World bank

Development Research Center

Discuss iun Papers

No. 17

RISK ATTITUDES OF SUBSISTENCE FARMERS I N NORTHEAST BRAZIL: A SAMPLING APPROACH

John L. D i l l o n and Pasqua le L. Scandizzo

- - '9 - - -

' r - 8 NOTE: Discuss ion Papers a r e pre l iminar , m a t e r i a l s c i r c u l a t e d - t o s t i m u l a t e

d i s c u s s i o n and c r i t i c a l comment. References i n p u b l i c a t i o n t o Discuss ion Papers should b e c l e a r e d wi th t h e au tho r ( s ) t o p r o t e c t t h e t e n t a t i v e c h a r a c t e r of t h e s e papers . The papers express t h e views of t h e au tho r and should no t b e i n t e r p r e t e d t o r e f l e c t chose of t h e World Sank.

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RISK ATTITUDES OF SUBSISTENCE FARMERS IN NORTHEAST BRAZIL: A SAMPLING APPROACH

J o h n L. D i l l o n and

PasquaZe L. Scandizzo

- John L. D i l l c m is a p r o f e s s o r i n t h e Department of A g r i c u l t u r a l Economics and Business@anagernent a t t h e U n i v e r s i t y of New England, Armidale , * - A u s t r a l i a . P a s q u a l e L. Scand izzo i s a n economist i n t h e World Bank, Washing ton .

2ISii ATTI1";DES Or" SUBSISTENCE FPSMERS IIJ iJONTilEAST 3PA ZIL : A SAMPLING APPROACH

J .L . D i l l o n and P.L. Scandizzo

Few would d i s a g r e e t h a t knowledge of p e a s a n t s ' cho ice behavior is

- i n p o r t a n t i n terms of bo th micro and macro s t r a t e g i e s f o r a g r i c u l t u r a l

devolopme-t. Doubtless f o r t h i s r ea son , t h e l a s t decade h a s wi tnessed a

v a r i e t y of r e s e a r c h and s p e c u l a t i v e commentary on peasan t s ' r eac t io r l s t o

u n c e r t a i n t y . These s t u d i e s might be c l a s s i f i e d under t h e headings o f :

( i ) economic an thropology , e.g. Johnson (1970, 1971) , L ip ton; ( i i ) econo-

m e t r i c s , e.g. D i l l o n and Anderson, Moscardi, Scandizzo, Wolgin; ( i i i ) farm

r i s k programming, e.g. Heyer, Low, Sanders and Hol landa , S c h l u t e r and Mount,

Wiens (1974); ( i v ) s e c t o r a l r i s k programming, e.g. Haze l1 and Scanclizzb

(1976) , Kutcher and Scandizzo (1976a); and (v) expected u t i l i t y ancl s a f e ty -

f i r s t t heo ry , e .g . H i e b e r t , Masson, O'Mara, Roumasset, Wharton, Wiens

A major element of nany of t h e s e s t u d i e s h a s been t h e modeling

and t e s t i n g of p a r t i c u l a r t h e o r i e s of peasant cho ice under u n c e r t a i n t y .

S t a r t i n g wi th a " reasonable" p o s i t i v e t heo ry , i t seems i t is noc d i f f i c u l t

t o f i n d 'keasonable" suppor t f o r i t through e i t h e r ~ i q d experiments o r '

L

r evea l ed choices . Peasan t s ' cho ices do appear t o be in f luenced by

u l rcer ta in ty and, i n p a r t i c u l a r , t o b e r b k a v e r s e on average. However, 4 s

t aken o v e r a l l , t h e l i t e r c t u r e a l s o g i v e s t h e impress ion t h a t any theory 0 -

E which recognizes t h e marginal impact o f 2 n c e r t a i n t y w i l l approximate . average peasant cho ice adequate ly enough. Convincing d i s c r i m i n a t i o n

b c t w c e n t h e d e s c r i p t i v e power of t h e v a r i o u s proposed t h e o r i e s ( c . g .

expected u t i l i t y , expected r e t u r n , s a f e t y - f i r s t , f ocus- los s , games a g a i n s t

n a t u r e ) w i l l r e q u i r e f a r more robus t t e s t s 3r t e s t s i t u a t i o n s than have s o

far been used. And, of course , d i f f e r e n t t h e o r i e s nay be a p p r o p r i a t e i n

d i f f e r e n t c i rcumstances over both space and t i m e .

The genesis of t h e p r e s e n t paper l a y i n t h e d e s i r e t o ob th in a

s a ~ p l e - b a s e d e s t i m a t e of t h e average v a l u e of t h e p o j x ~ l a t i o n r + s k co-

e f f i c i e n t i n t h e mean-standard d e v i a t i o n (E, a ) u t i l i t y f u n c t i o n

t o be used i n a s e c t o z a l programming a o d e l of Nor theas t B r a z i l . A s slhown

by Hazel1 and Scandizzo (1974, 1976) , t h e l i n e a r form of equa t ion (1) makes

i t extremely convenient i n s e c t o r a l modeling. Econometric a n a l y s i s b:y

Scandizzo and pa rame t r i c programming a n a l y s i s by Kutcher and Scendizz~o

(1976a) had a l r e a d y suggested an e s t i m a t e of about -1 a s t h e a p p r o p r i a t e

mean va lue . A s w e l l a s checking t h e s e e s t i m a t e s , a sampling approach I.

-

would a l s o y i e l d informa:iol? on t h e s t a t i s t i c a l d i s t r i b u t i o n of 4 a c r o s s

t he sampled popula t ion .

Our a p p r a i s a l of t h e d i s t r i b u t i o n of i s based on t h e r e s u l t s

of a sample survey of s u b s i s t e n c e farmers i n Nor theas t B r a z i l . I n making L , e

t h i s a n a l y s i s w e a l s o i n v e s t i g a t e t h e p o s s i b i l i t y t h a t poor peasan t s m y

respond d i f f e r e n t l y accord ing a s t o whether o r n o t t h e r e is u n c e r t a i n t y

abouc t h e s a t i s f a c t i o n of t h e i r s u b s i s t e n c e needs. - - *

d I n v s ing equa t ion (1) a s t h e b a s i s of our a n a l y s i s , ue mean t o

imply no more than t h a t i t may provide an adequate r e p r e s e n t a t i o n of

2 peasant r i s k behavior . Like t h e c l o s e l y r e l a t e d mean-variance ( E , a )

model, i t i s s u b j e c t t o c r i t i c i s m on both economic and psychologica l

2 Despi te t h i s t h e o r e t i c a l c r i t i c i s m , t h e u se of (E, u ) and ( E , u)

a n z l y s i s has r e c e n t l y been growing i n t h e a r e a of mathematical programming

r e l a r e d t o farm s imu la t i ons and a g r i c u l t u r a l s e c t o r m ~ d e l s a s , f o r example,

i n t h e work of Dean, H a z e l l , Haze l l and ~ c a n d i z z o (1974, 1976) , S c h l u t e r

and Mount, and Simmons and Pomreda . It seems t h a t i n most p r a c t i c a l

a p p l i c a t i o n s , t h e advantages of s p e c i f y i n g d e c i s i o n makers' cho ices

d i r e c t l y i n terms of t h e f i r s t two moments of t h e payoff d i s t r i b u t i o n

appear t o l a r g e l y outweigh t h e l o s s i n r i g o r , i f any (Samuelson).

