Family dynamics and household welfare in Cañete, Peru.
V. E. Cabrera & P. E. Hildebrand
University of Florida, College of Natural Resources and Environment. Gainesville, FL. USA.
ABSTRACT
Family composition is believed to be a major component in the capability of small farm
households to achieve sustainable development. In order to understand and test the effect of
household composition on overall farm household well being, a process simulation model was
developed. The model accounts dynamically for the birth, age and death of the members and for
the crops, livestock, and financial activities. Prices and yields were stochastic variables. Ten
typical Cañete households were simulated. Results in 10, 20 and 40-year runs showed that the
family composition has a great influence on economic stress. Smaller families were always
better off than large families. Only the 20-year run is illustrated.
INTRODUCTION
Cañete is a 24,000 ha valley on the west coast of Peru, one of the driest deserts in the world. The
land is highly parceled; there are about 5,000 farms and 80% of them are in hands of small
landholders (10 ha or less). Usually, small farms are family-centered households, where the main
source of labor comes from family members and the farm and the house are highly interrelated.
The typical Cañete farm has 5 ha of cultivable land divided into two fields, field 1 of 3 ha and
field 2 of 2 ha. Maize and sweet potatoes are raised in these two fields interchangeably; maize is
grown between September and December in field 1 and between February and June in field 2; in
the same way, sweet potato is grown between August and December in field 2 and between
March and July in field 1. Chickens are also raised all year long. The family house as well as
some storage compartments and the chicken house do not use crop land. The system boundaries
are the same as the farm border limits. The number of family members varies greatly, from twomember families to 10-member families. Low-resource income farms in Cañete have limited
access to credit opportunities.
Household composition is an important factor in low-resource farming systems. Sullivan (2000)
studying data of Senegal communities over a period of 40 years, found that household
composition drives the decision making process by determining needs, and the capacity of a
household to meet these needs.
Sullivan also found that households characterized by few adults and many young children would
be under relatively high stress; as children become adolescents or other adults join the
household, requirements and available resources change yet again. Grown children can
contribute to the labor pool as well as newly joined adults, which increase available labor even as
they increase total household consumption.
Data of a survey carried out in 1998 (Cabrera, 19991) was used as a baseline for this system
simulation. A random sample of 60 farmers was used in the survey; the database (an electronic
file) can be downloaded from Appendix C of the electronic publication. The interviewed farmers
were geographically stratified and completely randomly selected. For more details, see Cabrera
(1999) available via the Internet. Data were updated and, in a few cases recalculated, using 5year author expertise and non-published material from the “Valle Grande Rural Institute2”, a
local Non-Government Agency with 40-year of labor experience in the community.
The purpose of this study was test the hypothesis that family stress imposed by the existence of
many children would overcome and could even be advantageous after several years in the Cañete
community.
The objectives were:
1) Analyze the behavior of the financial variables versus different family compositions over
time for a typical farm in Cañete.
2) Assess risks of different family compositions and compute overall community
uncertainty.
THE MODEL
Farm scale simulation models are developed for different objectives. Authors use them for
assessing sustainability (Hervé et al, 2001; Sullivan, 2000; Shepherd et al, 1998; Hansen, 1996;
Kelly, 1995); estimating disruptions from policy changes (Kaya et-al, 2000; Litow, 2000;
Kruseman et al, 1998; Ruben et al, 1998, Dent et al, 1995); or testing new technologies to be
diffused (Grier, 2002; Bastidas, 2001; McGregor et al, 2001; Bernet et al, 2000; Cabrera, 1999;
Dalsgaard et al, 1997; Nyangito et al, 1996). Many late models aim to produce expert systems or
to develop decision support systems (Castelán-Ortega et al, 2001; Attonaty et al, 1999); several
include combined approaches working together (Shaffer et al , 2000; Neil et al 1999; Keating et
al 2001; Herrero et al, 1999).
These models are usually divided into Biological, Ecological, and Socio-economic modules.
Biological processes include crop production, livestock operations, and other biophysical
variables related to production. Ecological processes summarize the relationships of the farm
1
2
http://etd.fcla.edu/etd/uf/1999/amj9816/cabrera.pdf
http://www.irvg.org
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with the environment; and the Socio-Economic processes include variables that are related to
consumption, financial aspects, economic results and the like.
Even though most models include family as a farm component, family composition related to
household outputs as a particular interest of simulation was not found in the literature. In no case
were size, age, and composition simulated. In order to understand and test the effects of different
household compositions on limited resource farm household behavior, a simulation model was
developed. The model accounts dynamically for the birth, age and death of family members and
for crop, livestock, and financial activities.
Ten typical small farm households were chosen to be simulated using data from the survey.
