7
5.6
10.9
2.3
2.8
5.0
5.9

3.4
3.5
2.6
4.1
6.0
1.9
2.2
1.8
3.7

Area
planted
(acres)
2.3
2.4
1.3
1.5
3.2
0.9
0.7
1.2
1.9

Maize
Proportion of
total area
planted
0.63
0.68
0.60
0.42
0.65
0.53
0.37
0.70
0.56

Table 1.6: Changes in mean landholding, total area planted and area allocated to plots with
maize, by zone, 1997-2010
Zone

Total
landholding
(acres)

Coastal Lowlands
Eastern Lowlands
Western Lowlands
Western Transitional
High Potential Maize Zone
Western Highlands
Central Highlands
Marginal Rain Shadow
Overall

-0.2
-2.0
0.0
-0.9
-0.8
0.4
-0.8
-0.7
-0.1

Coastal Lowlands
Eastern Lowlands
Western Lowlands
Western Transitional
High Potential Maize Zone
Western Highlands
Central Highlands
Marginal Rain Shadow
Overall

-4.2
-31.0
-1.0
-15.6
-7.0
17.4
-28.1
-13.8
-12.5

27

Total area planted
in main season
(acres)

Area
planted
(acres)
Absolute change (1997-2010)
0.0
0.2
-0.5
-0.6
0.5
-0.1
-1.1
-0.2
-0.5
0.0
0.1
-0.1
-0.6
-0.3
-0.2
-0.2
0.1
0.1
% change
1.4
9.6
-17.8
-27.3
22.9
-5.7
-25.3
-16.4
-8.8
-1.1
7.5
-13.8
-24.7
-39.9
-10.8
-14.9
-11.1
-11.3

Maize
Proportion of
total area
planted
0.04
-0.07
-0.14
0.03
0.01
-0.11
-0.07
-0.05
-0.03

It is a common practice among smallholder farmers in Kenya to plant maize together with other
crops such as beans on the same plot. As shown in Table 1.7, planting maize alone on a plot was
a rare practice overall; a maize plot was generally intercropped with at least one other crop.
Besides, the average share of plots with intercropped maize in total maize area increased over time
(by 6 percentage points). This would be expected since declining landholdings impose constraints
on land available for production and encourages farmers to mix crops on the available cultivable
land. While intercropping is generally a good agronomic practice, it has little benefits to maize
yield if there are no beneficial interactions between maize and the other crop(s). Intercropping
maize with legumes, such as is common in Kenya, is beneficial to maize as legumes are nitrogen
fixers in the soil.
Table 1.7: Average share of monocropped and intercropped maize plots in total area planted and
in total area of plots with maize, 1997 - 2010

Year

N

1997
2000
2004
2007
2010
Total
Change (1997 2010)

1,499
1,441
1,396
1,335
1,306
6,977

1.4.2

Monocropped maize
area as % of …
Area
Total area
under
planted
maize
7.54
14.85
4.35
8.54
4.40
9.05
6.23
10.70
4.30
8.12
5.39
10.33
-3.23

-6.73

Intercropped maize area
as % of …
Area
Total area
under
planted
maize
51.70
85.15
52.74
91.46
50.03
90.95
48.82
89.30
50.30
91.88
50.77
89.67
-1.40

6.73

No. of other
crops on
intercropped
maize plots
1.6
2.8
2.4
2.5
2.2
2.3
0.7

Patterns and trends in land and labor productivity in maize production

In this section, we present and discuss patterns and trends in land productivity, family labor use
rate and labor productivity (returns to family labor) in maize production. As explained earlier, the
analysis is on the households’ largest plots planted with maize (monocrop or intercrop) and for the
years 2004, 2007 and 2010 for which labor data is available. We measure labor productivity in
28

terms of net returns to family labor-day, adjusted for inflation. Net returns is computed as gross
value of output for all crops planted with maize on the largest plot less the cost of variable inputs
used on the plot, and adjusted for inflation using Fisher’s ideal price index with 2004 quantities
and district median prices as the base. We disaggregate the analysis by various household and
spatial attributes to tease out relationships that might otherwise be masked by pooling the data.
Over time, average land productivity (net returns per acre) increased by 26% while family labor
average use rate declined by 16% between 2004 and 2010 (Table 1.8). Average labor productivity
(net returns to family labor) increased by 40%, a result of a combination of the increase in average
land productivity and a decline in family labor average use rate. It is important to note that the
decline in family labor average use rate was larger relative to the decline in the average planted
plot size, indicating an increase in average land-labor ratio. The reduction in family labor use rate
was compensated in part by increased use of hired labor, from an average of 17 to 19 person-days
per acre, representing an increase of about 12% between 2004 and 2010.
Table 1.8: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) over time (mean)

Year

N

2004
2007
2010
Total
% change (2004 - 2010)

1153
1098
1005
3256

Planted plot
size (acres)

Land
productivity
(Net revenue
per acre (Ksh))

Family labor
(Person-days
per acre)

1.5
1.5
1.3
1.4
-17.1

10744
11484
13565
11864
26.3

49.0
39.1
41.2
43.2
-16.0

Labor
productivity
(Net revenue
per family
labor-day
(Ksh))
609
933
854
794
40.3

Note: Net revenue values are in real terms
Across categories of landholding, average land productivity increased in the <5 acres and 5-10
acres categories but declined in the >10 acres category, while family labor average use rate

29

declined for all the categories (Table 1.9). Average labor productivity also increased for all
categories of landholding. The driving factor in the increase in average labor productivity for the
5-10 and >10 acres categories of landholding is the decline in family labor use rate rather than
positive changes in land productivity.
Table 1.9: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by landholding (mean)

Landholding
category

<5 acres

5-10 acres

>10 acres

Land
productivity
(Net revenue
per acre (Ksh))

Year

2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

Labor
productivity
(Net revenue
per family
labor-day
(Ksh))
379
578
601
521

N
698
726
719
2143

11489
12488
15016
13011

Family labor
(Person-days
per acre)
58.8
46.1
46.5
50.4

307
239
205
751

30.7
9057
9957
10302
9683

-20.8
38.3
29.2
31.9
33.6

58.7
788
1392
1063
1055

148
133
81
362

13.8
10727
8747
8947
9601

-16.8
25.0
18.7
17.0
20.9

34.9
1325
2047
2574
1870

-16.6

-31.9

94.3

Note: Net revenue values are in real terms
Levels of and changes in average land and labor productivity and family labor use rate
disaggregated by quintiles of population density are presented in Table 1.10. We observe several
patterns. First, total average land productivity generally increased as population density increased.
This relationship is much clearer in the non-parametric locally weighted scatterplot smoothing
(lowess) regression analysis presented in Figure 1.3. It shows a concave relationship between land
productivity and population density, indicating land productivity gains from agricultural
30

intensification efforts by households as population increases and landholdings become smaller up
to some point after which productivity gains diminish as population density increases (Muyanga
& Jayne, 2014) . Over time, average land productivity increased for households in all the villages
except those in the 1st quintile, mirroring the pattern observed in the disaggregation by landholding
categories above.
Table 1.10: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by population density (mean)
Quintile of
population
density

1st (lowest)

2

3

4

5th (highest)

N
227
218
208
653

Land
productivity
(Net revenue
per acre (Ksh))
12449
9419
10475
10809

Family labor
(Person-days
per acre)
32.0
23.8
27.3
27.8

Labor productivity
(Net revenue per
family labor-day
(Ksh))
1173
1881
1711
1581

236
219
200
655

-15.9
8947
11295
12442
10799

-15.0
43.9
34.9
40.9
40.0

45.8
519
771
733
669

226
222
198
646

39.1
9524
13119
13336
11928

-6.9
55.6
42.9
46.3
48.4

41.3
524
814
498
615

231
227
206
664

40.0
10223
11551
15924
12446

-16.7
52.4
42.9
46.7
47.4

-5.0
403
770
677
614

233
212
193
638

55.8
12602
12017
15777
13368

-11.0
60.9
50.9
45.4
52.9

67.9
437
425
611
486

25.2

-25.5

39.7

Year
2004
2007
2010
Total
% change
(2004 - 2010)
2004
2007
2010
Total
% change
(2004 - 2010)
2004
2007
2010
Total
% change
(2004 - 2010)
2004
2007
2010
Total
% change
(2004 - 2010)
2004
2007
2010
Total
% change
(2004 - 2010)

Note: Net revenue values are in real terms
31

Secondly, as expected, family labor total average use rate increased with increase in population
density. Over time, family labor average use rate declined in all the quintiles of population density,
with the 2nd quintile registering the least and the 5th quintile the largest decline. The decline over
time in family labor average use rate even in most densely populated villages suggests that
households were devoting more labor to other activities, either/both farm or/and non-farm
activities.
Lastly, there was an inverse relationship between total average labor productivity and population
density, as also shown in the lowess regression analysis results in Figure1.4, indicating the need
for faster growth in land productivity to sustain growth in returns to family labor as landholdings
shrink due to increasing population.

14000
13000
12000
11000
10000

Landproductivity(N
et valueof cropproductionperacre)

Figure 1.3: Locally weighted scatterplot smoother (lowess) of land productivity of maize and
village population density

0

200

400

600

800

Village population density (persons/square km)

32

1000

2000
1500
1000
500

Labour productivity (Net valueof production per familylabour-day)

Figure 1.4: Locally weighted scatterplot smoother (lowess) of labor productivity of maize and
village population density

0

200

400

600

800

1000

Village population density (persons/square km)

A notable observation across gender of household head is that total average land productivity,
family labor average use rate and labor productivity were higher in male- than in female-headed
households (Table 1.11), indicating a generally higher productivity of maize in male-headed
relative to that in female-headed households. Over time, both groups of households experienced
positive changes in average land and labor productivity and a decline in family labor average use
rate. It is important to note that 93% of female household heads did not have spouses and most
(87%) were widows. This contrasts sharply with male household heads 75% of who had spouses.
It implies that female-headed households in the sample lacked the support of one additional adult
in their farming activities and may be the reason they generally had lower productivity compared
to male-headed households.
The relationship between market access, represented by distance to paved road, and land and labor
productivity and family labor use rate is presented in Table 1.12. On average, most remote
households compared to their least remote counterparts had lower land and labor productivity and
family labor use rate. Figure 1.5 and Figure 1.6 also show that land and labor productivity each

33

generally has an inverse relationship with distance from a household to a tarmac road. This
indicates that better transport infrastructure implies better access to both input and output markets,
which may facilitate efficient use of inputs and family labor allocation, resulting in greater
productivity of both land and family labor.
Table 1.11: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by gender of household head (mean)

Gender of
household head

Female

Male

Land
productivity
(Net revenue
per acre
(Ksh))

Family labor
(Persondays per
acre)

N
223
263
257
743

10085
10238
12131
10847

45.5
35.9
39.3
39.9

Labor
productivity
(Net
revenue per
family
labor-day
(Ksh))
507
784
732
683

930
835
748
2513

20.3
10902
11876
14058
12165

-13.6
49.8
40.1
41.8
44.2

44.2
633
980
896
827

28.9

-16.1

41.5

Year

2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

Note: Net revenue values are in real terms
Table 1.12: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by distance to tarmac road (mean) (pooled sample – 2004 – 2007)
Quintile of distance to
tarmac road
1st (shortest)
2
3
4
5th (longest)
Difference (5th-1st)

N

Land productivity
(Net revenue per acre
(Ksh))

Family labor
(Person-days per
acre)

12057
11821
12738
13073
9502
-2555

39.1
43.7
43.8
44.0
47.1
8.0

828
547
689
582
610

Note: Net revenue values are in real terms

34

Labor productivity
(Net revenue per
family labor-day
(Ksh))
896
804
887
894
446
-450

14000
12000
10000
8000
6000

Land productivity (Net value of production per acre)

Figure 1.5: Locally weighted scatterplot smoother (lowess) of land productivity and distance to
tarmac road

0

20

40

60

Distance in kms from HH to tarmac road

1000
800
600
400
200

Labour productivity (Net valueof production per family labour day)

Figure 1.6: Locally weighted scatterplot smoother (lowess) of labor productivity and distance to
tarmac road

0

20

40

60

Distance from HH to tarmac road (km)

With respect to cropping system, Table 1.13 shows that total average land productivity and family
labor use rate were higher on intercropped than on monocropped plots, while total average labor
productivity was higher on monocropped than on intercropped plots. Over time, average land and
labor productivity increased while family labor use rate declined on intercropped plots. On
monocropped plots, both average land productivity and family labor use rate declined, while labor

35

productivity increased. It is worth noting that intercropped plots were significantly smaller than
monocropped plots, on average. These patterns mirror the results observed previously that
households with smaller landholdings had greater land productivity than those with larger
landholding, and labor productivity was greater for households with larger landholding.
Intensification of maize production involving intercropping with especially legumes may be useful
in increasing land productivity.
Table 1.13: Land and labor productivity and family labor use rate on maize intercrop and
monocrop plot (mean)

Cropping
system of
maize on plot

Intercrop

Monocrop

Year

2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

N

Land
productivity
(Net revenue
per acre
(Ksh))

Family
labor
(Persondays per
acre)

1059
959
892
2910

10938
11994
14343
12329

49.4
39.8
42.3
44.0

Labor
productivity
(Net
revenue per
family
labor-day
(Ksh))
602
893
745
742

94
139
113
346

31.1
8560
7967
7430
7953

-14.4
44.8
34.0
32.5
36.5

23.8
691
1209
1715
1234

-13.2

-27.5

148.2

Note: Net revenue values are in real terms
There were wide variations in average land and labor productivity and family labor use rate across
agro-ecological zones (Table 1.14). The total average land productivity was highest in the CH, one
of the most densely populated of the zones, and lowest in the CL. Family labor average use rate
was in the WH and CH zones, which had the highest population density. Total average labor
productivity was highest in the HPM zone, where family labor average use rate was also lowest,
and lowest in CL.
36

Over time, average land productivity increased in all the zones except HPM, CL and MRS, while
labor productivity declined only in CL. Family labor average use rate increased in all the zones
except the EL.
These results have important implications. First, the reduction in average land productivity in the
HPM zone, the most important maize producing region and where fertilizer and improved seed
variety adoption on maize is nearly complete, implies a problem in low response of maize to input
use. Research has shown that soil degradation is a major problem in Kenya’s agriculture, and soil
mining is a widespread concern not only in Kenya but in the entire Africa (Stoorvogel et al, 1993;
The Montpellier Panel, 2013). Increasing maize production on degraded soils is not feasible
without restoring soil fertility.
Secondly, both land and labor productivity were quite low in some zones, especially the Lowlands
where, coincidentally, use of external inputs such as fertilizer and improved maize varieties is
generally low. While it might be tempting to suggest that strategies to encourage widespread use
of external inputs in these zones would be beneficial in raising maize productivity, it is more
critical to recognize the necessity of agronomic practices that raise soil quality. Without building
soil fertility through proper agronomic practices, encouraging use of external inputs such as
fertilizers and improved seed varieties in these zones, despite their lower use rates, may not achieve
the needed productivity growth.

37

Table 1.14: Land and labor productivity and family labor use rate on maize plots (both monocrop
and intercrop) by agro-regional zone (mean)

Agro-ecological zone

Coastal Lowlands

Eastern Lowlands

Western Lowlands

Western Transitional

High Potential Maize Zone

Year

N

Land
productivity
(Net revenue
per acre
(Ksh))

2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

48
57
55
160

5603
8144
4724
6206

59.7
35.8
40.5
44.6

Labor
productivity
(Net revenue
per family
labor-day
(Ksh))
194
350
151
235

129
123
127
379

-15.7
6049
9950
13141
9692

-32.2
44.8
28.8
51.3
41.8

-22.6
303
684
487
489

117
146
140
403

117.3
4439
9280
7529
7267

14.5
45.6
33.6
32.4
36.7

60.6
160
793
458
493

149
141
143
433

69.6
9358
9839
13513
10887

-29.0
52.5
54.4
48.1
51.7

186.5
340
352
549
413

361
309
215
885

44.4
13194
10672
11466
11894

-8.4
40.3
33.0
32.7
35.9

61.5
1134
1552
1654
1406

-13.1

-19.0

45.9

38

Family
labor
(Persondays per
acre)

Table 1.14 (Cont’d)

Agro-ecological zone

Western Highlands

Central Highlands

Marginal Rain Shadow

Year

N

Land
productivity
(Net revenue
per acre
(Ksh))

2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

129
136
126
391

8992
11741
13249
11320

58.9
51.3
41.8
50.8

Labor
productivity
(Net revenue
per family
labor-day
(Ksh))
282
573
729
527

180
151
173
504

47.3
16817
19207
25673
20573

-29.1
58.5
39.4
47.3
48.9

159.0
664
1158
1025
936

40
35
26
101

52.7
11871
10976
5452
9909

-19.2
49.9
46.2
29.2
43.3

54.3
481
653
796
621

-54.1

-41.4

65.6

Family
labor
(Persondays per
acre)

Note: Net revenue values are in real terms
Lastly, the high and increasing average land productivity in the WH and CH, the most densely
populated zones, and WT and EL may suggest that sustainable intensification is taking place in
the zones. It is important to note that average plot sizes in WH and CH zones are the smallest and
a number of crops are intercropped with maize, which could also be among the reasons for the
high average land productivity levels. All the same, strategies to ensure sustained momentum in
increasing land productivity in these zones would be desirable, and lessons from these zones could
inform the design of appropriate strategies for increasing land productivity in other less densely
populated zones. It is also worth noting that there would be population density threshold beyond
which no land productivity gains would be realized or there would be a decline in land productivity
altogether (Josephson et al, 2014; Muyanga & Jayne, 2014; Ricker-Gilbert et al., 2014). Therefore,

39

strategies to stimulate growth in non-farm sectors would certainly be necessary to ease population
pressure on agricultural land.
Land and labor productivity (returns to land and to family labor) are also functions of use of other
inputs and agricultural technologies. We would expect productivity of family labor to increase
when farm operations are mechanized and when use of hired labor increases, if production
increases thereof are high enough to offset mechanization and labor hiring costs. We explore these
relationships in Tables 1.15 and 1.16. Total average land productivity and family labor use rate
were higher for households that did not at all use hired labor than for those that used (Table 1.15).
Average returns to family labor, on the other hand, was significantly higher for households that
also used hired labor than for those that did not at all use, indicating that returns to family labor is
much higher when a household is able to substitute hired for family labor. This implies that on
average, households who can afford to hire labor for maize production may benefit from
reallocating their labor from maize cultivation to activities with higher returns. Over time, both
groups of households had increased average land productivity, with the group that did not use hired
labor experiencing a larger increase. Average labor productivity increased more for households
that did not use hired labor than for those that used hired labor.
In Table 1.16 are patterns and trends in land and labor productivity and family labor use rate by
mechanized land preparation, a labor-saving technology. Data showed that mechanized land
preparation was more common on larger plots, on average. While total average land productivity
was significantly higher where land preparation was manual, total average labor productivity was
higher where land preparation was mechanized. This indicates that mechanized land preparation
does not really affect land productivity of maize but raises returns to family labor through reducing
family labor requirement. Indeed, family labor average use rate was higher where mechanization
40

was not used and much lower where it was used. Over time, average land and labor productivity
increased for both groups of households. However, average land productivity increased only
slightly for households that used mechanized land preparation. Family labor average use rate
declined for both groups of households, but the percentage decline was larger for those that did
not use mechanized land preparation.
1.15: Land and labor productivity and family labor use rate on maize plots (both monocrop and
intercrop) by hired labor use (mean)
Use of hired
labor

Not used

Used

Year

N

Land productivity
(Net revenue per
acre (Ksh))

2004
2007
2010
Total
% change (2004
- 2010)
2004
2007
2010
Total
% change (2004
- 2010)

462
446
390
1298

9709
12393
13835
11871

67.6
60.0
56.8
61.7

Labor productivity
(Net revenue per
family labor-day
(Ksh))
200
283
296
257

42.5

-16.0

47.9

11436
10862
13394
11860

36.6
24.8
31.3
31.0

882
1378
1208
1150

17.1

-14.5

36.9

691
652
615
1958

Note: Net revenue values are in real terms

41

Family labor
(Person-days
per acre)

Table 1.16: Land and labor productivity and land-labor ratio on maize plots (both monocrop and
intercrop) by mechanized land preparation (mean)
Use of
mechanized
land preparation

Not used

Used

Year
2004
2007
2010
Total
% change (2004 2010)
2004
2007
2010
Total
% change (2004 2010)

N

Land
productivity
(Net revenue
per acre (Ksh))

584
583
565
1732

11335
13693
16017
13656

Family
labor
(Persondays per
acre)
63.0
48.1
50.0
53.7

41.3

-20.6

64.0

10137
8983
10418
9828

34.6
28.9
29.8
31.3

838
1247
1138
1063

2.8

-13.9

35.8

569
515
440
1524

Labor productivity
(Net revenue per
family labor-day
(Ksh))
386
656
633
558

Note: Net revenue values are in real terms
We use expression (1.3) in the conceptual framework section to decompose percentage change in
labor productivity into its components – percentage change in land productivity and in land-labor
ratio – between two data points; 2004 and 2010 (Table 1.17). Overall, long-term labor productivity
increased by 36% on average, resulting from a combination of an increase in land productivity of
21% and in land-labor ratio of 16%. The increase in land-labor ratio was because of a decline in
family labor use rate. The fact that a little below half of the increase in returns to family labor is
contributed by increase in land-labor ratio due to reduced family labor use rate attests to the need
for faster growth in land productivity in Kenya’s maize sector, and in agricultural sector in general.

42

Table 1.17: Mean percentage change in labor productivity of maize (both monocrop and
intercrop) as the sum of percentage changes in land productivity and land-labor ratio, 2004-2010
Land
productivity
Overall
Farm size

Population density
quintile
Gender of household
head
Quintile of distance to
tarmac road

Cropping system

Agro-regional zone

Hired labor use
Mechanized land
preparation

<5 acres
5-10 acres
>10 acres
1st (lowest)
2
3
4
5th (highest)
Female
Male
1st (shortest)
2
3
4
5th (longest)
Intercrop
Monocrop
Coastal Lowlands
Eastern Lowlands
Western Lowlands
Western Transitional
High Potential Maize Zone
Western Highlands
Central Highlands
Marginal Rain Shadow
Not used
Used
Not used
Used

21.1
31.8
4.5
-42.2
-34.5
34.9
41.6
45.6
19.1
26.0
20.7
11.4
16.3
29.0
32.2
15.4
27.1
-18.2
-21.5
83.6
59.4
41.1
-33.2
40.4
57.0
-88.2
33.8
12.8
37.4
-0.3

Landlabor
ratio
16.3
21.3
19.0
65.8
26.7
2.8
12.9
4.8
31.2
19.8
15.2
12.4
21.3
15.5
32.4
2.0
9.7
65.1
32.0
-34.8
38.3
4.5
33.9
46.9
13.6
55.4
11.4
17.7
18.3
22.0

Labor
productivity
37.5
53.1
23.5
23.6
-7.8
37.7
54.5
50.5
50.3
45.8
35.9
23.8
37.5
44.5
64.7
17.4
36.9
47.0
10.5
48.8
97.7
45.6
0.7
87.3
70.6
-32.8
45.2
30.5
55.7
21.8

The overall picture about the sources of change in labor productivity can mask important details
regarding dynamics in the growth components across categories of farmers. For this reason, we
disaggregate labor productivity change and its components by the various categories of households
as in the analyses presented previously. By landholding, labor productivity increased for <5 acres
category, contributed by positive change in land productivity (32%) and in land-labor ratio (21%).
Again, it is important to note that the increase in land-labor ratio was because of a decline in family
43

labor use rate. For the 5-10 acres category of landholding, labor productivity increased by 24%,
contributed by 19% increase in land-labor ratio and only 5% increase in land productivity. Labor
productivity also increased for the >10 acres category of landholding, because of an increase in
land-labor ratio which outweighed the large decline in land productivity of 42%. These results
indicate encouraging gains in production intensification by households with smaller landholdings,
but a cause for concern about the lack of yield gains on larger farms, which are often relied upon
for producing marketable surpluses. Therefore, it should not be a surprise that there is an increasing
deficit in domestic supply of maize in Kenya (Kirimi et al., 2011).
The patterns in labor productivity changes observed across landholding categories are reflected in
the quintiles of population density. Households in the least densely populated villages had a decline
of 8% in labor productivity, contributed by a decline in land productivity of 35% and positive
change of 27% in land-labor ratio. On average, labor productivity increased for households in the
second to fourth quintiles of village population density, more because of positive change in land
productivity and less because of increase in land-labor ratio. For the fifth quintile of population
density, the increase in labor productivity was largely contributed by positive change in land-labor
ratio. It is important to keep in mind that the positive change we observe in land-labor ratio was
because of a decline in family labor use rate on maize plots and not increase in area planted with
maize, which declined over time.
Disaggregation by gender of the head of household shows positive change in labor productivity
for both male and female-headed households, because of increase in both land productivity and
land-labor.

44

Across quintiles of distance to paved road, an indicator of market access, labor productivity
increased for all the households but the increase was smallest for households furthest from paved
roads. This was due to a 15% increase in land productivity and 2% increase in land-labor ratio.
While intercropped plots registered positive change in labor productivity due to increases in land
productivity and land-labor ratio, monocropped maize plots had labor productivity increase
because of a large increase in land-labor ratio that outweighed the negative change in land
productivity.
A remarkable result across agro-ecological zones is the decline or small increase in labor
productivity in the HPM, CL and MRS zones, because of a decline in land productivity. Being the
most important maize producing region of Kenya, the dwindling maize yield in HPM zone
indicates the urgent need for ways to address the problems associated with low land productivity.
Both households that used and those that did not use hired labor on maize production had positive
change in labor productivity, because of positive change in land productivity and in land-labor
ratio. Disaggregation by type of land preparation shows that households that used mechanized land
preparation had a smaller increase in labor productivity because of a decline in land productivity.
It is worth noting that mechanized land preparation, larger landholdings and low population
density are highly correlated hence similar patterns in labor and land productivity changes.

