ARCIA3/A -1-- S, 0 S-
RISK, PERCEPTIONS OF PRICE AND YIELD UNCERTAINTY,
AND NEW TECHNOLOGY IN A SMALL FARM SETTING V/ j
Gustavo Arcia, S.R. Johnson and John H. Sanders*
Since 1978 the International Center for Tropical Agriculture (CIAT)
has been conducting. agronomic trials of new technologies on plots physi-
cally located on small farms. The principal rationale for what it is
known as on-farm trials is the need to assess new technologies in a more
realistic setting, devoid of the environmental and managerial bias
usually encountered at the experiment station [Sanders and Lynam]. CIAT
assumes that this additional screening, among other things, would help
avoid false expectations about technologies which are promising only
under ideal circumstances but which fail totally under more restrictive
biophysical constraints. This process of technology generation is also
used as vehicle for collecting information about the'farm which may
prove useful for future technology design.
The results from the on-farm trials, however, have not yet produced
sufficient information with respect to the probabilities of adoption.
Up to now, technologies tested in these trials are evaluated economi-
cally through partial budgeting and, in some cases, through mathematical
programming. This evaluation process is cost-effective due to its hier-
archic structure but it is not complete. As it stands, new technologies
may be evaluated ex-ante only under the assumption that the farmer's
decision process is fixed or given. Hence, if farmers perceive new
technologies as risky, then the evaluator tries to identify the sources
of risk. However, the mounting empirical evidence seems to indicate
that this decision process is not fixed but, in fact, can be favorably
modified if stimulated properly. [Perrin]. Risk, as estimated by the
on-farm trials process, may be represented by the variance of gross
revenue. This variance, as it turns out, may well be totally subjective
since, after all, the farmer's decision process is dependent on his per-
ception of the environment.
The principal hypothesis set forth in this paper is that if real
gross income variance of a new technology is lower than the subjective
variance, adoption will not occur. In addition, it is argued that risk
aversion, long touted as a deterrent to technology adoption, is not a
significant factor for the farmer's decision. Rather, inaccurate per-
ceptions by farmers of price and yield uncertainty are more important in
explaining the failure of low income farmers to adopt-new technologies.
These hypotheses were evaluated with normative programming experiments
using data from the on-farm trials conducted by CIAT in Huila, Colombia.
II. CIAT AND NEW BEAN TECHNOLOGY
Designing adequate technologies for small farms in developing
countries has turned out to be more complex than originally believed.
Partly due to an incomplete knowledge of the economic and biophysical
environment for peasant farmers, many technology packages envisioned as
answers for small farm development have been largely unsuccessful. As a
consequence, the International Research Center network has begun to
redefine the methodology and scope of research for small farms (Valdes,
Scobie and Dillon).
The more general systems approach to technology evaluation and
adoption that has evolved is a promising innovation. Initial prescrip-
tions for alleviating food problems in developing countries emphasized
new varieties for existing crops. However, these varieties were high
yielding under favorable conditions not usually found on small farms in
Latin America. This feature of the new technologies frequently resulted
in rapid adoption by the more affluent farmers, often widening income
differentials between the rich and the poor.
A major feature of the new systems approach to technology design is
a recognition of the importance of risk aversion for adoption. Adoption
of new technologies is hypothesized to depend both on the farm production
unit and the farmer's utility for income. Concave utility functions for
income imply the precautionary behavior.of peasant farmers. Peasant
farmers may be unwilling to jeopardize their present incomes for potential
gains from new technologies because of uncertainty about prices and
However, incorporation of risk aversion in analyzing farm decisions
has produced only mixed results. First, no general agreement on the
degree of risk aversion exists. Pioneering efforts of Dillon and Scandizzo
in Northeast Brazil and Binswanger in India have produced widely different
estimates of risk aversion (Dillon and Scandizzo; Binswanger). Second,
the degree to which risk aversion precludes technology adoption is not
yet well understood (Binswanger; Roumasset et al.).
CIAT is currently the only research institution conducting research
7 on field beans (Phaseolus vulgaris) on a large scale. This research
includes the evaluation of the anticipated benefits of a new technology
in terms of appeal to farmers and in terms of fit within the small farm
system. Measuring the potential compatibility between a new technology
and the small farm system is a linear programming problem. Measuring
the potential appeal to farmers, however, is a different issue involving
risk and risk aversion. Obviously, a quadratic programming problem.
The necessary data for this analysis were collected from 1978
through 1980 by means of the on-farm trials. Bean trials in 1978 eval-
uated seed quality, fertilizer use, and better agronomic practices
(Arcia and Sanders; Restrepo), showing that better agronomy practices,
including two weedings and opportune spraying, increased yields more
than 50 percent. A significant response to fertilizer was observed only
on low soil fertility plots. The farmer's own seed proved equal, if not
superior, to both selected and certified seed. These physical responses
were used in partial budget analyses to support economic recommendations.