The p l a a of t h e paper is a s fol lows. F i r s t we b r i e f l y o u t l i n e

t h e c h a r a c t e r i s t i c s of t h e sample and t h e i n t e rv i ewing procedure adoptled.

Xext w e p r e s e n t t h e r e s u l t s of t h e i n t e rv i ews and o u t l i n e two a l t e r n a t i v e

models of a n a l y s i s which a r z then used t o a p p r a i s e t h e ~ e a s a n t s ' r i s k

a t t i t u d e s .

SunpZe C"rzaracteristics and I,!teruiew Procedure

Our d a t a a r e based on two random samples r e s p e c t i v e l y c o n s i s t i n g

of 66 smal l farm owners and of 64 sharecroppers i n Canind6, a smal l county

l o c a t e d i n t he i n t e r i o r of t h e S t a t e of CearA i n Nor theas t B r a z i l . The

o v e r a l l group of 130 sma l l farmers c o n s t i t u t e d a pane l who were be ing

surveyed f o r t h e t h i r d yea r a s p a r t of a brcsder r e s e a r c h e x e r c i s e on

sma l l fa rmers i n v a r i o u s B r a z i l i a n r eg ions . I n t e rv i ews i n each yea r were

l a r g e l y conducted by t h e same group OF f i v e young female r e s e a r c h a s s i s -

t a n t s from the Un ive r s i t y of ~ e a r i ' s Department of A g r i c u l t u r a l Economics

(o f which they were a l s o g radua t e s ) . Recause of t h e i r l o c a l backgrounld,

c h a r m , i n t e l l i g e n c e and three- t ime c o n t a c t , t h e r e i s no doubt t h a t t h e s e

i n t e r v i e w e r s had e x c e l l e n t r appor t w i th t h e survey pane l and were ab1.e t o

nake good judgements about t h e thought fu lness and c r e d i b i l i t y of t h e

fa rmers ' respcnses .

The Canind6 a r t 3 5 . t y p i c a l of t h e S e r t a o , t h e semi- arid sub- -

r eg ion of Nor theas t B r a z i l . A g r i c u l t u r e i n t h e s e backlands Is very

p r i m i t i v e and of t h e slash-and-burn type w i t h hand hoes and p l a n t i n g s t i c k s .

There i s l i t t l e u s e of mechanizat ion, f e r t i l i z e r o r improved seeds . Food I

I I s h o r t a g e s , unemployment and m a l n u t r i t i o n a r e ch ron ic among t h e 30 m i l l i o n

i popu la t i on ; and because of extreme r a i n f a l l v a r i a b i l i t y l e a d i n g t o bo th

s e v e r e droughts and f l o o d s , a g r i c u l t u r e i n t h e SertZio i s a l s o exceedingly

r i s k y . For Canind6, Hargreaves r eco rds an average y e a r l y r a i n f a l l of 745

mm w i t h a 43 pe rcen t chance of r e c e i v i n g more than t h e average and w i t h 67

pe rcen t of t h e r a i n concent ra ted i n fou r months. The t y p i c a l p roduct ion

system i n t h e r eg ion invo lves t r e e c o t t o n a s a cash c r o p , corn and beans

grown toge the r f o r s u b s i s t e n c e u s e , and beef c a t t l e (Kutcher and Scandizzo,

1976b). Small ownars o r sharecroppers a r e t y p i c a l l y involved i n c rop

product ion w h i l e l a r g e l a n d l o r d s a r e mainly concerned wi th c a t t l e . A s

documented by Brcoks and Johnson (1970, 1911), f o r bo th sma l l owners and

sha rec roppe r s - though no t f o r l a r g e l and lo rds - y e a r t o yea r s u b s i s t e n c e a

i s extremely r i s k y and can have ca lami tous i m p l i c a t i o n s .

T a b l e 1 lists the sample means of v a r i o u s socio-economic

- - v a r i a b l e s . The d a t a r e f e r t o t h e farming yea r 1972-73 which-was average !c .. .

t o moderately good f o r a g r i c u l t u r a l p r o d u c t i c ; ~ and employment i n t h e (survey

r eg ion . A s t h e d a t a show, t he two samples a r e broadly s i m i l a r i n t h e i r

c h a r a c t e r i s t i c s , b u t the sharecroppers a r e s i g n i f i c a n t l y poorer , l e s s

C C

educated and younger than the srrall owners. I n a b s o l u t e t e r n s , wi th annual

per caput mean incomes of only $153 f o r owne-s and $90 f o r sharecroppers ,

t he f a m i l i e s of both groups a r e extremely poor on an i n t e r n a t i o n a l basir;. I

The 1975 survey of t he Cznind6 panel involved a n ex tens ive s e t

of socio-economic ques t ions t o which we were a b l e t o append a smal l s e t of

ques t ions regard ing s u b j e c t i v e p r o b a b i l i t i e s , e t h i c a l a t t i t u d e s t o

gambling, the use of omens, and r i s k preferences .

The r e s u l t s of t h e a n a l y s i s of t h e farmers ' s u b j e c t i v e probab:Llity

judgements, a t t i t u d e s t o gambling and use of omens have been repor ted by

Campos Mesquita and Di l lon . Af t e r some probing by t h e in t e rv iewers bo th

t h e sma l l owners and sharecroppers appeared t o be a b l e t o nominate y i e l d

p r o b a b i l i t i e s a s chances out of t e c implying on average , s i m i l a r l y behaved

s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n s f o r t h e y i e l d of beans, t h e i r main

subs i s t ence crop. These d i s t r i b u t i o n s were t y p i c a l l y l e s s concent ra ted

around t h e mean than a normal d i s t r i b u t i o n and p o s i t i v e l y s l a ~ c $ . A t t i -

tudes t o gambling and t h e use of omens were i n v e s t i g a t e d by zsk!.ng "he

s u b j e c t s n sma l l s e t of ques t ions concerning t h e i r opin ions on gambling,,

t h e i r p a r t i c i p z t i o n i n a c t u a l gambles and l o t t e r i e s , and t h e i r use of 1

n a t u r a l s i g n s and o t h e r omens i n farm dec i s ions . Responses ind ica t ed

l i t t l e differcnce=between srcall owners and sharecroppers . Some 30 percent '3

regarded gnmbling'as immoral; 80 percent had never en te red a b e t o r - - *

l o t t e r y ; and 40 e r c e n t s p e c i f i e d s i g n s (of which a t h i r d were o c c u l t ) I I -

in f l i ienc ing t h e i r p l a n t i n g dec i s ions .

