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Population Density and Fertility in Farm Households:A Study of the Millennium Development Authority Zonesin Ghana
Clement Ahiadeke • Dominic Demr Der
Received: 9 January 2012 / Accepted: 9 November 2012 / Published online: 20 December 2012� Springer Science+Business Media Dordrecht 2012
Abstract Agriculture is mainly a rural preoccupation, and about three quarters of the
population growth in developing countries emanate from agricultural households. Some
demographers posit that the agricultural system affects birth rates; in addition, population
pressures might put stress on agricultural land in farming communities. This paper focuses
on the population to land ratio in the Millennium Development Authority (MiDA) Enu-
meration Areas (EAs) in Ghana and tackles the important question: Do households adjust
to an increasing population/land ratio by having fewer children? The authors explore this
theme in the context of rural population density and fertility in the three MiDA zones,
drawing on data collected in 23 EAs in Ghana in 2008. The results suggest that fertility in
the MiDA zones can be affected by density if nothing is done to regulate population
density. The regression estimates for the pooled data show that all the coefficients are
negative and statistically significant at the 0.05 level or better. Thus, children ever born is
inversely correlated with density, agricultural production, female literacy and the trend
variable (year). The estimates from the cross-sectional data as well as the spatial coefficient
were consistent with those of the pooled data. The results under various model specifi-
cations are stable. We find from the Cox model that areas with higher education levels and
a lower share of individuals working in agriculture, both correlated with land use. Agri-
cultural production has at most a modest independent effect on fertility. Our findings
suggest that population density has a reasonable inhibiting effect on fertility in the MiDA
Zones.
Keywords Households � Fertility � Population density � Farming � Land �Agriculture
C. Ahiadeke (&) � D. D. DerInstitute of Statistical Social and Economic Research (ISSER), University of Ghana,P.O. Box LG 74, Accra, Ghanae-mail: [email protected]
123
Environ Dev Sustain (2013) 15:927–947DOI 10.1007/s10668-012-9419-8
1 Introduction
In the 1970s, demographers estimated that three quarters of the population increase in
developing countries took place within agricultural households (Yotopoulos 1978). The
significance of this estimation has not been lost on students of development from devel-
oping countries, particularly in view of the rapid scaling up of agricultural land use (Ningal
et al. 2008; Verburg et al. 2004). A growing body of work in this area then focused on the
causes and consequences of population increase and fertility in rural settings. Some of
these publications investigated the plausible notion that the agricultural system itself (type
of land tenure, type of technology, and quality and quantity of land) affected birth rates
(Carr et al. 2006).
The dynamics of population pressure on natural resources have brought about other
consequences, which in turn might strain the fragile balance between population and
environmental resources. Unfortunately, only scattered data (often for only one point in
time) are available to depict these evolutions (ISSER 2010). Among the consequences, the
most important are the fragmentation of family holdings through generational transfers and
the decline in agricultural production due to overcultivation.
Pingali et al.(1987) citing Boserup (1965) argue that population pressure does not
necessarily result in disastrous consequences, as it may lead to the evolution of farming
systems from land-using or natural resource-using systems, such as shifting cultivation to
land-saving and labor-intensive farming systems such as annual cropping systems. This
argument, however, has some shortfalls because while investment is required to establish
intensive farming systems (e.g., investment in the construction of irrigation facilities,
terracing, and tree planting), insufficient attention is paid to incentive systems which
ensure that the appropriate investment is made. It is widely recognized that investment
incentives are governed by land tenure or property rights institution, as it affects the
expected returns to investments that accrue to those who actually undertake them (Besley
1995). In sparsely populated areas of the Millennium Development Authority (MiDA)
zones, for example, the Afram Basin area, land is often owned and controlled by the family
where individual land rights are severely restricted, and benefits are shared widely among
members of extended families (Johnson 1972). If such communal ownership of land
prevails and persists, investment incentives are likely to be weak, hence stymieing
investments necessary for the intensification of farming systems (Besley 1995; Johnson
1972). Then, the extensive and natural resource-using farming systems may continue to be
practiced, contrary to the Boserupian hypothesis (Boserup 1965).
In this paper, we focus on population growth characteristics and the agricultural systems
(in particular, the ratio of population to land) in the MiDA zones in Ghana (Fig. 1) and try
to examine whether households adjust to an increasing population/land ratio by having
fewer children. By population characteristics here, we mean density (measured by land to
man ratio), fertility (defined in terms of measurable quantities like crude birth rate, child–
woman ratio, total fertility rate children ever born, etc.), family structure, inheritance
patterns, value of child labor, migration patterns, and other characteristics that could be
conducive to maintaining high fertility in a way as to depress land/man ratio in the zones.
For example, the value of child labor in traditional and transitional agricultural lands and
the potential importance of environmentally and socially determined risks as sources of
derived demand for children need not be overlooked in potentially fertile areas such as the
MiDA zones (Sutherland et al. 2004). We explore this theme in the context of rural
population density and fertility in the MiDA zones in Ghana, drawing on data collected in
23 Enumeration Areas or census districts in 2008. The relative availability of land during
928 C. Ahiadeke, D. D. Der
123
the current period of agricultural modernization in the zones may not be conducive to
higher fertility if population control (or family planning) activities do not accompany the
modernization process. For example, a study suggests that farm size boosts the number of
living children not by creating a demand for more children, but by increasing the supply of
children through higher natural fertility and child survival.
2 Background
To expand the mandate of the Institute of Statistical, Social and Economic Research
(ISSER) to provide technical leadership and direction to the MiDA project impact
assessment and evaluation in Ghana, the institute conducted two key surveys: a baseline
study and a Farmer-Based Organization (FBO) study to set the agenda for future evaluation
of the MiDA project impact. In this section, we identify the various data sets employed in
doing this study. It is also important to note that the FBO survey and the baseline survey
alongside with the Ghana Demographic and Health Surveys formed the main sources of
Fig. 1 Map of Ghana showing the MiDA zones
Population Density and Fertility in Farm Households 929
123
data used to establish the relationship between population density and land use in these
rural agricultural frontiers.