Results for repeated trials in 1979 indicated that better agronomy
again significantly increased yields on farms with adequate soil fer-
tility. Figure 1 summarizes the 1979 bean trial results for soils with
and without fertility problems and shows that application of improved
agronomic practices and fertilizer produced a yield improvement of 375
kg/ha in the low soil fertility plots. Based on similar results for the
two consecutive years of bean trials on 50 different farms, the better
agronomic practices option was selected for normative evaluation in a
programming model considering the whole farm system and admitting risk
III. DECISION MODEL WITH PRICE AND YIELD VARIATION
Two farm decision models were analyzed and compared. The first
used time series estimates for distributions of enterprise gross margins
as a measure of uncertainty. The second model used farmer's perceptions
of price and yield uncertainty, elicited experimentally. Both sets of
results were evaluated for alternative levels of risk aversion. Compari-
sons of results from the two models were examined for impacts of risk
aversion and perceptions of price and yield uncertainty on new technology
Farm Decision Model
Production responses for the new bean technology developed from the
farm trials were evaluated using the quadratic programming model,
Max U = cx 4(x'Qx)
Ax < b (1)
x > 0,
with c an (lxn) vector representing the expected gross margins for
enterprises or activities on a per unti basis, x the corresponding (nxl)
vector of activity levels, Q a (nxn) symmetric positive semidefinite
covariance matrix for gross enterprise margins, A an (mxn) coefficient
matrix, b the (mxl) vector of resource constraints, and 4 a scalar
reflecting aversion or preference for risk. Solutions of the model with
estimated values for production and margin coefficients provided optimum
farm diversification strategies for specified levels of risk aversion.
Additions of activities for the new bean technologies to this farm
decision model were used to evaluate ex-ante their impact on farm income
and resource use patterns.
The tableau sketched in Figure 2 illustrates the structure of the
quadratic programming model for analyzing the new bean technologies.
The model was annual, representing existing and selected or potential
farming activities for small farms in Southern Huila. Corn and beans
were assumed grown alone or in association. Along with tomatoes they
were the only semestral activities and therefore were modeled to permit
two plantings per year. Coffee, plantains, cassava, onions, and sugarcane
were the other cropping activities included in the decision model. For
these perennial crops, cost and income streams were represented for the
annual framework as annuity values.
All farm capital was assumed short-term, generated from loans and
labor or crop sales. Loans, private or public, following custom, were
assumed received'at the beginning of the first and second semesters and
repaid at harvest or at the end of the semesters. Capital was rationed
by adjustments in borrowing capacity and interest rates. Labor require-
ments of permanent crops were not discounted, the coefficients for the
model were averages of the quarterly labor requirements during the life
of the crop. However, labor restrictions were included in the decision
model to reflect'seasonal peaks in demand and management capacity.
Estimates for elements of A and b were developed using data from
the on-farm trials and adjusted in selected cases to reflect regional
averages and other secondary sources. Estimates of variances in gross
margins, the values for Q, as is typical of such analyses, were obtained
initially using published time series of prices and yields. These
estimators were products of random variables, yield and price and approxi-
mated using methods suggested by Bohrnstedt and Goldberger. Estimates
for means and variances of gross margins for new technologies were
calculated from farm trials data.
Covariances were estimated assuming correlations between existing
activities and the new beantechnologies to be the same as between
present bean technologies and the existing activities. Specifically,
calculations used the formula
cov(j,j') = pjjajoj., (2)
where pj,. was the correlation coefficient between gross margins for
activities j and j' and a. and a.i were corresponding standard deviations.
For example, from equation (2), the covariance between the gross margins
for the new bean technology say j* and an existing cassava activity j
was calculated as pjjai.oj where pjj, was the correlation-between gross
margin for cassava, j, and the gross margin from the existing bean
technology, j'. -Estimates for p, the risk aversion coefficient, were
elicited experimentally from farmers participating in the trials. The
methods of elicitation for p and results, similar to those obtained by
Dillon and'Scandizzo, have been reported in more detail elsewhere (Arcia
Difficulties with time series data for prices and yields were
numerous. Prices reported in secondary sources were typically aggregated
over both time, space and quality differences. For more commercial
crops, such as beans or brown sugar, prices reported were monthly aver-
ages. For subsistence crops such as plantains and cassava, prices
reported were monthly averages for marketed surpluses. Thus, the use of
secondary price series for estimating price risk posed important problems.
