Release Form
The undersigned certify that they have supervised, read and recommend to the Midlands State
University for acceptance a research a research project entitled: Estimating a maize production
function for Mazowe district submitted by Elias Chipatiso (R112185J)
In partial fulfilment of the requirements for the Bachelor of Commerce Economics Honors
Degree.
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Signature Student
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Date
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Approval Form
The undersigned certifies that they have supervised the student, Elias Chipatiso’s
dissertation entitled: Estimating a maize production function for Mazowe district,
submitted in partial fulfilment of the requirements of the Bachelor of Commerce
Economics Honors Degree at the Midlands State University.
Supervisor signature
Chapter 1
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Chapter 2
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Chapter 3
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Chapter 4
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Chapter 5
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Dedication
My dear family and friends
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ACKNOWLEDGEMENTS
I acknowledge all the tireless efforts of Dr Z Tambudzai who made this study a success. Special
thanks goes to Crispen Chipatiso, Bruce Munyaradzi Mafokosho and Mr & Mrs Magodo
whom provided financial support.
For your patience and understanding throughout the completion of this study, I would also like
to thank the department of economy staff for mentoring and guiding me for the past four years
and your kindness, this was a selfless sacrifice.
I would also like to thank Janet T Mupfawi, Wendy F Mauta, Victor S Utete and Tatenda E
Chingosho for proving a shoulder to lean on when I was falling.
Sincere thanks goes to all small-scale farmers in Mazowe District for their time and information
provided to carry out this research. Special appreciation to everyone who stood by me and
encouraged me to focus and be strong throughout the entire period of my study. Thank you for
appreciating me as a friend, classmate, brother and all roles I played in your life.
Finally ,I would like to thank God for sparing me and enabling me to through college life and
succeed.
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ABSTRACT
The main objective if the study is to estimate a maize production function in Mazowe
District for smallholder farmers. The study also attempts to investigate socio-economic
factors that affect maize production. A Cobb- Douglas function was used to estimate
production using primary data obtained through questionnaires. To ensure for unbiased
the model corrected for heteroscedasticity, results indicated that age, land size, household
size, amount used on seed and fertilizer were significant using the 2t rule of thumb, except
for capital which was not significant under this study. Though it as significant age had a
negative coefficient of -0.1608 and a t- statistic of -3.84.
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Contents
Release Form ........................................................................................................................................ i
Approval Form ..................................................................................................................................... ii
Dedication .......................................................................................................................................... iii
ACKNOWLEDGEMENTS ........................................................................................................................... iv
ABSTRACT ................................................................................................................................................ v
CHAPTER ONE .......................................................................................................................................... 1
1.0 Introduction to the study .............................................................................................................. 1
1.1 Background of the study ............................................................................................................... 1
1.2 Statement of the problem ............................................................................................................. 6
1.3 Objectives of the study .................................................................................................................. 6
1.4 Significance of the study................................................................................................................ 7
1.5 Hypothesis ..................................................................................................................................... 7
1.6 Organisation of the rest of the study ............................................................................................ 7
CHAPTER TWO ........................................................................................................................................ 8
Literature review................................................................................................................................. 8
2.0Introduction ................................................................................................................................... 8
2.1 Theoretical literature .................................................................................................................... 8
2.1.1 Special Production Functions ................................................................................................... 10
2.1.1.1 Linear Production Function (Perfect Substitutes) ................................................................. 10
2.1.1.2 Fixed Proportion Production Function (Perfect Complements) ........................................... 11
2.1.1.3 Cobb-Douglas Production Function ...................................................................................... 11
2.2 Empirical Literature..................................................................................................................... 13
CHAPTER THREE .................................................................................................................................... 18
RESEARCH METHODOLOGY .................................................................................................................. 18
3.1 Introduction ................................................................................................................................ 18
3.2 Model Specification .................................................................................................................... 18
3.3 Justification of Variables ............................................................................................................. 20
3.3.1 Capital ...................................................................................................................................... 20
3.3.2 Age ........................................................................................................................................... 21
3.3.3 Land .......................................................................................................................................... 21
3.3.4 Seed.......................................................................................................................................... 22
3.3.5 Fertiliser ................................................................................................................................... 22
3.3.6 Labour ...................................................................................................................................... 22
3.3.7 Household size ......................................................................................................................... 22
3.4 Estimation Procedure and Diagnostic Test ................................................................................. 23
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3.4.1 Heteroscedasticity ................................................................................................................... 23
3.4.2 Multicollinearity ....................................................................................................................... 23
3.4.3 Data types and sources ............................................................................................................ 23
3.4.4 Conclusion ................................................................................................................................ 24
CHAPTER FOUR ..................................................................................................................................... 24
RESULTS PRESENTATION AND ANALYSIS .............................................................................................. 24
4.1 Introduction ................................................................................................................................ 24
4.2 Diagnostic Test Results ............................................................................................................... 25
4.2.1 Multicollinearity Test Results................................................................................................... 25
4.2.2 Heteroscedasticity Test Results ............................................................................................... 26
4.2.3 REGRESSION RESULTS .............................................................................................................. 26
4.2.4 INTERPRETATION OF RESULTS ..................................................................................................... 27
4.3 CONCLUSION ................................................................................................................................... 29
CHAPTER FIVE ....................................................................................................................................... 29
POLICY RECOMMENDATIONS AND CONCLUSION ................................................................................ 29
5.0 INTRODUCTION ............................................................................................................................... 29
5.1 SUMMARY OF THE STUDY............................................................................................................... 30
5.2 POLICY RECOMMENDATION ........................................................................................................... 30
5.3 SUGGESTION FOR FUTURE STUDIES ............................................................................................... 30
5.4 LIMITATIONS AND DELIMITATIONS ................................................................................................ 31
5.4.1DELIMITATIONS............................................................................................................................. 31
5.5 CONCLUSION ................................................................................................................................... 31
List of Acronyms .................................................................................................................................... 32
List of Tables ..................................................................................................................................... 33
Reference List.................................................................................................................................... 34
Appendix 1 ........................................................................................................................................ 38
Appendix 2 ........................................................................................................................................ 46
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CHAPTER ONE
1.0 Introduction to the study
Agriculture has always been an important component of Zimbabwe’s economy and is key part
to the country’s efforts to reduce poverty. Government of Zimbabwe (2013) highlighted that
agricultural production was severely affected, resulting in the country depending on imports to
meet the demand for domestic consumption and industrial needs. Furthermore, these challenges
led to significant skills flight and erosion of private and public financing, thereby affecting
quality service delivery and achievement of the United Nations (UN) Millennium Development
Goals (MDGs). About 70% of the population depends on agriculture for food, income and
employment and it supplies 60% of the raw materials required by the industrial sector and
contributes 15-20 % of the Gross Domestic Product (GDP).The performance of the sector has
a strong influence on the rate of economic growth, economic stability, employment level and
demand for other goods as well as food security.
Zimbabwe is divided into five AGRO-Ecological Regions with rainfall and agricultural
patterns decreasing from region 1 to 5 (Vincent & Thomas 1961) and (Moyo 1994). The land
is divided into five natural regions on the basis of soil type and climatic factors. Natural regions
I, II and III are suitable for intensive crop cultivation and livestock raising, while regions IV
and V offer limited scope for crop agriculture but are suitable for livestock raising on a large
scale. The bulk of Mashonaland (West, East and Central), Midlands and Manicaland Provinces
are under regions I, II and III, while Matabeleland (North and South) and Masvingo Provinces
are under natural regions IV and V. The three Mashonaland Provinces constitute the
breadbasket of the country. Zimbabwe’s farming sector can produce, and has produced in the
past, exportable surpluses of maize and certain other food crops. But, as described earlier,
severe constraints have resulted in less than full capacity utilization of its natural resources.
1.1 Background of the study
A report has it that maize was introduced to Europe in 1942 from Southern and Central America
by Christopher Columbus and later spread to Africa (Okoruwa, 1997). Today maize has
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become Africa’s most important staple food crop and is grown by both large and small scale
farmers. Currently it is produced in most countries and is the third most planted crop after
wheat and rice (African Report 2013). Zimbabwe’s crop production is highly diversified
comprising of tobacco, maize, cotton, wheat, sorghum, soya beans and horticultural products.
Tobacco, cotton and horticultural products which are export crops are the most important in
terms of revenue generation. Maize is primarily for domestic consumption and is crucial to the
country’s food security. The country has not been meeting its national requirements for maize
and had to depend on imports and aid in order to meet domestic demand due to the decline in
agricultural production from year 2000.
2
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
2000
2001
2002
Area (ha in millons)
2003
2004
2005
Production (ton in millions)
2006
2007
2008
2009
Yield (kg/ha in thousands
Fig 1 Zimbabwe’s maize production from 2000-2009
Source: ZIMSTAT
Total maize production has declined from 1 619 651 million tonnes in 2000 to 1 240 000
in 2009 and to 600 000 tonnes (not on the graph) in 2012 against the national requirements
of 1800 000 tonnes. In 2012 a total area of 1.6 million hectares of maize were planted and
of this 722 577 hectares were written off due to a drought and the worst affected areas
included Masvingo, Manicaland and Matebeleland North (Government of Zimbabwe
2012). Efforts to revive the economy were dented by the drought that hit many parts of the
country during the 2011-12 cropping season. A strong adverse movement in production
of national maize, which accounts for the chief part of food production is evident from the
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past decade. In addition, the graph shows a drop in the average annual production of about
530 000 tonnes between the two periods before and since 2002. The reasons for the
downward trend, before the fast track land reform, include a continuing switch by the
large-scale commercial farms from maize, which became a Grain Marketing Board
(G.M.B) controlled crop, to other non-controlled crops such as tobacco, cotton, among
others. Recent decline (since 2002) were due to structural change triggered by land tenure
policies, lack of investment and funds domestically and externally in agriculture sector.
The newly settled farmers cultivate only about 50 percent of the total arable land allocated
to them owing to shortages of tractor/draught power, fuel, and investment in infrastructure
or improvements and absenteeism on the part of some new settler beneficiaries (Muzuri
2005). Large-scale commercial sector now produces less than one-tenth of the maize that
it produced in the 1990s (GoZ 2012). Increased frequency of drought combined with maize
production being on more marginal lands of the communal farmers with little no fertiliser
was noted by some experts to explain some of the long term negative trends.
