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This is to certify that the

dissertation entitled

Economic Efficiency and Returns to Scale of Communal
Area Agriculture in Zimbabwe and Implications for
Agrarian Reform

presented by

Bernard Kupfuma

has been accepted towards fulﬁllment
of the requirements for

Ph.D. . Agricultural Economics
degree m

 

 

gawwaés;

Major professor

Eric W. Crawford

Dam October 9, 1998

 

MSU is an Afﬁrmative Action/Equal Opportunity Institution 0- 12771

 

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ECONOMIC EFFICIENCY AND RETURNS TO SCALE OF COMMUNAL
AREA AGRICULTURE IN ZIJVIBABWE AND IMPLICATIONS FOR

AGRARIAN REFORM

By

Bernard Kupfuma

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁlment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

October , 1998

ABSTRACT

ECONOMIC EFFICIENCY AND RETURNS TO SCALE OF COlVIIVIUNAL
AREA AGRICULTURE IN ZINIBABWE AND IMPLICATIONS FOR
AGRARIAN REFORM

By

Bernard Kupfuma

The ﬁrst half of the twentieth century saw the creation of a dualistic agrarian structure
in Zimbabwe with European settlers occupying the choicest land while the indigenous
population was displaced into marginal areas. There is a large body of literature that supports
the inverse relationship between farm size and efﬁciency, implying that the small, low-input
communal area farms could be more efﬁcient than the large commercial farms. But
unavailability of data, among other reasons, makes it impossible to compare the efﬁciency
levels of communal area and commercial farms.

To determine the options for alleviating poverty in the communal areas, this study
seeks to establish the nature of returns to scale and level of economic efﬁciency of communal
area farms. Then household characteristics, resource endowments and other farm-level
factors are used to explain the variation in farm-level measures of economic inefﬁciency.
Generalized, multi-product translog cost functions were found to be more appropriate than
production ﬁmctions in handling the data collected by the Ministry of Agriculture during the
1988/89, 1989/90 and 1992/93 seasons.

The estimated cost functions exhibited decreasing returns to scale. A one percent
increase in all inputs would increase output by about 0.34, 0.25 and 0.72 percent during the

seasons 1988/89, 1989/90 and 1992/93, respectively. This suggests that there are

increasingly limited productivity gains if the supply of all farm inputs is raised at current
technology levels.

Measures of economic inefﬁciency were obtained from cost ﬁontiers estimated
assuming the distribution of the one-sided error term to be half-normal or exponential. The
average measures of economic inefﬁciency for the three seasons were between 11 and 27
percent. The minimum and maximum values were 10 to 13 percent, 12 to 46 percent and 10
to 21 percent for 1988/89, 1989/90 and 1992/92, respectively. Thus, on average, a program
to eliminate ineﬂiciency on communal farms would reduce costs by 16 percent which is
unlikely to signiﬁcantly change living standards in communal areas. Household
characteristics, resource endowments and fann-level factors were not signiﬁcant in explaining
the variation in farm-level inefﬁciency. These results supported the recommendation that a
careﬁilly planned and targeted technology development and transfer program is needed to

raise productivity and incomes in Zimbabwe’s communal areas.

DEDICATION

Happias, My Dearest Brother

iv

ACKNOWLEDGMENTS

I am heavily indebted to my major adviser, Professor Eric Crawford and members of
my committee, Professors John Strauss, Scott Swinton and Carl Eicher who in so many
different ways made it possible for me to complete this dissertation. It was through these
men’s intelligent and expert advice that I was able to steer through the turbulent waters of
graduate studies. This study is testimony of their diligence and commitment.

Several other individuals were instrumental in making this study a success. I could
not have made it without the support I got ﬁom Professor Mandivamba Rukuni who assisted
me in getting access to the vital deliberations of the Commission of Inquiry into Appropriate
Land Tenure Systems. It was from these deliberations that I was able to clearly deﬁne the
focus of this study. I also want to acknowledge the help I got from fellow colleague and
friend, Mr. L. Maﬁirirano at the Ministry of Agriculture, in getting access to the data used in
this study. So many other people made signiﬁcant contributions to the success of this study
during the period of data collection in Zimbabwe.

I I am also indebted to my sponsors, W. K. Kellogg Foundation and the Department
of Agricultural Economics at Michigan State University, who provided more the than
ﬁnancial support needed to complete this study. I am grateful to so many people within these
organizations who went the extra mile to ensure that my stay at Michigan State University
was comfortable. I particularly want to single out Dr Thorbum, Ms Rebecca Hernandez, Ms
Sally Altes, and Ms Gail McCoury from the Kellogg Foundation and Dr. Crawford, Dr.

Homer, Ms Noteboom, Dr. Eicher and Ms Sheryl Rich from Michigan State University. They
made it possible for me to concentrate on my dissertation even when the tides were high and
the destination beyond sight.

I drew a lot of inspiration from my family. Their constant encouragement and timely
advice kept me going. I also want to thank all of them for being so patient. I never felt like
we were so far away ﬁ'om one another. My fellow students in the Department of Agricultural
Economics as well as the African students at Michigan State University provided an excellent
working environment. I wish to express many thanks to my best and dearest ﬁ'iend, Nakazi
Ntlabati, who was “always there” with an oxygen mask whenever I needed it!. Nevertheless,
all these people are in no way responsible for the errors of commission and omission in this

study. These errors are totally my responsibility alone.

TABLE OF CONTENTS

TABLE OF CONTENTS .............................................. vii
LIST OF TABLES .................................................. xiii
LIST OF FIGURES .................................................. xvii
CHAPTER I: BACKGROUND AND INTRODUCTION ...................... l
l. 1 Introduction .............................................. 1

1.2 The Problem Statement ..................................... 5

1.3 Objectives and Hypotheses of the Study ......................... 8

1.4 Organization of the Study ................................... 12
CHAPTER II: THE ORIGINS OF THE DUALISTIC AGRARIAN STRUCTURE
IN ZIMBABWE .................................... 13

2.1 Agrarian Reform in National Development ...................... 13

2.2 The Agrarian History of Zimbabwe ............................ 15

2.2.1 Land Alienation: 1890-1980 ........................... 15

2.2.2 The Land Resettlement Program ........................ 19

2.3 Review of Agrarian Reform Literature ......................... 24

vii

2.3.1 The History of Agrarian Reform ........................ 24
2.3.2 Farm Size-Productivity Relationship ..................... 28
2.3.3 Labor Cost-Based Explanations of the Inverse Relationship . . . 29

2.3.4 Transactions Cost-Based Explanations of the Inverse Relationship

................................................. 32

2.3.53 The Inverse Relationship: Some Evidence ................. 35

2.4 Lessons for Southern Africa ................................. 40
2.5 Summary ............................................... 41
CHAPTER 111: DESCRIPTION OF ZIMBABWE’S COMMUNAL AREA
PRODUCTION SYSTEMS ........................... 44

3. 1 Introduction ............................................. 44
3.2 Communal Area Production Systems .......................... 45
3.3.1 Demographic Characteristics ........................... 46

3.3.2 Resource Endowment ................................ 48

3.3.4 Crop Production Enterprises ........................... 54

3.4 The Communal Areas in the 21" Century ....................... 64
3.5 Summary ............................................... 65

CHAPTER IV: METHODOLOGICAL ISSUES: A LITERATURE REVIEW . 68

4.1

Introduction ............................................. 68

viii

4.2

4.3

4.4

4.5

4.6

CHAPTER V:

5.1

5.2

5.2.4

Modeling the Production Technology .......................... 69

4.2.1 Flexible Functional Forms ............................. 70
4.2.2 Dual Versus Primal Models ............................ 71
4.2.3 Transcendental Logarithmic (T ranslog) Cost Function ....... 73
Further Extensions of Cost Functions .......................... 77
4.3.2 Incorporating Input Fixity ............................. 81
Estimating Economic Efﬁciency .............................. 83
4.4.1 Economic Efﬁciency ................................. 84
4.4.2 Parametric Measure of Economic Efﬁciency ............... 87
4.4.3 Non-Parametric Measure of Economic Eﬂiciency ........... 92
Methodology Cross-Checking ................... '. ........... 93
Summary ............................................... 95

CHARACTERISTICS OF COMMUNAL AGRICULTURAL

PRODUCTION DATA ............................... 97
Introduction ............................................. 97
The Cost Function Data .................................... 98
5.2.1 The Output Variables (Y9 ............................. 99
5.2.2 Prices of Variable Inputs (Pi) .......................... 101
Quasi-Fixed and Fixed Inputs (K9 ............................ 104
5.2.5 Environmental Variables (Li) .......................... 106

ix

5.2.6 Total Variable Costs (TVCQ ................................ 108

5.3 The Data Collection Instrument ............................. 109
5.4 Summary .............................................. 110
CHAPTER VI: THE COST FUNCTIONS AND ECONOMIES OF SCALE. . 112
6.1 Introduction ............................................ 1 12
6.2.1 Model Explanatory Power ............................ 113

6.2.2 Signiﬁcance of Parameter Estimates .................... 1 14

6.3 Testing for Econometric Regularity .......................... 118
6.3.1 Multicollinearity Problems ............................ 118

6.3.2 Heteroskedasticity Problems .......................... 122

6.3.3 Omitted Variables Problem ........................... 124

6.3.4 Problems of Measurement Errors ...................... 128

6.4 Testing for Regularity Conditions ............................ 130
6.5 Economies of Scale ...................................... 131
6.5.1 Economies of Scale Versus Economies of Size ............ 132

6.5.2 Testing for Constant Returns to Scale ................... 133

6.5.3 Measures of Economies of Scale ....................... 135

6.6 Summary .............................................. 139

CHAPTER VII: THE COST FRONTIER FUNCTIONS AND ECONOMIC

7.1

7.2

7.3

7.5

EFFICIENCY ..................................... 141
Introduction ............................................ 141
Estimates of Cost Frontier Functions and Economic Eﬂiciency ...... 142
7.2.1 Estimating Cost Frontier Functions ..................... 142
7.2.2 Cost Frontier Function Estimates ...................... 143
7.2.3 Estimates of Economic Efﬁciency ...................... 145
7.2.4 Discussion of Results ............................... 152

Determinants of Economic Ineﬂiciency in Communal Agriculture . . . . 154

7.3.1 Farm-Speciﬁc and Nonphysical Variables ................ 155
7.3.2 Regression Results ................................. 158
Summary .............................................. 162

CHAPTER VIII: SUMMARY, RECOMIVIENDATIONS AND CONCLUSION 164

8.1
8.2

8.3

8.4

Introduction ............................................ 164
Summary of Findings and Recommendations ................... 164
Policy Recommendations .................................. 167
8.3.1 Technology Development and Transfer .................. 168
8.2.2 Land Reform ...................................... 170
Limitations of the Study ................................... 171
8.4.1 Data Quality and Availability .......................... 172

8.4.2 Methodological Issues ............................... 173

8.5 Future Research Work .................................... 175
REFERENCES ..................................................... 177
APPENDIX ........................................................ 190

A.1: MINISTRY OF AGRICULTURE SURVEY QUESTIONNAIRE . . . 190
A2: FIGURES AND GRAPHS ................................. 199
A3: TABLES .............................................. 213

xii

Table1.l:

Table 2.1:

Table 2.2:

Table 3.1:

Table 3.2:

Table 3.3:
Table 3.4:

Table 3.5:
Table 3.6:

Table 3.7:
Table 5.1:
Table 5.2:

LIST OF TABLES

Percentage Contribution of Small and Large Scale Farmers to Total National
Agricultural Output in Zimbabwe, 1983-1992 ..................... 2
Zimbabwe; Land Allocations Aﬁer the Land Acts of 1931, 1951 and 1970
(million hectares). ......................................... 17

Zimbabwe: Percentage Distribution ofLand Area by Natural Region and Sub-

Average Arable and Fallow Land Owned by Communal Households in
Zimbabwe, 1990/91 ....................................... 49
Percentage of Households Using Purchased Inputs and AFC Credit in
Zimbabwe Communal Areas, 1989/90 ......................... 51
Farm Implements Ownership in Communal Areas of Zimbabwe, 1990/9153
Crops Grown on Communal Farms in Selected Areas in Zimbabwe, 1990/91

...................................................... 56
Crop Area, Yields and Return to Labor in Selected Areas of Zimbabwe 59

Fertilizer Application Rates on Maize in Selected Areas of Zimbabwe,

Livestock Ownership Patterns in Selected Areas of Zimbabwe, 1990/91 63
Descriptive Summary of Values of Farm Output Per Farm (Yi). ..... 100

Descriptive Summary of Prices of Variable Inputs, (Pi). ........... 103

xiii

Table 5.3:
Table 5.4:

Table 5.5:
Table 6.1:
Table 6.2:
Table 6.3:
Table 6.4:
Table 6.5:
Table 6.6:
Table 6.7:
Table 7.1:

Table 7.2:
Table 7.3:

Table 7.4:

Table 7.5:

Table A. 1:

Descriptive Summary of Quasi-Fixed and Fixed Inputs, (Ki) ........ 105
The Percentage ofF arms With Favorable Soil Types and Located in Favorable
Natural Regions ......................................... 107
Descriptive Summary of Total Variable Costs (T VCi) ............. 108
Unadjusted and Adjusted Coefﬁcients of Determination ( R2 and R2) . 113

Level of Signiﬁcance of Selected Coefﬁcients ................... 115
The Cook-Weisberg Test for Heteroscedasticity ................. 124
Results of the Ramsey Reset Test for Omitted Variables ........... 126
Results of the Speciﬁcation Link Test. ........................ 127
Tests for Constant Returns to Scale .......................... 134
Indicators of Economies of Scale (1) ......................... 136

Differences in Number of Statistically Signiﬁcant Coefﬁcients Between Cost
Functions and Cost Frontier Functions ......................... 144
Descriptive Summary of Economic Ineﬂiciency Estimates .......... 146
Test for Skewness, Kurtosis and Normality in the Distribution of Estimates
of Economic Inefﬁciency .................................. 151
Relationship of Economic Ineﬂiciency with Farm-Speciﬁc Variables; The
Half-Normal Case ........................................ 160
Relationship of Economic Ineﬁiciency with F arm-Speciﬁc Variables; The
Exponential Case ........................................ 161

Distribution of Small-Scale Farming Areas by Natural Regions ...... 214

xiv

Table A2:
Table A2:
Table A3:
Table A3:
Table A4:
Table A4:
Table A5:
Table A6:
Table A6:
Table A7:
Table A7:
Table A8:
Table A8:
Table A9:
Table A9:

Table A10:
Table A10:
Table All:
Table A11:

Cost Function Parameter Estimates, 1988/89 ................... 218
Cost Function Parameter Estimates, 1988/89; Cont. .............. 219
Cost Function Parameter Estimates, 1989/90 ................... 220
Cost Function Parameter Estimates, 1989/90; Cont. .............. 221
Cost Function Parameter Estimates, 1992/93 ................... 222
Cost Function Parameter Estimates, 1992/93; Cont. .............. 223
Correlation Coefﬁcients for Selected Variables ................. 224
Cost Frontier Parameter Estimates (Normal), 1988/89 ............ 225
Cost Frontier Parameter Estimates (Normal), 1988/89; Cont. ....... 226
Cost Frontier Parameter Estimates (Normal), 1989/90. ............ 227
Cost Frontier Parameter Estimates (Normal), 1989/90; Cont. ....... 228
Cost Frontier Parameter Estimates (Normal), 1992/93. ............ 229
Cost Frontier Parameter Estimates (Normal), 1992/93; Cont. ....... 230
Cost Frontier Parameter Estimates (Exponential), 1988/89 ......... 231
Cost Frontier Parameter Estimates (Exponential), 1988/89; Cont ..... 232
Cost Frontier Parameter Estimates (Exponential), 1989/90 ......... 233
Cost Frontier Parameter Estimates (Exponential), 1989/90; Cont ..... 234
Cost Frontier Parameter Estimates (Exponential), 1992/93 ......... 235
Cost Frontier Parameter Estimates (Exponential), 1992/93, Cont ..... 236

Figure 2.1:
Figure 3.1:
Figure 4.1:
Figure 6.1:

Figure 6.2

Figure 7.1:
Figure 7.2:
Figure Al:
Figure A2:
Figure A3:
Figure A4:
Figure A5:
Figure A6:
Figure A7:
Figure A8:

Figure A9:

LIST OF FIGURES

Diﬁ‘erences in Intensity of Labor Use Between Large and Small Farms . 30

Distribution of Livestock by Sector in Zimbabwe, 1987—1991 ........ 62
Illustration of Relative Economic Efﬁciency ..................... 85
Percentage Frequency Distribution of Correlation Coefﬁcients ...... 121
The Shape of the Long-run Cost Curve for Communal Areas ....... 137
Measures of Economic Inefﬁciency for the Half-Normal Case ....... 149
Measures of Economic Inefﬁciency for the Exponential Case ....... 150
Plot of Residuals on Total Arable Area, 1988/89 ................ 200
Plot of Residuals on Total Arable Area, 1989/90 ................ 201
Plots‘ofResiduals on Total Arable Area, 1992/93 ................ 202
Plot of Residuals on Farm Assets Value, 1988/89 ................ 203
Plot of Residuals on Farm Assets Value, 1989/90 ................ 204
Plot of Residuals on Farm Livestock Value, 1988/89 ............. 205
Plot of Residuals on Farm Livestock Value, 1989/90 ............. 206

Distribution of Farm-level Economic Ineﬁiciency; The Half-Normal Case,
1988/89. ............................................... 207
Distribution of Farm-level Economic Inefﬁciency; The Exponential Case,

1988/89. ............................................... 208

Figure A10:

Figure A1 1:

Figure A12:

Figure A13:

Distribution of Farm-level Economic Inefﬁciency; The Half-Normal Case,
1989/90. ............................................... 209
Distribution of Farm-level Economic Inefﬁciency; The Exponential Case,
1989/90. ............................................... 210
Distribution of Farm-level Economic Inefﬁciency; TheHalf-Normal Case,
1992/93. ............................................... 211
Distribution of Farm-level Economic Ineﬂiciency; The Exponential Case,

1992/93. ............................................... 212

xvii

CHAPTER I: BACKGROUND AND INTRODUCTION

1.1 Introduction

Zimbabwe’s economy is highly dependent on the agricultural sector. The agricultural
sector contributed 12.78 percent to the gross domestic product (GDP) during the six-year
period 1988 to 1993 (MOA, 1995). But although the contribution to GDP may be less
signiﬁcant, the overall economic performance is highly related to the performance of the
agricultural sector. In addition the bulk of the country's population (about 70 percent) resides
in the rural areas where they are dependent on agriculture for their livelihood. In terms of
direct employment, agriculture (including forestry and ﬁshery) accounts for about 24 percent
of people in formal employment. Agriculture also contributed an average of 47 .7 percent of
the total exports during the period 1981 to 1990 (MOA, 1995).

The agricultural sector is therefore viewed as a strategic sector in national economic
planning. The government's objectives for the agricultural sector are to ensure food security,
increase export earnings and to improve the economic and social position of small scale
farmers and their families. Raising living standards in rural areas is indeed a top priority of the
Ministry of Agriculture (MLAWD, 1993). The government's strategy to meet these
objectives, among other things, includes the provision of credit and access to input and output
markets to small-scale farmers, promotion of appropriate technology development and
transfer, resettlement of small scale farmers from overcrowded areas and development of
irrigation schemes and other essential physical infrastructure. These efforts are in line with
the shift in emphasis from large-scale commercial farming to small-scale agriculture aﬁer

independence in 1980.

Table 1.1: Percentage Contribution of Small and Large Scale Farmers to Total

National Agricultural Output in Zimbabwe, 1983-1992

 

 

 

Year Small Scale (%) Large Scale (%) National Agricultural Output
(Million Current ZWD)
1983 16.20 83.80 1,037
1984 19.90 80.20 1,351
1985 30.80 69.20 1,985
1986 28.20 71.80 2,116
1987 19.80 80.20 2,062
1988 27.90 72.10 2,582
1989 24.60 75.40 2,838
1990 28.30 71.70 3,755
1991 19.80 80.20 5,215
1992 14.00 86.00 4,184
Average 23.00 77.00 2,713

 

Source: Central Statistical Ofﬁce

The provision of services to the once neglected small scale farmers after 1980 resulted
in a major shiﬁ in the composition of national agricultural output. The contribution from
small scale farmers increased dramatically over the years. In terms of value of total output,
the percentage contribution of communal farmers rose from an average of 10 percent during
the 19703 to more than 20 percent in the 19803 (MOA, 1995). The percentage contribution
of small and large scale farmers to total national output is shown in Table 1.1. During the
ten-year period the contribution of small scale farmers remained well above 20 percent.

However, during the two-year period, 1991 and 1992, the percentage contribution of small

scale farmers to total national agricultural output has shown a declining trend. This could be
due to the low rainfall experienced during these years. The continued high frequency of
drought years is likely to reinforce this declining trend in the future. The performance of
small scale agriculture is highly dependent on rainfall since the bulk of these farmers are found
in semi-arid areas‘.

However, the most dramatic change in the composition of national agricultural output
after the implementation of the new 1980 government strategy was the increase in the intake
of maize and cotton from the small scale farmers as a percentage of total national intakes.
The small scale farmers’ contribution to national intakes of these two commodities increased
ﬁom less than 20 percent during the late 19703 and early 1980s to more than 50 percent
during the mid 1980s and onwards. However, these impressive achievements, the
independence dividend, came at some cost as the expansion of the support services that
enabled small scale farmers to attain these achievements involved huge ﬁnancial outlays from
the national treasury. The high costs of supporting small scale agriculture raised the question
of ﬁscal sustainability of these programs and therefore led to a rethink on the best ways to
spur small scale agricultural grth to increase the well-being of most small scale farmers,
especially those in the semi-arid areas.

The Economic Structural Adjustment Program (ESAP) initiated by the government
in 1991 to revitalize the economy strived to reduce the high costs of running a controlled
economy. In agriculture one of the aims of this program was to reduce the cost of supporting
small-scale agriculture using the institutions designed for large-scale commercial agriculture.

The program had profound eﬁ‘ects on the agricultural sector, particularly small scale

 

‘ More than 70 percent of communal areas are in Natural Regions IV and V; agro-
ecological regions that have the least average annual rainfall in the country.

3

agriculture. Under this program the state-controlled agricultural marketing authorities were
turned into private companies. However, initially the government owned all the shares of the
new companies with the intent of gradually selling them to individuals and private institutions.
The government has already given up over 40 percent of the stocks in two commercialized
parastatals, the Cotton Company of Zimbabwe and the Dairy Marketing Board.

The provision of services to small scale farmers was adversely affected by the
privatization of state corporations. In fact most of the new support services provided to small
scale farmers were scaled down if not completely stopped. For instance the number of grain
intake points in small-scale farming areas was cut from 148 in 1985 to less than 50 in 1992.
Similarly the number of loans by the Agricultural Finance Corporation (AFC) fell from 77,000
in 1986 to 23,000 in 1994. As a result only a few small-scale farmers have access to crop
intake points and/or are receiving less AFC credit. Most of these few fortunate farmers are
located in the high rainfall areas leaving the bulk of the small-scale farmers without access to
these essential services.

Some positive impacts are expected out of the ESAP program. ESAP is expected to
create a conducive environment for competition in the purchasing of agricultural inputs and
products. This will result in all farmers receiving market prices that are expected to direct
resource allocation in agricultural production as dictated by market forces. Questions still
linger about how agriculture can beneﬁt from the creation of a competitive environment given
the biological nature of agricultural production and the nature of the agricultural products
themselves. However, the main political question emerging from this is why should a
program that is supposed to boost economic activities to the beneﬁt of all so adversely aﬁ‘ect
the poorest section of society? Are the nation’s interests better served by a system that denies

more than 97 percent of impoverished small-scale farmers access to the much needed credit?

These are socio-political questions that ESAP has not yet adequately addressed.
Furthermore, it has been observed that farmers in developed econonries rely heavily on
subsidies for survival while their counterparts in the developing countries are heavily taxed
by the state (Bates, 1981). Thus as the Zimbabwean economy modemizes it is expected that

the demand for agricultural support services will increasez.

1.2 The Problem Statement

The impressive performance of the small scale farmers during the early eighties
attracted widespread international attention. However, the trend in agricultural production
since the mid-eighties has become a major problem for policy makers. During good rainfall
seasons the country experiences overﬂows of grain which are expensive to store. In fact the
government asked farmers to cut back on maize production in 1986 following a good
growing season. But when the rain is inadequate grain deﬁcits are commonplace necessitating
expensive grain imports. Communal area farmers are the most affected group during periods
of grain deﬁcits because the majority of them are located in the driest parts of the country.
Infrastructure in these low potential areas is not well developed to allow for timely
movements of imported grains (Eicher and Kupfuma, 1997). The challenge to policymakers
is to ﬁnd ways and means to ensure food supplies at reasonable cost during both surplus and
drought seasons.

Because the bulk of Zimbabwe’s communal area population is directly and indirectly
dependent on agricultural production for a livelihood, not only is it important to ensure

adequate supplies of agricultural commodities but to increase production on a sustainable

 

2 Bates’ assessment does not apply to most southern African countries that heavily
subsidized agriculture mainly for political reasons. These subsidies could not be maintained
and have become the subject of policy reform programs.

5

basis. The high annual average intercensal rate of population growth of 3.1 percent (1982-
1992) dictates that measures should be taken to spur communal area agriculture growth to
levels higher than that of the population. In fact over a third of the communal areas were
considered overpopulated in 1980 with close to 40 percent having three to ﬁve times the
estimated carrying capacity of human population (Whitlow, 1980). Thus the major challenge
is not only to smoothen the levels of production, but also to increase agricultural productivity
to a level that will ensure communal area farming families an acceptable standard of living.

The production problems in communal area agriculture are a product of two policies.
First, the advent of European settlers in the 18905 and the introduction of Land Acts of 1931
and 1940 resulted in the forced movement of communal farmers into areas with limited
agricultural potential. Then there was a belief that only large scale farms were the best
vehicles to modernize the countryside. Small farms were supposed to be consolidated and
their previous occupants absorbed in the modern industrial economy. Large scale mechanized
farms developed ﬁom state subsidies prematurely excluded small farmers from participating
in the modernization of agriculture. Communal area farms in Zimbabwe were created to be
reservoirs of cheap labor and hence never intended to be productive. Thus the current
problem of poverty in Zimbabwe’s rural areas is a product of both history and ﬂawed
economic development policies. The tragedy is that nothing signiﬁcant has been done to
reverse these past mistakes. In addition there is a dearth of information on communal area
agriculture productivity and resource use efﬁciency. Development programs are designed
mainly of the basis of “expert judgement”. For instance, the 1980 government emphasis on
extension, in terms of ﬁnancial support, seems to suggest that the perceived problem in

communal area agriculture is inefﬁciency in the use of resources.

Before a far-reaching program to reform communal agriculture can be implemented
it is important to empirically assess the efﬁciency of communal agriculture. The crucial
question is whether farmers are using available resources in such a way that there is no other
way that these same resources can produce more output. Stated another way, communal area
farmers would be efﬁcient if it is not possible to produce current levels of output using less
resource than those farmers use. If communal farmers are operating on the efficiency frontier
then the focus of development programs should be on expanding the frontier through
technology development and transfer and/or land redistribution. If farmers are not using
resources efﬁciently then the main development programs should include the timely provision
of inputs, appropriate and targeted technology development and transfer, improvement in the
physical infrastructure, and increased access to output markets to enable these farmers to
operate as close to the efﬁciency frontier as possible.

Information on the eﬁiciency of communal agriculture can also be an important input
to the debate on the economics of land reform. The crux of this debate is whether it is
economic to divide large estates into small farms. Studies elsewhere show that small farms
are more eﬁicient than large estates (Johnson and Ruttan, 1994; van Zyl, Binswanger and
Thirtle, 1995), . If communal farmers are similarly more efﬁcient than their counterparts on
larger farms then a land transfer program would serve both efﬁciency and equity concerns
and bring together “....the moral concern for the welfare of the small cultivator, the
technological discovery of his productive efﬁciency, and the economic ideal of social
efﬁciency in resource allocation..." (Putterman, 1983).

Zimbabwe’s communal areas urgently need to be rehabilitated so that the poor mral
households can be integrated into the national economy. Indeed the government realizes the

need for more eﬁcient use of land as part of plans to change existing patterns of land

ownership (MLAWD, 1993). Some communal farming areas are considered overpopulated
and productivity there would be signiﬁcantly improved by a land transfer program (Palmer,
1990). But some researchers also believe that there is considerable scope for increasing
productivity in some communal farming areas through improved agricultural management
practices (Cliﬂ‘e, 1989; Muir and Blackie, 1994). There are many ways of putting together
a program to rehabilitate communal areas depending on the assumptions made on the
eﬁciency with which farmers use available resources. This assumption has not been tested
quantitatively in Zimbabwe making it difﬁcult for anyone to make more informed decisions
concerning the improvement of communal area production systems. Policy making and
development program and strategies design has been seriously handicapped by the dearth of

information on this very critical issue.

1.3 Objectives and Hypotheses of the Study

This study is motivated by the problem of chronic poverty in Zimbabwe’s communal
farming areas. It is important at the onset to point out that this study is not intended to
provide a blueprint on how to eliminate poverty in the country side. A broad based inquiry
will be required to accomplish a task of this magnitude. The major objective of this study is
to quantitatively assess the economic efﬁciency of communal farmers in Natural Regions II,
I, “ III, IV and V in Zimbabwe with the hope that the information generated will be a vital input
into the design of economic development programs.

Information on economic efﬁciency is particularly valuable as an input in programs
such as agrarian/land reform. But, as demonstrated later on in this study, economic
considerations are not the only determinants of economic development. Some of the most

important preconditions for economic development are technological, political, social,

historical and sometimes even cultural (Eicher and Kupﬁrma, 1997). The scope of this study
allows us to concentrate only on estimating economic efficiency. Thus the main objective will
remain that of measuring the of economic efficiency of communal farms. Because this study
would be incomplete without addressing the other important preconditions, the discussion on
implications will be broadened to accommodate the other considerations of economic

development. Speciﬁcally this study has the following objectives:

1. To review the agrarian history of Zimbabwe and the literature on the relationship

between farm size and productivity.

2. To describe the general characteristics (demographic, resource endowment and
agricultural production practices) of communal farms using the results of a 1990

sample survey.

3. To review the literature on the empirical formulation of the relationship between
agricultural output and factors of production and the measurement of relative

economic efﬁciency.

4. To describe the speciﬁc characteristics of data collected from communal areas during
the 1988/89, 1989/90 and 1992/93 seasons before it is used to estimate translog cost

functions and ﬁ'ontier functions.

5. To estimate a generalized multi-product translog variable cost ﬁrnction and use the

function to determine the nature of economies of scale.

6. To measure the economic eﬁiciency of communal farmers in Zimbabwe during three
seasons; 1989/90, 1990/91 and 1992/93 using a generalized translog multi-product

variable cost frontier function.

7. To explain the variations in the estimated farm-level relative economic eﬂiciency using

agro-ecological, household and socioeconomic variables.

8. To draw the implications on future technical, economic and institutional reforms

aimed at “transforming” communal agricultural production.

To accomplish these objectives a three-year data set will be used covering the seasons
1988/89, 1989/90 and 1992/93. The choice of these seasons was based on the availability of
data and considerations about the normality of the seasons. The data for 1991/92 season is
not included because this season was quite atypical’. If data availability was not a problem,
one could have used panel data covering at least ﬁve agricultural seasons. This would have
hopefully captured the full length of climatic cycles in Zimbabwe.

The following hypothesized relationships will be tested as a way of fulﬁlling the above

objectives of the study:

* Communal area agricultural production systems in Zimbabwe exhibit constant returns

to scale.

3 Zimbabwe experienced the severest drought ever recorded in its history during the
1991/92 season.

10

* Communal area production systems are economically efﬁcient with an average
inefﬁciency of less than 10 percent.

‘k Farm-level economic inefﬁciency is inversely related to the years of education for
household head, years of farming experience, family size, value of farm animals, value
of farm implements and amount of remittances from relatives working off-farm.

* Farm-level economic inefﬁciency is positively related to farm size in line with the
inverse relationship hypothesis.

* Farmers who use credit, apply manure, winter-plough and buy modern inputs are
economically more efﬁcient.

* Small scale farms in high rainfall areas (Natural Regions II and HI) are more efﬁcient
than those in the low rainfall areas (Natural Regions IV and V).

* Farmers cultivating fertile soils (clays and loams) are more efﬁcient than farmers

cultivating infertile sandy soils.

In testing the above hypotheses, the following assumptions are explicit.

0 First, farmers are assumed to be able to choose input quantities and hence the total
cost to pay for producing a given level of output. The farmers cannot choose output
and input prices because they are exogenously given. As a result the cost function is
the best way to model the production decisions as compared to proﬁt and production
functions.

0 Because farmers produce several products and cannot change their factors of
production instantaneously, a generalized multi-product translog variable cost

function is employed.

ll

1.4 Organization of the Study

This study is divided into eight chapters. The ﬁrst chapter is a statement of the
problem, the objectives of the study and the hypotheses to be tested. In the second chapter
the agrarian history of Zimbabwe is outlined and the literature on the relationship between
farm size and productivity is reviewed. The third chapter describes the characteristics of
communal agricultural production system in detail using the 1990/91 sample survey results.
A literature review of the methods of measuring economic efﬁciency covering issues related
to ﬁrnctional form and the justiﬁcation for using the generalized multi-product translog
variable cost function are covered in the fourth chapter. Chapter ﬁve outlines the data used
in the estimating the generalized multi-product translog variable cost function. The results
of diagnostic tests of the data for econometric problems and regularity conditions tests are
presented in the sixth chapter. In this chapter multi-product translog variable cost functions
are estimated and tests for the presence of economies of scale are performed. The cost
frontier functions from which indicators of relative economic eﬂiciency are derived are
estimated in chapter seven. This chapter also presents results ﬁom relating measures of
relative economic eﬂiciency to farm-speciﬁc variables. Then a discussion of the implications
of the ﬁndings based on the observed relationship between relative economic efﬁciency
measures and the explanatory variables is presented. The last chapter is a conclusion of the
study and highlights implications of the ﬁndings from the study on policy formulation in

Zimbabwe. This chapter also identiﬁes future research areas and issues to be emphasized.

12

CHAPTER H: THE ORIGINS OF THE DUALISTIC AGRARIAN

STRUCTURE IN ZIMBABWE

2.1 Agrarian Reform in National Development

Rural poverty alleviation programs receive top priority in national economic
development planning. Since the majority of developing nations’ population resides and
works in rural areas, increasing agricultural productivity is a major component of rural
poverty alleviation. While there is considerable controversy on how exactly the pattern of
land ownership affects agricultural productivity, it is generally acknowledged that land rights
are an important institutional instrument for rural development (Berry and Cline, 1979). What
is needed is an agrarian structure that puts people to work (Eicher and Kupﬁlma, 1997).
Over time and across the whole world a lot of energy has gone into the search for that
agrarian structure that increase efﬁciency and farm incomes, eradicate poverty and direct the
economies onto a path that is economically, politically and socially sustainable. The main
reason why the United States agriculture is probably the most productive in the world is
because its family farm-based agrarian structure is inherently efﬁcient (Powelson, 1964).

As early as the early seventies it had become clear that policies that focus solely on
capital investment and output maximization could not spur the economies of developing
countries because they did not increase the participation of all members of society in
productive and socially useful labor (Dorner, 1972). These policies were derived from neo-
classical econorrrics which does not take into account the importance of institutions and time
in the process of development (North, 1993). This is not solely a result of too much reliance
on neo-classical economics but is a result of Cold War politics which considered agrarian

reform programs as Marxist-oriented. Now that the Cold War is over, the World Bank

13

development assistance activities, although still very much based on this neoclassical tradition,
institutional reforms, now include agrarian reform as an essential components as current
”country dialogues” and Eastern European assistance activities indicate (Platteau, 1992).

There are no signiﬁcant conﬂicts in deﬁning agrarian reform. Agrarian reform extends
beyond land tenure reform where land belonging to one group is taken away and transferred
to another group. It includes changes in the “legal or customary system under which land is
owned, the distribution of ownership of farm property between large estates and peasant
farms or among peasant farms of various sizes, land tenancy, the system under which land is
operated and its products divided between the operator and the owner, the organization of
credit, production and marketing, the mechanism through which agriculture is ﬁnanced, the
burdens imposed on the rural population by governments in terms of taxation, and the
services supplied by governments to rural populations such as technical advice and education
facilities, health services, water supply and communications” (Powelson, 1964; p. 65).

Agrarian reform is a continuous process that takes place as part of social change and
development. It is an integral part of the whole process of modernization involving the
economy, the social structure and cultural development. In Latin America agrarian reform
was triggered by some form of political revolution (Alexander, 1974). The extent of the
reform process (land reform versus agrarian reform) depends on how the revolution
succeeded in weakening the position of the old political power structures. The Zimbabwean
case is illustrative in this regard.

This chapter puts the agrarian problem in Zimbabwe into context by reviewing the
history of land alienation. This review raises the question of the relationship between farm
size and productivity. To answer this question the next section brieﬂy reviews available

evidence on the existence of an inverse relationship between farm size and productivity. The

14

last section seeks to answer the question whether it is justiﬁed for one to compare the
productivity of different farm sizes in Zimbabwe, given the available evidence of the existence
of an inverse relationship hypothesis. The experience of Latin American countries in
implementing agrarian reform programs is illustrative and will be used to draw some lessons

for Southern Aﬁican countries that are considering agrarian reform options,

2.2 The Agrarian History of Zimbabwe

The history of Zimbabwe is about a struggle for access to land especially aﬂer
European settlement at the turn of the 19‘h century. This section seeks to highlight the events
that have a profound impact on the development of the agrarian structure. This section
reviews the period starting with European settlement in the 1890s and chronicles the process
through which a dual agrarian system was developed. We then analyze the efforts of the new
majority government since independence in 1980 to reverse the past inequities in land

distribution.

2.2.1 Land Alienation: 1890-1980

The agrarian history of Zimbabwe took a dramatic turn with the arrival of European
"pioneers" from South Aﬁica in 1890. Initially drawn to the country by reports of large
. mineral deposits, many new settlers turned to agriculture aﬂer failing to ﬁnd mineral and gold
ﬁelds as large as speculated in the early pioneers’ reports. The initial impact of European
settlement was to stimulate surplus production from small-scale indigenous farmers through

the creation of markets, infrastructure and the introduction of the ox-plough‘ (Masters, 1994).

 

‘ The number of ploughs in use by Aﬁicans increased from 940 in 1905; to 16 900 in
1921; to 53 500 inl931 and to 133 000 in 1945 (Arrighi, 1970).

15

In fact the ﬁrst two decades of the twentieth century witnessed a phenomenal rise in surplus
crop production ﬁ'om the small-scale indigenous farmers (Muir, 1984).

But the new settlers found it difﬁcult to compete with the indigenous population for
land and agricultural markets. They lobbied the government to systematically remove
communal farmers from the choicest land and shunted them into reserves’. This method of
creating large estates was similar to experiences in Kenya, South Africa and Latin America
(Deininger and Binswanger, 1995; Alexander, 1977). The state helped settler farmers by
providing an extensive communication and marketing infrastructure and massive statutory
subsidies and "soﬂ" loans (Arrighi, 1970). The system of state marketing boards was created
during the 1930's to help the emerging large-scale commercial farmers whose initial focus was
on the export market to wrestle the now more lucrative domestic markets from the small scale
indigenous family farms. This was done mainly through price discrimination based on racial
lines (Muir, 1984).

In addition, during the early years of European settlement, 1900 to 1930s, a system
of demonstration farms and experiment stations was established (Arrighi, 1970). They
evolved to become the basis of a strong and efﬁcient technology development and transfer
system for European settler agriculture. This technology development and transfer system
was not designed to serve small scale agriculture and was part of the marginalization of small
scale indigenous agriculture. The ultimate aim was to reduce competition ﬁom these farmers
and force the indigenous population into becoming a labor reservoir for European settler

farms, mines and the emerging industrial sector. Thus, most of what is now communal areas

 

’ To allay the British government fears of abuse of indigenous people, the settler state had
among many explanations for land alienation that this was done in order to preserve the
”native culture" or that indigenous people were accustomed to farming the "thin sandveld"

(World Bank, 1986).
16

were never meant to be productive settlements. It is a product of contradictory policies by
the colonial government. On one hand there was a need to reduce competition from Africans
in industry as per the dictates of the “parallel development” doctrine while there was also a
desire for industrialization through the promotion of the growth of an internal market that
involve increased production by Africans (Arrighi, 1970).

Marginalization of small-scale indigenous farmers was accomplished through the
passing of several Land Acts (Rukuni, 1994). The Land Apportionment Act of 1931 became
the cornerstone of the land policy in the country. This Act sharply reduced the land available
to small-scale Aﬁican farmers. For the ﬁrst time, land ownership was divided along racial

lines. The resultant land distribution pattern is shown in the ﬁrst column of Table 2.1.

Table 2.1: Zimbabwe; Land Allocations After the Land Acts of 1931, 1951 and 1970

 

 

 

(million hectares).
Category 1931 Act 1951 Act 1970 Act
European Areas 19.67 18.96 18.11
Aﬁican Communal Areas 8.64 9.99 16.29
Aﬁican Purchase Areas 2.98 2.26 1.91
Unassigned Land 7.15 5.70 0.00
State Lands 0.24 1.58 2.73
TOTAL 38.68 38.49 39.04

 

Source: Roth, 1990.

The next signiﬁcant Land Act did not change the ownership structure signiﬁcantly.
The Land Husbandry Act of 1951 was enacted because of the growing awareness that the

reserves were not adequate to support the growing small-scale African farming population.

17

The potential of the land set aside for small-scale African farmers had been overestimated and
the indigenous African population growth underestimated. It also became apparent that the
Aﬁican population could not be absorbed by the expanding European-owned farms, mines
and industries. The aim of the Land Husbandry Act was, therefore, to reform African
husbandry and turn the African small scale farmers into capitalist entrepreneurs. The
distribution of land after the Land Husbandry Act is shown in the second column of Table 2. l.
The resultant pattern of land distribution is not signiﬁcantly different from that which
occurred after the 1931 Act. The percentage of land under European areas fell marginally
from 51 percent in 1931 to 49 percent after the 1951 Land Husbandry Act.

The administration of the Land Husbandry Act during the ﬁﬂies and sixties proved
difﬁcult as political agitation increased throughout the country“. In an attempt to resolve
these dimculties, the responsibility of administering the Tribal Reserves (to become known
as Communal Areas aﬂer independence in 1980) was partially transferred to local authorities
with the passage of the Land Tenure Act of 1970. This left the distribution of land at levels
shown in the third column of Table 2.1. Again this Act did not signiﬁcantly alter the agrarian
structure established in 193 1. The European areas, as a percentage of the total available area,
fell marginally to 46 percent. This Act was passed on the understanding that the state could
not guarantee every “unborn native” the right to own land. This pattern of land distribution
has since been preserved even after independence in 1980. In 1990, large scale farmers
owned about a third of the national agricultural land.

These legislative moves were not popular with most of the indigenous population.

As a result most of the small-scale farming population popularly and actively supported the

 

‘ The ﬁrst shots of the war against colonialism were ﬁred in 1966 near what is now
Chinhoyi, 110 km to the north of Harare.

18

ﬁfteen-year guerrilla war against settler colonialism (Chung, 1989). Land was at the center
of this revolution (Moyo, 1995). In the late seventies, the war had escalated to levels that
opened the possibility of a negotiated settlement. During the negotiations, two contradictory
issues had to be addressed; redistributing land to the landless majority and preserving the
"eﬁcient" large-scale commercial farming sector. The short-term effects of a rapid transfer
of land to land-hungry small-scale farmers would economically ruin the new nation as
experience in Mozambique had shown. In addition there was pressure from Frontline State’
leaders to accept peace at any cost. In what was considered a "crucial capitulation" the
nationalist liberation movements8 accepted a constitution that limited the scope of the
inevitable post-independent agrarian reform (Suba, 1989). The liberation movement
abandoned any expectations they had of pursuing a radical land reform program when they

agreed to a market-bound process of land acquisition (Moyo, 1994).

2.2.2 The Land Resettlement Program

The resettlement program implemented in Zimbabwe beginning in September 1980
was constrained by the Lancaster House Agreement. The Agreement stipulated that land
was to be acquired on a "willing—buyer-willing-seller" basis with the seller being paid
"promptly" and in a currency of his or her choice. In the absence of land taxation speculative
pricing resulted in very high land prices (Moyo, 1994). Though the Zimbabwean and British

governments equally split the costs of land acquisition, the high land values and Zimbabwe's

 

7 Frontline states are comprised of neighboring countries that actively supported the
struggle against minority rule in Zimbabwe, Namibia, and South Africa. The most inﬂuential
included Botswana, Mozambique, Tanzania and Zambia.