Similarly, secondary data for yields were aggregated. Crop yields
were aggregated across farms and geographic regions, generally biasing
variance estimates downward. Moreover, the reported statistics reflected
different crop technologies and differences in resource quality and
climate. Different ecosystems in a small farming environments can be
important in explaining observed behavior. Finally, time series on
yields for developing countries are often office estimates of extension
To overcome problems of accurately reflecting farmers' perceptions
of price and yield uncertainty, subjective or judgmental estimates of
distributions for yields and prices were elicited from the sample farmers.
The procedure for eliciting judgmental distribution has been applied in
a number of contexts (Chinn and Johnson; Jackson). Specifically, a set
of referenced gambles was given the farmer. From choices between succes-
sive referenced gambles, fractiles of the underlying judgmental distribu-
tions were obtained. These subjective price and yield distributions
were then utilized to estimate gross margin means and the covariance
matrix for the risk programming model.
Elicitation of subjective distributions has been a subject of
continuing discussion since Savage outlined the problem in a rigorous
manner (Savage). Due to their personal nature, doubts have been expressed
about the validity of elicited distributions in non-laboratory conditions
and the capacity of individuals to absorb the required pertinent informa-
tion (Hogarth; Hendrickson and Buehler; Hampton, Moore and Thomas;
Winkler). Accounting for these standard qualifications, interviews were
conducted for the farmers sampled to assess attitudes toward risk. The
questioning procedure was based on Raiffa's judgmental fractile method.2
This method attempts to find points in a cumulative distribution function
through the elicitation of equally likely probability intervals.
The elicited distributions revealed substantial differences between
time series estimates and values farmers associate with crop prices and
yields (Table 1). Subjective gross margin distributions tended to have
higher means and larger variances than those estimated from the time
series. The coefficients of variations in Table 1 show this relationship,
For instance, tomatoes, a crop with large price fluctuations within
the season as well as high vulnerability to pest attacks, presents a
time-series coefficient of variation similar to the time-series coeffi-
cient of variation for coffee, a very stable crop in terms of prices and
yields. The subjective assessment from farmers growing both crops,
however, reflects much more accurately the relative risks associated
with them. The subjective coefficient for tomatoes, it turns out, is
perceived by farmers to be more than double than the coefficient of
variation for coffee. Similar comparisons may be made with corn and
beans, as well as cassava.
Not surprisingly, the typical farm plan observed in Southern Huila
tends to follow the relative subjective risks. Hence, as table 2 indi-
cates, coffee is the first choice for farmers, accounting for more than
one-third of gross income, followed in succession by brown sugar and
beans (grown alone in or association with corn) in exactly the same
order as the subjective coefficients of variation.
Perennial crops were perceived as being less risky than annual
crops, and annual crops less risky than vegetable crops. Farmers in
semi-subsistence agriculture seem to diversify their farm plans in order
to compensate for inadequate food marketing structures, as well as
climatic risk. The results on the subjective distributions shown in
Table 1 seem to give additional information with respect to the patterns
of diversification: if income variation as perceived by farmers is an
index.of crop choice, then corn-beans should be preferred over cassava,
and both over tomatoes and onions. In this vein, it seems that the
larger the degree of risk aversion held by a farmer, the less diversified
his farm would be. In such cases farmers would tend to rely more and
more on labor sales (since wages are rigid and therefore not risky) and
on perennial crops. Such behavior would suggest the existence of farmers
who may be reluctant to invest on labor intensive activities in their
own farms, but ready to adopt labor saving technologies which would
enable them to sell labor during peak demand periods in the off-farm
labor market. Obviously, the large discrepancies between the estimates
from the two types of data suggested very different outcomes for farm
Application and Results
The study area, Southern Huila, Colombia, is a region that has been
the focus of research on beans for the past several years (CIAT, 1979).
As for other small farming regions, farms in Southern Huila were charac-
terized by diversified cropping, heavy labor use, and a myriad of cropping
patterns. Cassava, corn and plantains were the predominant home consumed
crops, while coffee, beans and brown sugar from sugarcane were the main
commercial crops. Tomatoes and onions were the principal crops on farms
near reliable sources of water. For the annual crops, the major planting
season began in March, the start of the first rainy period. Since
rainfall tended to be heavy during.the April, May and June, weeding
accounted for a large share of the farmer's time during this period.
Second semester plantings of beans started in late September with
the harvest ending in the middle of January of the following year. Corn
was not planted in the second semester due to the short second season
and lower rainfall. Bean plantings decreased considerably in the second
semester and tomatoes were planted only with irrigation. The farm labor
utilization pattern followed a series of peaks and valleys. This pattern
was further affected by the coffee harvest, from October to December.