45

1.5

Conclusions and implications for policy

Kenya’s agricultural productivity has generally been low and has stagnated over time. Aggregate
yield of maize, the most important staple crop, although showing a gradual upward trend in the
recent past, has a general downward trend over the past two and a half decades. In addition, farm
sizes have been shrinking over time as rural population densities rise and land sub-division occurs.
These have made Kenya increasingly dependent on food imports for its national food security. The
country is also foregoing opportunities to generate strong farm-nonfarm growth multipliers and
shifts in the composition of the labor force for economic transformation. This study focused on
maize and aimed to determine whether Kenya’s agricultural sector is changing in ways that are
promoting or retarding farm labor productivity and to understand the association between farm
labor productivity and population density, land scarcity and market access. We measured labor
productivity in terms of returns to family labor, which we consider most appropriate for
profitability of farming for agricultural households.
Six key results have emerged. First, average landholding declined by over 12% in 13 years while
average area planted declined by 11%. Maize is the single most important crop, occupying over
50% of total area planted. Over time, the average area of plots with maize for a household declined
by 11%.
Second, long-term labor productivity (returns to family labor) increased by 38% overall,
contributed by positive changes in land-labor ratio of 16% and land productivity of 21%. The
increase in land-labor ratio was because of a decrease in family labor use rate on maize plots. The
decline in family labor use rate was accompanied by increased use of hired labor. While many
factors that the scope of the analysis in this paper is incapable of identifying could explain the
46

decline in family labor use rate, one plausible explanation is that farm and non-farm activities of
higher returns might be attracting labor of smallholder farm families, making them to reduce their
labor in lower-value maize production.
Third, there was an inverse relationship between landholding and land productivity. The inverse
relationship was also observed between landholding and family labor use rate. Over time, labor
productivity increased substantially for the <5 acres category of landholding, contributed by
increase in land productivity (32%) and in land-labor ratio (21%). The labor productivity increase
for the 5-10 and >10 acres categories of landholding was mainly because of increase in land-labor
ratio rather than in land productivity. In fact, land productivity declined by 42% for the >10 acres
category of landholding.
Fourth, average land productivity and family labor use rate had direct relationships with population
density while labor productivity was inversely related with population density. Households in the
1st quintile of population density (least densely populated villages) had a decline of 8% in labor
productivity, contributed by a decline of 35% in land productivity and an increase of 27% in landlabor ratio. Labor productivity increased for households in all the other quintiles, more because of
increase in land productivity than the increase in land-labor ratio, except for the 5 th quintile (most
densely populated) where the contribution of land productivity increase was lower than that of
land-labor ratio increase.
Fifth, most remote households, in terms of distance to a paved road, compared to their least remote
counterparts had lower land productivity, higher family labor use rate and lower labor productivity,
on average. Although labor productivity increased for both households over time, the increase was

47

smallest for the households furthest from paved roads, because of smaller increases in land
productivity and land-labor ratio.
Lastly, there was a remarkably small increase in labor productivity (0.7%) in the HPM zone,
Kenya’s most important maize producing region, because of a 33% decline in land productivity.
These results provide important insights about Kenya’s farming sector in general and smallholder
agriculture in particular. First, the shrinking landholdings and the subsequent decline in area
planted among smallholder farmers puts the onus on strategies to achieve agricultural growth
through agricultural intensification and productivity growth. The sheer amount of area under maize
means that the crop remains fundamental to Kenyan agriculture and economy and land
productivity of maize will need to go up substantially for overall agricultural labor productivity to
rise appreciably over time. This means that we cannot just focus on diversifying into other crops
– that may be necessary but certainly not sufficient. Kenyan policy makers must also figure out
how to raise maize yield to raise the returns to labor in Kenyan agriculture overall. One of the
major causes of low and stagnated agricultural yields in Kenya is soil infertility (Government of
Kenya, 2014; Tittonell et al., 2008; Marenya & Barrett, 2007). Therefore, raising maize yield will
require addressing the soil infertility problem.
Secondly, we have shown that labor productivity increased in areas with smaller landholdings and
higher population density because of increase in land productivity, and declined or only slightly
increased in areas with larger landholdings and lower population density because of a decline in
land productivity. This suggests encouraging gains in production intensification by households
with smaller landholdings, but a cause for concern about the lack of productivity gains on larger

48

farms, which are often relied upon for producing marketable surpluses. Therefore, addressing
causes of declining yield on larger farms should be a priority.
Lastly, land-labor ratio increased even in villages with high population densities because
households reduced family labor use rate on maize. On one hand this suggests that households
may be devoting more labor to other activities, either/both farm or/and non-farm, that potentially
provide much higher returns to their labor than cultivating maize. Shifting of the labor force
involving movement of labor from farm to non-farm activities over time and accompanied by
increased land productivity can be viewed as part of structural transformation process, which will
by construct raise labor productivity in agriculture. This process appears to be taking place in some
high densely populated villages where both land-labor ratio and maize yield increased. On the
other hand, reduction of family labor in maize production might be based on “push” factors.
Haggblade et al (2005) note that labor can move from agriculture to rural non-farm sector
characterized by low-return activities because of low labor productivity in agriculture, low
opportunity cost of labor and declining real income of households. In the light of this argument,
reduction in family labor use rate on maize production may also be because of low or declining
maize yield. In such scenario, it is essential that underlying causes of low land productivity be
addressed to raise labor productivity.

49

APPENDIX

50

Figure A1.1 shows the relationship between village outmigration rate of the population 15 – 40
years of age. Outmigration rate is computed as the ratio of the number of persons aged 15- 40 years
that migrated out of the village to the number of village residents in that age bracket, multiplied
by 1000. The rate is thus interpreted in terms of number of out-migrants per 1000 population in
the 15 – 40 years age bracket in a village. The figure shows a general positive association between
village outmigration rate and population density. Marginal effects from a simple OLS regression
of village outmigration rate on population density and its quadratic term shows that on average,
and without accounting for other factors that might affect outmigration rate, additional population
density of 100 persons per square kilometer in a village is associated with an increase in migration
rate of 5 persons per 1000 population in the 15 - 40 years age bracket.

140
120
100
80
60

Outmigration rate (persons per 1000 population)

Figure A1.1: Relationship between youth outmigration rate and village population density
(lowess regression using pooled sample – 2000-2010)

0

200

400

600

800

Population density (persons per square kilometer)

51

1000

REFERENCES

52

REFERENCES

Argwings-Kodhek, G., Jayne, T. S., Nyambane, G., Awuor, T., & Yamano, T. (1999). How can
micro-level household information make a difference for agricultural policy making?
Selected examples from the KAMPAP survey of smallholder agriculture and non-farm
activities for selected districts in Kenya. Nairobi. Retrieved from
http://tegemeo.org/index.php/resources/publications/168-technical-reports/521-how-canmicro-level-household-information-make-a-difference-for-agricultural-policy-makingselected-examples-from-the-kampap-survey-of-smallholder-agriculture-and-non-farm-activ
Auer, L. (1966). Labour Productivity in Agriculture—a Conceptual Analysis. Canadian Journal
of Agricultural Economics/Revue Canadienne D’agroeconomie, 14(1), 29–39.
https://doi.org/10.1111/j.1744-7976.1966.tb02373.x
Barbier, E. B., & Hochard, J. P. (2014). Land degradation, less favoured lands and the rural
poor: A spatial and economic analysis.
Boserup, E. (1965). The conditions of agricultural growth. Population Studies, 20(1), 1–108.
https://doi.org/10.2307/2172620
Chamberlin, J. (2013). Market access and smallholder development in Kenya and Zambia.
Michigan State University.
FAOSTAT. (2014). FAOSTAT. Food and Agricultural Organization of the United Nations.
Retrieved from http://data.fao.org/ref/262b79ca-279c-4517-93deee3b7c7cb553.html?version=1.0
Government of Kenya. (2014). Soil suitability evaluation for maize production in Kenya soil
suitability evaluation for. Nairobi, Kenya.
Haggblade, S., & Hazell, P. B. R. (Eds.). (2010). Successes in African Agriculture. International
Food Policy Research Institute.
Haggblade, S., Hazell, P., & Reardon, T. (2005). The rural nonfarm economy: Pathway out of
poverty or pathway in? In International Food Policy Research Institute. The future of small
farms. Proceedings of a research workshop. Wye, UK.
Horneck, D. A., Sullivan, D. M., Owen, J. S., & Hart, J. M. (2011). Soil Test Interpretation
Guide (EC No. 1478). Corvallis, OR.
Jayne, T. S., & Rashid, S. (2013). Input subsidy programs in sub-Saharan Africa: A synthesis of
recent evidence. Agricultural Economics, 44, 547–562. https://doi.org/10.1111/agec.12073
Johnston, B. F., & Mellor, J. W. (1961). The role of agriculture in economic development. The
American Economic Review, 51(4), 566–593.
53

Josephson, A. L., Ricker-Gilbert, J., & Florax, R. J. G. M. (2014). How does population density
influence agricultural intensification and productivity? Evidence from Ethiopia. Food
Policy, 48, 142–152. https://doi.org/10.1016/j.foodpol.2014.03.004
Kirimi, L., Sitko, N., Jayne, T. S., Karin, F., Muyanga, M., Sheahan, M., … Bor, G. (2011). A
farm gate-to-consumer value chain analysis of Kenya’s maize marketing system (Working
Paper No. 44). Nairobi.
Lipton, M. (2005). The family farm in a globalizing world: The role of crop science in
alleviating poverty (2020 Discussion Paper No. 40). Washington, DC.
Marenya, P. P., & Barrett, C. B. (2007). Household-level determinants of adoption of improved
natural resources management practices among smallholder farmers in western Kenya.
Food Policy, 32(4), 515–536.
Muyanga, M., & Jayne, T. S. (2014). Effects of rising rural population density on smallholder
agriculture in Kenya. Food Policy, 48, 98–113.
https://doi.org/10.1016/j.foodpol.2014.03.001
Olwande, J., Smale, M., Mathenge, M. K., Place, F., & MithĂśfer, D. (2015). Agricultural
marketing by smallholders in Kenya: A comparison of maize, kale and dairy. Food Policy,
52, 22–32. https://doi.org/10.1016/j.foodpol.2015.02.002
Otsuka, K., & Larson, D. F. (Eds.). (2013). An African Green Revolution: Finding ways to boost
productivity on small farms. Dordrecht Heidelberg New York London: Springer.
https://doi.org/10.1007/978-94-007-5760-8
Pingali, P., Bigot, Y., & Binswanger, H. P. (1987). Agricultural mechanization and the evolution
of farming systems in sub-Saharan Africa. Economic Geography (Vol. 64). The Johns
Hopkins University Press. https://doi.org/10.2307/144242
Ricker-Gilbert, J., Jumbe, C., & Chamberlin, J. (2014). How does population density influence
agricultural intensification and productivity? Evidence from Malawi. Food Policy, 48, 114–
128. Retrieved from http://dx.doi.org/10.1016/j.foodpol.2014.02.006
Stoorvogel, J. J., Smaling, E. M. A., & Janssen, B. H. (1993). Calculating soil nutrient balances
in Africa at difference scales. Fertilizer Research, 35, 237–235.
https://doi.org/10.1007/BF00750642
The Montpellier Panel. (2013). Sustainable intensification: A new paradigm for African
agriculture. London.
The World Bank. (2008). World Development Report 2008: Agriculture for Development.
Washington, DC.
Tittonell, P., Corbeels, M., Wijk, M. T. Van, Vanlauwe, B., & Giller, K. E. (2008). Combining
Organic and Mineral Fertilizers for Integrated Soil Fertility Management in Smallholder
Farming Systems of Kenya: Explorations Using the Crop-Soil Model FIELD. Agronomy
54

Journal, 100(5), 1511–1526.
Tittonell, P., & Giller, K. E. (2013). When yield gaps are poverty traps: The paradigm of
ecological intensification in African smallholder agriculture. Field Crops Research, 143,
76–90. https://doi.org/10.1016/j.fcr.2012.10.007
Wambugu, S., Kirimi, L., & Opiyo, J. (2011). Productivity trends and performance of dairy
farming in Kenya (Working Paper No. 43). Retrieved from
http://tegemeo.org/index.php/resources/publications/166-working-papers/434-productivitytrends-and-performance-of-dairy-farming-in-kenya.html
Yeboah, K. F., & Jayne, T. S. (2016). Africa’s evolving employment structure (MSU
International Development Working Paper No. 48).

55

CHAPTER 2: FARMERS’ PERCEPTIONS OF SOIL FERTILITY AND
ADOPTION OF SOIL FERTILITY IMPROVEMENT PRACTICES

2.1

Introduction and Study Objectives

Soil infertility has been identified as a fundamental cause of low agricultural productivity in subSaharan Africa (Stoorvogel & Smaling, 1998; Sanchez et al., 1997), with nutrient depletion cited
as the major cause for the widespread soil infertility (The Montepellier Panel, 2013; Smaling et
al., 1997; Stoorvogel & Windmeijer, 1993). Stoorvogel & Windmeijer (1993) point out that
cropping intensity and land management are significant determinants of the rate of nutrient
depletion in soils once land use changes from natural vegetation to agriculture.
It is widely acknowledged that continuous cultivation of land without soil amendments in form of
nutrient replenishment and organic matter addition degrades soils and lowers crops response to
external inputs such as fertilizers (Sanchez et al., 1997; Lal, 2006; Tittonell & Giller, 2013).
Extractive land management practices deplete soil organic carbon (Lal, 2006), the main component
of soil organic matter. Soil organic carbon is essential for a range of soil chemical, physical, and
biological properties and is an overall indicator of soil health (Okalebo, Gathua, & Woomer,
2002;Lal, 2006; Horneck et al., 2011). Not least, soil organic carbon influences soil moisture and
nutrient holding capacities, microbiological activity, and soil structure and other physical
properties (Okalebo, Gathua, & Woomer, 2002; Lal, 2006; Horneck et al., 2011). Soil pH, an
important chemical property that influences soil nutrient availability to plants (McCauley, Jones,
& Olson-Rutz, 2017; IIASA/FAO, 2012) and is a measure of soil acidity, is also influenced by
land management practices. Although it is a naturally occurring process, Kunhikrishnan et al

56

(2016) point out that soil acidification on farms is mainly due to inappropriate use of chemical
fertilizers, in addition to improper management of organic materials on the farm. Continued
application of acidifying fertilizers such as DAP to soils with low pH and low organic matter can
further degrade the soil. When soils are degraded, raising productivity can be possible only through
management practices that add organic matter and nutrients and ameliorate soil acidity to restore
fertility (Lal, 2006; Chivenge et al., 2011; Kunhikrishnan et al., 2016).
In Kenya, studies have shown a remarkable increase in farmer adoption of fertilizer and improved
maize seed over time (e.g. Ariga & Jayne, 2009; Smale & Olwande, 2014), yet no growth in maize
yield has been visible over the last quarter century. Soil degradation because of continuous
cultivation without sufficient replenishment of soil nutrients, organic matter or both is one of the
main reasons for low agricultural productivity in general and poor maize yield in particular
(Government of Kenya, 2014; Tittonell et al., 2008; Marenya & Barrett, 2007). This implies that
continued use of fertilizers and improved maize varieties on their own cannot achieve the needed
growth in yield. It requires change of the current disproportionate emphasis by the government,
development agencies and non-governmental organizations on promoting chemical fertilizer use
to increase maize yield. There is a need to correct for the deficiency in soil fertility through
encouraging use of sustainable soil management practices.
Lal (2006) emphasizes the importance of sustainable management of soil resources to enhancing
soil fertility. Sustainable management includes agronomic practices that protect soil from erosion
and conserve moisture (e.g. zero and minimum tillage, mulching, terracing, contour farming, use
of soil bunds), and that recycle organic matter and add nutrients into the soil (e.g. use of manure,
compost and crops residues, and judicious application of chemical fertilizers). These practices,
apart from relying only on chemical fertilizers, enhance soil fertility by adding organic matter to
57

the soil, which increases soil organic carbon and, depending on some other factors, buffers soil pH
change (McCauley et al., 2017). They also improve water and nutrient use efficiency. Therefore,
encouraging widespread and sustained use of sustainable management practices that enhance soil
fertility should be a priority in Kenya if agricultural productivity growth is to be realized.
Many studies have explored factors that influence farmers’ adoption and use of agricultural
technologies and agronomic practices in Kenya. For example, Wainaina et al. (2016) used a
multivariate probit model to study factors that affect adoption of high yielding varieties of maize
seed, inorganic fertilizers and a range of soil management technologies (zero tillage, use of crop
residues, manure use and terracing and soil bunds). Using a similar analytical approach, Kamau et
al. (2014) studied adoption of soil conservation practices, inorganic fertilizers and a combination
of other soil fertility management practices (mulching, manure use, use of compost and planting
legumes). Marenya & Barrett (2009) applied a switching regression model to study factors that
affect use of inorganic fertilizer. Switching regression was used to determine how the factors affect
fertilizer use below and above a certain threshold level of soil carbon content. In another study,
Marenya & Barrett (2007) analyzed factors that affect adoption and dis-adoption of inorganic
fertilizer, manure, maize crop residue and agroforestry. Odendo et al. (2009) applied a logit model
to analyze adoption of inorganic fertilizer, manure, compost, and a combination of all three. These
studies have a common feature that they applied econometric methods to household- and/or plotlevel data to identify variables that explain adoption of agricultural technologies and agronomic
practices. They emphasize quantitative factors that affect adoption to inform policy prescriptions
for farmers’ adoption of agricultural technologies and agronomic practices. The often-considered
factors include social, demographic and economic characteristics of the farmer, institutional and
market conditions and environmental factors.
58

We can expect that farmers’ decisions regarding adoption of technologies and agronomic practices
that improve soil fertility may be influenced by, among other factors, what they think or know
about the fertility condition of their soil, their perceptions and knowledge about the technologies
and practices, and their ability to access the technologies and apply the practices. Few quantitative
studies exist about the correspondence of farmers’ perceptions about the fertility conditions of
their soils and measured soil fertility, and how those perceptions influence adoption (or use) of
soil fertility management technologies and agronomic practices. Two studies that have conducted
such analysis are Marenya et al (2008) and Berazneva et al. (2016). In an econometric framework
using data on a sample of plots in a region in Western Kenya, Marenya et al (2008) analysed the
relationship between farmers’ perceptions about soil fertility and laboratory measure of soil
carbon, which they used as a measure of soil fertility. The study also analyzed the relationship
between farmers’ subjective perceptions about impacts of fertilizer and statistically derived
marginal product of nitrogen use on maize and beans. The study concluded that observed crop
yields influenced farmers’ perceptions about soil fertility and impacts of fertilizer. The study by
Berazneva et al. (2016) used data from two locations in western Kenya and a nationally
representative sample in Tanzania to identify correlates of farmers’ reported perceptions about soil
quality and compare the perceptions with measured soil fertility. Similar to Marenya et al (2008),
Berazneva et al. (2016) found that farmers’ perceptions about soil quality was driven by crop
yields. Despite the dearth of studies in this area, it remains germane to understand farmers’
perceptions about soil fertility conditions and their influence on use of soil management practices
to support policy and extension efforts to address the acute problem of soil infertility and attendant
low agricultural productivity in Kenya.

59

This study has two objectives. The first is to assess maize farmers’ perceptions about the fertility
of their soils and compare these with measured soil fertility based on results from scientific test of
soil chemical properties. The second is to investigate farmers’ adoption (use) of soil fertility
management practices, with a focus on the influence of their perception of soil fertility. The
research questions guiding the study are as follows:
(a) What are farmers’ perceptions about the fertility of their soils? How do farmers’ perceived
and measured soil fertility compare? What informs farmers’ subjective judgement of soil
fertility?
(b) What is the relationship between farmers’ perceptions about soil fertility and their adoption
of soil fertility management practices?
This study differs in several ways from Marenya et al (2008), Berazneva et al. (2016) and the
studies highlighted above that analyzed factors that affect farmers’ adoption and use of agricultural
technologies and agronomic practices in Kenya. First, in the adoption analysis, we account for
cognitive aspects underlying farmers’ decision to apply various soil fertility management practices
by including their perception about the fertility condition of their soils among the explanatory
variables. Secondly, different from Marenya et al (2008), we use a soil fertility measure that
combines soil organic carbon, nitrogen and pH, based on recommended thresholds for optimal
maize growth in Kenya. While Berazneva et al. (2016) also used the three soil chemical properties
to construct measured soil fertility index, the threshold values they used to construct the index
were not based on recommended thresholds for optimal maize growth in Kenya despite the study’s
focus on maize plots. Thirdly, different from Marenya et al (2008), we analyze not only the
relationship between farmers’ perceptions and measured soil fertility, but also the relationship
60

between farmers’ perceptions and individual measured chemical and physical attributes of the soil.
This is important for identifying soil properties that might be underlying farmers’ perceived soil
fertility status. Lastly, our sample covers the primary maize growing areas of Kenya, making the
study most relevant to search for potential solutions to the problem of low and stagnated maize
productivity because of soil infertility.
2.2
2.2.1

Methods and Data
Conceptual Framework

Econometric methods have dominated studies about farmers’ use of soil fertility management
technologies and practices to generate explanations regarding factors that hinder or promote their
use. The adoption studies highlighted in the previous section for Kenya and many others have
often used farmer attributes such as gender and education, plot and farm level characteristics, and
institutional (market and policy) and environmental contexts as covariates in regression analyses
to arrive at the explanations. While the analyses are certainly useful in understanding farmer
adoption behavior, a limitation in many of them is lack of information about cognitive aspects that
underlie farmers’ decision-making regarding use of technologies and practices. Yet, it is hardly
disputable that farmers respond to a phenomenon, in this case soil fertility condition, based on,
among other factors, what they know or believe about it.
Although not common in studies about what influences farmers’ agricultural decisions, there is
increasing recognition and evidence that farmers’ values, perceptions and beliefs influence
decisions concerning soil conservation and fertility management (e.g. Pender & Kerr, 1998;
Enyong et al., 1999; Eckert & Bell, 2005; Asafu-Adjaye, 2008; Vignola et al., 2010; and Turner
et al., 2014). The research in this paper considers farmers’ perception about soil fertility and its
61

influence on decisions to apply selected fertility management practices. It uses two separate
analyses, but in a way that generates a unified understanding of the importance of farmers’
perception to soil fertility management in maize production in Kenya.
We suggest that a range of factors may influence farmers’ perceptions about the fertility of their
soils (Figure 2.1). Such factors may include socio-cultural influence (e.g. accumulated experience
in farming), environmental conditions (e.g. soil properties) and economic outcomes (e.g. crop
yield) (Halbrendt et al., 2014; Marenya et al., 2008; Desbiez et al., 2004; Corbeels et al., 2000).
These perceptions inform decisions regarding soil management practices to apply to influence
fertility for a desired production outcome (yield). The resulting outcome may then feedback to
inform future perceptions through economic outcomes and socio-cultural influence.
Figure 2.1: Conceptual framework for understanding farmers’ perceptions about soil fertility and
its influence on fertility management practices (Adapted from Halbrendt et al. (2014))

Socio-cultural
influence

Environmental
conditions

Perceptions
about soil
fertility

Soil fertility
management
practices

Influence
on soil
fertility
status

Production
outcome
(yield)

Economic
outcome

The first analysis entails estimating the extent of agreement between farmers’ perception about
(subjective judgement of) the fertility of their soils and fertility as measured from scientific test
results of soil chemical properties. The main idea is that farmers’ subjective conclusion about the
62

fertility condition of their soils might significantly differ from measured soil fertility. When this
happens, it would have undesirable implications about farmer knowledge of the fertility needs of
their soils and the appropriateness of soil management practices that they prioritize.
The second analysis examines the relationship between farmers’ perceived soil fertility and their
adoption (use) of soil fertility management practices. It applies an econometric modelling
framework for agricultural technology adoption.
Choice of soil fertility management practices is largely an economic decision. We motivate the
analysis using the agricultural household model originally developed by Singh et al. (1986) and
later extended by de Janvry et al. (1991) to explain farm household’s decision-making in settings
with semi-subsistence production and market failures. We assume non-separability of household
production and consumption decisions because agricultural households in Kenya are generally
semi-subsistent and often face numerous market imperfections. Input markets, for example for
inorganic fertilizers, are imperfect while markets for organic materials such as manure, compost
and crops residues are generally missing. Because of this, prices that guide farmers’ choices of
management practices are endogenously determined and depend on both household-specific
characteristics and characteristics of markets. Therefore, farmers’ objective is assumed to be utility
maximization rather than profit maximization.
We conceptualize adoption of fertility management practices in the context of random utility
framework as explained in Ben-Akiva and Lerman (1985) and applied in Marenya & Barrett
(2007), Ali & Abdulai (2010) and Kassie et al. (2011). Using the explanation in Ben-Akiva and
Lerman (1985) as the basis, we argue that when a farmer is faced with a feasible set of discrete
alternative management practices to choose from, the farmer will select that which generates the
63

greatest perceived utility. Assuming a linear utility function for practice 𝑔 for household 𝑖, utility
is represented as a function of observed and measured characteristics specific to a household and
plot, institutional factors, and environmental conditions ( 𝑽 ), and a stochastic term (𝜀 ). The
stochastic term captures the difference between the estimated and actual utility and accounts for
unobserved and unmeasured factors not in 𝑽

that affect utility. The probability of household 𝑖

adopting practice 𝑔 among a set of 𝐺 alternative practices available to it is equal to the probability
that the utility of practice 𝑔, 𝑈 , is at least as great as the utility of all other alternative practices
in 𝐺 . That is,
𝑃(

)

= 𝑃 𝑈 ≥ 𝑈 , ∀𝑗 ∈ 𝐺

=𝑃 𝑽 +𝜀

(2.1).

≥ 𝑽 + 𝜀 , ∀𝑗 ∈ 𝐺

The farmer faces a discrete choice of a soil fertility management practice that yields the greatest
utility, but we cannot observe the utility. What we do observe is whether a farmer has implemented
a practice. We thus proceed by specifying a latent variable function for practice 𝑔 for household 𝑖
as:
𝑇 ∗ = 𝑽𝒊𝒈 𝜷 + 𝜀

,

𝑇 = 1[𝑇 ∗ > 0]

(2.2),

where the latent variable 𝑇 ∗ represents net benefit to household 𝑖 from adopting practice 𝑔, 𝑇 is
an indicator variable that equals 1 if household 𝑖 adopts practice 𝑔 and 0 if not, and 𝑽 is a vector
of household, farmer and plot characteristics, institutional factors and environmental conditions
that explain heterogeneity in adoption of the practice. The vector 𝜷 represents parameters to be
estimated and 𝜀

is idiosyncratic error term. Among the farmer characteristics is our variable of

interest: farmer’s perception about the fertility of soil of the plot in question.