A major feature behind the variation in Zimbabwe’s economic growth is the agricultural sector
reliance on certain rainfall (Kinsey. 2010). Rainfall is highly variable in Zimbabwe, both from
one year to another, but also between different parts of the country. Recurrent droughts are a
normal feature of Zimbabwe’s climate and have had negative effects development, magnifying
existing poverty and vulnerability problems.
300
200
100
0
-100
-200
-300
-400
mm of rainfall above and below average
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Fig 2 Zimbabwe seasonal rainfall, deviation from the mean (1990-2007)
Adopted from: Unganai, 2011 based on Department of Metrological Services.
The season 1990-91 was a drought year followed by the worst drought for the century in 199192 with rainfall 77% below normal. The 2001/02 drought occurred in the first year that farmers
had land the Fast Track Land Reform making it harder for new farmers to become established.
Changes in rainfall between years, timing of rainfall and length of the season over time all
present increasing difficulties for communities in anticipating the climate conditions each
growing season.
Because maize is a staple crop, the minister of agriculture repeats government’s efforts to
ensure that each farming season becomes successful. The land reform through farm invasion,
was caused by the pre/post- colonial imbalances in land distribution. In 2001 the government
then properly re-allocated the grabbed land and corrected the land imbalances. Three quarter
of the land before the introduction of land acquisition policy belonged to 4500 whites and
constituted less than a percentage of the estimated 13 million population (Nebakwe 2002).
Utete (2003) found out that there were zero hectares for A1 resettlement farmers as of June
2002 and by July 2003, A2 farmers had 5.6 % while A1 had occupied 10.6% of the former
white’s commercial farmers. Six hectares of arable land were allocated to each A1 farmer.
Food security became a concern in Zimbabwe due to fast track land redistribution and Utete
report expected maize output to increase from farmers in areas with good land and rainfall
patterns. Tillage for A1 farmers was provided by District Development Fund (D.D.F) as
government mandate and charges differed depending if farmers provide own fuel (dry charges)
wet charges when the tractor comes with fuel. Most A1 farmers in Mashonaland province have
uncultivated fields and low agricultural produce making food security for the nation to remain
a major concern. Muzuru (20050 alluded to the uncultivated farms saying that some farmers
still take farming as part time employment. This therefore explains the need to identify the
characteristic features of A1 farmers in the area under study and estimate their production
function and see the relationship between inputs and output then come up with measures to
improve production in the district.
Mazowe District was selected because it has more A1 farmers as compared to other districts in
the province (CIMITY 2003), had faster resettlement than other districts, so farmers in Mazowe
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started meaningful production early. Furthermore, in Mazowe, Farmer Syndicate that were
formed assisted farmers in the procurements of inputs, peer education and team work on
farming.
Table 1: Mean range of maize hectares grown by farmers in the province for four years.
District
Shamva
Bindura
Mazowe
2003
2004
2005
2006
Range
0.73- 6.19
0.86- 4.83
1.80- 4.70
1.47- 3.35
Mean
3.4583
2.8437
3.2500
2.4063
Range
0.33- 4.77
0.94- 5.94
2.16- 5.02
1.66- 4.4
Mean
2.5385
3.4375
3.5938
3.0313
Range
1.35- 8.07
1.23- 6.51
2.44- 4.95
2.02- 6.04
Mean
4.7143
3.8667
3.6944
4.0278
Source: Mazuru N, Njaya T and Hanyani-Mlambo B (2007)
The total area under maize production had been generally declining over the years. Farmers
had wide differences in sizes of area allocated for maize production. Provincial sample average
of 3.60 ha and 3.1 ha for periods 2003 and 2006 were surpassed buy Mazowe district which
had 4.71 ha and 4.03 ha respectively.
Table 2: Average maize production per district from 2003-2006
District
2003
2004
2005
2006
Shamva
7.11
9.34
10.88
12.87
Bindura
8.18
9.85
10.84
8.73
Mazowe
13.64
11.94
13.72
17.43
Source: Mazuru N, Njaya T and Hanyani-Mlambo B (2007)
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Mazowe had dominance in both area under cultivation and in maize output because it received
rains earlier giving an advantage of early cropping than other districts. The standard deviation
suggest the coexistence of very good maize producers and small size producers.
1.2 Statement of the problem
The country needs about 2.2 million tonnes of the staple grain to feed its people annually. In
the 1990’s Zimbabwe was a net exporter of maize and as from 2000 there was a substantial
contraction in agricultural output that made the nation fail to meet its food requirements.
Empirical studies suggest that most under developed and developing countries are still facing
the problem of high poverty levels. This calls for improving yields of major staples, such as
maize for better food security and livelihoods of rural households. Thus, resources need to be
used in the most efficient way to achieve this objective. Further, improved efficiency is
expected to improve food security by cutting hunger halfway in 2015 (Amos, 2007).
In order to realize increased production farmers in developing countries need to efficiently
utilize the limited resources accessed for improved food security and farm income generation
(Amos, 2007). Mazowe district is part of the Mashonaland Central Province that has one
of the most productive communal lands, producing both food and cash crops. Maize is the
dominant crop however, the main sources of cash income include cotton, tobacco,
sunflower, soya beans and sugar beans production. Employment on A1 and commercial
farms is also an important source of livelihood. Maize is a strategic crop to the nation,
therefore the research seeks to assess ways of increasing production focusing on A1
farmers in Mazowe District.
1.3 Objectives of the study
The main objective of the study is to contribute to the literature of maize production by:

Estimating the relationship between maize output and the main traditional input
variables. These include seed, labour, capital and fertiliser.

Investigate some socio-economic factors that affect maize production in Mazowe
District.

To suggest policy measures to improve maize production in Mazowe district.
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1.4 Significance of the study
The study is important as it address a topical issue in the country. Problems associated with
low maize production in the country seeks remedies as they have grievous ending. Useful
agricultural knowledge will be contributed by the research towards the welfare of the nation so
as to reduce the level of poverty and high maize import bill for the country. Increasing maize
output will require multiple factors including technology, institutional changes and changes in
policies.
1.5 Hypothesis
H0: Maize production is not influenced by gender, age, irrigation, land, seed, fertiliser,
machinery, capital and labour.
H1: Maize production is influenced by gender, age, irrigation, land, seed, fertiliser, machinery,
capital and labour.
1.6 Organisation of the rest of the study
The rest of the dissertation is organised as follows: Chapter 2 contains review of the literature
in which theoretical and empirical review is discussed. Chapter 3 presents the methodology to
be employed for analysis. Chapter 4 contains empirical results and their interpretations.
Chapter 5 summarises the findings and policy recommendations as well suggestions for further
researches.
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CHAPTER TWO
Literature review
2.0 Introduction
It provides a theoretical framework which strengthens this study so as to propose sound policy
recommendations and it provides a foundation upon the current study is based upon. It is
categorised into theoretical and empirical literature review findings from different countries.
They are obtained using econometric models, empirical models and tests. Theoretical review
is based on common observation that have not been empirically tested to prove whether the
assertation made really occur in the real world. The information used is drawn from text books
and publications. The main idea of providing such works is to sightsee work done by others
and detect existing gaps and will also assist in constructing the model to be used in Chapter 3.
2.1 Theoretical literature
Economic theory is to a large extend about money, costs, prices, and markets, return on
investment, profit and similar economic concepts. However, the concept of production
economics is superior in that the limits of economic behaviour are defined by the technical
production possibilities. Production technology is the decisive factor regarding the quantity
produced and how it may be produced (Rasmussen 2013). Production technology is in its most
general form, a description of the relationship between input and output produced. The
description of production technical relationship is based on empirical observation of
relationships between inputs and output. Hence, a production function is defined as maximum
amount of output that can be produced (through the use of a given production technology) with
a given amount of input (Blank and Lynch 2001). Production of goods and services involves
transforming resources such as labour power, raw materials, and the services provided by the
facilities and machines into finished products. Semiconductor producers for example combine
the labour services provided by their employees and the capital services provided by the fabs,
robots and processing equipment with raw materials, such as silicon to produce finished chips.
The productive resources such as labour and capital equipment that a firm uses to manufacture
goods and services are called inputs or factors of production and the amount of goods and
services produced is the firms output. As the semiconductor example suggest, recall firms can
often choose one of the several combination of inputs to produce a given volume of output.
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The firm can produce a given number of chips using workers and no robots or using fewer
workers and many robots. The production function tells the maximum quantity of output the
firm can produce given the quantities of the inputs that it might employ. Production functions
are analogous to the utility function in consumer theory. Just as the utility function depends on
exogenous consumer tastes, the production depends on exogenous on technological conditions.
Overtime, these technological conditions may change, an occurrence known as technological
progress and the production function may shift. The production function equation tells the
maximum output a firm could get from given combinations of inputs however, inefficient
management could reduce output from what is technologically possible. Total production
function also known as single unit production function, shows how total output depends on the
level of input. It shows four notable properties from the example below
Table 3. Total Production Function
Inputs
Quantity
0
0
6
30
12
96
18
162
24
192
30
150
When inputs is zero, quantity will be zero, which means nothing can be produced without using
any inputs. Between input zero and the 12th input, output rises with an additional input at an
increasing rate (total production function is convex) thus there are increasing marginal returns.
When there are increasing marginal returns, an increase in inputs increases total output at an
increasing rate. Output rises with an additional input but at a decreasing rate from the 12th input
to the 24th input (total production function is concave). During this period there will be
diminishing marginal returns. An increase in inputs still increases output but a decreasing rate,
they set in when a firm exhaust its ability to increase productivity. When the quantity of inputs
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exceed 24, an increase in quantity of inputs results in a decrease in total output. During that
period there would be diminishing total returns.
There are two related but distinct notions of productivity that can be derived from the
production function that is average product and marginal product. Average product (AP) is the
average amount of output per unit of input. Mathematically, it can be represented as below:
𝐴𝑃 =
𝑇𝑜𝑡𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑝𝑢𝑡
It is also known as average physical product (APP)
The Marginal Product (MP) is the rate at which total output changes as the amount of inputs
are changing.
𝑀𝑃 =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑜𝑡𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑖𝑛𝑝𝑖𝑡𝑠
The MP is analogous to the concept of marginal utility from consumer theory. In most
production processes, as the quantity of one input increases with the quantity of another input,
the point will be reached beyond which the MP of that input decreases. This phenomenon,
which reflects the experience of real world firms, seems so pervasive that economists call it the
law of diminishing marginal returns.
