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ESSAYS ON APPLIED PRODUCTION ANALYSIS IN
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ESSAYS ON APPLIED PRODUCTION ANALYSIS IN AGRICULTURE
By

Zhiying X'u

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Agricultural Economics

2008

ABSTRACT
ESSAYS ON APPLIED PRODUCTION ANALYSIS IN AGRICULTURE
By
Zhiying Xu

This dissertation extends prior research under two important themes in
agricultural production study: technology adoption and crop production analysis. New
perspectives are incorporated into this dissertation under each research theme; in
particular, it underscores the relevance of agricultural input marketing system in
analyzing farmers’ input use in the context of developing countries, and the relevance of
agronomic principles to crop production analysis. New framework and methods
developed in this study are used to analyze fertilizer adoption and maize production in
Zambia.

Many governments in developing countries distribute fertilizer at subsidized
prices to stimulate small farmers’ agricultural productivity and food security. Prior
studies investigating the farmer and community characteristics associated with fertilizer
use largely fail to account for the effects of government input distribution programs on
farmers’ fertilizer purchase decisions. Using nationally representative rural household
panel data in Zambia, we distinguish between commercial and subsidized fertilizer
purchases and measure the “crowding in/out” effect of government input programs on
commercial fertilizer sales using a double hurdle modeling framework. Results indicate
that private sector fertilizer sales can decline substantially due to government programs.
In areas where private sector is not already active, government program may possibly

enhance commercial demand over the long run. Empirical studies explicitly modeling

 

 

farmers’ fertilizer purchase behavior within a dual marketing framework can provide
important insights for agricultural policy discussions in developing countries.

While raising small farmer fertilizer use and staple food productivity has been a
major goal of Zambian government’s agricultural policy, a recent survey of beneficiary
farmers indicates that government program has very little impact in terms of increasing
maize production and household incomes. In the second essay, we use nationwide panel
survey data to estimate maize production function and determine profitability of fertilizer
use under a range of small farm conditions in Zambia. Based on agronomic principles of
crop growth process, we develop a crop production function that distinguishes different
roles of inputs and examine the effects of various farm inputs, government programs, and
household socioeconomic characteristics on maize yield. Our analysis suggests that
fertilizer use is largely unprofitable under most smallholder conditions due to low yield
response rates and unfavorable price conditions. Programs to achieve the yield and
profitability potentials of fertilizer use will require efforts to ensure more timely delivery
of fertilizer, reduce input and output marketing costs and provide sensible extension

services to small farmers.

 

Copyright by
ZHIYING XU
2008

 

I dedicate this work to my parents and to the memory of my grandparents.

 

ACKNOWLEDGEMENTS

I would like to extend my gratitude to all those who have helped me and given me
support and encouragement over the entire dissertation process.

First and foremost, I would like to thank my dissertation committee. I was
fortunate to have worked with and learned much from these inspiring scholars and
teachers. I am grateful to my committee chair, Thom Jayne, for his guidance and support.
Not only was he available to discuss my research, he responded to various drafts of this
dissertation quickly and provided detailed comments. I greatly appreciate his support
which made the fruition of this work possible.

I would like to express my thanks to Robert Myers, Jefferey Wooldridge, Roy
Black, and Zhengfei Guan, who served on my committee and provided excellent
feedback on my research. I am grateful to Robert Myers and J efferey Wooldridge for
teaching me econometric and quantitative techniques, critical thinking, and effective
communication of ideas, through my coursework and dissertation research over the past
few years. Their expertise and assistance are greatly appreciated. My gratitude also goes
to Roy Black and Zhengfei Guan for providing valuable comments and ideas. I greatly
appreciate the contributions they have made to improve my dissertation.

Many other people on the faculty and staff of the Department of Agricultural
Economics helped me in various ways during my graduate studies. I am especially
thankful to Eric Crawford, Scott Loveridge, Steve Hanson, Scott Swinton, Songqing J in,
Cynthia Donovan, Jones Govereh, Margaret Beaver, Debbie Conway, Rosie Kelly, and

Xiao Zhen Li, for their support and assistance.

vi

My years at Michigan State University would not have been as enjoyable without
my friends and fellow students, especially Allan Fan, Yanyan Liu, Sarma Aralas, Wei
Zhang, Chris Wright, Sindi Kirimi, Honglin Wang, Epi Katjiuongua, Lara De Villa, Lili
Gao, F eng Wu, Feng Song, Fang Xie, Xuan Wei, Ping Yuan, Tomo Nagai, Andrew
Kizito, Ricardo Hernandez, Catherine Ragasa, and late friend Lesiba Elias Bopape. I am
grateful to them for their support.

I would like to thank my brother and sister-in-law for their support and
understanding. I give special thanks to my parents, Guangnan Xu and Shunai Gui, for the
unconditional love and encouragement they have always given me. I am deeply grateful

to them for supporting my aspirations over the years.

vii

 

 

TABLE OF CONTENTS
LIST OF TABLES ................................................................................. ix
LIST OF FIGURES .................................................................................. x
INTRODUCTION .............................................................................................................. l

ESSAY 1:
DO INPUT SUBSIDY PROGRAMS “CROWD IN” OR “CROWD OUT”
COMMERCIAL MARKET DEVELOPMENT? MODELING FERTILIZER USE

DECISIONS IN A TWO-CHANNEL MARKETING SYSTEM ...................................... 5
l . 1 Introduction ......................................................................................................... 5
1.2 Zambia’s Fertilizer Marketing System ............................................................... 8
1.3 Modeling Framework .............................................................................................. 10

1.3.1 Crowding in/out Effect .................................................................................... 10
1.3.2 Measuring “Crowding in/out” Using a Double Hurdle Model ........................ 12
1 .4 Estimation ......................................................................................................... 19
1.5 Data and Variable Construction .............................................................................. 20
1.5.1 Data .................................................................................................................. 21
1.5.2 Explanatory Variables ...................................................................................... 22
1.6 Findings ............................................................................................................. 23
1.6.] Estimation Results ........................................................................................... 24
1.6.2 Magnitude of the Crowding out Effect ............................................................ 27
1 .7 Conclusions ....................................................................................................... 29
REFERENCES ............................................................................................................. 45

ESSAY 2:

AN ASYMMETRIC CROP PRODUCTION MODEL AND THE APPLICATION TO

MAIZE PRODUCTION IN ZAMBIA ............................................................................. 48
2.1 Introduction ............................................................................................................. 48
2.2 Modeling Framework .............................................................................................. 53
2.3 Data and Econometric Issues .................................................................................. 55

2.3.1 Data .................................................................................................................. 55
2.3.2 Econometric Issues .......................................................................................... 56
2.4 Empirical Model ..................................................................................................... 59
2.5 Empirical Results .................................................................................................... 62
2.5.1 Attrition ............................................................................................................ 62
2.5.2 Production Function Estimation Results .......................................................... 63
2.5.3 Profitability of Fertilizer Use ........................................................................... 65
2.6 Conclusions ............................................................................................................. 67
REFERENCES ............................................................................................................. 78

viii

1“} uflfil

 

 

 

LIST OF TABLES

Table 1.1: Quantities of fertilizer procured by smallholder farmers, by type of supplier,
1995/ 1996 — 2005/2006 .................................................................................................... 32

Table 1.2: Definitions for variables .................................................................................. 33

Table 1.3: Fertilizer use patterns by source of procurement and by household wealth
status, 2002/2003 .............................................................................................................. 35

Table 1.4: Partial effect estimates of double hurdle model for fertilizer acquisition from
government program ......................................................................................................... 36

Table 1.5: Partial effect estimates of double hurdle model for fertilizer acquisition from
private sector ..................................................................................................................... 38

Table 1.6: Effects of government fertilizer program on total fertilizer consumption ....... 40

Table 1.7: Effects of government program on total fertilizer consumption by areas based

on percentage of households purchasing commercial fertilizer ........................................ 41
Table 1.8: Total changes in private sector sales ............................................................... 42
Table 2.1: Variable definition ........................................................................................... 69
Table 2.2: Means between attritors and non-attritors, 1999/00 ........................................ 70
Table 2.3: Coefficient estimates of empirical crop production fimction .......................... 71
Table 2.4: Estimates of partial effects ............................................................................... 73

Table 2.5: Estimates of marginal productivity of nitrogen and marginal value-cost ratio,
Zone IIA, AF ..................................................................................................................... 74

Table 2.6: Estimates of marginal productivity of nitrogen and marginal value-cost ratio,
Zone IIA, Non-AF ............................................................................................................ 75

Table 2.7: Estimates of marginal productivity of nitrogen and marginal value-cost ratio,
Zone 111, AF ...................................................................................................................... 76

Table 2.8: Estimates of marginal productivity of nitrogen and marginal value-cost ratio,
Zone 111, Non-AF .............................................................................................................. 77

ix

LIST OF FIGURES

Figure 1.1: Community-level (SEA) quantity of fertilizer acquired from private sector
versus from government program, 1999/2000 .................................................................. 43

Figure 1.2: Community-level (SEA) quantity of fertilizer acquired from private sector
versus from government program, 2002/2003 ................................................................. '. 44

INTRODUCTION

This dissertation consists of two essays. The first essay deals with agricultural
input use and the second essay deals with farm crop production, both in the context of
developing countries. Empirical analyses are based on rural household survey data from
Zambia.

In sub-Saharan Africa, farm productivity growth is widely recognized as a
precondition for broad based economic development. Achieving this productivity growth
is likely to involve, among many other things, much greater use of fertilizer by African
farmers. To this end, a number of approaches have been attempted over the past three
decades, including state subsidized distribution programs, targeted input credit programs,
free starter packs, interlinked credit-input-crop marketing arrangements, and
“liberalization” whereby private traders are encouraged to develop commercial input
marketing networks. In recent years, many African countries have re-instated fertilizer
subsidy programs to operate alongside commercial fertilizer distribution systems. Despite
these efforts, fertilizer use in sub-Saharan Africa has been consistently low and currently
stands at 9 kilograms per cropped hectare, by far the lowest of any region of the world.

The first essay is broadly motivated by an urgent need for research into
understanding the challenges of raising farmers’ fertilizer use and how best to meet these
challenges in sub-Saharan Africa. A double hurdle modeling framework is used to
analyze households’ fertilizer acquisition within the context of a dual input marketing
system. The theoretical model is applied to small-scale maize farmers in Zambia using

nationally representative household panel data. Zambian government agricultural policy

 

 

has focused on subsidized fertilizer distribution programs to increase farm productivity
and nurture the development of private sector in fertilizer distribution. Empirical studies
taking explicit account of dual input marketing system in modeling farmer input use can
provide important insights for agricultural policy discussions in developing countries.

This article goes beyond prior studies in three ways. First, it provides a
framework for estimating the degree of crowding in/out of private sector sales resulting
from government input subsidy programs, an important policy issue that has largely
lacked empirical foundation to date. Second, by explicitly distinguishing between
commercial and subsidized input purchases, the framework more accurately identifies
household and community characteristics affecting effective input demand as distinct
from those associated with acquisition of subsidized input. Third, it addresses some of the
problems affecting prior studies associated with controlling for unobserved household
heterogeneity. Relevant variables are almost always missing, such as between-household
variation in land quality, farmer skill, and risk attitude, which are hard to obtain or
difficult to measure. Unobserved household heterogeneity is controlled for in this essay
through panel data estimation method.

A recent assessment of the implementation and effectiveness of the government
fertilizer support programme (FSP) based on a survey of randomly selected 116
beneficiary farmers in Zambia indicates that F SP has very little impact in terms of
increasing maize production and enhancing household incomes and livelihoods. Several
factors were identified as responsible for reducing the effectiveness of the Programme:
Delays in input supply, inadequate supply of farm inputs, poor crop marketing

arrangements, high input prices and low output prices, and poor transport facilities,

among others. This highlights the need for an in-depth study of maize yield response to
fertilizer use, timeliness of fertilizer application and other crop management practices,
and profitability of fertilizer use under current small farm conditions to inform policy
process aimed at achieving sustainable increase in maize productivity and smallholder
incomes. These issues are addressed in the second essay.

While recognizing the importance of providing extension services to small
farmers, extension messages and fertilizer distribution programs in Zambia have been
based on one nationally recommended application rate, which largely ignores
heterogeneity in small farm conditions and differing market conditions. As fertilizer
remains an expensive input in many countries in sub-Saharan Africa, extension messages
and government programs promoting fertilizer use should emphasize technically viable
and economically efficient use of fertilizer, taking account of agroecological conditions,
complementary farming practices and cost-effectiveness of fertilizer application.

In recent years with greater availability of large farm survey data in developing
countries, there has been a rapid increase in the number of studies that used survey data
to estimate crop production functions at the farm level. The extent to which a
mathematical form of production function can approximate the actual input-output
relationships in field production depends crucially on the knowledge of these
relationships. Prior studies largely ignore agronomic principles of crop growth process
and treat all inputs symmetrically in production function specification. In addition,
simultaneity problem that often exists in empirical crop production analysis has not
received enough attention. The second essay deals with these issues with an application

to smallholder maize production in Zambia. By incorporating agronomic principles into

 

the specification of production function and by using panel data technique to address
simultaneity problem, we expect to obtain more precise estimates of the maize production

function and derive valid policy implications.

 

ESSAY 1:
DO INPUT SUBSIDY PROGRAMS “CROWD IN” OR “CROWD OUT”
COMMERCIAL MARKET DEVELOPMENT? MODELING FERTILIZER USE
DECISIONS IN A TWO-CHANNEL MARKETING SYSTEM

1.1 Introduction

Fertilizer use in sub-Saharan Africa currently stands at 9 kilograms (kgs) per
cropped hectare — by far the lowest of any region of the world. There is widespread
consensus that African farmers will need to make much greater use of fertilizer to
generate the growth in farm productivity needed to reduce poverty. However, there is
considerable debate about exactly how to achieve sustainable increases in fertilizer use in
sub-Saharan Africa.1 Over the past 30 years, a number of different approaches have been
attempted, including state subsidized distribution programs, targeted input credit
programs, free starter packs, interlinked credit-input-crop marketing outgrower
arrangements, and “liberalization,” whereby private traders are encouraged to develop
commercial input marketing networks in rural areas. A review of the literature reveals
mixed evidence and much debate about the appropriate roles of government and the
private sector in sustainably raising small farmers’ use of fertilizer (for reviews, see
Morris et al., 2007; Crawford et al., 2006; Dorward et al., 2004; Gladwin et al., 2002;
Minot, 2002).