64

Literature on adoption of the ‘Green Revolution’ technologies, for example inorganic fertilizers,
high yielding seed varieties and pesticides, have comprehensively documented factors that affect
adoption, including risk and uncertainty, capital constraints, credit constraints, farm size,
constraints in supply of complementary inputs and land tenure arrangement (Feder et al., 1985;
Kelly et al., 2003; Foster & Rosenzweig, 2010; Udry, 2010; Jack, 2011) . A distinctive feature of
this literature is that it does not explicitly include farmers’ perceptions among the variables deemed
to explain technology adoption decisions.
Another strand of literature has focused on adoption of soil management practices. The practices
include those that conserve water and soil and those that improve soil fertility, which may include
use of green revolution technologies, specifically mineral fertilizers. For example, Knowler &
Bradshaw (2007) review studies on adoption of conservation agriculture, which is a package of
soil and water conservation practices. They group the explanatory variables used in the studies into
characteristics of the farmer, household and farm, and exogenous factors (e.g. market prices,
extension services, and social capital). Farmer characteristics include perceived risk and attitudes
towards conservation. Studies by Kamau et al. (2014), Marenya & Barrett (2009) and Odendo et
al. (2009) examine factors that affect adoption of a range of soil management technologies, such
as zero tillage, use of crop residues, mulching, manure use, use of compost, use of inorganic
fertilizers, planting legumes, terracing, soil bunds and agroforestry. These studies use in the
adoption equations a range of explanatory variables, including plot biophysical characteristics,
farm household socio-economic characteristics, institutional factors such as proximity to markets,
and environmental conditions. However, the studies as well as those reviewed by Knowler &
Bradshaw (2007) do not take into account the role of farmers’ perceptions about the condition of

65

their soils, yet these would be expected to influence their decisions about adoption of soil
management practices.
As explained at the beginning of this section, there is increasing recognition that farmers’
perceptions matter in their decisions concerning soil fertility management and conservation (e.g.
Pender & Kerr, 1998; Enyong et al., 999; Eckert & Bell, 2005; Asafu-Adjaye, 2008; Vignola et
al., 2010; Turner et al., 2014). Failure to incorporate farmers’ perceptions in adoption decisions
might provide an incomplete account of important factors affecting those decisions. This is
especially important for Kenya, where there is urgent need for soil fertility improvement to raise
the generally low and stagnated or declining agricultural productivity.
2.2.2

Analytical Strategy

2.2.2.1 Farmers’ perceived and measured soil fertility
We use three approaches to compare farmers’ perceived and measured soil fertility. First, we apply
chi-square test for independence to determine whether there is a relationship between farmers’
perceived and measured soil fertility. Secondly, we use interrater agreement technique, as
explained in Fleiss et al. (2003) and applied by Kerr & Pender (2005) to farmers’ perceptions about
soil erosion in villages in India, to estimate the degree of agreement between farmers’ perception
about and measured soil fertility. The interrater agreement is measured using Cohen’s kappa
coefficient (Cohen, 1960). Kappa measures the degree of agreement beyond that which could be
expected by chance (Fleiss et al. 2003). It measures the degree of agreement between raters in
instances where the scales of ratings are categorical. To illustrate, consider dummy Table 1.1
below of data on agreement in ratings of soil fertility by farmers’ perception and by measurement.
Each of the cells, i.e. a, b, c and d, contains the proportion of all maize plots categorized as either
66

fertile or infertile by farmers and fertile or infertile by measurement. For example, cell a contains
the proportion of plots that are considered fertile according to both farmers’ perception and
measurement, while cell b contains the proportion of plots which the farmers assess as fertile but
are measured to be infertile. The kappa statistic is expressed as in (2.3) and ranges from -1 to +1:

𝜅̂ =

(

)

(2.3)

Table 2.1: Dummy table of data measuring agreement between farmers’ perception and
measured soil fertility
Rater
A
(Farmers’
perception)
Category 1 (Fertile)
Category 2 (Infertile)
Total

Rater B (Measured fertility)
Category 1 (Fertile)
Category 2 (Infertile)
a
b
c
d
p2
q2

Total
p1
q1
1

Landis & Koch (1977) and Fleiss et al. (2003) have suggested the following interpretations of
kappa ranges for degree of agreement:
Kappa (𝜅̂ ) value range:

Degree of agreement beyond chance:

Landis & Koch (1977):
𝜅̂ < 0.00

poor

0.00 < 𝜅̂ ≤ 0.20

slight

0.20 < 𝜅̂ ≤ 0.40

fair

0.40 < 𝜅̂ ≤ 0.60

moderate

0.60 < 𝜅̂ ≤ 0.80

substantial

𝜅̂ > 0.80

almost perfect

Fleiss et al. (2003):
𝜅̂ < 0.40

poor

0.40 < 𝜅̂ ≤ 0.75

fair to good

𝜅̂ > 0.75

excellent

67

Although useful in gauging the extent of agreement between two raters, the suggested ranges of
kappa and the agreement levels they represent are certainly arbitrary. We use both scales of
agreement in interpreting our results.
Lastly, we apply a probit model to estimate the association between farmers’ perception about and
measured soil fertility as well as measured individual physical and chemical properties of soil. The
aim is to explore whether there is a significant relationship between farmers’ perceived and
measured soil fertility and whether such a relationship holds when we account for the effects of
other relevant factors. The model takes the following form:
(2.4)

𝑌 = 𝑓(𝑀, 𝐹),

where 𝑀 represents measured soil fertility and 𝐹 represents other factors deemed to influence
farmers’ perceptions. 𝑌 is farmer’s perception about soil fertility and is a binary variable for the
probability of a farmer’s perception of the soil on a plot as fertile. We define for farmer 𝑖 a latent
measure of perceived soil fertility on a plot as 𝑌 ∗ , such that
𝑌 ∗ = 𝒁𝒊 𝜷 + 𝜀 ,

(2.5)

where 𝑖 = 1, … . , 𝑁, 𝒁 is a row vector of explanatory variables (𝑀, 𝐹) hypothesized to influence
farmer’s perception, 𝜷 is a column vector of parameters to be estimated, and  is a random error
term, here assumed to be distributed normal with a constant variance (i.e. 𝜀~𝑁(0, 𝜎 ) ).
In this latent variable setting, we observe only 𝑌 (i.e. whether a farmer indicates that a plot is
fertile or infertile):

𝑌 =

1 𝑖𝑓 𝑌 ∗ > 0 (𝑓𝑒𝑟𝑡𝑖𝑙𝑒)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (𝑖𝑛𝑓𝑒𝑟𝑡𝑖𝑙𝑒)
68

𝑌 ∗ > 0 ⇒ 𝒁𝒊 𝜷 + 𝜀 > 0 ⇒ 𝜀 > −𝒁𝒊 𝜷

(2.6)

So, in the probit model (Wooldridge, 2010) 𝑃(𝑌 = 1|𝒁𝒊 ) = 𝑃(𝑌 ∗ > 0|𝒁𝒊 ) = 𝑃(𝜀 > −𝒁𝒊 𝜷) =
𝑃

>

𝒁𝒊 𝜷

=ÎŚ

𝒁𝒊 𝜷

= 𝐺(𝒁𝒊 𝜷), where we set 𝜎=1 and effectively make the distribution of

the error term, 𝜀, standard normal density. 𝐺(. ) is a cumulative normal distribution function for
some continuous variable with a density 𝑔(. ). 𝑃(𝑌 = 0|𝒁𝒊 ) = 1 − Φ

𝒁𝒊 𝜷

= 1 − 𝐺(𝒁𝒊 𝜷) is

similarly derived. We obtain the estimates of 𝜷 using maximum likelihood estimation procedure.
The average partial effect of a continuous explanatory variable j, on the response probability (in
this case the probability of a farmer indicating that the soil on a plot is fertile) is derived as:
𝐴𝑃𝐸 = 𝛽 𝑁

(2.7)

∑ 𝑔(𝒁𝒊 𝜷)

For a binary explanatory variable k, the average partial effect on the response probability is
derived as follows:
𝐴𝑃𝐸 = 𝑁

∑ 𝐺 𝒁𝒊( ) 𝜷(

)

+𝛽

− 𝐺 𝒁𝒊(𝒌) 𝜷(

)

,

(2.8)

where 𝒁𝒊( ) is 𝒁𝒊 excluding the explanatory variable k.
We augment these analyses with mean comparison test of a range of soil physical and chemical
properties, plot attributes, input use, agronomic management practices, plot manager attributes,
and maize yield between farmers grouped according to their perceptions about soil fertility.
2.2.2.2 Adoption of soil fertility management practices
A number of studies on adoption of soil fertility management practices have found simultaneity of
adoption decisions of different practices by farmers (e.g. Marenya & Barrett, 2007; Kamau et al.,
69

2014; Kassie et al., 2015; Wainaina et al., 2016; Koppmair et al., 2017). Failure to account for
such simultaneity in econometric analysis of adoption decisions may compromise efficiency of the
estimates and make inferences inaccurate. Therefore, this analysis applies a multivariate probit
model because there are multiple soil fertility management practices for which adoption variable
is binary and farmers’ adoption decisions may be jointly made.
Multivariate probit model is like a seemingly unrelated regression for binary response variables.
We express the system of equations to be estimated as a series of equation (2.2) that match the
number of soil fertility management practices:
𝑇 ∗ = 𝑽 𝜷𝟏 + 𝜀
𝑇 ∗ = 𝑽 𝜷𝟐 + 𝜀
⋮
𝑇 ∗ = 𝑽 𝜷𝑮 + 𝜀

,

(2.9)

with 𝑇 = 1[𝑇 ∗ > 0] and 𝜺 |𝑽 ~𝑁𝑜𝑟𝑚𝑎𝑙 (𝟎, 𝛀) with unit variances. This means that the
marginal distributions conditional on 𝑽 are assumed to follow probit:
𝑃(𝑇 = 1|𝑽) = 𝚽 𝑿 𝜷 ,
2.2.3

𝑔 = 1, … , 𝐺

Data sources and variables

2.2.3.1 Data sources
The study uses household- and plot-level survey data on maize production in Kenya. The data
were collected by the Department of Agricultural, Food and Resource Economics at Michigan
State University under the Guiding Investments in Sustainable Agricultural Intensification in
70

Africa (GISAIA) research project implemented in seven countries in Africa. The project aimed to
influence policy environment to improve sustainable intensification of cereal crop production and
contribute to sustainable growth of agricultural productivity in Africa. In Kenya, the project
activities focused on efficiency and profitability of use of inorganic fertilizer and hybrid seed, and
agricultural land constraints and changing farm structure.
The first survey was conducted in 2014 from a sample of 650 farm households spread in five
counties. Sample selection followed a multistage procedure. Five counties were purposively
selected in the first stage based on two criteria: counties that are most important in maize
production to study maize yield response to inorganic fertilizer use; and highly densely populated
counties to study population density-intensification relationship. Uasin Gishu, Kakamega and
Trans Nzoia counties were selected for maize yield response study while Machakos and Kisii
counties were selected for population density-intensification relationship study. In the second
stage, two sub-counties were selected in Uasin Gishu, Kakamega and Trans Nzoia counties, with
one in each representing a locality perceived to be of low and the other of high maize yield response
to fertilizer. In Machakos and Kisii, two and three sub-counties, respectively, with highest
population densities within the county were selected. In the third and subsequent stages, Locations,
Sub-locations, villages and farm households in that order were randomly selected. The sample
distribution across the administrative units is shown in Table 2.2.
The second survey was conducted in 2016 on the same households as in the first survey, but the
number reduced to 623 because some of the households could not be reached for re-interview for
various reasons, including migration. This survey, however, did not necessarily target the same
maize plots that were cultivated in the 2014 survey. This means that the household-level data is
panel while plot-level data is not necessarily panel. While there was a question in the 2016 survey
71

questionnaire asking whether the largest maize plot (which is used in this study) was the same as
in the 2014 survey, the responses in the affirmative were not consistent with plot sizes compared
between 2016 and 2014. For that reason and because plot-level data is central in this study, the
data from the two surveys are treated as pooled cross sections rather than panel.
Plot-level data includes crop output, types and amounts of inputs used, soil management practices,
farmer’s perception about soil fertility, and soil physical and chemical properties and were
obtained for the largest maize plot cultivated by each household in the main season of 2013/2014
and 2015/2016 cropping years2. Willy, Muyanga, & Jayne (2016) document details about soil
sampling and testing procedures. On average, the share of the largest maize plot in a household’s
total area of plots that had maize in them in the main season was 83%, indicating that this analysis
captures the vast majority of maize produced by the farm households in the sample.
Table 2.2: Distribution of sample households across administrative units, 2014
County
Uasin Gishu
Trans Nzoia
Kakamega
Kisii
Machakos

Sub-county
Wareng
Eldoret West
Kwanza
Saboti
Kakamega North
Lugari
Bobasi
Marani
Kangundo
Kathiani
Machakos

Number of Sublocations
2
2
1
2
2
1
2
2
1
1
1
17

2

Number of
Villages
8
5
4
4
4
4
5
5
5
3
2
49

Number of
households
60
60
60
60
60
60
60
60
85
51
34
650

Agricultural production data collected in 2014 and 2016 pertain to 2013/2014 and 2015/2016 cropping year,
respectively.

72

2.2.3.2 Variables
Farmers’ perceived and measured soil fertility
Farmers’ beliefs and/or knowledge about the fertility condition of soil on their farms can partly
influence how they manage their agricultural production on the farm. However, such beliefs may
not necessarily reflect the actual soil fertility condition and thus may result in management
practices that mismatch the fertility needs of the soil. Farmers were asked to rate the fertility of
soil on their maize plots on a Likert scale of 1 (very infertile) to 4 (very fertile) based on their own
perceptions. Because of very low responses on the two extreme categories (1 and 4) we reduce the
scale to two categories - infertile (combining 1 and 2) and fertile (combining 3 and 4) to generate
a binary variable of farmer perceived soil fertility.
From the soil test data, we measure the fertility of soil on a plot using three chemical properties of
soil – total carbon (C), total nitrogen (N) and pH. IIASA/FAO (2012) suggest soil nutrient
availability and retention capacity as among seven soil qualities that affect crop performance.
Others are oxygen availability to roots, rooting conditions, toxicities, salinity and sodicity and
workability. The authors suggest that natural nutrient availability in the soil is essential for low to
medium input cropping, while nutrient retention capacity is especially important for effectiveness
of inorganic fertilizer use. Therefore, these two soil qualities are most relevant in the context of
maize production in Kenya where external input use is not that high and inorganic fertilizer use
appears not to generate significant yield gains. As explained earlier, soil organic carbon influences
a range of soil properties, including soil moisture and nutrient holding capacities, microbiological
activity, and soil structure and other physical properties and is often used as an indicator for soil
health (Okalebo, Gathua, & Woomer, 2002; Lal, 2006; Horneck et al., 2011). Soil pH influences
73

nutrient availability and serves as an indicator for micro-nutrient deficiencies (IIASA/FAO, 2012).
Together, IIASA/FAO (2012) suggest, soil organic carbon and pH are the best simple gauge for
soil health. Nitrogen is the nutrient required by plants in largest amounts and is often the limiting
nutrient in the soil.
We use threshold values for the properties as obtained from recommendations by the Kenya
government on critical levels of various soil nutrients and pH for maize growth (Government of
Kenya, 2014). A plot is measured as fertile if the soil has C≥ 2.7%, N≥ 0.2% and 5.5 ≤ pH ≤
7.0 and infertile if it does not meet at least one of these three thresholds. We compare the farmer’s
subjective rating (fertile or infertile) against the measured fertility rating (fertile or infertile) as per
these threshold values.
Correlates of farmer perception about soil fertility
For the probit model of the relationship between farmers’ perception about soil fertility and
individual soil physical and chemical properties, we use as explanatory variables a range of
measured soil properties. In addition, we control for other relevant plot and plot manager
characteristics. Texture is the only information about soil physical properties available in the data.
We classify soil texture based on relative percentages of sand, silt and clay and according to the
classification in (IIASA/FAO, 2012). Thus, we have four texture classes; sandy, loamy coarse,
loamy moderate, loamy fine and clayey soils. Among the soil chemical properties proposed by
Doran & Parkin (1994) as indicators that can be used to assess soil fertility include total organic
carbon, total nitrogen, soil pH, electrical conductivity and extractable (or plant-available)
macronutrients (P, K). Because total carbon and total nitrogen are highly correlated, we excluded
total nitrogen in the estimation. Soil pH measures acidity or alkalinity and its level affects
74

biological and chemical activity in the soil and affects availability of nutrients to plants. Lower pH
levels indicate greater acidity while higher values indicate alkalinity. Most crops require near
neutral levels of pH to grow best. Soil electrical conductivity is a measure of the amount of soluble
(salt) ions in the soil and is strongly correlated with many soil properties, particularly texture
(Grisso et al, 2009). We thus do not include it in the model. We include plant-available phosphorus
among the macronutrients because it is particularly important for crop growth and is sensitive to
soil acidity level.
The plot characteristics we include are farmer-reported slope, measured in categories – flat,
moderate and steep, and the number of years during the last decade the plot was in cultivation. We
include distance (in walking minutes) of plot from the homestead and plot manager’s education,
farming experience and gender to capture the effects of plot manager’s characteristics. To test
whether perception is correlated with information access, we include variables that measure area
physical infrastructure – distance to extension service provider, distance to town and distance to
paved road.
Determinants of adoption of soil fertility management practices
We consider five soil fertility management practices in the adoption analysis: inorganic fertilizer,
manure/compost, crops residue, legume intercrop and soil erosion control. Adoption of each of the
practices is measured as a binary variable, taking the value of 1 if a practice was implemented on
a plot and 0 if not. It is important to recognize that the variable for soil erosion control is not really
a measure of whether the farmer invested in soil erosion control during the cropping season but
whether there were soil erosion structures on the plot irrespective of when they were established.
This is because measures for soil erosion control such as terraces, grass strips and cut-off drains
75

tend to be relatively permanent, with regular or occasional maintenance. However, the data does
not have information about whether the farmer carried out any maintenance on the soil erosion
structures on the plot.
Adoption rates of the practices are presented in Table 2.3. Inorganic fertilizer is the most important
external inputs into maize production and which is accorded much attention by both the
government and farmers in efforts to raise maize productivity. It is important to note that adoption
rate of inorganic fertilizer is that high because a large part of the sample is concentrated in the
major maize growing regions – Uasin Gishu, Trans Nzoia and Kakamega. Because of their role as
the country’s grain basket areas, these regions have had a history of concerted promotion by both
the government and development agencies of adoption of fertilizers and improved maize varieties.
Manure and compost, in addition to supplying nutrients into the soil, increase soil organic matter,
and therefore organic carbon, which is beneficial for soil fertility as explained in the introduction.
Crops residue also add organic matter in the soil, and if used as mulch conserve moisture in the
soil and protect the topsoil from erosion that may result from direct impact of rain. Intercropping
maize with legumes, such as common beans, groundnuts and pigeon peas, enrich the soil with
nitrogen because they can fix atmospheric nitrogen into the soil. Soil erosion control, through
structures such as terraces, grass strips and cut-off drains, is beneficial in preventing soil loss and
loss of soil nutrients with it. It is our hypothesis that farmers may make joint decision regarding
adoption of some of these practices hence the need for simultaneous estimation of adoption
equations to ensure efficiency of estimated parameters.

76

Table 2.3: Adoption rates of various soil fertility management practices (N=1268)
Management practice
Inorganic fertilizer (1=yes, 0 otherwise)
Manure/compost (1=yes, 0 otherwise)
Crops residue (1=yes, 0 otherwise)
Legume intercrop (1=yes, 0 otherwise)
Soil erosion control (1=yes, 0 otherwise)

Mean
0.93
0.46
0.41
0.71
0.51

SD
0.26
0.50
0.49
0.45
0.50

Literature on adoption of soil fertility management practices have found a range of factors that
influences adoption (e.g. Marenya & Barrett, 2007; Odendo et al., 2009; Kamau et al., 2014; Kassie
et al., 2015; Wainaina et al., 2016; Arslan et al., 2017; Koppmair et al., 2017). We present the
descriptive statistics of the factors included in this analysis in Table 2.4. The factor of interest in
this study is farmer’s soil fertility perception, which most adoption studies do not include among
explanatory variables that explain technology adoption decisions. We include plot characteristics
among the factors since the condition of a plot, such as slope, may make particular practices better
suited to and necessary on it. The characteristics we include are slope and number of years within
the last decade the plot has been on cultivation. Plot manager characteristics include walking time
to the plot, whether the plot is owned, which is a measure of tenure security, and plot manager’s
education, gender and farming experience.
Three measures of household capital are included. Number of adults in a household represents
human capital in terms of labor, while group membership represents social capital. Group
membership may also act as a mechanism for access to information and credit, both of which have
been found to be important to technology adoption. Whether a household has non-farm income
may be an indicator of working capital, which is important for acquisition of external inputs such
as inorganic fertilizers and hired labor. The ability to hire labor may be important to adoption of
labor-intensive soil management practices such as manure/compost and crops residue use.

77

Table 2.4: Summary statistics of explanatory variables in the adoption estimation (N=1268)
Explanatory variables
Soil fertility perception (1=fertile, 0 otherwise)
Years of plot cultivation
Plot slope (1=moderate, 0 otherwise)a
Plot slope (1=steep, 0 otherwise)a
Plot size (acres)
Walking time to plot (mins)
Plot owned (1=yes, 0 otherwise)
Plot manager education (yrs)
Plot manager is female (1=yes, 0 otherwise)
Farming experience (yrs)
Active adults (#)
Group membership (1=yes, 0 otherwise)
HH has non-farm income (1=yes, 0 otherwise)
Livestock value (KES) (log)
HH landholding (acres)
Asset index
Distance to extension (km)
Distance to paved road (km)
Fertilizer price (KES/kg)
a

Mean
0.59
9.56
0.54
0.10
1.11
4.73
0.90
8.02
0.35
27.52
2.99
0.72
0.72
9.72
2.47
0.02
5.69
6.92
64.31

SD
0.49
1.55
0.50
0.30
2.19
10.85
0.30
3.86
0.48
16.22
1.75
0.45
0.45
3.13
25.81
0.07
5.07
6.87
18.09

Base category: flat

We measure household wealth using value of livestock, landholding and asset index. On one hand,
livestock are important because they produce manure and, therefore, may motivate manure use.
On the other hand, ruminants are often fed crops residue and thus presence of livestock may have
a negative effect on the adoption of the practice. Size of landholding may determine a household’s
motivation for agricultural intensification, with those having smaller landholdings having higher
propensity to apply intensification practices in a bid to maximize yield. Asset index, and indicator
of the capacity for access to resources, such as credit, is computed from a list of household assets
(agricultural and household) using principal component analysis. The index is based on the score
for the first principal component, which accounts for the largest variation in the data.

78

Information and market access conditions are proxied by distance to extension information and
distance to paved road. These variables are generally expected to have negative effects on adoption
of soil fertility management practices. Fertilizer price is included and is expected to be negatively
correlated with adoption of fertilizer and practices for which adoption is complementary to that of
fertilizer.
2.3
2.3.1

Results
Farmers’ perceived versus measured soil fertility

As explained in the previous section, farmers were asked to rate the fertility of soil on their largest
maize plots on a Likert scale of 1 (very infertile) to 4 (very fertile) based on their own perceptions.
Because of very low responses on the two extreme categories (6% for very infertile and 5% for
very fertile), we reduced the scale to two categories - infertile (combining 1 and 2) and fertile
(combining 3 and 4) thus resulting into a binary variable indicating farmers’ perception about the
fertility status of their plots as either fertile or infertile. Results show that overall, 59% of the plots
were perceived to be fertile while 41% were perceived to be infertile. Across regions (counties),
higher percentages of plots in Kakamega and Kisii were perceived to be infertile compared to those
in the other counties (Figure 2.2).
Using data from the laboratory test of physical and chemical properties of soil from the same plots
of which farmers subjectively rated fertility, we constructed a measure of fertility for each plot. As
explained in the preceding section, a plot was measured to be fertile if the soil had total C≥ 2.7%,
N≥ 0.2% and 5.5 ≤ pH ≤ 7.0 and infertile if at least one of these conditions was not met. Based
on this index, results show that 14% of the plots were measured to be fertile while 86% were
infertile. Figure 2.3 shows that incidence of soil infertility according to this measure was highest
79

in Kakamega, Machakos and Kisii in that order and lowest in Trans Nzoia and Uasin Gishu. It is
worth noting that population densities are higher in Machakos, Kisii and Kakamega than in Uasin
Gishu and Trans Nzoia, indicating that soil infertility problem could be worse in areas where land
scarcity is more acute.
Overall, farmer-perceived and measured fertility status of 46% of plots were consistent, about half
of the plots were rated as fertile by farmers but measured to be infertile, and less than 5% of the
plots were perceived as infertile but measured to be fertile.
Figure 2.2: Percentages of farmer-perceived fertile and infertile plots across regions
Uasin Gishu

36.75

Trans Nzoia

63.25

38.30

61.70

Kakamega

46.12

53.88

Kisii

46.58

53.42

Machakos

39.04

0

60.96

20

40

60

80

100

Percent of plots
Infertile

Fertile

Figure 2.3: Percentages of measured fertile and infertile plots across regions
Uasin Gishu

78.63

Trans Nzoia

21.37

60.00

40.00

Kakamega

98.28

Kisii

1.72

93.16

Machakos

6.84

96.70

0

20

40

3.30

60

80

Percent of plots
Infertile

Fertile

80

100

Using the chi-square test of independence between farmers’ perceived and measured soil fertility,
results show that overall, the two soil fertility ratings are not statistically independent at the 95%
confidence level (Table 2.5). However, the analysis separated by region rejects (at the 95%
confidence level) the null hypothesis of independence only in Machakos county. This suggests that
perceived and measured soil fertility are largely misaligned for majority of the plots, reflecting the
earlier description that 54% of the plots had farmers’ perceived inconsistent with measured soil
fertility.
The test results for the extent of agreement between farmers’ perceived and measured soil fertility
using the interrater agreement technique is presented in Table 2.6. Using the Landis & Koch (1977)
and Fleiss et al. (2003) scales of degree of agreement, the overall kappa value of 0.037, although
statistically significant, indicates only slight (Landis & Koch, 1977) or poor (Fleiss et al., 2003)
agreement beyond that which could be expected by chance between farmer perceived and
measured soil fertility. This conclusion also generally obtains in each of the five regions.

81

Table 2.5: Chi-square test of independence between farmer perceived and measured soil fertility
Overall sample
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 4.656 Pr = 0.031 ; Fisher’s exact = 0.032

Measured fertility
Infertile
Fertile
Total
463
59
522
630
116
746
1093
175
1268

Uasin Gishu
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 0.289 Pr = 0.591; Fisher’s exact = 0.622
Trans Nzoia
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 2.701 Pr = 0.100; Fisher’s exact = 0.132
Kakamega
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 0.0246 Pr = 0.875; Fisher’s exact = 1.000
Kisii
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 0.569 Pr = 0.451; Fisher’s exact = 0.605
Machakos
Farmer perceived fertility
Infertile
Fertile
Total
Pearson chi2(1) = 4.287 Pr = 0.038; Fisher’s exact = 0.056

82

Measured fertility
Infertile
Fertile
Total
66
20
86
118
30
148
184
50
234

Measured fertility
Infertile
Fertile
Total
60
30
90
81
64
145
141
94
235

Measured fertility
Infertile
Fertile
Total
105
2
107
123
2
125
228
4
232

Measured fertility
Infertile
Fertile
Total
103
6
109
115
10
125
218
16
234

Measured fertility
Infertile
Fertile
Total
129
1
130
193
10
203
322
11
333

Table 2.6: Kappa statistic measuring degree of agreement between perceived and measured soil
fertility
County
Uasin Gishu
Trans Nzoia
Kakamega
Kisii
Machakos
Overall sample

% agreement
41.03
52.77
46.12
48.29
41.74
45.66

% expected
agreement
42.41
47.66
46.25
47.05
39.76
43.61

Kappa

Std. Error

Z

Prob>Z

-0.024
0.098
-0.003
0.024
0.033
0.037

0.045
0.059
0.016
0.031
0.016
0.017

-0.54
1.64
-0.16
0.75
2.07
2.16

0.7044
0.0501
0.5624
0.2253
0.0192
0.0155

It is useful to understand how farmers’ perceived soil fertility correlates with measured fertility,
measured individual physical and chemical soil properties and other plot and farm characteristics.
Such information is helpful in identifying factors that contribute to heterogeneity in individual
farmers’ perceptions about soil fertility. As explained earlier, we explore this by estimating a probit
model where the dependent variable is the binary indicator of farmer’s perception about soil
fertility, and explanatory variables are measured soil fertility, selected soil physical and chemical
properties, other plot, plot-manager and area characteristics and maize yield. Before discussing the
probit model estimation results, we explore difference in means of a range of variables between
plots farmers perceived to be fertile and those perceived as infertile (Table 2.7).
On average, plots farmers perceived to be fertile were significantly richer in organic carbon and
nitrogen, had higher concentration of potassium and were less acidic (had higher soil pH) (Table
2.7). Perception about soil fertility, however, appears not to be associated with soil texture in a
significant way, as can be seen in the difference in the means of sand, silt and clay content between
perceived fertile and infertile plots. These statistics suggest that on average, farmers’ soil fertility
perception have some alignment with levels of individual soil chemical properties that influence
soil nutrient availability and retention capacity, and hence fertility. We revisit this conjecture when
discussing the probit model estimation results.