Peak labor demand periods during planting and harvesting tended to
affect only the quantity of labor supplied, not the wage rate. The
coffee harvest, however, produced an upward shift in demand for labor
with a corresponding wage increase. For example, wages during the
fourth quarter increased approximately 25 percent locally, creating an
additional disincentive for second semester production of labor intensive
Since farmers tended to cultivate four to six crops simultaneously,
labor requirements at planting and harvesting limited the area of produc-
tion. Credit sources were formal and informal: banks, relatives,
private lenders, middlemen, and shop-owners. Formal credit sources
charged low rates of interest but had a scarcity of funds and bureaucratic
Marketing for the farmers in the region occurred locally and usually
involved many intermediaries. Choices of the sale date for the cash
crops were dependent upon fixed "market days" in towns surrounding the
farms. Market information for cash crops, however, was quite limited.
Farmers usually knew the going price at the nearest locality for the
previous week, but the total amount available for sale fluctuated from
week to week, with farmers facing a relatively uncertain sale price.
Results for the risk programming model with time series and subjec-
tive distributions for enterprise gross margins are shown in Tables 3
and 4, respectively. In each table, solutions were provided for four
levels of risk aversion, from p = 0.05 most risk averse, to 4 = 0, risk
Time series estimates: In Table 3, optimal solutions for the model
based on time series data show that farm plans were dominated by annual,
labor intensive crops with indications of a downward bias in the impact
of crop risk. Corn-beans, beans grown alone, tomatoes and onions ac-
counted for more than 80 percent of gross margins for the most risk
averse assumption. As risk aversion decreased, farm plans shifted
gradually to the presumably "riskier" perennial crops such as coffee in
association with plantains. Note that as risk aversion is decreased,
the contribution of annual crops to income is diminished substantially,
by 38 percent of the gross marginor even more, as in the case of risk
Practically all available family labor was utilized on the farm and
even additional labor (not shown) was hired. The choice of annual crops
and, hence, labor utilization followed the relative risks indicated by
the time series data. However, these results, as well as the time
series data, tended to underestimate the relative risks associated with
each option. Such a shortcoming became evident from field observations
(see table 2) and from the farmer's own reports.
Farm enterprise composition changed drastically under the assumption
of risk neutrality. In the risk neutral case the mean gross margin
increased by 50 percent over the mean gross margin for the farm at the
low (4 = 0.05) risk level. New coffee area increased almost fourfold,
sugarcane production became important, and the corn bean association
activity diminished slightly. Farm capital utilization doubled over
that for the lowest level of risk aversion (p = 0.05). This drastic
change in the farm plan seems to indicate a strong downward bias in the
amount of risk reported by the time series as evidence by the predomi-
nance of annual crops in the programming solutions.
It was clear that the solutions were affected greatly by the presence
of even small amounts of uncertainty. These different solutions suggested
the importance of accurately reflecting the variance-covariance matrix
for gross returns. Interestingly, the solution for risk neutrality was
more consistent with the behavior traditionally associated with small
farm agriculture than that from the model incorporating risk aversion,
with permanent or multiperiodic crops being preferred over th more
capital and labor intensive annual crops, tomatoes' and onions.
Judgemental distributions: Optimal farm plans when gross margin
risk was based on farmer's perceptions showed a different.trend from the
time series results. The farm gross margin levels obtained under the
higher risk aversion assumptions (p = -0.5 and 4 = -0.25) were lower
than corresponding levels given the same aversion parameters but with
time series estimates of gross margin distributions (Table 4). This was
related directly to the larger values for perceived price and yield
uncertainty. As risk aversion decreased, however, this relationship was
reversed. Farm gross margins under the subjectively estimated distribu-
tions was higher for low risk aversion assumption than in the time
series model. The net effect, in terms of farm gross margin, for intro-
ducing the farmer's perceptions of gross margin distributions was to
significantly increase the consistency in farm behavior under differing
degrees of risk aversion.. That is, as risk aversion diminished, the
dependence on the less risky alternatives and alternatives and subsist-
ence activities (pasture and labor sales) was reduced in favor of more
crop production. This pattern was confirmed by the presence of corn-
beans, an annual cropping system, in the risk neutral situation, and by
the increased use of capital. Consistency in the choice of farm plans
under different levels of risk aversion was also shown by the more
gradual change in income resulting from the assumption of risk neutrality,
a change substantially less steep than in the time series model. The
lower reliance on subsistence and perennial crops helped explain the
degree of diversification found under risk neutrality. Farm diversifica-
tion, in the risk neutral case, was dependent not so much on risk aversion
as on the seasonality of labor and the complementary nature of farming
activities. For instance, harvest labor for coffee was needed at times
when the corn-beans activity was not in production. Also, brown sugar
could be produced year round.
The presence of labor sales in all the risk averse solutions indi-
cated an aspect of the decision problem hitherto overlooked, the influence
of the off-farm labor market. The labor market in Southern Huila,
albeit seasonal, was strong, both for labor use and wage rigidity. From
the field observations it was apparent that wages were rigid downward.