2.1.1 Special Production Functions
2.1.1.1 Linear Production Function (Perfect Substitutes)
In some production process, the marginal rate of technical substitution of one input for another
may be constant. For example, a manufacturing process may require energy in the form of
natural gas or fuel oil and a given amount can always be substituted for each litre of fuel oil.
In this case a marginal rate of technical substitution of natural gas for fuel is constant. In some
cases, a firm may find it that one type of equipment may be perfectly substituted for another
type. A linear production function is a production function whose isoquants are straight, thus
the slope of any isoquant is constant and the marginal rate of technical substitution does not
change as we move along the isoquant. A linear production function is of the form
Q = 𝑎𝐿 + 𝑏𝐾
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Where a and b are positive constants. In other words, the input in a linear production function
are infinitely (perfectly) substitute for each other.
2.1.1.2 Fixed Proportion Production Function (Perfect Complements)
Also known as Leontief production function, after economist Wassily Leontief who used it to
model relationship between sectors in a national economy. A production where the inputs must
be combined in fixed proportions are called fixed-proportions productions function and the
inputs in in fixed production function are called perfect complements. When inputs are
combined in fixed proportions, the elasticity of substituting is zero, because the marginal rate
of technical substitution along the isoquants of a fixed- proportion production changes from ∞
to 0 when we pass through the corner of the isoquant. Firms facing fixed proportion production
function have no flexibility in their ability to substitute among inputs.
2.1.1.3 Cobb-Douglas Production Function
It allows for some degree of substitutability among production input while Leontief production
function do not. It is an intermediate between a linear and fixed proportion production function.
Optimal output solutions will occur at points of tangency between isoquants and isocost curves
or in the case in the case of the Leontief function a corner solution will result. Hence, excepting
cases of the corner, marginal rates of technical substitution will equal slopes of isocost curves
at optimal production levels. It is given by the formula
𝑄 = 𝐴𝐿α Kβ
Where A, α, β are positive constants.
With the Cobb-Douglas production function, inputs can be substituted for each other, unlike a
fixed-proportion production function inputs can be used in variable proportions. Though the
rate at which inputs can be substituted they are not constant as we move along an isoquant, this
suggest that the elasticity of substitution for a Cobb-Douglas production falls somewhere
between 0 and ∞. In fact it turns out that the elasticity of substitution along a Cobb-Douglas
production as always equal to 1. Because it is thought to be a plausible way of characterising
many real world processes, it is often used by economist to study issues related to input
productivity or production costs. For, example Ballack S and Lynch L (1980-1990) estimated
the Cobb-Douglas production function to study the impact of “high performance” workplace
practices on worker productivity in United States firms.
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The introduction of the Cobb-Douglas regression into agricultural economics
In remembrance, it is not shocking that agricultural economist were prominent among those
who adopted the Cobb-Douglas regression as an empirical research tool. Agricultural
economists became a hot-bed of empirical research during the inter war period. Economists
were employed by the United States Department of Agriculture and the state supported longgrant colleges with the exception that they would conduct research into issues of interest to
farmers and agricultural policy makers. As a result training in statistical methods was
emphasized in graduate programmes in agricultural economics and many econometricians of
the inter war period came out of the field of agricultural economics (Rutherford 2009; Fox
1986). With their innovative use of regression analysis, Douglas production studies began to
appear. Agricultural economists were in a better position that economists in general to
understand them and were more likely to be intrigued by statistical issues they raised. For two
related and long-standing research areas in the field of agricultural economics, Douglas vision
of statistically estimating the production function of neoclassical economic theory was salient.
Banzhaf (2006) provides an excellent account of the emergence of agricultural economics in
the early 20th century as economists came to dominate the pre-existing research area of farm
management. Farm management encompasses the work of applied scientist in the early 1990’s,
whose research was intended to help farmers solve practical problems. As the experts who
could teach farmers how to apply the scientific knowledge from several disciplines to keep
their farms profitable in the face of shifting economic forces, early agricultural economists
envisioned a central role for themselves in this field. Based on their possession of a general
framework for thinking about the business decisions faced by farmers; the neoclassical theory
of the firm, agricultural economists claimed this role. They sought to bring order to the field
through the application of neoclassical theory, generating a body of research and knowledge
they called production economics. Common sense notion of the economy were being applied
in a haphazard and conflicting way, as economist moved into the field of farm management
they found a very empirical, practical but rather theoretical literature.
Research in production economics included the application of the logic of maximization to a
variety of situations arising in farming, such as allocating of labourers of varying efficiency to
cooperate inputs of efficiency (Waite 1936) or the multi enterprise farm which produced
multiple outputs requiring the same type of input (Benedict 1932). In principle, a properly
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estimated production function could prove a wealth of theoretically appropriate information to
guide farmers in their input and output decisions. The regression would yield not just ratios but
functions relating inputs to outputs, thus quantify the actions of the law of diminishing returns,
it would also reveal input substitution relationship. Indeed during the thirties some agricultural
economists had already produced estimates of the production relationship implied by the
neoclassical theory, including two way cross tabulations or bivariate regression involving one
input and one output (Hopkins 1930; Warren 1936; Menze 1942) but Douglas’s approach
offered a clear advantages over these earlier efforts. Its functional form easily handled several
inputs and parsimoniously captured the key assumptions of diminishing returns and when
estimated as a regression produced coefficients that were directly and easily interpretable as
elasticity’s of output with respect to inputs.
The hypothesis of this study is drawn from the Cobb-Douglas production function. The reason
for the choice of this view rests upon the argument that most empirical studies support its
postulations. Since it was developed by Knut Wicksell (1851-1926) and tested against
statistical evidence by Charles Cobb and Paul Douglas in 1928, the Cobb-Douglas function
form has been widely used to represent the relationship of an output to a set of inputs.
2.2 Empirical Literature
Africa was self-sufficient in goods and a leading agricultural exporter at the beginning of the
independence movement in 1960 and Asia was the epicentre of the world food crisis. By the
mid-1960s, Asia had launched the green revolution which at present adds 50 million metric
tonnes of grain to the world food supply each year. Although Asia struggles with issues of
household food supply, it is Africa, not Asia, which bears the brunt of the world food problem
(Byerlee, 1997). Africa’s food balance sheet has shifted from a surplus to deficit for example,
between the periods 1970 and 1985, food production went up by 1.5% while population grew
by 3%. This accelerated a decline in per capita food consumption, reducing average calorific
intake and
making Sub-Saharan Africa the only region in the world which experienced a
decline over time. Growing reliance on food imports, food aid, increasing degradation of the
natural resource base and increasing poverty are problems emanating from stagnation in food
production. Demand for food is expected to rise due to a double increase of 1.2 billion expected
in the human population by 2020. Food production gap in Africa demands fresh thinking and
urgent concentration of the mind by both scientists and policy makers. Two preconditions are
13 | P a g e
absolutely necessary for making an improvement on the downward spiral of poverty and
malnutrition in Africa. First, in most African economies, the driver to economic growth is
growth in agriculture. The majority of the population depends on agriculture, and an increase
in agricultural household income generate further rounds of spending that rouse economic
growth by increasing demand for rural non-farm products, as well as urban industrial products.
The second precondition is rapid technical change in food production (Byerlee, 1997).
Technology, institutional changes, infrastructure and changes in policy are crucial in providing
the momentum for a maize revolution. The importance of rice and wheat in Asia is equal to the
importance of maize in Eastern and Southern Africa because it is the dominant staple food. It
was introduced in Africa in the sixteenth century by Portuguese traders on the Eastern and
Western Africa coast and slowly moved inland through the incursion of slave traders who
valued maize as a storable and easily processed grain (Miracle, 1966).
Most of Africa’s population lives in rural areas and categorised by subsistence farming, poor
roads and other poor infrastructure, poor market information, low literacy levels and relatively
high levels of poverty levels. In addition to poverty, rural farmers use little or do not use some
inputs central for increased productivity (Chukwuji, et al., 2006). Sub Saharan African (SSA)
countries have drawn strategies of supporting poor farmers to eradicate poverty. Among
strategies, include increased agricultural output (productivity) through new technologies and
innovations like high yielding and disease resistant crops (Sentumbwe, 2007). New
technologies were further designed to enhance incomes of rural poor farmers and hence as a
means of accelerating economic development.
However, according to Wambui (2005), output growth is not only achieved by new
technological innovations but also through efficiency use of these technologies. Few studies
have been carried out to assess the allocative and technical efficiency of the rural farmers. Due
to scarce information and low literacy levels, most farmers in SSA may be still allocating
resources (inputs) in less suitable ways. A number of studies have noted an inverse relationship
between farm size and yields. Van Zyl (1995) points out that international evidence indicates
that a large-scale mechanised farm sector is generally inefficient especially when compared to
small-scale family type farming. Van Zyl's argument is supported by Adesina and Djato (1996)
who note that previous studies in Asia have tested for relative efficiency differences in terms
of farm size and found that small wheat farms in the Indian Punjab were more economically
efficient than large farms. The results from studies carried out in Pakistan contradicted those
14 | P a g e
of the Indian State. According to Alvarez and Arias (2004), some studies have also failed to
come up with concrete evidence of differences in the relative economic efficiency or its
components of technical or allocative efficiency, between small and large farms.
There have been different investigation of the production function in different parts of the
world in both developing and developed countries. Nasir (1990) has made an attempt to assess
and evaluate the production function in Kashmir agriculture for the period 1973-1986 and came
out against mass orchardisation in order to achieve regional self-reliance. Its analysis advocated
a thrust towards restructuring the basic input-output matrix to overcome the local supply gap.
He believes that reallocation of resources with capital intensity bias will promote growth and
employment potential of the agricultural sector in the state. The variables used in this study
were gross national output, land, rural population as a proxy for labour and annual capital
expenditure in rupees and a double log equation was used. The study concluded that marginal
of land is significantly greater than that of labour and capital inputs. Land has great potential
for growth and thus greater productivity owing to less capital intensive agriculture. The
marginal value of labour shows that, in farms the marginal return for each rupee spent on land
is profitable. Al-Najafi and Hussain (1993) estimated the production function in Iraq’s
agricultural sector during the period 1970-1986. The variables included in their study were
output (as a dependent variable) land, labour and capital as independent. The figure for land
was an index of total cropped area and capital included value of seeds, fertilisers, irrigation
charges, electricity, pest-cides, maintenance and other operational expenditures and a loglinear model was used.