83

Table 2.7: Mean comparison test of selected variables according to farmers’ perception about
soil fertility status
Farmer perception of soil
fertility status
Fertile (F)
Infertile (I)

Attributes
Plot characteristics
Total organic carbon (%)
Total Nitrogen %
Phosphorus (ppm)
Potassium (meq %)
Soil pH
Sand (%)
Silt (%)
Clay (%)
No. of years of plot cultivation in the past 10 years
Plot slope (1=flat, 2=moderate, 3=steep)

2.180
0.188
19.776
0.820
5.727
48.879
12.244
38.745
9.507
1.728

2.050
0.178
17.870
0.748
5.665
49.171
12.482
38.137
9.638
1.770

0.130**
0.00935**
1.906
0.0718*
0.0626**
-0.293
-0.238
0.609
-0.131
-0.0422

Input use on plot
Inorganic fertilizer use (1=yes, 0 otherwise)
Fertilizer rate (kg/acre) [users only]
Improved seed variety (1=yes, 0 otherwise)
Mechanized land preparation (1=yes, 0 otherwise)

0.913
81.723
0.928
0.532

0.948
80.741
0.927
0.450

-0.0354 **
0.982
0.000411
0.0820 ***

Agronomic practices on plot
Manure/compost use (1=yes, 0 otherwise)
Crops residue use (1=yes, 0 otherwise)
Maize-legume intercrop (1=yes, 0 otherwise)
Soil erosion prevention (1=yes, 0 otherwise)

0.472
0.401
0.685
0.504

0.454
0.427
0.757
0.519

0.0178
-0.0264
-0.0717 ***
-0.0151

1398.683

1183.586

215.1***

Local infrastructure
Distance to extension (km)
Distance to town (km)
Distance to paved road (km)

5.434
13.460
7.009

6.059
13.868
6.783

-0.625**
-0.408
0.226

Plot manager characteristics
Plot manager education (yrs)
Plot manager is female (1=yes, 0 otherwise)
Farming experience (yrs)
Walking time to plot (mins)
Plot owned (1=yes)
Observations

8.059
0.336
27.657
5.288
0.883
746

7.962
0.358
27.316
3.925
0.916
522

0.0973
-0.0218
0.341
1.362**
-0.0323 *
1268

Maize production
Maize yield (kg/acre)

*

Difference in
mean (F-I)

p < 0.10, ** p < 0.05, *** p < 0.01

84

Plots perceived to be fertile were on average located further from the homestead than those
perceived to be infertile. In addition, incidence of ownership (rather than renting) was lower for
plots perceived to be fertile than for those perceived to be infertile. This indicates that rented plots,
which the data show are on average located farther from the homestead than are owned plots, are
on average more likely to be rated fertile. It implies that, as would be expected, farmers who rent
plots for maize production have a higher likelihood to go for those they perceive to be fertile.
While inorganic fertilizer use was generally high (about 93% of the plots in total), results show
some association between the binary decision to use inorganic fertilizer and perception about soil
fertility: inorganic fertilizer use was more likely on plots perceived to be infertile than on those
perceived to be fertile. Whether this reflects conscious efforts by farmers to address perceived soil
infertility through use of inorganic fertilizer is a question deserving investigation. We explore the
possibility of this in the discussion of results on adoption of soil fertility management practices.
Conditional on use, however, mean application rates of inorganic fertilizer were statistically the
same between the two groups of plots. Incidence of mechanized land preparation was higher on
plots that were perceived to be fertile. Among agronomic practices, we only observe significantly
higher incidence of maize-legume intercrop on plots perceived to be infertile than on those
perceived to be fertile, while with regards to area infrastructure mean distance from extension
advice was shorter for plots that were perceived to be fertile than those that were perceived to be
infertile. As would be expected, the mean yield of maize was significantly higher on plots
perceived to be fertile than on those perceived to be infertile.
In summary, plots farmers perceived as fertile relative to those perceived to be infertile had, on
average, higher levels of individual soil chemical attributes that influence nutrient availability and
were less likely to have inorganic fertilizer applied. In addition, they were more likely to be
85

intercropped with legumes and had higher maize yield. Further, such plots were located farther
away from the homestead, suggesting that farmers viewed rented plots as more fertile.
Estimated marginal effects from a sequence of probit models of farmers’ perception about soil
fertility are presented in Tables 2.8 and 2.9. In Table 2.8 are the marginal effects of measured soil
fertility, along with other covariates, while in Table 2.9 are marginal effects of individual soil
properties, along with other covariates. The tables each has a sequence of five models to show the
behavior of the effects of measured soil fertility and individual soil properties when other
covariates are included. The other covariates are plot characteristics, maize yield, plot manager
characteristics, and area infrastructure. In all the specifications, regional effects are controlled for
using regional (county) dummy variables. A squared term for the soil pH variable was included in
the estimation of models in Table 2.9 to account for nonlinearity of soil pH, since in actual sense
extreme values of soil pH are associated with suboptimal conditions for plant growth.
In Table 2.8, model 1 shows that there is a positive but statistically weak correlation between
farmers’ perceived and measured soil fertility status, holding other things constant. Compared to
a plot measured to be infertile, a plot that is measured to be fertile has, on average, 7% higher
chance of being rated as fertile by a farmer. The small magnitude of the marginal effect of
measured soil fertility combined with its weak statistical significance strengthens the findings from
the interrater agreement through the Cohen’s kappa statistic and the chi-square test of
independence between farmers’ perceived and measured soil fertility. When we control for maize
yield, however, the weak significance of the association between farmers’ perceived and measured
soil fertility vanishes and the marginal effect of maize yield is positive and strongly significant
(model 2), a result that also obtains in models 3, 4 and 5, which have plot characteristics, plotmanager characteristics and area infrastructure, respectively. The negative and significant
86

marginal effects of steep slope dummy variable in models 3-5 is evidence that plot slope is
significantly associated with farmers’ perception about soil fertility. In addition, the negative and
significant marginal effect of distance to extension service provider indicates that access to
extension information may have influence on farmers’ perception about the fertility of their soils.
Table 2.8: Probit marginal effect estimates of the relationship between farmers’ perceived and
measured soil fertility
(1)
Measured
fertility
0.0732*

(2)
Maize yield

(0.0443)

(0.0441)

(0.0444)

(0.0443)

(0.0456)

0.0000513***
(0.0000146)

0.0000512***
(0.0000146)

0.0000510***
(0.0000147)

0.0000497***
(0.0000147)

Moderateb

-0.0252
(0.0309)

-0.0230
(0.0310)

-0.0243
(0.0310)

Steepb

-0.104*
(0.0556)

-0.111**
(0.0557)

-0.0991*
(0.0562)

No. of years of plot
cultivation

-0.0107

-0.00630

-0.00673

(0.00917)

(0.00955)

(0.00953)

0.000548

0.000563

(0.00399)

(0.00398)

-0.0168

-0.0168

(0.0301)

(0.0301)

0.000749

0.000667

(0.000948)

(0.000950)

Plot owned (1=yes)

-0.0558
(0.0487)

-0.0619
(0.0487)

Walking time to plot
(mins)

0.00256

0.00241

(0.00158)

(0.00158)

Dep var: Soil fertility
perception (1=fertile)
Measured fertility
(1=fertile)
Maize yield (kg/acre)

0.0707

Plot manager education
(yrs)
Plot manager is female
(1=yes)
Farming experience
(yrs)

87

(3)
(4)
(5)
Plot
Plot manager
Area
characteristics characteristics infrastructure
0.0711
0.0698
0.0719

Table 2.8 (cont’d)
Dep var: Soil fertility
perception (1=fertile)

(1)
Measured
fertility

(2)
Maize yield

(3)
(4)
(5)
Plot
Plot manager
Area
characteristics characteristics infrastructure
-0.00473*

Distance to extension
(km)

(0.00276)
Distance to paved road
(km)

-0.000476
(0.00298)

Regional dummies
Observations
LR 𝜒
Prob > 𝜒
Pseudo R

Yes

Yes

Yes

Yes

Yes

1268
11.19
0.0477
0.0065

1268
23.35
0.0007
0.0136

1268
28.22
0.0009
0.0164

1268
34.19
0.0019
0.0199

1268
38.72
0.0020
0.0225

Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01

Results in Table 2.9 are largely similar to those in Table 2.8. In model 1 of Table 2.9 where the
only covariates – apart from regional dummies – are individual soil properties, the marginal effects
of soil organic carbon and pH are positive and significant (albeit weakly). A unit increase in soil
pH is associated with 5% higher chance of the plot being rated as fertile by a farmer, while a onepercentage point increase in soil organic carbon content is associated with 3% higher chance of a
plot being rated as fertile by a farmer. These results strengthen the findings in Table 4 that farmers’
soil fertility perceptions have some reflection of levels of individual soil chemical properties that
influence soil nutrient availability. However, the statistical significance of the marginal effects of
soil organic carbon vanishes when we introduce other covariates in models 2-5, while that of soil
pH remains significant only in model 4. Like in Table 8, the marginal effect of maize yield remains
positive and significant in models 2-5 and that of the steep slope dummy is negative and significant
in models 3-5.
The evidence that the marginal effects of measured soil fertility (Table 2.8) and those of soil
88

organic carbon and pH (Table 2.9) become insignificant when other covariates are introduced is
evidence that farmers’ perceptions about soil fertility are based on factors other than measurable
soil attributes. The important factors that appear to influence farmers’ perception about soil fertility
are maize yield and plot slope, with maize yield showing a strong statistical correlation in all the
models in which it is included. This finding is consistent with that of Marenya et al (2008), who
suggested that famers may be prone to error in their soil fertility assessment given the many factors,
in addition to soil conditions, that influence yield. When observed yield levels is the primary
information on which farmers base their assessment of soil fertility status, they are likely to apply
soil fertility management practices that may not match the soil fertility needs and this can lead to
further soil degradation. The data in this research show that 39% of the plots in the sample had soil
pH values below the lower bound of the recommended optimal range of 5.5-7.0 while 52% had
values below the sample average of 5.7, which is barely above the lower bound of the range. In
the contrary, only 35% of the farmers acknowledged that their plots had soil acidity problems,
38% indicated there were no soil acidity problems on their plots, while the remaining 27% had no
idea regarding whether their plots had soil acidity problems. Therefore, it is not surprising that
majority of the farmers in the sample apply DAP, an acidifying fertilizer, in efforts to raise maize
yield.
Figure 2.4 shows that among the plots that had soil pH<5.5 (39% of plots), 44% had DAP applied
without manure or compost while 11% had neither DAP nor manure/compost application. About
35% had both DAP and manure/compost while 12% had manure/compost without DAP. A similar
pattern is observed on plots that had low organic carbon (<2.7%) (75% of plots), where majority
(44%) had DAP applied without manure/compost while 9% had neither DAP nor manure
application (Figure 2.5). About one-third of the plots had both DAP and manure/compost applied
89

while 17% had manure/compost only. The scenario in Figure 2.6 is most illuminating. Out of the
plots that had both low soil pH (<5.5) and low organic carbon (<2.7%), 46% had DAP applied
without manure/compost. These statistics show that even on plots that are low in soil pH and
organic carbon, and on which less-acidifying fertilizers and organic soil amendments should be
most appropriate, use of DAP without manure/compost is still the most common. But surprisingly,
despite producing a report that shows that soil acidity and low soil organic carbon levels are
widespread on farms in the major maize growing areas and providing recommendations for
appropriate types and amounts of fertilizer and manure to apply (Government of Kenya, 2014),
the government continues to subsidize DAP for maize production. These indicate deficiencies in
extension information and policy and exacerbates poor management of soil fertility.
Figure 2.4: Frequency distribution of DAP and manure use on plots with low soil pH (<5.5)
(39% of plots)

90

Figure 2.5: Frequency distribution of DAP and manure use on plots with low organic carbon
(<2.7%) (75% of plots)

Figure 2.6: Frequency distribution of DAP and manure use on plots with both low organic
carbon (<2.7%) and low soil pH (30% of plots)

91

Table 2.9: Probit marginal effect estimates of the relationship between farmers’ perception about
soil fertility and measured soil properties
Dep var: Soil fertility
perception (1=fertile)

(1)
Individual
soil
properties

(2)

(3)

Maize yield

(4)

(5)

Plot
Plot manager
Area
characteristics characteristics infrastructure

Total carbon (%)

0.0325*
(0.0196)

0.0297
(0.0196)

0.0305
(0.0198)

0.0292
(0.0198)

0.0305
(0.0202)

pH (value)

0.0506*
(0.0298)

0.0445
(0.0298)

0.0472
(0.0298)

0.0496*
(0.0301)

0.0448
(0.0303)

0.000783
(0.000752)

0.000775
(0.000746)

0.000589
(0.000752)

0.000531
(0.000752)

0.000554
(0.000752)

Loamy coarsea

-0.0976
(0.0971)

-0.0960
(0.0970)

-0.0971
(0.0964)

-0.0812
(0.0978)

-0.0791
(0.0974)

Loamy mediuma

-0.172
(0.190)

-0.158
(0.190)

-0.176
(0.188)

-0.160
(0.188)

-0.159
(0.187)

Loamy finea

-0.0160
(0.0910)

-0.0149
(0.0910)

-0.0119
(0.0903)

-0.000341
(0.0916)

-0.00123
(0.0912)

Clayeya

-0.0329
(0.0926)

-0.0346
(0.0925)

-0.0350
(0.0919)

-0.0193
(0.0932)

-0.0223
(0.0928)

0.0000484***
(0.0000146)

0.0000484***
(0.0000146)

0.0000477***
(0.0000147)

0.0000467***
(0.0000147)

Moderateb

-0.0355
(0.0313)

-0.0331
(0.0313)

-0.0338
(0.0313)

Steepb

-0.109*
(0.0564)

-0.115**
(0.0565)

-0.104*
(0.0570)

No. of years of plot
cultivation

-0.0102

-0.00570

-0.00609

(0.00917)

(0.00954)

(0.00953)

0.000819

0.000818

(0.00399)

(0.00398)

-0.0161

-0.0163

(0.0303)

(0.0303)

Phosphorus (ppm)

Maize yield (kg/acre)

Plot manager education
(yrs)
Plot manager is female
(1=yes)

Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
Notes: aSandy soil is the comparison category; b Flat slope is the comparison category

92

Table 2.9 (cont’d)
(2)

(3)

(4)

(5)

Maize yield

Plot
characteristics

Plot manager
characteristics

Area
infrastructure

0.000439
(0.000954)

0.000391
(0.000956)

Plot owned (1=yes)

-0.0563
(0.0487)

-0.0614
(0.0486)

Walking time to plot (mins)

0.00240
(0.00159)

0.00228
(0.00159)

Dep var: Soil fertility
perception (1=fertile)

(1)
Individual
soil
properties

Farming experience (yrs)

Distance to extension (km)

-0.00417
(0.00277)

Distance to town (km)

-0.00120
(0.00112)

Distance to paved road (km)

-0.000621
(0.00296)

Regional dummies

Yes

Yes

Yes

Observations
1268
1268
1268
20.86
31.67
36.78
LR 𝜒
0.0525
0.0027
0.0022
Prob > 𝜒
0.0121
0.0184
0.0214
Pseudo R
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
Notes: aSandy soil is the comparison category; b Flat slope is the comparison category

Yes

Yes

1268
42.14
0.0040
0.0245

1268
45.94
0.0045
0.0267

The data shows that 99% of the sample plots had not had their soils tested during the three-year
period prior to the 2014 survey when soil sampling and testing was conducted as part of the survey.
This confirms that farmers’ perceptions about soil fertility on their plots is largely not based on
knowledge about physical, chemical and biological attributes of soil. Farmers were asked in the
2016 survey to indicate what they consider to conclude that the fertility of soil is wanting. Table
2.10 displays the frequency distribution of farmer-reported indicators of soil infertility. The
statistics indicate that farmers overwhelmingly rely on crop performance, including crop health
(by look), growth and yield, to judge the fertility status of the soil. Farmers also use local
classifying attributes of soil such as color, texture and depth to assess soil fertility. Soil testing as
93

a way of knowing soil fertility status comes last in the list. This can be problematic because poor
crop performance may be a result of factors other than soil infertility, such as poor-quality seeds,
pests, and diseases that may not be visible to the farmer. In addition, even if poor crop performance
was because of soil infertility, it may not identify the exact deficiency in the soil that is contributing
to infertility. Meaningful diagnosis of deficiencies in the soil can be only through soil testing.
Therefore, the result that soil testing is generally a rare practice among maize farmers should raise
concern about the appropriateness of the soil fertility management practices they apply. This is
particularly important because the soils have been cultivated for a long time with intensity of
cultivation increasing (i.e. less fallowing as inferred from the number of years of cultivation during
the last decade). Indeed, it is not surprising that farmers’ perceived and measured soil fertility
largely mismatch in our analysis, and maize yield has stagnated or declined in the long term despite
evidence of increased use of inorganic fertilizers (mainly DAP) and improved seed varieties.
Table 2.10: Farmers’ reported indicators of soil infertility

unhealthy-looking plants
poor crop yield
retarded plant growth
soil color is different from what I expect
invasion by particular weeds
soil hard to work (hard to till)
texture is too coarse
texture is too fine
invasion by particular animals/organisms
soil is shallow
poor water infiltration
poor drainage
through soil testing

402
399
251
135
103
37
34
31
27
14
13
8
2

Percent of
responses
27.61
27.40
17.24
9.27
7.07
2.54
2.34
2.13
1.85
0.96
0.89
0.55
0.14

Total

1456

100

Indicators

Frequency

94

Percent of
cases
64.42
63.94
40.22
21.63
16.51
5.93
5.45
4.97
4.33
2.24
2.08
1.28
0.32
233.33

2.3.2

Adoption of soil fertility management practices

Before discussing the multivariate probit results of determinants of adoption of soil fertility
management practices in Table 2.12, we discuss the correlation matrix of the equations in Table
2.11. The positive and negative signs of the correlation coefficients indicate complementarity and
substitutability, respectively, in the decision to adopt the soil fertility management practices in
question. The statistical significance of some of the correlation coefficients indicates simultaneity
of adoption decisions and validates the suitability of multivariate probit to model adoption of the
soil fertility management practices. Inorganic fertilizer and manure/compost are significantly
substitutes, a finding that is consistent with Wainaina et al (2016) and Koppmair et al (2017) but
differs from Marenya & Barrett (2007) and Arslan et al (2017). This suggests that an average
farmer in our study may understand manure/compost and inorganic fertilizers as serving the same
purpose concerning soil fertility, which is not entirely the case. In addition to supplying nutrients
– mainly nitrogen – manure/compost adds organic materials into the soil and thus contributes to
enhancing soil quality characteristics that are associated with increased soil organic matter, and
therefore soil organic carbon, as explained earlier in the introduction. Inorganic fertilizer, on the
other hand, do not add organic matter into the soil, implying that efficiency of inorganic fertilizer
can be enhanced with concomitant application of manure/compost. Soil erosion control through
investment in structures such as grass strips, cut-off drains and terraces are substitutes with both
crops residue and inorganic fertilizer. The negative correlation of adoption between soil erosion
and crops residue could be driven by mulching, which, apart from using crops vegetative remains
to conserve moisture and enhance organic matter in the soil, also protects topsoil from erosion by
direct impact of rain. We also see a positive correlation between adoption of manure/compost and
legume intercrop.
95

Table 2.11: Correlation matrix for the regression equations
Manure/compost
Crops residue
Crops residue
0.0666
(0.0517)
Legume intercrop
0.102*
-0.0743
(0.0594)
(0.0540)
Soil erosion control
-0.0168
-0.181***
(0.0508)
(0.0475)
Inorganic fertilizer
-0.289***
-0.0196
(0.0895)
(0.0763)
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01

Legume intercrop

Soil erosion control

0.0481
(0.0537)
0.0369
(0.0829)

-0.156**
(0.0767)

The complementarities and substitutabilities of the soil fertility management practices have
important implications for policy and strategies to promote their use by farmers, since targeting
one practice for adoption can enhance or inhibit adoption of another. In Kenya, for example,
improving agricultural productivity through promotion of widespread use of inorganic fertilizers
has been a major strategy by the government, evident in fertilizer subsidy programs and, lately,
building of a fertilizer manufacturing plant. These initiatives, however, are not accompanied by
efforts to educate farmers about and promote use of organic soil amendments, such as use of
manure, compost and crops residue, which are necessary for building soil fertility and enhancing
efficiency of inorganic fertilizer use. Thus, the strategy may be portraying inorganic fertilizers as
the solution to the problem of soil infertility, making farmers to overemphasize use of inorganic
fertilizers and undermine organic soil amendments instead of looking at both as necessary
complements to enhance soil fertility for sustainable productivity improvement.
The effects of soil fertility perception on adoption shows that on average, the likelihood of applying
inorganic fertilizer on a plot is significantly lower when a farmer perceives the plot to be fertile
(Table 2.12). This may imply that plots that are viewed to be fertile are likely to be performing
well in maize production, the farmers’ main yardstick for soil fertility as we saw earlier, without
application of inorganic fertilizer. The finding may also imply that on average, farmers are inclined
to view inorganic fertilizer as a solution to soil infertility. This may be problematic if addressing
96

the soil infertility problem also requires, and it does on the maize plots in this study, soil
amendments that are different from what inorganic fertilizers do, such as correcting soil pH to
address acidity problems and increasing organic matter to increase soil organic carbon. This is
more likely what is happening in the major maize growing areas of Kenya where farmers have
sustained use of inorganic fertilizers on soils that are generally low in pH and have low organic
carbon levels in efforts to raise maize productivity. Soil fertility perception also has a negative but
statistically weak association with adoption of maize-legume intercropping.
Among plot characteristics, slope has an increasing effect on the likelihood of soil erosion control,
with erosion control structures more likely on moderate to steep relative to flat plots. Fertilizer
adoption is also more likely on plots that are steep relative to those that are flat. As would be
expected, plot size has a reducing effect on the probability of manure/compost use and use of crops
residue. This can be attributed to the bulkiness of the practices which makes them much labor
demanding and, therefore, much costlier to apply on large plots. In addition, availability of
manure/compost and crops residue, which competes with other uses such as livestock feeding, to
apply on large plots may be a challenge. Plot size, on the other hand, has a positive and significant
association with inorganic fertilizer use.
Plot distance from the homestead is negatively correlated with adoption of manure/compost and
crops residue, similar to findings of Kassie et al (2015). This may be because of the bulkiness of
manure/compost, which are often made in the homestead and transported to the farm. Similar to
findings by Kamau et al. (2014), Kassie et al. (2015) and Wainaina et al. (2016), plot ownership,
which implies tenure security, has a positive association with adoption of manure/compost. This
is expected since returns to manure/compost application is often not immediate and thus farmers
are more likely to apply manure/compost on plots for which they have assurance of continued use.
97

Table 2.12: Multivariate probit estimation results of factors affecting adoption of soil management practices (N=1268)

Soil fertility perception (1=fertile)
Years of plot cultivation
Plot slope (1=moderate)a
Plot slope (1=steep)a
Plot size (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Plot manager education (yrs)
Plot manager is female (1=yes)
Farming experience (yrs)
Active adults (#)
Group membership (1=yes)
HH has non-farm income (1=yes)
Livestock value (KES) (log)
HH landholding (acres)
Asset index
Distance to extension (km)
Distance to paved road (km)
Fertilizer price (KES/kg)
Trans Nzoia
Kakamega
Kisii
Machakos
Constant
*

Manure/ compost
Coef.
SE
0.124
(0.0809)
0.0593*
(0.0307)
0.0927
(0.0900)
0.208
(0.162)
***
-0.268
(0.0568)
***
-0.0262
(0.00618)
0.730***
(0.154)
0.0161
(0.0122)
0.0805
(0.0878)
-0.00100
(0.00286)
-0.00597
(0.0255)
-0.0791
(0.0937)
0.0421
(0.0973)
0.105***
(0.0147)
-0.000468
(0.00242)
0.636
(1.526)
-0.00937
(0.00850)
0.00177
(0.00883)
-0.000270
(0.00262)
-0.0650
(0.172)
***
0.533
(0.141)
0.522***
(0.160)
***
1.397
(0.169)
-2.736***
(0.433)

Crop residue
Coef.
SE
-0.0286
(0.0753)
-0.0407
(0.0250)
-0.0639
(0.0843)
-0.201
(0.151)
*
-0.0546
(0.0332)
**
-0.0118
(0.00467)
0.0840
(0.133)
**
-0.0249
(0.0112)
-0.0907
(0.0825)
0.000566
(0.00266)
**
0.0567
(0.0235)
-0.0183
(0.0881)
0.122
(0.0894)
-0.0139
(0.0132)
-0.0115
(0.00871)
**
2.187
(0.868)
-0.0153*
(0.00784)
0.00729
(0.00772)
-0.00391
(0.00248)
0.343**
(0.152)
***
0.531
(0.132)
1.014***
(0.150)
0.120
(0.151)
0.249
(0.367)

p < 0.10, ** p < 0.05, *** p < 0.01

Notes: Log likelihood = -3137.4466; Wald chi2(115) = 1037.21; a Base category: flat

98

Legume intercrop
Coef.
SE
*
-0.159
(0.0858)
-0.0475
(0.0290)
0.0275
(0.0956)
0.133
(0.170)
-0.0626
(0.0403)
-0.00142
(0.00409)
0.139
(0.146)
**
-0.0256
(0.0128)
0.264***
(0.0957)
0.00410
(0.00305)
-0.0202
(0.0259)
0.00246
(0.0998)
0.0913
(0.0993)
0.0146
(0.0145)
-0.0447***
(0.0127)
0.469
(1.041)
-0.00175
(0.00878)
-0.0159*
(0.00838)
-0.00194
(0.00275)
***
1.157
(0.163)
***
1.632
(0.155)
1.285***
(0.165)
***
1.021
(0.161)
0.320
(0.411)

Table 2.12 (cont’d)

Soil fertility perception (1=fertile)
Years of plot cultivation
Plot slope (1=moderate)a
Plot slope (1=steep)a
Plot size (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Plot manager education (yrs)
Plot manager is female (1=yes)
Farming experience (yrs)
Active adults (#)
Group membership (1=yes)
HH has non-farm income (1=yes)
Livestock value (KES) (log)
HH landholding (acres)
Asset index
Distance to extension (km)
Distance to paved road (km)
Fertilizer price (KES/kg)
Trans Nzoia
Kakamega
Kisii
Machakos
Constant
*

Soil erosion control
Coef.
SE
-0.0517
(0.0740)
0.0220
(0.0248)
0.447***
(0.0827)
0.297**
(0.147)
0.0397
(0.0329)
-0.000856
(0.00377)
-0.156
(0.129)
0.00565
(0.0110)
0.0321
(0.0807)
0.00123
(0.00262)
-0.0485**
(0.0231)
-0.0326
(0.0861)
0.237***
(0.0869)
0.0110
(0.0129)
0.0163*
(0.00910)
-3.241***
(1.109)
-0.00532
(0.00728)
0.00178
(0.00765)
*
-0.00467
(0.00242)
0.00887
(0.149)
-0.0445
(0.130)
0.137
(0.144)
0.489***
(0.148)
-0.334
(0.360)

p < 0.10, ** p < 0.05, *** p < 0.01

Notes: Log likelihood = -3137.4466; Wald chi2(115) = 1037.21; a Base category: flat

99

Inorganic fertilizer
Coef.
SE
**
-0.253
(0.128)
0.0379
(0.0384)
0.165
(0.140)
**
0.566
(0.243)
0.295***
(0.115)
0.0114
(0.00881)
0.246
(0.198)
0.0302
(0.0190)
0.179
(0.137)
-0.00327
(0.00401)
0.0502
(0.0429)
***
0.520
(0.145)
0.0481
(0.144)
0.00818
(0.0185)
-0.0294*
(0.0157)
5.051
(3.504)
0.0204
(0.0151)
-0.0144
(0.0130)
-0.00266
(0.00417)
0.0414
(0.254)
0.254
(0.233)
***
0.978
(0.350)
-0.672***
(0.246)
0.121
(0.570)

Contrary to expectations, plot manager education has reducing effects on the likelihood of
adoption of crops residue and maize-legumes intercrop and no significant effect on adoption of the
other practices. Kassie et al. (2015) and Wainaina et al. (2016) found a positive effect of education
of household head on adoption of manure and inorganic fertilizer while Arslan et al. (2017) found
a positive effect on adoption of soil and water conservation measures. Concerning gender, female
plot managers are more likely to intercrop maize with legumes compared to their male
counterparts.
As expected, number of adults, a measure of labor availability, is positively correlated with
adoption of crops residue, which may reflect the labor-intensive nature of the practice. However,
number of adults is inversely related with soil erosion control. As expected, and similar to findings
of Kassie et al. (2015), group membership, which is an indicator of social capital and may also
facilitate access to information and credit, has a positive effect on inorganic fertilizer adoption,
while the presence of non-farm income in a household has a positive effect on soil erosion control.
As expected, livestock wealth has a positive effect on manure/compost adoption, consistent with
Kassie et al. (2015) and Wainaina et al. (2016). Household landholding has an inverse relationship
with maize-legume intercropping and inorganic fertilizer adoption, suggesting that smaller
landholdings motivate agricultural intensification practices. Landholding has a positive association
with soil erosion control while the effect of asset index is positive on use of crops residue but
negative on soil erosion control.
The effects of distance to extension service provider, distance to paved road and fertilizer price are
negative and weakly significant on the adoption of crops residue, maize-legume intercrop and soil
erosion control, respectively. While the sign is as expected, the effect of fertilizer price on fertilizer
100

adoption is insignificant possibly because of little variation in fertilizer prices and the high rate of
adoption.
2.4

Conclusion and Implications

Soil infertility is a major problem in sub-Saharan Africa and is one of the main causes of
persistently low agricultural productivity. Soil degradation because of land management practices
that do not replenish soil nutrients and organic matter is the main cause of soil infertility. In Kenya,
low agricultural productivity in general and poor maize yield in particular, despite notable increase
in use over time of mineral fertilizers and improved maize varieties, is largely attributed to this
problem. A particular problem is that continued use of chemical fertilizers, especially acidifying
ones such as DAP, to soils with low pH and low organic matter can further degrade the soil.
Replenishing such soils requires applying organic materials such as compost or manure and
ameliorating soil acidity (Lal, 2006; Chivenge et al., 2011; Kunhikrishnan et al., 2016). Promoting
recycling of organic matter into the soil and judicious use of appropriate chemical fertilizers is a
necessary priority to improve agricultural productivity in general and maize yield in particular.
Several studies have explored factors that promote or hinder adoption of sustainable management
practices in Kenya and elsewhere. However, often not included in many of the studies is the role
of farmers’ perceptions about the fertility status of their soil in the adoption choice decisions of
alternative soil fertility management practices. Using household, farmer and plot-level data from
major maize growing areas in Kenya, this study has estimated correspondence between maize
farmers’ perceived and measured soil fertility and investigated the association between farmers’
perception about soil fertility and adoption (use) of soil fertility management practices.