' The Zimbabwe African National Union (ZANU) and Zimbabwe Aﬁican People Union
(ZAPU) formed the Patriotic Front as an alliance to ensure continued external ﬁnancial and
material support.

19

limited ﬁscal capacity9 limited the breadth of the ensuing resettlement program. The new
settlers were not asked to pay for the land on which they were resettled. The 52,000
households resettled by 1989 fell short of the 162,000 target (Palmer, 1990). Thus, by 1989,
416,000 people had been resettled on 2.7 million hectares bought from commercial farms.
The distribution of land by natural region and by farming sector is shown in Table 2.2. The
land under large-scale farms fell to 32 percent of the total national land. However, this 32
percent remains the prime agricultural land in the country. Table 2.2 shows that the land
acquired for resettlement purposes was mainly in the semiarid areas. Thus not only is the
proportion of the land for resettlement insigniﬁcant, but is also of poor quality.

Table 2.2: Zimbabwe: Percentage Distribution of Land Area by Natural Region

and Sub-Sector, 1990.

 

Land Use Natural Region'

I II III IV V X Tot.
Communal Areas 0.2 3.1 7.0 18.1 12.8 1.5 42.7
Large-scale Areas 1.2 9.8 5.6 9.7 5.7 0.1 32.1

 

Small-scale Areas - 0.6 0.7 1.5 0.5 0.2 3.5
Resettlement Areas 0.1 0.4 2.4 0.5 1.1 - 4.5
National Land 0.3 0.9 2.1 6.5 6.0 1.4 17.2
Total 1.8 14.8 17.8 36.3 26.1 3.2 100

 

Natural Regions are based on average annual rainfall. Natural Region I has the
highest average annual rainfall while Natural Region V has the lowest.

Source: Central Statistical Ofﬁce

 

’ Zimbabwe could not provide its share of the land acquisition budget partly because of
the devaluation of the Zimbabwe dollar against major currencies starting ﬁom 1981.

20

The implementation of the land resettlement program did not proceed at a pace
required by a government brought to power on a revolutionary ticket. As a result
government was under pressure to acquire more farms. In 1985 a Land Acquisition Bill was
passed requiring all willing sellers to ﬁrst offer their farms to the government for purchase.
If government lacked ﬁtnds to purchase the farms offered, the sellers were allowed to sell to
other buyers. Nevertheless, since the government did not have enough funds to purchase all
the farms oﬂ‘ered to it, very few farms were purchased for resettlement.

The second reason the resettlement program target was not met includes the inﬂuence
of the Commercial Farmers' Union (CFU)‘°. The CFU and its allies were successful in
lobbying the government to slow the Resettlement program by pointing out the importance
and eﬁiciency of large-scale farmers in generating foreign exchange earnings and
employment”. Resettled farmers would not only fail to match the productivity of the former
occupants, but would also cause considerable environmental damage because of their
inappropriate farming methods. The CFU has used its dominance over the emerging
independent and high proﬁle international media and ofﬁcial policy-making fora and
institutions to advance this point of view (Moyo, 1994). Accordingly, the business
community, black and white, and the urban elite regard the government land policy as

irrational and a mere political gimmick to garner votes for the ruling party come election

 

“’ The CFU is a powerful organization for large-scale, mainly white, farmers which actively
promote the interests of its constituency.

" To some researchers the centrality of large-scale commercial agriculture to the
agricultural success and economic survival of Zimbabwe is a myth (Weiner, e_t a1, 1985;
Riddell, 1978; Cliffe, 1988). The scepticism with the superiority of large-scale agriculture is
borne out of numerous ﬁndings in Asia and Latin America of an inverse relationship between
farm size and productivity.

21

time.12 What the CFU and its allies have done is to take advantage of the dearth of
information on government land policy to conﬁise public opinion (Moyo, 1994). The CFU
and its followers have therefore successfully stalled the resettlement program even though
they all agree that there is need for land redistribution as a statement from the CFU president
conﬁrms; “ ..... prior to and since Zimbabwe’s Independence the CFU understood and
accepted the need for land reform (Swanepoel, 1997).

The third reason for the slow pace of resettlement was the impressive performance
by small-scale farmers in the early and mid eighties that took off pressure from the polity to
effect land reform. For maize and cotton alone the contribution of small-scale farmers to the
marketed produce increased from 10 percent before independence to over 60 percent in less
than ten years aﬂer independence (Matanyaire, et al, 1992). It appeared that improvements
in access to markets, credit, and other services could effectively bring small-scale farmers into
the money economy. Thus resettlement, after all, appeared not to be important as a vehicle
for the empowerment of the rural poor. During the late eighties and early nineties crop
production growth rates in the communal areas have shown signs of stabilizing and sometimes
even declining (Jayne, et al, 1994). The universal empowerment of communal farmers is far
ﬁ'om being attained as over 80 percent of the beneﬁts were captured by 20 percent of the
communal area population who happens to be found in the high potential areas (Shumba,
1990). This has been used to show that rural socioeconomic problems cannot be resolved by
simply improving access to markets and other essential services. The bulk of small-scale
farmers in the marginal areas, most of whom are net-food buyers, have not beneﬁtted from

these programs (Jayne, Jones, Mukumbu and Jiriyengwa, 1997).

 

‘2 An editor of the only independent newspaper then, The Financial Gazette, dismissed
claims of land hunger as a mere excuse by government leaders to grab land.

22

The resettlement program sparked off several studies to evaluate the costs and
beneﬁts of replacing large-scale farmers with small-scale farmers. The earlier studies by
Kinsey (1982) and the Whitson Foundation (1983) found the costs of resettling the 162,000
families on large-scale commercial land potentially high. The pessimism in these studies is in
line with the belief that large farms are more efﬁcient than small farms (Weiner gt al, 1985).
But these studies used data that grossly underestimated the potential of the small-scale
farmers. Kinsey (1982) admitted that his analysis was based on the land use planners' models
which lacked dynamism and realism”. Dan Weiner e_t pl (1985) have challenged the myth of g
the efficient large-scale farmer by showing that, in terms of yields and output-input ratios,
resettlement and communal areas "can produce comparable yields to those of the large-scale
commercial farms with signiﬁcantly less inputs" in areas of comparable production pptential.
Matanyaire et al (1992) also concluded that “... resettlement can replace large-scale
commercial farms ......... without losses in total production” using crop yields of a cotton-
maize rotation. Both analyses were based on crop yields comparisons that do not account for
total farm productivity. To compare across farms of varying sizes, total farm productivity

measures should be used.

 

‘3 The planners’ ex ante models were not realistic because they lacked details on the
productivity levels of the resettled farmers. The ﬁgures and assumptions used were not
adjusted to take into account the effects of time as the new settlers adjusted to the new
environment.

23

2.3 Review of Agrarian Reform Literature

The controversy on whether it is economic to replace large scale with small scale
farms in Zimbabwe is not unique. The question of what the relationship between farm size
and productivity is like has dominated the literature on agrarian reform for a long time. In this

section the literature on the farm size-productivity relationship is reviewed.

2.3.1 The History of Agrarian Reform

Binswanger, Deininger and Feder (1993) documented the evolution of land relations
as societies evolve ﬁ'om land abundant to land scarcity settings, drawing heavily ﬁ'om
Boserup's theory of the evolution of farming systems. If land is abundant, the critical factor
is labor and there is no incentive to invest in land improvement. Degraded land is abandoned
for a period long enough for natural soil productivity restoration. Over time countries have
solved their demographic pressures by moving into new unoccupied lands (Powelson, 1964).
As human and livestock population pressure increases on limited land resources, the fallow
period becomes shorter. The land frontier is quickly exhausted and marginal land is opened
for cultivation. This, coupled with adoption of improved production practices, results in
continual cultivation.

With continual cultivation, especially on marginal land, land productivity-improving
investments become necessary. Then property rights over land become important since they
directly inﬂuence the uncertainty, perceived and real, of beneﬁts from investments made to
improve agricultural production. Property rights can take various forms depending on the
intensity of population pressure on land. When population pressure is very intense, the

likelihood of individuals demanding formal institutions that protect complete private property

24

rights is high. Informal laws are relied upon if the population pressure, and therefore, the
pressure for agrarian change is less intense.

History has shown that widespread change in property rights has mostly been
associated with revolutionary change (Alexander, 1977). The genesis of formalized property
thus might be from the bottom up in response to the inability of formal law to connect
property rights and ownership arrangements as deﬁned by informal law. The driving force
behind formalization is the potential beneﬁts generated by widespread, formal property rights
through low cost exchange that encourages specialization and thus greater productivity ﬁ'om
investments. This has been part of the modernization of agriculture in several cases around
the world.

The process of modernizing agriculture occurs in stages involving social
diﬂ‘erentiation between lower and upper classes (Kanel, 1971). The initial stages exhibit low
social differentiation with communal property relations dominating production. In the next
stages a rural elite that favors the establishment of the state to promote their interests
emerges. Feudalism and other similar systems correspond to these stages of evolution in land
relations. But other interest groups, such as industrialists and the urban elite, in alliance with
the oppressed cultivators, start to challenge the power of the rural upper class at the next
stage. This is the stage in which the demand for land reform is strongly expressed. The ﬁnal
stage of the evolution process involves a decisive shift of land relations from being based on
status to those governed by contract, stripping the tenure system of most of its political and
social dimensions (Kanel, 1971). This is the stage when economies are driven by market
forces with limited interventions by the state. One major difference between developed and
developing countries is that the economies of the former are more reliant on markets with

well-deﬁned and formalized property rights than the former.

25

But Binswanger et al (1993) point out that instances of smooth transformation of land
rights from communal to complete private rights are uncommon. Rarely are transitions to
formalized property rights unpremeditated. During the transformation process a class of
political and military elites can and do take advantage of their power to extract rents ﬁ'om the
cultivators. In India the caste system is used to this day to deny the “untouchables” access
to quality land (Mallick, 1992). In Latin America the establishment of the exploitative
hacienda system by the Spanish settlers aﬁer the conquest of the local villagers aptly
illustrates this phenomena (Williamson, 1997). The freedom of the small-scale cultivator is
restricted as the rural elite close most of their exit options to coercion.

If coercion cannot be used to extract rents, especially during the later stages of the
evolution of land relations, then the utility of the small-scale farmers must be reduced by
limiting their access to high quality land and through distorted policies. In Zimbabwe, South
Aﬁica and Kenya large landowners inﬂuenced their respective governments to pass laws and
regulations that marginalised small-scale farmers, who were then unorganized to resist (Orvis,
1997). The large scale farms have to survive on government support programs especially
those that drive the reservation price of small-scale cultivators’ labor down.

But exploitative production relations and large farmer-biased policies cannot be
sustained indeﬁnitely. As the economy develops the relation of ownership structure to the
social structure create stresses and conﬂicts that force the system to adjust resulting in the
emergence of new political coalitions (Kanel, 1971). In most of Latin America the large
estates did not only prevent a large part of the population from participating in the political
and economic markets but could not also supply the needs of a growing population and the
developing industrial sector (Alexander, 1974). In fact the main driving force for agrarian

reform in Latin America was the desire to break the political stranglehold of parasitic

26

landowners (Powelson, 1964). Thus eventually it is the internal contradictions within the
relationship between the cultivator class and the rural upper class over rights to expropriate
rents that are the source of the demise of these exploitative systems.

From the resultant political upheavals emerge wide variations in land relations evident
across the globe today. These include, among others, the Cuban type of revolution which
ended with the state owning all means of production, Mexico and its ejido system, South
Africa which have maintained the status quo, India and its caste system-based pattern of land
ownership and China which has now moved from state ownership to family farms. It is also
noteworthy that the Latin American land reforms had minimal impact since dualistic land
ownership structures still persist.” The dominant agrarian structure is therefore dependent
on who “wins” the struggle between the large landowners and the peasants. In Latin America
and Southern Aﬁica the anti-reform advocates (rural elite, agricultural capitalists and their
allies in urban areas) successfully contained the extent of effective land redistribution (De
Janvry, 1989; Moyo, 1994). In both cases the main argument of the anti-reform advocates
has been that of the superior performance of large estates, the peasants’ lack of managerial
experience due to high levels of illiteracy and the high cost extending the appropriate social
and physical infrastructure. The question that follows from this is whether large estates are
inherently more eﬁicient than small family farms that characterize peasant agriculture. The
section below explores this issue through a review of some of work done throughout the

world on the relationship between farm size and economic efﬁciency.

 

“ De Janvry, Marsh, Runsten, Sadoulet and Zabin (1989) reported that in 1980 large
estates accounted for 22 percent of farm units and occupied 82 percent of total area in Latin
America as a whole.

27

2.3.2 Farm Size-Productivity Relationship

The diﬁ‘erences in economic efﬁciency found between small—scale family operated
farms and large-scale farms are used to justify land reform. In the 19503 western
development economists believed that the key requirement for agriculture was to free labor
and other resources for industrial development and provide relatively cheap food for the
expanding industrial labor force (Dorner and Kane], 1971). It was further noted that large
plantations had ”well known economic advantages over the family size unit" (Lewis, 1954).
Large-scale farms were thus favored on the belief that they were technically more efﬁcient and
productive than small-scale farms. But by the 19603 some economists, citing the United
States as an example, believed that family owned and operated farms were better that large
estates operated by non-family labor on the basis of efficiency (Powelson, 1964). Even Lewis
had observed in the 19503 that the more successﬁrl organizational units for settlement
schemes in underdeveloped countries were small family farms because of their advantage as
social and economic units (Johnson and Ruttan, 1994). Thus even without the support of
empirical studies the relationship between productivity and farm size has since then been
speciﬁed as an inverse one.

Over time economists developed the Official Doctrine of Land Reform (ODLR), as
a radical departure from the traditional myth of the superiority of large-scale farming over
small scale agriculture (Platteau, 1991). The ODLR postulates an inverse relationship
between farm size and land productivity15 and is supported by the historical dominance of
small-scale family farming all over the world (Deininger and Binswanger, 1992). There are

two ways to explain the ODLR; the Labor Cost-based and the Transaction cost-based

 

‘5 Size here refers to area of the farm and not farm scale which refers to total economies
of size that involve all inputs. Land productivity is normally in terms of yield per unit area
with yield expressed in physical terms or in monetary terms.

28

explanations. There are no serious contradictions between these two approaches to
explaining ODLR. In fact the farm size to productivity relationship could be best viewed as

a result of the two processes. They are presented here separately to ensure clarity only.

2.3.3 Labor Cost-Based Explanations of the Inverse Relationship

The search for the causes for the inverse relationship dates to the time of classical
economics. J .8. Mill explained this relationship in terms of labor cost advantages of small
farms that exploit "imperfections" in the rural labor markets. The inverse relationship
between farm size and output per unit of land is due to the inverse relationship between farm
size and labor use. The inverse relationship between farm size and labor use is due to
diﬂ‘erences in labor costs between the two farm types; Labor Market Dualism. The basic
explanation of the dualism in the labor market is the difference in mode of employment
between large farms, which rely mainly on hired labor, and small farms that are dependent on
family labor. The market wages facing large farmers are higher than the cost of using family
labor on small family farms. This results in small family farms using more labor per unit area
than large farms. By using labor more intensively than large farms smaller farms put larger
proportions of the land they own under cultivation than large scale farms. There are various

ways to explain the differences in labor costs.

0 The original Mill's explanation of the inverse relationship was based on the
observation that individuals prefer to work on their own land. In neoclassical theory
it was noted that "the disutility of given quantities of work efforts is smaller when
these efforts are applied to one's own property than when they are made under the

control and on the account of another person" (Platteau, 1992; p 54). As a result the

29

effective cost of labor on small farms (its imputed price) is lower than on large ones.
Furthermore, the large farm workers' wives and children do not offer their labor to the
large farms. Thus as noted by Lipton (1974), small farmers end up producing more
output ﬁom a given bundle of inputs of (land and capital) because they use the labor

input more effectively.

0 The labor cost differences also arise from the egalitarian mode of income distribution
within small farm families (Platteau, 1992). The share of each member of the farm
family is the average product and not the marginal product. The former is greater than

the latter at the level small farms use labor“. Figure 2.1 illustrates this scenario.

Value (8)

\

Val? of Marginal Product

"\

% Value of Average Product
,""// / ‘\\\ /
/ f/J \\‘

\\ Labor
/7 \ Price

/ \\ \

\

Lb \ Ls
Labor (manhours)

 

 

 

 

 

Figure 2.1: Differences in Intensity of Labor Use Between Large and Small Farms

 

"5 This assumes that small farms operate within phase II of the production function when
the average product curve is above the marginal product curve.

30

A large farm would use labor up to point Lb on Figure 2.1 while a small family that
employs average product pricing would use more labor at Ls. For a family member
to leave the farm for alternative employment the market wage must at least be equal
to the average product of labor. The lower bound of the market wage is therefore set
at a level well above the marginal product of labor that is the real opportunity cost of
family labor. Thus small family farms end up using more labor than large hired labor-
based farms since the former can continue using labor beyond the point where the
marginal product of labor equals the market wage rate. In Figure 2.1 the marginal
product labor for a small family farm is below that of a large farm that utilizes hired

labor.

The market wage rate exceeds the marginal product of labor because of the
uncertainty in the rural labor markets especially in labor-surplus economies where
alternative employment opportunities are scarce. Thus even if small farm family
members are willing to be hired at market wages equal to the marginal product of
labor, the risk of ﬁnding off-farm employment results in the market wage being
discounted for the risk involved. The discounted market wage rate would be greater
than the marginal product of labor. When the probability of ﬁnding employment in
rural labor markets is low, assuming that small farm family members have no
preference for leisure, then rural labor markets will not clear. Thus small farms will
have more labor available than large farms which can only attract more labor at higher

market wage rates.

31

2.3.4 Transactions Cost-Based Explanations of the Inverse Relationship

The other way of explaining the differences in the cost of labor between family and
hired labor is the transaction cost approach (Platteau, 1992). Effective per unit costs of labor,
made up of direct wage costs and supervision costs, increase with increases in farm size. This
occurs because the supervision costs increase with farm size and operational scale. The
supervision costs are high because of the difﬁculty of monitoring the quality of the labor
eﬂ‘orts produced due to the variability and unpredictability of agricultural operations and
outcomes. This then becomes a classic principal-agent problem.

The variability and unpredictability of agricultural production activities lead to
information asymmetries between the employer/owner and the worker making it difﬁcult for
the employer to determine the extent to which the agent is responsible for the good or bad
outcomes. This is a typical incentive problem of both the moral hazard and/or adverse
selection type. The presence of exogenous risk thus makes small family farms more efﬁcient
in that the workers are the sole residual claimants of farm proﬁts. There are no incentive
problems on small family farms because monitoring the workers' effort is less important. In
addition family farmers have a more intrinsic knowledge of the biophysical attributes of their
land (Ellis, 1993). Thus Mill‘s original argument that guaranteeing individuals ‘the fruits of
their own labor and abstinence' eliminates the incentive problem remains intact and is the basis
of the higher efficiency of small family farmers. What we get out of the transactions costs
approach is that large non-family labor farms have to deal with the incentive problem at
positive transaction costs. They have to ensure, for example, that labor shirking and pilferage
of inputs by workers are avoided. This extra effort of labor supervision to avoid managerial

diseconomies increases the price of wage labor above that of family labor.

32

Managerial diseconomies of scale also mean that the per unit cost of labor increases
with farm size even when we consider small farms operated by family workers only. Platteau
(1992) thus noted that the inverse relationship can exist independently of production relations
in what is termed the "incentive dilution effect". The larger the family is, the more diluted the
shares of each member and thus the greater the incentive problem. Worker efﬁciency declines
or the cost of labor rises with the scale of operation.

Among large farms that rely on wage labor, researchers have found out that those
farms that have more family members staying on-farm were more efﬁcient than those that did
not, ceteris paribus. This led to what became known as Sen '3 reformulation of the
supervision cost argument. This reformulation is based on the effectiveness of avoiding
”supervising the supervisor" by entrusting the supervision of hired workers to family
members. This makes family labor a complement of hired labor but only up to a certain point
beyond which beneﬁts from substituting hired workers for family labor become negligible. Sen
used evidence ﬁ'om a study in Punjab (India) to prove that continuing to hire labor beyond
a certain point without more family labor available is difﬁcult. Large farms are often less
eﬁcient than small ones because shortages of family labor supply cannot be overcome
indeﬁnitely through hired labor.

Sen's reformulation illustrated that supervision problems can be reduced by reducing
the social distance" between the employer/owner and the worker or when the hired workers
work side by side with the employer. The social distance tends to increase with farm size.

The inverse relationship between farm size and productivity is also a result of the inverse

 

‘7 Social distance is a measure of the closeness of farm labor. The social distance between
family members is short by virtue of the family relationship. If a farm only hires a few
workers (2 or 3) relatives are most likely to be hired or the non-relatives are treated as
relatives, hence the social distance will be short.

33

relationship between social distance and wage labor's willingness to apply effort. If the social
distance is "short" then the effective per unit costs of hired labor are lower. Sen’s
reformulation to explain differences in labor costs seems to yield the recommendation that
large landowners should develop close personalized ties with their workers, if class relations
permit, so that they can lower their effective labor costs.

The other transaction cost-based observation is that subjective conditions, such as
preference for leisure and/or non-farm activities, by determining labor use also determine the
large farm equilibrium labor price. It may not be labor market condition alone (which assumes
that labor has no preference for leisure and non-fann work).

The transaction costs approach also enables us to explain why small family farms use
more family and hired labor per unit of land than large hired labor-based farms; and why the
marginal product of labor on the large farms is greater than the market wage rate and that it
increases with farm size. There is also a suggestion that agriculture sometimes experiences
diseconomies of scale (Johnson and Ruttan, 1994). The diseconomies of scale in agriculture
occur when the labor market fails or does not exist in the agricultural sector. Without a well-
functioning labor market, labor exchange activities become expensive such that the more hired
labor one uses the higher the transaction costs.

What emerges ﬁom the ODLR debate is an illustration of the constraints associated
with diﬁ‘erent farm structures. Large farms have to deal with the problems of controlling
labor, that is, an imperfect labor market. Hired labor is difficult to motivate. Family labor is
cheap and self-motivated. Large farms in many developing countries are usually owned by
absentee landlords and have been severely underutilized (Rukuni, 1994). Small farms on the

other hand have to deal with imperfect capital, and very oﬁen, political markets. The small

34

farmer-led agricultural growth strategy is constrained by the high costs of ensuring small
farmers access to capital markets and their transparency in political markets.

But the differences in farm sizes around the world is not only a product of imperfect
input markets. There are other reasons for the observed differences. Differences in the
relative availability of factors of production explain some of the differences in farm size across
nations. For instance countries that have relatively more land per capita have larger farms.
The United States farms are larger that those in Japan. Because of the relative shortage of
land and abundance of labor, Japan’s agrarian structure is based on small farms that use labor
intensively while the United States farms are relatively larger and dependent on the use of
mechanical inputs. In many developed countries small farms are being consolidated into
larger farms because with development the percentage of labor working in the agricultural
industry falls. The few who remain on farm are forced to use modern machinery to maintain
viability in the face of declining terms of trade. Thus farm sizes in developed nations are
becoming larger. It remains to be seen if this trend will be witnessed when developing
countries’ economies modernize.

Despite the differences in farm sizes observed around the world the argument that
small farms are more efﬁcient, economically and socially, than large farms remains strong.
The question that is addressed in the next section is whether there is consistence between
theoretical and empirical work on this subject. In other words what can we learn ﬁ'om the

empirical studies on the inverse relationship hypothesis?

2.3.5 The Inverse Relationship: Some Evidence
The continued survival of large-scale farming challenges strong theoretical literature

on the existence of the negative relationship between farm size and land productivity.

35

Theoretically, the inverse relationship hypothesis holds if both small and large farms use
identical technology and market imperfections and other policy induced distortions are absent.
Part of the upsurge in agricultural production in Kenya and Zimbabwe after independence is
attributed to the restructuring of distorted institutions that accompanied the reform of the
agrarian structure (Orvis, 1997).

The appraisal of the performance of Zimbabwe's Resettlement Schemes is
characteristic of the whole debate on what is the most productive farm type in Zimbabwe.
A vital question is whether land acquired for resettlement is being used as productively as it
was under previous owners (Matanyaire, et al, 1992). Muir and Blackie (1994) found the
productivity record of resettled farmers unimpressive and attributed the poor performance to
poor land quality and insecure tenure. They point out that most of the land used for
resettlement is marginal for crops in which resettlement farmers have shown a comparative
advantage and thus could not compete with the crops previously grown such as tobacco. The
Commission of Inquiry into Appropriate Agricultural Land Tenure Systems, while
acknowledging the problem of insecurity of tenure, was “impressed by the high standard of
farming” and concluded that the conventional wisdom that resettlement areas are
unproductive was not objective (Rukuni, 1994). The debate on the most productive farm
type in Zimbabwe, and indeed the whole question of agrarian reform, remains unresolved in
the absence of empirical studies (Moyo, 1994).

The experience in Kenya has been more conclusive than the Zimbabwean case. Kenya
witnessed a dramatic increase in output aﬂer the land titling schemes which were initiated
toward the end of the colonial period and pursued by post-independent governments (Migot-
Adholla, Place and Oluoch-Kosura, 1990). Hunt (1984) reported strong inverse correlation

between farm size and income, labor use, and marketed output per hectare. Migot-Adholla,

36

et al (1990) concluded ﬁ'om survey data that plot size was negatively related to yields for all
cropping patterns. Muir and Blackie (1994) attribute the success in Kenya to the high quality
of land on which smallholders were resettled. They were, unlike their Zimbabwean
counterparts, able to farm their new land more intensively than the previous owners without
causing serious land degradation.

There is empirical evidence ﬁ'om South Africa’ 3 commercial farming sector suggesting
that there is an inverse relationship between efﬁciency and farm size (van Zyl, Binswanger and
Thirtle, 1995). Using the data from the 1988 census of agriculture small farms (less than 500
hectares) had average gross margins per hectare over 17 and 42 times greater than the
average gross margin per hectare from middle farms (500 - 1000 hectares) and large farms
(over 1000 hectares), respectively. Small farms also employed about 23 and 22 times more
workers per thousand hectares than middle and large farms. Van Zyl et al (1995) also showed
that small-scale black farmers, when given adequate support, performed just as well as or
even outperformed their large-scale white colleagues.

Several studies on the inverse relationship have been conducted in several of Asian
countries with most of them being aﬂirmative. Among them, Yotopoulos and Lau (1973)
used a proﬁt function-based model to measure relative economic efficiency between groups
of farms based on Indian farm-level data. The study concluded that small farms were
relatively more efficient economically. Their superiority was due to both allocative and
technical efficiency. The study also found constant returns to scale in Indian agriculture.
These ﬁndings yielded a strong case for agrarian reform to increase both efﬁciency and equity.
But there are also a few studies, in India, that have conclusions to the contrary. Barnum and
Squire (1979) found no differences in relative economic efﬁciency between small and large

farms and thus found no basis for land reform other than for social and/or political objectives.

37

The main reason for the inverse relationship found in many studies is the dual labor
market hypothesis" (F eder, 1985). The universality of the dual labor market hypothesis as
an explanation of the inverse relationship has been weakened by lack of conclusive evidence.
In a 1979 review, Berry and Cline found some studies that refuted the inverse relationship
and showed positive or no relationship between farm size and productivity. Feder (1985)
showed that including market distortions helps explain the ambiguity of the observed
relationships between farm size and productivity. By proposing that supervision of hired
labor by family members improve the productivity, F eder (1985) was able to show that the
systematic relationship between farm size and productivity can be negative or positive. This
occurs though there are constant returns to scale and all farmers face the same prices.

In Latin America, most countries experienced a reduction in agricultural output a few
years after the reform, with the exception of Venezuela (Alexander, 1974). But this fall in
production is expected as Powelson (1964) observes that “it is scarcely possible to carry out
any change in land tenure without adverse effects on production” (p. 65). A study by Heath
(1992) in Mexico evaluating the impact of land reform on agricultural productivity concluded
that there were no major differences in productivity between privately operated land and ejido
(communal land) that resulted from agrarian reform. In Honduras, Larson (1997) found out
that efﬁciency was dependent not only on the nature of land markets but also on that of other
markets particularly credit.

Thus the fall in output immediately aﬂer agrarian reform is not a product of small

farms being inherently inefficient. The main reason why production did not fall in Venezuela

 

" The labor market is made up of the "family" labor market and the wage-labor market.
Because of high costs of searching for jobs with wages higher than the value of the average
product, it oﬁen occurs that the family labor market end up operating at a lower wage than
the wage-labor market. The difference in wages also gives rise to the duality.

38

was that the resettled farmers were lavishly supported by the government which drew from
its vast oil revenues. Resettled small farmers have not performed as well in other countries
because their governments could not afford to ﬁnance the establishment of the essential
physical, economic and social infrastructure. De Janvry et al (1989) and Williamson (1997)
reported the existence of acute landlessness in Latin America suggesting that the reforms
were not effective. Overally, however, the new agrarian structures have been able to not only
increase production to meet the needs of growing populations and developing industrial
sectors, but has effectively broken down the landlords’ hold over the lives of the peasants and
allowed peasants to participate in national politics (Alexander, 1974).

One crucial issue in the presentation of evidence on the existence of the inverse
relationship is the assumption of competitive capital and land markets. If these assumptions
are violated, then the relationship between farm size and productivity can take forms other
than the expected inverse relationship. What is the relationship between farm size and
economic efﬁciency in the real world? Speciﬁcally are small farms economically efﬁcient
relative to the large mechanized farms in Southern Africa?” Also, have past policies and
distortions affected the relationship between farm size and productivity in Southern Aﬁica?
An attempt to answer these question is made in the next section drawing from work down in

South Aﬁica and Zimbabwe.

 

’9 Southern Aﬁica includes all the countries that are members of the Southern African
Development Community (SADC) but in this study the focus is on those countries that have
dualistic agrarian structures such as Malawi, Namibia, South Aﬁica and Zimbabwe.

39

2.4 Lessons for Southern Africa

The review of studies on the relationship between farm size and productivity has
shown that, generally, small family-operated farms are more efﬁcient than large farms
especially when inputs markets are competitive (Berry and Cline, 1979). because of the way
these small family farms organize labor relations. This is particularly evident in cases where
factor markets exist and are not affected by distorting policies. If markets are imperfect
because of policy distortions, the relationship between farm size and economic efficiency will
not be an inverse one. Removing market imperfections would not only allow for efﬁciency-
farm size relations to properly manifest themselves but would also eliminate the societal
deadweight losses that they cause. Thus privileges and distortions that favor large farms
should, wherever possible, be removed to allow efficient markets to operate.

In many Southern Africa countries, markets reﬂect the distribution of power, rights
and privileges. This distribution favors large scale farming hence their dominance in the
economy as a whole and agriculture in particular. However, recent studies in South Aﬁica
report the presence of an inverse farm size-efficiency relationship despite an agrarian history
tailored speciﬁcally to entrench large scale farms (van Zyl, Binswanger and Thirtle, 1995).
An important issue here is whether there are gains in efﬁciency to be made from subdividing
the large scale farms in Southern Aﬁica.

Thus the most pressing question in Southern Africa is whether small farms are more
efﬁcient than large farms even in the presence of distorted input and output markets. The
other issue to be clariﬁed is how to create agrarian structure through, among other things,
leveling the playing ﬁeld not only to ensure no particular section of the society enjoys a
privileged position relative to others but also to enable society to maximize beneﬁts. Land

reform involving the subdivision of large scale farms is one of the main options given that

40

Southern Aﬁica has exhausted its land frontier. Unlike Latin America, the sub-region does
not have new unoccupied lands which makes the resettlement of marginalised small farmers
politically easy (Powelson, 1964). The other option, addressed in this study, is to look at
small-scale agriculture and examine whether it is possible to change production patterns in
ways that will eliminate poverty.

Accordingly the search for solutions should begin by looking at the way small scale
family farms have been operated. Are these farms economically efﬁcient? Ifthey are not,
what are the factors that explain inefficiency? Then what measures could be taken to ensure
that the current and future small family farms operate efficiently? In doing so, one should
recognize that the odds were staked against the small farmer all along. Policy distortions and
market imperfections were a result of eﬂ‘orts to marginalize small scale family farms and
promote large scale farming. The extend to which the results of an analysis of small scale
farm are dependent on these deliberate policy distortions and market imperfections should be

explored.

2.5 Summary

Zimbabwe’s agrarian history is a product of an era when large scale farms were
considered the primary vehicle to transform the economy ﬁ'om being agriculturally-base to
one based on industrial production. When the industrial sector failed to absorb all the labor
released when large scale farms were established, there was no attempt to change the agrarian
system so that it could provide opportunities for the majority of the population to work and
fully participate in the national political and economic markets. Instead, before independence,
in 1980, economic policies were enacted to entrench large scale farming and reduce the

competitiveness of small scale family farms. After independence, the new government

41

changed the focus of policy making to focus on communal farmers. The support
inﬁ'astructure that had been geared to serve a small number of large scale white commercial
farmers was expanded into the once neglected communal farming areas. In addition a market-
driven land redistribution program was implemented. These programs did result in a marked
change of the national agricultural system in terms of access to resources and production by
farm type. But the changes were not thorough enough to level the playing ﬁeld between
communal area and large-scale commercial farmers. Conditions have risen in Zimbabwe, and
in other Southern Aﬁican states, that call for changing the distribution of power, rights and
privileges in the use of land.

The central issue discussed in this chapter has been the economic justiﬁcation of
agrarian reform. The literature review revealed that there is an inverse relationship between
farm size and economic eﬂiciency when input markets are free of distortions. Labor market
imperfections turned out to be the main cause of the inverse relationship between farm size
and farm-level economic efficiency. The inverse relationship was explained using both the
labor cost-based and transaction cost-based explanations. What emerges ﬁ'om this analysis
is that, generally, small family farms are more efﬁcient than large scale farms because of the
way in which labor relations are organized. The only case when the farm size-efficiency
relationship is ambiguous is when there are capital market imperfections due to policies
enacted speciﬁcally to support large scale farms. Experience from Latin America indicate that
small farms should have access to inputs and essential support services for them to take ﬁrll
advantage of their comparative advantage in labor utilization. This provides valuable lessons
for Southern Africa countries that are trying to move from a dualistic agrarian structure to
one that put people to work. But without new unoccupied land on which to resettle landless

communal farmers, Southern Aﬁican countries need to look at how far they can increase

42

communal area production without engaging on the politically diﬁcult land redistribution.
Understanding the characteristics of current small scale agricultural production system is an

important step along this direction.

43

CHAPTER III: DESCRIPTION OF ZIMBABWE’S COMMUNAL AREA

PRODUCTION SYSTEMS

3.1 Introduction

The previous chapter describes in detail the creation of communal farming areas by
European settlers at the turn of the twentieth century and how from then on land has been a
festering political and economic problem in Zimbabwe. Also raised was the question about
the economic costs of the current agrarian structure and how it can be socially and morally
justiﬁed. What emerged as a challenge is devising ways and means to consistently ensure that
the nation’s natural resources are used for the beneﬁt of as broad a spectrum of Zimbabwean
society as is possible. Ensuring that the farming community uses the scarce production inputs
(land, labor and capital) is an important component of current and future development
programs.

Southern Aﬁican agrarian systems have not been changed ever since the advent of
European settlement. The current political and socioeconomic systems have effectively
preserved the old colonial structures and have resisted change. Political coalitions against
current agrarian structures have not grown to levels of strength and sophistication that can
generate change. Thus, similar to what Cardoso and Helwege (1992) noted in Latin America,
the economic poverty in communal areas reﬂects the political poverty were the communal
farmers lack the means for voicing their interests. Given that over 90 percent of land in
communal areas is not suitable for agriculture using available technology, the stresses and
conﬂicts generated by the current agrarian systems will eventually lead to an overhaul of the

system (Chasi and Shamudzarira, 1992).

44

The government realizes that improving the lives of the rural population should start
at the individual farm-level (WAWD, 1993). Rural infrastructural improvement is only a
necessary condition in this process. The suﬁicient condition is efﬁcient resource utilization
at the farm household level. To understand what is involved in improving the efﬁciency in
the use of farm resources by communal farmers, a detailed characterization is required.
Detailed characterization of communal agricultural production systems is also essential for
speciﬁcation of measures of farm productivity.

The purpose of this chapter is to provide such a characterization of the current
communal production systems. This characterization is based on a multi-visit survey of
communal farms by the Ministry of Agriculture (MOA) during the 1990/91 season. A brief
description of the survey instrument used to collect data reported in this chapter can be found
in the appendix. It is followed by a discussion of how to improve the productivity of
communal agriculture. The chapter ends with a summary of what lessons can be drawn ﬁ'om
the status of communal agriculture and how this information can be used in designing policies,

programs and strategies to alleviate poverty in communal areas.

3.2 Communal Area Production Systems

This section looks at three major features of communal farms; the demographic
characteristics of the communal households, the resource endowment levels and conditions,
and the agricultural production practices. This section primarily based on the 1990/1991
Annual Report of the Farm Management Data for Communal Area Farm Units published by
the then Ministry of Lands, Agriculture and Water Development (MLAWD)’3 Farm
Management Research Section. This annual report is based on a sample survey of 453

communal farmers in Natural Regions 1] (6.7%), III (16.4%), IV (3 1%) and V (45.9%). This

45

sample represents the distribution of communal farms by Natural Region with the exception
that provincial representation was not equal”. In addition the proportions for Natural
Regions IV and V should be reversed if they are to mirror the distribution of communal farms
by Natural Region. However, the similarity between these two Natural Regions makes this
reversal inconsequential. They are both considered unsuitable for crop production. An
attempt is made to compare and contrast the characteristics of households (especially
resource endowment and production practices) in the high potential (HP) Natural Regions
(II and III) and the low potential (LP) Natural Regions (IV and V). The ﬁndings ﬁ'om other

studies and surveys are also used in this characterization exercise.

3.3.1 Demographic Characteristics

Because most communal farm labor requirements are provided by family members,
several insights can be gained from examining the demography of farm households. It helps
in the determination of the availability of labor at the fann-level and helps in assessing the
quality of family labor. The most important demographic variables are on the household head
and the composition of the family.

Nearly 75 percent of the farms surveyed during the 1990/91 agricultural season were
headed by males with an average age of around 48 years. These household heads have been
farming for more than 17 years on average. Thus the households are headed by old and
experienced farmers considering that the average life expectancy is 53 years in Zimbabwe
(World Bank, 1995). Because of the near universal primary education of the Zimbabwean
population it is not surprising that the average years in school for household heads are above

eight years. This means that most of the farms are headed with people with more than just

 

2° Farmers from the two Matebeleland provinces were not included in this sample.

46

primary education.21 However, of the 75 percent of farms headed by males, 49 percent are
nonresident. Thus, the decisions on day to day activities are taken by women effectively
making the majority of communal households female-headed. As a result, efforts to
encourage efficiency in the use of scarce resources should involve women. The female
household heads have the same level of education as their male counterparts.

Family size is usually used as an indicator for the household’s labor force (Shumba,
1992). The average communal farm household consists of about nine members. Just more
than 52 percent of household members are female. Most of the family members are children
below the age of 15 (40 percent) who attend local schools. This coupled with the fact that
nearly 70 percent of the communal farm households have on average two of their members
residing away ﬁom the farm results in the total number of adult family members available for
farm work falling to between three and four”. Because few farmers use hired labor to work
on their farms, the three to four adult family members and the children attending local schools
are the main supply of farm labor. Labor availability becomes a limiting factor during peak
periods in the cropping calender such as seed-bed preparation, planting, weeding and
harvesting (Shumba, 1992).

The high percentage of young people in the rural population as shown by the
dependency ratio of nearly 50 percent is a great cause for concern. This phenomenon implies

that there is going to be more pressure on the already fragile communal environment unless

 

2‘ Primary education in Zimbabwe takes seven years to complete. Previously this used
to take eight years.

22 However, the high percentage of households with nonresident family members implies
that there are very strong linkages between farm and off farm activities. The strong farm to
oﬁ-farm linkage is ﬁlrther illustrated by the fact that remittances ﬁ'om the nonresident family
members make up more than 40 percent of the total annual household income.

47

the youngsters are absorbed elsewhere in the economy. The average percent of elderly people

(above 60 years) of just 4 percent means that the population structure is pyramidal.

3.3.2 Resource Endowment

As in any production process the main factors of production are land, labor and capital
assets. In the last section it was shown that communal farms rely exclusively on family
members for their labor requirements. On average, between three and four adults are
available to work on the farm. The next issue is to determine the average level of the other
inputs that these family members use in agricultural production activities.

The land tenure system in communal areas is based on customary law which gives
farmers usufruct rights over the arable land allocated to them by the traditional authorities.
They do not own the land they cultivate. Farmers are, therefore, not able to use their land as
collateral to borrow money for investments on-farm. However, some studies have concluded
that the claim that communal land tenure is constraint to land productivity is less compelling
(Heath, 1992; Rukuni, 1994). Farmers are not just interested in ownership but tenure
security. Communal land tenure, while not providing individual ownership, acts as a social
security system for the poor.

Communal farmers surveyed during the 1990/91 season had access to 4.83 hectares
of arable land on average. This means that, on average, an adult residing on-farm has more
than a hectare to work on. Communal farmers in the LP zones have more than two hectares

more arable land than their counterparts in the HP zones (Table 3.1).

48

Table 3.1: Average Arable and Fallow Land Owned by Communal Households in
Zimbabwe, 1990/91

 

 

Average Area Low Potential High Potential All Areas
Arable (hectares per household) 5.41 3.12 4.83
Fallow (hectares per household) 0.27 0 0.2

 

 

Source: MLAWD, 1993

The LP area farmers left about 5 percent of their land fallow (about a third of a
hectare on average per household) while farmers in the HP areas did not leave any land
fallow. This seems to suggest that, in terms of absolute sizes, the farmers in HP areas have
less arable land available to them while those in LP areas cannot put all the arable land they
own under crop production. However what HP farmers are missing in terms of the size of
the arable land is compensated for through the high quality of their land. It can also be
reasonably hypothesized that LP farmers are unable to cultivate all the land available to them
because of erratic rains that do not last for a period long enough to allow for the preparation
of all arable land. Some farmers stagger plantings as a way to minimize the risk of crop
failure in both the LP and HP zones (Shumba, 1985). Rainfall is an important variable in
communal area agriculture.

Although 6 percent of land under irrigation in Zimbabwe is on smallholder farms23 the
area under irrigation in communal areas as a percentage of the area under cultivation
nationwide is almost negligible (Rukuni and Makhado, 1994). Even in the small-scale

commercial farming sector and the resettlement schemes the area irrigated is less than one

 

2’ Smallholder here includes communal farms, small-scale commercial farms and
resettlement area farms.

49

percent of the total arable area while the large-scale commercial farmers irrigate 29. 1 percent
of their arable land (MOA, 1995). Thus while the bulk of the communal farmers is in the dry
areas there are no signiﬁcant irrigation projects and programs. It is mainly the availability
of capital to put up irrigation schemes that is a critical limiting factor to be included as a
variable in any analysis of agricultural production systems in Zimbabwe.

Communal farmers do not enjoy the same level of access to capital markets as
conunercial farmers do due to their inability to use land as collateral. Only 11.5 percent of
the farmers surveyed in 1990/91 received credit ﬁom the Agricultural Finance Corporation
(AFC)2‘ during the year 1989/90 as shown in Table 3.2. Table 3.2 shows that while nearly
36 percent of farmers in the better endowed Natural Regions use AFC loans, only less than
4 percent of farmers from the dry zones get loans from the AFC. This disparity may help to
explain why fewer LP area farmers, in percentage terms, buy inputs than HP area farmers
do”. It thus appears that farmers in the HP zones have more access to working capital than
LP area farmers. But it is the inability of all communal farmers to use their land as collateral
that prevent them ﬁ'om borrowing money from ﬁnancial institutions. With limited
participation in the capital markets, communal area farmers are unable to make the necessary

investments required for intensive and commercial oriented agricultural production.

 

2‘ The Agricultural Finance Corporation (AFC) is the only public-lending institution that
provides farmers with agricultural credit in Zimbabwe.

2’ Fertilizer and seed are the main inputs that communal area farmers purchase. A few
others also buy chemicals for pest, weed and disease control.

50

Table 3.2: Percentage of Households Using Purchased Inputs and AFC Credit in
Zimbabwe Communal Areas, 1989/90

 

 

Item Low Potential High Potential All Areas
Households buying Inputs 84.9 98.2 88.1
Households Receiving AFC Loans_ 3.7 35.6 11.5

 

Source: MLAWD, 1993

Another line of inquiry is to ﬁnd out how family income was used within the
household during the 1989/90 season with particular emphasis on the percentage of family
income that is used in capital investments. Most of the household income is spent on non-
agricultural expenditures such as food, clothing, school fees and other consumables. Capital
expenditure on agriculture as a percentage of non-agricultural expenditures is less than 4
percent. Only 45 percent of the capital expenditure on agriculture (or less than 2 percent of
non-agricultural expenditures) is on farm implements. It seems that limited access to capital
markets have a profound effect on on-farm investment and thus affect the level of efﬁciency
observed from one farm to another.