Al-Najafi (1988) estimated agricultural production function in Iraq using time series data for
the value of agricultural output as a dependant variable agricultural land, capital (fixed and
variable), labour (as number of men) as independent variables for the period (1970-1983). All
variables used in the estimation were at 1970 constant prices and express all variables in terms
of index numbers. The model applied were in the form of log-linear. Al-Remawi (1998),
estimated the determinants and growth resources in Jordanian agricultural sector. He applied a
Cobb-Douglas production function in order to estimate the relationship between the value of
agricultural output and total cultivated area in donums, labour force in agriculture, and
agricultural mechanism, chemicals, fertiliser and rainfall. A semi-log model was used with time
series data for the period 1975-1992 using the index number for the variables included in the
15 | P a g e
study. In the study all variables except rain where statistically significant and all signs were
positive except labour which was negative.
Hussain and Saed (2001) assessed and evaluated the crop production function parameters in
Jordanian’s agricultural sector during the period 1981-1996, in order to achieve regional selfreliance. The analysis advocates a thrust towards restructuring the basic input-output matrix to
overcome the local supply gap. Different forms of production were applied, log-log model,
linear, semi-log, inverse semi-log for all variables. All forms used exhibited positive signs and
the coefficient of determination (R2) was very high. The variables used in this study as
aggregate are output as dependent variable, while the independent variables where land, labour
and capital.
Cornia (1985) pointed out that those who adduce evidence for the inverse relationship used this
to advocate for the redistribution of land from large-scale farmers into smaller unit holdings.
In Zimbabwe, the Government believes that if some land is redistributed from the large -scale
commercial (LSC) farmers to the smallholder farmers there will be some increase in
productivity and improved income distribution for the people of the country (Ministry of
Information, 2001).
Sen (1982), as quoted by Alvarez and Arias (2001), found an inverse relationship between farm
size and yields per acre, giving rise to a set of follow-up papers that tried to confirm these
results. Kalaitzandonakes et al (1992) failed to find the best results when analysing the
relationship between technical efficiency and size, with the results changing depending on the
method used to estimate technical efficiency. Byiringiro and Reardon (1996) carried out a farm
productivity study in Rwanda. They found that there was a strong inverse relationship between
farm size and land productivity and the opposite for labour productivity. For smaller farms they
found some evidence of allocative inefficiency in the use of land and labour. This they
assumed, was due to factor market access constraints. They also found that farms with greater
investment in soil conservation had much better land productivity than farms with average
investment in soil conservation. Ajibetun, Battese and Daramola (1996) also investigated the
factors that influenced the technical efficiencies (TE) of smallholder croppers in Nigeria. They
used trans-log stochastic frontier production function instead of the Cobb-Douglas frontier
function because the latter did not adequately represent their data. The estimated technical
efficiencies of the sampled farmers varied widely, ranging from about 19 percent to 95 percent.
16 | P a g e
Their results also indicate that the technical inefficiencies of production of farmers are
significantly related to age and farming experience of the farmers, farm size and the ratio of
hired-labour to total labour used. The inefficiency of these smallholder farmers was not
significantly related to the size of farming operations of the farmers involved.
Bekele, Viljoen and Ayele (2002), investigated the effect of farm size on the technical
efficiency of wheat production in Central Ethiopia. The study covered the 2000/2001 cropping
season, and a multi -stage sampling method was used to sample 199 respondents. Farm size
was designated as the size of total cultivated land operated by the farm households and farms
greater than 2 hectares were classified as large farms while those whose farm size were equal
or less than two hectares were classified as small. They used yield of wheat per hectare as the
dependent variable. Among the independent variables they used land area, seed, fertilizer,
labour and traction. The maximum-likelihood estimates for the parameters of the stochastic
frontier were obtained using the program, FRONTIER, version 4.1 developed by Coelli in
1994. Their results indicated that differences in technical efficiency exist between small and
large farm groups owning more oxen; increased family size and more income per household
reduce inefficiency in both large and small farm sizes. Although these authors came up with
expected results the margin between their definition of large and small farm is rather too
narrow. Better results could have been obtained if the difference between a larger and smaller
farm was widened.
Battese and Hassan (1998) investigated the efficiency of cotton farmers in Vehari District of
Punjab, Pakistan. They analysed data from cotton farmers using a stochastic frontier production
function model, in which technical inefficiency effects are assumed to be a function of other
observable variables related to the farming operations. A questionnaire was used to collect
details about operations of the farms especially varieties grown, yields obtained, the use of
inputs like fertilizer, seed and pesticides. The sample size was 45 and the predicted technical
efficiencies of these cotton farmers ranged from 0,699 to 0,991, with the mean technical
efficiency estimated to be 0,930. This implies that, on average they were producing cotton to
about 93 per cent of the potential (stochastic) frontier production levels, given the levels of
their inputs and the technology being used. The empirical results also indicate that an increase
in land area under cotton would result in greater productivity of cotton for the farmers.
17 | P a g e
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Introduction
The major thrust of the chapter is to look into ways of data collection, types of data used in the
research, estimation procedures and possible relationship which exist between the variables
being examined. It also focuses on the analytical framework of the study and provides the
model used in carrying out the research, the variables to be included in the model both
explanatory and dependent variables and justification of these variables. The model and some
of the variables to be used emanates from the literature reviewed.
3.2 Model Specification
The study will use both primary and secondary data. Secondary data will be useful for
background information and to obtain a deeper understanding of the study. The main source of
secondary data would be previous studies conducted in the area of study and primary data will
be obtained from small holder farmers in Mazowe District. The area under study is located in
Mashonaland Central province, and has a population of 232 885 and 63 632 households
(Census 2012). It has 16 tracks of land with associated buildings devoted for agriculture and
there are 3 main bodies of water moving to a lower level of channel on land which are
Madzomba, Nyamasanga and Sawi. Morning sunrise at 06:05 and evening sunset at 17:48. It’s
rough GPS position Latitude. -17.51670, Longitude. 30.96670. There is no significant whether
temperature 110 C/ 520 F, wind 6.9 km/h East/North East and the clouds are clear (Travelling
Luck for Mazowe 2013). The research will use a Cobb-Douglas Function to represent the
relationship of an output to a set of inputs.
Q=ALαKβ ………………..1
Where Q= output,
A, α, β are constants
L & K are labour and capital respectively
Capital can be interchanged with labour without affecting output:
P (L; K) =b LαKβ…………………………………….2
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Where P = total production
L =labour input
K =Capital input
b= total factor productivity
α & β are the output elasticities of labour and capital.
Due to its flexibility, the stochastic frontier production function specification of the CobbDouglas model will be used in this. Defined in logarithmic form, the stochastic frontier
production function would be as follows
Log (Y) =β0 + β1ln (L) + β2ln (K) + β3ln (age) + β4ln (fert) + β5ln (hsehld) + β6ln (s) + β7ln
(land)
+V..................................................................................................3
Ln is the natural logarithm.
Y = output
β’s = regression coefficients
L= labour
K= capital
AG= age of the household in years
LA= area cultivated by the farmer
S = expenditure on seed
FERT= expenditure on fertiliser
Hsehld = household size
V = error term
19 | P a g e
Variables to be on the questionnaire
Independent variables
Definition
Values
Age
Age of the household in years
Actual age in years
Household size
Number of people staying at Actual number in figures
the farm
Land
Area cultivated by the farmer Continuous variable
for maize production
Seed
Expenditure on seed (ha) in Continuous variable
United States Dollars (USD)
Fert
Expenditure on fertiliser (ha) in Continuous variable
USD
Capital
Capital devoted for maize Continuous variable
production
Labour
Man hours worked per week
Continuous variable
Output
Number of bags harvested per Continuous
hectare
3.3 Justification of Variables
3.3.1 Capital
It is vital in determining the total production in agriculture. The relationship between capital
and output is expected to be positive in the study. Capital entails an increase capital goods or
purchasing them and is measure in USD, it includes tractors, ploughs and many other
machinery used. Development economics generally agree that lack of investment in agriculture
is fundamental cause of continuing decline in production in developing nations. Official
development assistance to agriculture has been declining over years and public investment have
been limited by budgetary pressure (Herald 14 September 2006). In this study Coudere and
Marijse’s argument is on smallholder was used. They argued that there is no variation in the
types of equipment these farmers use. To represent capital the equipment’s used for maize
production are used as proxies for their capital
20 | P a g e
3.3.2 Age
This variable measures actual age of the responded of the household in years. Younger farmers
are expected to be mechanically constrained than older farmers who are perceived to have
acquired resources. Therefore, it is hypothesised that age of household head and machinery
access are positively correlated. This is supported by an observation (Belete and Fraser 2003)
that older farmers are likely to have more resources at their disposal. Contrary Dlova, Fraser,
Belete (2004) found out that age is one of the factors that can affect the probability of a farmer
being succefull. The study concluded that older farmers are less capable of carrying physical
activities while younger ones are capable. They also added that they are more ready to adopt
to modern technology. Although farmers become more skilful as they grow older, the learning
by doing effect is attenuated as they approach middles age as physical strength starts to decline
(Liu and Zhung 2000). Similar conclusion were made by Awundu and Huff man (2000). The
reason for this is because the age pick up the effects of physical strength as well as farming
experience of the household age.
3.3.3 Land
The variable refers to the land size in hectares. Increase in land size may enhance production
if the land is effectively utilised. At the same time land will be available but not effectively
utilised. Effective utilisation will entail application of appropriate farm practises that will lead
to high physical output than otherwise would be the case. A number of studies have noted an
inverse relationship between farm size and yields. Van Zyl (1995) points out that international
evidence indicates that a large-scale mechanised farm sector is generally inefficient especially
when compared to small-scale family type farming. Van Zyl's argument is supported by
Adesina and Djato (1996) who note that previous studies in Asia have tested for relative
efficiency differences in terms of farm size and found that small wheat farms in the Indian
Punjab were more economically efficient than large farms. The results from studies carried out
in Pakistan contradicted those of the Indian State. According to Alvarez and Arias (2004), some
studies have also failed to come up with concrete evidence of differences in the relative
economic efficiency or its components of technical or allocative efficiency, between small and
large farms. Cornia (1985) pointed out that those who adduce evidence for the inverse
relationship used this to advocate for the redistribution of land from large-scale farmers into
smaller unit holdings. In Zimbabwe, the Government believes that if some land is redistributed
21 | P a g e
from the large -scale commercial (LSC) farmers to the smallholder farmers there will be some
increase in productivity and improved income distribution for the people of the country
(Ministry of Information, 2001).