101

Five key results have emerged. First, descriptive analysis results have shown that farmers’
perceived and measured fertility status of 46% of the plots were consistent, about half were rated
as fertile by farmers but measured to be infertile, and less than 5% were perceived as infertile by
farmers but measured to be fertile. In addition, farmers overwhelmingly relied on crops
performance to judge the fertility status of soil. Soil testing as a mechanism to understand the
fertility status of soil was extremely rare. Secondly, interrater agreement analysis has shown little
correspondence between farmers’ perceived and measured soil fertility. About half of the plots
were rated as fertile by farmers but measured to be infertile, suggesting substantial underestimation
of soil infertility problem among the maize farmers. Thirdly, probit model results have shown that
measured soil fertility and soil organic carbon and pH are significant predictors of farmers’
perception about soil fertility. However, these effects vanish upon introducing in the model the
maize yield variable for which the significance of the effect becomes persistent. Fourthly,
multivariate probit estimation results have shown that farmers’ soil fertility perception has a strong
relationship with the decision to apply inorganic fertilizer, but not soil fertility management
practices such as applying manure or compost. The likelihood of applying inorganic fertilizer
increases when a farmer perceives the soil to be infertile. In addition, farmers appear to regard
manure/compost and inorganic fertilizers as serving the same purpose concerning soil fertility,
thus treating them as substitutes.
These results have important implications for policy and extension efforts to explore ways to
improve management of soils for improved agricultural productivity. First, the lack of soil testing,
farmers’ reliance on crop performance as the main yardstick for judging soil fertility condition,
and the low correspondence between farmers’ perceived and measured soil fertility collectively
imply that farmers are applying management practices that may not match the fertility needs of
102

soil on their plots. This is exemplified by the result that there is persistent application of an
acidifying fertilizer (DAP) to maize and low application of organic soil amendments such as
manure and compost even on plots with soils that are low to very low in soil pH and organic
carbon. Data has shown that over 40% of the plots that were low in soil pH and soil organic matter
had DAP applied without manure or compost application.
Secondly, farmers’ higher adoption rate of fertilizer relative to other organic soil amendments,
their treatment of manure/compost and inorganic fertilizers as substitutes rather than complements
and the strong inverse relationship between farmers’ perception of soil fertility and the decision to
apply inorganic fertilizer may indicate deficiencies in policy and extension information. The
government promotes use of inorganic fertilizers, but without accompanying concerted efforts to
educate farmers about and promote use of organic soil amendments, which are necessary for
building soil fertility and enhancing efficiency of inorganic fertilizer use. This may erroneously
valorize inorganic fertilizers as the solution to the problem of soil infertility and lead farmers to
put less effort in the necessary complementary organic soil amendments, recognizing that manure,
compost and crops residue are not readily available and are not costless to obtain and their use is
labor intensive. In addition, the government continues to subsidize DAP, one of the acidifying
fertilizers, for maize production, despite its own report showing that low soil pH and organic
carbon levels are widespread on farms in the major maize growing areas. This policy disconnect,
together with lack of aggressive extension efforts to promote organic soil amendments, may be
perpetuating improper practices for soil fertility management thereby exacerbating soil
degradation.
There is a need for a shift in policy and extension focus to encourage farmers to pay greater
attention to organic soil amendments and judicious application of appropriate chemical fertilizers
103

to restore and sustain soil fertility. It is acknowledged that organic soil amendments are scarce and
several factors, such as ability to keep livestock for manure and labor availability for use of crops
residue, determine farmers’ access to and their application of them. However, there still needs to
be active policy and extension efforts, perhaps like those for encouraging chemical fertilizer use,
to encourage farmers to embrace their importance. In addition, policy actions that encourage
judicious use of appropriate chemical fertilizers are vital. In this regard, encouraging and
supporting farmers to test their soils and facilitating availability of fertilizers that are suitable for
the varied soil conditions should be desirable.

104

REFERENCES

105

REFERENCES

Ali, A., & Abdulai, A. (2010). The Adoption of Genetically Modified Cotton and Poverty
Reduction in Pakistan. Journal of Agricultural Economics, 61(1), 175–192.
Ariga, J., & Jayne, T. S. (2009). Private Sector Responses to Public Investments and Policy
Reforms The Case of Fertilizer and Maize Market Development in Kenya (IFPRI Discussion
Paper No. 921).
Arslan, A., Belotti, F., & Lipper, L. (2017). Smallholder productivity and weather shocks:
Adoption and impact of widely promoted agricultural practices in Tanzania. Food Policy, 69,
68–81. https://doi.org/10.1016/j.foodpol.2017.03.005
Asafu-Adjaye, J. (2008). Factors affecting the adoption of soil conservation measures: A case
study of Fijian cane farmers. Journal of Agricultural and Resource Economics, 33(1), 99–
117.
Berazneva, J., Mcbride, L., Sheahan, M., & David, G. (2016). Perceived , measured , and estimated
soil fertility in east Africa : Implications for farmers and researchers. In 2016 Annual Meeting,
July 31-August 2, 2016. Boston, Massachusetts: Agricultural and Applied Economics
Association.
Chivenge, P., Vanlauwe, B., & Six, J. (2011). Does the combined application of organic and
mineral nutrient sources influence maize productivity ? A meta-analysis. Plant Soil, 342, 1–
30.
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological
Measurement, XX(1), 37–46.
Corbeels, M., Shiferaw, A., & Haile, M. (2000). Farmers ’ knowledge of soil fertility and local
management strategies in (Managing Africa’s Soils No. 10).
de Janvry, A., Fafchamps, M., & Sadoulet, E. (1991). Peasant Household Behaviour with Missing
Markets : Some Paradoxes Explained. The Economic Journal, 101(409), 1400–1417.
Desbiez, A., Matthews, R., Tripathi, B., & Ellis-Jones, J. (2004). Perceptions and assessment of
soil fertility by farmers in the mid-hills of Nepal. Agriculture, Ecosystems and Environment,
103(1), 191–206.
Doran, J. W., & Parkin, T. B. (1994). Defining and assessing soil quality. Defining Soil Quality
for a Sustainable Environment.
Eckert, E., & Bell, A. (2005). Invisible Force : Farmers †TM Mental Models and How They
Influence Learning and Actions. Journal of Extension, 43(3), 1–7.
Enyong, L. A., Debrah, S. K., & Bationo, A. (1999). Farmers ’ perceptions and attitudes towards
106

introduced soil-fertility enhancing technologies in western Africa. Nutrient Cycling in
Agroecosystems, 53, 177–187.
Feder, G., Just, R. E., & Zilberman, D. (1985). Adoption of Agricultural Innovations in Developing
Countries : A Survey. Economic Development and Cultural Change, 33(2), 255–298.
Fleiss, J. L., Levine, B., & Paik, M. C. (2003). Statistical Methods for Rates and Proportions. John
Wiley & Sons, Inc.
Foster, A. D., & Rosenzweig, M. R. (2010). Microeconomics of Technology Adoption. Annual
Review of Economics, 2(1), 395–424.
Government of Kenya. (2014). Soil suitability evaluation for maize production in Kenya soil
suitability evaluation for. Nairobi, Kenya.
Grisso, R., Alley, M., Holshouser, D., & Thomason, W. (2009). Precision farming tools: soil
electrical conductivity. Virginia Cooperative Extension, 442(508), 1–6. Retrieved from
http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Precision+farming+tools:
+soil+electrical+conductivity#7
Halbrendt, J., Gray, S. A., Crow, S., Radovich, T., Kimura, A. H., & Tamang, B. B. (2014).
Differences in farmer and expert beliefs and the perceived impacts of conservation
agriculture. Global Environmental Change, 28(1), 50–62.
Horneck, D. A., Sullivan, D. M., Owen, J. S., & Hart, J. M. (2011). Soil Test Interpretation Guide
(EC No. 1478). Corvallis, OR.
IIASA/FAO. (2012a). Global Agro-ecological Zones (GAEZ v3.0). Laxenburg, Austria and Rome,
Italy.
IIASA/FAO. (2012b). Global Agro-ecological Zones (GAEZ v3.0). IIASA, Laxenburg, Austria and
FAO, Rome, Italy. iv. https://doi.org/10.1029/97GB03657
Jack, B. K. (2011). Market inefficiencies and the adoption of agricultural technologies in
developing countries. Literature review, Agricultural Technology Adoption Initiative.
Kamau, M., Smale, M., & Mutua, M. (2014). Farmer demand for soil fertility management
practices in Kenya ’ s grain basket. Food Security, 793–806.
Kassie, M., Shiferaw, B., & Muricho, G. (2011). Agricultural Technology , Crop Income , and
Poverty Alleviation in Uganda. World Development, 39(10), 1784–1795.
Kassie, M., Teklewold, H., Jaleta, M., Marenya, P., & Erenstein, O. (2015a). Understanding the
adoption of a portfolio of sustainable intensification practices in eastern and southern Africa.
Land Use Policy, 42, 400–411. https://doi.org/10.1016/J.LANDUSEPOL.2014.08.016
Kassie, M., Teklewold, H., Jaleta, M., Marenya, P., & Erenstein, O. (2015b). Understanding the
adoption of a portfolio of sustainable intensification practices in eastern and southern Africa.
107

Land Use Policy, 42. https://doi.org/10.1016/j.landusepol.2014.08.016
Kelly, V., Adesina, A. A., & Gordon, A. (2003). Expanding access to agricultural inputs in Africa:
A review of recent market development experience. Food Policy, 28(4), 379–404.
Kerr, J., & Pender, J. (2005). Farmers ’ perceptions of soil erosion and its consequences in India ’
s semiarid tropics. Land Degradation & Development, 16, 257–271.
Knowler, D., & Bradshaw, B. (2007). Farmers ’ adoption of conservation agriculture : A review
and synthesis of recent research. Food Policy, 32, 25–48.
Koppmair, S., Kassie, M., & Qaim, M. (2017). The influence of farm input subsidies on the
adoption of natural resource management technologies. Australian Journal of Agricultural
and Resource Economics, 61, 539–556. https://doi.org/10.1111/1467-8489.12220
Kunhikrishnan, A., Thangarajan, R., Bolan, N. S., Xu, Y., Mandal, S., Gleeson, D. B., … Naidu,
R. (2016). Functional Relationships of Soil Acidification, Liming, and Greenhouse Gas Flux.
Advances in Agronomy, 139, 1–71. https://doi.org/10.1016/bs.agron.2016.05.001
Lal, R. (2006). Enhancing crop yields in the developing countries through restoration of the soil
organic carbon pool in agricultural lands. Land Degradation & Development, 209(August
2005), 197–209.
Landis, J. R., & Koch, G. G. (1977). The Measurement of Observer Agreement for Categorical
Data. Biometrics, 33(1), 159. https://doi.org/10.2307/2529310
Marenya, P., Barrett, C. B., & Gulick, T. (2008). Farmers’ perceptions of soil fertility and fertilizer
yield response in Kenya. Retrieved from http://ssrn.com/abstract=1845546
Marenya, P. P., & Barrett, C. B. (2007). Household-level determinants of adoption of improved
natural resources management practices among smallholder farmers in western Kenya. Food
Policy, 32(4), 515–536.
Marenya, P. P., & Barrett, C. B. (2009). Soil quality and fertilizer use rates among smallholder
farmers in western Kenya. Agricultural Economics, 40, 561–572.
McCauley, A., Jones, C., & Olson-Rutz, K. (2017). Soil pH and organic matter. Nutrient
Management, (8), 1–16.
Odendo, M., Obare, G., & Salasya, B. (2009). Factors responsible for differences in uptake of
integrated soil fertility management practices amongst smallholders in western Kenya.
African Journal of Agricultural Research, 4(11), 1303–1311.
Okalebo, J. R., Gathua, K. W., & Woomer, P. L. (2002). Laboratory methods of soil and plant
analysis: A working manual (Technical Publication No. Volume 1).
Pender, J. L., & Kerr, J. M. (1998). Determinants of farmers’ indigenous soil and water
conservation investments in semi-arid India. Agricultural Economics, 19.
108

Sanchez, P. A., Shepherd, K. D., Soule, M. J., Place, F. M., Buresh, R. J., Izac, A. N., & Kwesiga,
F. R. (1997). Soil Fertility Replenishment in Africa : An Investment in Natural Resource
Capital. American Society of Agronomy and Soil Science Society of America, (51), 1–46.
Singh, I., Squire, L., & Strauss, J. (1986). A Survey of Agricultural Household Models : Recent
Findings and Policy Implications. The World Bank Economic Review, 1(1), 149–179.
Smale, M., & Olwande, J. (2014). Demand for maize hybrids and hybrid change on smallholder
farms in Kenya. Agricultural Economics (United Kingdom), 45(4).
Smaling, E. M. A., Nandwa, S. M., & Janssen, B. H. (1997). Soil Fertility in Africa Is at Stake.
American Society of Agronomy and Soil Science Society of America, (51).
Stoorvogel, J. J., & Windmeijer, P. N. (1993). Calculating soil nutrient balances in Africa at
different scales. Fertilizer Research, 35, 237–250.
Stoorvogel, J., & Smaling, E. M. A. (1998). Research on soil fertility decline in tropical
environments : integration of spatial scales. Nutrient Cycling in Agroecosystems 50:, 50, 151–
158.
The Montepellier Panel. (2013). Sustainable Intensification: A New Paradigm for African
Agriculture. London.
Tittonell, P., Corbeels, M., Wijk, M. T. Van, Vanlauwe, B., & Giller, K. E. (2008). Combining
Organic and Mineral Fertilizers for Integrated Soil Fertility Management in Smallholder
Farming Systems of Kenya: Explorations Using the Crop-Soil Model FIELD. Agronomy
Journal, 100(5), 1511–1526.
Tittonell, P., & Giller, K. E. (2013). When yield gaps are poverty traps: The paradigm of ecological
intensification in African smallholder agriculture. Field Crops Research, 143, 76–90.
https://doi.org/10.1016/j.fcr.2012.10.007
Turner, B. L., Wuellner, M., Nichols, T., & Gates, R. (2014). Dueling Land Ethics : Uncovering
Agricultural Stakeholder Mental Models to Better Understand Recent Land Use Conversion.
Journal of Environmental Ethics, (27), 831–856.
Udry, C. (2010). The economics of agriculture in Africa: Notes toward a research program.
AfJARE, 5(1), 284–299.
Vignola, R., Koellner, T., Scholz, R. W., & McDaniels, T. L. (2010). Decision-making by farmers
regarding ecosystem services: Factors affecting soil conservation efforts in Costa Rica. Land
Use Policy, 27(4), 1132–1142.
Wainaina, P., Tongruksawattana, S., & Qaim, M. (2016). Tradeoffs and complementarities in the
adoption of improved seeds , fertilizer , and natural resource management technologies in
Kenya. Agricultural Economics, 47, 351–362.
Willy, D. K., Muyanga, M., & Jayne, T. (2016). Can economic and environmental benefits
109

associated with agricultural intensification be sustained at high population densities ? A farm
level empirical analysis. In Invited paper presented at the 5th International Conference of the
African Association of Agricultural Economists, September 23-26, 2016, Addis Ababa,
Ethiopia.
Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
https://doi.org/10.1515/humr.2003.021

110

CHAPTER 3: TECHNICAL EFFICIENCY AND SOIL FERTILITY AND
AGRONOMIC PRACTICES IN MAIZE PRODUCTION IN KENYA

3.1

Introduction and Study Objectives

There has been a renewed interest about the role of agriculture in economic development in recent
years, with increased recognition that it is key to sustainable development and poverty reduction
in agriculture-based economies. This is particularly true of developing countries in sub-Saharan
Africa where over three quarters of the population is rural and majority of who depend almost
entirely on agriculture for livelihood (The World Bank, 2007; Haggblade & Hazell 2010).
Sustainable agricultural productivity growth is thus essential to broad-based sustainable economic
progress in these countries (The World Bank, 2007; Diao et al (2007), and fostering that growth
requires technological progress and/or efficiency improvement in management of productive
resources.
The problem of low agricultural productivity in sub-Saharan Africa has been majorly attributed to
soil infertility due to nutrient depletion (Stoorvogel & Smaling, 1998; Sanchez et al., 1997; The
Montepellier Panel, 2013; Smaling et al., 1997; Stoorvogel & Windmeijer, 1993). Soil nutrient
depletion is blamed on unsustainable land management practices that deplete soil organic carbon
pool (Lal, 2006) and accelerate soil acidification (Kunhikrishnan et al., 2016). Soils that are in
such depleted conditions result in reduced response of crops to external inputs such as fertilizers,
irrigation and high yielding crop varieties (Lal, 2006; Tittonell & Giller, 2013). This in turn lowers
productivity and reduces efficiency of input use.

111

In Kenya, soil degradation in terms of nutrient imbalance, diminished soil organic carbon pool and
high acidity is one of the main reasons cited for lack of growth in yield of maize (Government of
Kenya, 2014; Tittonell et al, 2008; Marenya & Barrett, 2007). Farmers have intensified use of
external inputs such as chemical fertilizers and high yielding maize varieties over time (e.g. Ariga
& Jayne, 2009, 2009; Smale & Olwande, 2014; Muyanga & Jayne, 2014), but evidence suggests
that aggregate maize yield has generally stagnated or declined. This implies that soil infertility
combined with agronomic practices that may not effectively respond to fertility needs of the soil
could be affecting maize response to external inputs.
Because there is little scope for land expansion in Kenya, the onus of increasing agricultural
production, particularly maize, is on increasing productivity, i.e. output per given amounts of
inputs. This can be achieved through technological change, increased efficiency in use of existing
technology and productive resources or both. This study is concerned with efficiency for two
reasons. First, when soils are degraded and farmers do not apply proper agronomic practices in
response to the actual conditions of the soil, they are unlikely to realize maximum yield possible
with the amount of inputs used under a given production technology. This means they are likely
to be technically inefficient. In this respect, knowledge of the level of technical efficiency of maize
farmers would be useful in determining potential productivity gains possible through better
agronomic management under existing technology. Information about specific factors that affect
variations in efficiency across farms can guide targeted policies to improve efficiency for widescale maize productivity improvement.
Secondly, higher yields because of increased amount of inputs may not necessarily imply higher
technical efficiency. A farmer may apply larger amounts of inputs and achieve higher yields but
remain far below the maximum yield possible with the amount of the inputs applied (Mochebelele
112

& Winter-Nelson, 2000). Therefore, improving technical efficiency is important for sustainable
agricultural intensification not only economically but also environmentally, since improper use of
certain external inputs such as inorganic fertilizers, pesticides and herbicides may potentially
degrade the environment and its productive resources.
Using a stochastic production frontier (SF) approach due to Meeusen & van Den Broeck (1977)
and Aigner et al (1977), this study estimates technical efficiency of maize farmers in Kenya while
controlling for soil fertility conditions and agronomic practices, and identifies factors responsible
for heterogeneity in technical efficiency across farms. The study addresses the following specific
questions:
(a) What is the technical efficiency level of maize farmers? How does technical efficiency
vary across farms? What does this mean for measures to improve maize productivity?
(b) What factors explain technical efficiency variations across farms?
(c) How important are soil fertility conditions and agronomic practices to agricultural
productivity and efficiency estimation?
A major contribution of this study is that it evaluates maize productivity and efficiency while
integrating soil fertility conditions and agronomic practices in the estimation, thus overcoming
omitted variable bias to which many studies that do not include these conditions and practices may
be prone. While studies have been conducted in Kenya and elsewhere on agricultural productivity
and efficiency, such studies have often inadequately specified or ignored environmental variables
mainly because of data limitations (e.g. Liu & Myers, 2009 and Kibaara, 2005 in Kenya;
Mochebelele & Winter-Nelson, 2000; Tiedemann & Latacz-Lohmann, 2013). Ali & Byerlee

113

(1991) suggest and Sherlund et al (2002) and Ekbom et al (2013) have shown that omitting
environmental production conditions from farm technical efficiency analysis would result in
biased and inconsistent estimates of the production frontier parameters and understated technical
efficiency. Maize-growing population in Kenya is quite heterogeneous and diversified, with
biophysical conditions under which farmers operate among the most important sources of
heterogeneity and diversity. These conditions affect farmers’ input choice decisions hence the need
to control for them in productivity and efficiency analysis.
3.3
3.3.1

Methods and Data
Conceptual Framework

The conceptual framework for technical efficiency is based on the seminal work of Farrell (1957).
In the context of a firm, Farrell (1957) defined technical efficiency (TE) as a firm’s ability to
maximize its production from a given level of inputs under a given technology. Farrell (1957)
illustrated this concept as in Figure 1 below, obtained from Coelli et al (2005). A firm is assumed
to produce one output, y, using two inputs, x1 and x2, under constant returns to scale technology.
Let SS’ represent the isoquant of a technically efficient firm. The isoquant represents the output
level that the perfectly efficient firm would produce given any combination of the two inputs, x1
and x2. A firm that produces at point P is technical inefficient because the input amounts can be
proportionally reduced while the output level is maintained. The distance QP represents the firm’s
technical inefficiency. The ratio QP/OP measures technical inefficiency of the firm. It is the
proportion by which all inputs could be downscaled to the technically efficient output level. The
ratio is one for a perfectly technically efficient firm. Technical efficiency is expressed as 𝑇𝐸 =
1 − 𝑄𝑃⁄𝑂𝑃 = 𝑂𝑄 ⁄𝑂𝑃 .

114

Figure 3.1: Input-oriented technical efficiency illustration (Coelli et al 2005)
S

P

x1/y

Q
S’

O

x2/y

This representation of the concept of technical efficiency is input-oriented and has input-reducing
focus (Coelli et al (2005). A useful analogous representation of the concept is in output-oriented
fashion, which views technical efficiency in terms of how much output could be proportionally
increased without reducing input amounts under the same technology. Consider a single input, x,
and single output, y, and decreasing returns to scale production technology, f(x), in Figure 3.2
(Coelli et al, 2005). A firm producing at point P is technically inefficient since the maximum output
possible with C amount of input is at D, which is on the production frontier. The ratio CP/CD
measures the technical efficiency of the firm producing.
The case of two outputs, y1 and y2, a single input, x, and constant returns to scale technology is
represented by Figure 3.3 (Coelli et al, 2005). Point A represents technically inefficient output
combination because for the given level of the input it is below the maximum possible output
combination, B, which is on the production possibility frontier (PPF) represented by the curve ZZ’.
The ratio OA/OB measures technical efficiency of a firm producing at point A. Using the notation
of Coelli et al (2005), a firm’s technical efficiency can also be generally represented as the distance

115

function at the firm’s input and output vectors, 𝑑 (𝐱, 𝐲), a representation that is useful in the case
of multiple outputs and inputs.

Figure 3.2: Output-oriented technical efficiency with one input and one output (Coelli et al 2005)

y

f(x)

D
B

A

P

O

x

C

Figure 3.3: Output-oriented technical efficiency with two outputs and one input (Coelli et al
2005)

D

y2/x

C

Z

B
B’
A
D’
O

Z’

y1/x

The next sub-section formalizes the framework for estimating a stochastic frontier production
function in the context of a single output and multiple inputs, the relevant context for this study.

116

3.3.2

Stochastic frontier analysis

Production is a process that transforms a set of inputs, 𝐱 ∈ R , into a set of outputs, 𝐲 ∈ R ,
through some technology represented by a production function. Figure 3.2 above is a graph of
production technology for the case of a single input and a single output.

The production

possibilities set is the input-output space bounded above by the production frontier, f(x). It is the
set of input-output combinations feasible with the production technology. The production
possibilities frontier, which is the upper boundary of the production possibilities set, is the set of
maximum output levels that can be produced from any given vector of inputs. Formally, the
production frontier can be represented as:
(3.1),

𝑓(𝐱) = max{𝑦: 𝑦 ∈ 𝑃(𝐱)}

where 𝑃(𝐱) is the production possibilities set, i.e. the set of vectors of output that is feasible to
produce for each vector of inputs.
The production frontier is the point of reference in determining technical efficiency of a producing
unit as illustrated in the conceptual framework. The input-output combination of each producing
unit, a maize farm in the context of this study, is either below or on the production frontier. Initially,
technical efficiency analysis was concerned with measuring how far below the production frontier
each producing unit operates. Later, the analysis has also often been concerned about factors that
explain variations in technical efficiency across producing units, to provide information that can
better guide policy interventions to improve efficiency.
There are two commonly used approaches to technical efficiency analysis. One approach is the
data envelopment analysis (DEA), which is non-parametric and uses mathematical programming
117

to estimate the efficient production frontier against which individual producing units’ outputs are
measured. A major criticism against DEA is that it does not separate inefficiency from random
error and considers all deviation from the frontier as inefficiency (Coelli 1995). Nevertheless, DEA
has the advantage that it neither requires a functional form for the production frontier nor makes
any distributional assumptions (Coelli 1995). This approach has not been widely applied in
efficiency studies in agriculture. The other approach is the stochastic frontier analysis (SFA),
which relies on functional form specification for the production frontier and distributional
assumptions about the error terms in the model (Coelli 1995). It applies econometric methods to
data on producing units to estimate parameters of the production frontier and inefficiency. Unlike
the DEA, the SFA approach explicitly separates inefficiency from random error.
This study applies the SFA approach to two cross sections of data on maize farms in Kenya to
estimate technical efficiency and identify factors that explain variations in technical efficiency
across farms. Stochastic frontier (SF) approach to technical efficiency analysis was originally
developed independently by Meeusen & van Den Broeck (1977) and Aigner et al (1977). The idea
and general setup of the stochastic production frontier in a cross-sectional data setting is as follows.
Suppose we have a sample of maize producing farms indexed by i=1, 2,…, 𝑁 and 𝑦 and 𝐱 ,
respectively, represent the output and a vector of inputs and other variables that affect the frontier
output. Let 𝑦 ∗ ≥ 𝑦 be the unobserved frontier output. We can define the frontier output as:
𝑦 ∗ = 𝑓(𝐱 ; 𝜷) + v ,

(3.2)

where 𝑓(𝐱 ; 𝜷) represents the production technology defining the frontier, 𝜷 is the parameter
vector to be estimated and v is statistical noise term which captures measurement and specification

118

errors. The observed (actual) output is defined as the frontier output minus a non-negative error
term, u ≥ 0, representing the farm’s inefficiency:
𝑦 = 𝑦∗ − u ,

(3.3)

If we express the actual and frontier output in terms of their natural logs, we can re-arrange (3.3)
and represent a farm’s technical efficiency measure as the ratio of actual to the frontier output as
shown in (4):
exp(−u ) =

(3.4)

∗

The stochastic production frontier model is as follows:
𝑦 = 𝑓(𝐱 ; 𝜷) + 𝜀 ,

(3.5)

𝜀 =v −u

(3.6)

v ~𝑁(0, 𝜎 ),

(3.7)

u ~ℱ

(3.8)

The error term, 𝜀 , has two components – the random error term, v , and the non-negative error
term, u , which represents inefficiency. It is assumed that the two components of the composed
error term are independent of each other and of 𝐱 . Aigner et al (1977) pointed out that the
inefficiency, representing deviation of a firm’s output from the frontier, originates from factors
under the control of the firm, such as management effort. The random error, v , indicates that the
frontier is stochastic and is a result of events that are not under a firm’s control and that can be
favourable and/or unfavourable, such as environmental shocks. The random error also results from
measurement and observation errors.