Moreover, seasonality of harvest labor had little effect on wages except
for coffee harvest. Apparently, farmers used slack periods for tending
to perennial crops, household activities, or simply leisure. Thus, the
prevailing wage rate in the area was the reservation wage for off-farm
labor. It is not surprising then, that at higher levels of risk aversion
the decision model indicated that farmers would have a preference for
riskless off-farm work rather than for risky annual cropping activities.
As risk aversion disappears, labor sales tend to disappear simply
because there are more activities in the farm plan. In fact, for risk
neutral farmers labor is totally utilized inside the farm. The behav-
ioral pattern hypothesized previously is thus confirmed: diversifica-
tion in the farm is not necessarily a direct consequence of risk or risk
aversion, but a consequence of a combination of risk aversion and risk
One final point to be made in this section is the selection of an
appropriate simulation model. It is fairly apparent that the model
incorporating the farmer's own perception of risk yields a smoother fit
with an additional intuitive appeal: in assessing the potential for
adoption of a new technology one needs to begin by examining the criteria
used for the adoption decision. Clearly, small farmers do not look at
time series data to help make their decisions. Hence a model with
subjective income variation is more appropriate for an ex-ante evaluation
even if there is chance that the farmer's perceptions may be at odds
with reality. As long as the criteria is properly assessed, the results
from the model simulations would have a better predictive ability with
respect to farmer's decisions than a model which relies exclusively on
time series data.
Regarding the choice of the appropriate risk aversion coefficient
the results are not as definite. The risk aversion coefficients elicited
from the interview farmer's fell within a range of -0.05 to -0.49 depend-
ing on the method utilized (Arcia). The risk neutral solutions, however,
are closer to the farm plan in table 2 than the solutions under risk
aversion. Can it be then concluded that risk aversion is not important?
No, at least from a mathematical standpoint. Weighing the variance-
covariance matrix of a risk programming model with increasing values of
p, the risk aversion coefficient, will always have a negative effect on
net income and perhaps on crop choice, simply because net income c x is
reduced by increasing amounts of O(X'QX) as the scalar p gets larger.
Whether or not 4 is.a relevant parameter in the decision making process
is still open to debate. The evidence set forth in this study seems to
indicate that risk neutral and mildly risk averse programming solutions
do resemble farm plans observed in Southern Huila. The farm plans under
strong risk aversion levels (p = 0.5), although internally consistent,
are not commonly found in the survey area.
Bean Technology Adoption
The impact of better agronomy for beans was measured through inclu-
sion of this enterprise as a new activity in the risk programming model.
This new activity had a higher mean gross margin than current bean
technologies, somewhat lower labor requirements, and slightly higher
capital requirements. The gross margin variance for the activity was
derived from the farm trials, in combination with the farmers yield
perceptions. In a.risk neutral context, this new bean technology domi-
nated the other bean technologies since it had a higher gross margin
Model results indicated that the new bean technology was not as
attractive to risk averse farmers (Table 5) as originally believed. The
activity for beans with better agronomy did not appear in the optimal
farm plan even at low levels of risk aversion. Under risk neutrality,
however, the beans with better agronomy did have an impact on farm
income and employment. The area allotted to bean cultivation increased
from zero to three hectares. Sugarcane and cassava become significant
activities in the farm plan and the coffee area increased slightly. The
expansion in the cultivated area increased the need for working capital
by almost 30 percent. Expected farm income or the mean gross margin for
the farm increased from 204,935 pesos in the case of lowest risk aversion
(0 = -0.05) to 270,015 pesos for the risk neutral farm, an increment of
31 percent. Moreover, most of the increase came from introduction of
the better agronomy practices for beans.
At the other levels of risk aversion studied, the impact of the new
bean technology was apparently nullified by the yield uncertainty per-
ceived by farmers. Finally, parametrically increasing capital and land,
yielded results not encouraging for adoption of the new bean technology.
That is, parametric increments in capital borrowing and land availability
did not bring about adoption of better agronomy bean technology when
risk aversion was a significant feature of the decision model.
With higher risk aversion, off-farm labor activities remained more
attractive than the new bean technology. With a coefficient of variation
for the subjective gross margin distribution of approximately 40.13, the
better agronomy bean technology ranked better than only tomatoes and
onions. Hence, the lack of impact of new bean technology in a risk
averse context was not surprising. Furthermore, the findings helped to
explain the low adoption rates by farmers reported in other studies.