In recent years, many African countries have re-instated fertilizer subsidy

programs to operate alongside commercial fertilizer distribution systems. The rising role

 

I For example, the Fertilizer Summit in Abuja (2006) and its resulting “Abuja Declaration” (2006),
endorsed by the African Union and its African member states, signaled the intention to scale-up the use of
fertilizer subsidies as a means to address rural poverty. Meanwhile, the recent World Bank fertilizer report
(Morris et al., 2007) strongly questions the contribution that fertilizer subsidies can make to sustained
poverty reduction in sub-Saharan Africa.

 

of state fertilizer subsidy programs reflects disillusionment in some quarters with the
private sector’s ability to stimulate small farmers’ use of fertilizer to levels deemed
essential for achieving rapid agricultural productivity growth and poverty reduction.
Dorward et al. (2004) contend that state-led input and output marketing policies featured
prominently in the “green revolution” successes achieved in Asia in the 1970s and 19805
and that similar programs will be needed in Africa. Moreover, some fertilizer subsidy
programs have been designed in such a way as to “crowd-in” private sector investment by
awarding contracts to firms for the distribution of subsidized fertilizer, which may reduce
the fixed costs of investing in commercial supply channels, and possibly raise the
effective demand for fertilizer among farmers who had not previously used it.

On the other hand, there are concerns that sustainable increases in fertilizer use
are blocked by a “catch-22” situation in which government fertilizer distribution
programs undermine the demand for commercially distributed fertilizer, which may
“crowd out” private investment in input marketing, and then justify the rationale for
continued government programs (Jayne et al., 2003; Pletcher, 2000). In this way, subsidy
programs designed to correct for temporary market failure or achieve other social and
developmental objectives may actually impede national policy objectives to achieve
sustainable growth in commercial fertilizer use.

There is a vast literature on fertilizer marketing in Africa using household survey
data, including many applied econometric studies attempting to understand the factors
affecting small farmers’ fertilizer use decisions.2 However, to our knowledge none of

these analyses have explicitly taken into account the parallel state and commercial

 

2 For reviews, see Morris et al., (2007), Kelly (2006), and Minot (2002). Specific country studies include
Abdoulaye and Sanders (2005), Chirwa (2005), Croppenstedt et a1. (2003), Isham (2002), Kaliba et al.
(2000), Minot et al. (2000), Adugna (1997), Nkonya et al. (1997), and Green and Ng’ong’ola (1993).

channels that characterize the input marketing situation in many African countries. As a
result, the applied literature to date is largely unable to inform important policy questions
about how the state and commercial input distribution systems interact to affect overall
fertilizer use, and specifically whether the state input distribution programs crowd-in or
crowd-out private sector input sales.

This study develops a double hurdle modeling framework for analyzing
households’ fertilizer purchases within the context of a dual input marketing system. We
then apply the theoretical model to small-scale maize farmers in Zambia using nationally
representative household panel data. Zambia, in southern Africa, provides an interesting
case to examine the interactions between government and private input distribution
channels and the measurement of “crowding in/out” of commercial fertilizer market
development. Zambian government agricultural policy has for the past several decades
focused on subsidized fertilizer distribution programs to increase farm productivity and
nurture the development of the private sector in fertilizer distribution.

This study has several innovations compared to prior studies. First, the study
provides a framework for estimating the degree of crowding in/out of private sector input
sales resulting from government input subsidy programs, an important policy issue that
has largely lacked an empirical foundation to date. Second, by explicitly distinguishing
between commercial and subsidized fertilizer purchases, the framework more accurately
identifies household and community characteristics associated with effective input
demand as distinct from those associated with acquisition of subsidized input. Household
characteristics affecting fertilizer acquisition from the two channels may be very

different; merging them together into one input demand function would be a source of

 

 

model mis-specification. Government programs often attempt to target poor households, 1'
while commercial fertilizer sales, being a function of effective demand, may be
accounted for mainly by relatively wealthy and educated farmers. Third, this study
addresses some of the problems affecting prior studies associated with controlling for
unobserved household heterogeneity. Relevant variables are almost always missing, such
as between-household variation in land quality, farmer skill, and risk attitudes, which are
hard to obtain or difficult to measure. Unobserved household heterogeneity is controlled
for through the use of panel data estimation method in this study.

The remainder of the paper is organized as follows. First, we briefly describe the
structure and behavior of fertilizer markets and the government fertilizer program in
Zambia. Section 3 presents a framework for measuring the crowding in/out effect of
government input programs on commercial fertilizer sales using a double hurdle
modeling approach that explicitly takes into account the effects of government subsidy
programs on households’ commercial fertilizer acquisition. Estimation techniques to
control for unobserved heterogeneity are also presented in this section. We then describe
the data and variable construction in Section 4, followed by the main findings in Section
5. Section 6 summarizes the main points of the study and considers possible implications

for public policy.

1.2 Zambia’s Fertilizer Marketing System
Promoting small farmers’ access to fertilizer has been a longstanding policy
concern in many African countries. For most of its history, fertilizer distribution in

Zambia was controlled by government. The financial burden and inefficiencies of the

public input subsidy programs prompted the legalization of private fertilizer trade in the
early 19903. However, almost continuously during the “liberalization” period, various
types of government credit and/or input subsidy programs have operated alongside the
emerging private distribution system. Starting in 1993, the government designated
private agents to distribute fertilizer on loan to “resource poor” farmers, and then to
recover the loans after harvest through purchasing maize from the loan recipients. In
each year since 1993, the loan recovery rate was never higher than 43 percent and was
typically below 30 percent (Govereh et al., 2002).

Starting in 2002, the government eliminated the fertilizer credit program and
initiated its Fertilizer Support Programme (FSP), which continues to this day. In both the
fertilizer loan program and the F SP, the scale, regions of delivery, and selection of
beneficiary farmers are determined by national and local government bodies and are
therefore exogenous from the standpoint of individual farmers. The Ministry of
Agriculture tender board invites private firms to submit tenders for procuring fertilizer
from international sources and deliver them to district depots (there are roughly 70
districts).3 Next, government selects local input distributors to deliver fertilizer from the
district depots to satellite depots and cooperative warehouses for subsequent release to
approved individual farmers at approximately 50% of the full retail cost. Hence, if the
government is distributing fertilizer in a particular area, a farmer who might otherwise
choose to purchase fertilizer at full price from a private dealer may perceive an advantage

in trying to acquire fertilizer from the government program instead. Despite these

 

3 Over the past several years, two firms have consistently been awarded these regional tenders.
Government generally pays these firms a flat commission for the distribution of fertilizer to the district
depots in each region. Some studies have concluded that the consistent awarding of tenders to two large
and prominent firms has caused other commercial firms to withdraw fi'om fertilizer distribution in Zambia
and has led to a more concentrated and oligopolistic market at wholesale level (Govereh et al., 2006).

government’s efforts over the last 15 years, overall fertilizer consumption has expanded l
slowly and only 20% of smallholder farmers used fertilizer in the 2002/2003 crop season.
An explicit objective of the government subsidy program is to nurture the
development of private fertilizer channels (GRZ, 2002). By contracting private firms to

distribute fertilizer on behalf of government, the Fertilizer Support Programme is
intended to reduce the fixed costs that private firms would otherwise face in developing
supply channels to remote rural areas, thereby “crowding-in” private investment. The
program is also intended to expand farmers’ effective demand for fertilizer over time.
Indeed, between 1999 and 2005, the volume of fertilizer distributed under government
programs has been roughly constant at 40,000 to 50,000 tonnes of maize, but private
sector fertilizer sales appear to have grown moderately (Table 1.1). Yet it is also possible
that the government’s distribution of large quantities of subsidized fertilizer, especially if
targeted to relatively wealthy farmers, could adversely affect investment in the fertilizer
market by private firms as well. There has been little evidence-based research to date to
help policy makers understand the extent to which their fertilizer promotion program
affects sales by the private sector and hence the long-term development of input markets

in a liberalized policy environment.

1.3 Modeling Framework
1.3.1 Crowding in/out Effect
The “crowding in/out” effect of government input subsidy programs can be

defined as the change in private sector sales caused by an increase in the amount of input

distributed under the government program: fig:— , where AGOVrefers to change in the

10

 

amount of input distributed by government, and APR] V refers to change in private sector
sales. The effect of government input subsidy program on total input consumption is

expressed as

ATOTAL __ A(GOV + PRIV) _1+ APRIV
AGOV AGOV AGOV

 

 

(1)

where ATOTAL refers to the change in total input consumption.

We divide the possible outcome of 9%? into three categories based on the

 

 

 

. APR] V
Sign of :
AGOV
(i) If M R1 V >0, then A—TflA—L— >1
AGOV AGOV
(ii) If APRIV =O,t en ATOTAL :1
AGOV AGOV

(iii) If A” R’ V <0, then 310—7349. <1
AGOV AGOV

 

If (i) is found to exist, this means that government distribution is contributing
positively to private sector sales, such that each additional unit of input distributed by the
government generates a more-than-one unit increase in total input consumption.
Condition (ii) implies that government programs have no effect on the volume of input
sold by private traders, i.e., the crowding in/out effect is zero. However, if condition (iii)
is found to exist, this means that each additional unit of input distributed by government
depresses or displaces sales by private traders and hence total input consumption rises by
less than one unit. Conditions (i) and (iii) are the mathematical representations of the

“crowding in” and “crowding out” effect.

11

 

1.3.2 Measuring “Crowding in/out” Using a Double Hurdle Model

Using the conceptual framework of double hurdle model used in the literature on
consumption of a variety of products (see e.g., Lin and Milon, 1993; Jones, 1989; Haines,
1988; Cragg, 1971), a household’s decision to participate in the fertilizer market and the

conditional decision to purchase a certain amount of fertilizer (q > 0) can be written as

P=P(ZI)
q=Q(22)

where p refers to the probability of market participation, q is the amount purchased, 21
and 22 are vectors of variables (they can be the same or different) that influence these

decisions by functions P(-) and Q(-) . The double hurdle model is a bivariate

generalization of the Tobit model and it allows the decisions about whether to purchase
and how much to purchase to be determined by different processes.

In the literature, factors typically entering input demand functions in developing
country studies can be divided into three major categories: household socio-economic
and demographic characteristics, input and output prices and indicators of market access
conditions, and agro-ecological attributes. In this study, we distinguish between input
acquisition from two channels — commercial and government, and examine the effects of
these variables on household fertilizer acquisition from each channel using the double
hurdle model framework. In addition to these variables, for the analysis of household
commercial channel fertilizer purchase we argue that it is important to explicitly model
the effects of government subsidy programs on farmers’ purchase of commercial

fertilizer, in areas where such programs exist. We construct a community-level variable

12

describing the government fertilizer program in a double hurdle model of commercial

fertilizer purchase. Consider a double hurdle model with the following structure’:
a:
(2) dit = int +aGt +QGtWit +927

d _ 1 ifd; > o

.t _

I 0 otherwise
a:

M“: = “is + 30: + (DGzWiz + “it

_ y; ify;>0andd,-,=l
yit — ,
O otherwrse

i=l,...,N; t=1,...,T

where the subscript it refers to the ith household during period t, dit is the discrete
fertilizer market participation decision, d; denotes the latent (unobservable) variable of
di, , yi, refers to the amount of commercial purchase, y; is the latent variable of yi, ,
x,-, and ki, are vectors of explanatory variables assumed to be exogenous (x,-, and kit
may contain the same or different variables), G, is the community-level government

program variable during period t, ei, and ui, are random errors that are normally

distributed, and 7, a, 6, /I, ,6, go are parameters to be estimated. If we assume that the
impact of G, depends on particular household characteristics such as wealth, Wit (which

are also included in xi, and kit ), then it would be appropriate to include interaction terms

 

" Government channel double hurdle model in this study can be written with a similar structure in equation
(2) without the 0, terms, and thus it is omitted.

13

such as G, w,, in (2).5 The specific forms for the distributions of discrete di, and

truncated-at-zero y,, can be expressed in terms of the normal distribution as follows:

P(dit:1lxit’Gt’Gtwit)= (D((yxi, +aG, +thWit)/O'e)

¢(0’it —lk,-, -,BG, ‘WtwitI/Uu) y', > O
O’uq)((/1kit+flGt+¢GtWit)/O'u) I

 

f(yit lkit,Gt,G,W,-,,and di, =1):

where P refers to the probability, f refers to the density function, “I” denotes conditional

on, (15 and (D are the probability density and cumulative distribution functions for the
normal distribution, 0'8 is the standard deviation of the normal distribution of 6,, , and

0,, is the standard deviation of the normal distribution of u,-, .

Both the quantity of fertilizer distributed under government programs and the
number of farm households in a community may affect an individual household’s
decision to purchase fertilizer at full price from a private trader. Other things equal, the
more subsidized fertilizer to be distributed in a particular community, the greater the
likelihood that farmers will receive it and therefore not need to purchase their fertilizer at
commercial prices from private retailers. The greater the number of farm households in
the community, the less likely it is that any individual farmer will be able to acquire a

given quantity of subsidized fertilizer to be distributed in that community. Based on

these considerations, we model the government program variable, G, , as the ratio of the

quantity of fertilizer distributed during period t by government in a region r where the ith

household is located, G0 Vr, , to the number of farm households in that region, N r, ,

 

S A priori, we might expect that poor households are less likely to buy commercial fertilizer, hence the
magnitude of crowding out would be lower than among wealthier households.

14

_Gon,

(3) Gt
Nrt

This modeling framework explicitly takes into account the effects of government

fertilizer programs on commercial fertilizer acquisition and thus reduces potential bias in

parameter estimates of x,, and k,, associated with omitted variable problems. We are

particularly interested in the research question of the extent to which government

fertilizer programs affect, either positively or negatively, commercial fertilizer sales when

. . V . .
other factors are held constant, re, the magnitude of % In equation (1).