Another group

a t t i t u d e s a s implied by

of ques t ions appra ised the fa rmers ' r i sk- bear ing

t h e i r choices between h y p o t h e t i c a l but r e a l i s t i c

T a b l e 1: Sone Socio-econonic C h a r a c t e r i s t i c s of Small Farmers

i n ~311ind<, ::orrheast B r a z i l , 1972-73

Vari ;,I11 c Srizill Owne~s Sharecroppers

Sanplc s i z e

P r o p o r t i o n i n r e g i o n

Av. age of f ami ly head

Av. s i z e of t~ouseho ld

Av. years of e d u c a t i o n of f ami ly head

propor t i b n of l i t e r a t e s

P r o p o r t i o n of imn ig ran t s

Av. cons \mpt ion of home-grown food (Cr $1 1,233

Av. n e t farm incone of household (Cr$ 1 4,810

Av. n e t t o t a l income of household (Cr $1 5,579

-' 8 r

Sources and no te s : Campos Mesquita and D i l l o n , Kutcher and Scandizzo .*

(1976G, P a t r i c k and F i l h o . $1 = ~ r $ 6 f 4 . - I -

JI? w

farm a l t e r n a t i v e s . These ques t ions f o r n t h e b a s i s of t h e empi r i ca l a n a l y s i s

i n t h i s paper and were geared t o f i n d i n g t h e c e r t a i n t y equ iva l en t s of r l s k y

p rospec t s i nvo lv ing known p r o b a b i l i t i e s .

Two types - of r i s k y p rospec t s were used, y i e l d i n g two s u b s e t s of

responses f o r each group of farmers. The f i r s t t ype involved only payoffs

above honsehold s u b s i s t e n c e requirercents. I n t h e s e , w h i l e t h e l e v e l (of I I I t o t a l income was a t r i s k , s u b s i s t e n c e was assured . The second type a f

r i s k y prospec t included the p o s s i b i l i t y of ea rn ing l e s s i n some y e a r s than

t h e amount of money necessary t o purchase t h e food d i r e c t l y produced and

consumed i n t h e farm ( taken a s a proxy f o r s u b s i s t e n c e ) , i . e . , i n t h e s e

ques t ions s u b s i s t e n c e was a t r i s k ,

Each r i s k y prospec t involved only two p o s s i b l e outcomes whose

p r c b a b i l i t i e s were provided a s f r equenc ie s and were maintained cons t an t

a t 0.75 ( '$3 yea r s o u t of 4") f o r t h e b e s t outcome and 0.25 ("1 yea r ou t of

4") f o r t h e wors t outcome. The payoff of t h e b e s t outcome i n t h e rislcy

p rospec t and/or of i t s a l t e r n a t i v e s u r e prospec t was p r o g r e s s i v e l y changed

u n t i l t h e s u b j e c t expressed i n d i f f e r e n c e between t h e r i s k y prospec t arrd

t h e s u r e prospec t - a t which p o i n t t h e s u r e prospec t . 1 . I

L

The v e r b a l formula t ion of t h c r i s k y p rospec t s involved not only -

p r o v i s i o n of t h e p r o b a b i l i t i e s a s de focto f r equenc ie s , bu t a@o r e f e r e n c e L

t o n definite-frame of t ime. We chose t o r e f e r t h e f r e q u e n c y ~ o f o u r

m d y e a r s because, t h i s was judged t h e minimum amount of time r equ i r ed t o make

t h e prospec t r e a l i s t i c t o t h e s u b j e c t . A s i n d i c a e d by p i l o t d i s c u s s i o n

with some of t h e farmers and a s confirmed by t h e i r answers t o the d i r e c t

q u e s t i o n s on y i e l d and s e a s o n a l p r o s p e c t s , t h e formal concept of

p r o b a b i l i t y per se is q u i t e a l i e n t o t h e way of r e a s o n i n g of t h e s m a l l

f a r m e r s i n t e r v i e v e d . 2 Thus, i t i s impor tan t t h a t t h e r i s k y p r o s p e c t s

p r e s e n t e d c l e a r l y c o n t a i n . n o t o n l y a g e n e r a l e lement of u n c e - i t a i n t y ( i . e . ,

t h e r e i s no g u a r a n t e e t h a t even t h e expec ted v a l u e of t h e p r o s p e c t is

a c h i e v e d o v e r a s m a l l i n t e r v a l of t i m e ) , b u t a l s o " d i s t r i b u t i o n a l " r i s k s

( i . e . , t h e p ~ s s i b i l i t y t h a t p a r t i c u l a r l y unlucky sequences o f bad y e a r s may

m a t e r i a l i z e ) . A s f o r t h e unequa l p r o b a b f l i t i e s used , we h y p o t h e s i z e t h a t

s m a l l f a r m e r s d i s p l a y an i n t u i t i v e r e a c t i o n t o summary s t a t i s t i c s of t h e

d i s t r i b u t i o n embedded i n a s i m p l e riskj p r o s p e c t , rather t h a n p o s s e s s i n g

any n a t u r a l m a s t e r i n g of t h e p r o b a b i l i t y c a l c u l u s .

The r e s u l t s f o r s u b s i s t e n c e a s s u r e d and s u b s i s t e n c e a t r i s k a r e

r e s p e c t i v e l y p r e s e n t e d i n T a b l e s 2 and 3 below. To f u l l y u n d e r s t a n d t h e s e

match ings of t h e r i s k y p r o s p e c t s w i t h t h e i r c e r t a i n t y e q u i v a l e n t s , two

f u r t h e r comments a r e needed. F i r s t , when a s w i t c h r a t h e r thal? i n d i f f e r e n c e

was e s t a b l i s h e d between t h e s u r e and r i s k y p r o s p e c t s , i t i s assumed f o r

s u b s e q u e n t a n a l y s i s t h a t i n d i f f e r e n c e p r e v a i l s a t t h e n i d p o i n t of t h z

i n c r e m e n t a l change, Seconc, d u e t o i n a d v e r t e n c e a r i s i n g from l a c k of p r i o r

knowledge, t h e sequence of q u e s t i o n s was r e g r e t t a b l y t e r m i n a t e d f o r some

s u b j e c t k b e f o r e r e a c h i n g c e r t a i n t y e q u i v a l e n c e . For t h e s u b s i s t e n c e -

a s su red s i t u a t i o n , most o f t h e s e s u b j e c t s were e x t r e m e l y r i s k a v e r s e and

only a few ex t remely r i s k p r e f e r r i n g .