Family. Family is a simulation module in itself. It keeps account of the number of members and
the age of each at any given time. The Family module classifies the members in 16 categories
according the age of each member (every 5 years, between 0 and 80 years).
The family module updates the age of each member every year. There are no deaths except the
members over 80 years. The members and their ages determine household consumption,
expenses, and labor available at any point of time with the following rules:
People in the Cañete valley work effectively 20 days a month. Labor can be sold (if extra labor is
available) or bought in any given month. Labor in the household is required for the crops and for
the animals. The sell/buy of labor has a constant value of US$ 3.5/day.
Chickens. There are limits to the number of chickens in the farm: When the number of chickens
reaches the minimum of eight (8) or maximum of fourteen (14), the family buys (8 units) or sells
(all above 14 units), respectively. The price of selling or buying a chicken varies between US$ 5
and 10, with a random probability. The chicken activity requires labor. Each animal requires 0.1
days of labor per month. Chickens also consume some maize and sweet potato produced in the
farm. Each chicken consumes 3.0 kg of maize and 1.5 kg of sweet potato each month.
The family consumes chickens. The number consumed in a month is a function of the total
number of family members, independently of the ages. Besides the regular chicken
consumption, the family consumes an extra chicken in the festivity months: December and July,
and two extra chickens in February, when the head celebrates his birthday.
Maize and sweet potato production. In order to produce maize and sweet potato, labor and
cash are required as well as land. The quantity of labor and cash varies according to the crop
physiological stages and the production season. Each crop has two harvestings in a year. Maize:
December and June, and Sweet Potato: December and July. The crop yields are based on the
range found in the 60-household survey, and it follows a stochastic process determined by a
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random number, between 4500 and 6000 Kg for maize and between 15000 and 25000 Kg for
sweet potato.
Maize grain and sweet potato storage. After the crops are harvested, the commodities flow to
storage. From the storage pool, the commodities can support the family and chicken
consumption (with the rates described above) or can be sold. The selling price varies, inside a
range found in the survey, with a random probability, between 0.15 and 0.18 US$/Kg for maize
and between 0.04 and 0.14 US$/Kg for sweet potato.
Cash and debt. Cash and debt are intimately linked. Money can flow from debt to cash
following some credit rules and cash must return to debt following some payment rules. In any
month, if the cash in the farm goes below US$ 2,000, the family obtains a credit of US$ 1,000.
If, after this loan, the family is not able to cover all its expenses, the family obtains another credit
of US$ 1,000, if it still is not enough, it obtains another US$ 1,000 credit and another and
another, successively up to a maximum of US$ 6,000 credit in any period of time. In any month,
the family pays at least 5% of the total debt, if the cash is lower or equal to US$ 4,000. But, if the
family cash is greater than US$ 4,000, then the family must pay all the money above US$ 4,000.
If the debt payment is greater than the current debt, then the payment must only equal the total
debt and pay it in full. The credit has a cumulative interest rate of 1.5% monthly.
Initial Conditions
STATE VARIABLE
CASH
DEBT
MAIZE
SWEET POTATO
MAIZE GRAIN
SW POT ROOT
CHICKENS
FAMILY
VALUE
1000
1000
0
0
500
800
14
5
UNITS
$
$
Kg
Kg
Kg
Kg
Units
Members
Table 1: Initial conditions of simulated Cañete farm
The initial family is composed at the beginning of the father (31) the mother (26) the
grandmother (61), and two infants (2 and 1). There are newborns in subsequent years 2, 3, and 5.
This is a typical family observed in the 60-household survey.
RESULTS
This initial family increases from 5 members to 8 in the fifth simulation year. It remains with 8
members until the 20th simulation year when the grandmother dies. From that point to the end,
there are 7 members, Figure 1. The symbols in this Figure represent, very approximately, the
number, gender, and age (related to symbol size) of present members at a given time. Notice how
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new members are integrated and aged through time (gender has no implications for this model).
In the simulation of this household, the family reaches the maximum stress point (high debt)
when many children and few adults are present and becomes “free” from debts in the 22nd
simulation year, when most of the members are adults. From then, the family starts accumulating
cash, ending with around US$ 75,000 in the last year.
Figure 1: Cash, Debt and approximate family composition simulated
SCENARIO ANALYSIS
Different family compositions were tested as different scenarios because of the importance of
composition in understanding the capability of households to achieve sustainable development.
Table 2 summarizes these 10 scenarios. The numbers represent the age of the members in the
first year of the simulation; negative numbers indicate new members who will be born in the
subsequent years, for example -11 means that there will be a new member in the year 11. The
initial family was scenario number 4.