First, based on the model estimates we test the hypothesis H0 that government

program has no effect on fertilizer acquisition from private sector, that is,

H0 :51, 6, ,6, (p = 0. Specifically, a and ,6 describe the effects6 of government program

G, on households’ commercial fertilizer acquisition and the amount of acquisition,

and 6/ and (o describe the effects of government program interacting with household

wealth w,, on fertilizer acquisition and the amount of acquisition respectively. If H0 can
not be rejected, it is considered there is no evidence of either crowding in or out, and thus
condition (ii) for equation (1) is supported. If H0 is rejected, it suggests that government

program affects commercial fertilizer acquisition. Particularly, if estimates of

a and/or ,6 are statistically significant whereas estimates of i9 and go are not, it suggests

 

6 It should be noted that under the nonlinear model assumptions, regression parameters a, 6/, ,6, and go are
not equal to the partial effects; nevertheless, the directions of regression parameters are the same as the
corresponding partial effects and the magnitude of partial effects are proportional to regression parameters.
See Green (2003) and Wooldridge (2002) for detailed discussion of partial effects and regression
parameters in nonlinear models.

15

that government program affects households’ commercial fertilizer acquisition, but the
effect does not vary by household wealth.

There is evidence of crowding out if coefficient estimates of a, 0, ,B, and go are
statistically significant and negative. To quantify the crowding out effect of government

. . . . . . . APR] V
program on commercral fertrlrzer sales In a regron r during perrod t, , we use
AGOV r,

 

estimates of partial effects, 07, 19, ,3, and a, as well as information on the number of

farm households ( N r, ), the number of households acquiring commercial fertilizer (nr, ),
the average amount acquired by a household among market participants (air, ), and the
average wealth level of households that acquire commercial fertilizer (172,, ). The

APR] V
AGOV

 

magnitude of ( j is expressed as
rt

 

 

(4) (APRIV) = (a + 6372,, )nrfir, + (1+ 5. + éwr, )nr, (E + gown)
AGOV ,, N,, N,.,

The volume of commercial fertilizer sales is affected by the government program
through changes in two sources: one is decline in the number of households acquiring
commercial fertilizer, and the other is decline in the amount acquired by those who
participate in the market. The right hand side of equation (4) which is comprised of two
parts shows the degree of change from each source respectively. The first part gives

estimate of the change in commercial sales due to some households no longer buying
from private traders. 61' + (937,, can be interpreted as the change in the percentage of

households purchasing commercial fertilizer from traders when the government program

variable G, increases by one unit. Thus, multiplying 07 + 67%,, by the number of

16

original market participant nr, , gives the estimate of the change in the number of

households purchasing commercial fertilizer, and further multiplying (C? + 5%,, )n,, by

the average purchase volume 21}, describes the change in the quantity of commercial
sales. The change, (a? + 19%, )nr,c7r, , is associated with a one-unit increase in the quantity

. . V . .
of G, . Because government program vanable G, 18 modeled as ——rt In equation (3),

rt
one-unit increase in G, is N ,, unit increase in the amount of government distribution in
region r (AGOVr, = N,,AG, = N r, ). The value (61' + 19%., )nrfir, is thus divided by the

number of households N,, to obtain the marginal effect of increasing government

fertilizer distribution in region r.
The second term of equation (4) is the estimate of the change in commercial sales

due to some households altering the quantity of fertilizer that they purchase in response to
changes in government fertilizer distribution. (1+ c? + 1917),, )n,, is the estimate of the
number of households that purchase from commercial retailers, and multiplying it by the
decline in the amount of fertilizer purchased by a market participant, ,3 + gov?" , gives the
estimate of the change in the amount of commercial fertilizer sales. For the same reason
discussed in the first part of the equation, we divide (1+ 6? + 5172,, )n,, (5’ + town) by N,,

to derive the marginal effect. Adding the two parts together gives the total decline in

private sector sales from a one-unit increase in government fertilizer distribution in a

17

region r during period 1. Consequently the ratio of change in total fertilizer consumption

 

 

. . . . . AT OTAL .
over change In government drstrrbutron, —— , rs
AGOV n
ATOTAL APR] V
(5) —— = 1+
AGOV r, AGOV r,
___1+(a~ + 6W” )nrtq-rt + (1+ (3 + 6W)? )nrt (:6 + éwrt)
N rt N rt

We further conduct simulation analysis and explore the magnitude of change in
aggregate commercial fertilizer sales during period t, (APRIV), , when government
distributes additional amount of fertilizer in areas where private sector operates. Using

expression in equation (4) we write (APR! V), as

 

 

k
APRIV
6 APRIV = AGOV
() < ). ZIAGOVji m
['21 rt
k .. ~_ _ ~ ~_ ~ -_
= Z ((a +9w,.,)n,.,q,.,. + (1 +0: +t9wr,)nr,(,6+(pwr,)](AGOV)
N N rt
r=l rt rt

where k is the number of regions chosen by the government programs. Equation (6)
suggests that the magnitude of change in commercial fertilizer sales depends on the
selection of regions as well as the selection of farm households by the government
programs, and the extent to which government programs increase fertilizer distribution in
these regions.

If the coefficient estimates of a, 6, ,6, and (p are statistically significant and

positive, then condition (i) is satisfied and it suggests that government fertilizer programs
crowd in private investment in input marketing. We measure this effect with a similar

approach discussed above. If not all coefficient estimates are statistically significant,

18

corresponding calculation is simplified by setting insignificant estimates at zero in
respective equations. We also apply above method to quantify crowding in/out effect

when parameter estimates have different signs.

1.4 Estimation

Controlling for relevant household characteristics in input demand functions is a
challenge due to unobserved household heterogeneity. Unobserved household effects can
be controlled for through the use of panel data in this research. We estimate the double
hurdle models using the correlated unobserved effects model (Chamberlain, 1984;
Mundlak, 1978), both with the pooled estimator and the random effects estimator.
Unobserved heterogeneity is explicitly taken into account in the Mundlak—Chamberlain
(hereafter M-C) approaches. Due to the incidental parameters problem], we do not

estimate a “fixed effects” double hurdle model which treats the unobserved effects 0,- as

additional parameters to estimate.

The M-C approach allows for correlation between unobserved heterogeneity c,-
and explanatory variables X ,- by assuming a conditional normal distribution of c,:
c,- | X ,- ~ Normal(r+)?i9‘, 03 ) 8, where X ,- is the vector of explanatory variables across

all time periods for household i, X,- is the average of X it , t=1,..., T, 2' and 6 are

 

7 Incidental parameters problem (Newman and Scott, 1948) arise with maximum likelihood estimation of
panel data models that treat unobserved effects as additional parameters to estimate, leading to inconsistent
estimators when N is large and T is small and fixed (Wooldridge, 2002).

8 An alternative is to have X,- in place of «I: in the linear expectation of the conditional distribution 6’ i X.

(Chamberlain, 1984); we use 37. (Mundlak, 1978) to conserve on parameters. The estimator of regression
coefficients on time-variant variables when having )‘(1 is the same as the fixed effects estimator (also called
within estimator) in linear models.

19

constants, and 03 is the constant variance of a,- in the equation 0, = 2' + A7,: + a, , where

a, has a normal distribution, a, |X,- ~ Norma1(0, 0-3). In practice, 2' is absorbed into

the intercept term and additional variables X,- , which include the time averages of all

explanatory variables except time-invariant variables, are added to the model. Using a
Wald test, we reject the hypothesis of zero correlation (5 =0) between unobserved
heterogeneity and explanatory variables, thus indicating that the M-C approach is
superior to the standard pooled model and the random effects model which assumes that

the unobserved heterogeneity Ci is independent of the explanatory variables X i- The

double hurdle model with the correlated unobserved effects characterized above is
estimated using both the pooled estimator with standard errors robust to serial correlation
and the random effects estimator. The M-C approach with pooled estimator does not
impose the assumption of conditional independence between dependent variables across
time t (Wooldridge, 2002). Although it does not consistently estimate parameters and
partial effects, we may still obtain approximate average partial effectsg. The random
effects estimator of the M-C’s device is the conditional maximum likelihood estimator
and fully efficient under the assumption of independence between dependent variables

across time conditional on the explanatory variables and unobserved heterogeneity ci.

1.5 Data and Variable Construction

 

9 Average partial effects are the partial effects averaged across the whole distribution of c,. See Wooldridge
(2002) for detailed discussion.

20

1.5.1 Data

Household data used in the current study are from three surveys, the 1999/2000

Post Harvest Survey (PHS), the linked First Supplemental Survey to the 1999/2000 PHS,
and the Second Supplemental Survey to the 1999/2000 PHS. These surveys, conducted
by the Central Statistical Office of the Government of Zambia, provide a two-year panel
dataset of 5,342 small and medium-scale farm households for the 1999/2000 and the
2002/2003 seasons. The PHS is a nationally representative survey using a stratified
three-stage sampling design. Census Supervisory Areas (CSAS) were first selected
within each district; one Standard Enumeration Area (SEA) was then sampled from each
selected CSA; at the last stage a sample of households were selected from a listing of
households within each sample SEA. The SEA is the most disaggregated geographic unit
in the data. An SEA in Zambia typically includes 2-4 villages of several thousand people.

These surveys cover detailed information on agricultural production as well as
household demographic and socioeconomic attributes. After excluding households in two
urban districts, and after dropping 451 other households due to missing information, our
sample reduced to 4,206 households in 70 districts. Because maize is the main staple
crop in the country and is the intended crop for fertilizer under the government subsidy
programs, we also confined the sample to households growing maize in both years of
analysis. The data set contains a panel of 3,189 maize-producing households with

detailed records of agricultural activities over the two seasons 1999/2000 and 2002/2003.

21

1.5.2 Explanatory Variables

Household socio-economic and demographic characteristics: Household
characteristics included in x” and k” are the value of household assets, landholding size”),
the age, gender, and education of the household head, the number of resident adult males,
females, and children in the household, binary variables for recent adult mortality,
whether a civil servant member is resident in the household, and whether the household
head or the spouse is related to the village headman. Holding other factors constant, asset
value, landholding size, education level of household head, and number of adults are
expected to positively influence commercial fertilizer purchase. The ceteris paribus
effects of other variables are unclear due to lack of straightforward theory and
inconclusive findings in the literature.

Market price and access conditions: F ertilizer-maize price ratioll is expected to
have a negative effect on farmers’ decision to use fertilizer. Community-level (SEA)
average prices for fertilizer and maize are used to derive price ratio because some
households did not purchase fertilizer or sell maize. Distance from a district town is used
as a proxy for transportation cost and access to markets. The distance variable is expected
to be inversely related to the probability and amount of fertilizer use.

Agro-ecological attributes: Incentives for purchasing commercial fertilizer are

expected to be higher for certain soil types and agro-zones because of better maize yield

response to fertilizer. Different yield response across soil types and agro-zones affects

 

10 Since household income is likely to be endogenous, there are advantages in empirical investigation to
use asset value and cropland size as proxies for wealth, which are accumulated over time and hence
arguably exogenous.

” Price ratio is used instead of separate prices of fertilizer and maize because of high collinearity between
these prices and the average price terms in the M-C models.

22

profitability of fertilizer use and thus we expect fertilizer demand to differ accordingly.
These agro-ecological attributes are SEA-level variables.

The Government program variable is defined as in (3), the amount of fertilizer
distributed under the government program in an SEA divided by the number of maize-
producing households in that SEA. We also examine the significance of the interaction
terms between government fertilizer program and household asset value and landholding
size. The definitions for dependent and explanatory variables used in this study are

presented in Table 1.2.

1.6 Findings

As a prelude to econometric estimation, we first provide some descriptive
statistics to provide basic features of the data. Table 1.3 shows the percentages of
households that acquired basal fertilizer and the average amount acquired among
households that obtained fertilizer from government fertilizer program and private sector
respectively. About 14 percent of the nationally-representative sample received
subsidized fertilizer from the government in the 2002/03 season, up from 9.7 percent in
1999/00. Just over 15 percent of households purchased fertilizer from private retailers in
2002/03, up from 13.6 percent in 1999/00. Those acquiring fertilizer from government
and those purchasing from retailers used similar amounts, around 120 kgs per household.
The government program appears to have targeted relatively wealthy farmers, who might
have otherwise purchased fertilizer from local retailers if they were not beneficiaries of
the government program. On average, households receiving government subsidized

fertilizer and households acquiring fertilizer from the private channel both have higher

23

incomes and asset levels, larger landholding sizes, and are closer to district towns than
households not acquiring any fertilizer. Wald-test results find significant differences in
all of these attributes when comparing fertilizer users (regardless of source) with non-
users. This provides some a priori grounds for suspecting that government fertilizer
distribution may to some extent displace commercial retailer fertilizer sales.

Figures 1.1 and 1.2 Show the quantity of fertilizer acquired from private traders
versus from the government program at the community level for each survey period
respectively. These graphs show that in some cases, government programs distributed
fertilizer in communities where farmers purchased very little from commercial retailers,
but in other cases, the government distributed fertilizer in areas where private retailers
Were actively selling fertilizer. Among the 356 communities in the nationwide sample,
the number of communities where both private retailers and the government programs
operated is 100 in the 1999/2000 season and 139 in the 2002/2003 season. During
1999/2000 (2002/2003), there are 35 (78) communities in which households only
received fertilizer from the government and no household purchased fertilizer from
private retailers, and in 73 (56) communities households only purchased fertilizer from

private retailers.

1.6.1 Estimation Results

Table 1.4 and Table 1.5 present estimates of the double hurdle model for
households’ fertilizer acquisition from the government program and from the private
sector, respectively. The M-C approach with both pooled estimator and random effects

estimator were used to estimate these models. Likelihood ratio test result from each

24

model rejects the hypothesis that there are no random effects, thus the random effects M-
C model is favored over the pooled M-C model.

Results in Table 1.4 show that households with larger landholdings are more
likely to be targeted by government programs and are allocated more fertilizer. The
negative effect of the squared landholding size in the consumption equation suggests that
the increase in government fertilizer allocation gets smaller as farm size rises.
Households located in agrozone IIA and III (which include the prime maize growing
areas of Zambia) increase the probability of being targeted by the government program.
Government programs tend to target households closer to the district towns and the
chance of being selected as a beneficiary is higher in 2002/03 than in 1999/00. The
probability of receiving subsidized program fertilizer as well as the amount of fertilizer
received increase with the educational attainment of the household head and with the
number of children.