The first of these data sources was the Ghana Living Standards Survey Round 5 Plus
(GLSS5?) (ISSER 2009) which served as the baseline data and an extension to the
previous Ghana Living Standards Survey Round 5. A Farmer-Based Organization (FBO)
survey was also conducted in 2009. The Farmer-Based Organization (FBO) survey was
conducted essentially to provide data for the training of farmers under the agricultural
transformation project. A very important element of the FBO data was to determine the
overall living conditions of farmers and their households. The surveys were planned over a
period of 3 years during the earlier part of the life of the project interventions. Approxi-
mately 1,200 FBOs were expected to benefit from the overall project intervention. The first
round of the FBO survey started in October 2008 covering 601 randomly selected FBOs.
Survey data were collected on 10 thematic areas, including demographic and household
characteristics, education, health, activity status, migration, household transfers, infor-
mation-seeking behavior, household assets, housing, agricultural activities, and nonfarm
enterprises of households. The information collected was to serve as the tool for measuring
the impact of the interventions planned under the FBO component of the MiDA project as
a whole. As was noted above, the GLSS5? was expected to provide information on
patterns of household consumption and expenditure at a greater level of disaggregation and
to provide the baseline information on various factors including population growth and
family planning activities, to support long-term monitoring of the MiDA project.
ISSER is currently analyzing the GLSS5? and the FBO data sets in preparation for
additional work in the MiDA zones. This analytical paper emanates from the baseline
survey of 2008 (ISSER 2009), the first round survey of FBOs in 2009 (ISSER 2010) and
the Ghana Demographic and Health Survey data sets over the period 1988–2008 which
supplied the fertility variables used in the analysis (see Fig. 2, for example). It was
important to use the fertility and some other demographic data from the Ghana Demo-
graphic and Health Surveys because we felt that these semi-longitudinal data sets would
help researchers understand better the intricacies involved in population change and
environmental factors. This would, in turn, serve as a base for future work on land/man
ratios in the zones.
Fig. 2 Average crude birth rate for high- and low-density MiDA communities. Source: Note that, since1988, Ghana has been collecting Demographic and Health Survey data with the support of MacroInternational with research grant from USAID. Using these data sets, projected Crude Birth Rates (CBR) for1988, 1993, 1998, 2003, and 2008 (GSS, NMIMR, and MI, various issues) were easy to estimate. Thesevalues were mapped onto Enumeration Areas in the MiDA communities captured by the DHS surveys andthe values graphed into Fig. 1 above
930 C. Ahiadeke, D. D. Der
123
3 Data and methods
The Millennium Development Authority (MiDA) intervention zones are classified into
three categories, namely the Southern Horticultural Belt (SHB), the Afram Basin, and the
Northern Agricultural Zone (see Fig. 1). In the Southern Horticultural Belt, emphasis is
placed on pineapple production as well as other horticulture that could boost the export
potentials of farmers. For beneficiary districts around the Afram River (Afram Basin), the
focal crops are cereals, and in the districts in the Northern part of Ghana (Northern
Agricultural Zone), the focal crop is mango cultivation in addition to other tree crops. The
overarching goal for emphasis in these crops is to increase the production and productivity
of high value cash and export crops and also to enhance the competitiveness of these high
value crops in these intervention zones. The intervention also seeks to emphasize inten-
sification of the cultivation of crops in the Southern Horticultural Belt, extensification in
the Afram Basin, and diversification in the Northern Agricultural Zone.
The three project zones covering 23 census districts (or Enumeration Areas) were
selected purposively, based on the earlier nationally representative Ghana Living Standards
Survey of 2005. About 230,000 individuals are expected to benefit directly from the
t interventions, while about one million people are expected to obtain indirect benefits. The
caution here is not to increase land/man ratios through migration and fertility factors as
MiDA modernizes agricultural productivity in the zones. Rather, the findings of this study
are expected to provide the demographic agenda for further analysis and evaluation as the
MiDA program evolves.
To link the FBO data to some important population variables that could not be calcu-
lated from the MiDA data sets, we created spacial files for the FBOs data containing
similar information in the MiDA zones in the Northern Zone, Southern Zone, and the
Afram Basin. These were then linked to the 5-year Demographic and Health Surveys in
Ghana over the period 1988, 1993, 1998, 2003, and 2008 to generate a pseudo-longitudinal
data to measure total fertility rates over the last 20 years. The files contained geographic
information on the boundaries of the administrative divisions of the MiDA-FBO zones.
3.1 Sample Design and Organization of Survey
Following the Demographic and Health Surveys, a two-stage sample design was used for
the Ghana Living Standards Survey and the Farmer-based Organization design as well. For
the FBO survey, the first stage involved selecting sample points or clusters from an updated
master sampling frame constructed from the 2000 Ghana Population and Housing Census
in the second half of 2007. A total of 621 clusters (census Enumeration Areas) were
selected from the master sampling frame. The clusters were selected using systematic
sampling with probability proportional to size. A complete household listing was con-
ducted in September 2007 in all the selected clusters to provide a sampling frame for the
second stage of the selection of households. The second stage of the selection involved the
systematic sampling of 15 of the households listed in each cluster. The primary objective
of the second stage selection was to ensure adequate numbers of completed individual
interviews to provide estimates for key indicators with an acceptable precision at the
district level. Other sampling objectives were to facilitate manageable interviewer work-
load within each sample area and to reduce the effects of intra-class correlation within a
sample area on the variance of the survey estimates. Because the design was not self-
weighting so household sample weights were computed and applied to the estimation of
the survey results. This was to facilitate the estimation of the true contribution of each
Population Density and Fertility in Farm Households 931
123
selected cluster in the sample. The main field work for the survey covered a 5-month
period (April–September 2008) in order to ensure that enough household baseline infor-
mation was taken before a significant number of MiDA interventions begun. [More
detailed information on sampling procedure for the MiDA and FBO surveys can be found
in ISSER (2009)].