The main capital assets in many communal farms are draft animals. Communal
agriculture is highly dependent on draft power. More than 74 percent of the households
surveyed in 1989/90 season owned cattle. For those who own cattle, each household, on
average, has of six animals. This would appear sufﬁcient for the provision of draﬁ power if
we do not take into account that this number may include non-draft power providing animals
such as calves. A survey of cotton farmers in 1995 showed that the farmers in most areas
have less than the required four draﬂ providing animals and in one case the number of draﬁ

animals was less than two (Mudhara, Anandajayasekeram, Kupfuma and Mazhangara, 1995).

51

Thus although most of the households surveyed owned cattle and donkeys for draft power,
a shortages of draft power at the household level exists. Farmers often resolve the shortage
of draft animals by combining and sharing spans while those who do not own draft animals
rely on borrowing from close relatives or hiring from neighbors (Mudhara, et al, 1995). Thus
access to draft power is an important factor in communal agriculture“.

The other important group of capital assets is farm implements. The implements of
interest here include ploughs, ox-drawn scotch—carts, cultivators, harrows and wheel barrows.
In both HP and LP areas, a majority (over three-quarters) of communal farm households own
the ox-plough which is used primarily for land preparation and planting. The other reasons
why the plough is the most common farm tool is its low price and ease of maintenance
(MLAWD, 1993). Motorized farm implements are less common because of the high costs
and the limited versatility (Moyo, Matanyaire and Norton, 1992). Most farmers in both the
LP and HP areas own scotch carts for farm transportation and cultivators for weed control
and to some extent marking of planting furrows. The absence of even a single farmer who
owns motorized farm implements such as tractors testiﬁes the degree of under-capitalization
in communal areas”. The percentage of farmers owning these implements are shown in Table

3.3.

 

2‘But access to draft power should be interpreted with caution. Access to draft power is
not equivalent to draft animal ownership. Extensive family ties allow households which do
not own draft animals varying degrees of access to draft power. Some households which do
not own draft animals behave like those who own because of the extended family ties which
are difficult to capture using a survey instrument.

2’ In 1987, of the 24,000 tractors used for agricultural production country-wide, only
1,500 (6.25%) were used by communal farmers (Moyo, et al, 1992).

52

Table 3.3: Farm Implements Ownership in Communal Areas of Zimbabwe, 1990/91
Farm Asset Low Potential High Potential

 

% Owning N° Owned % Owning N° Owned

 

Plough 75.7 0.9 77 1

Scotch Cart 30.2 0.7 26 0.4
Cultivator 12.3 0.1 43 .9 0.5
Harrow 12 0.1 9.7 0.1
Wheelbarrow 41.5 0.3 2.7 0.3

 

Source: MLAWD, 1993

There are no major signiﬁcant differences in the farm implements ownership pattern between
the HP and LP areas as shown in Table 3.3. The implements shown in Table 3.3 are
appropriate for small farms that are labor intensive. But it has been shown above that the
average family labor force of between three and four adults may not be enough to provide the
labor required on the more than four hectare farms in the absence of major capital
implements. The ownership of farm implements is expected to affect the level in farm-level
economic efﬁciency.

In summary communal farmers in both high and low potential areas do not have the
resources they would require to operate their farms adequately on a commercial basis. Land
is of poor quality. The capitalization of communal farms is almost nonexistent. Farm
implements are not up to the modern standards as the absence of tractor use seems to
suggest. Even the labor that many have said communal farmers have in abundance might be

on the low side (more than a hectare per adult residing full-time on—fann). It can be safely

53

concluded that there are genuine resource constraints (quality and quantity) on communal

farms in Zimbabwe.

3.3.4 Crop Production Enterprises

Communal agriculture consists of both crop and livestock enterprises. The major
crops in communal areas are maize (Zea mays), groundnuts (Arachis hypogaea) and cotton
(Gossypium spp). These crops’ average share of the national total value of crop production
during the ten-year period 1982 to 1991 was more than 75 percent. There are eight major
crops grown in the sample areas. They can be categorized as follows:

-Main Food Crops: - Mainly maize and groundnuts grown by most farmers and a

large portion of the harvest are retained for domestic consumption. However, these

crops also serve a double ﬁrnction as food and cash crops.

~Main Cash Crops: - The main cash crops include cotton, tobacco (Nicotiana
tabacum L.) and sunﬂower (Helianthus annuus) grown solely for sale. Cotton, unlike
sunﬂowers, is grown in speciﬁc areas notably where soils are clays or loams.

Tobacco is also grown in special areas.

°Other Crops: - The crops in this category are either not very popular with the
farmers or they are grown on a very small-scale basis in terms of the proportion of the
land on which they are grown. Most of these crops, which are mainly food crops for
domestic use, include small grains such as sorghum (Sorghum bicolor), pearl millet
(Pennisetum americanum), ﬁnger millet (Eleusine coracana) and bambara nuts

(Vigna subterranea).

54

The main livestock enterprises are cattle, goats and poultry. Livestock enterprises on
their own seem to contribute very little to the farm income other than acting as store of
wealth and insurance against unforeseen cash demands (N dlovu, 1994). However, livestock
enterprises are closely linked to the crop enterprises (Shumba, 1992). Crops beneﬁt from
livestock enterprises through the provision of draft power and manure. In many communal
areas crop residues are fed to livestock particularly cattle, goats, sheep, and donkeys. The
relationship between the two enterprises can be considered highly symbiotic.

The popularity of maize and groundnuts in communal areas is shown by examining
both the area under and the number of farmers growing the crop. This pattern is the same in
low potential and high potential areas as shown in Table 3.4. However, farmers in high
potential areas use a larger portion of their land to produce maize than farmers in the low
potential areas (42% versus 25%, respectively). The main reason for this pattern could be
that farmers in the low potential areas have access to larger pieces of arable land as pointed
out before. This seems to imply that there is more land pressure in the high potential areas
though this land may be more productive than that in low potential areas”. There is very little
difference between the HP and LP areas when it comes to other conventional crops listed in
Table 3.4 in terms of the proportion of farmers growing the crop and the proportion of the
area planted to the crop.

It has been argued that farmers in low rainfall areas should concentrate on growing
drought resistant crops. The pattern shown in Table 3.4 indicates that this recommendation
is not fully followed. Farmers in LP areas still grow drought-susceptible crops such as maize.

The choice of crops to grow is clearly not a function of amount of rainfall alone. Farmers

 

2‘ The other possible explanation for this phenomenon is that LP area farmers put a larger
proportion of their arable land to drought-resistant crops such as sorghum and millet as a way
of managing the risk associated with crop production in these areas.

55

have other factors to consider in their choice of an enterprise mix that include potential crop
yield and consumption patterns. Maize has taken the place of sorghum and millet as a staple
in low rainfall areas because of its higher yield, better taste as food and easy processing
(Kupfuma, et al, 1992). Farmers grow maize alongside sorghum and millet in low rainfall
areas so that if the maize crop fails they can always depend on the small grains (Shumba,
1992). However, if the maize crop succeeds, then the sorghum and millet harvested is either
sold or used for making beer. This point should not be ignored when considering programs

to alleviate poverty in the low rainfall areas of Zimbabwe.

Table 3.4: Crops Grown on Communal Farms in Selected Areas in Zimbabwe,

 

 

 

1990/91

Crop Grown Low Potential Areas High Potential Areas All Areas

% Farms %Area %Farms % Area %Farrns % Area

Growing Cropped Growing C ropped Growing Cropped
Maize 92.6 25.2 96.3 41.6 93.5 29.3
Groundnut 80.6 11.7 61.7 12.0 75.9 23.3
Cotton‘I 7.2 21.1 66.7 27.7 66.7 23.3
Sunﬂower 24.8 15.6 24.9 13.2 25.2 15.0
Pearl millet“I 37.3 15.0 n/a n/a 37.3 15.0
Finger millet 42.3 9.2 27.1 12.1 38.5 9.9
Sorghum‘" 23.3 11.3 n/a n/a 23.2 11.3
Barnbara nut 40.6 6.9 8.3 7.2 32.5 7.0

 

NOTES

" The cotton data in from enumeration areas where cotton is grown

“ Pearl millet is not grown in high potential areas (Chiweshe and Kandcya)

‘” Sorghum is not grown in high potential areas and the data reported exclude these areas

Source: MLAWD, 1993

56

Although cotton is the second largest agricultural foreign currency earner it did not
show up as a major crop in the sample in terms of area planted and/or the number of farmers
growing it because cotton is grown in speciﬁc agro—ecological zones. The crop does well on
heavy clay and loam soils. Thus cotton is grown in speciﬁc areas such as the north-central
Middleveld and Lowveld and the south eastern Lowveld”. Because of its high value its
contribution to total communal agricultural value is signiﬁcantly high to be considered a major
crop. This is also true for tobacco which is grown in speciﬁc areas. But even in areas where
the two cash crops are grown, maize and groundnuts are still major enterprises (Mudhara, et
al, 1995). In the 1990/91 survey cotton did not show up as a popular crop with farmers
because the enumeration areas were not major cotton growing areas (see Table 3.4).

Table 3 .4 shows the average farm’ 3 mix of crops in terms of the proportion of the area
devoted to each crop. As expected topping the list is maize which takes up close to a third
of the cropped area. The proportion devoted to other crops is close to even at around 10
percent with the exception in areas where cotton is grown. Here the area occupied by cotton
is close to a quarter of the total area under crops. The communal farming system is primarily
maize-based. Other crops do not have the same importance that farmers attach to the maize
crop

Table 3 .4 also shows that the main differences in crop mixes between LP and HP areas

is in the form of the proportion of arable area under sorghum and pearl millet. The two crops

 

2’ Zimbabwe is divided into three broad altitudinal planes/plateaus. The ﬁrst is a T-shaped
plateau that lays above 1,200 meters above sea level (masl) called the Highveld occupying 25
percent of the country; the Middleveld is a plateau laying between 900 and 1,200 masl and
covers about 40 percent of the country’s land; the third plateau is the Lowveld laying below
900 masl made up of the Zambezi basin to the north and the Limpopo and Save basins to the
south and south-east, respectively.

57

are not grown extensively in HP areas. In LP areas pearl millet and sorghum together take up
a quarter of the arable land that is available. It is, however, interesting that ﬁnger millet is
grown in all areas enumerated with more than 40 percent and 27 percent of the sampled
farmers growing the crop in the LP and HP areas, respectively. The same can be said of
bambara nuts raising the question on how best to promote the production, processing and
marketing of the crops or their by-products such that they graduate ﬁom being the
“forgotten” crops to enterprises that are beneﬁcial to a wider spectrum of small-scale farmers.

We have already noted the effect of agro-ecological conditions as the main factor that
inﬂuences the choice of crops farmers grow (Chasi and Shamudzarira, 1992). But agro-
ecological factors cannot explain why maize is still the dominant crop in the semi-arid zones.
There are other factors that explain these production patterns. A simple analysis of the
average yields and prices30 of the different crops in the two zones can provide some answers.
In Table 3.5 the average area planted, the average yield and the returns to the farmers own

labor is shown for each crop for the two zones.

 

3° The producer prices of sorghum and millets were equated to that of maize during most
of the 19803.

58

Table 3.5: Crop Area, Yields and Return to Labor in Selected Areas of Zimbabwe
Crop Grown Low Potential Areas High Potential Areas All Areas

 

 

Am Yield Labor Area Yield Labor Area Yield Labor
(ha) (t/lra) RoR' (ha) (t/lra) RoR' (ha) (t/ha) ROR'
($/lrr) ($/lrr) *** *" ($/ha)

 

Maize 1.38 0.99 0.46 1.28 3.59 0.7 1.73 1.45 0.52
Groundnuts 0.6 0.19 0.13 0.33 0.64 0.44 0.49 0.33" 0.2

Cotton 1.52 0.14 0 1.16 0.73 1.85 1.41 0.56 1.85
Sunﬂower 0.82 0.14 0.19 0.39 0.49 0.54 0.69" 0.25”“I 0.28
Pearl millet 0.81 0.8 0.12 n/a n/a n/a 1.49" 0.17” 0.12

Finger millet 0.5 0.25 0.19 0.36 0.44 0.19 0.66" 0.33" 0.19

 

Sorghum 0.59 0.1 0.11 n/a n/a n/a 0.7 0.17 0.11
Bambara 0.33 0.06 0.49 0.2 0.2 0.72 0.46" 0.18" 0.53
nuts

NOTES

‘ RoR stands for rate of return per man-hour of labor

” These averages have a coeﬂicient of variation that is greater than 30 percent.

*" The averages are computed from three years data 1988/89, 1989/90 and 1990/91.
Source: MLAWD, 1993

In terms of area planted and yield, maize is dominant in both LP and HP areas. As
shown by the three-year average data, only the area under cotton and pearl millet is close to
that of maize (cotton area higher than maize area in the LP areas). But the average yield for
pearl millet is way below that of maize. This is not surprising given the research effort that
maize has received over the years relative to other food crops and the attention farmers give
to their maize crop relative to other crops (Shumba, 1992). It is only close in the low
potential zones (maize average yields are 0. 99t/ha to 0. 8t/ha for pearl millet). However, when

it comes to returns to an hour of family labor, cotton dominates as shown in the All Areas

59

columns and the HP area column that represent some real cotton growing areas. Returns to
labor for maize are almost equal to those from bambara nuts even though the latter have a
very low average yield and demand more labor. If this crop is developed from production all
the way up to marketing then there is a good chance that farmers will be richly rewarded from
growing the crop. In the same light, the returns to labor for millets, sorghum and groundnut
are low compared with those from maize, cotton and bambara nuts.

The higher maize yields in comparison to other crops particularly cereals is because,
as the main staple, a lot of research work has been done to improve the crop". Maize is the
only cereal crop to which communal farmers in the selected areas apply chemical fertilizer.32

The levels of fertilizer application on maize in the two zones are shown in Table 3.6.

Table 3.6: Fertilizer Application Rates on Maize in Selected Areas of Zimbabwe, 1990/91

 

 

 

 

Type Low Potential Areas High Potential Areas
Basal Application (kg/ha)‘I ' 24 204
Top Dressing (kg/ha)” 29 181
Total Amount Applied 53 385
(kg/ha)
NOTES: “ This is Compound D fertilizer (7%N, 14%P, 7%K)

“ This is Ammonium Nitrate (34.5%N)
Source, MLAWD, 1993

The fact that more fertilizer is applied to maize grown in the high rainfall areas partly

explains why maize yields in the HP zone are higher than the yields in the LP zone. In Table

 

3' Numerous studies in Zimbabwe show that almost all farmers, including communal
farmers, use improved hybrid maize seed.

32 Cotton farmers are also reported as users of chemical fertilizers (Mudhara, et al, 1995)

60

3.6 farmers in the high potential areas apply more than seven times more fertilizer than
farmers in the semi-arid zones. This is driven by the high returns farmers get from growing
the crop as compared with the returns obtained in the semi-arid areas. They buy more inputs
and more households use AFC loans. This means that the farmers in these areas are relatively
more integrated into the monetary economy. In the LP zone, lower but more variable
expected yields discourages communal farmers from using fertilizers and chemicals on their
crops. However, the small-scale farmers in the HP areas occupy only a quarter of the total
small-scale farming area. The other three-quarters of the small-scale areas are relatively less

integrated into the market economy and is cause for concern.

3.3.5 Livestock Production Enterprises

Communal farmers own the bulk of the national cattle, sheep, pigs and goats herds
as shown in Figure 3.1. The ﬁve-year average numbers of livestock owned by the communal
and commercial farmers clearly show the dominance of the communal farmers. Communal
farmers owned more cattle, sheep, pigs and goats. However, communal farmers do not sell
their animals because in per capita terms the number of animals owned is too small. For
instance, the off-take, in terms of animals sold through formal markets, from communal farms
is less than 3 percent compared with 23 percent for commercial farmers (N dlovu, 1994). The
oﬁtake for the other smaller stocks is far less than that of cattle in communal areas. Livestock
play a role in small-scale agriculture that is different from that it plays in large-scale
commercial agriculture (providing draft power, store of wealth, insurance and food).

In small-scale agriculture livestock is an important input in crop production. Cattle
and donkeys are an important source of draft power for land preparation and other ﬁeld

operations. Farmers who have access to draft animals can plough their ﬁelds early enabling

61

them to beneﬁt from the higher yields associated with early planting (Shumba, 1992). Those
farmers without access to draft animals have to wait for those who have to ﬁnish planting
their ﬁelds before they can hire and/or borrow. As a result they end up planting late and thus
get poor yields. In addition livestock is also an important part of the nutrient cycle.
Livestock provide manure used to improve soil fertility and structure. Crop residues are an
important feed for livestock especially during the dry season. Efﬁciency in communal

agriculture is dependent on how best farmers exploit the crop-livestock interactions.

 

 

 

 

 

 

 

 

 

 

100
80. ........................ ....................... ....................... ....................... ........................
4 III III II: III
‘_ 60‘ ........................ ....................... ....................... ....................... ........................
g :::: :::: :::: ::::
o d
3 3535 3555 5555 . EEEE
0- 40., ........................ ....................... :::: ....................... ........................
20. ......................... . ................................. ....................... . ................................. . .......................
Cattle I sheep I Pigs I Goats

Livestock Type

 

IDConmerclolmCommmol ]

 

Figure 3.1: Distribution of Livestock by Sector in Zimbabwe, 1987-1991

62

Although communal farmers own the bulk of the national cattle, sheep and goat herds,
not every one of them own all these species of animals. Furthermore those who own
livestock, do not own them in numbers large enough for commercial livestock rearing and
neither do they keep livestock for the same reasons commercial farmers do. Table 3 .7 shows
that a quarter of farmers sampled in the 1990/91 season did not own cattle. It also shows the
ownership patterns for donkeys (which supply draft power in the semi-arid regions) and
goats.

Table 3.7: Livestock Ownership Patterns in Selected Areas of Zimbabwe, 1990/91

 

 

Item Low Potential Areas High Potential Areas All Areas

% Owning Cattle 74.4 74.4 74.4
Number Owned 6.1 4.9 5.8

%Owning Donkeys 20.2 2.9 15.9
Number Owned 0.7 0.1 0.5

%Owning Goats 77.5 52.5 71.2
Number Owned 6.? 2.6 5.6

 

Source: MLAWD, 1993

Other surveys in communal areas have reported higher percentages of communal
farmers who do not own cattle”. However, the average number of cattle owned is close to
other ﬁndings. The major point of interest is that while the percentage of cattle owners is the
same for both the HP and LP zones, the average number of cattle per household in HP areas
is less than that in LP areas by one animal. Fewer farmers in HP areas own donkeys and

goats when compared with LP area farmers. The farmers who own donkeys and goats in HP

 

3’ For instance, Shumba (1985) reported that about 48 percent of farmers survey in
Mangwende, a high rainfall area, did not own cattle. Mudhara et a1 (1995) reported from a
survey of cotton farmers that about 40 percent of the farmers were non-cattle owners.

63

areas own far less of these animals when compared with owners of donkeys and goats in the
LP areas. This pattern could be because there is more land per capita in the LP areas though
this land is of limited potential. In addition the LP areas are more suited to livestock rearing
than the HP areas according to the Vincent and Thomas’s 1961 study (Chasi and
Shamudzarira, 1992).

To summarize the communal farmers operate a system of crop-livestock enterprises
that has weak links with the market economy relative to large-scale commercial farmers. The .
production system is heavily dependent on rainfall. Livestock are an important input into the
crop enterprises such that it can be viewed as a capital input. Livestock provide crops with
manure and draft power services. The value of livestock changes in either direction
depending on the quality of the season and reproduction (appreciate or depreciate).
Livestock and human labor are the major inputs in crop production. It is only maize and
cotton that receive fertilizer and chemical inputs on a signiﬁcant scale. The production system
in communal areas is therefore less dependent on inputs from the market economy. It follows
that if these inputs are to be used to revolutionalize agricultural production in these areas then

some signiﬁcant changes in the delivery of these inputs have to be implemented.

3.4 The Communal Areas in the 21“ Century

There is no doubt that improving living standards in Communal Areas remains a
major challenge to policy makers as the new millennium approaches. Despite substantial
investments in improving small scale farmers’ access to markets and support services and
improvements in the rural infrastructure, the majority of communal area farmers remain
impoverished. The main beneﬁciaries of these investments have been the small scale farmers

in the high potential areas (Shumba, 1990). Nevertheless, even for these farmers in high

64

potential areas the “independence dividend”, caused by the improvements in access to support
services and markets, has proved short lived because of ﬁnancial sustainability problems.
Designing new initiatives to eradicate poverty in communal areas and integrate the communal
area population into national economic and political markets remains an elusive goal for all
concerned.

This chapter has characterize the communal production systems in order to put the
issue of eradicating poverty in the country-side into focus. By determining whether
communal agriculture is efﬁcient or not one is then able to screen the options that can be
employed to wipe out rural impoverishment. 1f communal area agriculture is efﬁcient, then
new technologies could be developed to shift the efficiency frontier outwards. The other
option is to expand the land frontier through redistributing underutilized and/or idle land. If,
on the other hand, communal area agriculture is not efficient then living standards in these
areas can be improved substantially by a program that focuses on changing the agricultural
management systems. The role of extension, crop management research, input delivery
systems and infrastructural development in such a program would be crucial. The
characterization has shown how urgent the rehabilitation of Zimbabwe’s country-side is to

ensure sustainable and peaceﬁrl development.

3.5 Summary

The production systems are described in terms of the demographic characteristics of
the households, household resource endowments and the production practices and patterns
that farm household use. Characterizing communal area production systems does not only
put the study into context but can be helpful when identifying factors that can be used to

explain the differences in efficiency in the use of available resources at farm-level. Ultimately

65

this characterization would help in identifying the critical areas where policy reform has a
potential of achieving gains toward the goals of creating an egalitarian society in and
rehabilitating the degraded communal lands of Zimbabwe.

In this chapter a communal area household, on average, consists of about nine
members with over 70 percent of them headed by males who have completed about eight
years of education. However, only three to four members reside and work ﬁrll time on farm
after adjusting for members attending school and/or working off farm. These four family
members work on between 3 to 5 hectares of arable land, on average. Most households
(88%) do not use formal credit sources to purchase inputs. Communal area production
systems are low-input systems that are heavily dependent on ox-drawn implements. Most
communal area farmers own cattle (74%), an ox-plough (over 76%) and a few other farm
implements.

Communal area farmers devote over 29 and 23 percent of their arable area to the main
crops, maize and ground nuts, respectively. The rest is used for other crops such as small
grains and cash crops depending on agro-ecological zones. Because of its position as a staple
food maize receives almost all of the fertilizer used on communal farm while other crops, with
the exception of cash crops like tobacco and cotton, receiving next to nothing. In addition
the improvements made on the maize crop through years of research have resulted in farmers
ﬁ'om low potential areas growing maize instead of the more drought-tolerant small grains.
As a result crop production in Zimbabwe’s communal areas is dominated by maize.

Livestock is an important enterprise in communal areas not only on its own but more
as an input into the crop production system. Livestock enterprises provide draft power and
manure to crop production and make use of crop residue as a source of food. It became clear

in this chapter that there was need to strengthen the low-input crop-livestock production

66

system in communal areas. In doing so there is need to ensure that the beneﬁts thereof are

as equitably distributed as is possible without sacriﬁcing elfrciency.

67

CHAPTER IV: METHODOLOGICAL ISSUES: A LITERATURE REVIEW

4.1 Introduction

The main objective of this study is to measure the economic efficiency of communal
area agriculture in Natural Regions II, III, IV and V. Measuring economic efﬁciency at the
farm-level is preferable, so that a relationship between the estimated indicators of economic
eﬁciency and variables that characterize communal area farm households can be speciﬁed.
Having explained the variation of the estimated indicators of economic efficiency from one
farm to the other, one can go on to draw policy implications and gain some insights into what
factors should be considered when crafting programs to rehabilitate communal area
agriculture in Zimbabwe.

Measures of farm-level efficiency are estimated from production, cost or proﬁt
frontier functions. These ﬁrnctions specify relationships between inputs and outputs. Since
it is possible to produce several output levels using the same bundle of inputs the production,
cost and proﬁt functions have often been deﬁned frontier functions. Production (proﬁt)
ﬁ'ontiers map the relationship between input bundles and the maximum level of output (proﬁt)
that these bundles can generate. Cost ﬁrnctions, on the other hand, are loci of the cheapest
input bundles that can be used to produce given output levels. The notion of duality links
production, proﬁt and cost ﬁrnctions". The best farm-level economic efﬁciency measures are

estimated using the best models of the production technology.

 

3‘ Duality theory speciﬁes that all the information that is contained in a production
function is embodied in the cost function such that by estimating a cost function one can
recover all the parameters that are in the production function. In other words the cost
function is dual to the underlying primal production function. The dual cost ﬁrnction allows
one to assume that ﬁrms choose inputs quantities so as to minimize the cost of producing a
certain level of output given exogenously determined input prices.

68

In this chapter the main thrust is to review the literature on the methods of estimating
production and cost functions and therefore economic efﬁciency indicators. The ﬁrst section
deals brieﬂy with how to specify the relationship between outputs and inputs with emphasis
on ﬂexible ﬁrnctional forms. An important aspect of the input-output relationship addressed
in this section is whether to use a cost function as opposed to a production function. The
second section reviews recent developments and the extension of the original production or
cost ﬁrnctions to make them more general and ﬂexible. Special emphasis is placed on the use
of a multi-product function versus a single product function and extensions that deal with
short run asset ﬁxities . Endogenization of pricing to take into account the existence of
imperfect markets and the modeling of the impact of technical progress while important are
not covered here. In the third section, the focus turns to how to use the estimated cost
functions that take into account these generalizations and extensions to estimate indicators

of economic efﬁciency.

4.2 Modeling the Production Technology

The economic concept of production functions, as it describes the technical process
through which inputs are transformed into outputs, has preoccupied the discipline of
economics for nearly two centuries. The advances made in the theoretical analysis of the
relationship between the levels of inputs and outputs, starting in the mid-nineteenth century,
were not matched by developments in empirical analysis (Bemdt, 1993). The ﬁrst attempt
to empirically analyze input-output relationships occurred in the 1928 with the development
of the Cobb-Douglas (C-D) function. Much of this early work focused on the use of
production functions as devices for macroeconomic studies on the distribution of income

between the two major inputs, capital and labor. But it was only after 1951 that Dean and

69

others started work on the empirical estimation of microeconomic production ﬁrnctions
(Greene, forthcoming). Most of the work on estimating the production function has involved
the modiﬁcation of the CD functional form to make it more ﬂexible and realistic. This
discussion on modeling the production process through a standard production function is
used here as a means to draw some insights on the estimation of frontier production ﬁlnctions.
The latter concept is an extension of the former. The extension involves imposing the
microeconomic theory-based constraint that a production function should be the maximum
output that is possible ﬁ'om a given bundle of inputs. As will be shown later, by not allowing
observations to lie above the production frontier (or below a cost frontier), this constrained
estimation of the production function naturally leads to the measurement of efﬁciency as the

difference between the observed and the estimated theoretical ideal.

4.2.1 Flexible Functional Forms

With the original C-D function, researchers could only estimate input value shares.
The main force behind the modiﬁcation of the C-D ﬁrnction into a constant elasticity of
substitution (CES) ﬁrnction was to enable researchers to estimate input substitution
elasticities (Berndt, 1993). Both the CD and CBS ﬁrnctions, however, proved restrictive as
they assumed constant returns to scale. The development of the Generalized Leontief
function and the Transcendental Logarithmic (Translog) ﬁrnctions made it possible for
analysts to estimate input-output relationships without having to restrict the magnitude of the
input substitution elasticities.

Conﬂict exists between structured and ﬂexible production technology models. The

more structure imposed on a model the better the estimates, as long as the imposed structure

70

is correct. The correct structure is usually not known. In such a situation, it is better to
estimate a sufficiently ﬂexible model and then test possible restrictions.

In this study a choice of what structure to impose on production technology has to
be made. As shown in the last chapter, communal agriculture farm-level technology is not
easy to characterize. The generalized translog structure that will be used to model communal
agricultural technology is a result of careful consideration of the data and characteristics of
the communal farmers. In reaching such a decision one should recognize that stronger

assumptions generate stronger results but strain one’s conscience more (Bauer, 1990).

4.2.2 Dual Versus Primal Models

Very often researchers are interested in ﬁrm-level production issues rather than the
issues for the whole industry. In competitive industries, prices are more exogenous than are
quantities. Entrepreneurs cannot choose prices when maximizing proﬁts in a competitive
market. Everyone is a price-taker. Instead, they choose input quantities to produce a given
level of output. Thus output levels and prices are exogenously determined. But when primal
functions, such as production ﬁrnctions, are used output, being the dependent variable is
endogenous and input quantities are exogenous. Thus these functions do not accurately
reﬂect what takes place in competitive markets. The dual ﬁmctions (mainly cost ﬁrnctions”)
became popular because their ability to reﬂect the relationships generated by competitive
markets. In addition the availability of disaggregated ﬁrm level data contributed to the 8
growth in the use of dual functions in empirical analysis of production technology.

However, there is debate on the appropriateness of primal versus dual ﬁrnction

estimation (Mundlak, 1996). The main issue of contention is the exogeneity of output

 

3’ With dual functions output and prices are exogenous.

71

quantities. In this study the dilemma is whether communal area agricultural production
systems are competitive given, on one hand, the large number of production units and, on the
other, input and output markets that are not completely competitive. If markets are
competitive all small farms would produce the same level of output, qe=Q/N3‘. In this case
the output level is exogenously determined. The cost ﬁrnction treats output as exogenous as
it would be under perfect competition scenarios.

But communal farmers usually face imperfect input and output market. It has been
long recognized that neoclassical framework does not adequately capture the decision making
process that characterize many small-scale semi-subsistence production systems (Ellis, 1993).
It appears plausible to assume that communal area farmers choose how much to produce and
then pick the cheapest input bundle to produce the chosen output level. The input and output
level decisions are endogenous. But the input prices are still exogenously determined. The
debate on the primal versus dual approaches thus is inconclusive in as far as it applies to
communal area agriculture”.

The dual function approach is used in this study because of its advantages when
estimating economic efﬁciency. Because a production ﬁrnction speciﬁes a theoretical
maximum output given the observed input choices by producers, one can only estimate
technical inefﬁciency. Technical inefﬁciency is speciﬁed as the extent to which output falls
below the theoretical maximum output given by the production function. By deﬁnition the

production function does not provide a framework from which one can estimate the extent

 

3‘ Q is the industry output determined by the equilibrium between the aggregate demand
and supply. N is the Optimal number of producers/suppliers.

3’ Simultaneous systems, which are used to handle cases with endogeneity problems, will
not be used because output (being endogenously determined on communal farms) is
expressed as the value of output. The endogenous output level is combined with exogenously
determined product prices.

72

to which observed input choices diverge from the Optimal levels dictated by cost minimization
or proﬁt maximization. Thus using cost ﬁrnctions provides a framework for addressing the
question of optimal input choices or allocative efﬁciency. In addition, these dual functions
allow the speciﬁcation of multiple product technologies and the estimation of economically
eﬁcient sets of input choices through the use of Shephard’s and Hottelling’s lemmas for cost
, and proﬁt functions, respectively. The second order conditions of a production function do

not indicate farm-level input choice decisions.

4.2.3 Transcendental Logarithmic (Translog) Cost Function

One of the most signiﬁcant developments in the generalization of the highly restrictive
OD and CBS production functions, using duality theory, took place around 1961 when
Heady and Dillon published a functional form that had second-degree polynomials with
quadratic and cross-terms added to the OD function.38 Heady and his colleagues at Iowa
State University were using experimental data to estimate input-output relationships using
diﬂ‘erent ﬁrnctional forms. When they included input combinations that are in stage III of the
production function (where the marginal products are negative) they found out that the CD ,
type functions became impractical. The third stage of production does not exist in OD and
CBS functions because of the constant returns to scale assumption. The ﬁrst-order
derivatives (marginal products) of these ﬁlnctions are always positive. As a result the team
headed by Heady had to develop a generalized functional form that allowed for all stages of

production. Experiments with Taylor’s series expansions as polynomial approximations to

 

3' This functional form was also developed independently by Christensen, Jorgenson and
Lau ten years later and became known as the Transcendental Logarithmic (Translog)
function.

73

unknown algebraic forms of the production process yielded what became the transcendental
logarithmic or translog function (Bemdt, 1993).

A non-homothetic translog cost function is presented here since it is very general
because the ratio of cost minimizing input demands can depend on the output level.
Assuming that there are ‘k’ input prices (P,) for the input quantities (Xi) used by a producer
to produce a single output (Y), and that Pi and Y are exogenous while X, and the total cost
of production (C) are endogenous, a non-homothetic translog cost function is speciﬁed as

follows:

k k k k
lnC = lnao + Z pimp, + 1213,,(1npy + Z 2 pumping.
i=1 1 21:1 k i=1 1:1 (1)
+ aylnY + Ednﬂnl’f + Zonrnpjnr, v iej
1:1

The symmetry conditions are imposed by letting Bu = [3],. The translog cost function is nicely
behaved” if it is homogeneous of degree 1 in input prices for a given output level. For this

to apply the following restrictions must be imposed:

213,. = 1, gay. = g9): = 24:6,, = 0

1:1 1 j r

Ifthe underlying production technology dictates that the cost function is homothetic then an
additional parameter restriction has to be imposed by letting the parameter 6,, in the translog
ﬁrnction to be equated to zero for all inputs. Constant returns to scale can also be imposed

if the parameter restrictions aW=0 and aY=l are made besides the homotheticity restriction.

 

3’ This means that all the parameters of the underlying production ﬁrnction can be derived
from such a cost function.

74

The translog ﬁrnction is reduced to a Cobb-Douglas function if all the Bu parameters are
restricted to zero.

The translog cost function can be estimated directly after creating the cross products
and quadratic variables. However, there are some efﬁciency gains if the optimal cost-
minirnizing input demand equations are estimated and transformed into cost share equations
(Bemdt, 1993). The translog cost function in equation (1) is differentiated with respect to
input prices. Employing Shepherd’s Lemma yields the optimal cost-minimizing input demand .

equations and the cost share equations:

6111C P1 (9C P/Y, 1‘
=—-—-=——= .+ .lnP.+6.nY=S.
dlnP, C 6P, C B' 124: pa I If] I (2)

 

The sum of Si’s for all inputs should equal unity. This is known as the “Adding-Up Condition”
which implies that with 11 inputs, k-l cost share equations are linearly independent. This
condition has several important econometric implications.

The number of parameters to estimate from these cost share equations can be reduced
by imposing restrictions. Among the most common restrictions are symmetry in parameter
estimates, homogeneity, homotheticity and constant returns to scale conditions. Because
residuals from the translog cost function and the cost-share equations that are used to
estimate farm-level economic efﬁciency are related, there is considerable debate about how
best to represent this relationship (O’Donnell, 1996). This additional problem has been
christened after Greene (The Greene Problem) will be brieﬂy discussed later on in this
chapter.

In the estimation of production and cost functions many researchers are interested in

estimating elasticities of substitution and own-price and cross-price elasticities. The

75

elasticities of substitution from a non-homothetic translog cost function are estimated as

follows:

Bi. + SIS, . ' B”. + S2 - S.
r} = ATS—J Vjaer; o". = $2 (3)

l j l

 

The cross-price and own-price elasticities from a non-homothetic translog cost function are,

respectively, estimated as follows:

[3 + SS + .
5 = —” 'j. V, 'ri; e = ’ 4
U S J u S ( )

I l

 

These elasticities are used for testing input substitution and effects of price changes. Because
the issue of input substitutions is outside the scope of this study, this subject will not be
pursued in detail with the exception of the elasticity of costs with respect to output (A). The

inverse of A is a measure of returns to scale and is estimated as follows;

 

A = —,
ecr
where (5)
V k
60, = 8”" = a, + Zoning + anlnY
Gilly ,2]

Estimating the elasticity of costs with respect to output allows one to test hypotheses about
the returns to scale. This returns to scale indicator is closely related to the measure of returns
to size as will be demonstrated later.

The other area of interest to researchers is to check whether the estimated translog

cost ﬁrnction is consistent with economic theory. Two of the most crucial conditions are to

76

ﬁnd out if the function is monotonic and if it is strictly quasi-concave in input prices. If the
cost function increases monotonically then all ﬁtted cost shares must be positive. Strict quasi-
concavity exists if the ka oii matrix is negative semi-deﬁnite for each observation. It is also
important that the condition that all cross-price elasticities sum up to zero is fulﬁlled to ensure

homogeneity as required by economic theory.

4.3 Further Extensions of Cost Functions

Modeling the production process has undergone substantial changes ever since the
Cobb-Douglas function was introduced around the 1930's. These changes came out of a
desire by several researchers to model the process of production without having to impose,
a priori, restrictions on the functional form or the parameters to be estimated. The
Generalized Leontief (GL) and the Translog Cost functions are products of these efforts and
are more ﬂexible and general than the original C-D functional form. However, the GL and
translog functional forms, though general and ﬂexible, cannot adequately handle real world
empirical work. Several extensions to the original formulations should be made to improve
their ability to reﬂect real world situations.

A translog cost ﬁrnction is used in this section to illustrate that there are some
important extensions to these generalized and ﬂexible functional forms that can improve their
capability to more accurately reﬂect real world situations. The extensions considered include
using multi-product versus single product speciﬁcations and handling ﬁxed inputs instead of
assuming that all inputs can be instantaneously transformed into output. The incorporation
of imperfections in input and output markets and the handling of the effects of technical
progress on factor demands and costs are also important considerations in the empirical

speciﬁcation of the production process. They are not reviewed in this section, not because

77

they are considered inconsequential, but because, when handling technical progress, a long
time series is essential.40 Endogenizing pricing in the product market to handle imperfect
competition may not be necessary since the large numbers of small-scale farmers (producers)
and the reforms taking place in agricultural commodity markets suggest a movement toward

competitive markets.

4.3.1 The Multi-Product Cost Function

Since the 19303, models of the production process have been presented as single
output functions. Yet ﬁrms do not always produce a single product. Many ﬁrms produce
more than a single product from a given bundle of inputs. Some ﬁrms producing a single
product cannot maintain uniform product quality characteristics and therefore have a
production function that is in many ways similar to that of a ﬁrm producing more than one
product. Thus, there are two types of multi-product ﬁrms; those that produce more than one
product, and those that produce a single product that is not uniform in terms of quality and
other physical product characteristics.

Failure to take into account the variation in physical output with respect to quality
attributes often results in speciﬁcation errors. Some researchers have solved this problem by
constructing hedonic measures of output as a function of the quality attributes of the product
in question. This is essentially transforming the output variable into a quality-adjusted
variable. The use of quality-adjusted output variable is most beneﬁcial when estimating factor
demand elasticities and economies of scope. The use of quality-adjusted output variables

applies to ﬁrms that produce a single product but with different quality attributes.

 

‘° Most researchers assume that the effects of technical progress are independent of the
temporal composition and characteristics of capital inputs implying that technical progress is
disembodied.

78

The quality-adjusted output variable cannot be used for a ﬁrm that produces more
than one product. Here a multi-product cost/production function should be speciﬁed. The
multi-product cost ﬁrnction recognizes the inherent danger of confusing economies of scale
and economies of scope“. The major advantage of a multi-product formulation is that it
allows more in-depth analysis of the effects of the various changes in the composition (scope
economies) and levels (scale/size economies) of output on the costs and factor demands. This
form of the multi-product speciﬁcation has become the most preferred in empirical work.

The total cost of producing ‘m’ outputs using ‘k’ inputs is generally expressed as
C(Y,P) where Y in a m><l column vector of output levels and P is a k><l column vector of
input prices. C(Y,P) is deﬁned to satisfy regularity conditions42 so that it is dual to a
transformation function T(Y,X), where X is a kx 1 column vector of input levels. This duality
condition between C(Y,P) and T(Y,X) ensures that the two ﬁinctions contain the same
information about the production process. The function C(Y,P) is assumed to be a translog
technology speciﬁcation. The multi-product translog cost ﬁrnction is a straightforward
extension and generalization of the single output case. The translog form of the multi-product

cost ﬁrnction can be represented as follows:

 

/ “ Economies of scale and size are concerned with the absolute size of the production unit
while economies of scope refer to the advantages or disadvantages associated with the
number of products that a single ﬁrm produces. It is not possible to separate the effects of
scope economics from scale/size economies without employing a multi-product function.

‘2 The regularity conditions in C are that (i) it is non-negative; (ii) it has real values, (iii)
it should be non-decreasing, (iv) it is strictly positive for nonzero Y, and (v) it be linearly
homogeneous and concave in X for each Y.

79

lnC = lnao + 2 any; + %Z aﬁanry + E Z ayrnxrnrj
k 1=1 l k i=1 k l=1j=1
+ Z Brlnpr + 32 Brr(lnPr)2 + 2:
i=1 i=1 i=1 j

ornrjnpj
r=l j

k
_l p lnPilnPj (6)

r]

k
:1 U

The main problem with equation (6) is that, because outputs are expressed in
logarithmic values, it does not permit output values to have zero values. If there are zero
values, the translog multiproduct cost function does not have ﬁnite representation (Caves,
Christensen and Tretheway, 1981). Caves et a1 (1981) proposed a Box-Cox metric as a way
to handle this problem. This metric replaces ln Yi in equation (6). Box and Cox speciﬁed the
metric (A) such that fi (Y,) = (Yi’L - l)/A, for all A e 0 and fi (Y,) = ln Yi for A = 0, where A is
always positive. Thus (Yf - 1)/A would replace lnYi in equation (7)“. The result is a
generalized translog multiproduct cost function (Caves, et a1, 1981). Eakin and Kniesner
(1988) developed a similar model which they termed “hybrid translog” multiple output cost
ﬁrnction. The extension to this model done by Atkinson and Comwell (1992, 1993) will not
be considered here because it requires the use of panel data.

One way to accommodate observations for which outputs are zero in to deﬁne the
logarithms of output not as log(Y) but log(Y+1). When output is zero the logarithmic value
computed this way will be zero. This study uses this approach because it is simpler than the

Box-Cox metric.

 

‘3 The limiting case of the Box-Cox metric is the natural log metric i.e.

Y’L - 1 -
1im£'——-—-)- = my!
to A 80

Following the way cost share equations are derived for single output translog cost
functions and using Shephard’s Lemma, the cost share equations of the generalized translog

multiproduct cost ﬁrnction are as shown below:

P/Y- at? P. aInC " "’
._i=__,_i=_'__ = ,+ .lnP.+ blnY'
C a], C aw, B, 12213,, , :2; ,, ( ) (7)

where ln(Y“) = ln(Y+1)
Once the cost share equations have been speciﬁed then the elasticities of substitution, own-

price and cross-price elasticities and other parameters can be estimated.

4.3.2 Incorporating Input Fixity

This discussion has implicitly assumed that all input can be instantaneously adjusted
to their long-run, full equilibrium levels. This assumption does not hold for many real world
situations. It is not always possible to change the level of inputs instantaneously in response
to changes in other variables such as input and output prices. This realization has lead many
researchers to develop a framework that recognizes that total costs consist of variable and
ﬁxed and/or quasi-ﬁxed costs. Quasi-ﬁxed costs correspond to inputs that cannot be
completely adjusted to their full equilibrium level within one production period. Making this
distinction is similar to differentiating between short-run cost functions (with some of inputs
being ﬁxed at levels that are not at their long-run full equilibrium) and long-run cost ﬁrnctions
(with all inputs being used at their full equilibrium levels).

In specifying the generalized translog multiproduct cost function two transformations
take place. First the total cost is replaced as a dependent left-hand side variable by the

variable cost variable and second the logarithms of the price of ﬁxed inputs, such as capital,

81

are replaced by the logarithm of the actual amount of the ﬁxed input used in production (for
example In Ki replaces 1n Pi for capital in equation (6)). The result is a generalized translog
multiproduct variable cost ﬁrnction. Thus the cost share equation derived from the
generalized translog multiproduct variable cost function, using Shephard’s Lemma, can be

written as shown in equation (8) below:

aanC P1X, H h m -
— = __ = . + .1nP. + .InP. + .InK. + oln Y.
amp, VC B! p” 1 M ' .5171!" ' .23 " (’) (8)

given that k = h+1.

In equation (8) the number of ﬁxed inputs (denoted K) is h and the number of variable inputs
is still k. This equation can then be used to estimate the elasticities and other parameters that
the researcher is interested in.

The generalized translog multiproduct variable cost function has the advantage that
one can calculate the shadow value of the ﬁxed inputs by differentiating this variable cost
function with respect to the ﬁxed inputs, i.e., aVC/aK. This shadow value is a one-period
reduction in variable costs when the quantity of K is increased by one unit everything else
being equal. In the short run this value is not expected to equal the market price of the ﬁxed
input that represents the long-run ﬁrll equilibrium price level for this ﬁxed input. Because it
is possible to deﬁne the full equilibrium level of the ﬁxed inputs as that amount that prevails
when the shadow value of the ﬁxed input equal the market value, distinguishing short-run
ﬁrnctions from the long-run function is feasible. This property also makes it possible to
distinguish between short and long term input substitution and own-price and cross-price
elasticities. By treating some inputs as ﬁxed and/or quasi-ﬁxed, the generalized translog
multiproduct variable cost function is sometimes called the generalized translog multiproduct

restricted cost function.