Table 1.5 presents estimation results of the double hurdle model for households’
fertilizer acquisition from private sector.‘2 Households purchasing fertilizer tended to
have larger landholdings. Amount of fertilizer purchase was also positively related to
farm size at a decreasing rate. The coefficients on the agrozone and soil variables indicate
that households having relatively favorable agroecological conditions are more likely to
acquire fertilizer, but after the decision to purchase fertilizer, these conditions appear not
to significantly affect the amount purchased per household, ceteris paribus. In addition,
households located farther from district towns are less likely to purchase fertilizer, which

was also found in the model of fertilizer acquisition from the government program. The

 

'2 Our sample includes communities where at least one household purchased fertilizer from private retailers
for at least one period.

25

fertilizer-maize price ratio is negatively related to the amount of fertilizer purchased, as
expected. The number of children and female adults in the household is positively
associated with the amount procured, but has no significant effect on the probability of
purchasing commercial fertilizer. Above findings suggest that the determinants of
fertilizer acquisition are likely to be different from those affecting how much to acquire.
We tested the double-hurdle model against the Tobit model for both the M-C pooled and
random effects models using likelihood ratio tests and rejected the hypothesis that the
Tobit model and double hurdle model are statistically equivalent. Therefore, a standard
Tobit model, which assumes that the processes which characterize the discrete choice and
the continuous choice are identical, would be inappropriate in analyzing households’
fertilizer acquisition behavior in our sample.

Focusing now on the main issue of this study, the model estimates from the M-C
pooled and random effects estimators both rejected the hypothesis that government
fertilizer programs in the community have zero effect on households’ fertilizer
acquisition from private sector. We further rejected the hypothesis that unobserved

heterogeneity c,- is uncorrelated with explanatory variables, implying that in the

traditional pooled and random effects models, the inability to control for unobserved
effects which are correlated with explanatory variables may lead to biased estimates.
Therefore, the M-C models are favored over the traditional pooled or random effects
models. In addition, the random effects M-C model is favored over the pooled M-C
model based on the likelihood ratio test result. Random effects M-C model estimates
show that the government fertilizer program variable G is negatively associated with the

probability of acquiring fertilizer from private sector, and the interaction terms G*ASSE T

26

and G*CLAND have negative effects on the quantity of commercial purchase. We
interacted the government fertilizer program variable and the year dummy and found no
significant effects. Above empirical evidence suggests that government fertilizer

programs may be crowding out rather than crowding in private fertilizer sales.

1.6.2 Magnitude of the Crowding out Effect

The effect of government fertilizer distribution on total fertilizer consumption by

small-scale maize farm households, [M] , is evaluated by equation (5) using
rt
, , ,_ ~ ~ 0 ~ -0.03
partral effect estimates of a = —0.0009, ,8=0, 6: 0 , go= 0 05 , number of households

(N r, ), number of households acquiring fertilizer from private sector (nr, ), average
acquisition amount ((7,, ), and the average asset level and cropland holding size of

households that acquired commercial fertilizer ( Wr, ). Table 1.6 presents estimates of

(ATOTAL)
AGOV ,,

The mean effect for each period is around 0.9, suggesting that a one-ton increase
in the quantity of government program fertilizer distributed in a community results in a
100-kg decline in the amount of fertilizer purchased from private traders, and hence an
overall 900-kg increase in total fertilizer use. The minimum and maximum values in
Table 1.6 indicate that the extent of displacement varies greatly across areas. Among the
communities with the largest crowding out effects, a one-ton increase in the quantity of
subsidized government fertilizer causes half of one-ton decline in the amount of fertilizer

sold by the private sector. Anecdotal information from some commercial fertilizer

27

distributors indicate that they often wait to see where government fertilizer subsidy
programs are occurring and then ship their fertilizer to other areas where they will not
compete against the subsidized fertilizer. Table 1.7 shows the crowding out effects by the
percentage of households purchasing fertilizer in an area in which both government and
private channels were operating.

We further derive aggregate change in private sector sales, (APR! V), , based on

equation (6). Table 1.8 presents the estimates when government program increases
fertilizer distribution by one ton in communities where both government and private
fertilizer channels were operating. As noted earlier, both the government program and
the private sector operated in 100 SEAS during 1999/2000 and 139 SEAS during
2002/2003, out of a total 356 SEAS.

Table 1.8 indicates that if government increases fertilizer distribution by one ton
in each SEA where private traders were already operating, such that the total amount of
government program fertilizer distributed to farmers increases by 100 and 139 tons, then
private sector sales in these areas will be reduced by around 8 and 10.56 ton for the two
periods respectively. Table 1.8 also presents the magnitude of crowding out in the ten
communities with the largest crowding out effects. The prospect of competing with
subsidized government fertilizer causes some private fertilizer traders to avoid stocking
fertilizer in that year, in anticipation of limited demand while the government program
operates. Unfortunately however, the cut-backs in private fertilizer distribution provides
the impression that the private sector is not adequately meeting effective demand for

fertilizer and is not a reliable supplier.

28

1.7 Conclusions

Parallel input marketing channels, featuring government and private distribution
channels are very common in developing countries. Some government fertilizer subsidy
programs are designed to nurture the development of commercial input marketing
systems. Yet there are concerns that such government programs may depress the
commercial demand for fertilizer and thus have unintended long-term consequences for
the development of sustainable input marketing systems to serve small farmers. There is
a dearth of empirical analysis to inform such policy debates. Most studies analyzing
farmer input use decisions do not consider the effects of government input subsidy
programs on farm demand for inputs. This study constructs household fertilizer use
models distinguishing between the two input channels and investigates the effects of
household socioeconomic and demographic characteristics, market access conditions,
agro-ecological attributes, and government fertilizer programs on household fertilizer
acquisition using nationwide household survey data in Zambia. We develop an approach
for quantifying the degree of crowding in/out of private sector fertilizer sales and overall
change in consumption due to government programs, which sold fertilizer to selected
beneficiaries in selected farming areas at 50% of the full cost.

For each channel the set of factors influencing whether to acquire (or receive)
fertilizer is found to be different from those that affect how much to acquire (or receive),
indicating the importance of a double hurdle approach in modeling household fertilizer
acquisition. Households’ landholding Size and proximity to district towns are correlated
with fertilizer acquisition from both channels. The correlation between these variables

and the commercial purchase of fertilizer is not surprising. However, the rationale for

29

many government input distribution programs is to meet the input needs of farmers in
remote areas where the private sector is perceived to be unwilling to operate. The finding
that proximity to towns and indicators of household wealth are positively correlated with
farmers’ receipt of subsidized government fertilizer suggests that the treasury costs of
these programs are being captured disproportionally by relatively wealthy farmers in
relatively accessible areas. Households targeted by government programs were more
likely to have purchased fertilizer from private traders if they had not had access to
subsidized government program fertilizer. These findings provide evidence of
contemporaneous crowding out effects. Over the entire country, an additional ton of
fertilizer distributed under the government program increased total fertilizer use by
roughly 700 kgs.

There may also be dynamic crowding in/out effects over time, yet our 2-year
panel study is only able to investigate contemporaneous effects. Future study can
investigate the potential lagged crowding in/out effects of government programs in a
given community on private sales in subsequent years by adding lagged terms of
government program variables in the panel data double hurdle model.

The findings in this study imply that government fertilizer distribution programs
may be more effective if they target areas where the private sector is not already active,
other things equal, and where a lack of knowledge and extension problems may provide
opportunities for subsidized distribution to facilitate learning so as to expand the
commercial demand for fertilizer over time. This may require appropriate management
extension messages to small farmers, and complementary investments in more fertilizer-

responsive seeds, physical infrastructure, and transport logistics, so that fertilizer use can

30

be made to be more profitable for farmers. These investments, coupled with targeted
promotional fertilizer use in areas where the private sector is not already active, would
promote the objectives of sustainable intensification of smallholder agriculture in sub-
Saharan Africa. On the other hand, as the findings of this study indicate, poorly targeted
fertilizer subsidy programs may be a costly way of crowding out the development of

commercial distribution systems without contributing much to sustainable intensification.

31

Table 1.1: Quantities of fertilizer procured by smallholder farmers, by type of supplier,
1995/1996 — 2005/2006

% of small farms using fertilizer on

 

 

maize Metric tons distributed
From government From private Government Commercial
programs traders programs sales“
(a) (b) (C) ((1)

1995/96 18.5% n.a. 61,141 69,000
1996/97 13.2% n.a. 65,577 108,000
1997/98 3.0% 12.3% 15,000 81,900
1998/99 6.0% 12.9% 43,028 65,912
1999/00 8.4% 8.4% 24,825 1 18,925
2000/01 3.5% 14.2% 23,975 81,307
2001/02 6.7% 17.4% 29,580 58,141
2002/03 13.9% 15.3% 54,120 74,485
2003/04 n.a. n.a. 76,927 11 1,850
2004/05 n.a. n.a. 54,094 129,295
2005/06 n.a. n.a. 57,130 148,486

 

Notes: * Commercial sales include purchases by smallholders and large-scale farmers, based on
government stated quantities distributed under government programs and private sector imports.
Sources: column (a) and (b) from Post-Harvest Surveys, Central Statistical Office (2002/03 is the
last year for which data is available); columns (c) and (d) from Agricultural Statistical Bulletins
(various years) and Ministry of Agriculture and Cooperatives files.

32

Table 1.2: Definitions for variables

 

 

Variables Definition

Dependent variables

BASAL_G 1 if household acquired basal dressing fertilizera from
government channel; 0 otherwise

BASAL_P 1 if household acquired basal dressing fertilizer from private
channel; 0 otherwise

QBASAL__G Quantity of basal dressing fertilizer from government channel
by the household (kilogram)

QBASAL_P Quantity of basal dressing fertilizer from private channel by the

Explanatory variables

household (kilogram)

Household socio-economic and demographic characteristics

ASSET

CLA ND
AGE

FEMA LEHH
ED UC
N__MA LE
N_FEMA LE
N_CHILD
HHDEA TH

S PDEA TH
ODEA TH

CSER VANT
RELA TED_HH

RELA TED_SP

Asset value including farm equipment, transportation
equipment, and livestock value (million Kwacha)

Area of cropland owned by the household (hectare)

Age of household head (years)

1 if household head is a female; 0 otherwise

Education of household head (years)

Number of male adults who live in the household

Number of female adults who live in the household

Number of children aged less than 15 who live in the household
1 if household head deceased within last 3 years of survey
season; 0 otherwise

1 if household head’s spouse deceased within last 3 years of
survey season; 0 otherwise

1 if any other adult deceased within last 3 years of survey
season; 0 otherwise

1 if household has civil servant member; 0 otherwise

1 if household head was related to village headman when he/she
procured land; 0 otherwise

1 if household head’s spouse was related to village headman
when he/she procured land; 0 otherwise

Market price and access conditions

PRICERA T10
DISTT OWN

Government fertilizer program
G

G *A SSE T
G *C LA ND
A gro-ecological attributes
ZONEIIA
Z ONEIIB
Z ONEIII
AF
A L
HG
F V

SEA-level basal fertilizer — maize price ratio
Distance to the nearest district town from center of SEA
(kilometer)

Ratio of quantity of government basal fertilizer distribution to
number of maize farm households in SEA (kilogram/household)
Interaction term between G and ASSET

Interaction term between G and CLAND

1 if SEA belongs to agro-zone IIA; 0 otherwise

1 if SEA belongs to agro-zone IIB; 0 otherwise

1 if SEA belongs to agro-zone III; 0 otherwise

1 if soil type is acrisols or ferrasols; 0 otherwise

1 if soil type is alisols or lixisols; 0 otherwise

1 if soil type is histosols or gleysols; 0 otherwise

1 if soil type is fluvisols or vertisols ; 0 otherwise

33

Table 1.2 (cont’d)

LR 1 if soil type is leptosols or regosols; 0 otherwise
Aggregate time eflect
YEAR2002 1 if survefieason is 2002/2003; 0 otherwise

 

Notes: ’ Farmers typically use two types of fertilizer on maize: basal dressing (compound D) and top
dressing (urea) at planting and weeding stage, respectively. Model estimates for top dressing are very
similar to those for basal dressing as households either did not acquire any of them or acquired them at
roughly a fixed ratio, 1:1, whether from private or government channel. Hence we only report model
estimates for basal dressing fertilizer in this study.

34

Table 1.3: Fertilizer use patterns by source of procurement and by household wealth
status, 2002/2003

Households receiving Households purchasing

 

fertilizer from fertilizer from Households not using

govemmerflogrgm commercial retailers fertilizer
Share of total
household sample 13.9% 15.3% 79.1%
Fertilizer acquired per
household (kgs) 122 120 0
Total household income
(000 kwacha) 804 774 266
Asset value
(000 kwacha per capita) 425 342 173
Landholding size
(ha per capita) 0.23 0.20 0.15
Distance to district town
(kms) 29.8 28.4 35.2

 

Source: Second Supplemental Survey, Central Statistical Office, 2004.