Summarizing the results, the utilization of time series variance in
risk programming models of small farm systems underestimates the risk
faced by farmers. Farm plans for the time series model emphasize the
production of onion and tomatoes which are usually grown by different
and more specialized producers. The results obtained with the model
with subjective variance indicate a different, albeit more consistent,
pattern: as farmers become more risk averse they first go into new
coffee technology, since coffee enjoys a stable (subjective) yield and a
fixed forward price. At higher degrees of risk aversion, however, the
amount of coffee grown is reduced, with a corresponding increment in
labor sales, a riskless activity. Hence, the available evidence indicates
that a risk model incorporating subjective risk is more appropriate for
the simulation of farm behavior.
A second important result relates to risk aversion and its interplay
with new bean technology. At high levels of risk aversion it is the new
coffee technology, rather than new bean technology, the one preferred in
the farm plan. Beans do not enter the solution except at risk neutrality.
However, and this is important, the risk neutral solutions are the ones
which come closest to observed farmers practices in the area.
Second, the results are useful for examining the importance of
risk aversion. The results shown indicate qualitative and quantitative
differences in risk modeling which need to be accounted for. Although
risk aversion has a negative effect on the farmer's objective function,
this effect has an economic meaning only when the risk aversion coeffi-
cient is the scalar of an appropriate matrix, in this case a subjectively
assessed variance-covariance matrix of gross margins.
The results presented here are intended to help clarify important
points in three areas of risk modeling for technology adoption and
design: (1) the value of subjective information, (2) the importance of
risk aversion, and (3) the impact of new bean technology. For the
first, the available evidence supports the use of subjective probabi-
lities in decision models for studying technology adoption. Farmers can
identify the variance.of gross margins from their farming activities in
a probabilistic framework and apparently use this information in enter-
Second, the results help assess the impact of new bean technologies
developed by CIAT. The new technology per se had limited impact on farm
income and employment. For risk averse farmers, the level of adoption
of the new technology was nil. For risk neutral farmers, the impact was
significant, with income increasing from 10 to 27 percent depending on
farm size. Risk averse farmers continued to work off the farm even in
the presence of the new bean technology. These results show that preli-
minary evaluations of judgmental perceptions of uncertainty can be
important for effective technology design, especially for peasant agricul-
ture where perceived uncertainties by researchers and targeted farmers
can be so different.
In addition, the results seem to clarify the reasons for farm
diversification. If risk is considered the main reason for diversi-
fication on a farm, then implicit in this argument is the mathematical
significance of risk aversion. The evidence shown here seems to suggest
that diversification is not only connected to risk aversion but to risk
perception as well. This difference is important because it indicates
that as risk aversion increases, subsistence farmers would tend to
diversify less, relying more on the labor market for subsistence.
The above assertion has important consequences for technology de-
sign. New technologies, to be attractive to farmers, need to fit into
the small farm system. Relaxing certain constraints which traditionally
have been accountable as restraining (e.g., land) does not imply imme-
diate adoption. Additionally, new technologies need to be perceived by
farmers to be equally or less risky than traditional technologies in
terms of gross revenues. Changes in the perception of risk may indicate
the need to redesign the on-farm trials to involve farmers more in the
testing process and to get them better acquainted with the real distribu-
tion of yields associated with the new technique. For price risk the
results indicate the need for a more efficient information system aimed
to keep farmers fully aware of market conditions. Again, this also
points out the need for better on-farm storage technologies for those
cases where market information suggests future increases in product
Finally, the decision process of farmers needs to be studied in
more detail. In particular, the variables which seem to affect percep-
tion the most need to be analyzed, as well as the possible methods which
may be devised to affect them.
Agricultural Economist, Research Triangle Institute, North Carolina;
Professor of Economics and Agricultural Economics, University of Missouri;
Associate Professor of Agricultural Economics, Purdue University. This
research was undertaken while the first and the last authors were at
CIAT (Centro Internacional de Agricultura Tropical).
The programming model formulation required distributions of gross
returns. Given the subjective distributions for prices and yields,
distributions of gross returns were simulated numerically and found well
approximated by the normal. Simple pproximations to compute parameters
for the gross margins distributions were then applied.
2The following is a.summary of Raiffa's judgmental fractile method.
For an example of the questionnaire used see Arcia. Similar
procedures can be found in Jackson, and Chin and Johnson.
Let fb be a value of a random variable X such that P(X < fo.b) =
f o.b. then its lowest possible value is f and its highest possible
value is fl.0 with f0.5 representing the mode of the distribution. Each
fob is called a "point b fractile" on the subjective CDF. The elicita-
tion procedure for each fractile in the distribution can proceed as
i) Find the lowest (fo.0) and the highest (f1.0) possible values
ii) Find the value of f0 such that it is equally likely for X to
fall above or below it.
iii) Find a value f0 25 such that it is equally likely for X to
fall below f0.25 or between f025 and f.5
iv) Find a value f 5 such that it is equally likely for X to fall
above f0.75 or' etween f0.5 and f0.75
Although this method permits elicitation of an arbitrarily large
number of fractiles, only five proved necessary for accurately reflecting
the farmer's information about yields and prices in Southern Huila.