82

The case for a generalized translog multiproduct variable cost function as a potential
model of communal agricultural production technology in Zimbabwe has been made. It
clearly does not take into consideration all the extensions proposed because of data problems
and sometimes the inapplicability of the situation that lead to these extensions to the situation
in Zimbabwe’s communal areas. It is hoped that the generalized translog multiproduct
variable cost function is general and ﬂexible enough to reﬂect the diverse production
processes in Zimbabwe’s communal farming areas adequately. In the next section the focus
turns to how to use the generalized translog multiproduct variable cost function to estimate

indicators of economic efﬁciency.

4.4 Estimating Economic Efficiency

The preceding sections have highlighted the problems associated with modeling the
production process. The main problems relate to the numerous choices that have to be made.
Some of the important decisions include whether to use dual (cost or proﬁt) or primal
(production) functions, structured or ﬂexible functional forms and the best mix of assumptions
for the modeling of the production process to be as realistic as is possible. The availability
of data have a decisive bearing on the ﬁnal choices to make when modeling the production
process. Once the decision on how to model the production process is made, the next step
is to consider another set of decisions concerning the estimation of economic efﬁciency using
production technology models.

It is important at this stage to reiterate the importance of distinguishing between
production or cost ﬁrnctions and frontiers when estimating indicators of efficiency.
Conventionally production or cost functions are estimated by ﬁtting an “average” function

over observations using techniques such as ordinary least squares. Even though this

83

procedure allows the representation of interesting technical aspects of production such as
economies of scale, size and scope, input substitution and input demand elasticities, the
“average” function is not adequately constructed to capture the theoretical deﬁnition of a
production or cost function. Theoretically a production (cost) ﬁlnction expresses the
maximum (minimum) amount of output (cost) obtainable from a given bundle of inputs using
a given technology (Aigner, Lovell and Schmidt, 1977). As such no producer can operate
above (below) a production (cost) function. The development of production or cost frontiers
provided a way to bridge the gap between theoretical and empirical work“. Production (cost)
ﬁ'ontiers are regressions that take into account the theoretical constraint that producers
cannot operate above (below) the frontier (Greene, forthcoming). It is from this constrained
estimation process that measures of economic efﬁciency naturally emerge as representations
of the distance between what producers do and the theoretical ideal that is deﬁned by the

frontier function.

4.4.1 Economic Efficiency

Economic efﬁciency holds whenever technical and allocative efﬁciency conditions are
satisﬁed. A technically efﬁcient farm cannot produce more output than the efﬁcient level
ﬁom a given input bundle. Thus there is no way of producing the current output level using
fewer inputs than currently employed. Allocative efﬁciency holds whenever a farm maximizes
proﬁts by equating the values of the marginal product of inputs to their respective input
prices. Thus one farm can be more economically efﬁcient than another due to differences in

technical and/or allocative efﬁciency.

 

“ Lau and Yotopoulos (1971) used a “meta” cost function to approximate a cost frontier
in line with economic theory.

84

The measurement of efﬁciency was popularized in a classic paper by Farrell (1957)
who noted that quantifying productive efﬁciency would enable empirical testing of theoretical
propositions about the relative efﬁciency of different economic systems. This process
involved modeling the transformation of inputs into outputs (the production technology). As
noted above, the production technology is normally described by means of a production or
cost frontier both of which are not known. The observed input and output data can be used
to construct the unknown production or cost frontiers empirically. Following the pioneering
work of Debreu (1951) and Farrell (1957) ﬁgure 4.1 graphically illustrates these two
components of economic efﬁciency using a conventional isoquant/isocost framework where

two inputs (X1 and X2) are used to produce a single output.

 

 

 

X2
r 8*
X0 = Observed Input Vector (X1, X2)
e Isoquant
Isoc/ost Line /
Px 2/ .
‘~ git—Kt = Technically Efficient Input Vector
ll " " -
~2:.,\.ge = Economically Efficient Input Vector
, , , 3*
Xa = Allocatrvely Efficrent Input Vector _\
O Px

Figure 4.1: Illustration of Relative Economic Efficiency

85

Figure 4.1 shows an inefﬁcient input vector X, used to produce some given level, say
Q,, of output that is mapped by an isoquant S'S'. An isocost line PxPx from given input
prices when combined with the isoquant yields a unique least cost combination of inputs to
produce the given output level. Debreu and Farrell measured technical efﬁciency using this

ﬁ'amework as shown below";

 

But although input vector Xt is technically efﬁcient, because it lies on the isoquant, it
is not economically efﬁcient. Output Q, can be produced using an input vector X, which
costs less than X,. Any producer who uses X, to produce Qc is both technically efficient
(located on the isoquant) and allocatively efﬁcient (produces Qc at least cost). Because input
vector X, costs the same as input vector X,, a measure of allocative efﬁciency can be
represented as follows;

lxal
IX l

f

0(a) =

 

Allocative efﬁciency can be measured only when price information is available. Thus the
measure of economic efﬁciency/total efﬁciency is a product of the two components of ﬁrm-
level efﬁciency; 0(e) = 0(t) * 0(a). Thus 0(e) can also be expressed as shown below;

1X01
IX |

0

0(e) =

 

 

‘5 [x] denotes the length of the input vector x.

86

These measures of efﬁciency, as shown in ﬁgure 4.1, represent the distance between the
observed input bundle X, and the theoretical ideal X,.

Estimating economic efﬁciency involves using available input use information (X, and
Pm) to derive X,, X,, X, and the associated measures of the components of economic
emciency. This can be done in two ways. We will outline parametric and non-parametric

approaches to estimating economic efﬁciency (technical and allocative eﬂiciency).

4.4.2 Parametric Measure of Economic Efficiency

One of the two main paradigms to estimate the production and/or cost frontiers is the
parametric approach. This is the most common and conventional approach that involves the
econometric estimation of a production or cost ﬁ'ontier. A generalized translog multiproduct
variable cost frontier function is an example of this approach where producers use 11 inputs
(Xi), purchased at given prices (P,) to produce m outputs (Yi) under an environment dictated
by h ﬁxed and quasi-ﬁxed factors (Ki) While the producer’s objective is to produce at
minimum cost, success is often elusive.

In the estimation process there is need, ﬁrst, to impose restrictions on the cost frontier
to account for regularity conditions, and, second, to specify an error structure that accounts
for the mistakes producers commit as they try to minimize costs. In the latter case, the error
structure is normally speciﬁed as consisting of two terms with an a priori distribution“.

Following Ferrier and Lovell (1990) if the cost frontier is a generalized multi-product

 

‘6 Aigner, Knox-Lovell and Schmidt (1977) suggested a two-part error term composed
of (a) the pure random noise, assumed to be normally distributed, and(b) an inefﬁciency term
that has a one-sided distribution. This one-sided distribution can be half-normal, exponential,
truncated normal or a two-parameter Gamma distribution.

87

translog, then the producers’ commonly observed total variable cost and observed input

variable cost shares can be written as follows;

m

m k h
anC, = lnor, + Zarnr,‘ + 2: amp, + Zyan" +-;-Za(ln1’,,'
i=1 i=1 i=1

1: h m m
”1%; B,,(lnP,,)2 + 1;}, Yrr(anrr)2 + Z: Z aylnYinan:

k :12}: 1:1}: It (12)
+ 22 am mp, + Z v, M M, + £26.,lnnilne
"11 1 HF i=1 1:1
m h
+ ZZpUInY" nKjl, + ZZAUlnPuanj, + 6,

1‘1 1 1 i=1 1:1

The k-l input variable cost share equations are as follows;

 

aIHVC _ P/Yj _ ‘5‘] m . h
alnP, - (75], _ Bf + Blimp}! + g BUMP" + gar/"Yr: T gAUIHK" + ”1t

Where the error terms are deﬁned as follows, a = rt, + to + v, and t1], = Q, + 1),, (Ferrier
and Lovell, 1990).

The above deﬁnition of error terms suggest that observed costs differ from efﬁcient
costs for three reasons. First, there is technical inefﬁciency captured by the term, rt, 2 0 and
is assumed to have half-normal distribution (rt,~ |N(0, o:)|) then allocative inefﬁciency
represented by a scalar, w 2 0, and random noise which producers cannot control, v, and
has zero mean (v,~N(0, 03.)). There are two components on the error term obtained when
the observed input share equations were estimated. Thus input shares diverge from the
eﬁcient input shares because of allocative inefﬁciency in the way producers use inputs as

shown by, O, which can be either positive or negative. The inﬂuence of factors beyond

88

producers’ control in input use causes random variations in observed input cost shares which
is represented by u], with a zero mean and constant variance. Thus p, does not have a zero
mean and is assumed to have the following normal distribution; p,.,~N(Q, , 0,9).

The relationship between the cost function and cost share equation error terms
remains an unresolved issue and hence a subject of intensive research effort. Greene (1980)
was the ﬁrst to realize the problem when he found out that treating the two error terms as
independent was an unsatisfactory restriction from a theoretical as well as practical point of
view. It is reasonable to expect that whenever there are errors in the way producers use
inputs then producers will not be able to produce at minimum cost. In other words higher
costs are a result of mistakes in the use of inputs. This problem has been christened the
“Greene Problem”.

Ferrier and Lovell’s solution to the Greene Problem was to assume that allocative
efﬁciencies were the same for all observations. They also assumed a close positive correlation
to between and 0, so that whenever there are errors in the way inputs are utilized producers
end up with higher costs. Their speciﬁcation takes care of the fact that costs are a result of
mistakes in the use of inputs and that those producers who commit relatively larger errors end
up with higher total variable costs. Thus when (2,- has a higher variance, the value of to is
expected to be correspondingly higher. This relationship between to and Q,’s was deﬁned as

follows;

a) = ZWJQJZ

P1

where ill,- are weights. Note that since 0) is a scalar, it is not possible to obtain producer-level

estimates of allocative inefﬁciency from such a formulation.

89

Maximum-likelihood techniques are usually employed to estimate the observed cost
ﬁontier and input cost share equations. The procedure yields not only the set of parameters
that describe the efﬁcient cost frontier and input cost share equations, but also a set of
parameters that shows the extent of divergences between the efﬁcient cost frontier and the
observed attempts by producers to minimize production costs. These include I), and their
variances, the weights, 11:,- and the variance of rt, After computing the estimate of allocative

eﬂiciency, (o, as shown above, technical efﬁciency estimates, 117,, can be calculated as follows;

. ~ . 6?.
1t,=(e,—w)><

Where the hat-notation denotes an estimated parameter. This approach will yield farm-level

estimates of technical efficiency and an average measure of allocative efﬁciency. To explain

variation in farm-level efﬁciency only measures of technical efﬁciency will be employed.
Kumbhakar (1991) extended Ferrier and Lovell’s formulation by imposing the

conditions of Shepherd’s lemma on the cost function residuals as shown below;

= as, - 6n, + 86)

Q!" I " 1 1
8 HP], 6 nPj, a nPj,

 

 

 

After imposing this relationship, Kumbhakar then formulated the log-likelihood ﬁinction that
takes into account the implications of this relationship on the efﬁciency components of the
cost function residuals (ie, 1:, +03). This formulation speciﬁcally applies to translog cost
functions that correspond to non-homothetic production ﬁrnctions. Although this extension
in itselfis not restrictive, it is not grounded in economic theory. The question is in what ways

can the level of input prices be related to inefﬁciency? Because the derivative of economic

9O

ineﬁciency with respect to input prices, or 0,, can be negative or positive, the direction of
causality is ambiguous.

The formulation of the relationship between the efﬁciency parameters in the cost
ﬁ'ontier ﬁrnction and the cost share equations that allows allocative efﬁciency to vary across
observations and is derived from economic theory remains a challenge to practitioners
working on ﬁontier models. The other challenge is to formulate this relationship in a way
that minimizes complexities during empirical estimation and biases in the resultant parameter
estimates. In this study separate measures of technical and allocative efﬁciency will not be
estimated because of the problems associated with their separation during estimation.

The advantage of the parametric approach is that it provides a consistent framework
for the econometric investigation of the indices measuring technical, allocative and scale
(scope and size) efﬁciency (Chavas and Aliber, 1993). However, the assumed functional form
cannot be tested statistically“7 and may introduce speciﬁcation errors (Fare, Grosskopf and
Kraft, 1987). The other problem with parametric estimation of production ﬁrnctions is the
inconsistency between the theoretical deﬁnitions of the ﬁinction as a maximum (or a cost
function as a minimum) coupled with the use of methods based on zero mean errors in the

estimation process (Hall and LeVeen, 1978).

 

‘7 For example, whenever a Cobb-Douglas production function is imposed, homotheticity
is prejudged even though no homotheticity test is performed. The same can be said of the use
of input and output price and quantity data as if the data was generated by perfect
competition when a dual ﬁrnction is employed. (Hanoch and Rothschild, 1972)

91

4.4.3 Non-Parametric Measure of Economic Efficiency

The two main non-parametric approaches to measuring economic efﬁciency are
deterministic frontier models and data envelopment analysis (DEA). They both use
mathematical programming as an algorithm to generate the measures of efﬁciency and closely
resemble each other. The main difference between the two non-parametric approaches is that
DEA does not impose an a priori parametric restriction on the production technology as
occurs when deterministic frontiers are employed. DEA procedures yield a piecewise, quasi-
convex hull around the observed data points in input space. The procedure strictly compares
observations to some observed best practice.

In non-parametric models observations deviate from the theoretical optimum due to
mistakes by producers only. Random errors are not taken into account. Both non-parametric
approaches rationalize observed data by a closed and convex production possibility set if the
input, output and price data are consistent with proﬁt maximization“. Thus the production
technology can be bounded without imposing restrictive parametric functional forms (Varian,
1984). In deterministic frontier models technology is parameterized, but the absence of
stochastic variation makes statistical inference impossible.

The non-parametric approach is an easy method to measure relative productivity that
can also handle production technologies with disaggregated inputs and multiple outputs
(Chavas and Aliber, 1993). When economic (technical and/or allocative) inefficiencies exist,
then the observed data are inconsistent with proﬁt maximization. Here there is no production

possibility set that rationalizes the observed data (Banker and Maindiratta, 1988). The

 

" An observed input, output and price data set 9 of n farms is rationalized by a production
possibility set T, if every input-output vector is contained in set T and is consistent with proﬁt
maximization relative to all other sets in 'f, for a given price vector (Banker and Maindiratta,
1988)

92

measures of the levels of inefﬁciency depend on the production possibility set to which they
are evaluated. The tightest, lower and upper bounds of measures of inefﬁciencies represent
the best description of the production frontier that can be constructed without imposing
structural restrictions such as a speciﬁc functional form. This production (cost) frontier is
obtained by ﬂoating a linear surface (hyperplane) on the "top" (bottom) of the observations.

The nonparametric approach's main weakness is that its estimates of economic
emciency cannot be subjected to tests of statistical signiﬁcance. The procedure does not yield
hypotheses tests (Cox and Chavas, 1990). This is because the model does not provide for
statistical noise, measurement errors and omitted variables errors. All deviations of
observations from the efﬁcient frontier are attributed to inefﬁciency. In addition the linear

hyperplane is sensitive to extreme points thus rendering most of the observations inefﬁcient.

4.5 Methodology Cross-Checking

The main objective of this study is to analyze the structure and efﬁciency of communal
agriculture in Zimbabwe. This can be done using parametric and nonparametric techniques.
Which technique is best? 13 it necessary analytically to compare the capability of the two
techniques to reveal consistently the same story about economic efﬁciency using the same
data set? The two techniques have different strengths and weakness. By comparing their
performance in estimating economic efﬁciency we shed light on the relative weights to attach
to their differences.

Ferrier and Lovell (1990) compared the ability of econometric and mathematical
programming (MP) techniques to reveal the structure of cost efﬁciency in banking accurately.
They compared the rankings of ﬁrms based cost efﬁciency estimates using the two techniques.

Technical efﬁciency rankings from the two techniques were positively correlated but were

93

insigniﬁcant. One reason advanced for this ﬁnding was the inability of the MP technique to
exclude statistical noise. Linear programmingis anon-stochastic technique. The econometric
approach used in the Ferrier and Lovell study was stochastic. Unlike the MP technique, the
econometric approach can account for pertinent institutional variables plus random noise.
The difference in the efﬁciency estimates from the two techniques can be attributed to the
difference in both structure and implementation of the two estimation techniques (Ferrier and
Lovell, 1990).

The question is can a stochastic MP technique produce results comparable to those
from a stochastic econometric model. Bjurek, Hjalmarsson and Forsund (1990) showed that
the differences in measures of structural efﬁciency using deterministic (non-stochastic)
parametric and nonparametric speciﬁcations were “surprisingly small”. Finding out if small
differences exist between measures of economic efﬁciency using stochastic parametric and
nonparametric speciﬁcations is an important analytical exercise. The problem has been how
to develop a stochastic nonparametric model of production technology. LP models are
hyperplanes ﬁtted on top of observations and cannot be compared with stochastic frontier
models that allow some observations to lie above and below the ﬁtted hyperplanes.

This study will not pursue the analytical goal of comparing parametric and
nonparametric frontier models due to two main reasons. First stochastic nonparametric
models have not been adequately developed. Developing a stochastic nonparametric model
comparable to the stochastic parametric model would be a major exercise that a separate
study can handle. Second, the similarity between the results from deterministic parametric
and nonparametric models coupled with the positive (though insigniﬁcant) correlation
between rankings based on a stochastic parametric model and a deterministic nonparametric

model (Ferrier and Lovell, 1990) suggests that stochastic parametric and nonparametric

94

models are likely to produce comparable results. This study will, therefore, concentrate on
the estimation of measures of economic efﬁciency using a stochastic parametric model - the

generalized translog multiproduct variable cost frontier function.

4.6 Summary

This chapter brieﬂy reviewed the relationship between factors of production and
output. Duality theory lead to the development of Translog Cost ﬁrnctions. These ﬁrnctions
are based on the theory that a cost function, by being dual to the production ﬁrnction,
captures all the information that is in the transformation ﬁrnction itself. The major advantage
of a cost ﬁlnction is that the way it is speciﬁed more accurately reﬂects the process which
farmers use to maximize proﬁts. In competitive markets farmers are often faced with a set
of output and input prices and have to produce a given level of output. Thus, they have to
minimize the costs of producing this output by choosing input quantities.

The ﬁrst extension discussed in this chapter covered the fact that farms like most
production units do not produce a single product. They have multiple outputs and have to
be modeled as multiproduct ﬁrms. The second extension discussed in some detail is to allow
for the fact that not all inputs can be instantaneously be transformed into the ﬁnal product
over the production period. In other words some inputs are ﬁxed in the short run. The
dependent variable was therefore changed into a variable cost variable and the amount of the
ﬁxed inputs used replaced the price of this input on the right-hand side. The ﬁnal product was
a generalized translog multiproduct variable cost function.

Generalized translog multi-product variable cost functions and frontiers were used as
the best representation of the relationship that characterizes the production process. To

estimate economic efﬁciency using this ﬁlnction an error term was added. A special feature

95

of this error term is that it can be decomposed into its constituent components. The normally
distributed component represents variability outside the farmer’s control. The other is due
to inefﬁciency at the farm-level. Measuring economic efﬁciency therefore involves
decomposing the error term into its constituent components. The other method of measuring
economic efﬁciency is the non-parametric approach that employs linear programming
techniques to ﬁt a hyperplane on the observed data points. This hyperplane becomes an
estimate of the cost frontier so that those farms that are above the hyperplane are considered
inefﬁcient. Efﬁcient farms are those that are on the hyperplane.

Results obtained from the two approaches of estimating economic efﬁciency are only
comparable if a stochastic nonparametric model is developed. The main intent of this study
is not to develop such a model but to analyze the structure and economic efﬁciency of
communal agriculture in Zimbabwe. The next chapter goes into the details of how to measure
the economic efficiency of small-scale farms in Zimbabwe by specifying the necessary data
transformations required when estimating a generalized translog multiproduct variable cost

function.

96

CHAPTER V: CHARACTERISTICS OF COMMUNAL AGRICULTURAL

PRODUCTION DATA

5.1 Introduction

This chapter describes the characteristics of the data used in this study to estimate cost
functions and frontiers from which farm-level efﬁciency measures are derived. Measures of
spread are presented for each of the variables that is included in the estimation of cost
functions and ﬁ'ontiers. As pointed out in the third chapter, the data were collected from
communal farmers by the Farm Management Section of the Economics Division of the
Ministry of Agriculture. The main purpose for collecting this data was to develop a data base
ﬁ'om which informed general policy decisions could be made.‘9 It must be noted that these
data were not collected primarily for the measurement of economic efﬁciency. However, the
data are detailed and comprehensive enough to permit the estimation of multi-product
translog cost functions and frontiers. But there are other techniques to estimate relative
economic efﬁciency, both modern and old, that cannot be used in this study because they
require specialized data which is unavailable.

This chapter is organized as follows: The ﬁrst section brieﬂy reviews the generalized
multi-product translog variable cost ﬁrnction. This is followed by sections describing the
variables used to estimate the cost functions and frontiers. These are output values, variable

input prices, quantities of ﬁxed and quasi-ﬁxed inputs and environmental variables”. The

 

‘9 The data collection program was designed when mechanisms for moving from a
controlled to a market-oriented economy were being debated with a view to implement them.
Information from communal areas was considered essential in managing the new economic
system.

5° The two environmental variables that are included in this study are soil quality and the
location of the farms in terms of natural regions.

97

quantities of variable inputs were used to calculate the total variable costs. The main focus
of these four sub-sections is to look at general patterns and variability across farms and across
seasons. The last section consists of a brief discussion of the Ministry of Agriculture data
collection instrument. The main intention is to identify the potential data gaps as well as
provide an overall assessment of the suitability of the data set for estimating translog multi-

product variable cost functions and frontiers

5.2 The Cost Function Data

The generalized translo g multi-product variable cost function (GTMVC), as speciﬁed
in the previous chapter, is made up of the total variable cost (TVC,) as the dependent variable;
output quantities (Yi), input prices (Pi), amounts of ﬁxed inputs (K,) and environmental
variables (L,) as independent variables. The GTMVC function is been speciﬁed as shown
below to illustrate the manner in which the above-mentioned variables make up the cost

ﬁrnction and cost frontiers.

In k h
1nVC, = rna, + Z: a,1nr,,‘ + 213.1% + Zy,an,, + é}: a,,(1nr,,’
=1

1: m m

E13 mum: %Evtan +E Ea.1nY.-I|an
1""... r. (16)
29,1111”, lnP + 22:“an an + £26,1n1',;1np,,

+
l l=1j=1 1=l j=l

i=1=
m h
+ ZZpUlnYu'anj, + ZZAUlnP an + r ,,,L + n,L,, + 6

i=1 j=1 1': l j: l

NI—e

Ma-

.—

f

98

The characteristics of the main components of cost function above are described in the next
sections. Although the variables are expressed in logarithmic form, the characteristics

discussed are for the original values of these variables.

5.2.1 The Output Variables (Y .)

The output variables in the GTMVC function is expressed in monetary values. To
avoid degrees of freedom problems, farm outputs were grouped into four categories. These
are maize, legumes, small-grains and cash crops". Output amounts and prices used to
construct this vector were obtained from the survey data. The prices used were either the
farm-gate (selling price less transport costs) for quantities marketed formally or the local
selling price for quantities sold locally and/or retained for family consumption. The price
indices for the legumes, small grains and cash crops are a summation of individual crop prices
weighted by the ratio of the value of that crop to the total value of the crop category. The
descriptive statistics of the total farm output levels (in nominal monetary terms) are shown

in Table 5.1 below.

 

" Farm output, Y, is a 4X1 vector (m=4). The legumes category consist of groundnuts,
bambara nuts, ﬁeld beans and cowpeas. Small grains include sorghum, pearl millet and ﬁnger
millet. Cash crops aggregates sunﬂower, cotton and tobacco. These crop categories, with
the exception of cash crops have similar uses, yield, price and production patterns.

99

Table 5.1:

Descriptive Summary of Values of Farm Output Per Farm (Y i).

 

 

 

 

 

 

1989 1990 1992

Crop Values Mean Max CV Mean Max CV Mean Max CV

(23) (23) (%) (23) (23) (%) (ZS) (zs) (%)
Maize $622 $11,711 143 $430 $2,728 113 $2,224 $26,857 116
Legumes $291 $12,895 258 $142 $2,236 176 $191 $3,540 217
Small Grains $87 $850 159 $75 $1,177 162 $259 $5,730 211
Cash Crops $137 $5,739 370 $57 $1,747 317 $339 $17,900 358
All Crops $1,137 $13,266 118 $704 $4,050 102 $3,012 $28,088 109

 

Farm output values vary considerably from one category to the other and from one
year to the other as shown by both the mean and maximum values in Table 5.1. The relatively
high coeﬁicients of variation (CV) show that the value of farm output also varies ﬁ'om one
farm to another. The variability is a combination of farm-gate price variation and the variation
in the physical output harvested. The values of farm output are more variable than the output
farm-gate prices. For instance, the CV’s for maize output for the three years are 112.8%,
113.4% and 106.2%, respectively. The CV’s for maize farm gate prices fro the three years
are 19.5%, 27.9% and 27.4%, respectively.

There are several reasons for the above pattern of variability. Physical farm output
varied from one farm to the other mainly due to the differences in agro-ecological
conditions”, crop management and access to service institutions. On the other hand, the year
to year variation in physical farm output is due to differences in rainfall and macroeconomic
conditions. Because output prices were determined by the government, they are expected to

be close to uniform from one farm to the other. The differences in prices from one farm to the

 

’2 This refers mainly to differences in amount of rainfall, although differences in soil type
are also very important.

100

other could only be due to differences market access in terms of distance to markets and
mode of transportation used. The price indices of crops marketed through informal channels
like legumes and small grains are more variable across farms because of the high variability
associated with these markets. The cash crops price index is more variable than the maize
price because of the mix of cash crops varies widely from one farm to the other. In addition
the unit prices of the three cash crops, cotton, sunﬂower and tobacco, are very different from
one another. Farmers also marketed their cash crops through different channels giving rise
to differences in the price that is realized at the fann-level. The resultant price index exhibits

this variability.

5.2.2 Prices of Variable Inputs (P,)

The main variable inputs used by communal farmers are labor and seed. Fertilizer and
chemicals are selectively used depending on region and crops grown. The prices of these
inputs are calculated at the farm-gate. The pattern of input use affects the farm-gate input
price indices. Chemicals are rarely used on crops other than cotton and tobacco. Thus
chemicals as an input are insigniﬁcant in communal agriculture because very few farmers
grow these two crops. Fertilizer is mainly used on maize in high rainfall areas and by the few
farmers who grow cotton’3 and tobacco. Thus the fertilizer and chemical price index is
dominated by the fertilizer price.

Seed is a major input on communal farms. Farmers purchase maize, cotton and
tobacco seed from formal sources consistently. The prices of these seeds are easily calculated

as purchase price plus the transport costs. In the case of other crops retained seed is used.

 

’3 Mudhara M (1995) found out from a survey of cotton farmers that the majority of
cotton growers do not use fertilizer.

lOl

The price of retained seed is calculated as the output price in local markets at planting time
plus the local transport costs involved.

The price of labor is difficult to determine because of the poor state of communal area
labor markets. In this study the price of labor is calculated as a shadow wage rate equal to
either the rate at which family members permanently staying on-farm are paid when they ﬁnd
temporary work locally or the wage rate paid to hired labor. The price of labor, thus depends
on what kind of off-farm work family members were able to get or the task for which hired
labor was sought. Different types of work entail different wage rates for both family members
working off-farm and hired labor. The determination of the price of labor is further
complicated by a myriad of kinship relationships and community arrangements that sometimes
determine what to pay for the bulk of farm work. The variability, shown in Table 5.2, in the
price of labor from one farm to the other reﬂects the difﬁculty of calculating a farm-speciﬁc

shadow wage rate.

102

Table 5.2: Descriptive Summary of Prices of Variable Inputs, (Pi).

 

 

 

Input Type 1989 1990 1992
Mean Max CV Mean Max CV Mean Max CV
(%) (%) (%)
Labor (Slhr) $0.68 $3.34 43 $0.89 $3.13 63 $1.18 $5.31 53
Fertilizer‘ ($Ikg) $1.01 $55.60 45 $0.57 $0.95 8 $0.33 $1.64 93
Maize Seed ($lkg) $1.17 $6.71 34 $1.64 $3.60 19 $1.40 $3.82 61
Legume Seed ($lkg) $1.45 $8.00 47 $1.14 $2.75 19 $2.74 $10.57 42

SmallGrainSwd($/kg) $1.21 33.00 27 $1.31 $2.15 11 31.47 $10.00 58
CashCropSeed($/kg)* $31.18 $64.00 265 $0.95 $9.16 97 $5.56 $250.00 513

 

 

 

 

 

 

AllSeedsIndex ($/kg) $1.18 $6.07 39 $1.44 $3.60 21 $1.54 $3.60 46
*Notes:

 

-Fertilizer also includes chemicals.

-The high variability in cash crop seed prices is because of the differences in per
unit prices of tobacco, cotton and sunﬂower as well as the fact that farmers grow
these crops using different combinations.

The mean shadow wage rate for communal farms increased consistently across the
years as shown in Table 5.2. But the price of purchased inputs like fertilizer and chemicals
and maize seed did not exhibit such a consistent trend. Fertilizer and chemical mean price
index fell from $1.01 during the 1988/89 season to $0.57 the following season and $0.33
three seasons later. The all seeds price index showed a consistently increasing trend masking
the irregular pattern exhibited by the constituent seed price indices. It is interesting to note
that farmers paid less for purchased inputs (mainly fertilizer and maize seed) in 1992/93 as
compared to what they paid three years before (1989/90). This is clearly due to the drought
relief program implemented after the 1991/92 season. Under this program, farmers received

close to free seed and fertilizer from the government and other non-govemmental

103

organizations. The program had the effect of reducing the average prices since “ﬁ'ee” inputs
are valued at the cost the farmers incurred to get them“.

Table 5.3 also reveals an interesting trend on wage rates. The wage rate variation
across farms (CV) did not change across the years as did that of other input price indices. For
instance the three season CV for the fertilizer and chemicals index was 45%, 8% and 93%,
respectively compared to 43%, 63% and 53%, respectively for the labor price. The fertilizer
and chemical price index CV has the same variation as that of the cash crop price index. This
similarity could be due to the differences in season samples. The 1989/90 season excluded

farmers from cotton growing areas (Kandeya).

5.2.4 Quasi-Fixed and Fixed Inputs (K,)

The other set of factors of production are the quasi-ﬁxed and ﬁxed inputs. Quasi-
ﬁxed input levels can be altered in a period which is shorter than that required for ﬁxed costs.
Livestock can be considered a quasi-ﬁxed input in communal agriculture while land and farm
assets (buildings and farm implements) are ﬁxed inputs. Land is expressed in hectares and
livestock and farm assets are expressed in terms of current Zimbabwean dollars. The data for
farm assets and livestock for 1992/93 were not available. The cost function for this season
will be devoid of these crucial variables with the exception of land planted to the different
categories of crops. The descriptive summary of the quasi-ﬁxed and ﬁxed inputs used in this

analysis is provided in Table 5.3, shown below.

 

5‘ The cost of acquiring “free” inputs was set at the time involved in attending the
meetings and the transport costs. While data on transport costs were collected from the
farmers, the time spent at the meetings (political party and village/ward development
committees) could not be determined.

104

Table 5.3: Descriptive Summary of Quasi-Fixed and Fixed Inputs, (Ki)

 

 

 

 

 

Input 1989 1990
Mean Maximum CV Mean Maximum CV
(%) (%)
Farm Assets $2,713.80 $30,592.50 145 $1,248.65 $12,177.00 135
Livestock $2,406.60 $12,237.00 82 $2,632.34 $20,281.00 108
Maize Area (ha) 1.56 7.40 64 1.77 8.70 74
Legume Area (ha) 0.50 3.60 109 0.70 5.33 111
Small Grain Area (ha) 0.71 20.90 198 0.74 8.20 145
Cash Crop Area (ha) 0.36 5.30 191 0.25 3.10 218
All Crop Area (ha) 3.12 23.40 71 3.46 16.93 77

 

The main observation from Table 5.3 is that there is more farrn-to-farm variation in
the value of farm assets compared to the value of animals owned by respondent farmers. The
seemingly signiﬁcant difference in ownership of farm assets between the two years could be
explained by the absence of farmers from Kandeya (a cotton growing area) in the 1989/90
sample. Being predominantly cotton farmers they are likely to own more farm assets than the
average non-cotton grower. It is not that they need special implements for growing cotton
but because of the higher farm income earned from cotton which allows them to acquire more
and/or improved farm assets.

The area under crops does not exhibit any major deviation from expectations.
Particularly interesting is the lower farm-to-farm variation in the area under maize compared
to other crop categories. The higher across farm variance in area under other crop categories

could be due to the fact that not all farmers grow all the crops making up the respective

105

categories . This is especially true for cash crop area where cotton and tobacco can only be
grown in areas with speciﬁc agro-ecological conditions. Generally the area under all crops

does not show major variations across farms.

5.2.5 Environmental Variables (L.)

Because agricultural production is a biological process, it is dependent not only on
quantity and quality of factors of production but also the quality of a number of environmental
variables. These variables determine the potential levels of output that can be obtained. The
main ones include the type of soil, topography, climatic factors (rainfall, temperature,
humidity, etc) and management. Because of data limitations it was not possible to include all
these variables in this study.

Soil type and location in terms of natural regions are the only two environmental
variable that are considered in this study. They are both presented as binary/dummy variables
where one stands for “favorable” soil type or natural region and zero otherwise. Red clays,
clays, clay loams, black clays, black and red loams and loams are categorized as favorable
soils. Sands and sandy loams constitute the less favorable soils category. Natural regions
I and II constitute favorable locations while natural regions [11, IV and V are less favorable
locations for agricultural production.

The soil data are only available for the 1989/90 season and there is very little to say
about the proportion of farms that have favorable soils over the years. As a result maize yield
is used as a proxy for soil type. Although yield data reﬂects management quality, it is the best
available variable to use as a proxy for soil type. The percentage of farms that have favorable
soils and are located in favorable natural regions during the three agricultural production

seasons are shown in Table 5.4 below.

106

Table 5.4: The Percentage of Farnrs With Favorable Soil Types and Located in

Favorable Natural Regions

 

 

 

Season soil types* natural regions Sample size

1988/89 na 48.2% 425

1989/90 44.4% 30.8% 331

1992/93 na 43.5% 368
Notes:

" na denotes cases were data is not available.

As shown in Table 5.4 the number of farms with good soils and located in favorable
natural regions are high enough to permit empirical analysis. Although the location of farms
in natural regions was predetermined in the design of the surveys which tried to mirror the
national distribution of the farming populations by natural regions, the percentage of farms
that are located in favorable regions is higher than the national average of around 25 percent.
The percentage of farms in favorable natural regions was closest to the national average
during the 1989/90 season. During the other two seasons the proportion of farms in these
regions is almost double the 25 percent national average. This over-representation of farms
in favorable natural regions is partly due to a disproportionate dropping of farms in the less
favorable regions from the study due to incomplete information. More farms in these areas
were left out of the analysis because low rainfall resulted in most of them producing negligible
agricultural products. They did not, as a result, have all the data that was required for this
study and were therefore dropped. But this over-representation does not have a signiﬁcant

impact on the results.

107

5.2.6 Total Variable Costs (TVC,)
The dependent variable of the cost ﬁrnction is a summation of labor, seed, fertilizer
and chemical costs incurred on farm. Each variable cost item is a product of the amount of

input used and the input’s farm-gate price. Table 5.5 below summarizes the farm-by-farm

Table 5.5: Descriptive Summary of Total Variable Costs (TVC,)

 

 

 

Season Minimum Maximum Average CV (%)
1988/89 $68.49 $5,909.85 $1,212.90 80.2%
1989/90 $99.20 $7,748.08 $1,631.69 84.3%
1992/93 $84.68 $16,014.43 $2,060.05 89.1%
Overall Mean $84.12 $9,890.79 $1,634.88 84.5%

 

The effect of the government-led drought relief program that provided farmers with
free seed and fertilizer is not as apparent in Table 5.5 as it was with prices of variable inputs
shown in Table 5.2 because variable costs are expressed in current terms. But the free seed
and fertilizer provided to farmers during the 1992/93 growing season did translate into lower
total farm variable costs if the total variable cost ﬁgures are expressed in real (inﬂation-
adjusted)’s terms. In 1989 dollars farmers paid $820.00 for farm inputs in 1992/93 compared
to $1212.90 in 1988/89. In other words, the $2060.05 used to buy inputs in 1992/93 bought
inputs that were worth only $820.00 in 1988/89. What might also have happened is that
farmers stopped buying the inputs they normally acquire because of a combination of the

availability of free inputs and large year-by-year increases in input prices. The impact of these

 

’5 The year-by-year inﬂation after 1990 rose to over 40 percent due to the 1991/92
drought and the initiation of the World Bank/IMF economic reform program, ESAP
(Economic and Structural Adjustment Program) in 1991.

108

changes in the macroeconomic environment on the use of purchased inputs and hence farrn-
1evel economic emciency will be explored later on in this study.

Table 5.5 also shows that farm-to-farm variation in the amount spent on farm inputs
remained close to constant over the three seasons. The CV only increased slightly from 80.2
percent in 1988/89 to 89 percent four season later. However, the farm-to-farm variation that

is shown by the variable costs CV is not as large as those for other variables discussed before.

5.3 The Data Collection Instrument

The questionnaire used to collect the data described in this chapter is reproduced in
summary form in the Appendix. As an instrument of data collection this questionnaire is fairly
detailed and comprehensive enough to cover the important farming and farming related
activities. But a good questionnaire does not generate an equally good data set without the
aid of the adequate planning of the data collection exercise itself. This starts with good
selection and thorough training of enumerators. During ﬁeld work there is need for frequent
monitoring of enumerators not only to ensure that the data is collected as planned but to solve
problems as soon as they occur and before they start to affect the quality of the survey output.
Given that the enumerators resided in the study areas for the whole season, monitoring and
evaluation became an expensive but essential input. Like all other public institutions, the farm
Management Section (FMS) did not have unlimited supply of funds at its disposal to carry out
this study. But the FMS team went all the way to ensure that the data collected was as
accurate as possible within the limits of the human and ﬁnancial resources available (MLAle
1990).

The survey questionnaire has three sections. The ﬁrst section, the Pre-season

questionnaire, captured demographic and household resource endowment data. It also

109

included an assessment of the farmers’ performance in the previous season. The next section
comprises the mid-season questionnaire that covers all farm-level operations ﬁ'om ploughing
to weeding. It also includes information on livestock transactions. The last section is a
questionnaire that seeks detailed data on harvesting and marketing activities, non-farm
income, overhead activities and livestock movements. The administration of these
questionnaires was the responsibility of carefully chosen and trained enumerators (research
assistants) who were permanently stationed at each site. Each enumerator collected data ﬁ'om
around 30 farmers, visiting each household once every four to six weeks. The crucial
question here is whether four to six weeks is not too long for farmers to recall accurately the
data as detailed as indicated by the questionnaires. A shorter tum-around period would have
been more appropriate if resources had permitted.

Again like most public institutions, the FMS had its fair share of professional staff
turnover and had to rely on the services of ﬂesh graduates, mainly from the local university
(MLARR, 1990). The FMS tried to ﬁll the gaps by using the services of technical advisers
who were experienced agricultural economists. Thus although ﬁ'equent staﬁ‘ changes could
have affected the quality of the output of the surveys there was enough professional expertise

to ensure that the data collected was the best that could possibly be assembled.

5.4 Summary

The data set used in this study generally exhibit wide across farm and season
variability. This characteristic reﬂects on the nature of communal agriculture even if one
controls for geo-physical (rainfall and soil type) and socio-economic factors. As pointed out
in Chapter II communal farmers are not a homogenous group. There are differences in

resource endowment and agricultural practices.

110

The ﬁrst four subsections examined the variability of the independent variables. The
variability of output values, being a combination of physical output variation and farm-gate
price variation was high with CV’s above 100 percent. This was mainly due to the variation
in physical output as output prices were controlled by the government. However, the
variation was similar across seasons. The variation in input prices was, in most cases, low
with CV’s around 30 percent. The exception was cash crop seed prices and the fertilizer and
chemicals price index during the 1992/93 season when there was a signiﬁcant change in crop
combinations in communal areas. The variation of quasi-ﬁxed and ﬁxed inputs ﬁ'om one farm
to the other is in many ways similar to that of output values. This indicates signiﬁcant
differences in household resource endowment levels. The two environmental variables, soil
type and natural region, were expressed as dummy variables. The was an insigniﬁcant over-
representation of farms with good soils and/or located in favorable natural regions.

The dependent variable in this study is the total variable costs at the farms. After
adjusting for inﬂation, it was evident that farmers spent less on inputs during the last two
seasons (1989/90 and 1992/93) than they did in 1988/89. Otherwise farm to farm variation
in nominal total variable costs remained relatively the same over the seasons. The main
conclusion is that all this variation in variables is as expected of cross-sections of such

breadth. There is sufﬁcient quality in the data sets to continue with the proposed analysis.

111

CHAPTER VI: THE COST FUNCTIONS AND ECONOMIES OF SCALE.

6.1 Introduction

The focus in this chapter is on estimating a generalized “hybrid” translog cost function
and obtaining measures of economies of scale. In the next section results of the estimated
cost function are presented. Then the econometric problems that are associated with the
empirical estimation of the cost function are examined next. This section covers econometric
problems such as heteroskedasticity, multicollinearity, errors-in-variables’6 and measurement
errors. The cost ﬁrnctions should also conform to economic theory. These are discussed
next and include homogeneity, homotheticity and constant returns to scale. This leads us
directly into the discussion on economies of scale and the implications of the estimates to
communal agricultural policy in Zimbabwe speciﬁcally and agrarian reform in general.
Measures of economies of scale provide important information on the question of optimal

farm sizes. The chapter closes traditionally with a short summary.

6.2 Estimating the Cost Function: The Results

The generalized translog multi-product variable cost function (GTMVC) was
estimated using ordinary least squares after all the variables were converted to logarithms.
Following Sil and Buccola (1995) Cowing and Holtmann (1982) Binswanger (1974) and
many others the input prices and total variable costs were normalized by the
fertilizer/chemicals price index to impose homogeneity in input prices. A different choice of

input price for normalization does-produce different results but this issue is not pursued here.

 

5‘ This includes the problems of omitted variables and measurement errors and the
different methods of correcting for these problems.

112

The estimated cost ﬁrnctions are presented in their entirety in the appendix (Tables A2-A4)
because of the large number of variables that were used to estimate these functions. This

section will summarize and highlight the main characteristics of the estimated parameters.

6.2.1 Model Explanatory Power

Generally the independent variables provide a reasonable degree of explanation of the
variability in total variable costs as shown by the unadjusted and adjusted coefﬁcients of
determination, R2 and R2, respectively. These are shown in Table 6.1. The adjusted
coefﬁcient of determination (R2) takes into account the number of independent variables used.
As expected, R2 is greater than R2. Using R2 one can conclude that, on average, the
independent variables explain well over 66 percent of the variation in total variable costs.

It is surprising that the 1992/92 costs ﬁrnction had higher R2 than the cost functions
estimated with data from the other two seasons. The 1992/93 cost ﬁrnctions did not include
two important ﬁxed inputs in communal area agriculture (farm asset and farm animals).
Fertilizer and seed use was distorted by the government drought relief program which
provided farmers with free seed and fertilizer. As mentioned earlier it was difﬁcult to assign
values to these “ﬁ'ee” inputs. The higher R2 for this season while puzzling could be due to

higher quality data as the team became experienced.

Table 6.1: Unadjusted and Adjusted Coefficients of Determination ( R2 and R’)

 

 

Season R2 R2
1988/89 78.6% 72.6%
1989/90 75.6% 66.1%
1992/93 89.6% 87.3%

 

113

Translog cost ﬁrnctions have more independent variables because of the inclusion of
cross terms. Coupling this with multi-product formulations, which also increases the number
of independent variables, results in a very large number of variables on the right-hand-side.”
Because R2 takes care of the problem of numbers of independent variables, the reasonably
high explanatory power is not simply due to the large number of right-hand-side variables.
However, other considerations should be taken into account for one to conclude that an

estimated model has sufﬁcient explanatory power.