35

Table 1.4: Partial effect estimates of double hurdle model for fertilizer acquisition from

government program

 

 

 

Probability of acquisition Quantity acquired
Variables (i) Pooled (ii) Random (i) Pooled (ii) Random
M-C Effects M-C M-C Effects M-C
ASSET -0.0027 -0.0026 0.75 -0.74"'
(0.0027) (0.0028) (2.35) (0.42)
CLAND 0.0266*** 0.0243*** 1414*" 519*"
(0.0039) (0.0031) (5.38) (0.36)
CLAND2 -0.0009*** -0.0008*** -0.53* -0.14***
(0.0003) (0.0002) (0.29) (0.02)
AGE 0.001 0.0009 1.18 0.09
(0.0006) (0.0006) (0.79) (0.1 1)
FEMALEHH 0.0159 0.0142 -8.04 1.98
(0.0337) (0.0368) (33.91) (8.13)
EDUC 0.0055M 0.0052" 2.38 1.00***
(0.0026) (0.0025) (1.92) (0.39)
N_MALE 0.0046 0.0043 -3.56 207*"
(0.0067) (0.0063) (5.65) (0.78)
N_FEMALE 0.0084 0.0077 0.12 0.28
(0.0072) (0.0068) (5.85) (0.90)
N_CHILD 0.0074*** 0.0068*** -0.02 094*"
(0.0025) (0.0024) (2.38) (0.35)
HHDEA TH 0.0062 0.0047 68.13 5.81
(0.0421) (0.0452) (52.63) (8.72)
SPDEA TH 0.028 0.0273 5.18 5.07
(0.0438) (0.0463) (26.40) (4.73)
ODEA TH 0.0016 0.0021 -21.23 -1.37
(0.0185) (0.0178) (20.37) (2.34)
CSERVANT 0.0638 0.0627 30.47 4.47
(0.0559) (0.0604) (24.08) (4.09)
RELA TED_HH -0.0107 -0.0104 -1.84 -1.97
(0.0094) (0.0082) (9.29) (1.51)
RELA TED_SP 0.0009 0.0005 9.61 2.30
(0.0157) (0.0147) (12.33) (1.85)
PRICERA T10 -0.0057 -0.0067 53.87 -0.38
(0.0388) (0.0344) (43.90) (5.92)
DISTI’OWN -0.0011*** -0.0011"‘** -0.38 -0.06*
(0.0002) (0.0002) (0.25) (0.03)
ZONE/IA 0.0472*** 0.0423" 98.69" 7.86
(0.0177) (0.0167) (44.94) (4.98)
ZONE/[B -0.0068 -0.0059 -27.84 3.79
(0.0237) (0.0227) (39.53) (10.11)
ZONE/ll 0.0581" 0.0535" 92.33" 7.93
(0.0227) (0.0224) (44.02) (5.09)
AF 0.0443*** 0.0399*** 1.30 -0.49
(0.0131) (0.0126) (12.13) (1.68)
AL 0.0252 0.0233 12.37 -0.04
(0.0178) (0.0168) (15.13) (2.05)
HG -0.0244 -0.0207 -42.51 -7.52
(0.0257) (0.0249) (35.32) (9.67)
FV -0.0032 -0.0031 -31.75 -8.80**
(0.0217) (0.02) (22.22) (3.78)
LR 0.0750*** 0.0718*** -7.49 1.99
(0.0183) (0.0187) (13.34) (1.88)

36

Table 1.4 (cont’d)

 

YEAR2002 0057*“ 0.0528*** ~50.85* 1.41
(0.0217) (0.0198) (26.36) (3 .29)
ASSET 0.007“ 0.0065" 2.35 3.14***
(0.0032) (0.0031) (2.29) (0.43)
A G E -0.0003 -0.0003 -0.91 -0.16
(0.0007) (0.0007) (0.87) (0.13)
FEWLEHH -0.0188 -0.0159 -46.97 -0.74
(0.034) (0.0362) (46.05) (8.84)
ED UC 0.0022 0.0019 -l.15 -0.45
(0.0029) (0.0027) (2.20) (0.45)
N_ A'L‘ILE 0.0098 0.009 0.96 0.28
(0.0082) (0.0076) (5.61) (0.88)
N _ FEMALE -0.0047 -0.004l 9.86 1.12
(0.0091) (0.0083) (6.99) (1.15)
N _ CHILD -0.0063“‘ -0.0059* 4.37 -0.80*
(0.0036) (0.0034) (4.13) (0.47)
WEE/17H 0.0498 0.0483 -70.66 -2.41
(0.06) (0.0623) (57.94) (10.21)
SPDEA TH ~0.0224 -0.0234 -10.05 0.14
(0.0619) (0.0575) (67.29) (8.03)
ODEA TH -0.0046 -0.0062 -7.48 -0.95
(0.0278) (0.0254) (30.35) (3.35)
CSERVAW 0.0304 0.0262 -25.96 10.16”
(0.0521) (0.0502) (31.10) (5.36)
PRICERA 770 -0.0401 -0.0365 -86.45 ~8.72
(0.0533) (0.0478) (62.79) (8.12)

 

Notes: Numbers in parentheses are standard errors. Asterisks(',",m) significant at 10%, 5%, and 1%,
respectively.

37

Table 1.5: Partial effect estimates of double hurdle model for fertilizer acquisition from
private sector

 

 

 

 

Probability murchase Quantity purchased
Variables (i) Pooled (ii) Random (i) Pooled (ii) Random
M-C Effects M-C M-C Effects M-C
ASSET 0.0029 0.0027 1.26 0.48
(0.0029) (0.0028) (0.82) (0.3 9)
CLAND 0.025*** 0.0209*** 22.80“ 627*“
(0.0052) (0.0042) (10.05) (0.80)
CLAND2 -0.0011*** -0.0009*** -0.88* -0.10*"‘
(0.0004) (0.0003) (0.46) (0.04)
AGE -0.0009 -0.0007 -0.23 0.005
(0.0007) (0.0006) (0.4 8) (0. 17)
F EMALEHH -0.0114 -0.01 14 29.93 0.45
(0.0358) (0.0272) (28.71) (13.01)
EDUC -0.0033 -0.0029 1.01 0.02
(0.0028) (0.0022) (1.63) (0.66)
N_MALE 0.0124“ 0.0095 7.35 0.69
(0.0073) (0.0059) (5.39) (1.48)
N_FEMALE 0.0038 0.0027 0.56 3.32"
(0.0083) (0.0061) (4.10) (1.53)
N_CHILD -0.0028 -0.0022 5.99“ 1.91* **
(0.0028) (0.00022) (2.55) (0.38)
HHDEA TH 0.0474 0.0435 -1 13.89“ -3.31
(0.0627) (0.0567) (62.96) (14.37)
SPDEA TH -0.0279 -0.0245 -3 1 . 13 -6.40
(0.0309) (0.0235) (27.59) (9.50)
ODEA TH -0.0309* -0.0245"' 10.37 1.55
(0.0160) (0.0126) (14.10) (4.84)
CSER VA NT -0.03 83 -0.0267 -10.36 -9. 19
(0.0380) (0.0246) (22.37) (7.59)
RELA TED_HH -0.0317*** -0.0262*** 4.72 -3.22
(0.0105) (0.0083) (10.94) (2.04)
RELA T ED__SP -0.0142 -0.01 1 1 -5.72 -0.81
(0.0170) (0.014) (7.77) (3.61)
PRICERA T10 0.0181 0.0134 -14.05 -14.22*
(0.0371) (0.03) (23.13) (7.47)
DISYTOWN -0.0015*** -0.0013*** -0.09 -0.06
(0.0003) (0.0002) (0.14) (0.05)
G —0.001 1*" -0.0009*** -0.03 -0.04
(0.0003) (0.0002) (0.1 1) (0.05)
G *ASSET 0.0001 0.0001 0.00 -0.03***
(0.0001) (0.0001) (0.01) (0.005)
G *CLAND -0.0001 -0.0001 0.00 -0.05 ** *
(0.0001) (0.0001) (0.02) (0.01)
ZONE/1A 0.1418*** 0.1178*** 20.51 12.77
(0.0254) (0.0214) (23.93) (12.43)
ZONEIIB -0.0501"‘ -0.0327 -30.24 8.62
(0.0304) (0.0225) (54.96) (21.50)
ZONE/II 0.1672*** 0.1614*** 10.60 13.05
(0.0383) (0.0394) (25.19) (12.60)
AF 0.0485*** 0.0428*"“" 2.03 -0.26
(0.0151) (0.0135) (9.60) (2.71)
AL 00356" 0.0325* 2.52 2.00
(0.0203) (0.0189) (9.53) (3.13)

38

Table 1.5 (cont’d)

HG -0.0147 0.0133 16.66 -6.68
(0.0369) (0.0258) (15.21) (9.44)
FV 0.0004 0.0022 8.39 -10.96*
(0.0262) (0.0212) (14.70) (5.77)
LR 0.0441** 0.0406** -6.02 0.56
(0.0202) (0.0186) (11.15) (3.27)
YEAR2002 0.0035 0.0033 18.29 8.56**
(0.0211) (0.0168) (14.26) (4.15)
——.4 55,; 7 0.0087" 0.0063* 252* 3.92***
(0.0038) (0.0035) (1.42) (0.49)
70—5— 0.0008 0.0006 0.17 -005
(0.0008) (0.0007) (0.52) (0.18)
m 0.0015 0.0024 -43.87 2.72
(0.0399) (0.0324) (37.51) (13.83)
m 0.0146*** 0.0122*** -0.44 1.04
(0.0032) (0.0026) (2.11) (0.64)
m -0.0187** -0.0142* -937 -2.92*
(0.0094) (0.0075) (7.19) (1.61)
W 0.0004 0.0008 3.72 -4.31**
(0.0105) (0.008) (6.13) (1.77)
m 0.0036 0.0029 -6.02 -1.67**
(0.0042) (0.0033) (4.19) (0.67)
m -0.0862 -0.0668 68.66 -8.98
(0.0799) (0.0614) (47.26) (20.42)
W 0.1082* 0.0914* 8.48 9.70
(0.0605) (0.053) (35.09) (10.89)
m 0.0377 0.031 -15.64 -4.65
(0.0312) (0.0251) (22.73) (7.40)
m 0.1105* 0.0877* 39.00 1725*
(0.0574) (0.0463) (29.66) (9.92)
m 0.0678 0.0604 -39.56 17.45
(0.0542) (0.0449) (49.14) (11.63)
6 0.0024*** 0.002*** 0.32 0.04
(0.0004) (0.0003) (0.20) (0.06)
W -00001 -0.0001 -0.04* 0.01
(0.0001) (0.0001) (0.02) (0.01)
o * CLA N15 0.0000 -0.0001 0.00 0.09***
(0.0001) (0.0001) (0.03) (0.01)

 

Notes: Numbers in parentheses are standard errors. Asterisks(j,",m) significant at 10%, 5%, and 1%,

respectively.

39

Table 1.6: Effects of government fertilizer program on total fertilizer consumption

 

 

Period Maximum Median Minimum Mean
1999/2000 0.99 0.936 0.758 0.92
20020003 0.99 0.946 0.52 0.924

 

40

Table 1.7: Effects of government program on total fertilizer consumption by areas based
on percentage of households purchasing commercial fertilizer

 

 

 

Percentage of households 1999/2000 2002/2003

purchasing commercial Average Average
fertilizer in an area in

which both government Number Of (w) Number Of [M]
and private channels were Areas AGOV rt Areas AGOV rt
operating

(0, 10%] 16 0.976 21 0.981

(10, 25%] 32 0.944 53 0.951
(25%, 50%] 35 0.911 44 0.917
(50%, 100%] 17 0.842 21 0.814

 

41

Table 1.8: Total changes in private sector sales
Change in

 

 

Total Change in Total Change in
Government .
. . . . Number of Areas Government Prrvate Sector
Drstrrbutron 1n . . .
Each Area (k) Drstrrbutron Sales
Period (A0010)? (AGOV), (APR! V),
(a) (b) (c) = (a)><(b) UsifiEquation (6)
1999/2000 1 ton 100 100 ton -8 ton
1 ton 10 10 ton -2.06 ton
2002/2003 1 ton 139 139 ton -10.56 ton
1 ton 10 10 ton -2.7 ton

 

42

300
J
o

200
1

100
1
0
..
O

O

 

 

0

 

SEA-level Fertilizer Quantity from Private Channel (ion)
0

I I

400

O—

1 0._ 200 300
SEA-level Fertilizer Quantity from Government Channel (ton)

Figure 1.1: Community-level (SEA) quantity of fertilizer acquired from private sector
versus from government program, 1999/2000

43

400
1

300
l

 

 

SEA-level Fertilzier Quantity from Private Channel (ton)
200
|

. O
48—3. 0 . . .
o o 0
"g o : . o
o o
0.. . '1’ .. .0 . .0
o— “o 0.. o o o. o o o
0

50 _ 100 150 200
SEA-level Fertilizer Quantity from Government Channel (ton)

Figure 1.2: Community-level (SEA) quantity of fertilizer acquired from private sector
versus from government program, 2002/2003

REFERENCES

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Adugna, T. 1997. “Factors Influencing the Adoption and Intensity of Use of Fertilizer:
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Handbook of Econometrics, Vol. 2: 1247-1318. North Holland, Amsterdam.

Chirwa, E.W. 2005. “Adoption of Fertilizer and Hybrid Seeds by Smallholder Maize
Farmers in Southern Malawi.” Development Southern Africa 22: 1-12.

Cragg, J .G. 1971. “Some Statistical Models for Limited Dependent Variables with
Applications to the Demand for Durable Goods.” Econometrica 39: 829-844.

Crawford, E., T.S. Jayne, and V. Kelly. 2006. “Alternative Approaches for Promoting
Fertilizer Use in Africa.” Agriculture and Rural Development Discussion Paper 22.
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Croppenstedt, A., M. Demeke, and M.M. Meschi. 2003. “Technology Adoption in the
Presence of Constraints: The Case of Fertilizer Demand in Ethiopia.” Review of
Development Economics 7: 58-70.

Dorward, A., J. Kydd, J. Morrisson, and I. Urey. 2004. “A Policy Agenda for Pro-Poor
Agricultural Growth.” World Development 32: 73-89.

Gladwin, C.H., A. Randall, A. Schmitz, and GE. Schuh. 2002. “Is Fertilizer a Public or
Private Good in Africa? An Opinion Piece.” African Studies Quarterly 6: 1-2.

Govereh, J ., T.S. Jayne, J. Nijhoff, H. Haantuba, E. Ngulube, A. Belemu, J. Shawa, A.
Banda, C. Donovan, and B. Zulu. 2002. “Developments in Fertilizer Marketing in
Zambia: Commercial Trading, Government Programs, and the Smallholder Farmer.’
Working Paper, Food Security Research Project, Lusaka, Zambia.

9

Govereh, J ., F. Mushimba, S. Haggblade, T.S. Jayne, and J. Shaffer. 2006. “Zarnbia’s
Fertilizer Support Programme (FSP): Insights from the 2002-03 Season.” Working
Paper, Food Security Research Project, Lusaka, Zambia.

45

Green, W.H. 2003. Econometric Analysis. Upper Saddle River: Prentice Hall.

Green, D.A.G., and DH. Ng’ong’ola. 1993. “Factors Affecting Fertilizer Adoption in
Less Developed Countries: An Application of Multivariate Logistic Analysis in
Malawi.” Journal of Agricultural Economics 44: 99-109.