3.2 Theoretical framework
It can be argued either explicitly or implicitly that almost all explanations of human
fertility have some decision-making ideas at their heart (Leibenstein 1981) not just at the
national level but also at the rural agricultural frontiers where populations tend to increase
with intensification (Carr and Pan 2002). At the very least, decision-making and population
planning play a role in situations where certain characteristics about an agricultural frontier
can mitigate incentives to reduce fertility. For example, abundant land but scarce capital,
infrastructure, and labor resources mean that investment in land is inefficient relative to
investment in labor and hence reproduction. In fact, research suggests that an exceptional
scarcity of wage-labor employment and schooling for women in remote and frontier areas
of a country may decrease the economic value of women’s time relative to that of children,
thus increasing fertility (Singh et al. 1985; Singh 1994). This is almost of necessity the case
if choice is in some way involved in fertility determination in frontier areas. The point
above suggests that a core population–environment interface in frontier environments turns
on the direct relationship between people and land. The available research on fertility–land
relationships generally supports the hypothesis that (1) where access to land is expanding
as in the MiDA zones, fertility rises; and, conversely, (2) land ownership suppresses
fertility. The literature tends to suggest that both the demand for labor on a larger farm and
the desire to expand landholdings as the family grows are considered the two primary
interpretations for the first hypothesis above (Chayanov 1986; Binswanger and McIntire
1987; Clay and Johnson 1992; Ellis 1993). The second hypothesis is explained, perhaps, by
the economic security imparted by land in lieu of children. The Philippines Rural Survey of
1952 (Hawley 1955), is, perhaps, the most striking study that positively links fertility and
farm size in which average total fertility varied from 4.8 to 7.0 per woman in her last
decade of childbearing as plot size increased from under 1 ha to over 4 ha.
Numerous researchers have examined the impact of land availability and/or farm size
on fertility behavior (Cain 1985; Clay and Johnson 1992; Easterlin 1976a, b; Hawley 1955;
Merrick 1978; Schutjer et al. 1983; Stokes 1984; Van Landingham and Hirschman 2001),
but these studies have been limited largely to historical and quantitative data. These may be
appropriate for indicating trends over time but such data do not explicitly clarify the
pathways and processes linking land to fertility decline.
Some researchers theorize that rural families deliberately produce more children
because of their need for more agricultural land and household labor (Caldwell and
Caldwell 1987; Lee 2001; Lee and Kramer 2002; Carr et al. 2006). While some theories
suggest that high fertility may be beneficial to farm families, yet the impact of different
land-use strategies or agricultural practices is not well known. When given similar access
to contraception, economic theories of fertility suggest that agriculturalists would prefer
(and achieve) greater family size than those engaged in less labor-intensive occupations.
In general, agriculture is more labor-intensive than cattle-raising, and agriculturalists on
marginal land with few technological implements have greater labor demands (Carr et al.
2006). The limited related research has indicated that the land–fertility relationship is
complex and fails to provide a definitive response to this conundrum.
932 C. Ahiadeke, D. D. Der
123
There is empirical evidence to show that in situations where agricultural land is rela-
tively scare, thus inducing a rational decision to reduce family size and undertake steps to
curtail reproduction, the reverse rather occurs. Various theories exist regarding why the
unexpected occurs, ranging from family planning program explanations (Robinson 1992)
to those positing a change in the direction of wealth flows, making children an economic
burden rather than a benefit (Caldwell 1982).
Kenya offers an interesting scenario, in that although it remains predominantly an
agricultural country, the rapid population growth that has occurred because of declining
mortality rates has resulted in a scarcity of land (Oucho 2000; Ovuka 2000). Although
fertility is declining, the population continues to grow at a rapid pace. With the current
total fertility rate at 5 children per woman and the attendant growth rate slowed to 2.3
percent, the projection is that more than seven million people will be added to the current
population of 32.4 million over the next 15 years (Population Reference Bureau 2004). In
essence, over 90 % of Kenya’s population resides on the 18 % of land area suitable for
agriculture, and there has been a serious decline in land/man ratio over the last half century
(APPRC 1998). The land–fertility dichotomy has resulted in the Easterlin argument which
advanced the development of the supply/demand framework for analyzing reproductive
decisions when using primarily an economic perspective. This idea led to the development
of a more specific component of the supply/demand framework (Easterlin 1976a, b).
The implication of this hypothesis is that as long as children provide labor then the
desire for large family size remains unchanged given that fertility is a conscious choice,
largely impacted by the need for additional labor in the fields or in the home. More recent
evidence of land–fertility interactions have framed the relationship between fertility and
landholdings in three ways:
(1) fertility increases in direct response to labor needs which are greater when more land
is owned (land needs drive family size goals (Carr et al. 2006; Coomes et al. 2001;
Binswanger and McIntire 1987; Chayanov 1986; Clay and Johnson 1992); (2) more
land is sought to meet the needs of growing family (i.e., family size drives lands (Carr
et al. 2006; Binswanger and McIntire 1987; Chayanov 1986); and (3) larger land
holdings may be indicative of higher socioeconomic status correlated with the
increased likelihood of infant and child survival (i.e., land holdings serve as a proxy
for socioeconomic status which in some cases leads to reduced mortality and
therefore higher fertility (Clay and Johnson 1992).
These positive land–fertility correlations have been documented in other developing
country settings (Stokes et al. 1986; Cain 1984); however, as noted by Carr et al. (2006),
the majority of related land–fertility research is conducted in settled agricultural areas. The
relationship between land and fertility in the context where land is abundantly available
and where the majority of the population are rural dwellers is an issue for further research,
particularly in frontier environments such as the MiDA zones. In essence, we conceive of
fertility as a function of variables such as the age of the population, the average income
levels, educational level, the occupational distribution, the locational distribution, and the
aspects of the population’s past history. If we change the variables, we expect to get
different results; but, we must keep in mind that in general we include variables either on
the basis of experience or because general knowledge of human behavior indicates they are
likely to have influence. Decision processes could be studied in a variety of contexts. For
our purposes, however, it would seem desirable to start such studies by exploring the
MiDA communities which are rural in nature. Some reasons come to mind: (1) those living
in rural communities are likely to exhibit a considerable amount of routine behavior, and
Population Density and Fertility in Farm Households 933
123
hence, this would appear to be a desirable context within which to study passive decision-
making (i.e., behavior ‘‘within a holding pattern’’) and (2) perhaps the most important
reason for doing rural studies is that most of the population of Ghana is rural-based and that
the population to land ratio has been decreasing because of natural population increase and
the persistent in-migration into frontier zones.
4 Demographic characteristics
Table 1 shows the summary statistics for the demographic measures at the Enumeration
Area levels for the FBO data. The selected rural settlements have a relatively youthful
population with an average age of 23 years compared to 43 years in the MiDA zones
altogether. This suggests that the FBOs are formed around the youth rather than older
people. Educational levels are low with an average of 3 years of completed schooling.
Almost 70 % of adults in the rural areas are into agriculture, and the average population
density is relatively high, particularly in the Southern and Afram Basin zones.