That is, more values for the fractiles resulted in similar distribution
estimates when protesting the approach. Letting Yi i = 0, ..., 4 be
the judgmental fractile value, the fractiles of the distribution can be
Y + Y
X = (Yo + 1 )/2
Y. + Y. Y. + Y.
X. = ( 1 i-1 + 1 1+1)/2; i = 1, 2, 3
Y + Y
X4= (Y4 + 4 3)
In turn, the mean and variance of the distribution is computed as,
Mean = I X.P. X
Variance = I (X -X P.,
where P. is the probability associated with each fractile.
Arcia, Gustavo. "Risk, Institutional Change and Technology Adoption
for Low Income Farmers: An Analysis of New Bean Alternatives for
the Southern Huila Region of Colombia, South America," Ph.D..
dissertation, University of Missouri, Columbia, Missouri, 1980.
Arcia, Gustavo and S.R. Johnson. "Risk Aversion, Farmers' Perceptions
of Price and Yield Uncertainty, and Technology Adoption in Small
Farm Agriculture." Mimeo. University of Missouri, 1981.
Arcia, Gustavo and John H. Sanders. "Ex-Ante Analysis of New Bean
Technology in Southern Huila." CIAT, Cali, Colombia, 1980.
Binswanger, H.P. "Attitudes Towards Risk: Experimental Measurement
in Rural India." ICRISAT, Hyderabad, India, 1979.
Bohrnstedt, G.W. and A.S. Goldberger. "On the Exact Variance of
Products of Ramdom Variables," Journal of the American Statistical
Association 64 (1969):1439-1442.
Centro Internacional de Agricultura Tropical (CIAT). Bean Program
1979 Annual Report. Cali, Colombia, April 1979.
Chin, Sean and S.R. Johnson. "Assessment of Judgmental Input Forecasting
Models," mimeo, University of Missouri, Columbia, Missouri, 1979.
Dillon, J.L. and P.L. Scandizzo. "Risk Attitudes of Subsistence Farmers
in North East Brazil: A Sampling Approach." American Journal
of Agricultural Economics 60 (1978):425-435.
Hampton, J.M., P.G. Moore and H. Thomas. "Subjective Probability'and its
Measurement." Journal of the Royal Statistical Society, Series A
Hendrickson, Arlo D. and Robert J. Buehler. "Elicitation of Subjective
Probabilities by Sequential Choices." Journal of the American
Statistical Association 67 (1972):880-883.
Hogart, Robin M. "Cognitive Processes and the Assessmnt of Subjective
Probability Distribtutions." Journal of the American Statistical
Association 70 (1975):271-289.
Jackson, Barbara B. "Assessing Probability Distributions for Uncertain
Quantities." Report #9-174-193. Harvard Business School, Cambridge,
Raiffa, H. Decision Analysis. Reading, Mass.: Addison-Wesley, 1968.
Restrepo, Luis F. "Evaluaci6n Agroecon6mica de Nuevas Tecnologfas, para
la Producci6n de Frijol en la Zona Sur del Huila-Colombia." .M.S.
thesis, Universidad Nacional de Colombia, Bogotg, 1979.
Roumasset, James, Jean-Mark Boussard, Inderyit Singh, eds. Risk,
Uncertainty and Agricultural Development. New York: Agricultural
Development Council, 1978.,
Sanders, J.H. and J.K. Lynam. "Evaluation of New Technology on Farms:
Methodology and Some Results From Two Crop Programs at CIAT.".
Agricultural Systems 9(1982):97-112.
Savage, L.J. "Elicitation of Personal Probabilities and Expectations."
Journal of the American Statistical Association 66(1971):783-801.
Valdes, Alberto, Grant Scobie and John L. Dillon, eds. Economics and
the Design of Small-Farmer Technology. Ames: Iowa State University
Winkler, R.L. "Probabilistic Prediction: Some Experimental Results."
Journal of the American Statistical Association 66 (1971):675-685.
"Scoring Rules and the Evaluation of Probability Asses-
sors." Journal of the American Statistical Association 64 (1969):
"The Assessment of Prior Distributions in Bayesian
Analysis." Journal of the American Statistical Association 62
(Kg/H'a) Lno." Fertility
New Variety, BAT-47
High Cheminc;l Inputs
HiJgh Chemiical Input s
Herbicide and Arnzan
No Chemical Inputs
2152 -~ "" -"'
iNv Variety, BAT-47
I p r ov ei.! A roL ,. 1 ..-;'/
High Chei;ical Inputs
i Frmor's Sped
impi'rcove. d Agro'w,.:-'r.y
Hiif-h Chmiacail TnplLLt.