6.2.2 Significance of Parameter Estimates

Parameter estimates are of econometric importance if they are both statistically
signiﬁcant and have the expected sign. Because of the large number of independent variables
used to estimate the cost functions, Table 6.2 does not show the signiﬁcance levels of the at“,
[3,, y, and A, parameters. In fact Binswanger (1974) pointed out although (1,, 11,, y, and A,-
are related to variable elasticities of substitution and of factor demand, they have little
economic meaning of their own. Since this study’s focus is not on elasticities of substitution,
little is lost by their omission from the discussion, especially at this diagnostic stage.

The purpose of table 6.2 below, and the accompanying discussion, is to highlight the
extent of parameter signiﬁcance for the estimated cost functions. It is also important to point
out that the parameter estimates, a, [1,, y, and A, shown in table 6.2 are not elasticities of
substitution. Elasticities of substitution in a translog formulation are variable and dependent
on other variables due to presence of cross terms. Thus the discussion here is lirrrited to just

comments on the signiﬁcance of the individual parameters. Little can be said about their signs

 

’7 In this study the GTMVC function with four crop categories, ﬁve variable inputs, three
ﬁxed inputs and two environmental variables had a total of 92 (1988/89 and 1989/90) and 67
ri t-hand-side variables (1992/93).

114

or can economic signiﬁcancy be determined. Detailed and complete sets of results are

presented in the appendix (Tables A2-A4).

 

 

 

Table 6.2: Level of Significance of Selected Coefficients
Variable 1988/89 1989/90 1992/93
p-value t-value B-value t-value B-value t-value

Constant 4.70 1.61 8.92 1.33 1.38 2.06
Labor Price 2.18 1.16 1.20 0.47 1.83 3.26
Maize Seed Price 0.33 0.19 -14.63 -2.72 0.39 0.99
Legume Seed Price 1.84 1.47 5.39 0.89 -0.26 -0.62
Small Grain Seed Price -0.20 -0.11 9.09 1.12 0.06 0.09
Cash Crop Seed Price -0.36 -0.28 2.95 1.37 0.63 1.41
Value ofMaizc 0.24 0.75 -0.39 -0.90 0.11 1.04
Value ofLegumes 9,28 1,_7_2_ 0.19 0.70 0.01 0.15
Value of Small Grains 0.23 1.37 0.93 2.88 0.18 2.48
Value ofCash Crops -0.11 -0.68 0.36 1.12 -0.05 -0.52
Total Crop Area 1.30 0.86 -4.45 -3.15 2.74 6.07
Value of Farm Assets -O.25 -0.72 0.06 0.09 na na
Value of Livestock -0.94 -2.57 -0.56 - l .04 na na
Soil Type 0.24 2.64 0.03 1.00 0.27 4.43
Natural Region -0. 12 -l .27 0.42 2.18 -0.10 -l.50

 

Notes: Signiﬁcant coefﬁcients are bolded (p=5%) and underlined (p=10%); na=not available.

The parameters shown in Table 6.2 above are not, estimates of elasticities of costs
with respect to the speciﬁed right-hand-side variables. The magnitude of each parameter
cannot tell us the percentage change in total variables cost that is brought about by a one
percent change in the independent variable. The fundamental inequality of cost minimization,
which states that if input prices increase total variable costs cannot decrease, cannot be

determined by simply looking at the sign of coeﬁicients on input prices. The additional effect

115

ﬁ'om cross-term must also be taken into account if one is to discuss the state of input

substitution by farmers. These partial effects can be represented as follows:

 

alntvc "'
= . + .1 P. + .I Z.

. The fact that input prices have negative coefﬁcients (labor is an exception) in one of the
three seasons is not a serious violation of the principles of the fundamental inequality of cost
minimization. But the change in coefﬁcient signs across seasons could be an indication of the
existence of data-related and/or econometric problems.

Ifhomotheticity is assumed then all inputs are normal so that costs are non-decreasing
in output. Output increases always increase variable costs. An increase in the value of output
is expected to increase variable costs, more so if the increase is due to change in the physical
output as compared to output price. If the increase in output value is due to an increase in
the product price, total variable costs can either increase or decrease depending on farmers’
objectives." In this exercise farmers are assumed to be proﬁt optimizers and the coefﬁcients
on the output variables are all expected to be positive. Table 6.2 shows that the coefﬁcients
on the value of maize (1989/90) and value of cash crops (1988/89 and 1992/93) are negative.
The validity of the proﬁt maximization assumption when dealing with communal area
agricultural production data is challenged by these results. Maybe the fact that communal
farmers pursue other goals such as meeting family food requirements can explain these results
where a price increase may not signiﬁcantly alter the production mix.

There is no theoretically valid basis on which to predict the sign of the coefﬁcients on

ﬁxed inputs. Increases in ﬁxed inputs can either reduce variable costs if there is an

 

" Iffarrners pursue proﬁt maximization only then an increase in prices will result in an
increase in output and hence total variable costs. But if farmers pursue other goals other than
proﬁt maximization then it is reasonable to expect other outcomes.

116

improvement in efﬁciency (less inputs are used) or increase costs if the input bundles are
unaﬁ‘ected. The coefﬁcients on farm assets and livestock are almost all negative except the
value of farm assets during the 1989/90 season. For increases in total area planted the
ﬁmdamental inequality of cost minimization should be expected to apply implying that the
coefﬁcient on total area planted should be positive. The results for 1988/89 and to some
extent 1992/93 conform to this expectation. But the coefﬁcient on total area planted for the
1989/90 season is negative and statistically signiﬁcant.

Despite the reasonable explanatory power shown by the coefﬁcients of multiple
determination, very few coefﬁcients are statistically signiﬁcant as shown in Tables 6.2 for the
selected parameters and the appendix (Tables A2-A4) for the quadratic and cross terms. Only
6, 12 and 9.6 percent of the coefﬁcients of the 1988/89, 1989/90 and 1992/92 multi-product
cost functions are signiﬁcant at 5 percent level, respectively. Similar percentages for 10
percent level of signiﬁcance are, respectively, 16, 18 and 25. However, there are coefﬁcients
that are economically signiﬁcant. For instance, table 6.2 shows large coefﬁcients, especially
for labor and the seed prices. But a percentage change in any one of these variables is not
determined by the magnitude of these coefﬁcients alone. Coefﬁcients from cross terms have
some inﬂuence as well.

Other than the observation that there was a large number of variables used to estimate
the GTMVC ﬁrnction and the assignment of crops grown into four categories to avoid

degrees of freedom problems”, there are other areas of concern. As a result the data will be

 

’9 Initially about 7 main crops were identiﬁed in communal areas. A translog function
involving 7 crops, seed prices and crop areas, a fertilizer and chemicals price index, a labor
wage rate and two ﬁxed input levels would end up with 350 independent variables. The
1988/89, 1989/90 and 1992/93 seasons have 425, 331 and 368 observations, respectively.

117

examined for the existence of econometric problems that should be taken care of when

estimating the cost functions and frontiers.

6.3 Testing for Econometric Regularity

The main purpose of this section is examine if the data presented in the last chapter
can be used to estimate a “well-behaved” cost ﬁrnction. The estimation of the cost ﬁrnction
employs a combination of least squares and maximum likelihood estimation techniques. A
ﬁrnction estimated using least square is “well-behaved” if does not violate the basic least
squares assumptions. Four econometric issues that will be examined include testing for the
presence of multicollinearity, heteroskedasticity, errors-in-variables and misspeciﬁcation
errors. Particular attention is given to how the presence of econometric problems affects the
residuals used to estimate farm-level economic efﬁciency. These issues are separately

discussed in detail below.

6.3.1 Multicollinearity Problems

Least squares estimation assumes that there is no relationship between independent
variables. If some independent variables are perfectly correlated then the signiﬁcance of the
parameter estimators of the collinear variables cannot be accurately determined. Collinear
independent variables result in large variances of the parameter estimates on these variables
making it possible that t-tests on these parameter estimates may turn out insigniﬁcant when

they should be signiﬁcant. The estimators themselves are neither biased nor inconsistent."o

 

‘° Because there will always be substantial correlation between independent variables,
multicollinearity is considered a problem when the correlation is perfect.

118

Multicollinearity often occurs in time series data where variables have a common
trend. This is not possible in this study. What is likely to result in multicollinearity is the
cluster sampling which was used to pick out the farmers involved in this study. Collinearity
in variables occurs in cluster sampling because of the proximity of respondents to each other.
But extra care was taken during cluster sampling to ensure that the problem of multicollinerity
is avoided (MLAWD, 1993).

There are informal and formal tests for collinearity in independent variables. The
informal tests include checking what happens to the signiﬁcance tests on coefﬁcients when
variables are added or subtracted and calculating a correlation matrix and “correcting” for
collinearity whenever the correlation coefﬁcient (p) is greater than 0.8.‘51 If the overall
regression coefﬁcient (R2) is larger than the R2 obtained from regressing an independent
variable on another then multicollinearity is not serious. If multicollinearity is found to be
serious the simple options available include collecting more data or dropping the offending
variable. Principal component approach can also be used to correct for this problem.
Otherwise very little can be done to correct for multicollinearity.

In this data set an effort was made to avoid multicollinearity. For instance, the prices
of fertilizer for the four crop categories were combined into a single index. Without this
index, problems would arise because the four prices for fertilizer corresponding to the four
crop categories would be highly correlated. Fertilizer types, compound D and ammonium
nitrate, are used in varying proportions in almost all crops. Because these two fertilizer types
comprise the bulk of fertilizer used by farmers on any crop their prices would dominate the

fertilizer price indices for the four crop categories.

 

" The signiﬁcance of multicollinearity as a statistical problem is diminished by the fact
that it does not affect the error term. As a result there is no absolute number that can be cited
as proof for the existence of multicollinearity and 0.8 is an arbitrary threshold.

119

Simple correlation coefﬁcients are used to test for the likelihood of multicollinearity
problems among the original independent variables. The quadratic and cross-terms were
omitted ﬁ'om the calculation of correlation coefﬁcients. Figure 6.1 shows the distribution of
absolute values of correlation coefﬁcients (p) between pairs of independent variables for each
of the three seasons. Figure 6.1 shows that there is insigniﬁcant correlation between
variables. Over 65 percent of p-values are less than 0.2 in the last two seasons. The variables
for the 1988/89 season show a different pattern of correlation. While the distribution of
correlation coefﬁcients peak in the 0.0-0.1 range for the last two seasons, the 1988/89 p-
values pick in the 0.2-0.3 range. But generally correlation between variables is insigniﬁcant

because the percentages of p-values that are greater than 0.4 are, in all cases, below 1 5 percent.

120

 

.................................................

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lllllllllllllllllllllllllllllllllllll llllllllllll

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0 1 i ‘ 1
1988/89 [989/90 [992/93
Seasons

 

Millage:

E 0.0-0.1 0.1-0.2 [:1 0.2-0.3
g 0.3-0.4 >0.4

Figure 6.1: Percentage Frequency Distribution of Correlation Coefficients

 

 

 

 

 

The pairs of independent variables with at least one correlation coefﬁcient p, that is
greater than 0.4 are presented in Table A5 in the Appendix. Table A5 shows that input prices
have quite a number of p-values that are greater than 0.4 against each other. Small grains,
legumes and cash crop seed prices have p-values greater than 0.4 in at least one of the
seasons with all other input prices. This leaves the maize seed and labor price pair as the only
one without p-values greater than 0.4 in any of the three seasons. But all input price pairs
have p-values that are, however, below the 0.8 threshold. In addition there is no pair of input

prices that have p-values greater than 0.4 for all the three seasons. Only three out of the nine

12]

pairs listed on Table A5 have p—values that are greater than 0.4 in two of the three seasons.
As a result there is little danger that input prices could pose serious multicollinearity
problems. Input prices were, therefore, left as they are.

There is only one pair of independent variables that exhibit signiﬁcant correlation. As
shown in Table A5 the p-values of cash crop area and cash crop value are 0.8 and 0.82 for
1988/89 and 1989/90, respectively. In fact, for all crop categories, the p-value for area and
value of output is greater than 0.4 in all seasons, with the exception of the maize area and
value of maize combination in 1989/90. Crop areas also have p-values that are greater than
0.4 against each other. All this indicates a high likelihood of a multicollinearity problem
involving the area planted variable. This emanates from the fact that land is deﬁned here as
the area planted while the value of a particular crop category is a product of the area planted
and the price of the ﬁnal output. Because the output price may be relatively uniform across
farms high correlation between area planted against value of output harvested or area planted
to other crops becomes highly likely.

Even though the easiest remedy to multicollinearity problems is to drop the offending
variables, we retain the land variable but modify it so as to minimize the probability of
multicollinearity. Land will be deﬁned as an aggregate value to eliminate correlations
between area planted and crop value, area planted to other crop categories and input prices.
The areas planted to crop categories and the value of the different crop categories harvested

appear to be the variables most likely to trigger multicollinearity problems.

6.3.2 Heteroskedasticity Problems
In this study heteroskedasticity problems deserve more attention than multicollenearity

because they affect the error terms. Heteroskedasticity exists when at least one of the

122

independent variables in correlated with the error term. The least squares assumption of
residuals having a constant variance is violated. While. the consistency of the parameters
estimated using least squares is not affected, it is not possible to subject these least squares
parameters to signiﬁcance tests, such as t-tests. Inference is less accurate because, although
the parameter estimates are unbiased, they are not the best parameter estimates in terms of
variance. In addition, the error terms do not exhibit the preferred form of constant variance.

Correcting for heteroskedasticity allows one to obtain unbiased parameters with the
lowest variance (i.e. best estimate). In this study we hypothesize that producers with higher
levels of farm assets, livestock and arable land are less risk averse and thus make decisions
that are likely to result in larger deviations from the economically optimal cost function. For
instance they are more likely to produce higher outputs than farmers who are less endowed
and hence are prone to commit bigger “mistakes” because of factors beyond their control as
well as inefﬁciency . We therefore hypothesize that least square residuals are correlated with
the quasi-ﬁxed and ﬁxed input variables. A simple test for heteroskedasticity is simple visual
inspection of a plot of residuals on the independent variables.

Figures A1 to A7 in the Appendix show plots of residuals on total arable area, value
of farm assets and value of livestock. The bulk of the observations on total arable area fall
between 2 to 10 hectares (or 0.7 to 2.3 in logarithmic terms) as shown in ﬁgures A1 to A3.
There is no clear pattern between total arable area and the residuals. “Mistakes” appear to
be uncorrelated, in any way, with size of holding. The same conclusion also hold for the
relationship between residuals and the value of farm assets and livestock.

The Cook-Weisberg test for heteroscedasticity was performed to further test for the

presence of heteroscedaticity. This procedure involves the modeling of the variance using the

123

ﬁtted values of the dependent variable. It produces a 3:} statistic that is used to test the null

hypothesis that the model has constant variance. The results are presented in Table 6.3.

Table 6.3: The Cook-Weisberg Test for Heteroscedasticity

 

 

Season xz-Statistic p-value
1988/89 5.88 0.02
1989/90 0.19 0.66
1992/93 0.19 0.66

 

The null hypothesis specifying the presence of constant variance can only be rejected
in one season; 1988/89. The other two seasons’ data does not have the heteroscedasticity
problem. The peculiar case of 1988/89 is difﬁcult to explain and goes to show that there are
other factors at work other than simple seasonal variations. On the whole, and in spite of the
1988/89 anomaly, the Cook-Weisberg test adds weight to the results of informal tests for

heteroscedasticity.

6.3.3 Omitted Variables Problem

This is the most serious problem that often arise in empirical analysis“. In this case
an important explanatory variable is omitted from the regression, for instance, because it is
difﬁcult to observe and hence cannot be easily measured. This omitted variable is

subsequently thrown into the error term affecting the t-tests on regression coefficients. The

 

‘2 Most regression analysis begin with the omitted variable test and nothing else can be
done before the omitted variable problem have been solved if it is found to exist.

124

problem is not merely the preciseness of t-test on regression coemcients. First, there is an
endogeneity problem if the omitted variable is correlated with other independent variables.
The often cited example in production economics is the diﬁculties of representing the
unobserved management and labor quality in estimating a production or cost function.
Management and labor quality are often correlated with observable inputs that are part of the
production or cost functions.

The second problem with omitted variables is that they “contaminate” the residuals
making it difﬁcult to ensure that only random noise and ineﬁiciency are in the residual. In the
example given above the variation in output or variable costs that is explained by the quality
of labor and management should be taken out whenever possible. But this would not be as
serious a problem if the intention is to measure economic inefﬁciency and if the quality of
management and labor were not correlated with farm input choices. What is crucial at this
stage is to ﬁnd out whether there is a problem of omitted variables.

The problem of omitted variables in this study can only be a result of errors in deﬁning
the cost function. Theoretically a short-run cost ﬁrnction similar to the one estimated in this
study, relates total ﬁrm costs to variable input prices, levels of ﬁxed costs and quasi-ﬁxed
inputs and output levels. There are few other possible explanatory variables that can be
considered omitted in this speciﬁcation other than the quality of labor, management
(incorporating education and experience), technology and other shifter variables. Since
management and labor quality are directly correlated with observable inputs levels, they cause
less problems when a cost function is used. A cost ﬁrnction does not have input levels as
independent variables. The indirect relationship between the unobserved management and
labor quality and output levels (that is, through input choices) can be ignored because other

factors affect output level more than management and labor quality. In addition, it is hard to

125

ﬁnd a proxy for management and labor quality that is not correlated with input levels and
hence indirectly to output levels.63 The technology used in the communal area production
system can be assumed to the same across farms (rainfed agriculture based on animal draft
power) as outlined in Chapter III.

The Ramsey Reset test for omitted variables estimates a regression model by
augmenting it with the second, third and fourth powers of the dependent ( or independent
variables, if so speciﬁed) variable. In the absence of omitted variables the coefﬁcients on these
powers of ﬁtted values are hypothesized to be zero. The results of the test that the
coefﬁcients on the second, third and fourth powers of the dependent variable are all equal to

zero are presented in Table 6.4 below.

Table 6.4: Results of the Ramsey Reset Test for Omitted Variables

 

 

Season F-value p-value
1988/89 1.83 0.14
1989/90 2.59 0.06
1992/93 0.82 0.48

 

From Table 6.4 we note that we cannot reject the null hypothesis (that the regression
model/cost function has no omitted variables), at 5 percent signiﬁcance level, in all three
seasons. At 10 percent signiﬁcance level there is evidence that there is an omitted variable
problem in the 1989/90 cost ﬁrnction. This is a surprising result in that exactly the same
variables are used in the ﬁrst two seasons. Could this omitted variable problem be attributable

to unobservable seasonal traits? There is nothing particularly striking about the 1989/90

 

‘3 The solution to this problem of unobservable variables is to ﬁnd proxy variables which
are as closely related to the unobservable variable as possible but not correlated to any of the
other independent variables.

126

season that could be pointed out as the cause of the omitted variable problem indicated in
Table 6.4. There is no variable in the 1989/90 cost ﬁrnction that is different from the 1988/89
model. Ifthe problem of omitted variables is more a product of missing than unobservable
variables one would expect to encounter this problem in the 1992/93 cost ﬁrnction. Data on
value of farm assets and livestock is missing for the 1992/93 season. Table 6.4 does not show
any evidence of omitted variables in the 1992/93 cost function. The problem of what was
omitted in the 1989/90 cost function is difﬁcult to resolve. We will look at speciﬁcation of
the dependent variable as a source of the omitted variable problem for the 1989/90 cost
function in particular and as an econometric problem of its own for all the three cost
functions.

It often occurs that when the dependent variable is mis-speciﬁed then the independent
variables will also be incorrectly speciﬁed. Following the work of Tukey ( l 949) and Pregibon
(1980) one can perform a test for model speciﬁcation (link test) based on the dependent
variable (StataCorp, 1997; Pregibon, 1980). A link test involves the regression of the
dependent variable on two variables; the predicted values of the dependent variable and the
square of the predicted values of the dependent variable (Y and Y2, respectively). The
coefﬁcient on Y is expected to be highly signiﬁcant. But the coefﬁcient on Y2 should not be
statistically signiﬁcant if there is no speciﬁcation problems. The results of regressing Y on
Y and Y2 are presented in Table 6.5 below;

Table 6.5: Results of the Specification Link Test.

 

 

 

Season R“ Constant Pred. Value (Y) Pred. Value Squared (Y2)
Coef. p- Coef. p-value Coef. p-value
1988/89 79% -0.58 0.42 1.17 0.00 -0.01 0.40
1989/90 67% -2.14 0.24 1.57 0.00 -0.04 0.24
1992/93 87% ~0.49 0.63 1.11 0.00 -0.01 0.63

 

‘ Note: R2 stands for adjusted-R2.

127

All the coefﬁcients on Y2 are not signiﬁcantly different from zero at 5 percent
signiﬁcance level (that is at p = 0.05). Table 6.5 also shows that, as expected, the coefﬁcient
on the predicted value, Y, is highly signiﬁcant. There is, therefore, no problems in the way
we speciﬁed the dependent variable, the total variable costs. Thus we cannot attribute the
problem of omitted variables noted in the 1989/90 cost ﬁrnction to problems in the
speciﬁcation of the dependent variable.

Because omitted variables present a more serious econometric problem than that of
heteroscedasticity, multicollinearity, and measurement errors the option of dropping the
1989/90 season’s cost function was seriously considered, even if this conclusion is reached
using 10 percent as the signiﬁcance level. We recognize that all of the cost functions in
general do not have all the variables that should be included (especially variables dealing with
farmer experience and education, farm-level technology and other shifter variables). In one
way or the other, there are missing variables in all cost functions because of the data problems
outlined before. It is impossible to go back to the ﬁeld to collect a new data set at this point
in time. We, therefore, include the 1989/90 cost ﬁlnction in the analysis and take note that
we should be cautious when interpreting the results that include this season. It also happens
that this is the only season that has data on farmer characteristics and resource endowments

which will be used to explain the variation in farm efﬁciency.

6.3.4 Problems of Measurement Errors
An endogeneity problem arises whenever one or more variables in a model are
measured with error and the recording errors are correlated with at least one of the

independent variables. When the recording errors are not correlated with independent

128

variables (other than the independent variable that is being recorded in error) parameter
estimates are unbiased and consistent. However, their large error variances result in imprecise
statistical tests leading to the conclusion that measurement error is a major problem even
when the recording errors are not correlated with other independent variables. Large error
variances lead to large standard errors and thus imprecise t-tests on the estimated parameters.

The recording errors can be committed when recording both the dependent and
independent variable. Unlike omitted variables, the problem of measurement error involves
dimculties in recording variables. What is observed is the measured and not the actual
variable because the latter cannot be observed. Recording errors may occur because of a
variety of reasons. Enumerators may not ask the appropriate questions leading to wrong
responses from the respondent farmers. On the other hand the questions may be appropriate
but the responses are wrong because respondents, for one reason or the other, are not willing
to provide the required information.

The measurement error problem deserves serious attention in this study because it
aﬁ‘ects the residual terms. One cannot guarantee that a particular data set was accurately
recorded. Concern here is not about the measurement errors that occurred because of
inadequate supervision and enumerator training, or the handling of recall data and sensitive
information. Even though there is no guarantee that these errors were absolutely avoided,
all imaginable means to minimize such errors were taken. This data set was extensively
cleaned by the ministry staff and by the author. Observations that had obviously outrageous
values were excluded from the data set. The measurement errors of concern are those
emanating from the difﬁculties involved in accurately recording the variables by the
respondents themselves. There is no way of handling this problem once the data has been

collected. Ifthe respondents cannot accurately record phenomena at their farms then there

129

must be ways put in place before data collection starts to enable enumerators to anticipate
such difficulties. It is hoped that the Farm Management Section of the Economics Division
of the Ministry of Agriculture had enough experience and expertise to handle such data

collection problems.

6.4 Testing for Regularity Conditions
To obtain a well-deﬁned cost function requires the imposition of assumptions on the
production technology (Chambers, 1986). The technology allows farmers to use factors of
production to produce different output sets. As a result the cost-minimization problem is
directly related to the production technology. Thus the properties of cost functions are
derived from the production function properties and vice—versa if the functions conform to
the regularity conditions that are based on economic theory. The main properties of
production ﬁrnctions such as monotonicity, concavity, non-emptiness (feasibility), non-
negativity and continuity give shape to cost functions. Chambers lists the following as
properties for a well-behaved cost function:
a). Non-negativity (No output produced at zero cost - inputs that are positively
priced lead to positive costs if positive outputs are to be produced)
b). Non-decreasing in input prices (An increase in input prices cannot reduce
costs - the fundamental inequality of cost minimization or monotonicity)
c). Concavity continuity in input prices (This rules out the possibility of an
optimal response to input price changes resulting in a decrease in costs and

that the function be twice differentiable“)

 

“ The Hessian or matrix of second order derivatives of costs with respect to input prices
must be negative semi-deﬁnite.

130

d). Positive linear homogeneity (Proportional changes in input prices do not

affect the level of cost-minimizing input bundles)

e). Non-decreasing in output (Minimum costs cannot be reduced by an increase

in the level of output)

It is not necessary to test for or impose all six conditions on the cost function in this
study. Some conditions, such as (c), are implicitly assumed to hold by design. The translog
functional form is twice diﬁ‘erentiable as it was developed primarily to capture all the three
stages of production (Rask, 1994). The other condition (a) stated above will not be
considered because it has a straight-forward interpretation. Homogeneity and homotheticity
(that costs should not be decreasing in output) are implicitly assumed. Binswanger (1974)
pointed out that one of the advantages of using a dual function, such as a cost function, is that
the function is homogeneous in input prices by design. Thus an increase in input prices will
always increase costs. In addition, the normalization of input prices and variable costs by the
price of fertilizer and chemicals imposes homogeneity on the cost function. Having assumed
the cost function to be homogeneous, it follows that it is also homothetic; for homogeneous
ﬁrnctions are a special sub set of homothetic functions (Debertin, 1986). The monotonicity
requirements (condition (b)) will not be examined because the cost functions are not

estimated as a system of equations incorporating cost share equations.

6.5 Economies of Scale

Measures of economies of scale in a translog speciﬁcation cannot be estimated at
farm-level. The measures are a ﬁrnction of several independent variables depending on how
the translog function is speciﬁed. These measures are calculated at the mean level of the

independent variables. In this section these indicators are estimated and, on the basis of these

131

estimates, implications are drawn on policy and program formulation for communal area

farmers in Zimbabwe and other similar Southern African countries.

6.5.1 Economies of Scale Versus Economies of Size

The concept of economies of scale is often conﬁrsed with economies of size to the
extent that they are often used interchangeably. Economies of scale expresses the
proportional change in output to proportional changes in all factors of production. In other
words if all inputs are increased by a constant factor, rt, output can increase by a factor less
than, equal to, or greater than rt, implying decreasing, constant and increasing returns to
scale, respectively. But in the real world such proportional changes in input bundles are rare
(Upton, 1996). Changes are normally not proportional due to the lumpiness or indivisibility
of durable inputs and the diﬂiculties in controlling and measuring inputs (Doll and Orazem,
1984). Economies of size is a measure of the output (cost) response to such non-proportional
changes in factors of production (input prices) (Derbetin, 1986). This is a more realistic
representation of what happens in the real world. But there are many non-proportional
changes in input quantities (prices) which yield diﬂ‘erent output (cost) responses, making the
measurement of economies of size difﬁcult. Thus a measure of economies of size is only
applicable to a particular non-proportional change in input quantities or prices. As a result
most empirical work has been on estimating measures of the easy-to-deﬁne economies of
scale (Derbetin, 1986).

While the two concepts are different it should be pointed out that these two concepts
are very closely related. Chambers (1986) pointed out that “at cost-minimizing points, a ﬁrm
exhibits increasing returns to scale if and only if it simultaneously exhibits increasing

returns to size.” and vice-versa (p. 72). Measures of the two concepts coincide at the cost-

132

minimizing points because indicators of returns to scale and returns to size represent the
response of output and cost in input space, respectively. Their difference come from the fact
that the two measures are based on different input combinations, with economies of size
concerned about movements of costs along loci of cost-minimizing points. Measures of
economies of scale are concerned with the response of output along the scale line from the
origin (Chambers, 1986). The two measures are particularly close when the production

function is homogeneous and homothetic.

6.5.2 Testing for Constant Returns to Scale

Agriculture, especially small-scale agriculture which does not use too many ﬁxed or
durable inputs (potential sources of scale economies), throughout the world is generally
characterized by constant returns to scale (Upton, 1996; van Zyl et al, 1995). This explains
much of the observed inverse relationship between farm size and efﬁciency (Barrett, 1993).
It is important, therefore, that a test for the presence of constant returns to scale precede the

calculation of the returns to scale parameters.

1. Constant returns to scale, according to Berndt (1993) can be imposed as follows;
2. Equating the sum of the input price (labor and seed) coefﬁcients to unit.

3. Equating to zero the sum of coefﬁcients on all cross terms involving input prices.
4. Equating to zero the sum of all coefﬁcients on cross terms involving input prices and

output variables.

5. Restricting to zero all the coefﬁcients of cross-term variables involving output values,
(that is, (1,, pij and 6,).

6. Equating to one the sum of coefﬁcients on the output value (Yi) variables (that is,

Ea,= 1 ).

133

The null hypothesis for these restrictions can be represented as follows;

EB=1; EB,=E6,=0

i=1

{Where q = 55:22am p = 11(2sz)- + m(k - m) giventhatk>m.}
aﬁ, pii and 6, =0
(Ear-=1)

These restrictions are tested together with the homotheticity restrictions. Table 6.6 below

shows the results of the three tests outlined above.

Table 6.6: Tests for Constant Returns to Scale

 

 

 

Season 1988/89

F-value p-value
1988/89 7.87 0.000
1989/90 24.46 0.000
1992/93 21.90 0.000

 

Table 6.6 shows the F-statistics and the associated signiﬁcance levels (p-values) for
testing the null hypothesis that the cost functions exhibit constant returns to scale (CRTS).
It is clear ﬁom the results that communal agricultural production did not exhibit constant
returns to scale during the respective three agricultural seasons. In all cases it is not possible
to accept the null hypothesis of the presence of constant returns to scale. This is unlike the

sugarcane case in Brazil which was tested for economies of scale by Kevin Rask (1995) using

134

a modiﬁed symmetric generalized McFadden cost ﬁrnction. Rask could not reject the
constant returns to scale hypothesis. Using non-parametric methods, van Zyl et al (1995)
found that only a little over 7 percent of farmers in the former South African homelands of
KaNgwane, Lebowa and Venda were large enough to be scale eﬂicient. But the later study
did not test for the presence of constant returns to scale making it hard to compare ﬁndings.

The absence of constant returns to scale means that communal farmers cannot expect
to double their outputs by simply doubling their input bundles. Without this option farmers
have to look for other means of improving productivity. It is, however, important to have an
idea about the direction of returns to scale in communal agriculture before delving into what
these other productivity-improving options could be. The choice set facing farmers whose
production system has increasing returns to scale is vastly different from the set available to
farmers with a production system experiencing decreasing returns to scale. The next section

presents the estimates of economies of scale.

6.5.3 Measures of Economies of Scale

Measures of economies of scale can be derived from the cost ﬁmction by
differentiating the log of costs with respect to log of output. The inverse of the elasticity of
costs with respect to output is a measure of returns to scale, (A). Using equation (16) and in

the absence of sample-mean scaling, this measure is as shown below;

1
A = —, where
e,.,.
m n h
_ ) .
8C, - a, + Z]: cry/111’]. + 21:91-11“: + 26017116.
I: 1:

(=1

135

Note that GCY stands for elasticity of costs (C) with respect to output (Y).
When the Pi, Yi and K, variables are scaled by their respective sample means prior to
converting to logarithms then all the log terms in the cost elasticity equation drop out at the

sample means. Thus the cost elasticity equation simpliﬁes to the following representation:

n n '1
ecr = 2a, - A = [212“.-
r= ,:

Increasing, constant or decreasing returns to scale exist when A is greater than, equal
to or less that one. It is important to note that A, like its elasticity of cost components, is a
local measure. These indicators of economies of scale are only applicable when the
percentage changes in farm input prices are within the proximity of the sample means. In
table 6.7 below, the economies of scale indicators calculated as the reciprocals of cost
elasticity and after scaling the input prices, values of output and the ﬁxed factors (Pi, Yi and

Ki variables) by their sample means are presented.

Table 6.7: Indicators of Economies of Scale (A)

 

 

Season Economies of Scale Indicator
1988/89 0.341
1989/90 0.245
1992/93 0.715

 

The measures of economies of scale that are displayed in table 6.7 indicate that
communal production is characterized by decreasing returns to scale. Thus when communal
farmers increase their scale of operation x-times the corresponding increase in output is less

than rate x. The average over the three seasons, for instance, implies that a one percentage

136

increase in all inputs will increase output by about 0.43 percent at the sample means. The
average measure for returns to scale for the ﬁrst two seasons at only 0.29 percent is much
lower than the overall average. There is need to examine the behavior of economies of scale
measures when sample means are changed so as to determine the optimal farm size at current
technology levels. This research work is left for ﬁxture initiatives.

The results shown in table 6.7 are best illustrated by a graph on the shape of the
communal area cost ﬁinctions. The possibility that it is a horizontal line is eliminated by the
absence of constant returns to scale illustrated in the preceding section. Following Ferguson

and Gould (1975), the U-shaped communal area cost function is presented in ﬁgure 6.2.

Costs

Lo -run ,
Cotslthurve

Increasing 5 Decreasing )
Returns to Scale 5 Returns to Scale

 

 

Output

Figure 6.2 The Shape of the Long-run Cost Curve for Communal Areas

137

The measures of returns to scale shown in Table 6.7 suggest that communal farmers
are operating in the decreasing returns to scale range that is shown in Figure 6.2 above. It
appears as if they have already moved beyond the range of increasing returns to scale. If the
farmers’ motives were just to maximize proﬁts then one would expect a downward
adjustment in the scale of operation. But communal area farmers are semi-commercial,
driven, ﬁrst and foremost, by the need to produce enough food for the family (Shumba,
1985). In such situations farmers use inputs beyond the economically optimal level (Barrett,
1993; Zimmerman and Carter, 1996; Larson, 1997).

In addition communal farmers do not operate in a perfect market, making some of the
predictions of economic theory incorrect. Facing decreasing returns to scale, communal
farmers need to employ new production techniques which depend on the supply of modern
inputs. But the input and output markets are not perfect. There is no market for communal
land, for instance. Capital and labor markets are also imperfect. Thus institutional barriers
could be among the important factors responsible for the observed agricultural production
patterns in communal areas. This raises the question whether some “institutional midwifery”
which hurries the birth of markets for land, labor and capital is necessary (Zimmerman and
Carter, 1996).

Conditions in communal areas continue to change due to the demographic pressure
and the changes in the external environment. New institutions are necessary to take full
advantage of the changing environment. Expanding use of inputs such as seed, labor,
fertilizer and chemical, land and capital inputs all can be instituted through markets regulated
by both formal and informal rules. That these are not well deﬁned for communal agriculture

is part of the legacy of this system of farming that was meant to provide modern industry and

138

commercial farms with cheap labor. The areas were never meant to be productive enough
to support a reasonable standard of living (Potts and Mutambirwa, 1997). These may all
explain why farmers operate in the decreasing returns to scale range when economic theory
suggests otherwise. This could well be highlighting the desperation that characterizes

communal agricultural production.

6.6 Summary

In this chapter estimates of translog cost ﬁinctions were presented. The independent
variables explained over 65 percent of the variation in farm-level variable costs. But less than
a quarter of the total number of coefﬁcients are signiﬁcant at 10 percent. Little could be said
about the signs of the coefﬁcients given the speciﬁcation of technology as a translog system.
The partial effect of a variable, say Pi, when technology is speciﬁed as translog is a
combination of HS coefﬁcient and those of other variables (other input prices, ﬁxed input and
output), say 21., with which Pi forms cross-terms. To ﬁnd out why such a small number of
variables have signiﬁcant coefﬁcients the cost models were examined for existence of
econometric problems.

The main econometric problems examined are multicollinearity, heteroskedasticity,
errors in variable and measurement errors. The last issue was limited to a mere discussion as
the measurement errors are unobservable and hence hard to handle. Multicollinearity was not
found to be a major problem because precautions were taken to create indices of input prices
such as fertilizer and chemicals and labor. Areas planted was found to be systematically
correlated to values of output for the corresponding crop categories as well as with other

variables and thus were collapsed into a single variable; total area planted.

139

Problems of heteroskedasticity were checked, ﬁrst, by simple plots of residuals on all
independent variables and then through the Cook-Weisberg (CW) test. The 1988/89 cost
function was the only one showing evidence of heteroskedasticity after the CW tests. More
attention was given to the problem of omitted variables. The Ramsey Reset test revealed that
only the 1989/90 cost function could have this problem if the rejection levels for tests of
signiﬁcance is set at levels higher than the traditional ﬁve percent. The speciﬁcation link test
revealed no problems at all with the speciﬁcation of the dependent variable.

The next set of tests covered economic regularity. Most of the regularity conditions
were not tested because the translog cost speciﬁcation implicitly assumes them to hold
especially homogeneity and, therefore, homotheticity. Thus the cost ﬁJnctions will be used
in this study and compared to estimates of cost frontier functions in the next chapter.

Measures of economies of scale were derived from the cost function estimated using
variables that were scaled by their means prior to being converted to logarithms. The most
striking ﬁnding was the presence of decreasing returns to scale in Zimbabwe’s communal
areas. This implies that, at current technology levels, an increase in the use of inputs only
generates a change in output (or cost saving) that is less than the rate by which inputs
quantities (prices) were changed. This has far reaching effects in terms of the
recommendations for institutional change. Communal farmers will need programs that change
more than just the input bundles. New technology will go a long way in ensuring that these
farmers operate at the desirable tail end of the increasing returns to scale range.

The tests for econometric and economic regularity revealed that the three cost
ﬁinctions have differences. To estimate a 1988/89 cost ﬁJnction heteroskedastic-robust
methods are best. Although the 1989/90 cost function has traces of the presence of the

omitted variable problem, it is the most “nicely behaved” cost function of the three.

140

CHAPTER VII: THE COST FRONTIER FUNCTIONS AND ECONOMIC
EFFICIENCY.

7.1 Introduction

The last two chapters described the data and the methods used to estimate translog
cost functions. It was possible to calculate indicators of economies of scale from estimated
cost functions. Although measures of returns to scale are important in determining
economically optimal levels of production they cannot be used to estimate economic
eﬁiciency of communal farms at individual farm-levels. Farm-level measures of economic
efﬁciency can be derived from translog cost ﬁontier functions. This chapter presents
estimates of farm-level economic efﬁciency and identiﬁes the factors determining cross-farm
variability in economic efﬁciency measures.

The chapter has three major sections. The ﬁrst section covers issues related to the
estimation of cost frontiers and measures of farm-level economic emciency. The main focus
of this section is the determination of the pattern of farm-level efficiency in communal areas
of Zimbabwe. Regression analysis is used in the second section to identify the factors that
cause variability in farm-level economic efficiency. The list includes household resource
endowment and demographic variables. Whenever available, data on physical farm
characteristics such as soil type are also used as possible explanatory variables for variation
in farm-level measures of economic efﬁciency. The aim of this analysis is to provide insights
to be used in the last chapter which draws implications on ﬁrture policy making on communal

area agricultural development. The chapter then closes with a short summary.

141

7.2 Estimates of Cost Frontier Functions and Economic Efﬁciency

The main issues related to the use of cost frontiers to measure economic efficiency
have been reviewed in detail in Chapter IV. Economic efficiency indicators will be derived
ﬁ'om the cost frontier by decomposing the error term into its constituent components of white
noise and the one-sided distribution of inefﬁciency. The assumptions that are necessary for

this process and the resultant estimates of economic eﬁiciency are presented in this section.

7.2.1 Estimating Cost Frontier Functions

When estimating cost frontiers one must make an assumption about the distribution
of the one-sided error term. Many studies have used half or truncated normal distributions
for the one-sided error (Greene, forthcoming). This raises questions on what distribution
should be considered as a reasonably adequate representation of the actual distribution of
farm-level technical and allocative errors. Economic theory does not dictate that mistakes be
distributed normally (Forsund, Lovell and Schmidt, 1980). It is legitimate to question why
we should expect farrn—level mistakes to be clustered near zero inefﬁciency. The same
question can be posed for other alternative speciﬁcations of the distribution of farm-level
errors. Economic theory does not provide enough light on such questions. Specifying the
distribution of the one-sided error term is a major assumption in the use of frontier models
to measure ﬁrm-level economic efﬁciency. Thus estimates of economic efﬁciency obtained
assuming half-normal distribution for the one-sided error term will be compared to estimates

when the one-sided error term is assumed to be distributed exponentially.

142

7.2.2 Cost Frontier Function Estimates

Cost frontier functions are different from those normally generated by least squares
techniques because while the latter represent an “average” line ﬁtted to minimize the sum of
squares of residuals, the cost frontier ﬁrnction is a line ﬁtted to map the observed least cost
for given levels of output. The difference between the two manifests itself in the form of
differences in coefficient estimates. Even though the frontier model is prone to the inﬂuence
of outliers, it possesses strong intuitive appeal because of the assumption that economic
agents aim to maximize utility by maximizing proﬁts through minimizing the production costs.
prroducer behavior is so deﬁned then a function that traces least cost observations is more
representative than one which deﬁnes an average through minimization of residual sum of
squares. The results from these two ways of representing production relations will be
subjected to comparative analysis.

Tables A9, A10 and All in the Appendix present the parameter estimates of the
translog cost frontier ﬁinctions when the one-sided errors are assumed to be distributed as a
half-normal for the 1988/89, 1989/90 and 1992/93, respectively. There is a slight difference
(third to fourth decimal) between coefficients shown in Tables A9, A10 and All and those
in Tables A2, A3 and A4. But the intercept term between the two sets of functions are
signiﬁcantly different. It is also interesting to note that cost functions have slightly more
variables which have statistically signiﬁcant coefﬁcients than cost frontier ﬁinctions, as

illustrated in Table 7.1.

143

Table 7.1: Differences in Number of Statistically Signiﬁcant Coefficients Between
Cost Functions and Cost Frontier Functions.

 

 

 

Type Cost ﬁmction Cost frontier (normal) Cost frontier (expon.)
p-leve1* 5% 10% 5% 10% 5% 10%
1988/89 10 12 8 10 9 10
1989/90 16 21 12 14 14 19
1992/93 15 19 9 13 9 13

 

I"Note: p-level stands for level of signiﬁcance.

In addition to the differences in numbers of statistically signiﬁcant coeﬁicients between
the cost frontiers and cost ﬁinctions shown in Table 7.1, there are also slight differences in
numbers of variables which have statistically signiﬁcant coefficients between half-normal and
exponential cost frontiers". The latter has more statistically signiﬁcant coefﬁcients than the
former. However, the differences between coefficients on corresponding variables across the
function types are almost negligible. This seem to suggest that the differences between
traditional (or average) cost ﬁanctions and cost frontier ﬁmctions is far from being complex.
Whilst the theoretical strength of the frontier model as a true representation of real world
phenomena seem adequate for one to recommend it over the “average” models, more work
needs to be done to close the gap which appears insurmountable theoretically but turns out
otherwise empirically. That the coefﬁcients in Tables A9, A10 and All have the same
interpretation as those of cost ﬁinctions shows that from both the theoretical and empirical
standpoints these two concepts of representing the production process tend to show similar

trends when it comes to characterizing the production process.

 

‘5 The half-normal and exponential cost frontiers are estimated assuming that the one-sided
error term has a half-normal and exponential distributions, respectively.

144

The discussion on cost ﬁ'ontier ﬁrnctions estimates would not be complete without an
examination of the variances of the two part error terms which are shown in Tables A9, A10
and Al 1. The across season differences in the cost frontier estimates are also apparent in the
variance of the random noise and the one-sided errors (of and 0,,2 , respectively). The
inefficiency errors dominate the random noise in terms of variance only in the ﬁrst season,
1988/89 as shown by the ratio A. The parameters 0 and A constructed from these variances
are all statistically signiﬁcant during the 1989/90 season. But a is also statistically signiﬁcant
in the other two seasons while A is insigniﬁcant in 1988/89 and signiﬁcant at 10 percent level
in 1992/93.

The cost ﬁontier functions with the one-sided error term distributed exponentially are
presented in Tables A12, A13 and A14 in the Appendix for the three seasons, respectively.
In addition to the differences in coefﬁcients and numbers of statistically signiﬁcant variables
noted above, the variances of the random and one-sided errors follow the same pattern as that
of the half-normal cost ﬁ'ontier functions. Both 0,, and 6 are statistically signiﬁcant in
1989/90 while 0,, is statistically signiﬁcant in the other two seasons and 6 is only statistically
signiﬁcant at 10 percent level in 1992/93. These patterns should be taken into account when

interpreting the measures of economic efﬁciency.

7.2.3 Estimates of Economic Efficiency

The variables described above were used to estimate levels of ineﬁiciency in
communal areas. Farm-level estimates of economic inefﬁciency, E(e"|ei) assuming that the
one-sided error term has a half-normal distribution are calculated as shown below following

Jondrow et al (1982):

145

EIevle} = of“.[ ﬁeA/o) - ﬂ]

1 - F(eA/o) a

In the case of the one-sided error term having an exponential distribution Jondrow et al
(1982) calculated E(e"|ei) as shown below assuming a = (alt!" + 0,10,.