GRZ (Government of the Republic of Zambia). 2002. “Implementation Manual for the
2002/2003 Agricultural Inputs Support Program.” Ministry of Agriculture and
C00peratives, Lusaka, Zambia.

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47

ESSAY 2:
AN ASYMMETRIC CROP PRODUCTION MODEL AND THE APPLICATION
TO MAIZE PRODUCTION IN ZAMBIA

2.1 Introduction

The majority of agricultural production in Zambia remains rainfed and based on
small-scale, subsistence family farming systems. Smallholder farmers that own less than
5 hectares of land, about 900,000 of them, comprise the vast majority of farmers in
Zambia. Zambian government agricultural policy has for the past several decades focused
on fertilizer subsidies and targeted credit programs to stimulate small farmers’
agricultural productivity, enhance food security and ultimately reduce poverty. Improving
maize productivity has been a major goal of the government policy. Over 70% of the
small-scale farmers grow maize as the major staple crop and they are responsible for 65%
of the maize production in the entire country. Agricultural marketing among smallholders
is dominated by maize sales (Govereh et al., 2003).

In 2002, the Zambian Government launched programs and policies under the
framework of the Poverty Reduction Strategy Paper (PRSP) which in the agricultural
sector included Fertilizer Support Programme (F SP), out-grower schemes, land and
infrastructure development, technology development, agriculture extension, and maize
marketing in support of small-scale farmers (PRSP, 2002/2004; World Bank, 2002a;
2002b). Despite government’s efforts over the past several decades, overall fertilizer
consumption has expanded slowly and maize yields remain at the level of 0.7 to 2.5 tons
per hectare falling far behind Latin America and south/southeast Asia. A recent
assessment of the implementation and effectiveness of the FSP based on a survey of

randomly selected 116 beneficiary farmers indicates that FSP has very little impact in

48

terms of increasing maize production and enhancing household incomes and livelihoods
(CSPR, 2005). Several factors were identified as responsible for reducing the
effectiveness of the Programme: Delays in input supply, inadequate supply of farm
inputs, poor crop marketing arrangements, high input prices and low output prices, and
poor transport facilities, among others. This highlights the need for an in-depth study of
maize yield response to fertilizer use, timeliness of fertilizer application and other crop
management practices, and profitability of fertilizer use under current small farm

. conditions to inform policy process aimed at achieving sustainable increase in maize
productivity and smallholder incomes.

While recognizing the importance of providing extension services to small
farmers, extension messages and fertilizer distribution programs in Zambia have been
based on one nationally recommended application rate of 200 kilograms of basal fertilizer
(compound D) and 200 kilograms of top dressing fertilizer (urea) per hectare of maize.
This one-size-fits-all recommendation largely ignores heterogeneity in small farm
conditions and differing market conditions. As fertilizer remains an expensive input in
many countries in sub-Saharan Africa, extension messages and government programs
promoting fertilizer use Should emphasize technically viable and economically efficient
use of fertilizer, taking account of agroecological conditions, complementary farming
practices and cost-effectiveness of fertilizer application.

In this article we examine maize yield response to a range of farm inputs,
determine profitability of fertilizer use by small-scale farmers, and identify the potential
to increase maize productivity and profitability of fertilizer use through public policy

tools. Empirical analyses are based on nationally representative panel household survey

49

data for 1999/00 and 2002/03 agricultural seasons in Zambia. Use of panel data sets
allows controlling for unobserved household/farm heterogeneity and thereby overcomes
the limitation of cross-sectional studies that may bias the results. In addition, use of a
nationally representative large sample enables generalization from the results to make
broader inferences.

Modeling and estimation of crop response functions has been of interest in
agricultural economics for decades. In crop response research many different functional
forms have been used including quadratic, Cobb-Douglas, transcendental logarithmic
(translog), Mitscherlich-Spillman, resistance, generalized power, and others (Dillon and
Anderson, 1990). In particular, flexible functional forms, such as quadratic (Lau, 1974)
and translog (Christensen, Jorgenson and Lau, 1971, 1973), that can achieve second-
order approximations1 to arbitrary functions have been widely used. A large number of
studies treated farm inputs symmetrically in the response function specifications.
Symmetric treatment of inputs basically ignores agronomic principles, where different
inputs are considered to contribute to crop growth through distinct processes. Failure to
take account of the underlying production process in modeling production functions may
lead to misspecification and inaccurate inferences (Guan et al., 2006).

In terms of econometric estimation, translog or quadratic production functions
contain parameters that increase quickly (or explosively) as the number of variables

increase, due to the large number of the square terms and interaction terms. Practitioners

 

' According to Lau (1974), there are two types of second-order approximations: differential approximation
(Diewert, 1971) and numerical approximation (Christensen, Jorgenson and Lau, 1973). Under the first
definition, a function H02) is a second-order approximation to another function G (y) at yo if the first and
second derivatives of the two functions are equal at yo; under the second definition, a function H(y) is a
second-order approximation of GO») if H(v)=G(y) at yo and, if in a prescribed neighborhood of yo, the
deviations of the approximation from the true function are constrained to be relatively small.

50

in production analysis generally face a dilemma: to avoid omitted variable bias, it is
necessary to include all relevant input information available. However, the explosive
increase in the number of parameters often quickly reduces the degrees of freedom and
poses a practical problem for econometric estimation. Consequently, many researchers
choose to limit the number of variables used in the model specification. To this end,
practitioners commonly adopt either of three strategies: 1) Start from a broader set of
variables and do the stepwise regressions, dropping the insignificant terms each step; 2)
Drop the variables that are considered to be the least important in the production process;
and 3) Aggregate inputs such as fertilizer, seed, etc. into a general category “variable
inputs”. Similarly, “capital” may include many things, such as machinery, equipment,
livestock, and building. It should be noted that all these strategies have problems. The
stepwise regression usually ends up with incomplete models as linear, cross and quadratic
terms may be dropped without theoretical justification. The resulting specification is
usually arbitrary and incomplete as far as second-order approximation is concerned. The
stepwise regression is not widely seen in the literature. Dropping an entire set of terms
associated with specific variables is more frequently seen, which is either based on
properly justified arguments or simply ad hoc choice. Although the resulting model
specification serves as a proper second-order approximation as such, the ad hoc choice of
variables could lead to misspecification. Aggregating inputs into a general category is a
more justifiable practice for theoretical and practical considerations. But the aggregation
would generally results in loss of valuable information and in some cases may lead to

aggregation bias (Griliches, 1957).

51

To summarize, concerns arise from the classic modeling mentality of second-
order approximation. Instead of looking into the underlying production process,
specifications based on second-order approximation, such as translog and quadratic, lack
theoretical underpinnings and are mainly employed for mathematical convenience.
Pursuing flexibility, these models claim to be able to approximate any unknown process
and are virtually “universal”. Though widely used in the agricultural economics literature,
traditional flexible functional forms per se have little to do with agriculture or economics.
Translog function does not allow concavity (Antle and Aitah, 1983), a basic principle in
economics. Lack of theoretical appeal and absence of relevant agricultural element make
it difficult, if not impossible, to make insightful inroads into empirical intricacies of most
agricultural complexes.

Some recent studies on crop response to pesticide and fertilizer have recognized
particular biophysical processes and integrated agronomic information into theoretical
framework and choice of functional forms (Lichtenberg and Zilberman, 1986; Babcock et
al., 1992; Paris, 1992; Chambers and Lichtenberg, 1994; Chambers and Lichtenberg,
1996; Carpentier and Weaver, 1997; Saha et al., 1997; Berck et al., 2000; Oude Lansink
and Carpentier, 2001; Holloway and Paris, 2002; Guan et al., 2005). Guan et al. (2006)
proposed categorization of inputs into growth inputs and facilitating inputs based on
agronomic principles. The complete production function consists of a crop-growth model
and a scaling function incorporating asymmetric treatment of growth inputs and
facilitating inputs. In their empirical crop-growth model, a translog function was
specified for modeling crop response to growth inputs. Translog specification has

limitations since it does not allow for concavity and zero input level. In our study, we

52

adopt the theoretical framework developed by Guan et al. and use a quadratic function for
modeling crop response to growth inputs. Quadratic function does not have the
limitations of translog function, so it is a more general treatment. These recent crop
response studies are either based on experimental data which only included water,
pesticide or nutrients as inputs, or based on farm level data but have a restricted set of
variables in the model. We use household-level survey data and extend the scope of
facilitating inputs used in Guan et al.’s study to include crop management practices,
household socioeconomic conditions, and government policies and programs that
presumably can affect actual farm yield. By controlling for a wide range of variables and
use of panel data techniques we expect to obtain more accurate estimates of crop yield
response to fertilizer.

The remainder of this article is organized as follows. We first provide the
modeling framework for crop response analysis. In the third section, we present data and
potential econometric issues. Empirical model is presented in the foruth section, followed

by estimation results. We conclude the article in the last section with closing remarks.

2.2 Modeling Framework

We adopt the conceptual framework recently developed by Guan et al. (2006)
for modeling crop production function. Agricultural inputs are dichotomized into grth
inputs and facilitating inputs based on agronomic perspectives on crop production levels

and different factors influencing these levelsz. Growth inputs are defined as those that are

 

2 1n agronomic literature, three distinct yield levels were proposed: potential, attainable, and actual yield.
These yield levels are determined by different growth conditions which depend on three groups of factors:
growth defining, growth limiting, and growth reducing factors. Growth defining factors such as weather
and species characteristics determine the potential yield, assuming there are no growth limiting and

53

directly involved in biological process of crop growth and thus essential for crop growth,
such as seed, nutrients, and water. Attainable yield is determined by the level of growth
inputs in a given biophysical environment, assuming no yield-reducing factors for
maximum yield such as weeds, diseases, pests, and imperfect labor and machinery
operation. These factors cause actual farm yield lower than the attainable yield.
Facilitating inputs are defined as those that are not directly involved in the basic
biological process, but can help create or alter growth conditions under which growth
inputs take effect. Guan et al. included labor, capital, and pesticides in this category. In
this study, we do not restrict the scope of facilitating inputs to crop management practices
alone; instead, yield gap between actual yield and attainable yield is hypothesized to be
also related to household socioeconomic characteristics and government policies and
programs. Through controlling for these factors that are likely to be correlated with farm
household’s input use decision, we expect to obtain more accurate estimates of the crop
production function, especially crop response to fertilizer that is of particular interest in
our study.

A general conceptual crop production function is written as:
(1) y = 000330)
where y is crop yield, x is a vector of growth inputs, and z is a vector of facilitating inputs.
Growth inputs x and facilitating inputs 2 affect crop output through different mechanisms

indicated by crop growth function G(-) and scaling function S (-) . Crop-growth function

G(-) determines the attainable yield level given the biophysical environment. The scaling

 

reducing factors. Attainable yield is lower than the potential yield due to growth limiting factors such as
water and nutrients. Yield gap between actual yield and attainable yield is caused by the growth reducing
factors such as weeds, pests, and diseases. In practice, potential yield is typically not achieved due to
growth limiting and growth reducing factors; also, it may not be economically viable to attempt to achieve
potential yield (Rabbinge, 1993; Van Ittersum and Rabbinge, 1997; Van de Ven et al., 2003).

54

function S(«) is defined in the interval [0, 1]. When S(x) reaches 1, i.e., when growth

conditions are optimal for a given level of grth inputs x, crop output y attains its
maximum value G(x). Actual yield is lower than the attainable yield and scaled down by
the factor S (-) under non-optimal growth conditions.

This modeling framework incorporates agronomic perspectives on crop
production levels and explicitly addresses distinct roles of different factors in crop growth
process. In field crop production, yield differences among farmers in the same area are
frequently observed because of different levels of growth inputs and facilitating inputs. In
empirical studies using farm data, we can estimate the crop production function with

explicit functional form specifications for G(-) and S(-) .

2.3 Data and Econometric Issues
2.3.1 Data

Household-level data used in this study are from three surveys, the 1999/2000
Post Harvest Survey (PHS), the linked First Supplemental Survey to the 1999/2000 PHS,
and the Second Supplemental Survey to the 1999/2000 PHS conducted by the Central
Statistical Office in Zambia. A panel dataset for two agricultural seasons 1999/2000 and
2002/2003 is available from these surveys. PHS is a nationally representative survey
using a stratified three-stage sampling design. Census Supervisory Areas (CSA) were
first selected within each district, next one Standard Enumeration Area (SEA) was
sampled from each selected CSA, and at the last stage a sample of households were
randomly selected from a listing of households within each sample SEA. The SEA is the

most disaggregated geographic unit in the data, which typically includes 2-4 villages of

55

several thousand people. Agro-ecological zone and soil type information is available at
the SEA level. The primary maize growing areas include Zone IIA (medium rainfall
areas) and Zone 111 (high rainfall areas) with dominant soil type Acrisols or F errolsols
(hereafter AF). In this study, crop production functions are estimated for four regions that
have distinct biophysical environments: Zone 11A soil type AF, Zone IIA soil type non-
AF, Zone 111 soil type AF, and Zone 111 soil type non-AF.

The output specified in this study is maize yield in kilogram (kg) per hectare.
Growth inputs address fertilizer, seed, and rainfall. We include nitrogen application rate
(the most important nutrient in maize growth) in kg per hectare", and the percentage of
basal fertilizer among total fertilizer applied in order to examine the effect of this variable
on maize yield’. Seed is specified as a dummy variable indicating whether hybrid seed
was used. Rainfall is annual district-level rainfall in millimeters. Facilitating inputs
examine the effects of a range of variables including mechanical or animal draught power
usage, maize area, timeliness of fertilizer application, fertilizer acquisition from
government program, extension service, characteristics of household head (age, gender,
and education), number of adults, and adult mortality. A year dummy is also included in

the model. Table 2.1 presents variable definition.

2.3.2 Econometric Issues

Simultaneity

 

3 It is calculated based on the amount of basal fertilizer (compound D) and top dressing fertilizer (Urea)
used per hectare and the nutrient components in these fertilizers. 100kg of Compound D contains 10kg
nitrogen (N), 20kg phosphorous (P), and 10kg potassium (K); 100kg Urea contains 46kg N.