Among all the main sources of land ownership, family heads appear as the most
dominant source of land for use (27.6 %), followed by other male relatives (22.8 %), chiefs
(16.0 %), nonrelatives (14.8 %), and other female relatives (10.2 %). By implication, the
family as a whole (i.e., family head, male relatives, and female relatives) is considered the
most important source of land, accounting for 60.6 % of total land owned or being used by
holders at the time of the 2008 survey. Government is seen as the least significant (1.6 %)
among the major sources of land ownership considered by the study.
The average household size in the Southern zone and the Afram Basin is nearly similar,
5.3 and 5.1 persons, respectively. The average in the Northern Zone is relatively large, 7.6
persons per household. Thus, although with the smallest population size, there appears to
be the potential for a rapid population growth in the Northern sector (ISSER 2009). More
detailed analyses from the same report (ISSER 2009) suggests that the average land sizes
of holders in the various MiDA intervention zones range from 1.1 ha in the Southern Zone
to 2.1 ha in the Afram Basin. Holders in the rural Northern Zone seem to own or use larger
sizes of land than their counterparts in the urban Northern Zone. While 25.3 % of indi-
vidual land holders in the rural Northern Zone possess or use land larger than 5 acres, only
21.3 % of their urban counterparts possess or use that much land. Contrary to this pattern,
Table 1 Some demographic and land-use characteristics of the MiDA-FBO zones
Characteristics MiDA zones
Southern Afram Basin Northern
Population density (persons per sq km) 174 131 134
Number of Households 647 1259 961
Average size of operational holdings (hectares) 1.1 2.1 1.6
Number of FBOs 129.4 (647) 251.8 (1259) 192.2 (961)
Population size (persons) 13,05,172 1,203,279 947,232
Area (in sq kilometers) 1,029,603 16,350 16,061
Mean household size 5.3 5.1 7.6
Average number of educational facilities 10.8 6.9 4.6
Source: MiDA GLSS5? survey, 2008
934 C. Ahiadeke, D. D. Der
123
holders in the urban Southern Zone have bigger portions of land than their rural coun-
terparts. In the urban Southern Zone, 19.7 % of land owners or users possess land larger
than 5 acres compared to only 10.0 % of their rural counterparts who also own or use land
larger than 5 acres. However, there appears to be no clear pattern of variation in land size
between rural and urban dwellers in the Afram Basin.
4.1 Population density
Population density in the MiDA zones was calculated as the number of people per square
kilometer. The total area of each MiDA zone was derived by adding up the areas of the
districts within the zone. The population of each zone was also obtained by summing up
the populations of the districts in each zone. The district populations were extracted from
the 2000 Population and Housing Census report and then projected to 2008, the year the
FBO data were collected. The areas of each district, the projected populations, and their
respective densities are also presented in Table 1.
The average population density for all the zones is 146 persons per square kilometer. It is
174 per square kilometer in the Southern Zone, 131 per square kilometer in the Afram Basin,
and 134 per square kilometer in the Northern Zone. These means, however, mask the
considerable spatial variations from 323 to 490 per square kilometer in some places. Also, the
overall average does not come close to the 790 per square kilometer population density
documented in the 2000 Population and Housing Census for parts of the Greater Accra
Region (GSS 2002). The data also represent the most complete picture of population density
and socioeconomic characteristics for most years between 1988 and 2008. Because DHS is a
repeated cross-section of individuals sampled from locations across the country including the
three MiDA zones, it was possible to compare the GIS locations for survey clusters.
4.2 Poverty levels
There was no ‘‘consumption module’’ in the MiDA-FBO data set in the 2008 study. In the
absence of comprehensive income variables of the households in the data set, it was not
possible to estimate the poverty status of the FBO member households. Thus, the poverty
level as calculated for the MiDA Ghana Living Standard Survey 5? (GLSS 5?)
descriptive report was superimposed on the districts. Thus, each district was assigned the
same poverty level as the GLSS5? report, since the data were collected in the same year
and around the same time.
5 Factors influencing disparate household sizes
Factors accounting for the differences in household size between the Northern and the
Southern zones or the rural and urban localities were examined. Also taken into consid-
eration were the desire for the large numbers of children and the different family systems in
the Northern and rural areas. These variables are considered in turn below.
5.1 Fertility patterns in the MiDA zone, 1988-2008
Figure 1 shows the average number of children ever born (CEB) for the various DHS
survey years for low and high-fertility areas for the three MiDA zones, categorized by
density (divided at the mean) to produce lower and higher density areas. The pattern
Population Density and Fertility in Farm Households 935
123
provides two clear features. On the one hand, the high-density areas appear to have lower
average birth rate, and on the other hand, CEB declined during the period 1988– 2008 (for
the high-density areas, from about 3.8 to 2.9; for the low-density areas, from 4.3 to 3.2).
Over the same period, population density increased by 19 % in the average settlement,
from 0.70 to 0.83 persons per acre. Thus, the over-time correlation of average CEB and
average density is negative. The cross-sectional correlations are also negative. At each of
the 10 years, higher density settlements tended to have lower births from -0.08 to -0.43,
with a mean of -0.18. Note that similar analysis was done using Crude Birth rates and
similar patterns were found.
These patterns suggest that fertility in the MiDA zones is affected by density. It is
important to note, however, that these zero-order relationships could be misleading,
because density could be related to other determinants of Zonal births. Assessing the effect
of zonal density on zonal fertility requires a multivariate model which we explored below.
5.2 Density and fertility
Various cross-national studies of fertility have consistently shown inverse relationship
between density and birth rate, controlling for the level of urbanization, economic devel-
opment and others, and the results for smaller units of analysis are almost consistent (Cut-
right and Kelly 1978; Firebaugh 1982; De Sherbinin et al. 2007). In the 1970s, several inverse
density–fertility relationships were observed in various units of analysis. Nevertheless, there
have been inconclusive results for household-level data for some agricultural villages.
Explanations of density effects vary with the exception of urbanization not being a candidate,
because most studies restrict the analysis to rural areas, or include measures of urbanization
(Firebaugh 1982). Some studies attribute density effects to ‘‘population pressure’’ without
elaborating on how such pressure might operate to inhibit fertility. Other studies are more
specific, particularly when it is argued that in Taiwan, high-density facilitates the acquisition
of birth-control information. Easterlin (1967a, b) (cited in Firebaugh 1982) suggested that
inheritance was the key link between density and fertility for the nineteenth-century United
States. This bequest theory was applied to rural Brazil, and the same outcome was found.