3.3.4 Seed
The use of hybrid maize seed produced by local seed companies or imported has gone down
due to their high cost and need for foreign currency. When this seed is not available on time
many farmers resort to using retained grain. Seed requirements are calculated by using the
recommended seed rates and forecast area to be planted next year and are included in the total
utilization. It is hypothesised that farmers with inadequate inputs are less likely to achieve
higher levels of production leading to lack of purchasing power for machinery and equipment.
3.3.5 Fertiliser
A number of studies established that fertiliser usage is positively related to output (Reardon et
al 1996). Conversely a farm unit that is too constraint to afford adequate amount of fertiliser
will most probably experience lower output. It is one of the land augmenting inputs that is
likely to enhance land productivity, thus an increase in fertiliser usage leads to higher yields
where rainfall is adequate. World Bank (2007) found out that an increased use of fertiliser
accounted for at least 20% growth in agriculture in developing world over the last 30 years.
The researcher expects a positive relationship between fertiliser and maize output.
3.3.6 Labour
Labour marginal productivity in traditional sectors was thought to be negative or zero and thus
it could be withdrawn without any reduction in the output. If the total output does not decrease
through withdrawal of some labourers (who make no contribution to the output), then utilising
the surplus of labour force in alternative occupation can increase national output. It was
recognised by some development economist that for agricultural sector in developing sectors
to perform these function, productivity must be through the application of new technology
(Meller 1979).
3.3.7 Household size
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3.4 Estimation Procedure and Diagnostic Test
The econometric package STATA, will be used to for estimation of the results. Each
independent variable will be tested for significance level on the dependent variable. The
ordinary least square (OLS) method of regression is used in this research.
3.4.1 Heteroscedasticity
Heteroscedasticity is a violation of one of the requirements of ordinary least squares (OLS) in
which the error variance is not constant. The consequences of Heteroscedasticity are that the
estimated coefficients are unbiased but inefficient. The variances are either too small or too
large, leading to Type I or II errors in the presence of Heteroscedasticity ( type I error leads
rejection of a true Null Hypothesis, while in type II error one accepts a false Null Hypothesis,
OLS is not BLUE (Best Linear Unbiased Estimator). However, in order to be sure of the level
of Heteroscedasticity, the Breusch Pagan test is used. Some of the methods used to correct for
Heteroscedasticity are transformation of data into natural logarithms and the generalized least
squares (GLS), also known as the weighted least squares (WLS).
3.4.2 Multicollinearity
Assumption 10 of the Classical Linear Regression Model (CLRM) is that there is no
Multicollinearity among regressors included in the model. The term Multicollinearity is due to
Frisch (1934). Originally it meant the existence a “perfect”, or exact linear relationship among
some or all explanatory variables of a regression model. If it is perfect, the regression
coefficients of the X variables are indeterminate and their standard errors are infinite. If it’s
less than perfect, the regression coefficients, although determinate possess large standard errors
(in relation to the coefficients themselves), which means the coefficients cannot be estimated
with great precision or accuracy. Whenever Multicollinearity is present the remedy is to drop
the variable with high R2 or do nothing, it results in wrong signs of the estimated parameters.
A correlation statistic that is greater than 0.8 reflect high correlation among variables (Barnes
et al 1978). Multicollinearity will be conducted on the null hypothesis that there is high
correlation between variables against the alternative that there is no high correlation.
3.4.3 Data types and sources
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Primary data will be collected from farmers using a survey method involving structured
questionnaire. DeVuas (2002) defined a questionnaire as a general term to include all
techniques of data collection in which each person is asked to respond to the same set of
questions in a predetermined order. Cross sectional data was obtained from A1 farmers in
Mazowe District. 354 self-administered questionnaires were used to randomly collect data
from a population size of 3963 farmers (Krejcie and Morgan 1960). Battese (1998) unless
random sampling methods are used in obtaining the sample of the farmers, the analysis of the
data may be of no benefit in making inference for the whole population. Thus, in-order to obtain
farm level data on inputs and output on maize and other variables which are important for the
study random sampling of farms was selected. It was not feasible for researcher to attempt to
collect data on all possible crops grown by the farmers in the population involved, because the
questionnaire may be too long and complicated to ensure high response rate and quality data
as noted by Battese (1998). This is why the study was restricted to the analysis of one of the
most important crops involved in the district which is maize. The student believes that the
questionnaire produced managed to collect precise data required to answer the research
question, as many authors for example (Bell 2005 and Oppenheim 2000) argue that it is far
harder to produce a good questionnaire.
3.4.4 Conclusion
To sum up, the chapter specified the model, justified the variables, and expressed the diagnostic
tests, and the data types and sources. The next chapter focuses on the results presentation and
interpretation
CHAPTER FOUR
RESULTS PRESENTATION AND ANALYSIS
4.1 Introduction
This chapter represents the results of the findings in the context of estimating a maize
production function. The data represented was collected from 354 smallholder farmers in
24 | P a g e
Mazowe district. The aim of this chapter is to highlight the input output relationship in maize
production. The chapter begins with the diagnostic checks test results, followed by regression
results and lastly marginal effects.
4.2 Diagnostic Test Results
4.2.1 Multicollinearity Test Results
The term Multicollinearity is due to Frisch (1934) that originally meant the existence of a,
“perfect”, or exact relationship among or some explanatory variables (Gujaratti, 2011). The
Multicollinearity test is carried under the null hypothesis that the explanatory variables are not
correlated against the alternative that there is correlation.
Table 4.1 Correlation matrix results
land1
seed1
fert1
K1
L1
age1
hsehld1
land1
1.0000
0.6197
0.6317
0.3065
0.5174
-0.1480
0.3566
seed1
fert1
K1
L1
age1
hsehld1
1.0000
0.5116
0.3842
0.3917
-0.2801
0.3465
1.0000
0.4579
0.4198
-0.0757
0.4111
1.0000
0.2388
0.1039
0.3446
1.0000
0.0288
0.3442
1.0000
0.1660
1.0000
As a rule of thumb, if the pairwise or zero order correlation coefficient between two regressors
is high, exceeding 0.8, multicollinearity is considered to be severe. Blanchard (1967) posited
that multicollinearity is essentially a data deficiency problem (micronumerosity). The
correlation table 4.1 shows the entries along the main diagonal which show variable’s own
correlation whilst pair-wise correlations that occur between explanatory variables are presented
by entries off the main diagonal. The researcher did not reject the null hypothesis that there is
25 | P a g e
no multicollinearity since there is no perfect multicollinearity therefore researcher adopts the
do nothing approach (Blanchard, 1967).
4.2.2 Heteroskedasticity Test Results
An important assumption of the classical linear regression model is that the disturbance term
in the population regression function are homoscedasticity, that is they all have the same
variance. Persisting in using the usual testing procedure despite Heteroscedasticity, whatever
conclusion drawn or inference made may be misleading.
Table 4.2 Breusch-Pagan/Cook-Weisberg test for heteroscedasticity
Chi2(1)
102.10
Prob > chi2
0.0000
The study tested the null hypothesis that the error variances are all equal versus the alternative
that the error variance are all multiplicative function of one or more variables. From table 4.2
shown above the alternative hypothesis states that the error term variance increases (decreases)
as the predicted values of Log Y increases for example, the bigger the Log Y increases, the
bigger the error variance. A large chi-square of 102.10 indicated that heteroscedasticity was
present. In-order to correct for heteroscedasticity the researcher used Robust Standard Errors
and it relaxed the assumption that the errors are identically distributed.
4.2.3 REGRESSION RESULTS
A Cobb-Douglas function was used to run estimates of a production function between the
dependant and independent variables. The outcome in the table below shows six variables that
contributed significantly to the production function. The variables are age, household, seed,
labour, fertiliser and land.
Table 4.3 Regression Results
Output1
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Coefficient
Robust
Error
Std t
P>t
land1
seed1
fert1
K1
L1
age1
hsehld1
_cons
0.231
0.433
0.245
0.012
0.167
-0.160
0.067
0.424
0.034
0.089
0.038
0.009
0.043
0.044
0.023
0.345
6.88
4.86
6.41
1.32
3.85
-3.63
2.97
1.23
0.000
0.000
0.000
0.188
0.000
0.000
0.003
0.219
Number of observation = 352
F (7,346)
=83.78
Prob >F
=0.0000
R-squared
=0.7798
Root MSE
=0.12192
4.2.4 INTERPRETATION OF RESULTS
Significance of the whole model is revealed by the F-statistic and the predictability capacity
was shown by the R2 (the coefficient of determination). The F statistic value of 83.78 far more
exceeds the required rule of thumb of 5. As ascertained by Gujarati (2004) it is apparent that
the null hypothesis of coefficients of explanatory variable being simultaneously equal to zero
is rejected. By the same token the p-value of F-statistic is 0.000 which is way less than 0.05
equally signifies the significance of the whole model. Meanwhile, R-squared shows goodness
of fit of a model as the value of R2 obtained is greater than 50%. The observed R2 is 0.7798
shows variables in the model better explains the variability of the dependent variable (maize
output). Approximately, 78 percent of the variation in the regressed (maize output) is due to
variation in seven explanatory variables that is land size, seedling, fertiliser, capital, labour,
farmer’s age and farmers’ household size. The remaining 22 percent is due to other stochastic
factors.
The regression results show that all variables except age of the farmer are positively related to
maize output. The results also shows that except capital all variables had a significant
relationship with maize output. The variable capital was insignificant because equipment
owned was used as a proxy for their capital. This results concurs with Condere & Marijses’s
(1998) whose argument was that there is no variation in the types of equipment smallholder
farmers use.