- r b ~ , i r i s u b - i ' ~ . s ~ Z t s and Ab te rw t i ve lduf?eb:; cf AnaZysis

Although t h e d a t a of T a b l e s 2 and 3 cannot be compared w i t h o u t

r e c o u r s e t o a f o r n a l model, a few p r e l i m i n a r y remarks a r e i n o r d e r .

0

0 0 l-i

ur-t*O\ r) - L ? c r \ l-i

. - - c

CJ X 3 0 0 0 w u a 4 4-1 a + 0. (It'd U a h P 0 (d U rO L'

l-i rd U

s

n n n N N N \ \ \ CA rn cn W W W

m m m N N N

0 0 0

u] -A

0 0 0 0 0 0 0 0 0 4 E 0 . 0 m o o a rn r n r l d N h l U . ra + 2 & $ & c n E-c 0 3

n n n 0 0 0 0 0 0 0 0 0 m m a + + $- C A W ~ w u w

F i r s t , t h e r e s u l t s i n d i c a t e an obvious q u a l i t a t i v e d i f f e r e n c e

between t h e s u b s i s t e n c e assured (S.A.) and t h e s u b s i s t e n c e a t r i s :k (S.R.)

cases . No owner and only a minimum number of sharecroppers disp1,ayed any

r i s k p re fe rence wheri subs i s t ence was a t r i s k , wh i l e a s i g n i f i c a n t number

of s u b j e c t s of both c a t e g o r i e s eppeared t o be eager t o t a k e r i s k s i n t h e

S .A. case.3 S ta t ed another way, i n spec t ion shows t h e S.A. r e s u l t s of

Table 2 t o be gene ra l ly compatible wi th a unidimensional u t i l i t y func t ion

having t h e money va lue cr <S + cash) a s crgument and d i s p l a y i n g ( e i the r

r i s k ave r s ion o r r i s k preference . I n c o n t r a s t , t h e S.R. r e s u l t s of Table

3 obviously tend t o imply a t~a-dimensional u t i l i t y func t ion w i t h S and

cash a s d i s t i n c . arguments, t h e func t ion being of e i t h e r s a f e t y- f i r s t o r

lex icographic form wi th S a s t h e dimension of prime concern.

Seconi , t he s m p l l owners appear on t h e whole t o b e more conserva-

t i v e than t h e sharecroppers , e s p e c i a l l y i f s u b s i s t e n c e i s a t r i s k . Although

i t i s obviously inlpossible t o draw any gene ra l conclus ion , t h i s r e s u l t does

sugges t , inter a l i a , t h a t sharecroppers f e e l more secu re a t cons iderably

lower l e v e l s of inco~ue than do smal l owners. This behavior would be

c o n s i s t e n t wi th t h e Friedman-Savage model, according t o which r i sk - t ak ing r e

0

behavior predominates above and r i sk-zvers ion beiow "ncrmal" income l e v e l s .

For t h e two groups considered an a l t s r n n t i v e exp lana t ion i s t h a t share-

.# c r ~ . ~ ~ c r s can s h a r e t h e i r r i s k s wi th ' t he landlord both through t h e formal - *

sha re arrangements and through t h e *formal but t r a d i t i o n a l patrorlal w

( f e u d a l ) r e l a t i o n between t h e landlord and h i s sharecroppers a s descr ibed

by Johnson (1970) .

Thi rd , f o r bo th t enu re types , a r e l a t i v e l y s t a b l e group of

extreme r i s k a v e r t e r s (ERAS) was s i n g l e d out by t h e ques t ions . Unlike t h e

r e s t of t he , ~ ? ! e c t s , who f r e e l y switched from a r i s k a v e r s e a t t i t u d e i n

. t h e S.R. ca se c s 1 r i s k n e u t r a l o r r i s k p r e f e r r i n g a t t i t u d e i n t h e S . A .

c a s e , most of t h e ERAS expressed a cons tan t r e l u c t a n c e t o bea r r i s k regard-

l e s s of t h e s u b s i s t e n c e v a r i a b l e .

Pas s ing now t o a more formal a n a l y s i s of t h e r e s u l t s , w e cons ider

t h e imp l i ca t ions of t h e s tandard (E, a ) model and of a s a f e t y- f i r s t

v a r i a n t of t h i s model.

Assuming t h a t t h e under ly ing u t i l i t y f u n c t i o n is l o c a l l y l i n e a r

i n t h e expected va lue and t h e s t anda rd d e v i a t i o n of t h e payoff , we can use

equat ion (1) t o w r i t e t he equat ion:

where E and a r e s p e c t i v e l y r ep re sen t t he mean and s t anda rd d e v i a t i o n of

t h e r i s k y prospec t and C.E. is i ts e l i c i t e d c e r t a i n t y equ iva l en t .

Equation (2) can be so lved f o r each respondent t o y i e l d e s t ima te s of h i s

c o e f f i c i e n t of r i s k p re fe rence .+. These e s t i m a t e s w i l l b e denoted + 1 , e

f o r t h e S.A. c a s e and +2 f o r t h e S.R. case. While i s a func t ion of

only the cash payoff l e v e l , (i i s a l s o a func t ion of t h e i n d i A d u a 1 ' I L

f a rmer ' s s u b s i s t e n c e l e v e l S as measured i n t h e socio-economic kurvey and - *

valued a t ioark+ p r i c e s . * - The two sets o r observa t ions can a l s o be combined by making use

of t he s a f e t y - f i r s t framework suggested by Baumol. I n t h i s c a s e we

hypothesize that. t h e s u b j e c t s respond accord ing t o a u t i l i t y func t ion

having a s arguments t h e expected va lue E of t he payoff and t h e o n e- t a i l

confidence i n t e r v a l E - Ku. Assuming l i n e a r i t y , we can w r i t e :

where t h e equat ion i s supposed t o hold, f o r t h e same $ and K , f o r both

t h e S . A . ( i = 1 ) and S.R. ( i = 2) prospects . We w i l l r e f e r t o t h e model

of equat ion (3) a s t h e ($, K) ~ o d e l .