Meanwhile, others posit that fertility tends to be lower in denser regions because children
cost more to bring up in these geographical areas. In the case of the three MiDA zones, there
could be at least two reasons for expecting a negative density effect: (a) population pressure
does not appear to affect density as large tracts of land are sparsely populated, (b) birth
control does not look imminent (as family control program in two of the zones is only about
2 % of the national average of 24 percept), and it is only in the southern horticulture zone that
land grabbing appears threatening (ISSER 2009).
5.2.1 Inheritance
Land scarcity creates a dilemma for the landholder. A surviving son is considered essential
to keep the land in the family particularly in most of the Northern settlements of the MiDA
zones. Arguably, as a result of the current high rural under-five mortality rate of 90 deaths
per 1,000 live births (GSS, GHS, and ICF Macro 2009), a large family is necessary to
insure a high survival rate. With the prevalence of the multigeniture norm, however, a large
family risks land shortage for inheritance relative to the family holdings, if many sons
survive. Once this happens, some of the children may migrate and others may be left
behind. But these activities are also a function of the current level of family planning
education programs and the general education support for the settlements. In other cases,
936 C. Ahiadeke, D. D. Der
123
couples may anticipate the density problem and try to limit fertility by having four (the
prevailing desired number of children GSS, GHS, and ICF Macro 2009) or less children.
Because the inheritance problem is more acute in higher density areas, we expect such
birth limitation to be more common in higher density communities.
5.2.2 Value of child labor
Microeconomic approaches to rural fertility stress that ‘‘the supply of and demand for
agricultural labor affect the demand for children in agricultural communities’’ (Rosen-
zweig and Evenson 1977, cited in Firebaugh 1982: 484). Studies including Firebaugh
(1982) and Carr et al. (2006) have shown that the value of child labor is very salient for
many farming households in the developing world. Child labor value in some communities
is determined largely by the availability of land. This is true even for the children of the
landless, who constitute a labor pool that can be used during peak seasons, such as harvest
times. Further, the labor pool is a community pool in that, children are most likely to work
on farms in their own communities, so it is the density of the community, and not some
aggregate, which principally determines child labor value.
5.2.3 Migration
High-density encourages migration, and migration erodes the social supports for high
fertility. Of the three MiDA zones, it is the Afram Basin that has experienced the most
migration unlike the Southern Horticultural Zone and the Northern Belt. In the Afram
Basin, for example, agricultural density (population/cultivated land) more than doubled
from 1975 to 1995. It is important to note that this paper focuses on rural-level density
effects, and not farm-level effects. This distinction is important, so the two levels of
analysis should not be confused. At the farm level, for example, the relationship between
farm size and family size could be reciprocal in that, farm size could adjust to family size
as well as the other way around. At the community level, this type of reciprocal effect is
not possible, because community land is fixed. For this reason inter alia, the results of a
community-level analysis of density and fertility do not necessarily apply to the rela-
tionship between farm size and family size within a community.
6 Other determinants of locality birth rate
Density could be correlated with other determinants of community birth rates, resulting in
inaccurate estimates of the density effect, if these other factors are not controlled for. These
determinants include agricultural production, female and male education, and some other
unknown factors.
6.1 Agricultural production
The likely effect of increased agricultural production is to lower fertility by delaying marital
cohabitation. Agricultural production in the 23 MiDA districts have been reviewed recently
and was found to be quite impressive in terms of quality and quantity (ISSER 2009).
The mean age at marriage for females is 20.8 years, while that for males is 25.3 years.
Both are significantly higher than the national mean age at first marriage (18.4 years). The
Population Density and Fertility in Farm Households 937
123
MiDA data indicated that 60.9 % of the population has ever been married. The indications
reveal that the rate is highest in the Northern zone (54.6 %), decreasing to 43.3 % in the
Afram Basin then to 38.7 % in the Southern zone. If these indicators are anything to go by,
then there is a high probability that agricultural production will have a negative effect on
birth rate. The expectation then is that a higher productivity relative to village fertility lay
in additional work, and not in additional income, brought by increased production. Some
might argue, however, from a microeconomic perspective, that agricultural production
should have a positive effect on fertility through its effect on income. This argument is
based on two assumptions: (1) that in these communities income has a positive effect on
fertility at the household level and (2) that there is no aggregation bias. Even if income
does affect fertility, quite possibly it is income relative to fellow community dwellers, and
not absolute income, which is critical. If so, the income effect at the community level
would be zero.
6.2 Female education
Several studies since the 1970s have suggested both at the individual and aggregate levels
that education has a negative effect on fertility (Firebaugh 1982; Coomes et al. 2001; Carr
et al. 2006). Although female education is critically important, its effects differ from
country to country. For example, in some low-literacy countries, the initial effect of
education might be to increase fertility.
Interpretations of the female education effect vary as some see female labor force
participation as the key: educated women command higher wages, so childbearing costs
more for educated women in terms of potential income foregone. However, this ‘‘income
foregone’’ argument seems irrelevant for farm households, because income opportunities
for farm village women are typically restricted to tasks which require no formal education
(clearing of land, for example). Other researchers focus on education’s probable effect on
knowledge and norms: Educated women are more likely to adopt nontraditional views on
family size, to use more effective birth-control methods and so on (Firebaugh 1982;
APPRC 1998; Van Landingham and Hirschman 2001). Other researchers also focus on
those being educated (the children) rather than on the educated and argue that education
raises the cost of children (Lee 2001; Lee and Kramer 2002). Whatever the case may be,
whether through its effects on adult norms or child costs (or both), we expect female
education to have a negative effect on fertility.
6.3 Female literacy
Female literacy was extracted from three variables in the MiDA-FBO data sets: the ‘‘age,’’
‘‘gender,’’ and the ‘‘can (name) read a phrase/sentence in English’’ variables. There is a
clear gender gap in terms of education in the zones: Only 5.8 % of women in the zones
compared to 14.1 % of men have secondary or higher levels of education. This is also
consistent with the finding of 43 % of women who have never attended school compared
with 30.2 % of men.
In terms of relationship between education and locality, the data indicate that the
proportion of adults who have never been to school is highest in the Northern zone
compared to the other two intervention zones. The figures suggest that while 61.4 % of the
adult population in the Northern zone has never been to school, only 23.8 and 25.9 % have
never been to school in the Afram Basin and Southern zones, respectively. The data also
indicate that on average, households spent GH¢122.7 annually (1.63 cedis = 1 USD at the
938 C. Ahiadeke, D. D. Der
123
time) on each member attending school or college. However, the annual average amount
spent varies by location. The urban Southern zone recorded the highest amount
(GH¢215.9) followed by the Northern zone with an annual average expenditure of
GH¢180.5 on education.