27 | P a g e
The results shows that an increase in any one of these except age of the farmer will increase
maize output. The significance of variables is measured by the t-statistic values. A variable is
said to be significant if its absolute t-statistic is greater than two or a neighbour of 2. From the
results all variables (except capital) are significant in explaining variation in maize output since
all t-statistic are greater than 2.
The results shows land size (Land1) coefficient of 0.231 which is positive and significant since
p-value is 0.000 and the t-statistic (6.88) is greater than 2, hence the relationship is significant
at all levels. This suggests a unit increase in land size result in 0.23 units increase in maize
output. The positive impact of land size on maize output was expected as testified by Cornia
(1985) who finds that an increase in land size have a direct positive relationship with output.
Results shows the coefficient of 0.433 which indicates a positive and significant as the p-value
is 0.000 and the t-statistic (4.86) is greater than 2, showing significantly that a percentage
increase on money spend on seed will lead to a 43.3% increase in maize output. The results are
in line with Benson (199), who observe that seedling is positively related to maize output
highlighting that an increase in money spend on seeds will increase maize output levels. The
results would be relevant to show most Zimbabwean maize farmers are unable to afford hybrid
seeds they use local seed which are cheaper. The implication is that locally unimproved maize
seed most farmer’s plant are significantly out-yield even those fertilised.
Basing again on the regression, results have shown that the coefficient of fertilizer (fert1) is
positive and significant as the p-value is 0.000 and the t-statistic (6.41) is greater than 2. There
is strong evidence that amount of fertiliser is positively related to maize productivity in
Zimbabwe. The results shows the coefficient of fertiliser as 0.245 which shows that a percent
increase in money spend on fertiliser is lease to about 25% increase in maize output. This result
reveals that a unit increase in fertiliser result in one quarter increase in maize output level. As
such, the results conform finding from various researchers who find that fertiliser plays a vital
role in maize productivity in agriculture.
Basing again on the regression, results have shown that the coefficient of Labour (L1) is
positive and significant as the p-value is 0.000 and the t-statistic (3.85) is greater than 2. There
is strong evidence that amount of labour is positively related to maize productivity in
Zimbabwe. The results shows the coefficient of labour as 0.167 which shows that a percent
increase in money spend on hiring an extra employee will lead to about 17% increase in maize
output. The findings of this study did not compliment that of Meller (1979) who establish that
28 | P a g e
labour marginal productivity was thought to be negative or zero and that labour can be
withdrawn without affecting output.
Basing again on the regression, results have shown that the coefficient of age (age1) is negative
and significant as the p-value is 0.000 and the t-statistic (3.63) is greater than 2. There is strong
evidence that as a farmer gets old this negatively affects productivity in Zimbabwe. The results
shows the coefficient of age as -0.16 which shows that a percent increase number of years will
lead to about 16% decrease in maize output. The findings of this study compliment that of
Belete and Fraser (2003) who find that youthful farmers are innovative than their older
counterparts.
The results have shown that the coefficient of household size (hsehld1) is positive and
significant as the p-value is 0.003 and the t-statistic (2.97) is greater than 2. There is strong
evidence that as farmers has more individuals as family members old this positively affects
productivity at the farm. The results shows the coefficient of age as 0.067 which shows that a
percent increase household size will lead to about 7% increase in maize output. The findings
of this study compliment that of Setumbwe (2000) who find that smallholders farmers mainly
depends on family free labour such that family size has a direct relationship with the output
farmers produces
4.3 CONCLUSION
This chapter presented and interpreted the results obtained from a Cobb-Douglas function. In
conclusion, only one variable capital proved to be insignificant and age showed an inverse
relationship with output. Chapter 5 will now highlight policy recommendation.
CHAPTER FIVE
POLICY RECOMMENDATIONS AND CONCLUSION
5.0 INTRODUCTION
After researching and presenting findings in previous chapters, this chapter dispenses the major
objective of empirical that is recommending policy makers courses of main action that can be
29 | P a g e
perused as remedies. It outlines summary of the study, policy recommendations, and
suggestions for future studies, limitations and delimitations of the study.
5.1 SUMMARY OF THE STUDY
In the first chapter of this research, the researcher briefly looked at the background of maize
production in Zimbabwe from previous years to date. Various trends on maize output were
highlighted. The chapter also highlighted the introduction of maize from Europe to Southern
and Central America and how it later spread to Africa. The main objective was to estimate the
relationship between maize output and main traditional inputs and investigate some socioeconomic factors which also affect maize production.
After establishing the objectives the researcher went on to look at related theoretical and
empirical literature as well as determinants of maize production. Most literature suggested that
socio-economic factors and traditional inputs factors have an impact on maize production.
In chapter 3, the researcher looked at the methodology used to estimate the maize production
function. The Cobb-Douglas function was used and found that al variables has a positive
relationship with output except for capital.
5.2 POLICY RECOMMENDATION
Due to a decline in agricultural production from year 2000, the country has not been meeting
its requirements for maize to feed its people. This was triggered by high seasonal rainfall
patterns deviating from the mean. This calls for investments in construction of more dams to
be used for irrigation, in order to reduce high import bill on maize and to eradicate poverty.
We also recommend that Agritex programmes should be introduced at community level. This
involves periodic visits by officer to farmers and educate them on maize farming. This
education may help improve the quality and yields on maize in Mazowe district.
5.3 SUGGESTION FOR FUTURE STUDIES
The researcher advises upcoming researchers to dwell on some areas which are very important
but due to some constraints he failed to cover the area and is perceived to be of paramount
importance, these include the importance of farmer education in enhancing productivity,
financial assistance of smallholder farmer through credit facility to purchase inputs and
30 | P a g e
irrigation among others. Future researchers should change the sample size of households that
may alter the significance of the variables.
5.4 LIMITATIONS AND DELIMITATIONS
•
Some information was restricted and considered confidential and this became lengthy
to the researcher to compile data
•
Availability of information on past researchers estimating maize production function
was very limited and the researcher had to use very old studies and other production
functions not of maize.
•
Financial constraint was the major problem as the researcher had to go through the
whole district, travelling using own transport.
5.4.1DELIMITATIONS
The research was only limited to smallholder farmers in Mazowe district but there are many
districts in the province and that random sampling was used to interview only farmers who
reside in the district.
5.5 CONCLUSION
A thorough research was embarked to estimate a maize production function for smallholder
farmers in Mazowe district. Objectives of the study cemented the background of the research
as was traced by the researcher. To attain the desired outcome both theoretical and empirical
review complemented the methodology used. Out of the seven explanatory variables in the
model, only one (capital) was not significant. In order to highlight some areas which require
attention for research the author offered some recommendation based on the findings of this
study.
31 | P a g e
List of Acronyms
AP
Average Product
BLUE
Best Linear Unbiased Estimator
CLRM
Classical Linear Regression Model
DDF
District Development Fund
GDP
Gross Domestic Product
GLS
Generalised List Squares
GMB
Grain Marketing Board
32 | P a g e
GoZ
Government of Zimbabwe
LCS
Large Commercial Scale
MDG
Milleminium Developmental Goals
MP
Marginal Product
OLS
Ordinary Least Squares
TE
Technical Efficiency
UN
United Nations
USD
Unites States Dollar
USDA
United States Department of Agriculture
WLS
Weighted List Squares
ZIMSTAT
Zimbabwe Statistical Agency
List of Tables
Table 1
: Mean range of maize (ha) grown by farmers in Mashonaland Province for 4
years.
2
: Average Maize production per district 2003-2006
3
: Total Production Function
33 | P a g e
4
: Variables to be on the questionnaire
4.1
: Correlation Matrix Results
4.2
: Bruesch- Pagan/ Cook Weisberg test for Heteroscedasticity
4.3
: Regression Results
Reference List
Awudu, A and Huffman, W (2000). Structure Adjustment and Economic Efficiency
of Rice Farmers in Northern Ghana. Economic Development and Cultural Change,
48: 503-519.
FAO. 2007 http://www.fao.org
Frisch R (1934) Statistical Confluence Analysis by Means of Complete regression system,
Institute of Economics, Oslo University
34 | P a g e
Gujaratti D (2004) Econometrics, 4th Edition, Mc Graw Hill Companies, New York
Liu Z. and Juzhong Z. (2000). Determinants of Technical Efficiency in PostCollective Chinese Agriculture: Evidence from Farm-Level Data. Journal of
Comparative Economics, 28:545-564.
Mellor J, W (1976) The Economics of Agricultural Development, Cornell University Press
World Bank (2007) Zimbabwe Country Profile and Statistic
Al-Najafi, S and Hussain, A (1993) Estimates of agricultural production function in Iraq: 19701986: An econometric analysis. Muta Journal for Research and Studies 8.5:79-93
Al-Remawi, A (1998) “Jordanian Agricultural Sector: Determinants and Growth Resources”
Journal for Research and Studies, Jerash University, 2.5
Banaeien, N and Zangeneh, M (2001) Estimating Production Function of Walnut Production
in Iran using a Cobb-Douglas Method, Original Research Paper 44.4
Banzhaf, H (2006) The other Economic Department: Demand and Value Theory in Early
Agricultural Economics, History of Political Economy 38: 9-38
Benedict, M (1932) The Opportunity Cost Basis of Substitution Method in Farm Management,
Journal of Farm Economics 14.3: 384-405.
Black, S and Lynch, M (2001) “How to compete: The impact of Workplace Practises and
Information Technology on Productivity”, Review of Economics and Statistics 83.3: 4343-445.
Douglas P (1976) The Cobb-Douglas Production Function once Again: Its history. In testing
and some new empirical values, Journal of political economy, 84.5:903-915
Fox, K (1986) Agricultural Economists as World Leaders in Applied Econometrics 1917-33,
American Journal of Agricultural Economics, 68.2:381-86.
Hopkins, J (1930) Interpretation of farm efficiency factors, Journal of farm Economics,
12.3:384-402.
Hussain, M and Saed A, J (1989) Econometrics: Theory and Application “Dar Wael
Publishing, Jordan, Amman.
Menze E (1942) An Economic Analysis of the length of feeding period in the production of
Hogs, Journal of farm Economics 24.2:518-523.
35 | P a g e
Rutherford M (2009) The USDA Graduate School: Government Training in Statistics and
Economics.1921-1945.
Waite N (1936) Combination of factors of different efficiency: Journal of Economics 18.4:930.
Warren S (1936) Statistical analysis in farm management research: Journal of farm economics
18.1: 169-179.