E(e"/e) = oiﬂ - a]
F(a)

Other variables are deﬁned as before. There are some differences between estimates of farm-
1evel inemciency when a half normal and a exponential distribution are compared. The
descriptive statistics (mean, standard deviation, minimum and maximum) of economic

inemciency measures are shown in table 7 .2.

 

 

 

 

Table 7.2: Descriptive Summary of Economic Inefficiency Estimates

Variable 1988/89 1989/90 1992/93 Average
Norm. Exp. Norm. Exp. Norm. Exp. Norm. Exp.

Mean 0.114 0.110 0.218 0.206 0.143 0.137 0.158 0.151

Std. Dev. 0.003 0.002 0.034 0.031 0.013 0.010 0.017 0.014

Minimum 0.100 0.106 0.119 0.176 0.098 0.126 0.106 0.136

Maximum 0.121 0.126 0.284 0.460 0.166 0.210 0.190 0.265

Cases 425 425 331 331 368 368 375 375

 

 

 

 

 

Notes: ‘Norm.’stands for the half-normal distribution case, ‘Exp.’ is the case when the
exponential distribution is assumed and ‘Std. Dev.’ is the standard deviation.

Overall across-season average economic ineﬁiciency estimates shown in Table 7.2

indicate that communal farmers are about 15 percent inefﬁcient. Thus communal farmers can

146

Overall across-season average economic inefﬁciency estimates shown in Table 7.2
indicate that communal farmers are about 15 percent inefficient. Thus communal farmers can
improve production by simply eliminating this 15 percent inefficiency. Although the average
for the half-normal case is slightly higher than the average for the exponential case, the two
methods seem to yield the same results on average. The variability of the average estimates,
as shown by the standard deviations, is similar between the two methods. However,
diﬁ‘erences do occur when one considers the case of the most efﬁcient and inefﬁcient farmers.
In the half-normal case the least efficient farmer would be 19 percent off the efﬁciency
ﬁ'ontier as compared to 27 percent for the exponential case. On the other hand the most
efﬁcient farmer for the half normal case would be 1 1 percent off the efficiency frontier against
14 percent for the exponential case.

The real story is shown by the season by season measures of economic inefﬁciency.
As expected there is some signiﬁcant across season variation in farm-level efficiency as shown
by the mean, minimum and maximum values in Table 7.2. The most inefficient farm for all
the half-normal cases was off the efficiency frontier by 28.4 percent during the 1989/90
agricultural season. On the other hand the most efficient farm was only off the frontier by 9.8
percent during the 1992/93 season. Average seasonal inefficiency fluctuated between 11.4
and 21.8 percent. The variability of efficiency estimates from one farm to the other during
the 1989/90 season was higher than that of the other seasons as shown by a higher coefficient
of variation (CV) of 16 percent compared to 3 and 9 percent for the 1988/89 and 1992/93
seasons, respectively.“ The efficiency measures for the 1988/89 season produced the lowest

mean, standard deviation and maximum value. The 1992/93 are closest to the average values.

 

“ The coefﬁcient of variation (CV) is obtained by dividing the standard deviation by the
mean. A rule of thumb in social science research is that a CV of less than 30 percent indicates
acceptable variability.

147

The exponential cost frontier functions produced estimates of economic efficiency that
have a similar pattern in terms of descriptive statistics. Examining the exponential cases
reveals the most inefﬁcient farmer was off the efficiency frontier by 46 percent in 1989/90
as compared to 23 percent for the half-normal case during the same season". The most
eﬁicient farm for the exponential cases was off the frontier by l 1 percent in 1988/89. We also
note from Table 7 .2 that the 1989/90 estimates of economic inefficiency are not only higher
than the overall averages but are more variable across farms. Variations in inefficiency from
farm to farm followed the same pattern shown in the half-normal case with CV’s of 2, 15 and
7 percent for the three respective seasons. Farm-to-farm variation, as measured by CV’s,
was lower than the variation in the half-normal case in all three seasons. This shows that the
estimates from the exponential cases are clustered together more than those from the half
normal case even though the former has the highest estimates of inefficiency.

Table 7.2 shows some differences in economic inefficiency estimates across the three
seasons. To further explore the nature of the differences of economic inefficiency measures
across seasons, we superimpose all three seasons into two plots, one for the half-normal case
and the other for the exponential case. The economic ineﬁiciency estimates were rearranged
in ascending order for clarity of presentation. These plots are shown in Figures 7.1 and 7.2.

In both ﬁgures the 1989/90 estimates are notably higher than the other seasons while
the 1988/89 estimates are not only the lowest but are consistently uniform. In the half normal
case (ﬁgure 7.1) the 1988/89 estimates do not get beyond the half-way mark of the10 to 15
percent range. But the other seasons’ estimates have a broader range especially the estimates

for the 1989/90 season. The same pattern is evident in the exponential case with the 1989/90

 

‘7 The farm that was 28.4 percent inefﬁcient in the half-normal case is not the same as the
one that was off the frontier by 46 percent.

148

estimates having the widest range of all the three season estimates. Estimates for the 1988/89
season are again consistently within the narrowest range of between 11 and 15 percent.
However, the exponential estimates have a ﬂatter slope than the half-normal estimates
implying lower across farm variability. The similarity in pattern once again indicates that the

two methods of estimating economic inefficiency yield reasonably similar results.

 

   

 

    

1989/90

1 992/93

 

 

Economic lnefﬂciency (%)

 

 

 

' v i

1 45 89 1 33 1 77 221 265 309 353 397

Observations

Figure 7.1: Measures of Economic Inefficiency for the Half-Normal Case

The differences in levels of estimates of economic inefﬁciency across the three seasons
could be due to factors such as rainfall and other seasonal factors. The unpredictability of the
rainfall season in Zimbabwe in general and communal areas in particular is considered to be

one of the main factors affecting productivity (Chasi and Shamudzarira, 1992). False seasonal

149

starts and mid-season droughts can eliminate whole plantings. Most farmers stagger their
plantings as a way to hedge against the risk of false starts and mid-season droughts (Mudhara,
et. al., 1995). The actual nature of the inﬂuence of rainfall cannot be pinpointed in the

absence of data on rainfall and its distribution in the sample areas.

 

l 989/\90

   
 

 

1992/93

20%

 

Economic lnefﬁciency (%)

 

 

101

1988/89

 

 

 

'

1 45 89 153 67 221 255 309 353 397

Observations

Figure 7.2: Measures of Economic Inefﬁciency for the Exponential Case

The above analysis has been based on measures of spread. Our next task is to
examine the distribution of the economic inefficiency estimates. The histograms for both half-

normal and exponential cases for each season are shown in Figures A8 to A13 in the

150

Appendix. These histograms allow us to examine whether there exists any difference in the
distribution of economic ineﬂiciency measures across the seasons and between the two cases.

What emerges ﬁom Figures A8 to al3 is that there is a difference in the nature of the
distribution of estimates on the basis of method. The estimates from the half-normal cases
all appear to have a distribution that is skewed to the right. The distributions are all
approximately normal. On the other hand estimates from all exponential cases have
distributions that are skewed to the leﬁ with a thinning right-hand side tail. The associated
measures of skewness and kurtosis shown in Table 7.3 conﬁrm that there is signiﬁcant
skewness and that the distributions are not normal. The thickness of the tails of the
distributions shown in Figures A8 to A13 do not conform with those of a normal distribution.

Table 7.3: Test for Skewness, Kurtosis and Normality in the Distribution of

Estimates of Economic Inefficiency

 

 

 

Season Case Skewness Kurtosis Test for Normality
1988/89 Normal -O.78* 380* 34.21“
Ex??ﬂ‘.’.‘.‘.t.l§! ............ .2. ' 13:“. ....... l 1'67.* .......................... 1.19:: ....................
1989/90 Normal -0.56* 243* 18.80"
......................... P? mania- 3402082”
1992/93 Normal -0.77* 3.23 2643*
Exponential 284* 1452* l.n.*

 

* signiﬁcant at 1 percent

In. stands for very “large number”.

Table 7.3 conﬁrms the pattern of skewness and kurtosis in the distributions of
economic inefﬁciency measures. Unlike the exponential case, the half-normal cases’
distributions have negative indicators of skewness. In addition all the indicators of skewness

and kurtosis signiﬁcantly indicate non-normality except for the kurtosis in the half-normal

151

case of the 1992/93 season. The test for normality (joint signiﬁcance of skewness and
kurtosis) also conﬁrms that none of the distributions have a normal distribution. These results
show us that the two methods produce different distributions of inefficiency measures. What
these distributions indicate is whether farmers are clustered towards the most efﬁcient end or
the ineﬂicient end of the distribution. The distribution of exponential case estimates shows
that farmers are clustered towards the efficient end. On the other hand, the distribution of the
half-normal case estimates of economic inefﬁciency show that only a few farmers are on the
most eﬁicient end. Having said this one should note that the most efficient end for the
exponential distribution start at level well beyond the medians of the distributions of the half-
normal case estimates. In addition we have no theoretical background on which to base any

expectations on what the ideal distribution of farm-level inefﬁciency should be.

7.2.4 Discussion of Results

The main highlight of this chapter is that on average communal farmers are between
11 and 22 percent inefﬁcient as shown on table 7.2. Overally it was noted that farmers are
oﬂ’ the economic optimum by between 10 and 46 percent. These rates are comparable to
what other studies have found in other parts of the world. Van Zyl et. al. (1995) found the
mean inefﬁciency relative to the best practice farms in the South African small-scale sector
ranging between 52 and 64 percent. Bravo-Ureta and Evenson (1994) found out that on
average peasant farmers in eastern Paraguay were economically inefﬁcient by 60 percent for
cotton and 48 percent for cassava. But in the North West Frontier Province of Pakistan,

small farmers were 1 1.5 percent inefficient (Parikh, Ali and Shar, 1995). The Pakistan results

152

are closer to those found in this study not only in terms of the average estimates but also in
the wide variations in estimates ﬁom one farm to the other".

The average inefﬁciency ranging between 11 and 22 percent means that on average
between 11 and 22 percent of the cost incurred could have been avoided without any loss in
output. These observations on their own do not lead to any conclusion about the communal
farmers’ level of economic eﬁciency. Clearly it is not possible to expect zero eﬁciency in
any production process. Some losses should always be expected even when the process is
automated. The question then is what is acceptable level of inefficiency. There are no clear-
cut answers to this question because this is equivalent to asking what is the expected or
acceptable ineﬁciency attributable to random events which are beyond the control of the
producers. With communal farmers some inefﬁciency is expected because of the importance
that is given to meeting the family’s subsistence needs. Farmers deviate from eﬁciency
ﬁ'ontier because they use shadow values, based on family subsistence needs, to allocate
resources at the farm. Again it is not easy to express this expectation in quantitative terms.

In chapter I it was hypothesized that communal farms would be considered eﬁcient
if the average inefﬁciency is below an arbitrarily determined ﬁgure of 10 percent. If this
ﬁgure is accepted as a threshold for determination of economic eﬁiciency, then we can
conclude that communal farmers are eﬁcient. Even though they can produce current levels
of output at lower costs, the cost savings would be, on average, between 1 and 12 percent“.

Thus, at current technology levels there are no signiﬁcant gains for communal farmers if they

 

" Parikh, Ali and Shar reported a range of between 3 and 42 percent for their estimates
of economic inemciency.

”The ﬁgures 1 and 12 percent are obtained from subtracting the hypothesized
“acceptable” 10 percent from the means levels of inefﬁciency shown in Table 7.2 that range
between 11 and 22 percent.

153

are to rearrange production so as to be closer to the frontier. In other words communal
farmers are relatively close to the efficiency frontier.

The above conclusion does not change signiﬁcantly if the distribution of the one-sided
error term is assumed to be exponential. The three season average of economic inefficiency
estimates ranges between 11 and 21 percent. Thus farmers would save about the same
amount of costs that was found for the half-normal case if they take measures to produce at
least 10 percent from the efficiency frontier. The cost savings of up to 12 percent are not
economically signiﬁcant. This change would not generate the changes in production that
would result in revolutionary change in the lives of communal farmers and their families. But
the change would still bring modest gains.

7.3 Determinants of Economic Inefficiency in Communal Agriculture

The next step is to identify factors responsible for the observed economic inefﬁciency.
Most of the socio-economic factors are not taken into account in the estimation of the cost
frontier ﬁinction following the dictates of the two-step procedure of estimating economic
efﬁciency”. The critics of this procedure argue that all variables should be incorporated
directly into the frontier models (Bravo—Ureta and Evenson, 1994). But estimating the
ﬁ'ontier models this way assumes that the variables directly affect efficiency and thus is at
odds with those who contend that socio-economic variables have an indirect effect on
production and hence efﬁciency (Kalirajan, 1991). Only further research can resolve this
relatively new and developing controversy in the literature on the estimation of ﬁrm efﬁciency.
In this study the estimated cost inefficiency are related to various farm-speciﬁc and

nonphysical explanatory variables.

 

7° The two-step procedure involves measuring farm-level efficiency ﬁrst and then
estimating a regression model where efficiency is expressed as a function of socio-economic
variables.

154

Because of unavailability of data it is not possible to relate cost inefficiency to farm-
speciﬁc and nonphysical variables for all the three seasons. Ifone had a choice of the season
that is representative of all the three seasons one would pick 1988/89. However, there is no
data on the proposed explanatory variables for this season. But it is the 1989/90 season for
which data on farm-speciﬁc and nonphysical data is available. As outlined in the preceding
chapter, the only blemish on the 1989/90 data is that it produces a cost model that has
evidence (at 6% signiﬁcance) of problems of omitted variables. But the 1989/90 cost model,
like the other models, is homogenous making it possible for us to make inference on the
underlying primal ﬁrnction. In fact there is no season with a perfect cost model as illustrated
in the last chapter. Thus there is no major loss in accuracy in identifying the determinants of

cost inefficiency ﬁ'om the 1989/90 data.

7.3.1 Farm-Speciﬁc and Nonphysical Variables
Farm-speciﬁc variables that may affect inefficiency include farm size, farm assets, farm
animals, annual cash remittances, soil type and location of the farm in terms of agro-
ecological consideration. The hypothesized relationships between these variables and fann-
level ineﬂiciency are as follows:
> As argued throughout this study, farm size is expected to be positively related to
farm-level inefficiency.
> The value of farm assets and farm animals are expected to be inversely related to

farm-level inefﬁciency as these two would allow ﬂexibility in farm operations.

155

3* Families that receive remittances from relatives working elsewhere should also be
more efficient because they have a reduced cash constraint. This contributes to farm
working capital".
> Farms that have fertile soils and/or are located in good natural regions are expected
to be closer to the efficiency frontier than those that are not. The soils variable is
expressed as a dummy variable with all sandy soils classiﬁed as poor and red and

black clays and loams classiﬁed as rich soils. Similarly location is presented as a

dummy variable with farms located in natural regions 11 and III classiﬁed as good

location and those in natural regions IV and V classiﬁed as poor location.

There are several nonphysical variables that could explain farm-level inefficiency. In
this exercise three variables characterizing the head of the household are used as explanatory
variables. These are age of the household’s head, years of education and years of farming
experience. The hypothesized relationship between these variable and farm-level inefﬁciency
is speciﬁed as follows:
> The number of years of education for the household head is expected to be inversely

related to inefficiency because farmers with more education are expected to commit

less mistakes.
> The household head’s years of experience in farming is also expected to be inversely

related to farm-level inefficiency in similar fashion to the expected effect of the years

of education on inefficiency.

 

7' This might appear to be at odds with the famous T.W. Schulz’s “poor but efficient”
hypothesis. But this hypothesis is an observation that farmers can be allocatively efficient
without being technically (and hence economically) efficient. In this study the focus is on
economic eﬂiciency which implies both technical and allocative efficiency.

156

> There is no clear relationship to assign between inefficiency and age. Because age
and experience should be positively correlated the former is dropped from the
analysis.

> The other household variable included in this exercise is the size of the farm work
force that includes adults and children”. Farms with more workers are expected to
be more efficient than those with less.

The other nonphysical variables used in this exercise include access to input markets
and use of credit. Access to input markets is represented by a dummy variable based on
whether the farmer bought inputs or not. Use of credit is expressed as a dummy variable
where one is assigned to farmers who used credit and zero to those who did not. An
important nonphysical variable not used in this exercise, because of data unavailability, is
access to extension.
> Farms that use purchased inputs are expected to be more efficient than those that do

not rely on these modern inputs.
> Similarly farmers who use credit are expected to be more efficient that farmers who

do not have access to credit.

We also look at two of the most common practices on communal farms; winter-
ploughing and use of manure. While these two practices might appear as indicators of
diﬁ’erent technology at the farms, it is their dependence on farm resources and most probably
farmer education and experience that persuade us to incorporate them in this analysis.
Winter-ploughing allows moisture conservation and better germination in the event of early

planting. Early planting have been shown to be associated with higher yields in the communal

 

n A family member aged between 15 and 70 years is taken as an adult-equivalent. A child
aged between 5 and 15 years or an adult older than 70 years provides 75 percent of an adult-
equivalent work.

157

areas (Shumba, 1985). Manure applications are known to improve the organic matter content

of soils. The inﬂuence of manure could be affected by use of fertilizer. These two inputs

have a synergistic effect. The use of manure and winter-ploughing are represented by dummy

variables. The hypothesized relationships are as follows:

> The farmers who winter-plough their ﬁelds should be more efficient than the farmers
who do not.

> Farmer who use manure as a source of organic matter to replenish soil fertility are

expected to be more efficient.

7.3.2 Regression Results
The relationship between estimated economic (cost) inefficiency and the various

explanatory variables is expressed as shown below:

EIE, = a0 + BIEDUC, + 525mm + p,W0RK, + mm,
+ BsLNVA. + I36LNLV. + MARE/W,- + BsBUY.

+ BgAFC, + prEG, + pHSOIL,
+ pawn/Pr + BI3MANUI + 6'

Where the dependent variable, EIE is the estimated measure of economic ineﬁiciency that is

obtained when the distribution of the one-side error term is assumed to be either half-normal

or exponential. In both cases EIE is expressed as a percentage.

158

The 13 independent variables are shown in the above equation are as follows:

1. EDUC = Years of education for the household head

2. EXPE = Years of farming experience for the household head

3. WORK = Number of adult equivalents working on-farm

4. AREA = Farm size (arable area)

5. LNVA = Logarithm of Value of farm implements and assets

6. LNLV = Logarithm of Value of farm animals

7. AREM = Amount remitted from relative working off-farm

8. BUY = Dummy variable for farmers who buy inputs

9. AFC = Dummy variable for farmers who use credit

10. REG = Dummy variable for natural agro-ecological regions

11. SOIL = Dummy variable for soil type

12. WINP = Dummy variable for farmers who winter-plough

13. MANU = Dummy variable for farmers who use manure

The two equations were estimated through ordinary least squares since the
relationship. The estimated parameter coefficients ((1,, and [3,) and t-ratios are presented in

tables 7.4 and 7.5.

159

Table 7.4: Relationship of Economic Inefficiency with Farm-Specific Variables; The

 

 

 

Half-Normal Case

Variable Label Variable Description Coefficient t-ratio
a0 Constant 22.1159 18.153"
0, Years of Education for Household Head -0.0563 -1.978**
[32 Years of Farming Experience -0.0082 -O.443
[33 Number of Adult Equivalents Available -0. 1017 -0.917
[3, Total Arable Area Available -0.0990 -1.562
[3, Logarithm of Value of Farm Assets 0.2799 1.429
B, Logarithm of Value of Farm Animals 0.1797 1.101
[3, Amount Remitted 0.0004 1.260
B, Purchased Inputs -1.5658 -2.932*"'
09 Use of Credit -0.4138 -0.673
[3,0 Natural Region -0.5567 -1.016
[3,, Soil Type 0.0353 0.218
[3,2 Winter-plough -1.2871 -2.669"‘ *
0.3 UseofMa9939 ____________________________ -. 919‘}? ______ - 9.??1 ......

Other Statistics: R2 = 0.091; R2 = 0.052; F(13, 305) = 2.35**

Notes: *"‘ = signiﬁcant at 5 % level; * = signiﬁcant at 10 % level

 

160

Table 7.5: Relationship of Economic Inefficiency with Farm-Specific Variables; The

Exponential Case

 

 

 

 

 

 

Variable Label Variable Description _--- Coefficient t-ratio
a0 Constant 21.2895 19.819”
B, Years of Education for Household Head 0.0409 1630*
B2 Years of Farming Experience -0.0106 -0.650
B3 Number of Adult Equivalents Available 0.0202 0.207
B, Total Arable Area Available 0.0750 1.343
B, Logarithm of Value of Farm Assets -0. 1812 1.049
B6 Logarithm of Value of Farm Animals -0.2447 -1.700"'
B7 Amount Remitted -0.0002 -0.575
B: Purchased Inputs 1.1647 2.473"
B9 Use of Credit -0.1940 -0.353
Bm Natural Region 0.7736 1.602
0,, Soil Type -0. 1 109 -0.776
B,2 Winter-plough 0.8752 2.058"
Bu 28.9953499939 ____________________________ 9 .5311 ..... 1245

Other Statistics: R2 = 0.067; R2 = 0.028; F(l3, 305) = 1.69’“

Notes: ** = signiﬁcant at 5 % level; * = signiﬁcant at 10 % level

 

The relationships represented by the coefficients shown in Tables 7.4 and 7. 5 have low
explanatory power. Collectively, the explanatory variables account for only 5 and 3 percent
of the variation in economic inefficiency for the half-normal and exponential cases,

respectively. However, these levels of explanatory power are typical of regression models

161

involving cross-sectional data. Furthermore, out of the 14 estimated coefficients (13 variables
and a constant), only 4 (constant, years of education, purchase of inputs and winter-
ploughing) are statistically signiﬁcant at 5 percent for the half-normal case. In the exponential
case, on the other hand, 3 and 6 coefficients are statistically signiﬁcant at 5 and 10 percent,
respectively. Of those variables that are signiﬁcant, the use of purchased inputs have the most
economically signiﬁcant coefficient even though use of these inputs only reduces ineﬂiciency
by 1.6 percent in the half-normal case. The coefficients shown in tables 7.4 and 7.5 are not
signiﬁcant economically even if they were statistically signiﬁcant.

In addition the number of variables with the expected signs are low (8 and 7 for the
half-normal and exponential cases, respectively). The signs on the variables differ between
the half-normal and exponential cases. Only Years of Farming Experience and Use of Credit
have the same signs in the two cases. Thus, the results shown in Tables 7.4 and 7.5 cannot
be used to draw strong policy recommendations. These results are used with the caveat that
they do not fully explain the relationship between farm-level efﬁciency and farm-level

characteristics.

7.5 Summary

This chapter presented the cost frontier and measures of economic inefficiency.
Economic inefficiency estimates were derived assuming the distribution of the one-sided error
term to be either half-normal or exponential. The two cases produced results that were
similar in terms of magnitude but different in terms of distribution. The main ﬁnding of this
process was that, on average, communal farmers are 15 percent inefficient. All of the three
seasons’ measures of inefficiency were within a range of 10 to 46 percent. There was

considerable across season variation.

162

Only the 1989/90 data was complete and detailed enough for an analysis of the
relationship between measures of economic inefficiency and 13 farm-speciﬁc variables
comprising of variables describing the household head, the resource endowment, and other
farm-level nonphysical factors. As is typical of regression models involving cross-sectional
data, the explanatory power of this relationship as shown by the coefficients of determination
(R2) was low. The signs on the coefficients were in line with expectations on 8 and 7
occasions for the half-normal and exponential cases, respectively. But only three of the 13
variables had coefficients that had the expected sign and at the same time were statistically
signiﬁcant at 5 percent level. The relationship was therefore found to be relatively

insufficiently informative to be used for deductive purposes.

163

CHAPTER VIII: SUMMARY, RECOMMENDATIONS AND CONCLUSION

8.1 Introduction

The objective of this chapter is to summarize the main ﬁndings of this study and then
draw some policy recommendations and conclusions. First, a summary of the main ﬁndings
are provided. The outline of this section closely follows that of the study. Then policy
recommendations that are based on the ﬁndings of the study are provided next. In the next
section these recommendations are qualiﬁed by a short discussion on the theoretical and
practical shortcomings of the study. The gaps identiﬁed in this section are the basis of the
recommendations for ﬁrture research work that are covered as part of concluding remarks in

the last section.

8.2 Summary of Findings and Recommendations

Zimbabwe’s agrarian structure is partly a creation out of the belief that large scale
fanns and estates are the best vehicle to transform an agricultural-based society into one
dependent on industrial production. It is also a product of policies that sought separate
development of the country’ s population on a racial basis. When the industrialization strategy
failed to structurally transform the economy, the system was not adjusted accordingly. In fact
policies were enacted to entrench large scale farming and reduce the competitiveness of small
scale family farms. However, close to half of the land in Zimbabwe is under communal
farming making any policy or program seeking to exploit the full productive potential of land
unrealistic if it ignores what is happening in communal areas.

The second chapter presented the literature on the inverse relationship between farm
size and economic eﬁiciency. Small farms are often more eﬁicient economically than large

farms even if capital and land markets are distorted in favor of large farms. This inverse

164

relationship between farm size and economic efficiency is due, mainly, to the dual nature of
the agricultural labor markets which allows small family farms to use labor more intensively
and incur less supervision costs than large, hired labor dependent farms. As shown in this
literature review, there are few studies in Africa in general, and Southern Africa in particular,
that address this issue even though farm size-efficiency issues are becoming increasingly
important as the land frontier is closing due to rapid population growth. This was one of the
motivation of this study. Data limitations, however, did not permit a comparison of
communal and commercial farmers in Zimbabwe.

The third chapter is a presentation of the characteristics of communal agriculture. The
description of communal area household demographic characteristics, household resource
endowments and the production practices and patterns that farm household use helps identify
the factors that explain the use of available resources at farm-level. This characterization
revealed that communal farmers operate a low-input system of crop—livestock enterprises that
have weak links with the market economy. Livestock and human labor are the major inputs
of crop enterprises. Crop production, as the main occupation, is not dependent on the
markets for inputs. The inputs that farmers purchase regularly are maize, cotton and tobacco
seed and fertilizer. But fertilizer is not widely used and when used it is applied at levels lower
than official recommendations.

The main purpose of the fourth chapter was to examine ways of expressing the
relationship between factors of production and output which is important in the measurement
of the eﬂiciency of communal agriculture. From the review of models relating factors of
production and output, duality theory afforded us an easier way of empirically estimating the
input-to-output relationship. Chapter four made the case for using dual functions to reﬂect
the process farmers use to maximize proﬁts given a set of output and input prices and a level

of output. The extension of the cost function to a generalized translog multi-product variable

165

cost function allows the estimation of a more general and ﬂexible function that does not
involve imposing restrictive assumptions. It is this general and ﬂexible translog multi-product
variable cost functional form that was used to estimate frontier ﬁinctions and, hence, the
estimates of farm-level economic efficiency.

Before using the recommended general and ﬂexible translog multi-product variable
cost firnction to represent the relationship between factors of production and output in
communal areas, the variables involved were described. As shown in the ﬁfth chapter the
variables used to estimate cost ﬁJnctions and frontier functions vary widely across farms and
seasons. This reﬂects the inherent variability characteristic of communal agriculture due to
geo-physical (rainfall and soil type) and socio-economic factors. The data, as shown in the
sixth chapter, produced estimates of generalized multi-product translog variable cost function
where the independent variables explained over 65 percent of the variation in farm-level
variable costs. But only a few variables have signiﬁcant coefficients suggesting that there
could be some econometric problems.

The main econometric problems examined were multicollinearity, heteroskedasticity,
errors in variable and measurement errors. Multicollinearity was not found to be a major
problem because precautions were taken to create indices out of variables (input prices and
area planted) which were found to be systematically correlated to values of output and with
each other. There was no signiﬁcant evidence of heteroskedasticity except in the 1988/89 cost
function. The omitted variable problem appears to exist in the 1989/90 cost function only if
the signiﬁcance level is set above the standard ﬁve percent.

The conformity of the cost ﬁrnctions with economic theory is assumed by the way the
translog cost ﬁrnction is speciﬁed. The most important conditions that are implicitly assumed

include concavity, homogeneity and homotheticity.

166

Measures of economies of scale were calculated from cost ﬁrnctions derived ﬁ'om
variables that were scaled by their means prior to being converted into logarithmic values.
The most striking ﬁnding was the presence of decreasing returns to scale in Zimbabwe’s
communal areas. This suggests that communal farms need more than just an increase in input
supply if they are to increase production signiﬁcantly. New technologies are required so that
farmers have an opportunity to produce outside the decreasing returns to scale region.

The main ﬁnding from estimating cost frontier functions and measures of economic
ineﬁciency was that, on average, communal farmers are 15 percent inemcient. All of the
three seasons’ measures of inefficiency were within a range of 10 to 46 percent. But there
was considerable across-season variation. Data availability only allowed the use of the
1989/90 data to relate measures of economic inefficiency to 13 farm-speciﬁc variables
comprising of variables describing the household head, the resource endowment, and other
farm-level physical and nonphysical factors. The explanatory power of this relationship was
low and a signiﬁcant number of coeﬁcients were not statistically signiﬁcant. The signs on
the majority of the coefficients changed depending on whether the distribution of the one-

sided error term was assumed to be half-normal or exponential.

8.3 Policy Recommendations

One of the major ﬁndings of this study is that there is economic inefficiency averaging
between 11 and 22 percent and an overall range of between 10 and 46 percent in communal
area agriculture in Zimbabwe. However, most farms are clustered around the mean range of
11 to 22 percent and an overall mean value of 15 percent. This means that current output
levels can be produced using less resources or more preferably, more output could be
produced using the same bundles of inputs that farmers currently use. If ineﬁiciency is

eliminated then, on average, production can be increased by up to 15 percent. This cannot

167

result in signiﬁcant changes in the living standards of the majority in communal areas. In
aggregate terms this may be a signiﬁcant change. But at the household level a 15 percent
increase over an already small output level is unlikely to make much of a difference. Clearly
the changes in production required for communal areas to break out of poverty will have to
be more than that obtained from just eliminating the estimated inefficiency. This leaves
unanswered the question of what is the most viable and appropriate mix of programs and

policies that will rehabilitate communal areas and revolutionalize overall living standards.

8.3.1 Technology Development and Transfer

Technology transfer is recommended in cases where farmers are found to be
economically inefficient. After ﬁnding levels of economic inefficiency ranging between 48 and
60 percent among peasant cassava and cotton growers in Paraguay, Bravo-Ureta and
Evenson (1994) recommended extension programs to move farmers towards the efﬁciency
ﬁ'ontier. Van Zyl et al (1995) also recommended intensiﬁcation of extension efforts in the
former homelands of South Africa when they found economic inefficiency levels ranging
between 52 and 64 percent. In such cases extension specialists would provide farmers with
information on the best use of existing technologies. If the extension programs succeed in
transferring the technologies to the farmers then, at most, production at fann-level would
increase by 60 percent. This could result in signiﬁcant changes in income and subsistence
levels.

Technology transfer may also be recommended in cases where farmers appear to be
economically efficient but are unaware of the availability of new production technologies

and/or how best to use them”. The low levels of inefficiency that are observed may be

 

’3 This occurs because the estimated frontier is basically a loci of the “best practices” by
farmers using information available to them. The question of what is the true frontier will be
discussed later on in this chapter.

168

reﬂecting a case where farmers are located on an efficiency frontier that is lower than the
potential deﬁned by the unknown technology. As a result care must be taken to ensure that
frontier functions are estimated from samples of farmers that have access to information on
how to use the best production technology available. Otherwise the estimates of economic
efﬁciency may end up being used to recommend inappropriate policies and programs.

In cases where the estimated economic inefficiency level is relatively small, as is the
case in the communal areas of Zimbabwe and the North West Frontier Province of Pakistan
(Parikh, Ali and Shar, 1995), the impact of extension programs would be greatly reduced.
Farmers are operating close to the efﬁciency frontier and can only signiﬁcantly increase
production if they move up to a new frontier. New agricultural technology developed for
communal area conditions create new efficiency frontiers and allow farmers to use current
resources to produce higher output levels. Investments in technology development have
produced high payoff levels in the past. The rates of return to past investments in maize and
cotton research and extension in Zimbabwe, averaging over 40 percent, were signiﬁcantly
higher than the opportunity cost of public ﬁmds (Kupﬁrma, 1994; Mudhara, et al, 1996).
New technologies should be developed speciﬁcally for communal agriculture based on the
faith that history will repeat itself as demonstrated by the fact that past well-planned
technology development and transfer investments generated high rates of return. The main
question is whether the success achieved from agricultural research approaches designed to
solve commercial agricultural problems could be replicated using new agricultural research
approaches that focus on the problems of semi-subsistence small family farms whose primary
aim is providing sufficient food for the family

To develop new and appropriate technology and transfer it to farmers requires that
sufficient ﬁnancial and manpower resources be committed over a long period of time (20 to

25 years). The availability of resources and time constrain the process of producing new

169

technology. Furthermore, the process is not definite as there is no guarantee that a new
technology will be developed and when. The main question then is whether there is enough
time to wait until science can accomplish all the tasks that society needs and expects. It is for
this reason that the technology development planning process should be thorough and be
managed by the best minds that agricultural sciences can provide. But science can provide
more efficient and effective means to organize national resources in the process of production
if investments in science are increased to enable the development of more comprehensive and
better calibrated scientiﬁc models. Science, in various forms, has sustained and shaped the
development of societies throughout the history of mankind even at times when popular belief
on its utility was negative. Ultimately it is the political will and resolve of national
governments that determine the ability of each nation to take full advantage of agricultural

science as a tool for economic and social development.

8.2.2 Land Reform

In addition to technology development, land reform programs are often recommended
when farmers are operating on or close to the efficiency frontier. Farmers are resettled on
land taken from inefficient users or newly opened for agricultural use. The objectives of such
a program include efﬁciency and/or equity. Without data from the other farm types in
Zimbabwe it was not possible to identify the most efficient farm type raising the question of
what would be foregone if other types of farms are transferred to communal farmers. Thus
this study does not provide enough evidence for one to recommend land transfers in
Zimbabwe. The efficiency of other farm types have to be established in order to give an
indication of the opportunity costs of land reform programs. Furthermore, the economic and
environmental cost of implementing land reform programs and the time it takes for the new

settlers to restore current production levels should all be taken into account.

170

However, many land reform programs are often implemented for egalitarian purposes
and to stem the political agitation that normally accompanies inequality in access to land. In
Zimbabwe there is general agreement, even among the commercial farmers, that there should
be some redistribution of land for the beneﬁt of the landless and near landless residents of
communal areas (Swanepoel, 1997). Power relations based on class play a major role here.
Indeed the success of a land reform program is dependent on the balance of power between
the new and old political coalitions. But these issues are beyond the scope of the economics
discipline which offers limited insights into the process that is predominantly social and
political (Zimmerman and Carter, 1996). Because a land reform program involves changing
the land ownership structure, measures must be taken to change the social and political
relations to minimize the inevitable conﬂict. But changing social relations and political
coalitions is, admittedly, a difficult process to set in motion. Often it is the spontaneous
emergence of strong socio-political coalitions that permits land transfers. In Zimbabwe
reports of land invasions by communal area residents that began to appear in the popular
press since June 1998, indicate that the pressure for a far-reaching land redistribution program
is mounting. In fact, spontaneous settlements have been more successful than those that are

planned and tightly managed (Kinsey and Binswanger, 1993).

8.4 Limitations of the Study

This study, like many others of its type, has a number of shortcomings despite
considerable efforts to circumvent them. In this section we will resist the urge to address all
identiﬁed shortcomings. We will concern ourselves with just two shortcomings (data quality
and availability and methodological issues) that we believe to have signiﬁcantly affected the

outcome of this study. This does not in anyway mean that the shortcomings apparent in this

171

study but not addressed here can be assumed away as insignificant. They do affect the study’s

outcomes, and all opportunities to avoid them were taken ﬁill advantage of.

8.4.1 Data Quality and Availability

As in many quantitative studies, there is always a problem of insufficient data. This
study is no exception. The data used in this study were not collected speciﬁcally for this
exercise. As a result some data that are speciﬁc to estimating measures of economic
efficiency were not available. When data was retrieved from the Ministry of Agriculture data
ﬁles, some important variables could not be obtained. For instance, we could not locate the
1988/89 and 1992/93 data on household characteristics. In addition, a lot of observations had
to be thrown out because certain key variables were missing. This reduced the sample sizes
signiﬁcantly and affected the quality of the analysis.

Besides data availability problems, there are problems of data quality. The fact that
we had no control over the data collection process leaves us with limited options to improve
data quality. Because of the timing of this study, it was not possible to go back to the ﬁeld
to cross check the values which were found to be out of expected ranges. The only option
at our disposal was to delete such observations from the analysis. Through this thorough data
cleaning exercise, some control over data quality was exerted. Most of the quality control,
such as in-ﬁeld supervision and data entry, was performed by the Ministry of Agriculture staff.

The question often asked about poor data availability and quality is whether it is
prudent to go ahead with the analysis. The answer is straight-forward when it is judged that
no reasonable conclusions can be reached from analysis based on insufficient and/or poor
quality data. But the line that separates when to and not to proceed with analysis using data
with such problems is hard to draw. Most often the decision to use problem data is based on

the realization that no other better quality data is likely to be available in the near future and

172

that there is urgent demand for information that such an analysis would provide. Sometimes
such analysis will provide important indications that can aid decision making. When decisions
are being based on no information at all, there may be merit in proceeding with the analysis

so as to provide the policy-making process with some information.

8.4.2 Methodological Issues

The other major weakness of the study has both methodological and philosophical
dimensions that are hard to disentangle fully in a discussion like this. Following Forsund, et
al (1980) this study raised the issue of what a cost frontier stands for as compared to an
“average” cost function. The deﬁnition of a cost frontier as a loci of minimum levels of costs
that can be attained to produce a given level of output, given a set of input prices, leaves us
asking whether the minimum is with respect to the sample, the population or the technically
feasible scenario. The ﬁrst two deﬁne the best-practices observed and are used in the
estimation of both deterministic and stochastic frontier ﬁinctions. The question here is do
these converge to or approximate the true cost frontier" as deﬁned by the best available
technology (or the third scenario). 1f farmers are not aware of the best available technology
then the practice of using the observed best-practices as a basis for constructing a frontier
function and calculating measures of inefficiency is clearly ﬂawed. There are several obstacles
that could prevent communal farmers from knowledge of the true frontier. Whatever these
are, the bottom line is that we may end up using the ‘wrong’ frontier to evaluate the efficiency

of a production system. Our inability to estimate frontier ﬁrnctions that incorporate ‘known’

 

7" The true cost frontier must be deﬁned by the minimum levels of costs with respect to
the technically feasible levels which are well known by farmers as competitive markets do not
have information asymmetries.

173

gaps between current practices and the best practices poses a methodological development
problem that has to be resolved.

Somewhere in this study we pointed out the problem of assigning to the one-sided
error term a known distribution without theoretical grounding. There is no way of knowing,
apriori, how fann-level inefficiency is distributed. Even though alternative speciﬁcation of
the one-sided error term allows some form of sensitivity analysis, the question of the
theoretical basis of the distribution assumption still remains. This study imposed these
distributions without sufficient theoretical justiﬁcation. There were differences in the
distribution of economic efficiency estimates between the half-normal and exponential cases.
When the two sets of economic efficiency estimates were regressed on farm-level variables
they produced different results. These observations call for ﬁthher investigation of the a
priori distribution of farm-level economic efficiency to establish, on a theoretical basis, the
distribution that best represents real world circumstances.

Several other methodological shortcomings are apparent in this study. In most cases
methodological developments have lagged behind theory and desire. This is particularly true
if one considers the “Greene Problem”. Theory suggests that the errors made in using inputs
translate into higher costs. But the development of a functional form that takes this
relationship into account continues to this day, close to 20 years aﬁer Greene discovered this
problem. In this study this problem was not taken into account because of the absence of
appropriate methods. The separation of technical and allocative efficiency was thus not

possible without adequately resolving the “Greene Problem”.

174

8.5 Future Research Work

Given the data problems encountered in this study, there is need to collect new data
sets speciﬁcally for estimating efficiency, and then to compare results. There is also need to
estimate the efﬁciency levels of other farm types (resettlement areas, small-scale commercial
and large-scale commercial) and, if possible, compare results across farm types. Estimates
of economic efﬁciency obtained from panel data sets should be compared to estimates from
cross-sectional data sets

The observed differences in estimates of economic efficiency when the assumption
about the distribution of the one-sided error term changes is an issue that needs ﬁrrther
investigation. Are mistakes made by agricultural producers distributed as half-normal, gamma
or exponential? Under what circumstances would each of these distributions apply? Is there
something that can be gleaned from production or economic theory in general to help identify
the most appropriate distribution? Future methodological studies should try to answer some
of these questions.

The suggestion that technology development and transfer and land reform programs
are possible intervention tools to develop communal areas demands studies based on ex ante
evaluations of the beneﬁts and costs involved. There also should be in-depth evaluations of
other agricultural and non-agricultural options. Most communal areas are located in areas
not suitable for crop production at all. Maybe in these areas, agriculture is not the most viable
option of using available resources. It may be that communal farmers could specialize in
producing other types of goods and services from which they can earn sufficient income to
meet their food and non-food needs through purchases. Studies that address this issue
should pay particular attention to institutional reforms (especially food markets) necessary for

this to work effectively and efﬁciently.

175

The other area that researchers have shied away from is the factors determining the
formation and development of farmer organization and institutions. Interest should be on the
dynamics of such organizations and institutions and how they can contribute to changes that
are as complex as agrarian reform. One of the crucial issues is the different ways that can be
employed to improve the effectiveness of organizations that are set up to serve many and
geographically dispersed poor farrners._ The economics discipline has tended to leave this area
to political and other social science disciplines. But the developments in institutional
economics offers the best promise for the discipline of economics to contribute signiﬁcantly
to a proper understanding of the political and social organizational issues that characterize

small-scale farming.

176

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189

APPENDIX

A.1: THE MINISTRY OF AGRICULTURE SURVEY QUESTIONNAIRE

190

MEISTRY QF LANDS, AGRICULTURE AND RURAL RESETTLEMENT
(Farm Management Research Section - FMRS)

EQQRD 050 - ﬁenoral Information

19. Enumerator

20. Name of Head of Household
21. Village

22. District

23. Number of Years Farming

 

 

 

 

 

RE 100 - i e onomic haracteri tic
1. Ask for a full list of all the household members and indicate whether resident (R) or non-
resident (N) next to name.

 

FNamelR/N lRelationship Age Sex Attending Highest Principal Approx.
to Head of M/F School? Ed. Level Non-farm Annual
[Household Y/N Occupation Remittance

 

 

 

 

 

 

 

 

 

 

 

 

 

REQQRD 150 - Inventory of Assets

ASSET CODE QUANTITY AGE ORIGINAL COST CURRENT SALE
($) VALUE (3)

 

 

 

 

 

 

 

 

 

 

191

ASSET CODES

..................................................................................................................................................................................

 

Ox-plough PL Spraying Equipment SE
Harrow HA Hoes HO
Ox-cultivator CV House (mud & thatched) MT
Scotch cart SC House (brick & thatched) BT
Wheel-barrow WB House (brick & corrugated) BC
Water cart WC Storage facilities SF
Chains CH Picks PI
Axes AX Shovels SH
Maize shellers MS Others (Specify) OT

 

RECORD 200 - Farm Structure/Characteristics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Plot/Field Last Year Number Area Approximate Soil type
Number of paces (ha) distance from (ode)
Main Minor homestead
Crop Crop (km)
(or fallow) (if any)
Garden
Total Arable Area (ha) -------------- (NB 1 acre = 0.4 ha)
SOH. TYPE CODES:

 

{Black Clayey BC Red Clayey RC

    
   

Sandy Soils S Sandy Loamy SL

Loamy Soils L Other (Specify)

192

REQQRD 250 - Livestock Composition

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Type Number Health Uses in Value per Animal
of Condition Order of (8)
Animals Importance
1 2 3 3
CATTLE
Bulls
Cows
Oxen
Heifers
Steers
Calves
HEALTH CODES:
01 Excellent 03 Average/Reasonable
02 Good 04 Poor
USE CODES:
DR Draught EX Exchange of Animals LO Lobora (bride mic?)
MA Manure BR Breeding ME Meat (home use)
SA Sale of Animals PR Prestige/Status EG Eggs
SM Sale of Meat TR Transport Other (Specify)

 

 

193

REOORD 350 - Pre-Rainv Season Operations

Did you do winter ploughing last season?

1.
2.

Did you apply (a) manure?
(b) fertilizer?
Did you purchase inputs such as seeds?

Did you receive an AFC loan last year?