119

The main objective of SFA is to disentangle inefficiency (u ) from random error (v ) in the
composed error term. To achieve this, estimation of the model often relies on assumptions about
statistical distributions of the random error, v , and the inefficiency term, u , and usually uses
maximum likelihood (ML) procedure. Meeusen & van Den Broeck (1977) and Aigner et al (1977)
both assumed a zero-mean normal distribution for v , which has been widely maintained in SFA
studies. For the inefficiency component, u , Meeusen & van Den Broeck (1977) assumed
exponential distribution with a single parameter, i.e. u ~ℰ(𝜎 ), while Aigner et al (1977) assumed
half normal distribution, i.e. u ~𝑁 (0, 𝜎 ). The next step in ML estimation after making
distributional assumptions is to derive the log-likelihood function of the model, which is thereafter
maximized with respect to the parameters and parameter values obtained.
Based on their assumption of mutual independence of v and u and their distributions, Aigner et
al (1977) derived the density function of the composed error term, 𝜀 , and obtained the loglikelihood function of the ith observation as follows:

− 𝑙𝑛(𝜎 + 𝜎 ) + 𝑙𝑛𝜙

𝐿 = −𝑙𝑛

where 𝜇∗ =

;

𝜎∗ =

+ 𝑙𝑛Φ

∗
∗

(3.9)

; 𝜙(∙) is a standard normal density function; and Φ(∙) is a

standard normal cumulative distribution function (cdf). Upon maximizing the sum of the loglikelihood function over individual observations, the parameter estimates, i.e. 𝜷, 𝜀̂, 𝜎 , 𝜎 , and
subsequently the values of 𝜇̂ ∗ and 𝜎∗ are obtained.
The model parameters are then used to derive technical inefficiency index as 𝐸(𝑢 |𝜀 ) according
to Jondrow et al (1982) and technical efficiency scores as 𝐸(exp(−𝑢 )|𝜀 ) according to Battese &
120

Coelli (1988). Jondrow et al (1982) showed the distribution of 𝑢 conditional on 𝜀 to be truncated
normal with mean 𝜇∗ and variance 𝜎∗ , i.e. (𝑢 |𝜀 )~𝑁 (𝜇∗ , 𝜎∗ ). Based on this distribution, the
technical ineffiency scores by Jondrow et al (1982) and efficiency scores by the Battese & Coelli
(1988) methods, respectively, are predicted as:

𝑢 = 𝐸(𝑢 |𝜀 ) =

∗

∗
∗
∗
∗

(3.10)

+ 𝜇∗

𝐸(𝑒𝑥𝑝(−𝑢 )|𝜀 ) = exp(−𝜇∗ + 𝜎∗ )

∗
∗

∗
∗
∗

(3.11)

There have been tremendous developments in methods and empirical applications of SFA
following the initial studies by Meeusen & van Den Broeck (1977) and Aigner et al (1977).
Kumbhakar & Lovell (2000 and Parmeter & Kumbhakar (2014 provide detailed accounts of the
developments. Early studies focused on finding flexible distributions for the inefficiency term. For
example, Stevenson (1980) proposed gamma distribution and a truncated (at 0) normal
distribution, which allowed for zero and non-zero modes in the distribution of inefficiency, while
Greene (1980) proposed a gamma distribution for the inefficiency term.
Jondrow et al (1982) developed the method for estimating observation-specific technical
inefficiency parameters as discussed above, overcoming shortcomings in earlier methods that
estimated only average inefficiency score over a sample of producing units. However, the Jondrow
et al (1982) method assumes that the technical inefficiency parameter is independently and
identically distributed. This assumption is problematic in cases where technical inefficiency is
correlated with characteristics of producing units.

121

Kumbhakar, Ghosh, & McGuckin (1991), Reifschneider & Stevenson (1991), Huang & Liu (1994)
and Battese & Coelli (1995) extended the stochastic frontier methodology to estimate the
production frontier and explicit relationship between inefficiency and exogenous factors in a single
step. This estimation procedure solves the bias problem inherent in the two-step estimation process
which had dominated in earlier studies (see Wang & Schmidt (2002) for a discussion about the
bias in a two-step procedure). Caudill & Ford (1993), Caudill, Ford, & Gropper (1995), Hadri
(1999) and Wang (2002, 2003) considered stochastic frontier models that address
heteroscedasticity problem through parameterizing the pre-truncated variance of the inefficiency
term, u , and noted that ignoring heteroscedasticity may lead to biased inefficiency estimates. This
contrasts with the case in linear models where heteroscedasticity in the error term may affect only
the precision of coefficient estimates.
Wang & Schmidt (2002) introduced the idea of scaling property in the context of cross-sectional
data while Alvarez et al (2006) discuss models with the property but in the context of panel data
and identify its advantages. Models with the scaling property have the feature that changes in the
exogenous factors hypothesized to affect inefficiency change the scale but not the distribution of
the inefficiency component of the error term. Alvarez et al (2006) propose a procedure for selection
of the inefficiency model.
The first studies to apply panel data methods to stochastic frontier analysis were Pitt & Lee (1981)
and Schmidt & Sickles (1984), both of which assumed time-invariant technical inefficiency. The
time-invariant assumption would be acceptable in short panels but obviously is practically
questionable in long period panels. Another implication of this assumption is that unobserved
producer-specific effects that are time-invariant are interpreted as inefficiency, which may bias
estimated inefficiency scores. An additional shortcoming of the conventional fixed-effects model
122

is that it requires sufficient variability of data over time for each producing unit because it uses
within estimation. Little within-variability of data for producing units would produce imprecise
fixed-effects estimates. In addition, it is not possible to include time-invariant covariates, such as
gender, in the model.
To overcome some of the limitations of the conventional panel data methods, later studies using
panel data relaxed the time-invariant assumption and considered time-varying inefficiency (e.g.
Kumbhakar, 1990; Cornwell, Schmidt, & Sickles, 1990; Battese & Coelli, 1995). However, the
models used in these studies still confound time-invariant unobserved producer-specific effects
into inefficiency. In efforts to overcome this problem, Greene (2005) extended panel data methods
to the stochastic frontier models and developed what he calls “true fixed-effects” (TFE) and “true
random-effects” (TRE) stochastic frontier models. A key feature of these models is that they treat
inefficiency as time-varying and at the same time separate time-invariant unobserved producerspecific effects from inefficiency. The TFE stochastic frontier model, however, faces the incidental
parameters problem (Neyman & Scott, 1948). This problem arises because the number of fixedeffect parameters (the incidental parameters) to be estimated increases as the sample size increases
while the time dimension is fixed, resulting in inconsistent estimates of the incidental parameters.
Greene (2005) found that while the incidental parameter problem does not affect the model slope
parameters, it biases model residuals, therefore affecting technical inefficiency estimates, which
are based on the residuals. Some analysts, for example Wang & Ho (2010), Chen, Schmidt, &
Wang (2014) and Belotti & Ilardi (2015), have proposed estimation methods to resolve this
problem.
While its estimation is not problematic, a limitation of the TRE stochastic frontier model is that it
does not allow for correlation between time-invariant unobserved producer-specific effects and
123

explanatory variables in the model, which can lead to biased estimates. Some analysts have
proposed adjustments to the TRE specification of stochastic frontier model using MundlakChamberlain device (Mundlak, 1978; Chamberlain, 1984; Wooldridge, 2010) to account for
correlation between time-invariant unobserved producer-specific effects and covariates in the
model (e.g. Farsi, Filippini, & Kuenzle, 2005; Abdulai & Tietje 2007; Filippini, Hunt, & Zorić
2014; Filippini & Greene, 2016; Griffiths & Hajargasht, 2016). The authors note that unlike in the
random effects linear model with a normal error term where adjustment using the MundlakChamberlain device results in coefficient estimates that are similar to within estimators, the
coefficient estimates from the adjusted TRE stochastic frontier model are not similar to within
estimators. This is because the adjusted TRE stochastic frontier model has asymmetric composed
error term and estimation is by maximum likelihood. Nevertheless, the authors suggest that using
the device in TRE stochastic frontier model reduces heterogeneity bias because some correlation
between time-invariant unobserved producer-specific effects and explanatory variables is
captured. However, what remains unknown is the extent to which the heterogeneity bias is reduced.
Despite the methodological efforts in SFA to disentangle time-invariant unobserved producerspecific effects from inefficiency, Chen et al. (2014) observe that a philosophical question remains
as to whether these effects are part of inefficiency, as assumed by the models that do not distinguish
them from inefficiency, or heterogeneity to control for in estimating inefficiency. Some analysts
have recently suggested that the ‘true’ inefficiency measure may lie in between the two extreme
positions and proposed extensions of stochastic frontier panel data models to disentangle persistent
inefficiency from time-invariant unobserved producer-specific effects (e.g. Colombi, Martini, &
Vittadini, 2011; Kumbhakar, Lien, & Hardaker, 2014; Filippini & Greene, 2016).

124

The methodological developments in SFA are impressive, but great variability exists in results
obtained from using different models. For example, Kumbhakar, Lien, & Hardaker (2014) apply
six panel data models in SFA of technical efficiency in Norwegian grain farming and obtain quite
different results for each of the models. They conclude that there is no model that can be said to
measure inefficiency “correctly”. This places the onus of model choice in an empirical study using
SFA on a careful understanding of the research context and the nature of data available.
We present model choice and estimation strategy next.
3.3.3

Model choice and estimation strategy

3.3.3.1 Model choice
The focus of the study is on estimating farm-level technical efficiency while controlling for
environmental conditions, and identifying factors that affect technical efficiency variation across
farms. It exploits some of the methodological advances discussed above and applies them to pooled
cross sectional data to meet these objectives. Reflecting on the objectives and the data, the study
applies the model proposed by Wang (2002), which combines features of the model of Kumbhakar,
Ghosh, & McGuckin (1991), Huang & Liu (1994) and Battese & Coelli (1995) (KGMHLBC) and
that of Caudill & Ford (1993), Caudill, Ford, & Gropper(1995) and Hadri (1999) (CFCFGH).
Indexing producing units (maize farms in this case) by 𝑖 = 1,2, … , 𝑁, we express the model in a
cross-sectional setting as follows:
𝑦 = 𝑓(𝐱 , 𝐰 ; 𝜷, 𝜽) + 𝜀

(3.12)

𝜀 = 𝑣 −𝑢 ,

(3.13)

𝑢 ≥0

125

𝑣 ~𝑁(0, 𝜎 ),

(3.14)

u ~𝑁 (𝜇 , 𝜎 ),

(3.15)

𝜇 = 𝒛 𝜹,

(3.16)

𝜎 = exp(𝒛 𝝉),

(3.17)

where 𝑦 is the output, 𝑓(𝐱 , 𝐰 ; 𝜷, 𝜽) represents the production frontier, 𝐱 is the vector of inputs
and includes one, 𝐰 is a vector of environmental conditions (soil fertility conditions and
agronomic practices) and 𝜷 and 𝜽 are the corresponding parameter vectors to be estimated. The
term 𝑣 represents random error that accounts for measurement and specification errors and 𝑢 is
a non-negative random term representing inefficiency. A zero-mean normal distribution is
assumed for 𝑣 (3.14) while 𝑢 is assumed to have a truncated normal distribution with mean 𝜇
and variance 𝜎 (3.15) both of which are functions of 𝒛 ((3.16), (3.17)). The vector 𝒛 (which
includes one among the elements), represents exogenous factors hypothesized to influence
inefficiency, while 𝜹 and 𝝉 are the corresponding parameter vectors to be estimated. It is
assumed that 𝑣 and 𝑢 are independent of each other and of 𝐱 and 𝐰 .
The KGMHLBC and CFCFGH models differ in that the former allows the exogenous factors, 𝒛 ,
to influence inefficiency through the mean, 𝜇 , of the pre-truncated distribution of 𝑢 while the
latter accounts for heteroscedasticity through the variance of 𝑢 , that is, the exogenous factors are
allowed to influence inefficiency through the variance, 𝜎 , of the pre-truncated distribution of
𝑢 . Wang (2002) demonstrates that allowing the exogenous factors to influence inefficiency
through both the mean and the variance allows for a non-monotonic relationship between
inefficiency and exogenous factors. In addition, Kumbhakar & Lovell (2000) note that disregard

126

for heteroscedasticity results in biased estimates of the production frontier parameters and
technical ineffciency estimates.
It is important to acknowledge the limitation that the modelling approach used here does not
accommodate the possibility that some maize farms may be fully efficient. Rho & Schmidt (2015)
suggest that if some producing units are fully efficient, the traditional stochastic frontier model we
apply is mis specified and may result in biased production frontier and inefficiency estimates.
Although this study does not apply them, recent efforts to accommodate the possibility of some
units being fully efficient include Kumbhakar, Parmeter, & Tsionas (2013), Tran & Tsionas (2015)
and Rho & Schmidt (2015).
3.3.3.2 Estimation strategy
The SFA requires specifying a function for the production frontier, 𝑓(𝒙 , 𝒘 ; 𝜷, 𝜽). Many
production functions in the literature possess the quasi-concavity property suggested by producer
theory and 𝑓(𝒙 , 𝒘 ; 𝜷, 𝜽) can take any of those forms. However, the Cobb-Douglas and translog
production functions are two most commonly used specifications for the production frontier in
SFA studies. The Cobb-Douglas functional form has the advantage that it is easier to estimate
(because of fewer parameters) and the results are easier to interpret. However, it restricts output
elasticities to be constant and elasticity of substitution between inputs to unity. The translog
functional form is a generalization of the Cobb-Douglas functional form, and is more flexible
because it does not impose restrictions on the elasticities; it allows elasticity of substitution to vary
from point to point on the production function. However, the translog functional form requires
estimation of many parameters (because of interaction terms) and the results are more difficult to
interpret than in the Cob-Douglas. Because of its flexibility, we use the translog functional form,
127

and test its suitability against the Cobb-Douglas specification. The model we estimate, i.e.
equations (12a), (16) and (17), is specified below:
Frontier:
ln 𝑦 = 𝛽 + ∑ 𝛽 𝑙𝑛 𝑥

+ ∑ 𝛽 𝑙𝑛 𝑥

+∑ ∑

𝛽 𝑙𝑛 𝑥 𝑙𝑛(𝑥 )

(3.18)

+ ∑ 𝜃 𝑤 + 𝛼𝑇 + 𝜀
Inefficiency:
𝜇 =𝛿 +

𝛿 𝑧

𝜎 = 𝑒𝑥𝑝 (𝜏 + ∑ 𝜏 𝑧 )
In the model (3.18), i, j, and s index maize farm, input, and environmental variable (soil fertility
attribute or agronomic practice) respectively; 𝑦 is output; 𝒙 is the input vector; 𝒘 is the vector of
environmental variables (soil fertility conditions and agronomic practices); and 𝜷 (also containing
the intercept) and 𝜽 are parameter vectors associated with inputs and their interaction terms and
environmental variables, respectively. As explained earlier, Kenya’s maize production is quite
diverse with respect to environmental conditions. These conditions, such as soil fertility, are likely
to affect maize yield while at the same time conditioning farmers’ input use decisions. Failure to
control for such conditions may result in biased production frontier and inefficiency estimates. We
also include a dummy variable for year of the survey, 𝑇, to control for year differences and 𝛼 is its
associated parameter. 𝜀 = 𝑣 − 𝑢 is the composed error term. The vector 𝒛 in the inefficiency
equations represents exogenous factors that influence technical efficiency and (𝜹, 𝝉) are the
corresponding parameter vectors to estimate.

128

Model (3.18) is estimated in a single step using maximum likelihood (ML) procedure as outlined
earlier. The log-likelihood function is presented in Wang (2003) and technical efficiency estimates
are obtained using Battese & Coelli (1988) method (equation (11)). The model is specified with
and without including the environmental variables to understand the importance of controlling for
environmental production conditions in agricultural productivity and efficiency estimation.
3.3.4

Data sources and variables

3.3.4.1 Data sources
The study uses household- and plot-level survey dataset on maize production in Kenya described
in section 2.2.31. In addition, the study uses rainfall data obtained from the Climate Hazards group
Infrared Precipitation with Stations (CHIRPS) dataset, developed in support for the United States
Agency for International Development Famine Early Warning Systems Network (FEWS NET)

(Funk et al., 2015). The dataset comprises high resolution (0.05°), daily, 5-day mean, and
monthly precipitation that spans over 30 years (see Funk et al., 2015 for details). Household-level
GPS coordinates were used to extract from the dataset daily precipitation data for growing periods
of 2013/2014 and 2015/2016 main seasons of maize production. The daily precipitation data were
summed over the growing period for each season to generate data on amount of rainfall for that
season. All households within a sub-location had the same rainfall amount because they were
within the same 0.05° x 0.05° grid.

129

3.3.4.2 Variables
Output variable
The frontier part of the stochastic frontier model specifies the relationship between output and
inputs, soil fertility conditions and agronomic management practices. The output variable is maize
yield per acre. Because intercropping maize with other crops, especially common beans, is the
norm rather than an exception in Kenya, and because it is not possible to meaningfully apportion
inputs applied on a plot to maize production, it is necessary to adjust for intercropping in
calculating maize output on a plot. We create an output index for intercropped maize plots using
the following method proposed by Liu & Myers (2009):

𝑦 =

∑

,

(3.19)

where 𝑦 is the output index on plot 𝑖, 𝑦 the yield of crop 𝑗 on plot 𝑖 and 𝑃 the sub-county median
price of crop 𝑗, computed from producer prices reported by the sample households that sold crop
𝑗. Crop 1 is maize, so that 𝑃 is the price of maize.
Input variables
The inputs are inorganic fertilizers, maize seed, labor, and mechanization 3. Because maize farmers
often use a wide range of fertilizers and in varied amounts and because different fertilizers have
different amounts of macronutrients, it is reasonable to use amounts of macronutrients rather than
the quantity of fertilizer applied in the production frontier equation. Compound inorganic

3

While farmers also use organic materials such as manure and compost, we consider their application among
agronomic practices because farmers apply them with a long-term view of improving the fertility condition of the
soil rather than for production in a growing season.

130

fertilizers often have three macronutrients - nitrogen (N), phosphorus (P) and potassium (K). The
nutrient composition of the compound fertilizers is identified by percentages of nitrogen (N),
phosphate (P2O5) and potash (K2O) (Maguire, Mark, & Flowers, 2009), which, as a standard
practice internationally, are normally labeled on fertilizer packaging (bags). Such labeling helps
in determining the amount of the macronutrients in each quantity of fertilizer and is, therefore,
useful to decisions about appropriate fertilizers and quantities to apply. For example, the most
commonly used planting fertilizer for maize in Kenya is diammonium phosphate (DAP), which
has the composition (formula) (18:46:0). This means that any amount of DAP has 18% N, 46%
P2O5 and 0% K2O. To get the amount of each macronutrient applied on a plot, first we need to
know the percentage of phosphorus (P) in the available phosphate (P 2O5) and potassium (K) in the
water-soluble potash (K2O), then multiply these with the respective composition percentages and
eventually by the amount of fertilizer applied. P constitutes approximately 43.6% of P 2O5 while K
constitutes 83% of K2O. Continuing with the DAP example, it means that any amount of DAP
contains 18% N, about 20% (0.436*46) P and 0% (0.83*0) K. The remaining 62% is filler material.
Another fertilizer among many that farmers use is NPK (23:23:23). Any amount of this fertilizer
contains 23% N, 10% (0.436*23) P and 19% (0.83*23) K, and the remaining material is filler. We
compute the amount of the macronutrients from all the fertilizers that farmers reported for their
largest maize plots. Because of the fertilizer formulations, farmers apply the macronutrients in
fixed proportions when they use inorganic fertilizers. There is thus likely to be high collinearity in
the amount of N, P and K applied on a plot. Indeed, data shows a high correlation coefficient of
0.74 between N and P applied to maize plots. Therefore, we use the amount of N as a measure of
the amount of fertilizer applied to a plot. The use of N to represent fertilizer amount is reasonable
since nitrogen is the most important and often limiting nutrient in the soil.

131

Maize seed is measured as quantity (in kg) of seed planted per acre. Because not all farmers planted
improved seed varieties (i.e. hybrid or open pollinated variety (OPV)), we control for the effects
of improved seed variety using a dummy variable.
We measure labor as person-days per acre. It constitutes family labor by adult household members,
hired labor and any other labor that is neither family nor hired. Data on children’s labor is available
for only 2014 and is excluded from the analysis for that reason and because of lack of a standard
factor for converting it into adult-equivalent labor. As in Liu & Myers (2009), only labor on preharvest activities is included in the analysis because harvest and post-harvest activities are not
expected to have significant effects on maize yield.
The effect of mechanization is captured through a dummy variable for tractor and/or oxen use in
land preparation and/or planting, the two pre-harvest activities for which mechanized operation is
most common and data were collected.
Although we measure output and inputs in terms of amount per unit area, we also include plot size
explicitly in the frontier function so as not to impose constant returns to scale of the production
technology in land.
Soil fertility conditions
As explained earlier, a major contribution of this study is in controlling for the effects of soil
fertility conditions and agronomic practices in evaluating technical efficiency. This overcomes
potential omitted variable bias to which many studies that do not do so may be prone. Soil fertility
conditions affect the responsiveness of crops to inputs, especially fertilizers, and so it is important
to control for variability in these conditions in a production function estimation. Because of data

132

limitations, some studies have used geographical location dummies and average soil fertility
conditions at larger geographical scales (e.g. Liu & Myers, 2009; Sheahan, 2011). However, soil
fertility conditions can dramatically vary even within a very small geographical area, so using
average soil conditions for large geographical areas to represent soil fertility on cultivated plots
certainly does not accurately capture the variability in soil fertility across the plots. This study
overcomes that limitation by using plot-level measures of soil physical and chemical properties to
control for the effects of soil fertility status on maize yield.
Doran & Parkin (1994) propose a selection of physical, chemical and biological properties of soil
that can be useful as indicators for assessment of soil fertility. Based on the soil data available for
this study, we control for soil fertility using measured soil physical and chemical properties. Soil
texture, a physical property, is a measure of relative proportion (by weight) of clay, silt and sand
particles in a soil. Texture influences many soil properties, including drainage, water holding
capacity, erodibility, organic matter content and aeration. We measure soil texture in terms of sand
content (i.e. percentage sand). Soils higher in sand content have lower water holding capacity and
organic matter content, which is important for nutrient storage and availability to plants. We expect
maize yield to vary inversely with sand content in the soil.
Among the soil chemical properties proposed by Doran & Parkin (1994) as indicators that can be
used to assess soil fertility include total organic carbon, total nitrogen, soil pH, electrical
conductivity and extractable (or plant-available) macronutrients (P, K). Total carbon and total
nitrogen are indicators of soil fertility and potential crop productivity of the soil and are highly
correlated. We therefore use amount of total carbon in the soil, measured in percentage. Soil pH is
a measure of soil acidity, which affects biological and chemical activity in the soil. Lower pH
levels indicate greater acidity while higher values indicate alkalinity. Most crops require near
133

neutral levels of pH to grow best. Electrical conductivity of soil is a measure of the amount of
soluble (salt) ions in the soil. It varies depending on a host of soil properties, including texture,
water holding capacity, organic matter content and cation exchange capacity. Electrical
conductivity is thus strongly correlated with many soil properties, particularly texture (Grisso et
al, 2009), and, for this reason, we do not include it in the model. We include plant-available
phosphorus among the macronutrients because it is particularly sensitive to soil acidity.
Agronomic practices
Agronomic practices refer to farm management actions that farmers take to improve soil fertility,
enhance utilization of agricultural production resources and improve the environment. While such
practices are many and cut across different aspects of the farm, this study concentrates on the group
of practices often targeted at improving soil fertility to increase crop production. A dummy
variable for use of manure (animal or green) or compost on the plot is included to capture the
effects on maize yield of management practices that improve soil fertility. Addition of manure or
compost increases soil organic matter, which acts as a reservoir of nutrients in forms that are
available to plants and improves soil structure, maintains soil tilth and minimizes erosion (Bot &
Benites, 2005). Also included are dummy variables for use of crop residues and intercropping
maize with legumes (e.g. common beans, cowpeas, pigeon peas). Crop residues, upon
decomposition, add organic matter into the soil while legumes fix nitrogen in the soil hence
improves soil fertility.
To control for the effects of rainfall on maize yield, we include two variables; rainfall amount and
rainfall stress during the growing season. We measure stress as the fraction of 20-day periods that
received less than 40 mm of rain during the growing season. Rainfall stress is important because
134

it captures rainfall distribution over the growing period. Maize crop demand for water varies with
growth stages and it is important that at every stage there is sufficient supply of water for better
yield potential. We control for other differences in environmental, policy and market conditions
through county dummy variables. This is very important because since 2012 Kenya’s department
of agriculture, livestock and fisheries has been under the management and policy directives of
respective county governments, which operate independently in terms of policies and programmes
they prioritize and implement.
Exogenous factors influencing efficiency
Kagin, Taylor, & YĂşnez-Naude (2015) note that theory offers little guidance on what explains
technical efficiency and suggest that its analysis is primarily an empirical endeavor. However,
literature has established existence of statistical relationship between technical efficiency and a
range of contextual characteristics under which farms operate. We thus follow the existing
literature (e.g. Yang et al., 2016; Kumbhakar et al., 2014; Liu & Myers, 2009; Wang, 2002; Battese
& Coelli, 1995; Kumbhakar et al., 1991) in selecting the variables that go into the inefficiency part
of the stochastic frontier model. Factors that affect efficiency are primarily those that often
influence a farmer’s management capacity of the production process. It is possible that different
groups of farmers can use the same type and amounts of inputs and operate under the same
environmental conditions but produce different output levels. Such differences can be explained
by factors that affect how they manage their production process.
We use education to control for human capital and measure it as the education level of the plot
manager. Kumbhakar et al. (1991), Battese & Coelli (1995), Liu & Myers (2009) and Yang et al.,
(2016) found a positive relationship between education and technical efficiency. Also related to
135

human capital are skills acquired through experience in farming and so we include as a measure
of experience the number of years the plot manager’s household has been in farming. To control
for the effects of gender on technical efficiency, we include a dummy variable for female plot
manager. It is widely acknowledged that women relative to men are generally disadvantaged in
terms of agricultural productive resources, including human capital.
A farmer’s incentives to invest in long run productivity improvement can be affected by the
attributes of their land, including tenure security (Besley, 1995). Location of the cultivated plot
can also affect its management, with plots near homesteads receiving greater attention because
they are easily reachable and monitoring them should be more convenient. Research has also found
inverse farm size-productivity relationship and farm size-technical efficiency relationship (e.g.
Benjamin, 1995; Kagin, Taylor, & YĂşnez-Naude, 2016). These show that it is important to control
for the effects of farmers’ land attributes in inefficiency estimation. We use a dummy variable for
plot ownership to control for effects of tenure security. Two measures are used to control for the
effects of land size – household total landholding and the size of the maize plot. We also include
distance from the household’s dwelling to the maize plot.
Farmers’ perceptions and/or knowledge about the fertility condition of soil on their farms can
partly influence how they manage their agricultural production on the farm. However, such
perceptions may not necessarily reflect the actual soil fertility condition and thus may result in
management practices that mismatch the needs of the soil. If this happens, it may have undesirable
influence on technical efficiency. We control for the effects of deviation of farmers’ perceptions
about the fertility conditions of their soils from measured fertility as determined from soil test
results. Farmers were asked to rate the fertility of soil on their maize plots on a Likert scale of 1
(very infertile) to 4 (very fertile) based on their own perceptions. We reduce the scale to two
136

categories - infertile (combining 1 and 2) and fertile (combining 3 and 4) - because of very low
responses on the two extreme categories (1 and 4). From the soil test data, we use three chemical
properties of soil – total carbon (C), total nitrogen (N) and pH - and their threshold values as
obtained from recommendations by the Kenya government on critical levels of various soil
nutrients and pH for maize growth, to determine whether a soil is infertile or fertile. A plot is fertile
if the soil has total C≥ 2.7%, N≥ 0.2% and 5.5 ≤ pH ≤ 7.0. We compare a farmer’s rating (fertile
or infertile) against the rating using these threshold values, and construct a binary variable for
farmer perception deviation that takes the value of 1 if the farmer’s rating differs from the rating
using threshold values and 0 otherwise.
We control for the effects of extension services using distance to extension service provider. While
suitable variables to capture effects of extension services include number of visits to extension
service provider and whether a farmer received extension advice, such information is,
unfortunately, lacking in the data.
We exclude from the analysis maize plots with any of the following characteristics: 1) intercropped
plots for which the share of maize in total value of crops output is less than 20% because the focus
of the study is on maize; 2) less than 0.2 acres in size because of potential for measuring error in
computing rates of input use; 3) labor use rate of less than 3 or more than 3000 person-hours per
acre; and 4) maize yield less than 80kg/acre. Ultimately, the analysis uses 1102 pooled plot
observations in 621 households. Summary statistics of the variables is presented in Table 3.1.