Ingosi, Abner. 2005. Economic Evaluation of Factor Influencing Maize Yield in the
North Rift Region of Kenya. Masters of Science Thesis, Colorado State University
Government of Zimbabwe (2013) Planning Bulleting: First Quarter, Volume 2
Government of Zimbabwe (2013) Zimbabwe Agenda for Sustainable Socio-Economic
Transformation: October 2013-December 2018
Feresu, S. Manjengwa, J. Chimhou A (2013) Understanding poverty promoting well-being and
Sustainable Development
Maddison, D., M. Manley, and P. Kurukulasuriya. 2006. The impact of climate change on
African agriculture: Aricardian approach. CEEPA Discussion Paper no.15. University of
Pretoria, South Africa
Okoruwa, A. E. (1997). Utilization and Processing of Maize. IITA Research Guide 35. IITA
Ibadan, Nigeria.
APPENDICES
Appendix 1: Questionnaire
MIDLANDS STATE UNIVERSITY
FALCULTY OF COMMERCE
DEPARTMENT OF ECONOMICS
36 | P a g e
My name is Elias Chipatiso level 4.2 student from MSU with registration number R112185J
studying towards a Bachelor of Commerce Economics Honours Degree. I am currently doing
a research: Estimating a maize production function for smallholder farmers in Mazowe
District in partial fulfilment of my degree. I would like to find out the factors that affect maize
output in the area under study. The responses to this questionnaire will be confidentially
treated, and strictly be for academic purposes only.
Instructions

No names required on this questionnaire

Tick where necessary
1. Gender
Male
2. Age of household head
3. Household size
Female
………
………
4. Is your maize production under irrigation?
Yes
No
5. Land size used for maize production (in hectares)
…………..
6. Which farming equipment’s do you own?
Hoes
Ox-drawn ploughs
Tractor
scotch cart/ trailer
7. Do you own any not mentioned above, if yes please specify?
…………………………………………………………
8. What type of inputs do you use and how much do they cost?
Items
37 | P a g e
Type
Amount
hectare)
(Kg’s
per Value in USD
Seed
Fertiliser
Chemicals
Other
9.
10.
How many bags of maize do you get per hectare?
………………..
What level of agricultural training have you attained?
None
Master Farmer
Cert-Diploma
Other
11.
How many hours do you spend in the field per day? …………
12.
How many days do you work in the field per week?
....................
Appendix 2: Data Set
Output land
seed
fert
K
L
35
3.5
42
144
800
20
1.5
23
99
800
40
4.7
46
102
1500
38
3
38
96
620
45
5
40
136
600
38
2
33
136
750
49
4.5
40
102
900
47
4
46
170
850
39
3
40
100
650
44
4.5
46
105
740
48
3.5
46
170
800
51
5.5
46
165
6500
38 | P a g e
age
45
30
40
36
49
42
49
42
30
42.5
41.5
49
hsehld
45
60
40
38
63
52
49
47
39
44
48
51
6
4
6
4
7
8
9
6
6
9
6
11
37
47
39
40
44
20
26
45
42
40
41
46
37
40
47
51
15
17
39
44
46
46
48
49
47
41
37
50
49
49
15
35
50
45
36
47
42
39
49
44
40
51
37
35
44
40
39 | P a g e
2
4
2.5
3.5
4
2.5
3
4
3.8
4
3.4
4.6
2.5
2.9
3.5
5
1.2
1.5
3
3.6
3.9
3.5
4
4.2
5
5.5
1.5
5.5
3.5
4
1.4
3
5.5
5
3.5
4
3.5
3
3.7
3.8
3.5
4.6
3.5
3.5
3
3.25
38
44
40
40
42
23
22
48
40
44
46
40
36
40
44
48
23
23
30
40
40
44
42
40
42
42
38
46
40
46
21
40
46
44
35
42
40
38
40
46
38
46
35
42
42
42
93
101.4
99
100.41
136
90
66
140
136
102
132
165
70
99
120
170
64
62
75
132
136
140
165
136
170
124
144
170
155
160
96
108
155
136
93
130
125
102
150
120
124
165
96
120
140
124
700
900
650
1200
1250
500
600
1600
1250
1800
3500
4000
800
1500
1300
3500
350
450
700
1300
4200
4000
6000
6500
5200
3500
1550
6570
3000
3500
450
720
5500
3600
550
6200
5000
900
3700
3000
2800
6500
1120
650
5600
2500
40
40
41.25
49
45
32
41.25
45
40
36
42
44
40
42
44
49
28
30
36
40
42
40
35
41.25
35
52.5
28
45
42
41.25
20
36
41.5
37.5
20
40
41.25
28
30
40
41.25
45
42
40
36
35
63
47
39
40
51
64
68
45
42
40
63
66
37
40
47
51
61
69
39
44
46
51
48
49
47
65
37
51
51
49
63
60
50
45
36
47
42
39
49
68
71
51
66
35
44
40
4
8
9
7
7
4
4
9
7
4
7
9
5
8
6
8
4
7
4
6
8
4
7
8
7
6
5
8
9
6
3
6
7
7
5
4
7
2
7
5
15
14
5
7
10
6
37
49
43
37
39
44
42
35
48
52
49
47
39
41
52
46
35
20
40
38
50
38
49
47
39
44
48
51
37
47
39
40
37
50
49
49
15
35
50
45
36
47
42
39
49
44
40 | P a g e
2
4
4.2
1.5
2.8
3
3.5
2
4.5
5
5
3.5
3.8
3.5
4
2.9
3.5
2
4.7
3
5.5
5
4.5
4
3.5
4.5
3.5
5.4
2.25
4
3.6
3.5
1.5
4.5
3.5
4
1.5
3
5.5
5
3
4
3.5
4.5
2.5
3.5
40
46
48
24
44
40
45
40
40
50
40
44
46
42
46
44
42
38
46
44
40
42
40
44
40
42
40
46
38
48
40
42
44
40
40
40
40
40
46
44
42
40
42
42
40
46
99
110
136
96
100
145
120
96
124
141
136
124
120
140
155
136
102
70
124
96
170
99
136
165
100
155
132
231
132
220
132
198
120
231
160
155
66
102
170
210
120
165
136
115
150
120
600
550
4500
6500
1200
6700
4200
520
1200
5000
1700
1700
6500
5700
5200
6000
6500
1900
2000
1700
2300
750
1560
1650
750
5200
5500
6500
4500
4300
2500
4000
1600
6570
3000
3500
900
720
6000
4700
2500
6200
2800
3500
4000
2700
25
44
50
35
45
52.5
40
45
49
42
30
41.25
30
52.5
30
42
45
25
40
45
49
36
42
41.25
30
52.5
41.5
37.5
40
40
41.25
49
28
30
30
41.25
20
28
41.5
37.5
35
40
36
40
42
44
37
49
43
69
53
44
67
58
54
52
49
70
61
41
62
58
45
60
40
38
63
52
49
47
39
44
48
51
63
47
39
40
37
51
51
49
63
60
50
45
36
47
42
39
49
68
4
7
7
9
12
8
9
3
6
13
8
5
9
4
12
9
5
4
9
4
6
8
4
6
4
6
7
9
4
8
5
9
7
8
5
6
3
6
11
7
4
4
7
2
7
7
40
51
37
35
37
40
37
47
43
37
39
35
20
40
38
45
38
49
47
39
44
48
51
37
47
39
40
44
20
37
50
49
49
15
35
50
45
36
47
42
39
49
44
40
51
37
41 | P a g e
3.5
5
2.8
3.5
3
3.5
2
3.75
4
2.2
3.5
3.5
1.2
4.7
3
5
3
4.5
4
3.5
4.5
5.4
5.5
3.5
4
4.5
3.5
4
2
1.5
5.5
3.5
4
1.4
3
5.5
5
3.5
4
3.5
3
3.7
3.8
3.5
4.6
3.5
44
46
48
42
42
42
40
42
48
40
40
42
40
46
44
42
42
46
50
42
42
40
40
35
46
42
40
42
23
38
46
40
46
21
40
46
44
35
42
40
38
40
46
38
46
35
124
165
120
120
130
136
90
100
93
85
100
102
66
124
96
160
93
124
136
100
165
170
235
132
215
124
132
165
70
144
170
155
160
96
108
155
136
93
130
125
102
150
120
124
165
96
1500
6000
4250
1700
2650
1750
1600
1550
4500
6500
2500
6500
4600
1400
620
2400
6600
560
900
5600
740
640
680
4500
650
600
550
4500
6500
1550
6570
3000
3500
450
720
5500
3600
550
6200
5000
900
3700
3000
2800
6500
1120
41.25
45
40
36
35
30
25
30
39
35
45
20
28
40
45
49
42
30
41.25
30
52.5
41.5
40
40
41.25
49
35
40
28
45
42
41.25
20
36
41.5
37.5
20
40
41.25
28
30
40
41.25
45
42
71
51
66
35
44
40
37
49
43
69
53
45
60
40
38
63
52
49
47
39
44
48
51
63
47
39
40
51
64
37
51
51
49
63
60
50
45
36
47
42
39
49
68
71
51
66
8
9
7
4
6
5
5
4
7
9
5
5
4
9
4
6
8
6
6
5
4
8
9
6
7
4
5
7
4
5
8
9
6
3
6
7
7
5
4
7
2
7
5
15
14
5
35
44
40
37
49
43
37
39
44
42
35
48
52
49
47
39
41
52
46
35
20
40
38
45
38
49
47
39
44
48
40
41
46
37
40
47
51
15
17
39
44
46
46
48
49
35
42 | P a g e
3.5
3
3.25
2
4
4.2