If no, What are the reasons?

Yes/No
Yes/No
Yes/No
Yes/No
Yes/No

 

EOORD 300 - Cropping Patterns (Previous Seoson)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

iPlot Crop Area Sales Gifts &/or Retention Distance Means of lCost of Soil
lio. (fallow)lhvstd xchanges bags ito point Transport Transport Type
(ha) Qty Total Qty Reason 0f sale iper bag
bags value bags (km) (S)
SOIL TYPE CODES:
Black Clay Soils BC Red Clay Soils Rc\
Sandy Soils S Sandy Loams SL
Loamy Soils L Other (Specify)

Note: Ifinter-cropped show both crops on the same plot number.

 

RECORD 380 - Input Stocks

 

 

 

 

 

[Crop

Input

Source

LCode

Quantity

Total Means of

Cost Transport

Transport
Charge

Month & Year lComments
of Purchase

 

 

 

 

 

 

 

 

 

REOORD 400 - Land Preparations

 

 

 

 

Cropbperation(s)

0.

Draft power
Own/hired
cost (8)

Adult labor hrs

Child labor hrs

Area

 

OwnlI-IiredlCost

Own Hired Cost

overed

Comments

 

 

 

 

 

 

 

 

 

194

 

 

 

 

 

 

RECORD 450 - Planting Operations

 

lMo. &

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Crop Draft Power Adult labor hrs. Child labor hrs. Seed Used Fertilizer Used
No. of
days Own/hired Own Hired Cost Own 'red Cost [Type Qty Area Type Qty
CW6) Planted ert.
REOORD 500 - Chemical Application
Crop Fertilizer/ lMonth No. of Area Adult labor hrs. Child labor hrs. Comments
Chemicals days (ha)
Type by Own liired Cost Own Hired Cost
REOORD 550 - Weeding Operations
Crop Operation to. of Area iDraft power Adult labor hrs. Child labor hrs Calculations
ays covered
(ha) Own/hired Own Hired Cost Own Hired Cost
Cost
REOORD 600 - Harvesting (up to grain preparation)
Crop Operation IMO. o. of Adult labor hrs Child labor hrs. Area Quantity Transport Home
pays Own Hired Cost Own Hired ﬂost Loads Bags lMethod Dist. Cost

 

 

 

 

 

 

 

 

 

 

 

195

 

 

 

 

 

 

 

 

 

 

 

OPERA TIONS:

 

        
     
       
   

Millets, S/F lower, Rice G/Nuts, R/NutsLowpeas Maize

1. Cutting heads 1. Lifting 1. Cutting
2. Transporting 2. Transporting 2. Stacking
3. Threshing 3. Plucking 3. Threshin
4. Winnowing 4. Drying 4. Bagging
5. Bagging 5. Winnowing

6. Bagging

RECORD 650 - Marketing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Crop IMo. Sales Gifts and Receptions Transport Market
Exchanges to market
Qty Value Qty Reason Qty Value Type/ Cost Type [Distance
@388) (3) (13388) (13388) (5) [Form (3) (km)
MARKET TYPE CODES;
Local shop/store LS Local farmer LF
Cooperative COOP GIVHB depot GMB-D
GMB collection point GMB-CP GMB approved buyer GMB-A

Others (Specify)

   

RECORD 700 - Overhead Expenditures: Repairs and Maintenance

 

 

Operation Items Repairs Done Material Costs Labor hours

Own Hired Cost

 

 

 

 

 

 

 

 

 

 

 

196

RE RD 700 - Overhead Ex enditures: Purchases and New Constructions

 

Operation Items Approximate Material Costs Labor hours

useful life Own Hired Cost

 

 

 

 

 

 

 

 

 

 

 

OVERHEAD ITEMS:
Eguipmont Facilities \

 

   
     
 

l. Ploughs 5. Shellers 1. Fences 5. Contour ridges
2. Yokes & harnesses 6. Planters 2. Dams 6. Drainage ditches
3. Scotch carts 7. Harrows 3. Kraals 7. Houses

 

4. Cultivators 8. Others 4. Storage 8. Others

      

    

RECORD 750 - Non-Farm Activities

1. Ask the family whether they are in activities outside their normal farnring business such
as handicraft, cutting grass, being hired out, brewing and selling beer, etc.

 

 

2. Ask for the amount received as remittances.
Activity(ies)/Source Family members Income generated Uses/Comments
involved* (cash or in kind)

 

M F m f

 

 

 

 

 

 

 

 

 

 

 

* MEMBER CODES:
M — Male Adults m —- Male Children
F -— Female Adults f — Female Children

197

RECORD 800 - Ch_angs in Livestock Numbers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Animal pening Livestock Number Month Value Sale of Produce iLivestock [Cost
Type Stock Change Received Operation (8)
(number) |Code or Paid Item Code Qty Value (specify)

[Bulls

ows
[Oxen

eifers

teers
[Calves
I[Others
LIVESTOCK CHANGE CODES;

S - Sales B - Births D0 - Donations Ou

P-

Purchases

SL — Slaughtered

D—
0.

Deaths

Others (specify)

198

D1

Donations In

 

 

APPENDIX

A2: FIGURES AND GRAPHS

199

 

1.5

1.0‘

.51

 

 

 

_

D
____..
ll—O

 

0.0

Residuals

-51

-1.0t

 

-1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0

Figure Al:

m!
...s
O
at
U!
N
O
N
0|
or
0

Log of Total Arable Area
Plot of Residuals on Total Arable Area, 1988/89

200

3.5

 

2.5
2.0‘
15q

19. I,

i. W: ii 11H 11 ll
’1 H H ' .

ll‘

 

Residuals
‘1‘

'_C

=__.

 

 

 

 

 

 

 

 

-5 1

1 l

 

 

 

 

 

 

 

l

l l
r

l

-1.0‘

 

 

 

1.5 2.0 2.5

“I
O

0.0

Log of Total Arable Area
Figure A2: Plot of Residuals on Total Arable Area, 1989/90

201

 

3.0

 

20

15‘

101

51

 

 

 

 

Residuals

00

-1.0‘

 

45

 

 

 

 

 

 

 

 

 

 

 

', ‘. ll:
11 ,1th ,.ﬂl

 

 

 

 

'

 

 

 

00

Figure A3:

I I U U i

.5 1D 15 20 25

Log of Total Arable Area
Plots of Residuals on Total Arable Area, 1992/93

202

3D

 

1.5

10‘

5|

 

 

 

 

 

0.0

Residuals

-1.0‘

 

 

 

-1 .5

 

 

 

l , .
hi i i :1 j I
Jill] i .l if 1 I:' l '

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure A4:

10

and
or
‘1
m
to

Log of Farm Assets Value

Plot of Residuals on Farm Assets Value, 1988/89

203

11

 

2.5

2.0 "

15‘

1.0‘

Residuals
‘2

 

 

 

0.0

-.5 ‘

-1.0‘

-1.5

 

 

, 1 All i l 5:.
ll ‘1 1111 1w I'lu‘l ..

 

 

 

Figure A5:

Log of Farm Asset Values
Plot of Residuals on Farm Assets Value, 1989/90

204

GI

10

 

15

1.0l

5i

 

 

 

 

0.0

Residuals

-51

-1.0‘

 

-1 .5

 

 

 

#—

 

" T ‘ . i" 1|
i] . ll 1 "I _’l

 

 

 

 

 

 

 

 

 

 

 

. l (lull, l“ W "

l .
lull
ill '

I

 

 

 

 

 

Figure A6:

we
on

4 3 5
Log of Livestock Values
Plot of Residuals on Farm Livestock Value, 1988/89

205

01

10

 

2.5

2.0 ‘

15‘

1.0‘

Residuals
‘1‘

 

 

ill I i ll I II. “I II II

 

0.0

-5'

-1.0‘

 

-1 .5

 

 

 

 

Til» . I
II“: II II II"‘II I

 

 

Figure A7 :

I I i

4 6 8 10

Log of Livestock Values
Plot of Residuals on Farm Livestock Value, 1989/90

206

12

Frequency
72

 

-I

.I

 

 

 

10.0 10.2 10.4 10.6 10.8 11.0 ll.2 11.4 11.7 [1.9
Economic lneﬂ‘iciency (%)

Figure A8: Distribution of Farm-level Economic Inefficiency; Half-Normal Case,

1988/89.

207

Frequency

 

an
IV

 

 

 

10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 [2.4
Economic Ineﬁ‘iciency (%)

Figure A9: Distribution of Farm-level Economic Inefficiency; Exponential Case,

1988/89.

208

Frequency
48

 

36" ——————————————————————————————————————————————

 

 

   

26. 7

11.9 13.5 15.2 [6.8

Economic Inefﬁciency (%)

Figure A10: Distribution of Farm-level Economic Inefficiency; Half-Normal Case,

1989/90.

209

Frequency
136

 

 

 

 

 

 

17.6 20.5 23.3 26.1 29.0 31.8 34. 7 37.5 40.3 43.2

Economic lneﬁiciency (%)

Figure All: Distribution of Farm-level Economic Inefficiency; Exponential Case,

1989/90.

210

Frequency
5.?

 

 

 

   

9.8 10.5 11.2 11.9 12.6 13.2 [3.9

Economic Inefﬁciency (%)

Figure A12: Distribution of Farm-level Economic Inefficiency; Half-Normal Case,

1992/93.

211

Pfequency
146

 

35‘

 

 

 

12.6 13.4 14.3 15.1 15.9 16.8 17.6 18.5

Economic Inefﬁciency (%)

Figure A13: Distribution of Farm-level Economic Inefficiency; Exponential Case,

I992/93.

212

APPENDIX

A3: TABLES

213

 

 

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mama. 80. 309.30... NEE—020 0m m mean—Ea. wane 0: 80.0 83:83:: @353.
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manna—:8“. main—a 209.30: 5880: 309.30: 2:: Em: 309.30: 2:: Em:
39.3 33.2 80 men 039.30: enoemE new. 530 9.9—mg aux
comma 88.80. mama—:0: 038.08.

 

M058” GEE Ea mgeg Bow.

214

Lnntvc
Lnnpl
Lnnms
Lnnls
Lnnss
Lnncs
anm
anl
Luvs
anc
Lnta
ana
Lnlv
anlpl
anlms
anlls
anlss
anlcs
anlvm
anlvl
anlvs
anlvc
anlta
anlva
anllv
ansms
ansls
an sss
anscs
ansvm

ansvl

VARIABLE NAMES (Tables A2-A4 and A6-Al l)

Logarithm of Total Variable Costs

Logarithm of Labor Price

Logarithm of Maize Seed Price

Logarithm of Legume Seed Price

Logarithm of Small Grains Seed Price

Logarithm of Cash Crop Seed Prices

Logarithm of Maize Output Value

Logarithm of Legume Output Value

Logarithm of Small Grains Output Value

Logarithm of Cash Crop Output Value

Logarithm of Total Crop Area

Logarithm of Value of Farm Assets

Logarithm of Value of Livestock

Logarithm of Labor Price * Logarithm of Labor Price

Logarithm of Labor Price * Logarithm of Maize Seed Price

Logarithm of Labor Price * Logarithm of Legume Seed Price

Logarithm of Labor Price * Logarithm of Small Grain Seed Price

Logarithm of Labor Price * Logarithm of Cash Crop Seed Price

Logarithm of Labor Price * Logarithm of Maize Output Value

Logarithm of Labor Price * Logarithm of Legume Output Value

Logarithm of Labor Price * Logarithm of Small Grains Output Value

Logarithm of Labor Price * Logarithm of Cash Crop Output Value

Logarithm of Labor Price * Logarithm of Total Crop Area

Logarithm of Labor Price * Logarithm of Farm Asset Value

Logarithm of Labor Price * Logarithm of Livestock Value

Logarithm of Maize Seed Price * Logarithm of Maize Seed Price

Logarithm of Maize Seed Price * Logarithm of Legume Seed Price

Logarithm of Maize Seed Price * Logarithm of Small Grain Seed Price
Logarithm of Maize Seed Price “ Logarithm of Cash Crop Seed Price

Logarithm of Maize Seed Price * Logarithm of Maize Output Value

Logarithm of Maize Seed Price * Logarithm of Legume Output Value

215

ansvs
ansvc

ansta

ansva

anslv
Lnlsls
Lnlsss
Lnlscs
Lnlsvm
Lnlsvl
Lnlsvs
Lnlsvc
Lnlsta
Lnlsva
Lnlslv
Lnssss
Lnsscs
Lnssvm
Lnssvl
Lnssvs
Lnssvc
Lnssta
Lnssva
Lnsslv

anscs

ansvm

ansvl
ansvs
ansvc
ansta
ansva

anslv

anmvm

Logarithm of Maize Seed Price * Logarithm of Small Grains Output Value
Logarithm of Maize Seed Price * Logarithm of Cash Crop Output Value
Logarithm of Maize Seed Price * Logarithm of Total Crop Area
Logarithm of Maize Seed Price "‘ Logarithm of Farm Asset Value
Logarithm of Maize Seed Price * Logarithm of Livestock Value
Logarithm of Legume Seed Price * Logarithm of Legume Seed Price
Logarithm of Legume Seed Price * Logarithm of Small Grain Seed Price
Logarithm of Legume Seed Price * Logarithm of Cash Crop Seed Price
Logarithm of Legume Seed Price * Logarithm of Maize Output Value
Logarithm of Legume Seed Price * Logarithm of Legume Output Value
Logarithm of Legume Seed Price * Logarithm of Small Grains Output Value
Logarithm of Legume Seed Price * Logarithm of Cash Crop Output Value
Logarithm of Legume Seed Price * Logarithm of Total Crop Area
Logarithm of Legume Seed Price * Logarithm of Farm Asset Value
Logarithm of Legume Seed Price * Logarithm of Livestock Value
Logarithm of Small Grain Seed Price * Logarithm of Small Grain Seed Price
Logarithm of Small Grain Seed Price * Logarithm of Cash Crop Seed Price '
Logarithm of Small Grain Seed Price * Logarithm of Maize Output Value
Logarithm of Small Grain Seed Price * Logarithm of Legume Output Value
Logarithm of Small Grain Seed Price * Logarithm of Small Grains Output Value
Logarithm of Small Grain Seed Price * Logarithm of Cash Crop Output Value
Logarithm of Small Grain Seed Price * Logarithm of Total Crop Area
Logarithm of Small Grain Seed Price * Logarithm of Fami Asset Value
Logarithm of Small Grain Seed Price * Logarithm of Livestock Value
Logarithm of Cash Crop Seed Price “ Logarithm of Cash Crop Seed Price
Logarithm of Cash Crop Seed Price * Logarithm of Maize Output Value
Logarithm of Cash Crop Seed Price "‘ Logarithm of Legume Output Value
Logarithm of Cash Crop Seed Price * Logarithm of Small Grains Output Value
Logarithm of Cash Crop Seed Price * Logarithm of Cash Crop Output Value
Logarithm of Cash Crop Seed Price "‘ Logarithm of Total Crop Area
Logarithm of Cash Crop Seed Price * Logarithm of Farm Asset Value
Logarithm of Cash Crop Seed Price * Logarithm of Livestock Value
Logarithm of Maize Output Value * Logarithm of Maize Output Value

216

anmvl

anmvs

anmvc

anmta

anmva

anmlv
anlvl
anlvs
anlvc
anlta
anlva
anllv
ansvs
ansvc
ansta
ansva
anslv
ancvc
ancta
ancva
anclv
Lntata
Lntava
Lntalv
anava
analv
Lnlvlv
anyld
Soildv
Naredv

Logarithm of Maize Output Value * Logarithm of Legume Output Value
Logarithm of Maize Output Value * Logarithm of Small Grains Output Value
Logarithm of Maize Output Value * Logarithm of Cash Crop Output Value

Logarithm of Maize Output Value * Logarithm of Total Crop Area
Logarithm of Maize Output Value * Logarithm of Farm Asset Value

Logarithm of Maize Output Value * Logarithm of Livestock Value
Logarithm of Legume Output Value * Logarithm of Legume Output Value
Logarithm of Legume Output Value * Logarithm of Small Grains Output Value
Logarithm of Legume Output Value * Logarithm of Cash Crop Output Value
Logarithm of Legume Output Value * Logarithm of Total Crop Area
Logarithm of Legume Output Value * Logarithm of Farm Asset Value
Logarithm of Legume Output Value * Logarithm of Livestock Value
Logarithm of Small Grains Output Value * Logarithm of Small Grains Output Value
Logarithm of Small Grains Output Value * Logarithm of Cash Crop Output Value
Logarithm of Small Grains Output Value * Logarithm of Total Crop Area
Logarithm of Small Grains Output Value * Logarithm of Farm Asset Value
Logarithm of Small Grains Output Value * Logarithm of Livestock Value
Logarithm of Cash Crop Output Value * Logarithm of Cash Crop Output Value
Logarithm of Cash Crop Output Value * Logarithm of Total Crop Area
Logarithm of Cash Crop Output Value * Logarithm of Farm Asset Value
Logarithm of Cash Crop Output Value * Logarithm of Livestock Value
Logarithm of Total Crop Area * Logarithm of Total Crop Area
Logarithm of Total Crop Area * Logarithm of Farm Asset Value
Logarithm of Total Crop Area * Logarithm of Livestock Value
Logarithm of Farm Asset Value * Logarithm of Farm Asset Value
Logarithm of Farm Asset Value * Logarithm of Livestock Value
Logarithm of Livestock Value * Logarithm of Livestock Value
Logarithm of Maize Yield (per hectare)

Dummy Variable for Soil Type
Dummy Variable for Natural Region

217

Table A2:

Cost Function Parameter Estimates, 1988/89

 

 

 

 

Source I 53 df Number of obs 425
--------- +--------—----—-----------—---- F( 92, 332) = 13.23
Model I 281.767943 92 3.06269503 Prob > F = 0.0000
Residual l 76.8721046 332 .231542484 R-squared = 0.7857
--------- +--------------—-------—------- Adj R-squared = 0.7263
Total I 358.640048 424 .845849169 Root MSE = .48119
lnntvc Coef. Std. Err. t P>|t| [95% Conf. Interval]
lnnpl 2.181935 1.876374 1.163 0.246 -1.509145 5.873016
lnnms .32642 1.708949 0.191 0.849 -3.035313 3.688153
lnnls 1.841902 1.253991 1.469 0.143 -.6248666 4.308671
Inns: -.1978079 1.825438 -0.108 0.914 —3.788691 3.393076
lnncs -.3453092 1.247514 -0.277 0.782 -2.799337 2.108719
lnvm .2375073 .3166138 0.750 0.454 -.3853147 .8603293
lnvl .2753739 .1603579 1.717 0.087 -.0400717 .5908196
lnvs .2348941 .1713046 1.371 0.171 -.1020851 .5718733
lnvc -.1078715 .1594815 -0.676 0.499 -.4215932 .2058502
lnta 1.301403 1.519228 0.857 0.392 -1.687124 4.28993
lnva -.2465336 .342116 -0.721 0.472 -.9195219 .4264548
lnlv -.9414897 .3662787 -2.570 0.011 -1.662009 -.22097
lnplpl .4928374 .7163851 0.688 0.492 -.9163888 1.902064
lnplms .5713693 1.439168 0.397 0.692 -2.259668 3.402406
lnplls -1.112583 1.29843 ~0.857 0.392 -3.666771 1.441605
lnplss -.280558 1.588426 -0.177 0.860 -3.405206 2.84409
lnplcs -.0766641 .8536051 -0.090 0.928 -1.755821 1.602492
lnplvm -.1356581 .1219556 -1.112 0.267 -.3755613 .1042451
lnplvl -.064935 .0699666 -0.928 0.354 -.2025687 .0726988
lnplvs .0879258 .0636784 1.381 0.168 —.0373383 .2131899
lnplvc .0960029 .0770975 1.245 0.214 —.0556583 .2476641
lnplta -.0062507 .5570305 —0.011 0.991 -1.102005 1.089504
lnplva -.1705082 .1083388 -1.574 0.116 -.3836253 .0426088
lnpllv .1556421 .1229563 1.266 0.206 —.0862295 .3975136
lnmsms -.2810722 .7042502 -0.399 0.690 —1.666427 1.104283
lnmsls —1.435706 1.409949 -1.018 0.309 -4.209267 1.337855
lnmsss —1.325868 1.443191 -0.919 0.359 -4.164818 1.513083
lnmscs .163998 1.046098 0.157 0.876 -1.893817 2.221813
lnmsvm -.0247498 .167273 -0.148 0.882 —.3537983 .3042988
lnmsvl -.0333283 .0805488 -0.414 0.679 ~.1917787 .1251221
lnmsvs -.0948619 .0775081 .224 0.222 -.2473308 .0576069
lnmsvc .0260666 .0890902 .293 0.770 -.1491858 .201319
lnmsta .1846572 .7228257 .255 0.799 —1.237239 1.606553
lnmsva .1462234 .1323523 .105 0.270 -.1141315 .4065784
lnmslv .10494 .1568918 .669 0.504 -.2036873 .4135673
lnlsls -.6999541 .4353748 .608 0.109 -1.556395 .156487
lnlsss -.4132391 1.218865 .339 0.735 -2.810911 1.984433
lnlscs -.4675326 1.172373 .399 0.690 -2.773749 1.838684
lnllvn. .2330831 .0995754 .341 0.020 .0372048 .4289614
lnlsvl .0461964 .0600599 .769 0.442 -.0719496 .1643424
lnlsvs .032191 .053128 .606 0.545 -.072319 .136701

 

218

Table A2: Cost Function Parameter Estimates, 1988/89; Cont.

 

 

 

lnntvc I Coef. Std. Err. t P>ItI [95% Conf. Interval]
lnlsvc I -.0353689 .0677167 -0.522 0.602 -.1685767 .0978389
lnlsta I .2274562 .3684577 0.617 0.537 -.4973498 .9522623
lnlsva I .0043063 .0839675 0.051 0.959 -.l608691 .1694817
lnlslv I ~.1322264 .0982885 ~1.345 0.179 -.3255731 .0611203
lnssss I -.8773263 1.004936 -0.873 0.383 —2.854171 1.099518
lnllos I 2.781 1.238367 2.246 0.025 .3449651 5.217036
lnssvm I *.0265365 .1338814 ~0.l98 0.843 ~.2898993 .2368263
lnssvl I -.0609989 .0638254 -0.956 0.340 -.186552 .0645543
1nssvs I -.0298169 .0765842 -0.389 0.697 -.1804684 .1208346
lnssvc I -.0386804 .0772922 -0.500 0.617 -.1907245 .1133638
lnssta I -.4685351 .6172766 -0.759 0.448 -l.682802 .7457314
lnssva I .1270251 .1272372 0.998 0.319 -.1232678 .3773179
lnsslv l .1274581 .1404135 0.908 0.365 -.1487541 .4036703
lncscs I .0210311 .1201704 0.175 0.861 -.2153604 .2574226
lncsvm I -.0991596 .0889305 -1.115 0.266 -.2740979 .0757788
lncsvl I .0335114 .0454315 0.738 0.461 -.0558586 .1228813
lncsvs I —.0399392 .0388103 -1.029 0.304 -.1162844 .036406
lncsvc I .0124298 .0395662 0.314 0.754 -.0654022 .0902618
lncsta I -.4432274 .4405551 -1.006 0.315 -1.309859 .4234038
lncsva I -.1032881 .0786219 -1.314 0.190 -.257948 .0513719
lncslv I .122084 .0848856 1.438 0.151 -.0448975 .2890654
lnvmvm I .0036215 .0224437 0.161 0.872 —.0405284 .0477713
luv-v1 I ~.0255003 .0109565 -2.327 0.021 -.0470532 -.0039474
lnvmvs l .0086399 .0105224 0.821 0.412 -.0120591 .029339
lnvmvc l -.0042758 .015292 -0.280 0.780 -.0343571 .0258056
lnvmta l -.ll87173 .0966813 ~1.228 0.220 -.3089025 .0714679
lnvmva I -.0085343 .0189474 -0.450 0.653 -.0458063 .0287377
lnvmlv I -.0059888 .0184947 -0.324 0.746 -.0423703 .0303927
lnvlvl I .032456 .013815 2.349 0.019 .00528 .0596321
lnvlvs l -.0078824 .005934 ~l.328 0.185 -.0195554 .0037906
lnvlvc I .0025828 .0061715 0.419 0.676 -.0095573 .0147229
lnvlta I -.0043365 .0548101 -0.079 0.937 -.1121553 .1034823
lnvlva I -.0102527 .0090707 -1.130 0.259 -.0280959 .0075906
lnvllv I -.0001593 .010569 -0.015 0.988 -.02095 .0206315
1nvrvn I .0620153 .018722 3.312 0.001 .0251866 .098844
luvavc I -.0182048 .0067742 -2.687 0.008 -.0315307 -.004879
lnvsta l -.0719635 .0532357 -1.352 0.177 -.1766854 .0327584
lnvsva I -.0101671 .0109954 ~0.925 0.356 -.0317967 .0114624
lnvslv l -.0106479 .0119428 -0.892 0.373 -.034141 .0128452
lnvcvc I .0483224 .017032 2.837 0.005 .0148181 .0818267
lnvcta I .0085238 .0564768 0.151 0.880 -.1025736 .1196212
lnvcva I -.0046636 .011541 -0.404 0.686 -.0273664 .0180392
lnvclv I .0101124 .0143769 0.703 0.482 -.018169 .0383938
lntata I -.2651539 .6034283 -0.439 0.661 -l.452179 .9218711
lntava I .0225956 .0821455 0.275 0.783 -.1389957 .1841869
lntalv I .1698425 .104068 1.632 0.104 -.0348733 .3745584
lnvava I -.0043682 .0283801 -0.154 0.878 -.0601957 .0514593
invalv I .0440943 .01937 2.276 0.023 .0059909 .0821977
lnlvlv l .0257843 .0335216 0.769 0.442 -.0401572 .0917259
lnnyld I .2417465 .0916578 2.637 0.009 .0614432 .4220498
naredv I -.1197627 .0943709 ~1.269 0.205 -.305403 .0658775
_cons I 4.700692 2.921266 1.609 0.109 -1.045832 10.44722

 

 

219

Table A3: Cost Function Parameter Estimates, 1989/90

 

 

 

 

 

Source I 35 df MS Number of obs = 331
--------- +----------------------———----- F( 92, 238) = 8.00
Model I 163.350063 92 1.77554416 Prob > F 0.0000
Residual I 52.8250064 238 .221953808 R—squared a 0.7556
--------- +---------------------~-------— Adj R-squared = 0.6612
Total I 216.175069 330 .655075967 Root MSE = .47112
lnntvc I Coef. Std. Err. t P>It| [95% Conf. Interval]
lnnpl I 1.202693 2.538294 0.474 0.636 —3.797699 6.203086
Inna. I -14.62855 5.37043 -2.724 0.007 -25.2082 -4.048905
lnnls l 5.39497 6.095133 0.885 0.377 —6.612329 17.40227
lnnss l 9.089892 8.085755 1.124 0.262 —6.838895 25.01868
lnncs I 2.946817 2.14524 1.374 0.171 -1.279265 7.1729
lnvm I -.3934095 .4357339 -0.903 0.368 —1.251797 .4649782
lnvl I .1855843 .2651913 0.700 0.485 —.3368377 .7080063
luvs I .9271844 .322376 2.876 0.004 .2921095 1.562259
lnvc I .3618935 .3220547 1.124 0.262 -.2725483 .9963353
lat: I -4.446299 1.410127 -3.153 0.002 -7.224224 -1.668374
lnva I .057471 .6648002 0.086 0.931 -1.252173 1.367115
lnlv I -.5566243 .5338295 -1.043 0.298 -1.608258 .4950098
1np1p1 I -2.148327 .675764 -3.179 0.002 -3.479569 -.8170844
lnplms l 1.391912 1.414696 0.984 0.326 -1.395012 4.178836
lnplls I -.6479844 1.544934 -0.419 0.675 —3.691476 2.395507
lnplss I .9792789 1.804431 0.543 0.588 -2.575418 4.533975
lnplcs I .4177538 .4698497 0.889 0.375 —.5078414 1.343349
lnplvm J -.1564965 .0904241 -1.731 0.085 -.3346303 .0216372
lnplvl I .0529845 .0695169 0.762 0.447 -.0839625 .1899316
1np1va I -.1298038 .0665668 -1.950 0.052 -.2609391 .0013315
lnplvc I -.1251304 .0670772 —l.865 0.063 —.2572713 .0070105
lnplta I .7261927 .3321205 2.187 0.030 .0719215 1.380464
lnplva I -.1322473 .1242058 -1.065 0.288 -.3769304 .1124358
lnpllv I .0520916 .1221693 0.426 0.670 -.1885796 .2927628
lull-s I 4.543392 1.750686 2.595 0.010 1.094573 7.992211
lnmsls I .161141 4.687577 0.034 0.973 —9.0733 9.395582
lnmsss I .5426468 3.675511 0.148 0.883 -6.698042 7.783336
lnmscs l .1781339 .9871572 0.180 0.857 -1.766547 2.122815
lanswn I .4598778 .231185 1.989 0.048 .0044476 .915308
lnmsvl I -.2078598 .146235 -1.421 0.157 -.4959401 .0802204
lnmsvs I .0124977 .1518466 0.082 0.934 -.2866372 .3116326
lnmsvc I .0950556 .1585101 0.600 0.549 —.2172064 .4073176
lnmsta I .7963968 .6330115 1.258 0.210 -.4506241 2.043418
lnmsva I .2945237 .2861697 1.029 0.304 -.2692253 .8582727
lnmslv I .2496788 .236321 1.057 0.292 -.2158693 .7152269
lnlsls I .4043474 2.862709 0.141 0.888 -5.235137 6.043831
lnlsss I -2.540515 5.58096 -0.455 0.649 -13.5349 8.453872
lnlscs I -1.379248 1.447098 -O.953 0.341 -4.230004 1.471508
lnlsvm I -.1126675 .2314556 —0.487 0.627 —.5686307 .3432957
lnlsvl I .0728604 .1424487 0.511 0.609 -.2077609 .3534818
lnlsvs I -.2297092 .2489734 -0.923 0.357 -.7201823 .2607638

 

220

Table A3:

Cost Function Parameter Estimates, 1989/90; Cont.

 

 

 

 

 

1nntvc I Coef. Std. Err. t P>|t| [95% Conf. Interval]
lnlsvc I -.1253353 .1728307 -0.725 0.469 -.4658085 .2151379
lnlsta I .5812628 .9832944 0.591 0.555 -1.355809 2.518335
lnlsva I .129506 .3463019 0.374 0.709 -.5527023 .8117142
lnlslv I -.2746906 .2492875 -1.102 0.272 -.7657824 .2164012
lnssss l -6.799468 4.12991 -1.646 0.101 -l4.93531 1.336379
lnsscs I -1.342388 1.787939 -0.751 0.454 -4.864595 2.179819
1nssvm I .1116485 .3421449 0.326 0.744 —.5623705 .7856676
lnssvl I .0029353 .1833645 0.016 0.987 -.3582894 .36416
lnscva I -.4828878 .2272007 -2.125 0.035 -.930469 -.0353066
lnssvc I -.1016463 .1987065 -0.512 0.609 -.4930944 .2898018
lnalta I 2.675578 1.064143 2.514 0.013 .5792365 4.77192
lnssva I -.4549504 .4136745 -1.100 0.273 -1.269881 .3599806
lnsslv I .2443025 .3691593 0.662 0.509 -.4829345 .9715395
lncscs I -.0836028 .5714187 -0.146 0.884 -1.209287 1.042081
lncsvm I -.1042513 .0706205 -1.476 0.141 -.2433723 .0348698
lncsvl I .0123016 .0570347 0.216 0.829 -.1000556 .1246589
lncsvs I .0735846 .0677236 1.087 0.278 -.0598296 .2069988
lncsvc I .070232 .0547382 1.283 0.201 -.0376013 .1780652
lncsta I -.2793334 .3554489 -0.786 0.433 -.9795611 .4208942
1ncsva I .0134336 .1082024 0.124 0.901 -.1997232 .2265904
lncslv I -.0041358 .0788617 -0.052 0.958 —.1594919 .1512204
lnvuwn.l .1172194 .0271108 4.324 0.000 .0638115 .1706273
lnvmvl I -.0261498 .0148381 -1.762 0.079 -.0553806 .0030811
lnvmvs I -.0153507 0120771 -1.271 0.205 -.0391423 .008441
luv-N0 I -.0533866 .0163154 -3.272 0.001 -.0855275 —.0212456
lnvmta I -.0109863 .0500879 -0.219 0.827 -.1096584 .0876859
1nvuwa.l -.0500821 .0211264 -2.371 0.019 -.0917007 -.0084636
lnvmlv I .0171595 .0145297 1.181 0.239 -.0114637 .0457826
lnvlvl I .059724 .0188591 3.167 0.002 .022572 .096876
lnvlvs I -.0075347 .007738 -0.974 0.331 -.0227784 .0077089
lnvlvc I .0016778 .0084253 0.199 0.842 —.0149198 .0182754
lnvlta I .0228468 .0351981 0.649 0.517 -.0464928 .0921864
lnvlva I .0117911 .0153529 0.768 0.443 -.0184538 .0420361
lnvllv I -.012975 .0126127 -1.029 0.305 -.0378219 .0118718
lnvsvs I -.0378805 0263479 -1.438 0.152 -.0897855 .0140244
lnvsvc I -.0037913 .0078067 -0.486 0.628 -.0191703 .0115877
lnvsta I .0687325 .0391645 1.755 0.081 -.0084208 .1458858
lnvsva I -.003433 .0160604 -0.214 0.831 -.0350718 .0282058
lnvalv I .0142546 .0152231 0.936 0.350 —.0157347 .0442439
lnvcvc I .0599644 .027669 2.167 0.031 .0054569 .1144718
lnvcta I -.0658737 .0442775 —1.488 0.138 —.1530995 .0213521
lnvcva I .0145258 .0171449 0.847 0.398 -.0192493 .0483009
lnvalv I -.0002904 .0136466 -0.021 0.983 -.0271738 .0265931
lntata I -.2057172 .2666095 -0.772 0.441 -.730933 .3194986
lntava I -.0171117 .0849263 -0.201 0.840 -.1844149 .1501916
lntalv I -.038378 .065963 -0.582 0.561 -.168324 .0915679
lnvava I .049942 .0438982 1.138 0.256 -.0365367 .1364206
lnvalv I -.0076695 .0324114 -0.237 0.813 -.0715194 .0561805
lnlvlv I .0463611 .0362729 1.278 0.202 -.0250957 .117818
soildv I .0258822 .026022 0.995 0.321 —.0253807 .0771451
narodv I .4220394 .1947231 2.167 0.031 .0384385 .8056402
_cons I 8.917189 6.707242 1.329 0.185 —4.295954 22.13033

 

221

 

 

 

 

Table A4: Cost Function Parameter Estimates, 1992/93
Source I 55 df MS Number of obs = 368
--------- +-----------------—------------ F( 67, 300) = 38.74
Model I 334.96306 67 4.99944866 Prob > F = 0.0000
Residual I 38.7163969 300 .129054656 R-squared = 0.8964
--------- +---—----------—--—-—--—------- Adj R-squared = 0.8733
Total I 373.679457 367 1.01820016 Root MSE .35924
1nntvc I Coef. Std. Err. t P>|t| [95% Conf. Interval]
lnnpl I 1.827252 .560909 3.258 0.001 .7234372 2.931066
lnnm: I .3862968 .3885023 0.994 0.321 -.3782379 1.150832
lnnls I -.2555809 .4157097 -0.615 0.539 -1.073657 .5624955
lnnss I .0618437 .6819459 0.091 0.928 -1.28016 1.403847
lnncs I .6278361 .4469642 1.405 0.161 -.2517461 1.507418
lnvm I .1070234 .1028707 1.040 0.299 -.0954162 .309463
lnvl I .0113246 .0775311 0.146 0.884 -.1412491 .1638982
luvs I .1766903 .0712737 2.479 0.014 .0364305 .31695
lnvc I -.0490335 .0941514 -0.521 0.603 -.2343143 .1362473
lnta I 2.741386 .4520063 6.065 0.000 1.851881 3.63089
lnplpl I -.1027808 .1442423 -0.713 0.477 -.3866357 .1810741
lnplms I -.1283844 .1011693 -l.269 0.205 -.3274757 .0707069
lnplls I -.0170987 .111635 -0.153 0.878 -.2367856 .2025882
lnplss I .1738935 .2044089 0.851 0.396 -.2283634 .5761504
lnplcs I -.1456388 .162008 -0.899 0.369 -.4644549 .1731772
lnplvm I -.0220948 .0677983 -0.326 0.745 -.1555153 .1113258
lnplvl I .0563623 .0215182 2.619 0.009 .0140165 .0987082
lnplvs I -.0171901 .0295818 -0.581 0.562 -.0754042 .041024
lnplvc I .0195656 .0252926 0.774 0.440 -.0302078 .0693389
lnplta I -.1217912 .199872 -0.609 0.543 -.5151l98 .2715375
lgmsms I .2738252 .1573819 1.740 0.083 -.0358871 .5835375
lnmsls I -.049289 .091957 —0.536 0.592 -.2302515 .1316736
lnmsss l .0533736 .1247252 0.428 0.669 -.1920735 .2988206
lnmscs I -.089509 .118636 -0.754 0.451 -.322973 .1439551
lnmsvm I -.0423044 .0474763 -0.891 0.374 -.1357333 .0511244
lnmsvl I -.0166178 .0162461 -1.023 0.307 -.0485886 .0153529
lnnnva I .0409057 .0180293 2.269 0.024 .0054258 .0763856
lnmsvc I -.0081391 .0185343 -0.439 0.661 -.0446127 .0283345
lnmsta I -.1899358 .1355995 -1.401 0.162 -.4567824 .0769108
lnlsls I -.0415439 .1168973 -0.355 0.723 -.2715864 .1884987
lnlsss I -.0356604 .1747543 -0.204 0.838 -.3795599 .3082391
lnlscs I .0455543 .1231488 0.370 0.712 -.1967906 .2878991
lnlsvm I .0327537 .0490417 0.668 0.505 -.0637556 .129263
lnlsvl I .0038648 .0152738 0.253 0.800 —.0261925 .0339221
lnlsvs I -.0119814 .0185338 -0.646 0.518 -.0484541 .0244913
lnlsvc I -.0182276 .0256717 -0.710 0.478 -.068747 .0322919

 

222

Table A4: Cost Function Parameter Estimates, 1992/93; Cont.

 

 

 

 

 

1nntvc I Coef. Std. Err. t P>It| [95% Conf. Interval]
1nlata I .2882071 .1489551 1.935 0.054 -.0049221 .5813364
lnssss I -.0004937 .2081956 -0.002 0.998 -.4102024 .4092149
lnsscs I -.0187019 .1579172 -0.118 0.906 -.3294677 .2920638
lnssvm I .0229546 .0780258 0.294 0.769 -.1305926 .1765018
lnssvl I -.0505484 .027704 -1.825 0.069 —.1050672 .0039704
lnssvs I -.046639 .0329268 —1.416 0.158 -.1114358 .0181579
lnssvc I -.0185912 .0281233 -0.661 0.509 -.0739352 .0367527
lnssta I -.1404483 .1868296 -0.752 0.453 -.5081107 .2272142
lncscs I .1012175 .0707728 1.430 0.154 -.0380565 .2404915
1nccvn.| -.1031952 .0497309 -2.075 0.039 -.2010607 -.0053297
lncsvl I -.0121678 .019923 -0.611 0.542 -.0513744 .0270388
lncsvs I .0380602 .0262543 1.450 0.148 -.0136056 .089726
lncsvc I .0270311 .0112711 2.398 0.017 .0048506 .0492116
lncsta I .0804236 .1753737 0.459 0.647 —.2646948 .4255419
lanNn.I .045051 .0187918 2.397 0.017 .0080707 .0820314
lnvmvl I .0005212 .0103431 0.050 0.960 -.019833 .0208754
anﬂNI I -.0186616 .0083746 -2.228 0.027 -.0351419 -.0021812
lnvmvc I .0008506 .0105827 0.080 0.936 -.0199751 .0216763
lawnta I -.1392231 .060189 -2.313 0.021 -.2576692 -.020777
lnvlvl I .0406757 .0123428 3.295 0.001 .0163862 .0649652
lnvlva I -.0047385 .0037059 —1.279 0.202 -.0120314 .0025544
lnvlvc I -.0010041 .0033728 -0.298 0.766 -.0076414 .0056333
lnvlta I -.0367877 .0288515 -1.275 0.203 -.0935646 .0199892
lnvsvs I .007991 .010888 0.734 0.464 -.0134354 .0294175
lnvsvc I .0125826 .0042362 2.970 0.003 .0042461 .0209191
lnvstagl -.0625456 .0325369 -1.922 0.056 —.1265752 .0014839
lnvcvc I .0217 .0120156 1.806 0.072 -.0019455 .0453454
lnvcta I -.0299407 .033284 -0.900 0.369 -.0954404 .035559
lntata I -.2934997 .3249412 —0.903 0.367 —.9329525 .345953
lnnayld I .2652344 .0599377 4.425 0.000 .1472828 .383186
naredv I -.1018572 .0679297 -1.499 0.135 -.2355362 .0318218
‘_oons I 1.381531 .6713047 2.058 0.040 .0604689 2.702594

 

223

Table A5: Correlation Coefﬁcients for Selected Variables

 

 

 

 

 

 

 

 

Variable Pairs 1988/89 1989/90 1992/93
Area is Output: Maize Area*Value of maize 0.47 0.16 0.43
Legume Area*Value of Legumes 0.65 0.53 0.69
Small Grain Area*Small Grains Value 0.70 0.70 0.72
Cash092.458.94419592291116 ________________ ‘1 -§9 _______ 0. .69 ______ ‘1 43...
Area yg Area; Legume Area*Maize Area 0.13 0.49 0.25
Legume Area*Sinall Grain Area 0.52 0.38 0.14
Maize Area‘Casli Crop Area __ 0.36 0.22 0.40
m Small Grains Seed Price*Labor Price 0.38 0.32 0.74
Small Grains Seed Price*Maize Seed Price 0.53 0.26 0.43
Small Grains Seed Price*Legume Seed Price 0.47 0.33 0.63
Small Grains Seed Price*Cash Crop Seed 0.24 0.32 0.52
Legume Seed Price*Labor Price 0.20 0.23 0.66
Legume Seed Price*Maize Seed Price 0.43 0.30 0.28
Legume Seed Price*Casli Crop Seed Price 0.21 0.18 0.44
Maize Seed Price*Casli Crop Seed Price 0.40 0.20 O. 18
Cash Srop Seed Price*Labor Price 0.26___ 0.63 0.49
Aga vs Prices: Small Grains Area*Labor Price 0.05 -0.43 0.01
Small 05211153921999:250.9599423196 ........... 0. .12 ______ £52.----:'11§.-
b rs: Maize Value*Cash Crop Value 0.41 0.25 0.25
Small Grain Value*Labor Price 0.04 -0.43 0.03
Small Grain Value’l'Casli Crop Seed 0.25 -0.43 -0. 18
Livestock Value*Farm Assets Value 0.23 0.51 na

 

Note: The two p-values 2 0.8 are bolded. na = not available.