MEMBER
1
2
3
4
5
6
7
8
9
10
11
1
61
31
26
1
2
-2
-3
-5
-7
-9
-11
2
61
31
26
1
2
-2
-3
-5
-7
-9
3
61
31
26
1
2
-2
-3
-5
-7
4
61
31
26
1
2
-2
-3
-5
SCENARIOS
5
6
61
61
31
31
26
26
1
1
2
2
-2
-2
-3
7
61
31
26
1
2
8
61
31
26
1
9
61
31
26
10
31
26
Table 2: Age of family members in household in the first year of simulation.
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Table 3 shows the proportion in the population of “these kinds” of scenarios. It is impossible to
cover all the family compositions with all the ages in different times; so, these kinds of scenarios
are only approximations to the scenarios run.
MEMBER
Number
of Members
Frequency
Probability
“These kinds” of SCENARIOS
4
5
6
7
1
2
3
8
11
10
9
8
7
6
5
0
0.00
2
0.03
4
0.07
9
0.15
10
0.17
5
0.08
8
0.13
9
10
4
3
2
7
0.12
11
0.18
4
0.07
Table 3: Family members and probability of occurrence.
The family of the first (1) scenario starts with five members, the parents, the grandmother and
two children of 1 and 2 years. In the years 2, 3, 5, 7, 9, and 11 new members are born. Finally,
the household totals 11 until the grandmother dies in year 20, when the total number becomes 10.
In the following scenarios, there is one less member born, until scenario seven (7) when the
family does not have any new born after the simulation starts.
Thirty simulations were run for each scenario. Cumulative Probability Distribution, Mean and
Variance relationships, and Box Plots were used to analyze the outputs (CASH less DEBT, or
NET CASH) over 10, 20 and 40 years. Figure 2 summarizes the Net Cash outputs for the 20-year
simulation. In the 20 year period, scenarios 1, 2 & 3 maintain high debt indexes, scenario 4 & 5
have 10% and 25%, respectively, chance of getting out of debt.
Table 4 shows the proportion of each “kind of” composition family and the probability of success
(assuming that success in 20 year period is to stay out of debt). The total population success is
the sum of all partial probabilities; 0.6392 means that 63% of the families will be able to make it
in 20 years, considering family composition as the driving factor inside the household.
“These kinds” of SCENARIOS
Probability
of success
Population
Proportion
Population
Success
1
2
3
4
5
6
7
8
9
10
0.00
0.00
0.01
0.11
0.28
0.93
1.00
1.00
1.00
1.00
0.00
0.03
0.07
0.15
0.17
0.08
0.13
0.12
0.18
0.07
0.0000
0.0000
0.0007
0.0165
0.0476
0.0744
0.1300
0.1200
0.1800
0.0700
Total
Population
Success
0.6392
Table 4: Probability of Cañete farm family’s success after 20 year simulation.
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A
CUMULATIVE PROBABILITY
A
1.00
0.90
1
0.80
2
3
0.70
4
0.60
5
0.50
6
0.40
7
0.30
8
0.20
9
0.10
10
0.00
-60000
-40000
-20000
0
20000
40000
60000
80000
100000
120000
NET CASH
B
120000
100000
80000
80000
8
NET CASH
MEAN
100000
40000
7
20000
6
0
5
-20000
-40000
120000
9
60000
1 2
-60000
0.00E+00
60000
40000
20000
0
4
3
C
140000
10
-20000
-40000
-60000
5.00E+07
1.00E+08
1.50E+08
VARIANCE
2.00E+08
2.50E+08
3.00E+08
1
2
3
4
5
6
7
8
9
10
SCENARIO
Figure 2: 20-Year Risk Analysis. A) Cumulative Probability Distribution of Net Cash; B) Mean
vs. Variance plot; C) Box Plot Distribution of Net Cash.
CONCLUSIONS AND RECOMMENDATIONS
Families with fewer members were better off after 20 years. With more members, the expenses
and consumption exceed the benefits from additional labor.
The ability of households to hire inexpensive labor (available all the time), is a big factor
explaining the above results. Labor in the community is not a limiting factor. The relatively high
expenses for family members and the consumption rates are, overall, bigger than the member’s
contribution to farm income, independent of age.
Further research should look carefully to other labor options as children grow. In this case, offfarm labor earned the same as hiring labor on farm. Further research should also look at the
gender factor, which was not included in this study.
Simulations like this are quite useful to represent complicated flows between system components
and to represent long-term dynamic interactions. However, it has limitations for the decision
variables, which have to be rule-controlled but stochastic. Combinations of linear programming
with this kind of simulation might provide additional benefits for studying small farm systems.
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Contact Information:
Victor E. Cabrera
University of Florida
2126 McCarty Hall,
Gainesville, FL 32611
Phone: 352-392-5830 x 435
Fax: 352-392-7127
vcabrera@ufl.edu
Paper for ORAL presentation
Theme: Farming systems knowledge and information systems
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