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 I. Introduction
 II. CIAT and new bean technolo...
 III. Decision model with price...
 Footnotes
 References
 Figures and tables






Group Title: Risk, perceptions of price and yield uncertainty, and new technology in a small farm setting
Title: Risk , perceptions of price and yield uncertainty, and new technology in a small farm setting
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Permanent Link: http://ufdc.ufl.edu/UF00075663/00001
 Material Information
Title: Risk , perceptions of price and yield uncertainty, and new technology in a small farm setting
Physical Description: 24 leaves : ; 22 cm.
Language: English
Creator: Arcia, Gustavo
Johnson, S. R
Sanders, John H
Publication Date: 1981
 Subjects
Subject: Agriculture -- Economic aspects   ( lcsh )
Agricultural innovations   ( lcsh )
Farms, Small   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographic references (leaves 23-24)
Statement of Responsibility: Gustavo Arcia, S.R. Johnson and John H. Sanders.
General Note: Typescript.
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Bibliographic ID: UF00075663
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 85773516

Table of Contents
    I. Introduction
        Page 1
    II. CIAT and new bean technology
        Page 2
        Page 3
    III. Decision model with price and yield variation
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Footnotes
        Page 21
        Page 22
    References
        Page 23
        Page 24
    Figures and tables
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
Full Text
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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*

I. INTRODUCTION

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


*" ARCIA3/A


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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

yields.

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.





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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

averse behavior.

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

adoption.


1





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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)
x

subject to:

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





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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.
J J




ARCIA3/A


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

and Johnson).

Subjective Distributions

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

agents.

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.





ARCIA3/A -8-



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 Method

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,

clearly.

For instance, tomatoes, a crop with large price fluctuations within

the season as well as high vulnerability to pest attacks, presents a





ARCIA3/A -9-



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





ARCIA3/A


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

planning models.

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


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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

crops.

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

procedures.

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

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

neutrality.

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


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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

neutrality.

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


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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


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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

perception.

One final point to be made in this section is the selection of an

appropriate simulation model. It is fairly apparent that the model


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AKCIA3/A -15-



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.


__





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, ^


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

distribution mean.

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.




AnRinA3/n M



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.


ADPT A1/A


_1 7








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.

Conclusions

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-

prise selection.

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


ARCIA3/A


-18-




ARCIA3/A -19-



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

pri.ce.




ARCIA3/A -20-



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.




ARCIA3/A -21-



FOOTNOTES

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) =
o,b o.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-
o.b
tion procedure for each fractile in the distribution can proceed as

follows:

i) Find the lowest (fo.0) and the highest (f1.0) possible values
for X.

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




ARCIA3/A


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

estimated by

Y + Y
X = (Yo + 1 )/2
2


Y. + Y. Y. + Y.
X. = ( 1 i-1 + 1 1+1)/2; i = 1, 2, 3
2 2


Y + Y
X4= (Y4 + 4 3)
2


In turn, the mean and variance of the distribution is computed as,

4
Mean = I X.P. X
i=O '


4
Variance = I (X -X P.,
i=0


where P. is the probability associated with each fractile.


-22-





ARCIA3/B


REFERENCES


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
136 (1973):21-42.

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,
Massachusetts, 1974.

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.


-23-




ARCIA3/B


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
Press, 1979.

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):
1073-1078.

"The Assessment of Prior Distributions in Bayesian
Analysis." Journal of the American Statistical Association 62
(1969):776-800.


-24-





















Yields With
(Kg/H'a) Lno." Fertility


Without a
Fertility Problem


New Variety, BAT-47
Improved Agronomy
High Cheminc;l Inputs

Farmer's Seed
Tmprov.:d Agronomy
HiJgh Chemiical Input s

Farlncr'f Sceed
inpr.)ve(! Agronomy
Herbicide and Arnzan


Farmer's Seed
Improved Agrunomy
No Chemical Inputs


Yield
Increase
(Kg/Ha)
-1105


2152 -~ "" -"'
iNv Variety, BAT-47
i40-l.020-'i0 Kg/Hia
N-P-K
I p r ov ei.! A roL ,. 1 ..-;'/
High Chei;ical Inputs

i Frmor's Sped
20-60-20 Kg/i-
I-P--K


1493


Fanner's Fields
Monocnul tur


Farmer's Fiels
Associated Croppini;


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 .
Colonmbij, .1979.