137

Table 3.1: Variable description and summary statistics (N=1102)
Variable
Output
Maize yield index
Inputs
Nitrogen amount in fertilizer
applied
Maize seed
Pre-harvest labor
Improved maize seed
Mechanized land preparation
Agronomic practices
Manure/composed use
No. of crops
Maize intercrop with legume
Use of crop residue
Soil fertility conditions
Total organic carbon
Plant available phosphorus
Soil pH
Soil Texture
Main season rainfall
Moisture stress (Fraction of 20-day
periods with <40 mm of rainfall)
Inefficiency predictors
Education of plot manager
Gender of plot manager
Experience of household in farming
Farmer perception of plot fertility
Consistency of farmer perception
and measured plot fertility
Plot size
Household land holding
Distance to plot
Household owns plot
Distance to extension service

Unit of
measure

Mean

Kg/acre

SD

Min

1256.15 842.86

81.14

Median

Max

1089.32 7800.00

Kg/acre

19.57

16.48

0.00

16.26

109.00

Kg/acre
Personhours/acre
1=yes, 0=no
1=yes, 0=no

9.50
229.05

2.81
217.90

2.00
3.00

10.00
172.00

20.00
2484.00

0.94
0.54

0.24
0.50

0.00
0.00

1.00
1.00

1.00
1.00

1=yes, 0=no
Number
1=yes, 0=no
1=yes, 0=no

0.44
2.18
0.72
0.42

0.50
1.10
0.45
0.49

0.00
1.00
0.00
0.00

0.00
2.00
1.00
0.00

1.00
9.00
1.00
1.00

% (value)
Parts per
million (ppm)
Value
% sand
mm
(0-1)

2.12
17.77

0.86
18.90

0.22
0.20

2.00
12.40

4.93
168.00

5.62
50.00
843.72
0.13

8.03
88.10
3294.94
0.60

years
1=female,
0=male
years
1=fertile,
0=infertile
1=consistent,
0=inconsistent
acres
acres
Walking time
(minutes)
1=yes, 0=no
km

138

5.67
0.51
4.40
48.13
18.83
7.55
1015.36 692.67 263.08
0.21
0.16
0.00
7.97
0.35

3.88
0.48

0.00
0.00

8.00
0.00

17.00
1.00

27.51
0.59

16.07
0.49

1.00
0.00

25.00
1.00

87.00
1.00

0.47

0.50

0.00

0.00

1.00

1.15
3.20
4.75

2.08
5.40
10.65

0.20
0.00
0.00

0.50
1.50
2.00

30.00
49.00
180.00

0.89
5.75

0.31
4.98

0.00
0.10

1.00
5.00

1.00
40.00

3.4

Results

Model diagnostic test results are discussed first, followed by maximum likelihood estimation
results of the stochastic frontier production function, and, finally, technical efficiency estimates
and implications.
3.4.1

Model diagnostic test results

3.4.1.1 Likelihood ratio test of presence of technical inefficiency
We test for the presence of technical inefficiency using the likelihood ratio test procedure as
outlined in Kumbhakar, Wang, & Horncastle (2015). We compare the log likelihood ratio of OLS
regression against that of maximum likelihood estimation of the Wang (2002) stochastic frontier
model, in which both the pre-truncated mean and variance of technical inefficiency are functions
of exogenous variables. We conduct the test with and without environmental variables (soil
fertility conditions and agronomic practices) in the estimation equations, and use the flexible form
of the translog specification for the production frontier. The likelihood ratio (LR) statistic is
computed as -2[L(H0 )-L(H1 )]. L(H0 ) is the log-likelihood value of the OLS regression (restricted
model) while L(H1 ) is that of the stochastic frontier (unrestricted model). The degree of freedom
is the number of restrictions, which in our case is 22; i.e. 11 parameters in each of the pre-truncated
mean and variance of the inefficiency term. The LR statistic is compared to the critical values of
the mixed chi-square distribution. Results show that the LR statistic is 112.509 when
environmental variables are included and 116.167 when environmental variables are not included.
Both are larger than the critical value of 39.664 at 1% significance level. We thus reject the null
hypothesis of no technical inefficiency irrespective of whether environmental variables are
included in the estimation. The OLS regression results are in Table A3.1 in the Appendix.

139

3.4.1.2 Production frontier functional form test: translog vs Cobb-Douglas
We conduct a likelihood ratio test comparing the suitability of the translog functional form
(unrestricted model) against the Cobb-Douglas functional form (restricted model) for the
production frontier. We conduct the test separately for the model specification with and without
environmental variables. The number of restrictions is equal to the quadratic and interaction terms
in the translog functional form, which in this case is six. In the model specification with
environmental variables, the LR statistic of the test is 41.70 with p<0.001, while in the
specification without environmental variables the LR test statistic is 33.48 with p<0.001.
Therefore, the translog functional form fits the data better than the Cobb-Douglas irrespective of
whether environmental variables are included in the production frontier equation. Maximum
likelihood estimation results of the Cobb-Douglas production frontier (with and without
environmental variables) are in Table A3.2 in the Appendix. Subsequent tests and analyses proceed
with the flexible translog functional form specification for the production frontier.
3.4.1.3 Stochastic frontier model test
This study uses the Wang (2002) model in which both the pre-truncated mean and variance of
technical inefficiency are modelled as functions of exogenous variables, thus combining features
of the model of Kumbhakar, Ghosh, & McGuckin (1991), Huang & Liu (1994) and Battese &
Coelli (1995) (KGMHLBC) and that of Caudill & Ford (1993), Caudill, Ford, & Gropper (1995)
and Hadri (1999) (CFCFGH) models. For completeness, we test the suitability of this model
against the KGMHLBC and CFCFGH models. We also test its suitability against the truncatednormal model of Stevenson (1980) in which exogenous variables do not influence the distribution
of inefficiency. We use LR test where the Wang (2002) model is the unrestricted model and the
others the restricted models. We conduct the tests for the specifications with and without
140

environmental variables. Test results are shown in Table 3.2 (Maximum likelihood estimates of
the restricted models are presented in Table A3.3 in the Appendix). Clearly, the Wang (2002)
model best fits the data. Further, rejection of the Stevenson model in favor of the Wang (2002)
model affirms that inefficiency is affected by the exogenous factors as specified in the Wang
(2002) model. Subsequent analyses and results are based on the Wang (2002) model.
Table 3.2: Likelihood ratio test results of the Wang (2002) model against KGMHLBC, CFCFGH
and Stevenson models

Models

No. of
restrictions

With
environmental
variables

With environmental
variables

LR
statistic

pvalue

LR statistic

pvalue

5%
critical
value

Decision

Wang vs
KGMHLBC

10

33.73

0.0002

25.58

0.0044

18.307

Reject
KGMHLBC

Wang vs
CFCFGH

10

31.04

0.0006

28.68

0.0014

18.307

Reject
CFCFGH

Wang vs
Stevenson

20

97.89

0.0000

97.51

0.0000

31.410

Reject
Stevenson

3.4.2

Stochastic production frontier estimation results

The joint maximum likelihood estimates of the frontier part of model (3.18), specified in flexible
translog functional form, are presented in Table 3.3. The estimation was conducted with and
without environmental variables and both sets of results are presented. Likelihood ratio test shows
that the model specification with environmental variables fits the data better; the LR statistic (with
13 degrees of freedom) is 139.95 with p<0.001. Under the specification with environmental
variables, maize yield is positively and significantly correlated with fertilizer (N) and seed. The
positive and significant coefficients of the first and second order terms of the fertilizer variable
indicates that for the entire range of the data, increased use of nitrogen fertilizer would, on average,
141

have increasing effects on maize yield. Although weakly significant, the negative sign on the
second order term of fertilizer and labor indicate that the two inputs are substitutes. As expected,
maize yield is positively correlated with use of improved seed varieties. In addition, yield has a
positive association with mechanized land preparation. There is an inverse relationship between
maize yield and plot size, which is consistent with findings in majority of empirical studies on
farm size-productivity relationship (see Barrett, 1996; Barrett, Bellemare, & Hou, 2010; Carletto,
Savastano, & Zezza, 2013). The positive association of maize yield with the number of crops on a
plot indicates that on average, intercropped maize plots would have higher yield than monocropped
plots.
The coefficient estimates of the production frontier without environmental variables included are
qualitatively similar to those in the specification with environmental variables. The only major
differences are that in the specification without environmental variables, the coefficient on the first
order term for fertilizer is not statistically significant at any reasonable significance level, while
the coefficient on improved seed is strongly significant.
Regarding environmental variables, manure/compost use, higher total organic carbon in the soil
and soil pH are each associated with higher maize yield. Holding other things constant,
manure/compost use is associated with approximately 15% higher maize yield, on average, while
the coefficient on soil pH indicates that increasing the pH by 10% is associated with 1.7% increase
in maize yield, suggesting that the sample maize plots are acidic, on average. Indeed 39% of the
plots in the sample had soil pH values below the recommended minimum of 5.5, and 52% had
values below the sample average of 5.7. Therefore, high soil acidity on maize farms in Kenya is
an issue that needs to be addressed.

142

Table 3.3: Stochastic production frontier estimates
Response variable: Log of maize yield
Explanatory Variables
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
lnN x lnN
lnseed x lnseed
lnlabour x lnlabour
lnN x lnseed
lnN x lnlabour
lnseed x lnlabour
Improved seed (1=yes)
Mechanized land preparation (1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant
𝜎
Log-likelihood
Observations

With environmental
variables
Coefficient

Std. error

0.249*
0.814**
-0.0549
0.128***
-0.221
0.0169
-0.145
-0.0636*
0.0944
0.127*
0.147***
-0.149***
0.117***
0.177***
0.142***
-0.0711
0.0367
0.0460*
-0.00162
0.171***
-0.00181
0.0000409
-0.217
-0.137**
-0.341***
-0.697***
-0.377***
3.933***
-1.623***
-863.1077
1102

0.149
0.384
0.173
0.0250
0.186
0.0229
0.0991
0.0366
0.118
0.0762
0.0511
0.0285
0.0203
0.0555
0.0363
0.0497
0.0351
0.0276
0.00101
0.0357
0.00159
0.0000369
0.136
0.0585
0.0717
0.0868
0.0833
0.732
0.101

Without environmental
variables
Std.
Coefficient
error
0.178
0.840**
0.0271
0.145***
-0.104
0.00820
-0.126
-0.0760*
0.0409
0.292***
0.252***
-0.120***
0.0825***
0.282***

0.162
0.415
0.184
0.0261
0.199
0.0234
0.105
0.0403
0.126
0.0793
0.0478
0.0335
0.0174
0.0369

4.310***
-1.563***
-933.0820
1102

0.771
0.132

*

p < 0.10, ** p < 0.05, *** p < 0.01
Note: aUasin Gishu is the comparison county

Coefficients on the other environmental variables – plant available phosphorus, soil texture (sand
content), rainfall and moisture stress – are not statistically significant although all but plant
available phosphorus have expected signs. The unexpected sign of the coefficient on plant
143

available phosphorus is similar to results found by Ekbom et al (2013) in their study of effects of
soil capital on maize productivity in central Kenya. They attribute their result in part to high soil
acidity, which, as explained earlier, has the effect of causing phosphorus to form insoluble
compounds, which makes it unavailable to plants. In highly acidic soils, tests may indicate high
levels of phosphorus but phosphorus deficiency in plants may occur and reduce output.
The input coefficients in Table 3.3 are not quite informative by themselves about the relationship
between maize yield and the inputs because the interaction terms confound such relationships. We,
therefore, computed output elasticities of the inputs, which have straightforward and meaningful
interpretation. The elasticity estimates were computed for each plot and the means are presented
in Table 3.4. Output elasticity of N is particularly of interest, since fertilizer often seems to be the
most limiting input in maize production and which has drawn much interest among policy makers
and researchers in Kenya and the region. The average elasticity of N is 0.262 when environmental
variables are controlled for. This estimate is statistically larger than the 0.226 average estimate
without controlling for environmental variables (a paired sample t-test of difference in mean has
t= 59.815). In both model specifications, the elasticities vary considerably across the counties, with
Uasin Gishu having the highest and Machakos the lowest estimates. The elasticity estimates for N
compare well with those obtained by other researchers using data from Kenya. For example,
Mghenyi (2015) found output elasticity of N of 0.18 while Liu & Myers (2009) found it to be
0.224 among hybrid maize seed users and 0.209 among local seed users. These studies, however,
did not control for environmental variables.

144

Table 3.4: Maize output elasticity with respect to inputs (mean)
With environmental variables
Fertilizer
Seed
Labor
(N)

Without environmental variables
Fertilizer
Seed
Labor
(N)

Uasin Gishu

0.317
(0.00887)

0.294
(0.00706)

0.0336
(0.00262)

0.293
(0.0101)

0.504
(0.00484)

-0.00154
(0.00260)

Trans Nzoia

0.290
(0.00891)

0.330
(0.00661)

0.0463
(0.00243)

0.260
(0.0101)

0.521
(0.00482)

0.00594
(0.00265)

Kakamega

0.295
(0.00765)

0.362
(0.00688)

0.0431
(0.00210)

0.263
(0.00868)

0.536
(0.00473)

0.00425
(0.00228)

Kisii

0.241
(0.00678)

0.421
(0.00684)

0.0593
(0.00197)

0.200
(0.00767)

0.572
(0.00451)

0.0198
(0.00202)

Machakos

0.174
(0.00839)

0.470
(0.00781)

0.0745
(0.00223)

0.123
(0.00952)

0.611
(0.00529)

0.0399
(0.00251)

Overall

0.262
(0.00401)

0.376
(0.00372)

0.0517
(0.00112)

0.226
(0.00458)

0.550
(0.00248)

0.0141
(0.00119)

County

Standard errors in parentheses
Note: Elasticities are computed at plot level

The average elasticities of seed are 0.376 and 0.550, respectively, with and without controlling for
environmental variables, and vary across the counties, with the estimates highest in Machakos and
lowest in Uasin Gishu, an exactly opposite pattern to the one for the elasticity of N. Liu & Myers
(2009) estimated elasticities of seed to be 0.336 and 0.293 among hybrid and local seed users,
respectively, while, surprisingly, Mghenyi (2015) found a negative elasticity of -0.3 for seed.
Output elasticity of labor averages 0.0517 and 0.0141 for the specification with and without
environmental variables, respectively, and differs across counties. These estimates are quite
different from those obtained by Liu & Myers (2009) (0.177 and 0.300 among hybrid and local
seed users, respectively) but are close to Mghenyi's (2015) estimate (0.04).
The elasticity estimates point to the importance of controlling for environmental variables in
agricultural production function estimation. Controlling for soil fertility conditions is especially
145

important for accurate estimation of the effects of fertilizer on yield. This point will be clearer
below when we discuss technical efficiency estimates and, subsequently, marginal physical
product of the inputs.
3.4.3

Technical efficiency estimation results

The main aim of this study is to estimate technical efficiency of maize farmers and identify factors
responsible for variation of technical efficiency across farms, and to understand how important it
is to account for environmental conditions in the analysis. We first present results on the marginal
effects of exogenous factors on technical inefficiency from the joint maximum likelihood
estimation of model (3.18). Next, we discuss technical efficiency estimates and how these vary
across regions (counties), and the difference in the estimates when we do and not account for
environmental conditions. Marginal products of the variable inputs are also computed and
compared across regions to understand regional variations in potential output response to the
variable input use.
3.4.3.1 Determinants of technical (in)efficiency
Marginal effects of exogenous variables on the unconditional mean and variance of inefficiency
are presented in Table 3.5. The marginal effect on unconditional mean measures how expected
inefficiency changes when the exogenous variable in question increases, while marginal effect on
unconditional variance measures the effect of an increase in the exogenous variable on uncertainty
of technical inefficiency (Wang, 2002; Kumbhakar et al., 2015). It is important to note that for
continuous variables, a negative sign of the marginal effect on expected inefficiency implies an
increasing effect on the level of technical efficiency for a positive change in the variable, and vice

146

versa. For binary variables, a negative sign of the marginal effect on the expected inefficiency
implies that technical efficiency is, on average, higher compared to the base (omitted) category.
Table 3.5: Marginal effects of exogenous determinants of technical inefficiency (sample means)

Marginal effect

Bootstrap
std. error

Without environmental
variables
Marginal
Bootstrap
effect
std. error

-0.0213***
-0.0546***
-0.191***

0.000340
0.00592
0.00716

-0.0144***
-0.0221***
-0.236***

0.000170
0.00698
0.00295

-0.0286***

0.00643

-0.0502***

0.00322

-0.0478***
0.000746***
-0.00240***
0.328***
0.000207*
-0.00193***

0.000953
0.000190
0.000151
0.0171
0.000120
0.000188

-0.0812***
-0.00659***
-0.00220***
0.0651***
0.00154***
-0.00137***

0.00193
0.000266
0.0000797
0.00253
0.000130
0.000138

-0.0103***
-0.0636***
-0.144***
-0.0523***

0.000223
0.00283
0.00490
0.00272

-0.00630***
-0.0754***
-0.144***
-0.0554***

0.0000938
0.00242
0.00275
0.00143

-0.0218***
-0.000672***
-0.00216***
0.0849***
-0.000572***
0.00000600

0.000444
0.0000624
0.0000841
0.00360
0.0000424
0.0000500

-0.0256***
-0.00581***
-0.00186***
0.0112***
-0.000379***
0.000549***

0.000362
0.000137
0.0000429
0.000416
0.0000305
0.0000344

With environmental variables
Variables
Mean function (𝜇)
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with
soil test (1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Variance function (𝜎 )
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with
soil test (1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Observations

1102

1102

*

p < 0.10, ** p < 0.05, *** p < 0.01
Note: A negative sign of the marginal

effect on the mean function implies a contribution to
efficiency while a positive sign is a contribution to inefficiency for a positive change in the
variable.
We observe qualitatively similar (in terms of signs) marginal effects of the exogenous variables
between the model specification with and without environmental variables. The only exception is
147

in the landholding variable in the mean function for which the effects are positive in the
specification with but negative in that without environmental variables. Quantitatively, however,
the marginal effects are quite different between the two model specifications but with no distinct
pattern, although the magnitudes of the effects are generally small in both specifications. With
respect to the unconditional mean and variance in each of the two model specifications, the signs
of the marginal effects of nearly all the exogenous variables are the same. We focus the discussion
on the marginal effects in the model specification with environmental variables.
On average, both the level and uncertainty of technical inefficiency tend to reduce with increased
education level of plot manager, plot size and distance to plot, and when plot manager is female,
while they tend to be higher when the plot is owned (rather than rented). Increased farming
experience has a decreasing effect on the level of technical inefficiency. Increased landholding and
distance to extension service provider have increasing effects on the level but decreasing effects
on uncertainty of technical inefficiency. These effects are largely as expected, except for the effects
of gender of plot manager, distance to plot, plot ownership and landholding. The unexpected effect
of distance to plot and plot ownership may reflect management efforts farmers put on rented plots,
which the data show are located on average three times farther from the homestead than are owned
plots. Paying rent on a plot may incentivize a farmer to apply management practices for better crop
yield to increase returns to investment. The effects of gender of plot manager contradicts findings
by other studies that have shown that female-headed households are more technically inefficient
than their male-headed counterparts (e.g. Liu & Myers, 2009).
Concerning farmer perception about soil fertility status, the first notable result is that farmers that
view their plots as fertile have, on average, 19% lower technical inefficiency than do their
counterparts that consider their plots infertile. They also have less uncertainty of inefficiency. The
148

second is that those whose perceptions of the fertility status of their plots are consistent with that
determined from soil test have 2.9% lower technical inefficiency than do those with inconsistent
view and they also have less uncertainty of inefficiency, although these are only significant at 10%
level. These effects indicate the importance of farmer perceptions about the fertility conditions of
their soils and underscores the need for farmer access to information that can enhance their
knowledge about correct soil fertility conditions on their farms.
3.4.3.2 Technical efficiency estimates
Technical efficiency estimates were computed using Battese & Coelli (1988) method:
𝐸(𝑒𝑥𝑝(−𝑢 )|𝜀 ). Figure 3.4 shows kernel densities of technical efficiency for model specification
with and without environmental variables. Clearly, technical efficiency estimates based on the
model specification with environmental variables are higher compared to those based on the
specification without environmental variables. The mode of technical efficiency for the
specification with environmental variables is around 0.83 while it is around 0.79 for the
specification without environmental variables. The distribution of efficiency estimates is leftskewed in both specifications. Descriptive statistics in Table 3.6 show that technical efficiency
ranges from 0.12 to 0.99, with the mean at 0.76, for the specification with environmental variables,
while without environmental variables the estimates range from 0.19 to 0.98, with mean at 0.70.
The difference in the two means is statistically significant (t=9.021, p<0.001). This is evidence
that failure to account for the effects of environmental variables in SFA underestimates technical
efficiency, a finding that is consistent with Sherlund et al (2002) in a study of technical efficiency
in rice production in Ivory Coast.

149

2
0

1

Density

3

4

Figure 3.4: Kernel density of technical efficiency estimates

.2

.4

.6

Technical efficiency
With EV

.8

1

Without EV

Table 3.6: Technical efficiency estimates (mean)
County
Uasin Gishu
Trans Nzoia
Kakamega
Kisii
Machakos
Overall

With environmental variables
Mean Median Minimum Maximum
0.751 0.798
0.123
0.985
0.766 0.783
0.305
0.983
0.750 0.785
0.248
0.984
0.740 0.769
0.303
0.952
0.747 0.797
0.169
0.917
0.751 0.789
0.123
0.985

Without environmental variables
Mean Median Minimum Maximum
0.755 0.784
0.217
0.978
0.738 0.754
0.314
0.981
0.669 0.707
0.218
0.893
0.629 0.659
0.191
0.895
0.683 0.727
0.205
0.892
0.696 0.730
0.191
0.981

Note: Technical efficiency estimates are computed using Battese & Coelli (1988) method: 𝐸(𝑒𝑥𝑝(−𝑢 )|𝜀 )

While the pattern of the difference in technical efficiency estimates between the two model
specifications remains qualitatively the same within each county, except for Uasin Gishu where
there appears to be hardly any difference, it is notable that controlling for environmental variables
makes significant difference in the average technical efficiency estimates in Kisii, Kakamega and
Machakos. Wald test shows that differences in average technical efficiency across the five counties
is statistically significant only in the specification without environmental variables, suggesting that
after controlling for environmental variables, technical efficiency in maize production is pretty
150

much the same across different regions of Kenya. These results affirm that failure to account for
differences in environmental conditions can give misleading results on the level of technical
efficiency and its variation across regions.
Using equation (4) and estimated technical efficiency levels, we computed frontier maize yield
and generated inefficiency-induced foregone output. Results show that inefficiency-induced maize
yield loss in model specifications with and without environmental variables is 0.34 and 0.45 tonnes
per acre, respectively (Table 3.7). Because technical efficiency is underestimated in the
specification without environmental variables, the computed foregone yield appears to be higher.
Nevertheless, the yield loss of one third of a tonne/acre is substantial, given that the average
reported (actual) yield is just 1.3 tonnes/acre. Across the counties, yield losses due to inefficiency
are highest in Uasin Gishu and Trans Nzoia and lowest in Kisii (in the model specification with
environmental variables).
Table 3.7: Actual, frontier and foregone output (mean)
County
Uasin
Gishu
Trans
Nzoia
Kakamega
Kisii
Machakos
Overall

Actual
output
(kg/acre)

With environmental variables
Frontier output Foregone output
(kg/acre)
(kg/acre)

Without environmental variables
Frontier output Foregone output
(kg/acre)
(kg/acre)

1497

1921

424

1912

416

1563

1985

423

2042

480

1213
846
1128
1256

1548
1087
1415
1599

336
241
287
343

1728
1272
1525
1702

515
425
398
446

Note: Foregone output computed at the mean of actual and frontier output

Results on average marginal product (MP) of fertilizer (N), seed and labor are presented in Table
3.8. The marginal products are computed for each plot from the elasticity estimates. Overall, the
MP of N, seed and labor are all positive, on average, suggesting that at the current average
151

application rates, farmers would realize positive maize yield returns if they increased their rate of
use of each of the inputs. There is significant variation in the average MP of inputs between the
two model specifications. Focusing on the specification with environmental variables, the MP of
fertilizer is 18.63 kg/acre, on average, and varies considerably across the counties. The MP of N
is particularly high in Trans Nzoia and Uasin Gishu but below the total average in Kisii and
Kakamega. The result on the MP of N is pretty close to those found by Mghenyi (2015) (14.81
kg/kg) and Marenya & Barrett (2009) (17.64 kg/kg). It is worth noting that Marenya & Barrett
(2009) controlled for some soil properties and other environmental production conditions while
Mghenyi (2015) did not. It is interesting to note that Mghenyi's (2015) estimate is only slightly
larger than our estimate in the specification without environmental variables (13.01 kg/kg).
Therefore, the fact that the estimate by Mghenyi (2015) is much lower than ours, which is larger
than Marenya & Barrett (2009)’s estimate, affirms that omission of environmental variables from
agricultural productivity analysis can lead to biased results.
The MP of seed averages 44.9 kg/kg while that of labor is quite low (0.15 kg/person-hour). These
also vary across the counties, with Machakos having the highest MP of seed and Kisii the lowest.
Trans Nzoia has the highest MP of labor while Uasin Gishu has the lowest and is negative. Our
estimate of the MP of seed is incomparable to Mghenyi (2015) who found a large negative estimate
(-49.70 kg/person-hour) (Marenya & Barrett (2009) did not include seed among the inputs in their
estimation). However, our estimate of MP of labor, although above that of Marenya & Barrett 's
(2009) estimate of 0.08 kg/man-day, is equally quite low.

152

Table 3.8: Marginal product of inputs
County

With environmental variables
Labor
Fertilizer
Seed
(kg/person(N) (kg/kg) (kg/kg)
hour)

Without environmental variables
Labor
Fertilizer
Seed
(kg/person(N) (kg/kg) (kg/kg)
hour)

Uasin Gishu

20.11
(2.237)

39.14
(1.417)

-0.356
(0.212)

12.97
(4.994)

62.36
(1.363)

-1.478
(0.319)

Trans Nzoia

21.65
(0.569)

46.36
(1.480)

0.365
(0.0207)

16.92
(0.596)

68.87
(1.507)

-0.134
(0.0331)

Kakamega

17.02
(0.376)

44.11
(1.443)

0.242
(0.0150)

15.91
(0.336)

70.26
(1.790)

-0.0501
(0.0180)

Kisii

14.55
(0.404)

37.51
(1.144)

0.177
(0.00985)

11.90
(0.514)

57.97
(1.513)

0.0706
(0.0106)

Machakos

19.57
(1.885)

56.48
(2.081)

0.318
(0.0521)

7.417
(4.195)

72.12
(1.974)

0.177
(0.0551)

Overall

18.63
(0.619)

44.88
(0.727)

0.150
(0.0450)

13.01
(1.339)

66.46
(0.756)

-0.284
(0.0681)

Standard errors in parentheses
3.5

Conclusion and implications

Sustainable agricultural productivity growth is essential to broad-based economic progress in
agriculture-based economies. This is particularly relevant in many sub-Saharan African countries
where agriculture plays a major role as livelihood source for majority of the population. Yet,
agricultural productivity growth in these countries is stymied by, among other things, widespread
soil infertility mainly because of improper land management practices.
In Kenya, soil infertility combined with agronomic practices that may not effectively respond to
fertility needs of the soil is manifest in the stagnation of aggregate maize yield over time despite
increasing mineral fertilizer application and planting of improved maize varieties. Because there
is virtually no land for expansion to increase agricultural production, the onus is on increasing

153

agricultural productivity through technological change, increased efficiency in use of existing
technology and productive resources or both.
This study focused on technical efficiency in maize production in Kenya. The first objective was
to understand the level of technical efficiency in smallholder maize farming and its variation across
farms, and the factors that are responsible for that variation with a focus on farmers’ subjective
soil fertility perception. The second was to evaluate the importance of controlling for
environmental production conditions (soil conditions and agronomic practices) in agricultural
productivity and technical efficiency estimation. The study applied the stochastic production
frontier approach due to Meeusen & van Den Broeck (1977) and Aigner et al (1977).
Three key results have emerged from the study. First, maize farmers in Kenya are generally
technically inefficient and the level of technical efficiency varies across regions. The mean of
technical efficiency is 0.75 when environmental variables are controlled for and 0.70 without
controlling for them in the model estimation. On average, the inefficiency-induced foregone maize
yield is 0.34 tonnes/acre when environmental variables are controlled for and 0.45 tonnes/acre
without controlling for environmental variables.