Solving equat ion (3) f o r JI and K y i e l d s , a f t e r some s i m p l i f i -

c a t ion :

wherc R i ( i = 1.2) i s t h e c o e f f i c i e n t ~f v a r i a t i o n of t h e i - t h r i s k y

prospect . r

From equat ion (3) we have

(6) a u / a ~ = -ILK - w

Hence r i s k ave r s ion p r e v a i l s when both $ and K a r e of t h e same qign;

r i s k n e u t r a l i t y !f $ or K a r e zero ; and r i s k p re fe rence if $ and K

a r e of d i f f e r e n t s ign . The c o e f f i c i e n t i s somewhat analogous t o

., - :- -;ire of r i s k p r e f e r e n c e s i r , ce , from equa t ion ( 3 ) , ~ u / ~ ( K u ) = -I)

-. - .'. < - 1 > - 1 - -- = E ( X ) -t ; 0 f o r K < Ri and I) 7 0 f o r K > R

/ i The para-

_ _ _ , .. - %., - :n t h e o t h e r hand, measures another dimension of r i s k p re fe r ence

s z r 2 -Lt *--eccly r e l a t e s t o t h e p r o b a b i l i t y l e v e l r equ i r ed by t h e s a f e ty- -

' - - - -I- - m - n t nes t ed i n tfie u t i l i t y func t ion . I n f a c t , by Tchebychev's

K C ~ ~ & Z , 2e cbn e s t i m a t e t h e upper bound o~ t h e s a f e t y - f i r s t p r o b a b i l i t y

zs shown by equa t ion (6) , by i n c o r p o r a t i n g Baumol's c r i t e r i o n w e - 4 =I-,-== e f f e c t a decomposition of t h e degree of r i s k p r e f e r e n c e i n t o

: ~ = - - ~ Z % z a t i v e components: a s t anda rd d e v i a t i o n p r e f e r e n c e component

s - 1 - i ~ - = 3 r i t y o r s a f e t y- f i r s t component K. This i s a l s o appa ren t i f

e7-2 -.-- -. equa t ion (3) by a p o s i t i v e l i n e a r t r ans fo rma t ion t o a form

a%n-s-ms tc e q u a t i o n (2) , v i z . :

. I '-- - 1 . BT*; 1. - 1 + I ) K ] and U" (C.E.) denote t h e transformed repres -

i f Q and U(C. E. ) r e s p e c t i v e l y . - - 2 - - . _ _ - I I.- - m

--4Y..--c ~ 3 f the R i s k Attitude Estimates - - * I

. 25-ren t h e s e two s imple models of a n a l y s i s , w e cons ide r now t h e

T t -=;--< - - - -=wing from t h e i r a p p l i c a t i o n . 4

I-. 0

< m

'I'he ( E , 0 ) Model

The l e f t s i d e of Table 4 summarizes t h e r e s u l t s from t h e (El a )

model f o r t h e c a s e w i t h s u b s i s t e n c e no t a t r i s k , r e p o r t i n g i n t e r v a l s of

e s t i m a t i o n f o r and t h e corresponding f r equenc i e s f o r owners.

11s a l r e a d y appa ren t from Table 2 , owners and sha rec roppe r s appear t o r e a c t

d i f f e r e n t l y , on average , t o s i m i l a r r i s k y p rospec t s . A s t h e socio-economic

c l i a r a c t e r i s t i c s of t h e two groups a l s o d i f f e r a able 1 ) , however, a s imp le i

comparison of t h e means of $ does n o t s u f f i c e t o e s t a b l i s h t h a t e i t h e r

group tends t o b e more r i s k a v e r s e than t h e o t h e r . The q u e s t i o n was then L

addressed by performing a m u l t i v a r i a t e l i n e a r d i s c r i m i n a n t ana..ysis5 on t h e

two groups cons ide r ing both t h e v a l u e s of and some of t h e most

important socio-economic and a t t i t u d i n a l v a r i a b l e s cons idered i n t h e survey.

Some of t h e r e s u l t s of t h i s a n a l y s i s a r e r e p o r t e d i n Table 5.

Table 5: Discr iminant Analys i s of Owners versus , Sharecroppers

Standardized

Var i ab l e Discrim. Funct . F t e s t

C o e f f i c i e n t s For I n c l u s i o n

1 *

Age

1975 A g r i c u l t u r a l Income

1974 T o t a l Income - Value of home grown food 3. % 5.229

E Family S i z e I

-3.2 0.425 Rel ief t h a t b e t t i n g i s

immoral 0.251 1.4413

78% of known c a s e s c o r r e c t l y c l a s s i f i e d

x 2 = 13.291.

17.

A s T a l l e 5 shows, when a sirr~ltavieous comparison of t h e charac-

t e r i s t i c s of t h e two groups is made, sharecroppers appear t o be s i g n i f i -

c a n t l y poorer ( a t l e a s t i n terms of t h e home grown food v a r i a b l e ) and

younger t han t h e owners but no t s ign i f i can tzy l e s s ave r se t o r i s k . Also,

a s p l o t t i n g of t h e f r equenc ie s shows, t h e d i s t r i b u t i o n s of t h e es t im3ted

+l's f o r t h e two groups appear t o be normal except f o r t h e i r l e f t- hand

t a i l s corresponding t o t h e extreme r i s k a v e r t e r s . To t e s t t h i s hypo th~es i s

of no rma l i ty , we combined t h e two groups of non-ERA obse rva t ions and f i t t e d

a normal curve. The r e s u l t of t h i s e x e r c i s e was indeed p o s i t i v e . A normal

d i s t r i b u t i o n wi th a mean of zero and a va r i ance of 0.21 f i t s t h e non-E:RA

obse rva t ions very wel l . (Pearson goodness of f i t t e s t is s i g n i f i c a n t a t

t h e .001 l e v e l . )

The i n t e r p r e ~ z t i o n t h a t sugges t s i t s e l f , a t t h i s p o i n t , i s t h a t

two subpopula t ions appear t o u n d e r l i e t h e r i s k p re fe rence d i s t r i b u t i o n and

t h a t they appear t o c u t a c r o s s t h e a pr ior i owner- sharecropper t e n u r e

d i s t i n c t i o n . The f i r s t subpopulat ion, which we may c a l l t h e r i s k n e u t r a l

fa rmers , appears t o account f o r t h e major i ty of t h e s u b j e c t s (about 701

pe rcen t of t h e t o t a l ) and d i s p l a y s n i c e l y normal d i s t r i b u t i o n behavior

a . * around t h e p e r f e c t r i s k- n e u t r a l i t y po in t ( = 0 The second subpopula-

t i o n , i n c o n t r a s t , is composed of those s u b j e c t s s t r o n g l y ave r se t o r i s k - - C (IS1 < - 1 .25 ) . A s w e were a b l e t o e s t ima te only a lower bound of '3

m

= -1.73 f o r most 6f t h e s e s u b j e c t s based on a C.E. equal t o t n e worst lly

I.