224

Table A6: Cost Frontier Parameter Estimates (Normal), 1988/89

 

Limited Dependent Variable Model - FRONTIER I
Maximum Likelihood Estimates

 

 

I

I l

I Dependent variable LNNTVC I

I'Weighting variable ONE I

I Number of observations 425 I

I Iterations completed 1 I

l LM Stat. at start values .1958422 I

I LM statistic kept as scalar LMSTAT l

I Log likelihood function ~239.6463 I

I Variances: Sigma-squared(v)= .15929 I

I Sigma-squared(u)= .05938 I
IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZ|>z] I Mean of XI
Constant 4.893544276 3.4337953 1.425 .1541
LNNPL 2.181983173 2.4065727 .907 .3646 .80323966
LNNMS .3264582826 2.5551009 .128 .8983 1.1506815
LNNLS 1.842231828 1.7399391 1.059 .2897 1.2757095
LNNSS -.1980276613 2.2348253 -.089 .9294 1.1731809
LNNCS -.3444927219 1.5411917 —.224 .8231 1.0593265
LNVM .2373514274 .34837318 .681 .4957 5.6776400
LNVL .2752270691 .17616423 1.562 .1182 3.8561645
LNVS .2348215065 .18665202 1.258 .2084 2.6761662
LNVC -.1078956901 .17207737 -.627 .5306 1.5420195
LNTA 1.304619173 1.8180294 .718 .4730 1.3768872
LNVA -.2464832254 .37679493 -.654 .5130 6.9843414
ENBV -.9416201250 .42490622 —2.216 .0267** 7.2387206
LNPLPL .4928432807 .81598021 .604 .5459 .35264508
LNPLMS .5716469600 1.8308136 .312 .7549 .47413023
LNPLLS -1.112870780 1.5030105 -.740 .4590 .52011633
LNPLSS -.2803768953 2.0986495 -.134 .8937 .48300873
LNPLCS -.7687189600E-01 .82368682 -.093 .9256 .44125415
LNPLVM -.1355962113 .13982783 -.970 .3322 4.5397799
LNPLVL -.6492315483E-01 .70224913E-01 -.925 .3552 3.1599528
LNPLVS .87939107863—01 .762237438-01 1.154 .2486 2.1743363
LNPLVC .95990415318-01 .82156302E-01 1.168 .2427 1.1233033
LNPLTA -.6627057221E-02 .61698791 -.011 .9914 1.1045645
LNPLVA -.1705106307 .12000435 -1.421 .1554 5.4945124
LNPLLV .1556508409 .15519951 1.003 .3159 5.7795826
LNMSMS -.2811024468 1.1026848 —.255 .7988 .69533029
LNMSLS -1.435700146 1.7832386 -.805 .4208 .75118869
LNMSSS -1.325669578 2.0255354 -.654 .5128 .69234133
LNMSCS .1638671609 1.4529255 .113 .9102 .63482545
LNMSVM -.24699818338—01 .21640788 -.114 .9091 6.4134497
LNMSVL -.333011214SE-01 .93746336E-01 —.355 .7224 4.5211933
LNMSVS -.94840606OSE—01 .99271237E-01 -.955 .3394 3.2383088
LNMSVC .26072656478-01 .977655828-01 .267 .7897 1.5378683
LNMSTA .1839824705 .91554811 .201 .8407 1.5711864
LNMSVA .1462058492 .15921985 .918 .3585 7.9290467
LNMSLV .1049926927 .21734019 .483 .6290 8.2586770
LNLSLS -.7000308309 .54952665 -1.274 .2027 .86196438
LNLSSS -.4133817472 1.8276461 —.226 .8211 .76679446
LNLSCS -.4676086955 1.3761356 -.340 .7340 .69123221
LNLSVI’ .2330942678 .11414206 2.042 .0411** 7.1940733
LNLSVL .46211098688-01 .651617058-01 .709 .4782 5.0395316
LNLSVS .32190412788—01 .70187979E-01 .459 .6465 3.4851812
LNLSVC -.35382351858-01 .703758283-01 -.503 .6151 1.7808488

 

225

Table A6: Cost Frontier Parameter Estimates (Normal), 1988/89; Cont.

 

 

 

 

IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZI>z] I Mean of XI
LNLSTA, .2273775403 .45224341 .503 .6151 1.7521162
LNLSVA .43114425048-02 .10630259 .041 .9676 8.8511575
LNLSLV -.1322267101 .12304719 -1.075 .2826 9.1747954
LNSSSS -.8773549385 1.4579156 -.602 .5473 .72085685
LNSSCS 2.780844230 1.4588899 1.906 .0566* .63646762
LNSSVM -.2651320733E-01 .19454247 —.136 .8916 6.6022275
LNSSVL -.6099576707E—01 .845911788-01 -.721 .4709 4.5318528
LNSSVS -.298207009BE-01 .95114637E-01 -.314 .7539 3.1687438
LNSSVC -.386765447ZE-01 .81601355E-01 -.474 .6355 1.6734754
LNSSTA. -.4686571716 .75083500 -.624 .5325 1.6067637
LNSSVA .1270511741 .15456794 .822 .4111 8.1772232
LNSSLV .1274686306 .15790916 .807 .4195 8.4663002
LNCSCS .20992704668-01 .14047115 .149 .8812 . 8022330
LNCSVM -.9918842473E-01 .10868331 -.913 .3614 5.8871905
LNCSVL .33519495888-01 .441081658-01 .760 .4473 4.3953617
LNCSVS -.3993180999E-01 .43286984E-01 -.922 .3563 3.1205264
LNCSVC .12442679388-01 .423231888-01 .294 .7688 1.3180145
LNCSTA -.4434617813 .44677157 -.993 .3209 1.4398880
LNCSVA -.1033097455 .886591238-01 -1.165 .2439 7.1770890
LNCSLV .1220961543 .10538005 1.159 .2466 7.6063538
LNVMVM .36180226328-02 .237653128-01 .152 .8790 17.168468
LNVMVL -.2549823674E-01 .126589983-01 -2.014 .0440** 21.954498
LNVMVS .86417609708-02 .109537828-01 .789 .4302 14.482953
LNVMVC -.4272400601E-02 .163729933-01 —.261 .7941 10.230055
LNVMTA -.1187615901 .11025806 -1.077 .2814 7.9468257
LNVMVA -.8530289904E-02 .210352878-01 -.406 .6851 39.979292
LNVMLV -.5982512326E-02 .203003868—01 -.295 .7682 41.701333
LNVLVL .32453711908-01 .147408603-01 2.202 .0277** 10.772224
LNVLVS -.788409066OE-02 .57632540E—02 -1.368 .1713 12.442016
LNVLVC .25823914258-02 .59542981E-02 .434 .6645 5.5281200
LNVLTA -.4311669969E—02 .574065998-01 -.075 .9401 5.6226780
LNVLVA -.1024877944E-01 .88413892E-02 -1.159 .2464 26.213959
LNVLLV -.1575229266E-03 .107597908-01 -.015 .9883 28.396614
LNVSVS .62012425743-01 .218374428-01 2.840 .0045** 6.3346163
LNVSVC -.18203760863-01 .725549722-02 -2.509 .0121** 2.6501878
LNVSTA -.7193950867E-01 .625505118-01 -1.150 .2501 3.8566413
LNVSVA -.1016568374E-01 .111620828-01 -.911 .3624 18.189565
LNVSLV -.1064889125E-01 .133163968-01 -.800 .4239 19.744443
LNVCVC .48319723272-01 .158718282-01 3.044 .0023** 4.2986908
LNVCTA .8521775292E-02 .624819198-01 .136 .8915 2.3162624
LNVCVA -.4661715577E-02 .132191198-01 —.353 .7244 11.846978
LNVCLV .1011247294E-01 .160034898—01 .632 .5275 12.017633
LNTATA. -.2655047518 .68106890 -.390 .6967 .99972989
LNTAVA .22512754968-01 .88404666E-01 .255 .7990 9.6564848
LNTAVL .1697879963 .11428770 1.486 .1374 10.124702
LNVAVA -.4373806024E-02 .30619464E-01 -.143 .8864 25.464669
LNVALV .44102384868-01 .229346328-01 1.923 .0545* 51.002857
LNLVLV .2578586366E—01 .332054688-01 .777 .4374 27.078326
LNMILD .2417886430 .99201799E-01 2.437 .0148** 2.5989920
NAREDV —.1197881190 .10363613 -1.156 .2477 .48235294
Variance parameters for compound error
Lambda .6105714285 1.3013953 .469 .6390
Sigma .4676312961 .15708671 2.977 .0029**

 

226

Table A7: Cost Frontier Parameter Estimates (Normal), 1989/90.

 

Limited Dependent Variable Model - FRONTIER
Maximum Likelihood Estimates

Dependent variable LNNTVC
Weighting variable ONE
Number of observations 331

|
I
I
I
l
Iterations completed 1 l
I
I
I
l
l

 

 

LM Stat. at start values 4.674091

LM statistic kept as scalar LMSTAT

Log likelihood function -214.0113

Variances: Sigma-squaredIv)= .12644

I Sigma-squaredIu)= .24783

IVariable I Coefficient I Standard Error Ib/St.Er.IP[|Z|>z] I Mean of XI
Constant .7772335521 6.3785334 .122 .9030
LNNPL .5210438104 2.6534721 .196 .8443 .88227558
LNNMS -6.690481867 5.4033328 -1.238 .2156 1.3461501
LNNLS -2.966153603 6.7364816 -.440 .6597 1.0946537
LNNSS 19.18680248 9.4817718 2.024 .0430** 1.1917822
LNNCS 1.012341742 2.2277577 .454 .6495 .87544951
LNVM -.3094579460E-01 .58076913E-01 —.533 .5941 5.1916238
LNVL -.1028003032 .524013022-01 -1.962 .0498** 3.3436941
LNVS .3972262313E-01 .663670358-01 .599 .5495 2.4289928
LNVC -.1227581354E-01 .665809908-01 -.184 .8537 1.2108494
LNTA —1.969701153 1.2839181 -1.534 .1250 1.3503719
LNVA -.4310299014 .64216650 -.671 .5021 6.4394190
LNLV .2408067145 .61138016 .394 .6937 7.1224702
LNPLPL -1.467898809 .65152898 —2.253 .0243“I .44421681
LNPLMS .9933825368 1.6117261 .616 .5377 1.1952261
LNPLLS .3599382788E-Ol 1.6172621 .022 .9822 .97472234
LNPLSS .6112676341 1.9704567 .310 .7564 1.0611853
LNPLCS .1444241103 .48743527 .296 .7670 .85741185
LNPLTA .5682847196 .29018407 1.958 .0502** 1.1531831
LNPLVA -.9609940601E—01 .13510063 -.711 .4769 5.7166342
LNPLLV -.3805862534E-01 .12920669 -.295 .7683 6.2404563
LNMSMS 1.792155066 2.1743747 .824 .4098 .91544618
LNMSLS 4.382639890 5.1525647 .851 .3950 1.4783277
LNMSSS -5.334549118 4.2774921 -1.247 .2124 1.6075868
LNMSCS .4608088842 1.1987046 .384 .7007 1.1898211
LNMSTA .3151551741 .60467220 .521 .6022 1.8096588
LNMSVA .4671132134 .32227365 1.449 .1472 8.6643952
LNMSLV .2217408306 .24882709 .891 .3729 9.5547595
LNLSLS .3112810544 3.1965202 .097 .9224 .60582448
LNLSSS -1.418344412 6.4771925 -.219 .8267 1.3081353
LNLSCS -1.274695525 1.6894039 -.755 .4505 .96675937
LNLSTA .3908017850 1.1458301 .341 .7331 1.4742554
LNLSVA .7644700964E-01 .44037046 .174 .8622 7.0536661

 

227

 

 

 

 

Table A7: Cost Frontier Parameter Estimates (Normal), 1989/90; Cont.
IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZ|>z] I Mean of XI
LNLSTA .5828917791 1.2502375 .466 .6411 1.4742554
LNLSVA .1313592922 .41945716 .313 .7542 7.0536661
LNLSLV -.2744981641 .31214573 -.879 .3792 7.7836915
LNSSSS -6.790416780 4.7474827 -1.430 .1526 .71444207
LNSSCS -1.343078918 2.2486285 -.597 .5503 1.0553449
LNSSVM .1108473992 .37142407 .298 .7654 6.1849992
LNSSVL .3464399774E-02 .20123759 .017 .9863 3.9735414
LNSSVS -.4827733890 .23115928 -2.088 .0368** 2.8560128
LNSSVC -.1015097675 .20302900 -.500 .6171 1.4613889
LNSSTA 2.673631853 1.2455863 2.146 .0318** 1.6050268
LNSSVA -.4537575738 .45778804 -.991 .3216 7.6773717
LNSSLV .2436891462 .48116575 .506 .6125 8.4697311
LNCSCS -.8398519409E-01 .77095273 -.109 .9133 . 6587571
LNCSVM -.1043201132 .85380186E—01 -1.222 .2218 4.5742041
LNCSVL .1213096090E-01 .80583728E-01 .151 .8803 2.8111466
LNCSVS .7384121734E-01 .10159421 .727 .4673 1.7128804
LNCSVC .7021557131E-01 .75509990E—01 .930 .3524 1.1680506
LNCSTA -.2794617518 .43004486 -.650 .5158 1.1189231
LNCSVA .1347734249E—01 .15083783 .089 .9288 5.6747968
LNCSLV -.41628646088-02 .11856165 —.035 .9720 6.1372630
LNVIVI .1171707572 .318907693-01 3.674 .0002** 15.034542
LNVMVL -.2612736678E-01 .15988950E-01 -1.634 .1022* 18.658161
LNVMVS -.1535455265E-01 .12714494E-01 -1.208 .2272 13.156604
LNVMNC -.5339736403£-01 .178387323-01 -2.993 .0028** 7.2448809
LNVMTA -.1098301642E-01 .52853673E-01 -.208 .8354 7.0971665
LNVMVA -.5011451932E-01 .22992053E-01 -2.180 .0293** 34.048816
LNVMLV .1718559580E-01 .14501450E—01 1.185 .2360 37.755287
LNVLVL .5962107979E-01 .210433138-01 2.833 .0046** 8.3137646
LNVLVS -.7526445470E-02 .80267059E—02 -.938 .3484 9.2734422
LNVLVC .1678094331E—02 .88701116E-02 .189 .8499 5.1565872
LNVLTA .22896303738-01 .38803408E-01 .590 .5552 4.9709757
LNVLVA .1178580592E-01 .15192934E-01 .776 .4379 21.970795
LNVLLV -.1298801152£-01 .13457597E-01 -.965 .3345 24.610321
LNVSVS -.37884100008-01 .27166357E-01 -1.395 .1632 5.7703077
LNVSVC ~.3780957023E-02 .97998630E-02 -.386 .6996 3.5028585
LNVSTA .68843752758-01 .38667027E-01 1.780 .0750* 3.8055501
LNVSVA -.3464481027E-02 .17292436E-01 -.200 .8412 15.558662
LNVSLV .1424871785E~01 .16862878E—01 .845 .3981 18.204183
LNVCVC .60029037372-01 .28057839E-01 2.139 .0324** 3.0405703
LNVCTA -.6584018253E-01 .52185943E-01 -1.262 .2071 1.9298398
LNVCVA .1455979709E-01 .20267770E—01 .718 .4725 7.8488264
LNVCLV -.3000040342E-03 .161526458-01 -.019 .9852 8.7199356
LNTATA -.2062284820 .26995003 -.764 .4449 1.0491833
LNTAVA -.1704889315E-01 .96171312E—01 —.177 .8593 8.8268865
LNTALV -.3839771417E-01 .75927476E-01 -.506 .6131 9.8744344
LNVAVA .49895162218-01 .48209386E-01 1.035 .3007 21.489860
LNVALV -.7613587438E-02 .30282753E-01 -.251 .8015 46.825796
LNLVLV .46330783303-01 .40056964E-01 1.157 .2474 26.539769
NARRDV .4219532343 .19466332 2.168 .0302** .30815710
SOILDV .25865332768-01 .23680105E-01 1.092 .2747 .44410876
Variance parameters for compound error
Lambda 1.377449627 .37731683 3.651 .0003**
Sigma .5231786230 .79397240E-01 6.589 .0000**

 

228

Table A8: Cost Frontier Parameter Estimates (Normal), 1992/93.

 

Limited Dependent Variable Model - FRONTIER
Maximum Likelihood Estimates

Dependent variable LNNTVC
Weighting variable ONE
Number of observations 368

l
I
|
|
I
Iterations completed 1 l
l
|
|
I
I

 

 

LM Stat. at start values 4.012769

LM statistic kept as scalar LMSTAT

Log likelihood function —106.6425

Variances: Sigma-squared(v)= .07063

I Sigma-squared(u)- .09515

IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZI>z] I Mean of XI
Constant 1.627588802 1.0290454 1.582 .1137
LNNPL 1.826944604 .61554564 2.968 .0030** 1.7388216
LNNMS .3858863009 .44938862 .859 .3905 1.7544106
LNNLS -.2555987795 .51206082 -.499 .6177 2.4087634
LNNSS .6238316734E-01 .95436376 .065 .9479 1.9325746
LNNCS .6278538246 .73049927 .859 .3901 2.2196989
LNVM .1069955173 .18403930 .581 .5610 7.1497868
LNVL .1134199332E-01 .80990643E-01 .140 .8886 2.5772566
LIV! .1767130073 .765295678-01 2.309 .0209** 3.5580386
LNVC -.4902568099E-01 .11708982 -.419 .6754 1.8032684
BETA 2.741694143 .61785318 4.437 .0000** 1.2177632
LNPLPL -.1027754640 .19958054 -.515 .6066 1.7349561
LNPLMS -.1283803882 .13317240 -.964 .3350 3.2156495
LNPLLS -.1708235439E—01 .11963948 -.143 .8865 4.5787074
LNPLSS .1739499845 .27395870 .635 .5255 3.6779324
LNPLCS -.1456767491 .20381653 —.715 .4748 4.1173248
LNPLVM -.2206361393E-01 .76401174E—01 -.289 .7727 12.276423
LNPLVL .56364291632-01 .25351088E-01 2.223 .0262** 4.1970061
LNPLVS -.1718485404E-01 .32826838E-01 -.524 .6006 6.2314152
LNPLVC .1955703071E-01 .27341206E-01 .715 .4744 2.9012274
LNPLTA -.1218152085 .23590245 -.516 .6056 2.0627293
LNMSMS .2739238099 .18403744 1.488 .1366 1.7652662
LNMSLS -.4922317208E-01 .11280427 -.436 6626 4.3899015
LNMSSS .5327312242E-01 .18631819 .286 .7749 3.5756691
LNMSCS -.8951055778E-01 .15051083 -.595 .5520 3.9873081
LNMSVM -.4226055304E-01 .52519259E—01 -.805 .4210 12.525402
LNMSVL -.1662030866E-01 .20101089E-01 -.827 .4083 4.8336116
LNMSVS .4090297380E-01 .189754572-01 2.156 .0311** 6.4994562
LNMSVC -.8135033920E-02 .21109158E-01 -.385 .7000 3.3089376
LNMSTA -.1899932224 .15913041 ~1.194 .2325 2.2211818
LNLSLS -.4144775329E-01 .14345356 -.289 .7726 3.2874154
LNLSSS -.3578668376E-01 .23425728 -.153 .8786 5.0346705
LNLSCS .4555439635E—01 .17466476 .261 .7942 5.6522160
LNLSVM .3275066490E-01 .63106255E-01 .519 .6038 17.130738

 

229

 

 

 

 

 

 

 

Table A8: Cost Frontier Parameter Estimates (Normal), 1992/93; Cont.
lVariable I Coefficient I Standard Error Ib/St.Er.IP[IZI>z] I Mean of XI
LNLSVL .3858075601E-02 .179207548—01 .215 .8295 5.7799213
LNLSVS -.11983684238-01 .23078430E-01 -.519 .6036 8.7345313
LNLSVC -.1823903559E—01 .330253238—01 -.552 .5808 4.6003379
LNLSTA .2881939328 .18826551 1.531 .1258 2.9281693
LNSSSS -.4627973547E-03 .41907754 -.001 .9991 2.0720305
LNSSCS -.1863367650E-01 .23212085 -.080 .9360 4.5477349
LNSSVM .2288422372E-01 .10033773 .228 .8196 13.768926
LNSSVL -.505402624OE-01 .36935255E-01 -1.368 .1712 4.7765119
LNSSVS -.4663176071E-01 .45651631E-01 -1.021 .3070 6.9350380
LNSSVC -.1857588631E-01 .392569328-01 -.473 .6361 3.2810114
LNSSTA -.1403606280 .29947805 -.469 .6393 2.3254654
LNCSCS .1011902080 .10240267 .988 .3231 2.7695815
LNCSVM -.1031923864 .809672938-01 -1.274 .2025 15.864477
LNCSVL -.1216330283E-01 .27416737E-01 -.444 .6573 5.8213300
LNCSVS .38046969858-01 .350035748-01 1.087 .2771 7.5331993
LNCSVC .2703426776E-01 .14896241E—01 1.815 .0695* 4.1236235
LNCSTA .8039532208E-01 .23174766 .347 .7287 2.6731814
LNVMVM .4506088241E-01 .215226713-01 2.094 .0363** 26.352182
LNVMVL .5173073996E-03 .11101620E-01 .047 .9628 19.539507
LNVMVS -.18663296038-01 .101204718-01 -1.844 .0652* 25.387309
LNVMVC .84954376548-03 .12390089E-01 .069 .9453 13.795925
LNVMTA -.1392406094 .91887603E-01 -1.515 .1297 8.9188446
LNVLVL .40675002873-01 .12408608E-01 3.278 .0010** 7.2792272
LNVLVS -.4739722696E—02 .392651948-02 -1.207 .2274 9.3476876
LNVLVC -.1003527223E-02 .37632005E-02 -.267 .7897 5.5334338
LNVLTA -.3678220352E-01 .30551572E-01 —1.204 .2286 3.4941215
LNVSVS .7985421508E-02 .112287363-01 .711 .4770 9.6837998
LNVSVC .1258006710E-01 .42519136E-02 2.959 .0031** 5.6222526
LNVSTA -.6252298038E-01 .33864508E-01 -1.846 .0649* 4.6983002
LNVCVC .2170191625E-01 .12344899E-01 1.758 .0788* 5.8700932
LNVCTA -.2993842678E-01 .33525111E-01 -.893 .3718 2.7917639
LNTATA -.2936388608 .37218142 -.789 .4301 .83817794
LNMZYLD .2652325563 .62205832E-01 4.264 .0000** 2.8355027
NAREDV -.1018358194 .76422914E-01 -1.333 .1827 .43478261
Variance parameters for compound error
Lambda 1.160691602 .61187706 1.897 .0578*
Sigma .4071648028 .59393046E-01 6.855 .0000**

 

230

Table A9: Cost Frontier Parameter Estimates (Exponential), 1988/89

 

Limited Dependent Variable Model - FRONTIER I
Maximum Likelihood Estimates

 

 

l

I |

I Dependent variable LNNTVC I

I Weighting variable ONE I

I Number of observations 425 I

I Iterations completed 1 I

I LM Stat. at start values .1389457 I

I LM statistic kept as scalar LMSTAT I

I Log likelihood function —239.6800 I

I Exponential frontier model I

I Variances: Sigma—squaredIv)= .16732 I

I Sigma-squaredIu)= .01355 |
IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZ|>z] I Mean of XI
Constant 4.815517570 3.4111612 1.412 .1580
LNNPL 2.181983173 2.3954090 .911 .3623 .80323966
LNNMS .3264582826 2.5472688 .128 .8980 1.1506815
LNNLS 1.842231828 1.7374942 1.060 .2890 1.2757095
LNNSS -.1980276613 2.2233682 -.089 .9290 1.1731809
LNNCS -.3444927219 1.5357355 —.224 .8225 1.0593265
LNVM .2373514274 .34676732 .684 .4937 5.6776400
LNVL .2752270691 .17584309 1.565 .1175 3.8561645
LNVS .2348215065 .18537877 1.267 .2053 2.6761662
LNVC -.1078956901 .17159372 -.629 .5295 1.5420195
LNTA 1.304619173 1.8111123 .720 .4713 1.3768872
LNVA -.2464832254 .37553758 -.656 .5116 6.9843414
LNEV -.9416201250 .42227158 -2.230 .0258** 7.2387206
LNPLPL .4928432807 .81272897 .606 .5442 .35264508
LNPLMS .5716469600 1.8288617 .313 .7546 .47413023
LNPLLS -1.112870780 1.4998752 -.742 .4581 .52011633
LNPLSS -.2803768953 2.0890015 -.134 .8932 .48300873
LNPLCS -.76871896OOE—01 .82380024 -.093 .9257 .44125415
LNPLVM -.1355962113 .13868126 -.978 .3282 4.5397799
LNPLVL -.6492315483E-01 .70142058E-01 -.926 .3547 3.1599528
LNPLVS .8793910786E-01 .758619298-01 1.159 .2464 2.1743363
LNPLVC .9599041531E~01 .819943058-01 1.171 .2417 1.1233033
LNPLTA -.6627057221E-02 .61402897 -.011 .9914 1.1045645
LNPLVA -.1705106307 .11973370 -1.424 .1544 5.4945124
LNPLLV .1556508409 .15415090 1.010 .3126 5.7795826
LNMSMS -.2811024468 1.0912982 -.258 .7967 .69533029
LNMSLS -1.435700146 1.7757728 -.808 .4188 .75118869
LNMSSS -1.325669578 2.0230134 -.655 .5123 .69234133
LNMSCS .1638671609 1.4476762 .113 .9099 .63482545
LNMSVM -.2469981833E-01 .21603266 -.114 .9090 6.4134497
LNMSVL -.3330112145E-01 .94282443E-01 -.353 .7239 4.5211933
LNMSVS -.9484060605E-01 .99596014E-01 -.952 .3410 3.2383088
LNMSVC .2607265647E-01 .97336013E-01 .268 .7888 1.5378683
LNMSTA .1839824705 .91168935 .202 .8401 1.5711864
LNMSVA .1462058492 .15854853 .922 .3564 7.9290467
LNMSLV .1049926927 .21585487 .486 .6267 8.2586770
LNLSLS -.7000308309 .54690707 -1.280 .2006 .86196438
LNLSSS -.4133817472 1.8219619 —.227 .8205 .76679446
LNLSCS -.4676086955 1.3711002 -.341 .7331 .69123221
LNLSVM: .2330942678 .11467624 2.033 .0421** 7.1940733
LNLSVL .4621109868E-01 .64972573E-01 .711 .4769 5.0395316
LNLSVS .32190412788-01 .70148287E—01 .459 .6463 3.4851812

 

231

 

 

 

Table A9: Cost Frontier Parameter Estimates (Exponential), 1988/89; Cont.
IVariable I Coefficient I Standard Error Ib/St.Er.IP[IZ|>z] I Mean of XI
LNLSVC -.3538235185E-01 .70101441E-01 -.505 .6137 1.7808488
LNLSTA .2273775403 .45015007 .505 .6135 1.7521162
LNLSVA .4311442504E-02 .10598710 .041 .9676 8.8511575
LNLSLV -.l322267101 .12256044 -1 079 .2806 9.1747954
LNSSSS -.8773549385 1.4505772 -.605 .5453 .72085685
LNSSCS 2.780844230 1.4540841 1.912 .0558* .63646762
LNSSVM -.2651320733E-01 .19356805 -.137 .8911 6.6022275
LNSSVL -.6099576707E-01 .842705028-01 -.724 .4692 4.5318528
LNSSVS -.2982070098E-01 .94730785E-01 -.315 .7529 3.1687438
LNSSVC -.3867654472E-01 .81338187E-01 -.476 .6344 1.6734754
LNSSTA -.4686571716 .74803367 -.627 .5310 1.6067637
LNSSVA .1270511741 .15397522 .825 .4093 8.1772232
LNSSLV .1274686306 .15718866 .811 .4174 8.4663002
anscs .2099270466E-01 .14000058 .150 .8808 . 8022330
LNCSVM -.9918842473E-01 .10855207 -.914 .3609 5.8871905
LNCSVL .3351949588E-01 .43939319E-01 .763 .4455 4.3953617
ansvs -.3993180999E-01 .43293197E-01 -.922 .3563 3.1205264
ansvc .1244267938E-01 .421637928-01 .295 .7679 1.3180145
LNCSTA -.4434617813 .44505783 -.996 .3190 1.4398880
ansva -.1033097455 .88123135E-01 -1 172 .2411 7.1770890
ansrv .1220961543 .10495784 1.163 .2447 7.6063538
LNVMVM .3618022632E-02 .23681327E-01 .153 .8786 17.168468
nuvuvr -.2549823674E-01 .126061133-01 ~2.023 .0431u 21.954498
LNVMVS .8641760970E-02 .10939562E-01 .790 .4296 14.482953
LNVMVC -.4272400601E-02 .16230414E-01 -.263 .7924 10.230055
LNVMTA -.1187615901 .10983482 -1.081 .2796 7.9468257
LNVMVA -.8530289904E-02 .20965336E-01 - 407 .6841 39.979292
LNVMLV -.5982512326E-02 .20213776E-01 -.296 .7673 41 701333
nuvrvr .32453711902—01 .14702261E-01 2.207 .0273** 10.772224
LNVLVS -.788409066OE-02 .577783218—02 -1.365 .1724 12.442016
LNVLVC .25823914258-02 .59348816E-02 .435 .6635 5.5281200
LNVLTA -.4311669969E-02 .571488668-01 - 075 .9399 5.6226780
LNVLVA -.1024877944E-01 .88139707E—02 —1.163 .2449 26.213959
LNVLLV -.1575229266E-03 .10735097E-01 -.015 .9883 28.396614
nuvsvs .6201242574E-01 .21754202E-01 2.851 .0044** 6.3346163
nuvsvc -.1820376086E-01 .72299261E-02 -2.518 .0118** 2.6501878
LNVSTA -.7193950867E-01 .62348068E-01 -1.154 .2486 3.8566413
LNVSVA -.1016568374E-01 .11125237E-01 -.914 .3608 18.189565
LNVSLV -.10648891258—01 .13233235E-01 -.805 .4210 19.744443
nuvcvc .48319723278-01 .157968268-01 3.059 .0022** 4.2986908
LNVCTA .8521775292E-02 .62272348E-01 .137 .8912 2.3162624
ancva -.4661715577E-02 .131589608-01 —.354 .7231 11.846978
LNVCLV .1011247294E-01 .15907020E-01 .636 .5250 12.017633
LNTATA -.2655047518 .67866134 —.391 .6956 .99972989
LNTAVA .22512754968-01 .87898840E-01 .256 .7979 9.6564848
LNTAVL .1697879963 .11396079 1.490 .1363 10.124702
LNVAVA -.4373806024E-02 .30476408E—01 -.144 .8859 25.464669
nuvanv .4410238486E-01 .22682248E-01 1.944 .0519** 51.002857
LNLVLV .2578586366E-01 .33028987E-01 .781 .4350 27.078326
LNHYLD .2417886430 .99130070E-01 2.439 .0147H 2.5989920
NAREDV -.1197881190 .10339076 -1.159 .2466 .48235294
Variance parameters for compound error
Theta 8.590372227 18.315128 .469 .6390
Sigmav .4090507191 .651967413-01 6.274 .0000**

 

232

Table A10: Cost Frontier Parameter Estimates (Exponential), 1989/90

 

Limited Dependent Variable Model — FRONTIER I
Maximum Likelihood Estimates

 

 

 

 

 

I

I |

I Dependent variable LNNTVC I

I Weighting variable ONE |

I Number of observations 331 I

I Iterations completed 1 |

I LM Stat. at start values 6.501468 |

I LM statistic kept as scalar LMSTAT I

I Log likelihood function -164.5451 I

I Exponential frontier model I

I Variances: Sigma-squaredIv)= .11870 I

l Sigma-squared(u)= .04090 I
lVariable I Coefficient | Standard Error lb/St.Er.|P[IZI>z] I Mean of XI
Constant 8.728353212 8.2870870 1.053 .2922
LNNPL 1.195173504 2.8345563 .422 .6733 .88227558
ENNIS -14.64737130 6.1796176 -2.370 .0178** 1.3461501
LNNLS 5.348154992 8.2475338 .648 .5167 1.0946537
LNNSS 9.145605495 9.4684551 .966 .3341 1.1917822
LNNCS 2.949294706 2.7485416 1.073 .2833 .87544951
LNVM -.3915471509 .43552847 -.899 .3686 5.1916238
LNVL .1844759243 .27023104 .683 .4948 3.3436941
ENVS .9275496661 .31266273 2.967 .0030** 2.4289928
LNVC .3613435623 .36165097 .999 .3177 1.2108494
ERIK -4.444700967 1.4892708 -2.984 .0028** 1.3503719
LNVA .5517143286E-01 .70008155 .079 .9372 6.4394190
LNLV -.5572006410 .62133406 -.897 .3698 7.1224702
ENPLPL -2.148329038 .76940117 -2.792 .0052** .44421681
LNPLMS 1.395392148 1.8420922 .758 .4487 1.1952261
LNPLLS -.6558077930 1.7739150 -.370 .7116 .97472234
LNPLSS .9890554844 2.1935657 .451 .6521 1.0611853
LNPLCS .4176391935 .57490701 .726 .4676 .85741185
LNPLVM -.1564474102 .82076860E—01 ~1.906 .0566* 4.5698587
LNPLVL .5300758934E-01 .78873006E-01 .672 .5015 2.8809659
LNPLVS -.1298936598 .76168718E-01 -1.705 .0881* 1.8034776
LNPLVC -.1250359879 .82203910E-01 ~1.521 .1282 1.0992641
ENPLIA .7267371372 .32288909 2.251 .0244** 1.1531831
LNPLVA -.1324007118 .14177467 -.934 .3504 5.7166342
LNPLLV .5205533096E-01 .14324477 .363 .7163 6.2404563
LNHSMS 4.535577918 2.0932064 2.167 .0302** .91544618
LNMSLS .2063299026 5.6972364 .036 .9711 1.4783277
LNMSSS .5282460132 4.4428317 .119 .9054 1.6075868
LNMSCS .1733663403 1.6255476 .107 .9151 1.1898211
LNMSVM .4597363171 .24435079 1.881 .0599* 6.9811986
LNMSVL -.2073052726 .18287678 -l.134 .2570 4.4672883
LNMSVS .1225181177E-01 .20712408 .059 .9528 3.2334759
LNMSVC .9466529399E-01 .19940217 .475 .6350 1.6376282
LNMSTA .7953529663 .79501241 1.000 .3171 1.8096588
LNMSVA .2937634298 .36992505 .794 .4271 8.6643952
LNMSLV .2503738356 .30812137 .813 .4165 9.5547595
LNLSLS .4320744816 3.4457634 .125 .9002 .60582448
LNLSSS -2.589362893 6.1145441 -.423 .6719 1.3081353
LNLSCS -1.373664130 1.8483524 -.743 .4574 .96675937
LNLSVM -.1130971792 .23542576 -.480 .6309 5.6946340
LNLSVL .7292086828E-01 .19360356 .377 .7064 3.6291793
LNLSVS -.2299063679 .27369986 -.840 .4009 2.6301577

 

233

 

 

 

 

Table A10: Cost Frontier Parameter Estimates (Exponential), 1989/90; Cont.
lVariable I Coefficient I Standard Error Ib/St.Er.IP[IZI>z] I Mean of XI
LNLSVC -.1248766448 .28742869 -.434 .6640 1.3314201
LNLSTA .5828917791 1.2276473 .475 .6349 1.4742554
LNLSVA .1313592922 .40542361 .324 .7459 7.0536661
LNLSLV -.2744981641 .29951531 -.916 .3594 7.7836915
LNSSSS -6.790416780 4.6722604 -l.453 .1461 .71444207
LNSSCS -1.343078918 2.1937264 -.612 .5404 1.0553449
LNSSVM .1108473992 .36408508 .304 .7608 6.1849992
LNSSVL .3464399774E-02 .19628103 .018 .9859 3.9735414
nnssvs -.4827733890 .22496563 «2.146 .0319** 2.8560128
LNSSVC -.1015097675 .19706800 -.515 .6065 1.4613889
ENSSIA 2.673631853 1.2167171 2.197 .0280** 1.6050268
LNSSVA -.4537575738 .45703790 -.993 .3208 7.6773717
LNSSLV .2436891462 .46815271 .521 .6027 8.4697311
LNCSCS -.8398519409E-01 .74802506 -.112 .9106 .46587571
LNCSVM -.1043201132 .83767788E-01 -1.245 .2130 4.5742041
LNCSVL .12130960903-01 .77413479E-01 .157 .8755 2.8111466
LNCSVS .73841217348-01 .97556745E-01 .757 .4491 1.7128804
LNCSVC .70215571313-01 .7251464BE-Ol .968 .3329 1.1680506
LNCSTA -.2794617518 .41888265 -.667 .5047 1.1189231
LNCSVA .1347734249E-01 .14543915 .093 .9262 5.6747968
LNCSLV -.41628646OBE-02 .11295242 -.037 .9706 6.1372630
LNVNVI .1171707572 .30954828E-01 3.785 .0002** 15.034542
LyyMVL -.2612736678E-01 .15540308E-01 -1.681 .0927* 18.658161
LNVMVS -.153545526SE-01 .lZ602284E-01 -1.218 .2231 13.156604
ENVIVC -.5339736403E-01 .17378214E-01 -3.073 .0021** 7.2448809
LNVMTA -.1098301642E-01 .51227923E—01 -.214 .8302 7.0971665
LNVINI -.501145193ZE-01 .227912182-01 -2.199 .0279** 34.048816
LNVMLV .17185595803-01 .14419664E-01 1.192 .2333 37.755287
LNVBVL .59621079793-01 .202929993-01 2.938 .0033** 8.3137646
LNVLVS -.7526445470E-02 .77459270E-02 -.972 .3312 9.2734422
LNVLVC .16780943318-02 .85313713E-02 .197 .8441 5.1565872
LNVLTA .22896303738-01 .37318747E-01 .614 .5395 4.9709757
LNVLVA .11785805928-01 .149102528-01 .790 .4293 21.970795
LNVLLV -.1298801152E-01 .13291297E-01 -.977 .3285 24.610321
LNVSVS -.37884100008-01 .264330348-01 -l.433 .1518 5.7703077
LNVSVC -.3780957023E-02 .94258034E-02 —.401 .6883 3.5028585
LNVSTA .68843752758-01 .37729793E-01 1.825 .0681* 3.8055501
LNVSVA -.3464481027E—02 .166529528-01 -.208 .8352 15.558662
LNVSLV .14248717858-01 .16388681E—01 .869 .3846 18.204183
LNVCVC .60029037373-01 .27434197E-01 2.188 .0287** 3.0405703
LNVCTA -.6584018253E-01 .501315448-01 -1.313 .1891 1.9298398
LNVCVA .1455979709E-01 .19631003E-01 .742 .4583 7.8488264
LNVCLV -.300004034ZE-03 .15636141E-01 -.019 .9847 8.7199356
LNTATA -.2062284820 .26426703 -.780 .4352 1.0491833
LNTAVA -.1704889315E-01 .95030148E-01 -.179 .8576 8.8268865
LNTALV -.3839771417E-01 .74856142E-01 -.513 .6080 9.8744344
LNVAVA .49895162218-01 .47074227E-01 1.060 .2892 21.489860
LNVALV -.7613587438E-02 .29968423E-01 -.254 .7995 46.825796
LNLVLV .4633078330E-01 .38889218E-01 1.191 .2335 26.539769
HIREDV .4219532343 .19435845 2.171 .0299** .30815710
SOILDV .25865332768-01 .23284518E—01 1.111 .2666 .44410876
Variance parameters for compound error
Theta 4.944528311 2.3607572 2.094 .0362**
Signav .3445318724 .48332369E-01 7.128 .0000**

 

234

Table A1 1:

Cost Frontier Parameter Estimates (Exponential), 1992/93

 

I Limited Dependent Variable Model - FRONTIER I

Maximum Likelihood Estimates

 

 

I I

I Dependent variable LNNTVC I

I Weighting variable ONE I

I Number of observations 368 I

I Iterations completed 1 I

I LM Stat. at start values 2.124636 I

I LM statistic kept as scalar LMSTAT |

I Log likelihood function ~107.l903 I

I Exponential frontier model I

I Variances: Sigma—squared(v)= .08349 I

I Sigma-squared(u)= .02171 I
IVariable I Coefficient | Standard Error Ib/St.Er.IP[IZ|>z] I Mean of XI
Constant 1.528820402 1.0107048 1.513 .1304
LNNPL 1.826944604 .60796336 3.005 .0027** 1.7388216
LNNMS .3858863009 .44172618 .874 .3823 1.7544106
LNNLS -.2555987795 .50186893 -.509 .6105 2.4087634
LNNSS .6238316734E-01 .93314582 .067 .9467 1.9325746
LNNCS .6278538246 .70215579 .894 .3712 2.2196989
LNVM .1069955173 .17980905 .595 .5518 7.1497868
LNVL .1134199332E-01 .79463301E-01 .143 .8865 2.5772566
nnvs .1767130073 .755828192-01 2.338 .0194** 3.5580386
LNVC -.4902568099E-01 .11460677 -.428 .6688 1.8032684
LITA 2.741694143 .60902887 4.502 .0000** 1.2177632
LNPLPL -.1027754640 .19357022 -.531 .5955 1.7349561
LNPLMS -.1283803882 .12992241 -.988 .3231 3.2156495
LNPLLS -.1708235439E-01 .11730852 -.146 .8842 4.5787074
LNPLSS .1739499845 .26630597 .653 .5136 3.6779324
LNPLCS -.1456767491 .19823708 -.735 .4624 4.1173248
LNPLVM -.2206361393E-01 .74645303E—01 -.296 .7676 12.276423
LNPLVL .56364291633-01 .246785983-01 2.284 .0224** 4.1970061
LNPLVS -.1718485404E-01 .32074637E-01 -.536 .5921 6.2314152
LNPLVC .1955703071E-01 .26770717E-01 .731 .4651 2.9012274
LNPLTA -.1218152085 .23064624 —.528 .5974 2.0627293
LNMSMS .2739238099 .18082231 1.515 .1298 1.7652662
LNMSLS -.4922317208E-01 .10994377 -.448 .6544 4.3899015
LNMSSS .5327312242E-01 .18104428 .294 .7686 3.5756691
LNMSCS -.8951055778E-01 .14703149 -.609 .5427 3.9873081
LNMSVM -.4226055304E-01 .51693643E-01 -.818 .4136 12.525402
LNMSVL -.1662030866E-01 .19753625E-01 —.841 .4001 4.8336116
LNMSVS .40902973808-01 .186647183-01 2.191 .0284** 6.4994562
LNMSVC -.8135033920E-02 .20475571E-01 -.397 .6911 3.3089376
LNMSTA ~.1899932224 .15552644 -1.222 .2219 2.2211818
LNLSLS -.4144775329E-01 .14032223 -.295 .7677 3.2874154
LNLSSS -.3578668376E-01 .23038107 -.155 .8766 5.0346705
LNLSCS .4555439635E-01 .17157991 .265 .7906 5.6522160

 

235

 

 

 

 

 

 

Table All: Cost Frontier Parameter Estimates (Exponential), 1992/93, Cont.
IVariable I Coefficient I Standard Error Ib/St.Er.IP[|ZI>z] I Mean of XI
LNLSVM .3275066490E-01 .61406950E-01 .533 .5938 17.130738
LNLSVL .38580756018-02 .174824528-01 .221 .8253 5.7799213
LNLSVS -.1198368423E—01 .22511185E-01 -.532 .5945 8.7345313
LNLSVC -.1823903559E-01 .32048903E-01 -.569 .5693 4.6003379
LNLSTA .2881939328 .18245556 1.580 .1142 2.9281693
LNSSSS -.4627973547E-03 .41763218 -.001 .9991 2.0720305
LNSSCS -.1863367650E-01 .22768809 -.082 .9348 4.5477349
LNSSVM .2288422372E-01 .98798291E-01 .232 .8168 13.768926
LNSSVL -.505402624OE-01 .35901030E-01 -1.408 .1592 4.7765119
LNSSVS -.4663176071E-01 .44456366E-01 -1.049 .2942 6.9350380
LNSSVC -.1857588631E-01 .38421196E-01 -.483 .6288 3.2810114
LNSSTA -.l403606280 .29128616 -.482 .6299 2.3254654
LNCSCS .1011902080 .988624128-01 1.024 .3060 2.7695815
LNCSVM -.1031923864 .77586744E-01 -1.330 .1835 15.864477
LNCSVL -.1216330283E-01 .26557839E-01 -.458 .6470 5.8213300
LNCSVS .3804696985E-01 .341051603-01 1.116 .2646 7.5331993
LNCSVC .2703426776E-01 .14624235E-01 1.849 .0645* 4.1236235
LNCSTA .80395322088-01 .22509628 .357 .7210 2.6731814
LNVMVM .45060882413-01 .211006553—01 2.136 .0327** 26.352182
LNVMVL .5173073996E-03 .10829083E-01 .048 .9619 19.539507
LNVMVS -.1866329603E-01 .994978348-02 -1.876 .0607 25.387309
LNVMVC .84954376548-03 .12147886E-01 .070 .9442 13.795925
LNVMTA -.1392406094 .90509404E-01 -1.538 .1239 8.9188446
LNVBVL .4067500287E-01 .12159024E-01 3.345 .0008** 7.2792272
LNVLVS -.4739722696E-02 .38623162E-02 -1.227 .2198 9.3476876
LNVLVC -.1003527223E-02 .36954016E-02 -.272 , .7860 5.5334338
LNVLTA -.3678220352E-01 .30044830E-01 -1.224 .2209 3.4941215
LNVSVS .7985421508E-02 .11038799E-01 .723 .4694 9.6837998
LNVSVC .12580067102-01 .42191948E-02 2.982 .0029** 5.6222526
LNVSTA -.6252298038E-01 .33276391E-01 -1.879 .0603* 4.6983002
LNVCVC .2170191625E-01 .12192080E-01 1.780 .0751* 5.8700932
LNVCTA -.2993842678E-01 .32758646E-01 -.914 .3608 2.7917639
LNTATA -.2936388608 .36232763 -.810 .4177 .83817794
ENMZYLD .2652325563 .61163489E-01 4.336 .0000** 2.8355027
NAREDV -.1018358194 .75054036E-01 -1.357 .1748 .43478261
Variance parameters for compound error
Theta 6.786365303 3.5898432 1.890 .0587*
Signzv .2889524560 .340057253-01 8.497 .0000**

 

236

I'IIICH GQN STRTE UNIV LIBRARIE

I IIIIIIII III IIIIIIIIIIIIII III I||II||8II| II II

III IIII