. Fr. r, ... ..; ."." --.!
; 20- cil)-2-0 C ..
.No :th. Nr C -.ir.: i i :i
Summary of cn-ffatm ban t cnon.yv t. : *i :: ,, :i LMa,
o Fig c uri 1 .
,' i -
3 535 -
--- --- --- 4c- - ------- -- -- --
Sn ri. e-':p: CIAT, iAnnuiii.l Rt)por-I., 197'.;, (; l.1 ,
ilnui~~ L~3 u JOC"
-wi ..., --
.F "'': P.O
. .... b'~.,
F. -: t y,:p:'-y
i ., 1,46
'. c Tnspar c:-nt "
.-rodc'* Transfer 31,t:.1
Maxiar;a Debt Capacity
FBgure 2. Schematic illustration of the Structure for the Risk Programming Model
' rns tit
1 ... 1
TINE SERIES AND SUBJCLVE Di RMB ONS, i' OF GROSS M VENUES
FOR SOu'THERN HUILA (n =-- 30)
Deviat i onb
Corna-eans' 35,130 44,794 2,239
casa -2 45,570 21,136 7,653
BrJown Sugar 32,113 51,590 12,024
Co fee-Planzains 53,289 36,986 9,209
Toat D.ei 124,131 157,922 24..8
. n 79,530 106,043 2
L.0 W.A. Dollar -- ,'.O ?. sM os.
Prefse only on 25 percent of he farms.
Present only on 14 percent of the farms.
Time Series Subjective
objective of of
standard Variation Variation
aviation (%) (%)
14,031 6.37 31.32
7,284 16.79 34.46
13,805 37.4a 26.76
8,851 17,28 23.93
18.035 20.03 55.74
16,51i Ai ."U 5 .753,
. . . .. .. .. ... .. .
_ ~~_~ ~~
Typical Farm Plan for a Medium Size Farm
in Southern Huila
(Hectareas) Percent of Total
Crop Total Area=15.8 Has. Gross Revenue
Low Technology Caturra
Coffee-Plantains 3.0 34.41
Sugarcane 3.0 26.42
Cassava 1.0 6.11
Beans 1.5 19.37
Corn-Beans 0.5 6.41
Pasture 6.8 7.24
"a ble 3
OQUDRATIC PROGRAMMING SOLLTIO'N I NDER TIME-SERIES '"AiIIC:, LOCAL
3EAC: TECHNOLOGY, AND ESTI:l'TTED c'::REaSs OF RISK AVERSION FOR
S>LALL F.',RMS IN S' t!HEN- HUILA
F_ rm Size, 15.8 Hectares
Crop Area (Hectare)
Low Te-chnol aogy
. .' I, ,
1 72, 191
6 = 0
1.0 U.S. Dollar = 40.0 Pesos
* ee -'3
-t :. -
- -- ----- ---' --
Quadratic Solutioi s _
T. ai ize. t 5.8 H"c=3res
Quadratic Lolutuio s Linear Solution
--0.5 --0.25 -0.05
113,227 16.(9h1 204,935 248. 70
IS as i resSs
i.:~ U~. )13:~r= 40-1 Pa" ;0
FARM PLANNING UNDER SUBJECTIVE VARi..[': C ~AT il'AN
TECHNOLOGIES AND ESTIMATED I'PE;RF:; OF :RLS
AVERSION FOR SMALL FARMS 0I
SFarm ;le, .S Hi,.:.',r- __
Quadratic S'olui ,- i. .. ...n.ution
Crop Area (Hectares)
Old Cof teec
Ag"rronomy ( CAT)
H n].c hold, Pastures,
:rnd Othc.r Acti.vi t:es
C pi Lln Borrowin
( I' .so' )
('01 ," '\
, -,' ')
:'7 0 15
. 1 .ni
SI ,' 77
1.0 lU.S. Dollar = 40.0 Pesos.
. 1 =.-0.5 0 = -0.23"
1 7 i
FARM PLANNING UNDER SUBJECTIVE V I-,i !:.'i, C.IAT BEAN
TECHNOLOGIES AND ESTIMATED DECRRES OF RISK
AVERSION FOR SMALL FARMS TIN
Farm Si.ze, 15.8 Hectare..
Quadratic So 'il: i'i.l~
Crop Area (Hectares)
and Other Activities
, = -0.5
t = -0.25
1.0 U.S. Dollar = 40.0 Pesos.
__~I______~II______ ___ __
___ I~_ ____ _______ ______
I ; I -
i, i -,rr," Solution
i = -0.05
, ) ,, 8