S.A. payoff , we do n6 t have s u f f i c i e n t information t o say anyth ing on

t h e i r d i s t r i b u t i o n , except t h a t i t appears t o be much more

l e p t o k u r t i c than the normal.

Binodal ' ty and b r a c h i - v e r s u s l e p t o k u r t i c c h a r a c t e r i s t i c s o f

o p p o s i t e segments of a d i s t r i b u t i o n a r e c h a r a c t e r s q u i t e f r e q u e n t i n

p o p u l a t i o n s i n t r a n s i t i o n under n a t u r a l s e l e c t i o n s t r e s s (Huxley) . We

might s p e c u l a t e t h a t such a stress is m i g r a t i o n o r , a s i n n a t u r a l

s e l e c t i o n , t h e i n c r e a s i n g h a r d s h i p imposed by p o p u l a t i o n growth i n a

r e s o u r c e- s c a r c e c l i m a t i c a l l y- u n s u r e environment . The s t r u c t u r e of t h e

p o p u l a t i o n , o r i g i n a l l y based on r i s k n e u t r a l i t y , i s p e r h a p s b e i n g skewed

i n f a v o r of t h e r i s k a v e r t e r s s i n c e t h e y a r e t h e more l i k e l y t o s u r v i v e

and e k e o u t a n e x i s t e n c e i n t h e f a c e of t h e i n c r e a s i n g a t t r a c t i o n of t h e

u rban s e c t o r .

P e r h a p s a n i d e a of t h e c h a r a c t e r i s t i c s of t h e $ d i s t r i b u t i o n

of t h e ERA g roup o r of t h e f u t u r e o v e r a l l d i s t r i b u t i o n o f r i s k p r e f e r e n c e s

oE s m a l l f a r m e r s i n t h e Ser t i lo c a n b e g i v e n by t h e e s t i m a t e s of $ f o r

6 t h e c a s e of s u b s i s t e n c e a t r i s k , i .e . , $2. The r e s u l t s of t h i s

a n a l y s i s , r e p o r t e d i n t h e r i g h t s i d e o f T a b l e 4 , show v e r y skewed, unimodal

d i s t r i b u t i o n s c e n t e r e d around - 1.2 f o r small owners and - 0.9 f o r s h a r e-

c r o p p e r s . I t is i n t e r e s t i n g t o n o t i c e how v e r y c l o s e t h e s e mean e s t i m a t e s

are t o t h e v a l u e s of -1 s e l e c t e d by p a r a m e t r i c i t e r a t i o n by H a z e l 1 and C

Scand izzo (1976) and Kutcher and Scand izzo (1976a) f o r u s e i n t h e i r r i s k -

o r i e n t e d n g r i c u l t u r o l s e c t o r models , and t o t h e v a l u e s e s t i m a t e d by

econometric methods by Mnscardi and Scand izzo .

- An a l t e r n a t i v e e x p l a n a t i o n of t h e aon-normal s h a p e s of t h e $

C 1

and d i s t r i b u t i o n s might l i e i n t h e i n f l u e n c e o f o t h e r p o p u l a t i o n

v a r i a b l e s g i v i n g r i s e t o v a r i a t i o n s i n r i s k p r e f e r e n c e between i n d i v i d u a l

s u b j e c t s . To t h i s end, u s i n g r e g r e s s i o n z n a l y s i s , we c o n s i d e r e d a s

p o t e n t l o t explana tory v a r i a b l e s t h e same v a r i a b l e s used i n t h e d i s c r i m i n a n t

f u n c t i o n a n a l y s i s . These e f f o r t s were unsuccess fu l .

The ( 9 , K ) Model

-

Consider now t h e r e s u l t s of combining our S.A. and S.R. obser'va-

t i o n s u s ing t h e framewcrk developed i n equa t ions (3) t o (8) . Based on

equa t ions (4) and ( 5 ) , Tables 6 and 7 r ~ s p e c t i v e l y r e p o r t t h e d i s t r i b u t i o n s

of 9 and K by i n t e r v a l s of estinate. I n bo th c a s e s we f i n d ve ry f l a t

d i s t r i b u t i o n s a lmos t of t h e uniform type. The estimates of $ < -1

( c o n s t i t u t i n g 35 pe rcen t of t h o s e f o r sma l l owners and 39 p e r c e n t of t hose

f o r sha rec roppe r s ) do n o t appear t o b e s e n s i b l e s i n c e they imply a ~ / a E < 0. 7

ilowever, t h e d i s t r i b u t i o n of t h e e s t ima ted K ' s does appear t o be bounded by

r ea sonab le v a l u e s and is p a r t i c u l a r l y i n t e r e s t i n g a s i t i m p l i e s q u i t e

p l a u s i b l e v a l u e s f o r t h e p rob t ib i l i t y l e v e l of t h e s a f e t y - f i r s t element.

Based oc equa t ion ( 7 ) , which i s t h e most conse rva t ive form of ~ c h e b ~ c h e v ' s

i n e q u a l i t y , t h e ave rage upper bound on t h e s a f e t y - f i r s t p r o b a b i l i t y l e v e l

is 32 pe rcen t f o r s m a l l w n e r s and a more conse rva t ive 16 pe rcen t f o r

sharecroppers . I f t h e payof f s were symmetric, t h e s t r o n g e r form of

2 Tchebychev's i n q u a l i t y w i t h a p r o b q b i l i t y l i m i t of 1 / 2 ~ imp l i e s ha lv ing t

t he se upper bounds. The 2 a t a t h e r e f o r e sugges t t o u s t h a t , f o r Northea~st

Llrazi l , r ea sonab le e s t i m a t e s of an average s a f e t y - f i r s t p r o b a b i l i t y l e v e l - '2 - -- LA"

a g d i s t i n c t from an upper bound - l i e i n t h e ranges of from 1 2 t o 24 ~c!r- *

c s t f o r smal l owners and 6 t o 12 pe rcen t f o r sha rec roppe r s . E I

Using ave rage va lues of $ and K (wi th I$ cons t r a ined t o > - IL - s o as t o n e e t t h e r e q u i r m e n t of a p o s i t i v e l i n e a r t r ans fo rma t ion ) , we can

a l s o c a l c u l a t e an e s t i m a t e of t h e m a n r i sk- pre fe rence parameter +' of