,' i -


L
(


Yield
crease
Kg/Ha)
1 257


Yields
(Kg/Hla)
1857



1752



1 '99




3 535 -


--- --- --- 4c- - ------- -- -- --


1172


Sn ri. e-':p: CIAT, iAnnuiii.l Rt)por-I., 197'.;, (; l.1 ,











ilirin


XLI';- :iflt]U2


ilnui~~ L~3 u JOC"


*--i '-q',


Labor
Sales


-wi ..., --


S' "*


.F "'': P.O


Pr ducrion


P auction






1 -


I.I' "',^46


. .... b'~.,


-Wily Labtr


Cera-inr Cp-ital
First SernesterC


F. -: t y,:p:'-y


i ., 1,46


-1


'".4


-. -


'. 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


3-


' rns tit
Transte-


max


-kI ...


I



(icr1


... (1+r,


1 ... 1


'am ly
Labor
Use


Sriln.:










Table j

TINE SERIES AND SUBJCLVE Di RMB ONS, i' OF GROSS M VENUES
FOR SOu'THERN HUILA (n =-- 30)


Time Seri-es
Gross
Revenue"
(Pesos)


Subjective
Gross
Revenue
(Pesos


MT'iae Series
Standard
Deviat i onb


Su
SD
D.


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
Coefficient Coefficient
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,
. . . .. .. .. ... .. .


.rop ,


_ ~~_~ ~~





V.


TABLE 2

Typical Farm Plan for a Medium Size Farm
in Southern Huila


Area
(Hectareas) Percent of Total
Crop Total Area=15.8 Has. Gross Revenue

Low Technology Caturra
Coffee-Plantains 3.0 34.41
and
Old Coffee

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







.I


"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


Linear Solution


_- Lem


= -0.5


(prss .s)
(P-acs)


131,054


Crop Area (Hectare)

High Technology
Coffee-Piancain

Low Te-chnol aogy
Coffee-PIrntains


0..4


) .9

".2 .


. .' I, ,
0-'*- ,:


50,000


= -0.25


167,646


1.55 :


2.1


50,000


S-0.05


1 72, 191
I/ .-.'L/


] .76


0. 13


2. 0


I .79


50,000


6 = 0


248,780


1.0 U.S. Dollar = 40.0 Pesos


* ee -'3


-t :. -


75,000


- -- ----- ---' --


Quadratic Solutioi s _


1 .3








".4













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




1.38 .


















IS as i resSs
v:

i.:~ U~. )13:~r= 40-1 Pa" ;0





4 t.


Table 5

FARM PLANNING UNDER SUBJECTIVE VARi..[': C ~AT il'AN
TECHNOLOGIES AND ESTIMATED I'PE;RF:; OF :RLS
AVERSION FOR SMALL FARMS 0I
SO'IUTHER!KN HULLA


SFarm ;le, .S Hi,.:.',r- __

Quadratic S'olui ,- i. .. ...n.ution


I term


Gross Margin
(Pa os)


Crop Area (Hectares)

Hligh Technology
Corfpee-Planta ins

Low Te'chnology
Gof fo-Pl'.antains

Old Cof teec

Sugarcane'

Beans, letter
Ag"rronomy ( CAT)

C ;ssva

H n].c hold, Pastures,
:rnd Othc.r Acti.vi t:es

.abor Sales


C pi Lln Borrowin
( I' .so' )


113,227


1 .38


0.81


13.61


169,05


('01 ," '\


, -,' ')


:'7 0 15


1.87


0.67

2.2,


. 1 .ni


SI ,' 77


1.0 lU.S. Dollar = 40.0 Pesos.


. 1 =.-0.5 0 = -0.23"


1 7 i











Table 5

FARM PLANNING UNDER SUBJECTIVE V I-,i !:.'i, C.IAT BEAN
TECHNOLOGIES AND ESTIMATED DECRRES OF RISK
AVERSION FOR SMALL FARMS TIN
SOUTHERN HULA


Farm Si.ze, 15.8 Hectare..


Quadratic So 'il: i'i.l~


I tem


Gross Margin
(Pesos)

Crop Area (Hectares)

High Technology
CouCcc-Plantains

Low Technology
Goffee-Plantains

Old Coffee

Sugarcane

Beans, Better
SAgronomy (CIAT)

C assava

Household, .Pastures,
and Other Activities

Labor Sales
(Man Days)

Capital Borrowing
(Pesos)


, = -0.5


113,227


1 .38


0.81


13.61


180



11,477


t = -0.25


169,051


1.87


0.67

2.21


2'04,5


5.-f '


11.05


168



57,260


1.0 U.S. Dollar = 40.0 Pesos.


270.015


a,
* '


'1. 5


, :.O0


__~I______~II______ ___ __


___ I~_ ____ _______ ______


I ; I -


i, i -,rr," Solution


i = -0.05


, ) ,, 8




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