These forgone yield levels are significant

considering that the reported (actual) yield averaged only 1.3 tonnes/acre. Secondly, estimation of
technical efficiency without controlling for environmental production conditions in the model
results in underestimated technical efficiency levels, as evident in the dissimilar results between
the model specifications with and without environmental variables. Lastly, results have shown that
farmers that view their plots as fertile have, on average, 19% lower technical inefficiency than do
those that consider their plots infertile. In addition, farmers whose perceptions about the fertility
status of their plots are consistent with measured soil fertility have 2.9% lower technical
inefficiency, on average, than do those with perceptions that do not match measured soil fertility.
154

We conclude that smallholder farmers are technically inefficient and inefficiency varies across
regions. Therefore, different regions may require different strategies to improve farmers’
management of inputs to raise maize productivity. The result that farmers’ perceptions about soil
fertility explains variation in technical efficiency underscores the importance of farmers’ access to
information that can enhance their knowledge and understanding about the correct soil fertility
conditions on their farms. Such information would help them make better choices about
appropriate inputs and agronomic management practices to apply. Finally, failure to account for
environmental production conditions in agricultural productivity analysis may produce results that
are less accurate and unreliable.

155

APPENDIX

156

Table A3.1: OLS regression results
Response variable: Log of maize
yield

*

With environmental
variables
Coefficient Std. error

Without environmental
variables
Coefficient Std. error

0.229
0.639
-0.0599
0.154***
-0.102
0.0250
-0.140
-0.0745*
0.0727
0.189**

0.160
0.417
0.186
0.0263
0.200
0.0251
0.107
0.0387
0.125
0.0785

0.162
0.721*
-0.0645
0.141***
-0.140
0.0281
-0.0968
-0.0697*
0.0660
0.217***

0.162
0.423
0.189
0.0265
0.203
0.0255
0.109
0.0392
0.127
0.0797

Explanatory Variables
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
lnN x lnN
lnseed x lnseed
lnlabour x lnlabour
lnN x lnseed
lnN x lnlabour
lnseed x lnlabour
Improved seed (1=yes)
Mechanized land preparation
(1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant

0.199***

0.0540

0.198***

0.0549

-0.106***
0.117***
0.209***
0.179***
-0.0488
0.000824
0.0277
-0.00151
0.172***
-0.00226
0.0000648*
-0.209
-0.0738
-0.304***
-0.602***
-0.275***
3.596***

0.0267
0.0213
0.0585
0.0384
0.0523
0.0375
0.0289
0.00107
0.0376
0.00169
0.0000390
0.147
0.0616
0.0758
0.0911
0.0878
0.791

-0.117***
0.109***
0.274***

0.0269
0.0182
0.0364

-0.0748
-0.351***
-0.558***
-0.342***
4.538***

0.0588
0.06 30
0.0789
0.0776
0.763

Adjusted R-squared
Observations

0.385
1102

0.359
1102

p < 0.10, ** p < 0.05, *** p < 0.01

157

Table A3.2: Maximum likelihood results of stochastic frontier model with Cobb-Douglas
specification
Response variable: Log of maize yield
Frontier
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
Improved seed (1=yes)
Mechanized land preparation (1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant
𝜎
Inefficiency
Mean function (𝜇)
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with soil test
(1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Constant
*

With environmental
variables
Coef.
Std. error

Without environmental
variables
Coef.
Std. error

0.203***
0.0192
***
0.470
0.0570
0.0384
0.0234
0.106
0.0762
0.143***
0.0523
-0.156***
0.0298
0.110***
0.0209
***
0.209
0.0553
0.145***
0.0374
-0.0565
0.0506
0.0559
0.0360
0.0389
0.0296
-0.00164
0.00102
0.155***
0.0365
-0.00193
0.00164
0.0000426 0.0000382
-0.191
0.138
-0.109*
0.0593
-0.344***
0.0716
***
-0.725
0.0881
-0.372***
0.0852
4.363***
0.314
-1.624***
0.110

0.172***
0.510***
0.0419*
0.147*
0.133**
-0.189***
0.0970***
0.293***

0.0186
0.0575
0.0232
0.0786
0.0532
0.0320
0.0181
0.0345

-0.0890
-0.380***
-0.675***
-0.424***
5.194***
-1.559***

0.0568
0.0604
0.0765
0.0767
0.204
0.123

-0.0471**
-0.0726
-1.430**

0.0234
0.182
0.716

-0.0462**
-0.170
-0.733***

0.0183
0.123
0.185

-0.631**

0.280

-0.455***

0.173

-0.146**
0.0418*
-0.00418
-0.442
0.00498
0.00284
1.193***

0.0659
0.0215
0.00802
0.269
0.0146
0.00772
0.435

-0.276***
0.0365***
-0.000623
-0.585**
0.0142*
-0.00164
1.476***

0.0935
0.0130
0.00480
0.260
0.00750
0.00551
0.286

p < 0.10, ** p < 0.05, *** p < 0.01

158

Table A3.2 (cont’d)
Response variable: Log of maize yield

*

With environmental
variables
Coef.
Std. error

Variance function (𝜎 )
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with soil test
(1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Constant
Log-likelihood
Observations

-883.959
1102

Without environmental
variables
Coef.
Std. error

-0.0204
-0.103
0.560*

0.0300
0.203
0.301

-0.00747
0.117
-0.0173

0.0321
0.214
0.249

0.617***

0.236

0.538*

0.280

0.0570
-0.142***
0.00794
1.133**
-0.000173
-0.00666
-1.700**

0.0826
0.0527
0.00810
0.472
0.0182
0.00853
0.809

0.167
-0.157**
0.0115
2.666
-0.0167
-0.00313
-3.382*

0.108
0.0798
0.00988
1.739
0.0178
0.00828
1.970

p < 0.10, ** p < 0.05, *** p < 0.01

159

-905.144
1102

Table A3.3: Maximum likelihood results of stochastic frontier model of KMHLBC
Response variable: Log of maize yield
Frontier
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
lnN x lnN
lnseed x lnseed
lnlabour x lnlabour
lnN x lnseed
lnN x lnlabour
lnseed x lnlabour
Improved seed (1=yes)
Mechanized land preparation (1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant
𝜎
Inefficiency
Mean function (𝜇)
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with soil test
(1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Constant
Log-likelihood
Observations
*

With EV
Coef.
Std. error

W/o EV
Coef.
Std. error

0.228
0.795**
-0.0752
0.133***
-0.174
0.0215
-0.162
-0.0507
0.0740
0.137
0.149***
-0.148**
0.118***
0.191***
0.144***
-0.0630
0.0307
0.0302
-0.00186*
0.164***
-0.00191
0.0000419
-0.222
-0.119**
-0.325***
-0.656***
-0.346***
4.155***
-1.730***

0.179
0.398
0.184
0.0267
0.192
0.0235
0.101
0.0459
0.122
0.0835
0.0515
0.0682
0.0209
0.0601
0.0404
0.0568
0.0369
0.0288
0.00103
0.0364
0.00163
0.0000380
0.147
0.0599
0.0734
0.0887
0.0995
0.947
0.405

0.0819
0.870**
-0.0424
0.127***
-0.227
0.0130
-0.0971
-0.0282
0.0590
0.166**
0.182***
-0.310***
0.115***
0.277***

0.159
0.414
0.182
0.0256
0.200
0.0239
0.107
0.0375
0.121
0.0767
0.0571
0.0686
0.0178
0.0353

-0.0862
-0.362***
-0.644***
-0.453***
5.617***
-2.276***

0.0563
0.0611
0.07 72
0.0774
0.761
0.363

-0.0628
-0.102
-0.795
-0.221

0.130
0.318
1.929
0.708

-0.0228***
-0.00623
-0.281***
-0.0681

0.00596
0.0417
0.0584
0.0531

-0.188
0.00829
0.0000886
0.184
0.00226
-0.00474
0.884*
-879.972
1102

0.316
0.0334
0.00859
0.319
0.0115
0.0110
0.463

-0.167***
-0.00135
-0.000753
0.0463
0.00291
-0.00214
1.600***
-901.194
1102

0.0476
0.00556
0.00203
0.0659
0.00397
0.00141
0.287

p < 0.10, ** p < 0.05, *** p < 0.01

160

Table A3.4: Maximum likelihood results of various stochastic frontier model of CFCFGH
Response variable: Log of maize yield
Frontier
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
lnN x lnN
lnseed x lnseed
lnlabour x lnlabour
lnN x lnseed
lnN x lnlabour
lnseed x lnlabour
Improved seed (1=yes)
Mechanized land preparation (1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant
𝜎
Inefficiency
Variance function (𝜎 )
Plot manager education (yrs)
Plot manager is female (1=yes)
Soil fertility perception (1=fertile)
Farmer perception consistent with soil test
(1=yes)
Plot size (acres)
HH landholding (acres)
Walking time to plot (mins)
Plot owned (1=yes)
Distance to extension (km)
Farming experience (yrs)
Constant
Log-likelihood
Observations
*

With EV
Coef.
Std. error

W/o EV
Coef.
Std. error

0.233
0.785**
-0.0717
0.132***
-0.179
0.0211
-0.154
-0.0555
0.0800
0.150*
0.151***
-0.154***
0.117***
0.189***
0.145***
-0.0622
0.0380
0.0281
-0.00186*
0.167***
-0.00205
0.0000439
-0.226
-0.116**
-0.322***
-0.660***
-0.337***
4.091***
-1.693***

0.151
0.393
0.176
0.0251
0.190
0.0230
0.101
0.0372
0.120
0.0767
0.0513
0.0291
0.0207
0.0557
0.0368
0.0501
0.0356
0.0275
0.00101
0.0362
0.00162
0.0000377
0.138
0.0585
0.0719
0.0880
0.0839
0.748
0.117

0.170
0.924**
-0.0659
0.120***
-0.229
0.0213
-0.125
-0.0456
0.0661
0.174**
0.144***
-0.168***
0.104***
0.267***

0.152
0.400
0.179
0.0253
0.194
0.0233
0.102
0.0377
0.122
0.0782
0.0523
0.0291
0.0178
0.0348

-0.101*
-0.368***
-0.623***
-0.404***
4.920***
-1.666***

0.0558
0.0606
0.0758
0.0754
0.724
0.116

-0.0751***
-0.177
-0.830***
-0.122

0.0214
0.145
0.220
0.179

-0.0711***
-0.113
-0.905***
-0.174

0.0206
0.141
0.220
0.179

-0.221**
0.000220
0.00188
0.301
0.00357
-0.00460
0.200
-878.626
1102

0.0979
0.0169
0.00708
0.234
0.0136
0.00469
0.389

-0.230**
-0.00153
0.00326
0.198
0.00799
-0.00521
0.364
-902.744
1102

0.0988
0.0167
0.00692
0.222
0.0133
0.00466
0.376

p < 0.10, ** p < 0.05, *** p < 0.01

161

Table A3.5: Maximum likelihood results of various stochastic frontier model of Stevenson
(1980)
Response variable: Log of maize
yield
Frontier
Log of fertilizer (lnN)
Log of seed (lnseed)
Log of labor (lnlabour)
lnN x lnN
lnseed x lnseed
lnlabour x lnlabour
lnN x lnseed
lnN x lnlabour
lnseed x lnlabour
Improved seed (1=yes)
Mechanized land preparation
(1=yes)
Log of plot size
No. of crops on plot
Year dummy (1=2016)
Manure/compost use (1=yes)
Maize-legume intercrop (1=yes)
Crops residue use (1=yes)
Total organic carbon
Phosphorus
Soil pH
Sand content
Rainfall
Moisture stress
Transnzoia county dummya
Kakamega county dummya
Kisii county dummya
Machakos county dummya
Constant
𝜎
Log-likelihood
Observations
*

With EV
Coef.
Std. error

W/o EV
Coef.
Std. error

0.167
0.834**
-0.110
0.147***
-0.186
0.0261
-0.154
-0.0433
0.0728
0.160**
0.179***

0.156
0.406
0.183
0.0256
0.193
0.0242
0.102
0.0394
0.124
0.0770
0.0516

0.0984
1.004**
-0.104
0.134***
-0.239
0.0302
-0.118
-0.0352
0.0477
0.183**
0.168***

0.158
0.410
0.184
0.0258
0.196
0.0244
0.104
0.0404
0.126
0.0790
0.0525

-0.0981***
0.118***
0.190***
0.166***
-0.0696
0.0205
0.0385
-0.00147
0.165***
-0.00159
0.0000504
-0.224
-0.0962
-0.307***
-0.586***
-0.265***
4.167***

0.0256
0.0208
0.0568
0.0375
0.0513
0.0365
0.0282
0.00105
0.0367
0.00165
0.0000381
0.142
0.0599
0.0733
0.0881
0.0843
0.781

-0.107***
0.104***
0.255***

0.0257
0.0179
0.0351

-0.0916
-0.362***
-0.568***
-0.332***
4.963***

0.0570
0.0616
0.0762
0.0755
0.754

-1.728***
-912.054
1102

0.136

-1.649***
-937.162
1102

0.142

p < 0.10, ** p < 0.05, *** p < 0.01

162

REFERENCES

163

REFERENCES

Abdulai, A., & Tietje, H. (2007). Estimating technical efficiency under unobserved heterogeneity
with stochastic frontier models: application to northern German dairy farms. European
Review of Agricultural Economics, 34(3), 393–416.
Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic
frontier production function models. Journal of Econometrics, 6, 21–37.
Ali, M., & Byerlee, D. (1991). Economic efficiency of small farmers in a changing world: A
survey of recent evidence. Journal of International Development, 3(1), 1–27.
Alvarez, A., Amsler, C., Orea, L., & Schmidt, P. (2006). Interpreting and testing the scaling
property in models where inefficiency depends on firm characteristics, 201–212.
https://doi.org/10.1007/s11123-006-7639-3
Ariga, J., & Jayne, T. S. (2009). Private Sector Responses to Public Investments and Policy
Reforms The Case of Fertilizer and Maize Market Development in Kenya (IFPRI Discussion
Paper No. 921).
Barrett, C. B. (1996). On price risk and the inverse farm size – productivity relationship. Journal
of Development Economics, 51, 193–215. https://doi.org/10.1016/S0304-3878(96)00412-9
Barrett, C. B., Bellemare, M. F., & Hou, J. Y. (2010). Reconsidering conventional explanations
of the inverse productivity-size relationship. World Development, 38(1), 88–97.
https://doi.org/10.1016/j.worlddev.2009.06.002
Battese, G. E., & Coelli, T. J. (1988). Prediction of firm-level technical efficiencies with a
generalized frontier production function and panel data. Journal of Econometrics, 38(3),
387–399. https://doi.org/10.1016/0304-4076(88)90053-X
Battese, G. E., & Coelli, T. J. (1995). A model for technical inefficiency effects in a stochastic
frontier production function for panel data. Empirical Economics, 20, 325–332.
Belotti, F., & Ilardi, G. (2015). Consistent inference in fixed-effects stochastic frontier models.
Benjamin, D. (1995). Can unobserved land quality explain the inverse productivity relationship?
Journal of Development Economics, 46(1), 51–84. https://doi.org/10.1016/03043878(94)00048-H
Besley, T. (1995). Property Rights and Investment Incentives: Theory and Evidence from Ghana.
Journal of Political Economy, 103(5), 903–937. https://doi.org/10.1086/262008
Bot, A., & Benites, J. (2005). The importance of soil organic matter: key to drought-resistant
soil and sustained food production. FAO Soils Bulletin.
https://doi.org/10.1080/03650340214162
164

Carletto, C., Savastano, S., & Zezza, A. (2013). Fact or artifact: The impact of measurement
errors on the farm size-productivity relationship. Journal of Development Economics, 103,
254–261. https://doi.org/10.1016/j.jdeveco.2013.03.004
Caudill, S. B., & Ford, J. M. (1993). Biases in frontier estimation due to heteroscedasticity.
Economics Letters, 41(1), 17–20.
Caudill, S. B., Ford, J. M., & Gropper, D. M. (1995). Frontier Estimation and Firm-Specific
Inefficiency Measures in the Presence of Heteroscedasticity. Journal of Business &
Economic Statistics, 13(1), 105–111. https://doi.org/10.1080/07350015.1995.10524583
Chamberlain, G. (1984). Panel Data. In Handbook of Econometrics (Vol. II, pp. 1247–1318).
https://doi.org/10.1016/S1573-4412(84)02014-6
Chen, Y., Schmidt, P., & Wang, H. (2014). Consistent estimation of the fixed effects stochastic
frontier model. Journal of Econometrics, 181(2), 65–76.
https://doi.org/10.1016/j.jeconom.2013.05.009
Coelli, T. J. (1995). Recent developments in frontier modelling and efficiency measurement.
Australian Journal of Agricultural Economics, 39(3), 219–245.
Coelli, T. J., Rao, P. D. S., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to
efficiency and productivity analysis (Second). New York: Springer Science+Business Media
Inc.
Cornwell, C., Schmidt, P., & Sickles, R. C. (1990). Production frontiers with cross-sectional and
time-series variation in efficiency levels. Journal of Econometrics, 46, 185–200.
Diao, X., Hazell, P., Resnick, D., & Thurlow, J. (2007). The Role of agriculture in development:
Implications for sub-Saharan Africa. Washington, D.C., USA. https://doi.org/153
Doran, J. W., & Parkin, T. B. (1994). Defining and assessing soil quality. Defining Soil Quality
for a Sustainable Environment.
Ekbom, A., Alem, Y., & Sterner, T. (2013). Integrating soil science into agricultural production
frontiers. Environment and Development Economics, 18, 1–18. Retrieved from
http://journals.cambridge.org/abstract_S1355770X13000089
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical
Society, 120(3), 253–290.
Farsi, M., Filippini, M., & Kuenzle, M. (2005). Unobserved heterogeneity in stochastic cost
frontier models: an application to Swiss nursing homes. Applied Economics, 37, 2127–
2141.
Filippini, M., & Greene, W. (2016). Persistent and transient productive inefficiency : a maximum
simulated likelihood approach. Journal of Productivity Analysis, 45, 187–196.

165

Filippini, M., Hunt, L. C., & Zorić, J. (2014). Impact of energy policy instruments on the
estimated level of underlying energy ef fi ciency in the EU residential sector. Energy Policy,
69, 73–81.
Funk, C., Peterson, P., Landsfeld, M., Pedreros, D., Verdin, J., Shukla, S., … Michaelsen, J.
(2015). Climate Harzads Group. https://doi.org/10.1038/sdata.2015.66
Government of Kenya. (2014). Soil suitability evaluation for maize production in Kenya soil
suitability evaluation for. Nairobi, Kenya.
Greene, W. H. (1980). Maximum likelihood estimation of econometric frontier functions.
Journal of Econometrics, 13, 27–56.
Greene, W. H. (2005). Fixed and random effects in stochastic frontier. Journal of Productivity
Analysis, 23, 7–32.
Griffiths, W. E., & Hajargasht, G. (2016). Some models for stochastic frontiers with
endogeneity. Journal of Econometrics, 190, 341–348.
Grisso, R., Alley, M., Holshouser, D., & Thomason, W. (2009). Precision farming tools: soil
electrical conductivity. Virginia Cooperative Extension, 442(508), 1–6. Retrieved from
http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Precision+farming+tools:
+soil+electrical+conductivity#7
Hadri, K. (1999). Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function.
Journal of Business & Economic Statistics, 17(3), 359–363.
https://doi.org/10.1080/07350015.1999.10524824
Haggblade, S., & Hazell, P. B. R. (Eds.). (2010). Successes in African agriculture: Lessons for
the future. Baltimore: The Johns Hopkins University Press.
Henningsen, A. (2014). Introduction to econometric production analysis with R (Draft version).
Department of Food and resource Economics, University of Copenhagen.
Huang, C. J., & Liu, J. (1994). Estimation of a non-neutral stochastic frontier production
function. Journal of Productivity Analysis, 5, 171–180.
Jondrow, J., Lovell, C. A. K., Materov, I. S., & Schmidt, P. (1982). On the estimation of
technical efficiency in the stochastic frontier production fucntion model. Journal of
Econometrics, 19, 233–238.
Kagin, J., Taylor, J. E., & YĂşnez-Naude, A. (2015). Inverse Productivity or Inverse Efficiency?
Evidence from Mexico. The Journal of Development Studies, 388(December), 1–16.
https://doi.org/10.1080/00220388.2015.1041515
Kagin, J., Taylor, J. E., & YĂşnez-Naude, A. (2016). Inverse Productivity or Inverse Efficiency?
Evidence from Mexico. The Journal of Development Studies, 52(3), 396–411.
https://doi.org/10.1080/00220388.2015.1041515
166

Kibaara, B. W. (2005). Technical efficiency in Kenya’s maize production: An application of the
stochastic frontier approach. Colorado State University.
Kumbhakar, C. S., & Lovell, C. A. K. (2000). Stochastic Frontier Analysis. Cambridge:
Cambridge University Press.
Kumbhakar, S. C. (1990). Production frontiers, panel data, and time-varying technical
inefficiency. Journal of Econometrics, 46, 201–211.
Kumbhakar, S. C., Ghosh, S., & McGuckin, J. T. (1991). A generalized production frontier
approach for estimating determinants of inefficiency in US . dairy farms. Journal of
Business & Economic Statistics, 9(3), 279–286.
Kumbhakar, S. C., Lien, G., & Hardaker, J. B. (2014). Technical efficiency in competing panel
data models : a study of Norwegian grain farming. Journal of Productivity Analysis, 41,
321–337.
Kumbhakar, S. C., Wang, H.-J., & Horncastle, A. P. (2015). A practitioner’s guide to stochastic
frontier analysis using stata. New York: Cambridge University Press.
Kumbhakar, S. C., Parmeter, C. F., & Tsionas, E. G. (2013). A zero inefficiency stochastic
frontier model. Journal of Econometrics, 172(1), 66–76.
Lal, R. (2006). Enhancing crop yields in the developing countries through restoration of the soil
organic carbon pool in agricultural lands. Land Degradation & Development, 209(August
2005), 197–209.
Liu, Y., & Myers, R. (2009). Model selection in stochastic frontier analysis with an application
to maize production in Kenya. Journal of Productivity Analysis, 31, 33–46.
https://doi.org/10.1007/s11123-008-0111-9
Maguire, R., Mark, A., & Flowers, W. (2009). Fertilizer Types and Calculating Application
Rates (Publication No. 424–35). Virginia Cooperative Extension. Communications and
Marketing, College of and Life Sciences, Virginia Polytechnic Institute and State
University.
Marenya, P. P., & Barrett, C. B. (2007). Household-level determinants of adoption of improved
natural resources management practices among smallholder farmers in western Kenya.
Food Policy, 32(4), 515–536.
Marenya, P. P., & Barrett, C. B. (2009). Soil quality and fertilizer use rates among smallholder
farmers in western Kenya. Agricultural Economics, 40, 561–572.
Meeusen, W., & van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas
production functions with composed error, 18(2), 435–444.
Mghenyi, E. (2015). The impact of agricultural credit on demand for factors of production , farm
output , and profitability in Kenya. Michigan State University.
167

Mochebelele, M. T., & Winter-Nelson, A. (2000). Migrant labor and farm technical efficiency in
Lesotho. World Development, 28(1), 143–153.
Mundlak, Y. (1978). On the Pooling of Time Series and Cross Section Data. Econometrica,
46(1), 69. https://doi.org/10.2307/1913646
Parmeter, C. F., & Kumbhakar, S. C. (2014). Efficiency analysis : A Primer on recent advances.
Foundations and Trends in Econometrics, 7(3–4), 191–385.
Pitt, M. M., & Lee, L.-F. (1981). The measurement and sources of technical inefficiency in the
Indonesian weaving industry. Journal of Development Economics, 9, 43–64.
Reifschneider, D., & Stevenson, R. (1991). Systematic departures from the frontier : A
framework for the analysis of firm inefficiency. International Economic Review, 32(3),
715–723.
Rho, S., & Schmidt, P. (2015). Are all firms inefficient? Journal of Productivity Analysis, 43(3),
327–349.
Sanchez, P. A., Shepherd, K. D., Soule, M. J., Place, F. M., Buresh, R. J., Izac, A. N., &
Kwesiga, F. R. (1997). Soil Fertility Replenishment in Africa : An Investment in Natural
Resource Capital. American Society of Agronomy and Soil Science Society of America, (51),
1–46.
Schmidt, P., & Sickles, R. C. (1984). Production frontiers and panel data. Journal of Business &
Economic Statistics, 2(4), 367–374.
Sheahan, M. B. (2011). Analysis of fertilizer profitability and use in Kenya. Michigan State
University.
Sherlund, S. M., Barrett, C. B., & Adesina, A. A. (2002). Smallholder technical efficiency
controlling for environmental production conditions, 69, 85–101.
Smale, M., & Olwande, J. (2014). Demand for maize hybrids and hybrid change on smallholder
farms in Kenya. Agricultural Economics (United Kingdom), 45(4).
Smaling, E. M. A., Nandwa, S. M., & Janssen, B. H. (1997). Soil Fertility in Africa Is at Stake.
American Society of Agronomy and Soil Science Society of America, (51).
Stevenson, R. E. (1980). Likelihood functions for generalized stochastic frontier estimation.
Journal of Econometrics, 13, 57–66.
Stoorvogel, J. J., & Windmeijer, P. N. (1993). Calculating soil nutrient balances in Africa at
different scales. Fertilizer Research, 35, 237–250.
Stoorvogel, J., & Smaling, E. M. A. (1998). Research on soil fertility decline in tropical
environments : integration of spatial scales. Nutrient Cycling in Agroecosystems 50:, 50,
151–158.
168

The Montepellier Panel. (2013). Sustainable Intensification: A New Paradigm for African
Agriculture. London.
The World Bank. (2007). World development report 2008: Agriculture for development.
Washington, DC: The World Bank.
Tiedemann, T., & Latacz-Lohmann, U. (2013). Production Risk and Technical Efficiency in
Organic and Conventional Agriculture – The Case of Arable Farms in Germany. Journal of
Agricultural Economics, 64(1), 73–96.
Tittonell, P., Corbeels, M., Wijk, M. T. Van, Vanlauwe, B., & Giller, K. E. (2008). Combining
Organic and Mineral Fertilizers for Integrated Soil Fertility Management in Smallholder
Farming Systems of Kenya: Explorations Using the Crop-Soil Model FIELD. Agronomy
Journal, 100(5), 1511–1526.
Tittonell, P., & Giller, K. E. (2013). When yield gaps are poverty traps: The paradigm of
ecological intensification in African smallholder agriculture. Field Crops Research, 143,
76–90. https://doi.org/10.1016/j.fcr.2012.10.007
Tran, K. C., & Tsionas, M. G. (2015). Zero-inefficiency stochastic frontier models with varying
mixing proportion: A semiparametric approach. European Journal of Operational
Research.
Wang, H. (2003). A Stochastic Frontier Analysis of Financing Constraints on Investment A
Stochastic Frontier Analysis of Financing Constraints on Investment : The Case of Financial
Liberalization in Taiwan, 21(3), 406–419. https://doi.org/10.1198/073500103288619016
Wang, H.-J. (2002). Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic
Frontier Model. Journal of Productivity Analysis, 18, 241–253.
Wang, H.-J., & Schmidt, P. (2002). One-step and two-step estimation of the effects of exogenous
variables on technical efficiency levels. Journal of Productivity Analysis, 18, 129–144.
Wang, H., & Ho, C. (2010). Estimating fixed-effect panel stochastic frontier models by. Journal
of Econometrics, 157(2), 286–296. https://doi.org/10.1016/j.jeconom.2009.12.006
Willy, D. K., Muyanga, M., & Jayne, T. (2016). Can economic and environmental benefits
associated with agricultural intensification be sustained at high population densities ? A
farm level empirical analysis. In Invited paper presented at the 5th International
Conference of the African Association of Agricultural Economists, September 23-26, 2016,
Addis Ababa, Ethiopia.
Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
https://doi.org/10.1515/humr.2003.021
Yang, J., Wang, H., Jin, S., Chen, K., Riedinger, J., & Peng, C. (2016). Migration, local off-farm
employment, and agricultural production efficiency: evidence from China. Journal of
Productivity Analysis, 45(3), 247–259. https://doi.org/10.1007/s11123-015-0464-9
169