Table 6 : Prequency Distribution of $

T ~ i b l c 7: Frequency 1 ) i s t l - i i i u t i on of K and I Z S S O C ~ S C C ~ Values

of thz Safety-First Prcb25ility Linit

--- - ti ProSaLi li ty L i l c i t (TI,) A1 1 All

I n tc'rv:11 ( f rorn Tchsbycl~~~v's I n e q u a l i ty) rXmcrs Sharecroppers P -- --- -

Variance of K 6.05 11.70

Variance of PL 0.04 0.008

equat ion (8). This y i e l d s va lues of -0.66 f o r smal l owners and -0.27 f o r

sharecroppers . These e s t i m a t e s a r e n o t too d i f f e r e n t from those f o r $ 1

of Table 4 and again i n d i c a t e a g r e a t e r degree of r i s k ave r s ion mong

small owners than among sharecroppers . -

Using r eg res s ion a n a l y s i s wi th t h e same s e t of p o t e n t i a l explana-

t o r y v a r i a b l e s a s t r i e d wi th $ and , w e a l s o at tempted t o exp la in 1

v a r i a t i o n i n + and K. Though marginal ly more s u c c e s s f u l , no s t r o n g

r e s u l t s were obtained.

Conc Zttsions

The r e s u l t s t h a t we have repor ted concern r e sea rch condulcted i n

t h e f i e l d , i n very l i t t l e t ime, and a s a n addendum t o a l a r g e r socio-

economic r e sea rch p r o j e c t concerned wi th small farmers i n B r a z i l . Because

of t h e c o n s t r a i n t s t h a t t ime, l o g i s t i c s and human f a c t o r s imposed, our

approach was n e c e s s a r i l y pragmatic. By n e c e s s i t y w e had t o d ispense wi th

most of t he s o p h i s t i c a t i o n s t h a t u t i l i t y measurers have developed s i n c e

von Neumann and Morgenstern f i r s t presented t h e expected u t i l i t y model.

I n consequence, we cannot b e s u r e t h a t b i a s e s due t o p r o b a b i l i t y prefer-

ences and ave r s ion o r love f o r gam5liffg may no t have d i s t o r t e d our

empir ica l a n n l y s i s . - - Nonetheless , t h e pragmatic ipproach d id have, we f e e l , t h e ?

Ir

advantage of p e r m i t t i - g the c o l l e c t i o n of a s i z e a b l e sample of worthwh&Le P I -

observa t ions on peasants ' r i s k preferences . Though t h e ques t ions we used

were n e c e s s a r i l y h y p o t h e t i c a l , they were geared t o ob ta in ing farmers '

responses i n t h e context of r e l a t i v e l y r e a l i s t i c s i t u a t i o n s and were no t

confined t o t h e game-type francwork t y p i c a l ~ f most o t h e r s t u d i e s of r i s k

p re fe r ence .

The e s t i m a t e s ob ta ined s t r i k e us a s q u i t e r ea sonab le and appea l i cg

b o t h t o common sense and t o our d i r e c t pe rcep t ion of t h e behavior and

mo t iva t ion of sma l l farmers i n t h e semi- arid B r a z i l i a n Nor theas t . Although

some of t l e va lues of t h e r i s k p re fe r ence parameter Q, f o r t h e r i s k y

p rospec t s w i t h s u b s i s t e n c e a s su red run coun te r t o t h e conventional. wisdom

t h a t a l l peasan t s a r e r a t h e r r i s k ave r se , t h e i r d i s t r i b u t i o n s u g g e s t s t h a t

t h e conven t iona l wisdom v a l u e s do c h a r a c t e r i z e one of t h e modes of t h e d

popula t ion . For t h e c a s e w i t h s u b s i s t e n c e a t r i s k , on t h e o t h e r hand, t h e -, c'

va lues e s t ima ted f o r h g e n e r a l l y i n d i c a t e r i s k a v e r s i o n and t h e i r means

c l o s e l y match those es t imated by both econometr ic and mathematical program-

ming techniques f o r peasant fa rmers i n B r a z i l and f o r Mexico. F u r t h e r ,

w i t h bo th s u b s i s t e n c e a s su red and s u b s i s t e n c e a t r i s k , small owners were

g e n e r a l l y more r i s k a v e r s e t han sha rec roppe r s - probably due t o the r i s k -

s h a r i n g a s p e c t s of t h e t r a d i t i o n a l f e u d a l r e l a t i o n betwten landlord? and

sha rec roppe r s i n t h e r eg ion (Johnson, 1970). - Regre t t ab ly , w e were unable w i t h e i t h e r sma l l owners o r share-

f L

croppers t o f i n d any adequate exp lana t ion f o r t h e v a r i a n c e of r i s k .

a t t i t i l d e s a c r o s s t h e sample i n terms of t h e set of p o t e n t i a l explana tory

socio-economic v a r i a b l e s t h a t we i n v e s t i g a t e d . - w The o v e r a l l p i c t u r e provided by our d a t a appears t o v a l i d a t e t h e

q u a l i t a t i v e hypotheses advanced f o r r i s k p r e f e r e n c e s of s u b s i s t e n c e

fa rmers (e.g. Johnson, 1971) and, i n p a r t i c u l a r , t h e hypo thes i s t h a t they

a r e l i k e l y t o fo l l ow sane t y p e of s a f e t y - f i r s t approach whenever t h e

s a t i s f a c t i o n of b a s i c needs may be a t r i s k . The v a r i a b l e most used t o

measure s u b s i s t e n c r showed, however, such a l a r g e variation t h a t i t was

imposs ib le t o ds termine what i s t h e c r i t t c a l element t h a t t h e fanner

cons ide r s i~ d e t e r n i n i n g h i s s e c u r i t y o r s u r v i v a l l e v e l . This conclus ion

c a l l s f o r a b e t t e r understanding of t h e i n t e r a c t i o n between t.he ? rodur t ion

and consumption behavior of peasant hous&oids. Though t h i s endeavour w i l l

be t h e s u b j e c t of another s tudy , t h e p resen t paper w i l l hopeful ly be

in s t rumen ta l i n sugges t ing some of t h e r e l e v a n t ques t ions tha,t r e sea rch

has t o f a c e i n t h i s f i e l d . Not l e a s t , w e hope t h a t o a r a n a l y s i s has shorn

t h a t i t is p o s s i b l e v i a s imple but purpos ive ques t ion ing t o e l i c i t meanhg-

f u l information on peasant a t t i t u d e s p e r t i n e n t t o r u r a l devel.opment.