1.5
2.8
3
3.5
2
4.5
5
5
3.5
3.8
3.5
4
2.9
3.5
2
4.7
3
5.5
5
4.5
4
3.5
4.5
3.5
4
3.4
4.6
2.5
2.9
3.5
5
1.2
1.5
3
3.6
3.9
3.5
4
4.2
3.5
42
42
42
40
46
48
24
44
40
45
40
40
50
40
44
46
42
46
44
42
38
46
44
40
42
40
44
40
42
40
44
46
40
36
40
44
48
23
23
30
40
40
44
42
40
42
120
140
124
99
110
136
96
100
145
120
96
124
141
136
124
120
140
155
136
102
70
124
96
170
99
136
165
100
155
132
102
132
165
70
99
120
170
64
62
75
132
136
140
165
136
144
650
5600
2500
600
550
4500
6500
1200
6700
4200
520
1200
5000
1700
1700
6500
5700
5200
6000
6500
1900
2000
1700
2300
750
1560
1650
750
5200
5500
1800
3500
4000
800
1500
1300
3500
350
450
700
1300
4200
4000
6000
6500
800
40
36
35
25
44
50
35
45
52.5
40
45
49
42
30
41.25
30
52.5
30
42
45
25
40
45
49
36
42
41.25
30
52.5
41.5
36
42
44
40
42
44
49
28
30
36
40
42
40
35
41.25
45
35
44
40
37
49
43
69
53
44
67
58
54
52
49
70
61
41
62
58
45
60
40
38
63
52
49
47
39
44
48
40
63
66
37
40
47
51
61
69
39
44
46
51
48
49
45
7
10
6
4
7
7
9
12
8
9
3
6
13
8
5
9
4
12
9
5
4
9
4
6
8
4
6
4
6
7
4
7
9
5
8
6
8
4
7
4
6
8
4
7
8
6
20
40
38
45
38
49
47
39
44
48
51
37
47
39
40
45
20
40
40
37
50
49
49
15
35
50
45
36
47
42
39
49
44
40
51
36
47
42
39
49
44
40
51
37
35
37
43 | P a g e
1.5
4.7
3
5
2
4.5
4
3
4.5
3.5
5.5
2
4
2.5
3.5
4
2.5
3.6
3.5
1.5
4.5
3.5
4
1.5
3
5.5
5
3
4
3.5
4.5
2.5
3.5
3.5
5
3
4
3.5
4.5
2.5
3.5
3.5
5
2.8
3.5
3
23
46
38
40
33
40
46
40
46
46
46
38
44
40
40
42
23
40
42
44
40
40
40
40
40
46
44
42
40
42
42
40
46
44
46
42
40
42
42
40
46
44
46
48
42
42
99
102
96
136
136
102
170
100
105
170
165
93
101.4
99
100.41
136
90
132
198
120
231
160
155
66
102
170
210
120
165
136
115
150
120
124
165
120
165
136
115
150
120
124
165
120
120
130
800
1500
620
600
750
900
850
650
740
800
6500
700
900
650
1200
1200
500
2500
4000
1600
6570
3000
3500
900
720
6000
4700
2500
6200
2800
3500
4000
2700
1500
6000
2500
6200
2800
3500
4000
2700
1500
6000
4250
1700
2650
30
40
36
49
42
49
42
30
42.5
41.5
49
40
40
41.25
49
45
32
41.25
49
28
30
30
41.25
20
28
41.5
37.5
35
40
36
40
42
44
41.25
45
35
40
36
40
42
44
41.25
45
40
36
35
60
40
38
63
52
49
47
39
44
48
51
63
47
39
40
51
64
39
40
37
51
51
49
63
60
50
45
36
47
42
39
49
68
71
51
36
47
42
39
49
68
71
51
66
35
44
4
6
4
7
8
9
6
6
9
6
11
4
8
9
7
7
4
5
9
7
8
5
6
3
6
11
7
4
4
7
2
7
7
8
9
4
4
7
2
7
7
8
9
7
4
6
40
37
47
43
37
39
35
20
40
38
45
38
49
47
39
44
48
51
37
47
39
40
47
39
40
44
20
26
45
42
40
41
46
37
40
47
51
15
17
39
44
46
46
48
49
47
44 | P a g e
3.5
2
3.75
4
2.2
3.5
3.5
1.2
4.7
3
5
3
4.5
4
3.5
4.5
5.4
5.5
3.5
4
4.5
3.5
4
2.5
3.5
4
2.5
3
4
3.8
4
3.4
4.6
2.5
2.9
3.5
5
1.2
1.5
3
3.6
3.9
3.5
4
4.2
5
42
40
42
48
40
40
42
40
46
44
42
42
46
50
42
42
40
40
35
46
42
40
44
40
40
42
23
22
48
40
44
46
40
36
40
44
48
23
23
30
40
40
44
42
40
42
136
90
100
93
85
100
102
66
124
96
160
93
124
136
100
165
170
235
132
215
124
132
101.4
99
100.41
136
90
66
140
136
102
132
165
70
99
120
170
64
62
75
132
136
140
165
136
170
1750
1600
1550
4500
6500
2500
6500
4600
1400
620
2400
6600
560
900
5600
740
640
680
4500
650
600
550
900
650
1200
1250
500
600
1600
1250
1800
3500
4000
800
1500
1300
3500
350
450
700
1300
4200
4000
6000
6500
5200
30
25
30
39
35
45
20
28
40
45
49
42
30
41.25
30
52.5
41.5
40
40
41.25
49
40
41.25
49
45
32
41.25
45
40
36
42
44
40
42
44
49
28
30
36
40
42
40
35
41.25
35
40
37
49
43
69
53
45
60
40
38
63
52
49
47
39
44
48
51
63
47
39
40
47
39
40
51
64
68
45
42
40
63
66
37
40
47
51
61
69
39
44
46
51
48
49
47
5
5
4
7
9
5
5
4
9
4
6
8
6
6
5
4
8
9
6
7
4
5
8
9
7
7
4
4
9
7
4
7
9
5
8
6
8
4
7
4
6
8
4
7
8
7
41
37
50
49
49
15
35
50
45
36
47
35
20
40
38
45
38
49
47
39
44
48
40
20
40
38
50
38
49
47
39
44
48
51
37
47
39
40
15
35
50
45
36
47
42
39
45 | P a g e
5.5
1.5
5.5
3.5
4
1.4
3
5.5
5
3.5
4
3.5
2
4.7
3
5.5
5
4.5
4
3.5
4.5
3.5
4
2
4.7
3
5.5
5
4.5
4
3.5
4.5
3.5
5.4
2.25
4
3.6
3.5
1.4
3
5.5
5
3.5
4
3.5
3
42
38
46
40
46
21
40
46
44
35
42
42
38
46
44
40
42
40
44
40
42
40
44
38
46
44
40
42
40
44
40
42
40
46
38
48
40
42
21
40
46
44
35
42
40
38
124
144
170
155
160
96
108
155
136
93
130
102
70
124
96
170
99
136
165
100
155
132
102
70
124
96
170
99
136
165
100
155
132
231
132
220
132
198
96
108
155
136
93
130
125
102
3500
1550
6570
3000
3500
450
720
5500
3600
550
6200
6500
1900
2000
1700
2300
750
1560
1650
750
5200
5500
1800
1900
2000
1700
2300
750
1560
1650
750
5200
5500
6500
4500
4300
2500
4000
450
720
5500
3600
550
6200
5000
900
52.5
28
45
42
41.25
20
36
41.5
37.5
20
40
45
25
40
45
49
36
42
41.25
30
52.5
41.5
36
25
40
45
49
36
42
41.25
30
52.5
41.5
37.5
40
40
41.25
49
20
36
41.5
37.5
20
40
41.25
28
65
37
51
51
49
63
60
50
45
36
47
45
60
40
38
63
52
49
47
39
44
48
40
60
40
38
63
52
49
47
39
44
48
51
63
47
39
40
63
60
50
45
36
47
42
39
6
5
8
9
6
3
6
7
7
5
4
5
4
9
4
6
8
4
6
4
6
7
4
4
9
4
6
8
4
6
4
6
7
9
4
8
5
9
3
6
7
7
5
4
7
2
49
44
40
51
37
35
44
40
37
39
35
20
40
38
45
38
49
47
51
37
3.7
3.8
3.5
4.6
3.5
3.5
3
3.25
2.2
3.5
3.5
1.2
4.7
3
5
3
4.5
4
4.6
3.5
40
46
38
46
35
42
42
42
40
40
42
40
46
44
42
42
46
50
46
35
150
120
124
165
96
120
140
124
85
100
102
66
124
96
160
93
124
136
165
96
3700
3000
2800
6500
1120
650
5600
2500
6500
2500
6500
4600
1400
620
2400
6600
560
900
6500
1120
Appendix 3: Diagnostic Test Results
Heteroskedasticity Test Results
. hettest
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of Output1
chi2(1)
=
Prob > chi2 =
102.10
0.0000
Multicollinearity Test Results
46 | P a g e
30
40
41.25
45
42
40
36
35
35
45
20
28
40
45
49
42
30
41.25
45
42
49
68
71
51
66
35
44
40
69
53
45
60
40
38
63
52
49
47
51
66
7
5
15
14
5
7
10
6
9
5
5
4
9
4
6
8
6
6
14
5
. correlate land1 seed1 fert1 K1 L1 age1 hsehld1
(obs=352)
land1
seed1
fert1
K1
L1
age1
hsehld1
land1
seed1
fert1
K1
L1
age1
hsehld1
1.0000
0.6197
0.6317
0.3065
0.5174
-0.1480
0.3566
1.0000
0.5116
0.3842
0.3917
-0.2801
0.3465
1.0000
0.4579
0.4198
-0.0757
0.4111
1.0000
0.2388
0.1039
0.3446
1.0000
0.0288
0.3442
1.0000
0.1660
1.0000
Appendix 4: Regression Results
47 | P a g e
.
reg Output1 land1 seed1 fert1 K1 L1 age1 hsehld1, robust
Linear regression
48 | P a g e
Number of obs
F(7, 344)
Prob > F
R-squared
Root MSE
Output1
Coef.
land1
seed1
fert1
K1
L1
age1
hsehld1
_cons
.2309796
.4334195
.2446988
.0121101
.1666394
-.16023
.0670454
.4243635
Robust
Std. Err.
.033573
.0890937
.0381859
.0091805
.0433389
.0440841
.0225907
.3447032
t
6.88
4.86
6.41
1.32
3.85
-3.63
2.97
1.23
P>|t|
0.000
0.000
0.000
0.188
0.000
0.000
0.003
0.219
=
=
=
=
=
352
83.78
0.0000
0.7798
.12192
[95% Conf. Interval]
.1649453
.2581826
.1695915
-.0059469
.0813967
-.2469383
.0226122
-.2536277
.2970139
.6086564
.3198061
.030167
.251882
-.0735217
.1114787
1.102355