6.4 Rural–Urban dimensions
Many studies have found an inverse relationship between fertility and the type of place of
residence. It is usually assumed that fertility is lower in urban areas than in rural com-
munities. However, the focus in this study is the community; the measure of urban–rural
composition (the absolute number of population) is differentiated by the size of the pop-
ulation. For rural areas, the population must be 500 people or less, thus making urban–rural
definition dichotomous. For the two broad MiDA communities, there is no clear-cut dis-
tinction between urban and rural. In this regard, the individual-level and community-level
relationship need not be the same.
Let uf = urban fertility rate, rf = rural fertility rate, and R = ratio of scheduled urban
population to the rural population. Suppose that urban definition affects fertility at the
individual-level, that is uf = rf, then we have two basic cases to consider.
Case I (no contextual effect). Here uf and rf for a community are not related to com-
munity R. Hence, total community fertility rate, which is a function of uf and rf, depends on
the relative sizes of the urban and rural schedules, that is, on R. For example, if uf [ rf,
then a zone with larger R will have higher fertility rate.
Case II (contextual effect). In the case of contextual effects, uf and/or rf are related to
community R. The possibilities here are numerous. For example, an urban community
within a rural setting can encourage high fertility, so when R is small, we expect uf to be
large. If rf is unaffected by R, then (total) community fertility rate is negatively related to
R. But R could also affect rf. Perhaps when R is small, the rural people feel less threatened,
thereby depressing rf. Alternatively, a small R could lead to higher rf: The rural population
often constitutes a cheap labor pool for urban dwellers, and when their labor pool is
relatively small, child labor is more likely to be important to the urban dwellers. In any
case, the basic point here is that such contextual effects are likely, and when they occur, the
community-level and individual-level relationships will differ.
6.5 The model and estimation procedure
The essence of the model employed here is to determine the relationships between land use
and demographic variables in the study areas. In this paper, the basic model estimated is a
linear regression of the form:
CEBit ¼ aþ b1DENSITYi;t�1 þ b2PRODi;t�1
þ b3%MALELITi;t�1b4%FEMLITi;t�1B5YEARþ eit ð1Þ
(i = 1, 2,…, 23; t = 1988, 1990,…, 2008)where CEBit is children ever born for each of
the 23 Enumeration Areas within the MiDA zone over time t; DENSITY is community
population/community land area; PROD is farm production per capita; %MALELIT and
%FEMLIT are male and female literacy rates, respectively; eit is error term.
Equation (1) describes ‘‘pooled’’ cross-sectional and time series data, that is, 23 Enu-
meration Areas each at 11 points in time 10, because the independent variables are lagged
1 year for a total N of 242.
Population Density and Fertility in Farm Households 939
123
We also include the age of the respondent to avoid biased estimates because age
structure (a) affects crude birth rate and (b) could be correlated with the explanatory
variables in the Eq. (1) above. Preliminary estimates show that the percentage of the
female population has no independent effect on CEB, and this variable was subsequently
dropped from the analysis.
Because there are missing data on key variables, our regression estimates are based on a
combination of cross-sectional (across zones) and time series (over time) covariance.
Analyses of such ‘‘pooled’’ data are not common place in demography, and two obser-
vations are in order. First, pooled data can reduce to more familiar data structure (Hannan
and Young 1977, cited in Firebaugh 1982). Among the possibilities, the best often is cross-
sectional analysis with outcome variable at time 1 as predictor. This approach, of course, is
quite inefficient, in that it ignores all the data for the intervening years. The approach is
used here to supplement and confirm the analysis of the pooled data. The chief attraction of
the cross-sectional, lagged outcome variable approach is that it enables one to use more
refined measures. For example, with the cross-sectional, lagged outcome variable, we can
use the 1988 Demographic and Health Surveys of Ghana (i.e., from 1988 to 2002), or
adjustment years, thereby minimizing the interpolation necessary for the pooled data (see
Table 2; note that community birth records are not usually kept, especially in rural areas,
so interpolation was found necessary to make adjustments). Further, a refined measure of
density is available with the cross-sectional, lagged outcome variable: household/cultivated
land area, instead of total population/total land area.
In addition, there are two basic econometric approaches to analyzing pooled data: the
‘‘error components’’ approach and the generalized least squares (GLS) approach. Each has
its advocates, and it is premature to say that one is superior to the other. In fact, GLS and
Table 2 Description of variables and data sources for pooled and cross-sectional data
Variable Component Data SourcesPooled data Cross-sectional data
CBR N = number ofbirths eachyear
Births collected from DHS1988–2008 sources
Used 5 year DHS averages tosmooth out short-term fluctuations(that is 1989 is 1988–1992 averageand 2009 is 2008—MiDA sample)
D = populationin thousands
Census, DHS sources, andMiDA
No interpolation needed for 2008.Minimal interpolation needed for1988
DENSITY N = Population See above Number of households interviewedin 2008
D = Land Total MiDA zone land. Someland area (constant overtime)
Cultivated land area 2008
PRODUCTION D = Population See above See above
%FEMLIT N = Literatefemalepopulation
Source: MiDA communitiesextrapolated from DHS dataat 5 year intervals1988–2008
Minimal interpolation needed
D = TotalfemalePopulation
Same as above Minimal interpolation needed
Source: MiDA GLSS5? survey, 2008
940 C. Ahiadeke, D. D. Der
123
error components make fundamentally different assumptions about the structure of the
error term, so in a given analysis, one must consider which set of assumptions is more
reasonable. The error components method, for example, decomposes the error term eit into
two components: a unit-specific component li and a well-behaved component vit (Hannan
and Young 1977; StataCor 2009). A time-specific component could also be included
(StataCor 2009), but time-specific effects are unlikely in our case. Recall that Eq. (1)
includes YEAR to capture any linear time trend. Here, li represents the community-
specific effects on CEB which (a) are not captured by the explanatory variables in Eq. (1)
and (b) are constant over time. Such community-specific effects are likely here. Age
structure in particular is an important determinant of community fertility rates (measured
here by CEB); however, it does not look stable, as the FBO data appears to produce mean
younger ages than the older age segments in the MiDA communities in general. Similarly,
if some communities consistently underreport births, or if some communities have better
access to family planning programs, that would be reflected in li. In short, the error
components approach seems quite appropriate for use in this study.