4 Farmers adopting fertilizer typically used basal and top dressing at 1:1 ratio.

56

In previous empirical studies of crop production function using nonexperimental
farm data, Simultaneity problem has not received enough attention. Farm inputs such as
fertilizer and seed are unlikely to be random because farmers can control input use.
Deaton (1997) pointed out that farm input use is unlikely to be independent of land
quality, thus inputs are at least partly determined by crop yield. As a result, the usual
estimates of the production function using cross-sectional farm data are likely to suffer
from simultaneity bias. Simultaneity in this context can be considered as an omitted
variable problem where land quality is missing. Land quality and farmer Skill are
unobserved heterogeneity, and it is precisely the correlation between unobserved
heterogeneity and observed explanatory variables that is the source of difficulty in cross-
sectional study of crop production function ((Deaton, 1997). Use of panel data makes it
possible to get closer to the ideal experimental situation than a single cross section since
it allows comparison of the same observation unit under different circumstances and use
of that unit as their own control. Panel data techniques are employed in this study to
control for unobserved heterogeneity and obtain consistent estimates of model parameters.

In addition, explanatory variables indicating presence or absence of government
programs are unlikely to be random if these programs are not assigned randomly to the
treatment (for example, household). In a randomized experiment, a dummy variable
indicating the presence of government program will be uncorrelated with the error term
and the usual cross-sectional estimates will be consistent. However, government
programs are often not implemented as randomized experiments; on the contrary, they
are often targeted to certain population. The econometric problem of evaluating the

impact of government programs is similar to that encountered in estimating the effects of

57

farm inputs. It is the correlation between unobserved heterogeneity and the presence of
government program that causes simultaneity bias and invalidates cross-sectional
evaluation, and again panel data can be used to address this concern (Deaton, 1997). In
this study, government program variables such as provision of extension service and
subsidized fertilizer are unlikely to be random. There iS empirical evidence that
households targeted by the government’s fertilizer program tend to be wealthy farmers in
accessible areas (Xu et al., 2007). In the case of purposeful allocation, cross-sectional
analysis can overestimate the program’s true impact if unobserved heterogeneity is not

controlled for in the model.

Attrition

Attrition is a common problem in panel survey data. Some households
interviewed in the first round of survey are lost from the second round, leading to a
reduction in the number of households in the panel. Reasons for sample attrition in
developing countries may include household migration, dissolution due to head death,
household split-off, or refusal5 (Deaton, 1997). Investigation of sample attrition is
necessary because nonrandom attrition can cause the panel sample unrepresentative of
the population of interest and potentially bias the empirical result.

Potential attrition bias can be tested using the methods suggested in the literature
(Becketti et al., 1988; Fitzgerald et al., 1998a; Maluccio, 2004). First, a baseline sample
of the households in the first survey is divided into two groups: those that remain (non-

attritors) and those that are lost in the second survey (attritors). Sample averages of

 

5 Refusal rates are relatively low in developing countries, which may be related to low opportunity cost of
time or cultural attitudes (Maluccio, 2004).

58

variables are then compared between the two groups to examine whether they are
significantly different by attrition status. While univariate comparison can provide useful
information about relevant attributes of attritors and non-attritors, it is not a formal test
for potential attrition bias. In other words, if the underlying crop production functions for
the two groups are the same, we can still obtain unbiased estimates of the population
model using the subsample of non-attritors. A formal test can be conducted by using the
full sample in the first period and estimating a crop production function which
incorporates an attrition indicator and interaction terms between the indicator and other
explanatory variables. Joint significance test of the attrition indicator terms will
determine whether the model is statistically different between the two groups. If they are
jointly insignificant, the hypothesis of homogeneous production function cannot be
rejected, therefore inferences about the population crop production function based on the
subsample of non-attritors will be valid. If they are jointly significant, attrition bias may
be present and it can be corrected for using the inverse probability weighting method

(Woodridge, 2002; Fitzgerald et al., 1998a, b).

2.4 Empirical Model
Under the general framework (1), we specify functional forms for the crop-growth

function G(-) and the scaling function S(-) in our empirical application of maize

production in Zambia. Instead of the translog function used in the literature (Guan et al.,

2006), we propose to use the quadratic firnction for G(-) because it permits concavity and

zero input. Concave yield response curves are consistent with most observable biological

59

relationships Since excessive amount of fertilizer or rainfall can adversely affect crop
growth. A quadratic model for the crop-growth function G(-) is specified as:
(2) 0,, = alN,, + azBSLPCTi, + a3RAINi, + a4HYBDi, + a1 1N3 + alzNi, x BSLPCT}, +

a13Ni, x RAIN” + a14Ni, x HYBDi, + azzBSLPC7},2 + (123 BSLPCY}, x RAIN,, +
a24BSLPCT,-, x 1117313,, + a33RAIN§ + a34RAIN,, x HYBD,,

where N, BSLPC T, RAIN, H YBD are growth inputs defined in Table 2.1, and a] —-a 34

are parameters to be estimated.

In specifying the scaling ftmction S(-) , we extend the scope of the facilitating
inputs used in the literature to include crop management practices, government programs,
and household socio-economic characteristics. We use the exponential form that does not
impose monotonicity on the input-output relationship (Guan et al. 2006):

(3) 5,, = exp[—(,BO + ,BIONTMi, + ,BZDRTPWi, + ,63MZAR + ,64EXTNSN,, + ,B5GVCHNL,, +
fl6ADUL7}, + ,B7AGE + flgEDUC + ,BgFEMHD + ,BWMRTLTi, + ,6] 1YEAR,)2]

where 0NTM, DRTP W, MZAR, EXT NSN, GVCHNL, ADULT, AGE, EDUC, FEMHD,

MRTLT, and YEAR are facilitating inputs defined in Table 2.1, and ,60 — ,6 1 1 are

parameters to be estimated.
With the two functions specified above, maize production function is now written
as:
(4) YIELD” = (al N,, + azBSLPCTi, + 5831641117,, + a4HYB ,, + a] 1N5 + a1 2N,-, x BSLPCY}, +

(11301,, X RAIN” +a14N,-, X HYBDi, + (122BSLPCT,,2 + 0:23BSLPC7}, X RAIN” +

a24BSLPC7}, x HYBD,, + a33RA1N§ + a34RAINi, x HYBD,, ) exp[—(,BO + ,6.0NTM,-, +
,BZDRTPWi, + ,63MZAR + ,64EXTNSNi, + Escrow/n, + ,B6ADULTi, + 57.4015: +

,BgEDUC + ,BgFEMHD + ,BIOMRTLTi, + E] lYEAR,)2]+ f,- + u,,

60

where YIELD is maize yield in kilogram per hectare, f,- iS unobserved household

heterogeneity, and u,, is random error assumed to be i.i.d. N(0, 0'2 ). We use the

approach developed by Mundlak (1978) and Chamberlain (1984) (hereafter M-C
approach) to control for unobserved heterogeneity f,- , which is assumed to have the form:
(5) f,- =r+)?,~y+a,~

where 2?,- is a vector of the averages of inputs X11 across time periods, I is constant, y is

a parameter vector, and a,- is distributed as i.i.d. MO, 03, ) and independent of 21,, .

Parameters a1 — a 34 , ,60 — ,B 1 1 , r, y, 02 , and 03 are estimated using maximum

likelihood estimation method (MLE). Under regularity conditions, MLE is asymptotically

unbiased and efficient.

We can determine whether unobserved heterogeneity is correlated with 2?,- by the
joint significance test of )1. If the hypothesis H0 :y=0 is rejected, there is evidence of

unobserved heterogeneity which is correlated with )7,- , thus parameter estimates of the
crop production function will be inconsistent if the function is estimated ignoring the
unobserved heterogeneity f,- .

Taking the expectation of YIELDi, in equation (4) conditional on X ,- and taking

partial derivative with respect to N it , we get

(6) 6[E(YIELD,, | X, )] / 6M, = (a1 + 2611 1N“ + a1 ZBSLPCTi, + a13RA1Ni, +
a14HYBDi,)exp[—(,B0 + ,BIONTMi, + ,BZDRTPWi, + ,B3MZAR +
fi4EXTNSNi, + ,BsGVCHNLi, + ,B6ADUL7}, + ,B7AGE + ,BgEDUC +

,BgFEMHD + ,BIOMRTLY}, + p, 1YEAR,)2]

61

which is the partial effect of N i, on the expected YIELDi, . It is also the marginal
productivity of N i, , i.e., the change in expected YIELDi, as a result of adding an

additional unit of N it , ceteris paribus. As reflected by the formula in (6), marginal

productivity of nitrogen is allowed to depend on the nitrogen level as well as the levels of
all the other explanatory variables. Partial effects of other continuous variables can be
derived similarly by taking the partial derivative of equation (6) with respect to the
variable. Partial effect of a dummy variable is derived as the difference between the

expected yields when the dummy variable changes from 0 to 1.

2.5 Empirical Results
2.5.] Attrition

The sample of households in the first round of survey is divided into two sub-
samples: attritors and non-attritors. Table 2.2 shows estimates of the variable means and
differences in the means between the two groups in 1999/2000. For example, for region
Zone IIA soil type AF, results from equality of means tests indicate that households that
were re—interviewed in the second round of survey on average had larger maize area,
higher basal fertilizer percentage, more adults per hectare, and were located in regions
with less rainfall. A higher percentage of non-attriting households used animal or
mechanical draught power in land preparation and were headed by a male. The averages
of other variables are not significantly different between the two subsamples.

Univariate comparison provides information on the unconditional means of
variables. Whether these differences in means will cause attrition bias, i.e., whether the

underlying crop production function will differ by attrition status is unknown from the

62

univariate analysis. To examine potential attrition bias, a formal test described in Section
3.2.2 was performed. Using the sample for the first period, crop production function in (4)
was expanded to include an attrition indicator and the interaction terms between the
indicator and explanatory variables. The function was then estimated for each
agroecological region. The attrition indicator terms are jointly insignificant in all models,
suggesting estimation of the crop production function based on the non-attriting sample is

unlikely to have attrition bias problem in our study.

2.5.2 Production Function Estimation Results

Parameter estimates of the crOp production function are presented in Table 2.3.

Joint significance test of the average terms reject the hypothesis H0 : y=0 in (5),

suggesting unobserved heterogeneity is correlated with the averages )Ti. Estimates of

partial effects are presented in Table 2.4. Different estimates of the production function
for the four distinct regions indicate that estimation of a single crop production function
for the entire country without distinguishing different biophysical environments can lead
to spurious estimates.

Results in Table 2.4 Show that except household head characteristics including
age, gender, and education level (A GE, EDUC, and FEMHD), the effects of other
explanatory variables on maize yield are statistically significant for at least one of the
four regions. The directions of partial effects are generally consistent with our
expectations. Specifically, for Zone IIA soil type AF, nitrogen, timely availability of
fertilizer, use of animal or mechanical draught power, and fertilizer acquisition from

government channel (N, 0NTM, DRT P W, and GVCHNL) has a positive effect on yield,

63

whereas rainfall, extension service, and recent adult mortality (RAIN, EXT NSN, and
MRTLT) has a negative effect on yield. The positive coefficient on fertilizer acquisition
from government channel implies that household acquiring fertilizer from the
government program have a higher average yield than those purchasing fertilizer from the
commercial retailers, possibly because these farmers have adopted better crop
management practices or reported maize production level higher than their actual harvest
in order to demonstrate the program is effective on their farms. Negative effect of rainfall
at its 50th percentile indicates that the amount of rainfall during the two seasons may
have been excessiveé. Extension service has a negative effect, suggesting
recommendations offered by extension service were rather counterproductive. Results for
the other three regions Show that for Zone IIA soil type non-AF, nitrogen, percentage of
basal fertilizer, adoption of hybrid seed, use of draught power, and number of adults per
hectare has a yield increasing effect, whereas rainfall, maize area, and adult mortality has
a yield decreasing effect. For Zone 111 soil type AF, yield is positively associated with
nitrogen, adoption of hybrid seed, timely availability of fertilizer, use of draught power,
fertilizer acquisition from government channel, and adult mortality. For Zone 111 soil type
non-AF, nitrogen, timely availability of fertilizer, and extension service has a yield
increasing effect, whereas rainfall, use of draught power, and fertilizer acquisition from
government channel has a yield decreasing effect.

Marginal productivity of nitrogen (MPN) is of particular interest in our study.
Table 2.4 shows that nitrogen has a positive and significant effect on maize yield for all
the four regions. We further derived estimates of MPN at varying levels (25, 50, and 75

percentiles) of nitrogen and other explanatory variables that have significant interaction

 

6 Rainfall in both years was normal to above normal compared to 1995-2005 means.

64

effects with nitrogen for each region (Tables 2.5-2.8). As expected, marginal productivity
of nitrogen declines as nitrogen increases implying a concave response curve for all
regions. Timely availability of fertilizer has a significant and positive effect on marginal
productivity of nitrogen in two areas, Zone IIA soil type AF and Zone 111 soil type non-
AF. This demonstrates that fertilizer application in a timely manner can contribute
substantially to the productivity gains achievable from fertilizer use. Marginal
productivity of nitrogen is negatively associated with rainfall in Zone 111 soil type AF,
indicating excessive amount of rainfall can cause a decrease in fertilizer efficiency.
Results for some regions Show that maize area is positively related to marginal
productivity of nitrogen suggesting farmers with larger maize area may have adopted
better cultural practices to make fertilizer more efficient, and higher marginal
productivity of nitrogen for households with fewer adults per hectare of maize (thus more
maize area per adult) could result from these households using better practices to improve

fertilizer efficiency.

2.5.3 Profitability of Fertilizer Use
Based on the estimates of marginal productivity of nitrogen (MPN), marginal
value-cost ratio (MVCR) of applying nitrogen was computed as

MP N x P maize
PN

 

(7) MVCR =

where Pmaize is the price of maize per kilogram and PN iS the price of nitrogen per

kilogram7. The numerator indicates marginal value productivity (MVP) of nitrogen.