Finally to verify the effects of the timing of initial FBO activity in the communities, we
estimate the Cox proportional hazard model of the form:
kcðtjGc; bÞ ¼ koðtÞ expðGc0bÞ ð2Þ
where kc (t|Gc, b) is the community-specific hazard rate; ko(t) is the baseline hazard rate;
t is the year in which the community obtained FBO coverage (here t = 2008 for all
communities); and Gc is the set of community-specific demographic and land–use-related
factors.
The Cox proportional hazards model allows us to estimate the relationships between
land use and demographic variables semi-parametrically. This model does not make
assumptions about the form of ko(t) (which is unidentified here) but does assume the hazard
rate around multiplicatively (Cameron and Trivedi 2005).
7 Results
Table 3 gives the matrix of correlation coefficients for the pooled data. Children ever born
is inversely correlated with density, agricultural production, and female literacy. CEB is
Table 3 Zero-order correlation, pooled data
CEB Density Production %FEMLIT %MALELIT
Density -0.25
Production -0.19 -0.03
%FEMLIT -0.27 0.01 0.15
%MALELIT -0.23 0.01 0.27 0.07
Year -0.38 0.19 0.08 0.62 0.67
Age -0.23 0.12 0.33 0.06 0.34
Mean
SD
N 2,231
Source: MiDA GLSS5? survey, 2008
Population Density and Fertility in Farm Households 941
123
also inversely correlated with density, agricultural production, female literacy, and the
trend variable (YEAR). This is consistent with Fig. 1, which pictured a decline in CEB
over the period of study. This decline is not limited to the MiDA zones only, because the
Ghana Demographic and Health survey also projected a similar decline for Ghana as a
whole. Table 2 also gives the means and standard deviations; from the means we can
characterize the ‘‘average FBO village in the average year’’ in the following way: About
one-third of the communities are in urban setting, slightly over a fourth of the females are
literate, land is not critically scarce (if distributed equally, each resident would have
0.56 ha, or about 1.4 acres), and 37 babies are born per 1,000 women.
Table 4 gives the regression estimates for the pooled data. The results are consistent
with expectations. All the coefficients are negative and statistically significant (at the 0.05
level or better). The estimated effects are really not very large, however; the largest b(standardized regression coefficient) is 0.27.
Tables 5 and 6 give the estimates for the cross-sectional data. The results closely
parallel those for the pooled data. As it were, CEB is inversely correlated with all the
independent variables (Table 5). The pattern of result for the partial coefficients (Table 6)
also tends to confirm the results from the pooled data. The coefficients for density, female
literacy, and urban–rural settlement are all negative. The coefficients for production are
also negative, but quite small. These coefficients rarely attain statistical significance at the
conventional 0.05 level. What is quite informative is the stability of the results under
various specifications. Table 6 gives the coefficients for four specifications. In each case,
denser communities tended to have lower birth rates in 2008, controlling for per capita
agricultural production, percentage female literate, proportion rural, and 1988 children ever
born. Similarly, communities with higher female literacy tended to have lower children
ever born, all things being equal; communities that are urban tended to have relatively
lower birth rates, other things, being equal.
We find from the Cox model that a number of proxies for agricultural land-use appear to
be important in driving timing. Thus communities with both higher education levels and a
lower share of individuals working in agriculture were seen to have typically correlated
with land use. The relationship between education and land use is quite strong at baseline.
Table 4 Determinants of children ever born in the MiDA zones: regression estimate for the pooled data
Explanatory variablea bb bc Cox
Population density -0.06*** -0.27 0.283
Agriculture production -0.03** -0.13 -0.492***
Female education (in years) -0.18** -0.23 0.066***
Average age -0.26** -0.22 0.098***
Average education (in years) 0.017*** 0.038*** 0.065***
Year -0.35* -0.15 0.19
R2 (adjusted) 0.77 0.39
N 2,231 2,231 2,220
Source: MiDA GLSS5? survey, 2008
* Significant at 0.05; ** significant at 0.01; *** significant at 0.001a See notes for Table 3b Metric regression coefficientc Standardized regression coefficient
942 C. Ahiadeke, D. D. Der
123
Let us consider the findings for the other determinants of community children ever born.
We expected agricultural production to depress fertility in the high-density areas. The
results are somewhat not exactly so. Agricultural production has at most a modest
Table 5 Zero-order correlation, cross-sectional data
2008 CEB 1998 CEB Production %Femlit Density Age
1988 CEB 0.69
Production -0.32 -0.21
%Femlit -0.36 0.02 0.05
Age -0.07 0.33 0.27 -0.05 0.43
Density -0.26 -0.04 -0.22 -0.30 0.27
Mean 34.2 41.5 116.0 33.5 34.3 25.4
SD 6.8 10.9 100.2 11.3 7.4 11.3
Source: MiDA GLSS5? survey, 2008
2008 CEB average number of births, 1988–2009, divided by 2008 population * 1,000
1988 CEB average number of births, 1987–2000, divided by 1988 population * 1,000
Production farm output per capita, 2008
%FEMLIT percentage of female literate, 2008
Age age as recorded in 2008 survey
Density households per square kilometer of cultivated land, circa 2008
Table 6 Determinants of 2008 CEB: regression estimates for cross-sectional data with lagged CEB usingvarious models
Explanatory variables Model
Baselinea Male birthsb Sex ratioc Lag modeld
be bf b b b b b b
Household density -0.17 -0.24 -0.23 -0.35 -0.26 -0.24 -0.18 -0.26
Agricultural productiong -0.02 -0.07 -0.03 -0.15 -0.02 -0.09 -0.03 -0.08
% female literate -0.25** -0.35 -0.23 -0.32 -0.27** -0.36 -0.26* -0.38
Age -0.25 -0.26 -0.08 -0.07 -0.24 -0.26 -0.33 -0.25
1988 crude birth rate 0.55** 0.76 0.39* 0.54 0.56** 0.69 0.46** 0.77
R2 (adjusted) 0.67 0.20 0.70 0.66
N 2,231
Source: MiDA GLSS5? survey 2008
* Significant at 0.05; ** significant at 0.01a Uses variables as described in Table 4b Uses male births, 1987–1988, to estimate 1988 CEB, and male births, 1998–2008, to estimate 2008 CEB(in case female births are underreported)c Baseline model with community sex ratio controlled ford Lags production, female literacy, and yeare Metric regression coefficientf Standardized regression coefficientsg These results are not due to the skewed distribution of agricultural production. The results are the samewhen the skew is eliminated by taking the logarithm of production
Population Density and Fertility in Farm Households 943
123
independent effect on fertility. The coefficient is always negative but even in the one case
where it is significant, the b is only -0.15. This finding, however, serves as baseline
information for evaluating any impact that innovations in agricultural productivity in the
MiDA communities may have on fertility. It also serves as a challenge to family planning
activities nationwide.
With regard to female education, most studies of fertility conclude that female edu-
cation reduces fertility. This study is no exception as the coefficient here is negative and
moderately large (the median b is -0.35) (see Table 6). The results from the rural com-
munities illustrate how relationships sometimes depend on the level of aggregation. The
rural children ever born had to be estimated, yet at the community level, the correlation
coefficients and the partial regression coefficients are negative. The weight of the evidence,
then, suggests that living in urban communities has a negative effect on fertility. A possible
explanation would be that the ready availability of labor in the urban areas drives down the
result value of child labor; however, the data do not speak directly to this point.
7.1 The effect of density
Our results show that population density has a moderate inhibiting effect on fertility in the
MiDA communities. This is particularly so in the Southern Horticultural Zone. As evident
in Tables 4 and 6, the beta coefficients for density are consistent, ranging from -0.23 to
-0.35. The estimate of b (pooled data) is -0.47. If population density increased by one
person per square kilometer, other things being consistent one would expect the CEB to
decrease by 0.047. Saying it differently, if density increased by, say 10 % in the average
community, other things holding constant, we would expect CEB in the community to
decrease by 0.84 or 2.3 %. Note that the percentage decline in CEB does not match the
percentage increase in population. This means that, at least for the short run, if a com-
munity population (and hence density) increases, we expect the number of births to
increase although birth rate declines.
8 Discussions and Conclusion
This paper’s main focus is on the characteristics of population growth and agricultural
systems in the MiDA zones in Ghana. We also wanted to find out whether households
adjust to an increasing population/land ratio by having fewer children. We did this study in
the Millennium Development Authority (MiDA) zones in Ghana using two data sources:
GLSS 5? and FBO, which were the surveys conducted by the Institute of Statistical, Social
and Economic Research (ISSER). These data sets were supplemented with the Ghana
Demographic and Health Surveys carried out over the past 20 years. A two-stage sample
design was used to select samples for data collection in the three MiDA zones covering 23
Enumeration Areas or communities.
The variables of key interest to this paper were population density, fertility patterns,
value of child labor, male, and female literacy rates. The average population density for all
the zones was found to be 146 persons per square kilometer. Fertility patterns were studied
by averaging the number of children ever born for low- and high-fertility areas for the three
MiDA zones over a number of years. This was then categorized by density to produce
lower and higher density areas. The patterns suggest that fertility in the MiDA zones is
affected by density and high-density settlements tend to have lower birth rates. Community
density and availability of land on the other hand are both determinants of child labor
944 C. Ahiadeke, D. D. Der
123
value, but the principal determinant was found to be community density since children are
more likely to work on farms in their own community, than in other communities. Literacy
rate for males was higher than for females, and with respect to women, education was
found to have a negative effect on fertility. This could be due to the fact that educated
women have a higher tendency to adopt nontraditional views on family size, and they also
use more effective birth-control methods. Children ever born (CEB), community density,
farm production per capita (PROD), male and female literacy rates (% MALELIT,
%FEMLIT), and year were employed in a linear regression model to depict their rela-
tionship with land use.
The results show that children ever born is inversely correlated with density, agricul-
tural production, female literacy, and the trend variable year. A decline in CEB over the
study period was observed which is not limited to MiDA zones only but to Ghana as a
whole since a similar pattern was projected from the DHS survey. Denser communities,
high female literacy rate, and communities that are urban tended to have lower birth rates
compared to the other determinants. A number of proxies for agricultural land-use seem
important in driving timing. Thus communities with higher education levels and a lower
share of individuals working in agriculture were seen to have typical correlations with land
use. Agricultural production was seen to have an independent effect on fertility, which is
surprising, since it was expected to depress fertility in the high-density areas. Population
density on the other hand was seen to have a moderate inhibiting effect on fertility,
suggesting that if a community density (population) increases, the number of births is
expected to increase while birth rate declines.
This paper attempts to understand fertility behavior in relation to land use in the MiDA
zones in Ghana (an agricultural frontier area being supported by the George Bush—a
former American President’s initiative). We feel that this is an important topic for eco-
logical and population planning reasons. Population planning because the southern horti-
cultural zone appears to be experiencing high density while the rest of the zones are
relatively sparsely populated giving rise to in-migration and higher-than-average fertility.
With regard to the ecological importance of the research, we note that agricultural
expansion within the tropical world is the primary factor in deforestation in most agri-
cultural countries. Most forest conversion for agriculture is done by small farm families,
and household size has been consistently linked as a key determinant to deforestation in
such environments. The result of this study, therefore, underlies the need to accompany
frontier land development projects with population programs.
The paper has shed light on the population/land ratio interrelationships in the three
MiDA zones in Ghana. Particularly, we have critically examined one environmental
condition (density) in these zones, and the results are suggestive that increasing density
does dampen fertility. Stemming from the results of this paper, it is argued that fertility
may respond to environmental conditions in the poorer communities of the MiDA zones in
Ghana if nothing is done about planning for the future. In consequence, a factor to consider
for policy planning is the possible response of rural fertility to increasing land scarcity.
It appears that current levels of land use does not pose a threat to the population–fertility
dichotomy, and it would be good for planners to maintain or improve upon this pattern by
introducing population programs that keep land use and population density at equilibrium.
These findings lead to an acceptable conclusion that increasing density does reduce fer-
tility, and current levels of land use is not a threat to the population–fertility issue.
Acknowledgments This paper benefitted from Contract Number 4101103-01 between the MilleniumDevelopment Authorities (MiDA) and the Institute of Statistical Social and Economic Research (ISSER)
Population Density and Fertility in Farm Households 945
123
Farmer-Based Organisation (FBO) Survey Round 1, 2008. The original paper forms part of the 3 analyticalreports. The current version is an improvement upon the analytical report and has benefited significantlyfrom two anonymous reviewers and the editors of this journal.
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