 

7 PN was calculated using the basal and top dressing fertilizer prices and their nutrient component
information. Let x denote the amount of each fertilizer required for 1kg of nitrogen given the 1:1

65

Technically, marginal value-cost ratio greater than one would imply fertilizer use by
itself is profitable if no additional cost is incurred. This is not likely to be the case due to
the transaction cost. For this reason as well as the risks associated with fertilizer use,
experienced researchers have found that MVCR of 2 or greater is generally required to
find farmers using fertilizer in any appreciable amounts (Crawford and Kelly, 2002). Our
paper adopts this convention and considers marginal value-cost ratio of at least 2 as an
indicator that fertilizer use is likely to be profitable.

Equation (7) indicates that MVCR is higher for higher MPN or higher output-

input price ratio 5141-49. Estimates of MVCR are presented in Tables 2.5-2.8. Results
N

Show that majority of cases have MVCRs less than two. For example, Table 2.5 shows
that for Zone IIA soil type AF, only one case out of 18 cases has MVCR above 2 during
the first period and 7 cases have MVCRs above 2 during the second period. At the given
levels of marginal productivity of nitrogen, fertilizer use appears to be profitable at its
full market cost for a minority of smallholder farmers. On the other hand, a large
proportion of government fertilizer recipients (approximately 15% in our sample) may
find fertilizer use profitable since they were able to acquire fertilizer at roughly half of
the retail price and this would effectively double the MVCR values.

The last column in Tables 2.5-2.8 shows the level of nitrogen (N *) at which
MVCR is equal to 2 for each case. Nitrogen applied at a level lower than N * has a higher

marginal productivity and thereby a higher marginal value-cost ratio for profitable use of

 

application ratio of two types of fertilizers, based on the nutrient component information we have 10%x+
46%x=1. Solving for x yields x=l .79kg, that is, 1kg of nitrogen costs approximately 1.79kg of basal and
top dressing, therefore the formula for calculating PM is 1.79><(basal price per kg + top dressing price per

kg).

66

fertilizer. The recommended nitrogen application rate by Zambia extension message
(116kg of nitrogen per hectare of maize from 200kg of basal fertilizer and 200kg of top
dressing) is higher than the N * in these tables, suggesting fertilizer applied at the
recommended level is unlikely to be economically viable under current market prices and

most smallholder conditions.

2.6 Conclusions

Using two-year panel household survey data from Zambia, this study estimates
maize production function adopting the conceptual framework recently developed in the
literature. This framework incorporates agronomic perspectives on the underlying process
of crop growth and thereby addressing the problem of identical treatment of inputs in the
traditional quadratic and translog models. Unobserved household heterogeneity is
controlled for using the Mundlak-Chamberlain’s approach.

Empirical results indicate that maize yield is positively associated with fertilizer
and timely availability of fertilizer, while inappropriate extension message and excess
amount of rainfall can have yield decreasing effect. Estimates of marginal value-cost
ratio of nitrogen for a range of small farm conditions are generally low due to the low
yield response rates to nitrogen and unfavorable price conditions. Only for beneficiaries
of government fertilizer program that purchased input at a much lower price does
fertilizer use appear to be clearly profitable. These findings suggest that small farmers
may lack incentive to purchase commercial fertilizer even for those having the capacity
and resources to do so, which may explain why only a small proportion of small farmers

(15%) acquire fertilizer commercially in Zambia. Strategies to make fertilizer use more

67

profitable for small farmers will require efforts to raise yield response rates and reduce
input and output marketing costs. Our study finds empirical evidence that farmers’ ability
to acquire fertilizer on time has a strong positive effect on maize yield as well as maize
yield response to fertilizer. Subsidized fertilizer under government programs in Zambia
has often been distributed late. These programs have also caused uncertainty for private
traders who first assess whether subsidized government fertilizer will be circulated in a
certain area of operation before deciding to sell fertilizer (Govereh et al., 2003). These
dynamics give rise to the late acquisition of fertilizer through both public and private
channels. Fertilizer use in an appreciable amount is unlikely to be profitable until efforts
are made to ensure more timely delivery of fertilizer. Moreover, the extension service
may consider revising their recommended fertilizer application rates both by region and
by smallholder characteristics taking into consideration whether fertilizer is available on
time and whether they acquired fertilizer through government program or commercial
retailers at full cost. All of these factors are shown to influence the profitability of

fertilizer use in Zambia.

68

 

 

Table 2.1: Variable definition
Variable Description
YIELD Maize yield (kg/hectare)
N Nitrogen application (kg/hectare)
BSLPC T Percent of basal fertilizer over total fertilizer application
RAIN Rainfall (mm)
HYBD l=used hybrid seed
0N TM 1=basal fertilizer available on time
DRTPW l=used animal or mechanical draught power in land preparation
MZAR Maize planting area (hectare)
EXT NSN l=received extension service
GVCHN 1=acquired fertilizer from govemment channel
ADULT Number of adults (above age 14) per hectare of maize
AGE Age of household head
EDUC Years of schooling of household head
F EMHD 1=female household head
MRTLT 1=adu1t mortality within past three years
YEAR 1=2002 season

 

69

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70

Table 2.3: Coefficient estimates of empirical crop production function

 

 

Zone IIA Zone IIA Zone 111 Zone III
Parameter AF non- AF AF non-AF
42.519" 17.472‘ 22.692" 44.464"
Cl1 (N) (0.000) (0.030) (0.005) (0.000)
-10.891 2.515 -30.607 4.736
92 (BSLPC 7’) (0.516) (0.832) (0.034.). (0.859)
-2449” ~6.819" -2944 -3.83
Cl3 (RA/N) (0.001) (0.000). (0.000). (0.000.)
-972.07” -241.97‘ 447.99 433.64
(14 (HYBD) (0,000) (0.000) (0.000) (0000),
N2 .01 12" -0039‘ -0.009 -0.117
011 1( ) (0.000) (0.020) (0.508) (0.000)
-0043 0.108 0.109 0.199
a12(N x 3511’”) (0.725) (0.157) (0.226) (0.182)
-0.008 -0.006 -0.012‘ -0.021
0113 (N x RAIN) (0.320) (0.395) (0.021) (0.011.).
0.129 -0.445 1.225 12.229
0L14W x HYBD) (0.969) (0.863) (0.719.) (0.003.)
72 0.38” 0.18‘ 0.209 0.319
0‘22 (BSLPC ) (0.004) (0.029) (0.031) (0.024)
-0013 -0.016 0.002 -0023
Cl23 (BSLPCT " RAIN) (0.391) (0.102) (0.883) (0.197)”
-7.1 0.439 3.468 -36.291
“24 (BSLPCT " HYBD) (0.248) (0.907) (0.510) (0.000)
N2 0.001 0.004“ 0.002" 0.002”
Cl33 (RA’ ) (0.098) (0.000) (0.000.) (0.002)
1.897' 0.667“ -0.439 ‘ 0.809‘
“34W” x HYBD) (0.000) (0.000) (0.008) (0.020)
-0.72" -0.796” -0.199 0.933“
‘30 (0.003) (0.000) (0.509) (0.002)
0.456 -0.065 -0.134 -l.l36 ‘
‘31 (0NTM) (0.102) (0.153) (0.594) (0.002)
-0109 -0.013 0.075 0.006
‘32 (DRTPW) (0.281) (0.604) (0.750) (0.980)
0.336“ 0.099“ 0.205“ 0405”
B3 (MZAR) (0.000) (0.000) (0.008) (0.001)
-0. 109 -0042 0.349 0.1 13
BMW/V5”) (0.297) (0.069) (0.300) (0.371)
1.61 1” -0.083‘ -0533 0271
B5 (G VCHNL) (0.000) (0.043) (0.603) (0.370)
-0.226" -0017" -0.068‘ 0.011
56(ADU”) (0.000) (0.002) (0.039) (0.728)
0.001 -0.001 -0.006 0.004
97““) (0.901) (0.313) (0.274) (0.481)
-0.013 -0.008 -0.014 0.014
[’8 (EDUC) (0.492) (0.204) (0.495) (0.478)
0.063 0.017 -0.230 -0.274
59(FEMHD) (0.615) (0.538) (0.477) (0.107)
—0.242 -0007 -0054 -0.06
BIOWRT”) (0.154) (0.826) (0.771) (0.729)
0.218 0.222“ 1.130 -0.131
5” (YEAR) (0.058)” (0.000). (0.141) (0.383)
-93.672 2666.69 ‘ 2820.19" 3217.24”
70 (0.000) (0.000) (0.000) (0.000)

71

Table 2.3(cont’d)
71W)
7265????)
73(m)
14(fifi35)
”(07547)
“(Tiff—W)
77(m)
”(ENS—N)
YMW)
How—DOW)
Y 11 (El—'3)
7mm)
71305—517715)
11AM)

0,2

03

Number of observations

3.365‘
(0.039)
-7.946“
(0.001)
2.096“
(0.000)
-4.091“
(0.000)
264.94“
(0.000)
255.17“
(0.000)
1 10.03”
(0.000)
-69. 1 76”
(0.000)
189.00”
(0.000)
5.515
(0.725)
-2.803
(0.335)
-0.056
(0.996)
-0.l6l
(0.635)
-300.59“
(0.000)
848000“
(0.000)
220000"
(0.000)
1414

2.789‘
(0.021)
.4833‘
(0.018)
0.614“
(0.007)
129.38”
(0.000)
23.331”
(0.000)
301.98”
(0.000)
1 10.94“
(0.000)
-90.781“
(0.000)
29.547”
(0.000)
-15.1
(0.256)
-2773
(0.372)
-0049
(0.997)
-0.159
(0.703)
-339.76"
(0.000)
920037“
(0.000)
163700"
(0.000)
2338

0.081
(0.954)
-l.268
(0.700)
-064“
(0.004)

81.402“
(0.000)
285.58"
(0.000)
317.94“
(0.000)

-37.838”

(0.000).
57.426
(0.000)
215.16“
(0.000)
-7.797
(0.520)
-2.747
(0.330)
-0052
(0.997)
-0. 160
(0.540).
290.09
(0.000)
800724“
(0.000)
1 19000“
(0.000)
982

-1 . 147
(0.623)
-1.717
(0.721)

-1064”
(0.000)

-336.44"
(0.000)

410.96“
(0.000)

-104.71"
(0.000.).

-3.845

(0.009)
195.66“
(0.000)

-131.22“

(0.000)
0.965
(0.942)
-2.766
(0.589)
-0.063
(0.997)
-0.l63
(0.8802.

23.761
(0.000)

720296“
(0.000)

1 16000“
(0.000)

586

 

Note: Numbers in parentheses are p-values. rand " indicate estimate is significantly different from

zero at 5% and 1% significance level, respectively.

72

Table 2.4: Estimates of partial effects

 

 

 

Zone 11A Zone 11A Zone 111 Zone 111
AF non-AF AF non-AF
Variable 1999/00 2002/03 1999/00 2002/03 1999/00 2002/03 1999/00 2002/03
N 7.80‘ 11.70' 6.75' 9.34' 8.45' 10.67' 5.73' 7.19‘
(0.002) (0.000) (0.000) (0.000) (0.000) (0.007) (0.014) (0.007)
BSLPCT 4.61 6.92 5.46‘ 7.55‘ 0.18 0.23 11.11 13.95
(0.068) (0.062) (0.026) (0.026) (0.971) (0.971) (0.077) (0.051)
RAIN -0.51‘ -0.76‘ -062‘ 086' 0.34 0.43 -0.62‘ -0.78‘
(0.007) (0.002) (0.000) (0.000) (0.077) (0.094) (0.049) (0.019)
HYBD 121.38 184.25 303.24‘ 369.83‘ 237.72’ 278.69‘ -165.26 -121.42
(0.090) (0.084) (0.000) (0.000) (0.004) (0.013) (0.160) (0.390)
0NTM 201.06 201.96 110.17 116.43 339.48 244.4 405.36 407.10
(0.000) (0.000) (0.233) (0.239) (0.000) (0.005) (0.009) (0.000)
DRTPW 267.49‘ 270.34‘ 328.08‘ 328.71‘ 287.41‘ 345.4‘ -104.66‘ -104.65‘
(0.000) (0.000) (0.000) (0.000) (0.002) (0.000) (0.000) (0.000)
MZAR .4054 -48.17 -205.11‘ -208.90‘ -867‘ 73.74 -323 -3.49
(0.308) (0.292) (0.000) (0.000) (0.028) (0.192) (0.971) (0.971)
EXTNSN -56.90‘ -54.06‘ -4.17 -0.98 -65.96 191.13‘ 196.51‘ 196.60‘
(0.001) (0.008) (0.927) (0.984) (0.286) (0.009) (0.000) (0.000)
GVCHNL 122.54 183.28‘ 139.65 148.89 408.91‘ 126.16 -13353‘ -133.56‘
(0.065) (0.000) (0.082) (0.083) (0.000) (0.510) (0.035) (0.037)
ADULT 27.33 32.47 35.76 36.42 29.24 -24.87 0.09 0.10
(0.280) (0.276) (0.001) (0.001) (0.132) (0.343) (0.970) (0.970)
AGE -0.06 -0.08 2.76 2.81 2.59 -2.2 0.03 0.04
(0.904) (0.904) (0.295) (0.298) (0.307) (0.359) (0.971) (0.971)
EDUC 1.53 1.81 16.5 16.8 6.51 -553 0.11 0.12
(0.522) (0.517) (0.192) (0.197) (0.448) (0.518) (0.971) (0.971)
FEMHD -8.03 -9.30 -3591 -36.29 88.69 -62.66 -2.51 -2.54
(0.661) (0.657) (0.539) (0.535) (0.198) (0.326) (0.969) (0.969)
MRTLT -27565‘ -26864‘ -325.51‘ -325.21' 305.47‘ 277.39‘ 23.27 23.23
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.079) (0.099)

 

Note: Numbers in parentheses are p-values. ' indicates the estimate is significantly different from
zero at 5% or higher level. Partial effects are evaluated at HBRD, 0N TM, DRTP W, EXT NSN,
GVCHNL, FEMHD, MRTLTequal to zero, and N=(45.90, 49.19, 82.28, 74.67), BSLPCT=(50, 50, 50, 50),

RAIN=(892.6, 892.6, 1086.3, 1087.9), MZAR=(1.215, 1.215, 0.75, 0.81), ADULT=(3, 3, 4, 4), AGE=(44, 44,

44,46), EDUC=(6, 7, 7, 7), the 50 percentiles of households with N>0 for each agroecological region.

73

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77

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80

   

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