Anderson, J . R . , J L. D i l l on and J . B . Hardaker. A g r i c u l t u r t l 3 e c i s i o n

Analys i s . h e s : Iowa S t a t e Un ive r s i t y P r e s s , 1976.

Baumol, W. "An Expected Gain-Confidence Limit C r i t e r i o n f o r P o r t f o l i o

Se lec t ion" . Managemeat S c i . 10 (1963) : 174-82.

Brooks, R.H. " ~ r o u g h t and Pub l i c P o l i c y i n Nor theas t e rn B r a z i l : A l t e r -

n a t i v e s t o S t a rva t ion" . P r o f e s s i o n a l Geographer 25 (1973):

Campos Mesquita, T . , and J .L. Di l lon . "Alguns Aspectos dos Pequenos

A g r i c u l t o r e s do Serti lo do Ceard, d i a n t e do Risco". Estudos

Agrar ios (INCRA, B r a s i l i a ) 1 (1976): 1-12.

Coombs, C .H . "A Review of t h e Mathematical Psychology of R:Lsk and

Risk- Taking" . Department of Psychology, Un ive r s~ i ty of

Mischigan, W P 2.eport No. 72-6, 1972. - Dean, G.W. " F i r n Theory i n c o r p o r a t i n g Growth and Risk: I n t e g r a t i o n

i n t o Farm Management Research". Suppl. t o I n t e r n a t . J.

A g r a r ~ . ~ n A f f a i r s , 1975, pp . 110-20.

D i l l o n , J .L . , and J.X. Anderson. " Al loca t ive E f f i c i e n c y i n T r a d i t i o n a l

A g r i c u l t u r e and Risk", Amer. J. Agr. Econ. 53 (1971): 26-32.

E i senbe i s , Robert A. and R.A. Avery. Discr iminant Anclysio and

C l a s s i f i c a t i o n Procedures , Lexington Books, 1972. a . I

Hargreaves, G . H . Monthly P r e c i p i t a t i o n P r o b a b i l i t i e s f o r Nor theas t

B r a z i l . Department of A g r i c u l t u r a l and i r r i g a t i o n - . Engineering, Utah S t a t e ~ n i v e r q t ~ , Logan, 1973.

L

- l i a z e l l , P.B. R . "A Linear A l t e r n a t i v e t o Q u a d r a t i c and Semf-Variance

8 Programming i n Farm Planning unTer unce r t a in ty" . Arner . J. . Agr. Econ. 53 (1971): 53-L2.

H a z e l l , P.B.R., and P.L. Scandizzo. " ~ o m p e t i t i v e Demand S t r u c t u r e s

under Risk i n A g r i c u l t u r a l L inear Programming ~ o d e l s " .

Amer. J. Agr. Econ. 56 (1974): 235-44.

i l a z e l i , P.B.R., and P.L. Scandizzo. "opt imal P r i c e I n t e r v e n t i o n P o l i c i e s

when Product ion i s Risky f' . Developmeat Research Center , World

Bank, Washington, 1976, mimeo.

deyer , J . "An Analys is of Peasant Farm Product ion under Condi t ions of

~ n c e r t a i n t y " , J; Agr. Econ. 23 (1972) : 135-45.

H iebe r t , L.D. "Risk, Learning and t h e Adoption of F e r t i l i z e r Responsive

Seed Var i e t i e s" . Amer. J. Agr. Econ. 56 (1974): 764-8.

Huxley, J. Evolut ion i n Action. New York: Harper, 1953.

Johnson, A.W. Sharecroppers of t h e Serti lo: Economics and Dependence on a

B r a z i l i a n P l a n t a t i o n . S tanford Un ive r s i t y P r e s s , 1970.

1 .-. Johnson, A.W. " Secur i ty and Risk- taking among Poor Peasants : A B r a z i l i a n

Case". Stud. Econ. Anthrop. AS7 (1971) : 143-50.

Kutcher, G.P., and P.I.. Scandizzo. "The Nor theas t B r a z i l Modelling E f f o r t :

A Progress Fteportf1. Development Research Center , World Bank,

Washington, 1976a, mineo.

Kutcher, G.P., and P.L. Scandizzo, eds. The Economics of Farming i n North-

e a s t Braz i l : Report on a Regionwide Survey. Development Research

I Center , World Bank, Washington, 1976b, mimeo.

Lip ton , M. "The Theory of t h e Optimizing peasant" . J . Dev. Stud. 4 (1968):

327-51.

Low, A.R.C . " ~ e c i s i o x Flaking under Uncer ta in ty : A Linear Programming . f

Model of Peasant Farmer ~ c h a v i o r " . J. Agr. Econ. 25 (1974):

311-22. - - Masson, R.T. " U t i l i t y Funct ions wi th Jump D i s c o n t i n u i t i e s : Some ~ a d e n c e

I and 1mplic;ations from Peasant ~ g r i c u l t u r e " . Econ. Irtquiry 5 2

Moscardi, E.R. "A Metho,iology t o Study A t t i t u d e s toward Risk: t h e Case

of t h e Puebla Pro jec t" . CIMMYT, Mexico C i t y , 1975, mimeo.

I O'Mara, G.T. "A Decis ion Theore t ic View of t h e ?Iicroeconomics of

I Technique Dif fus ion i n a Developing country". Ph.D. t h e s i s ,

I Stanford Un ive r s i t y , 1971.

4 " - iii -

P a t r i c k , G.F., and J.J.C. F i lho . "Low-income Groups i n B r a z i l i a n Agricul-

tu re : A Progress ~ e p o r t ' ' . Purdue Un ive r s i ty , Agric. Exp. S t

Bul. No. 79, La faye t t e , 1975.

Rounasset, J . A . "Est imating t h e Risk of A l t e r n a t e Techniques:: Nitrogenous

F e r t i l i z a t i o n of Rice i n t h e Phi l ippines" . Rev. Mctng. Agr. con. - 42 (1974): 257-94.

Samuelson, P.A. "The Fundamental Theorem of ?o:ctfolio

Analysis i n Terns of Means, Variances and Higher Moments". Rev. Econ. S tud ie s 37 (1970): 537-42.

Sanders , J . H . , and A.D. Hollanda. "Designing New Technology f o r Small

Farmers: A Case Study i n a Semi-arid Area of t h e Br(azi1ian

~ o r t h e a s t " . Department of A g r i c u l t u r a l Econcmics, Federa l

Univers i ty of Cear5, F o r t a l e z a , 1975, mimeo.

Scandizzo, P.L. " D i s t r i b u t i o n a l E f f e c t s of P r o d u c t i v i t y Inc reases : A

Case Study i n NE ~ r a z i l " . Develapment Research Centre , World

Bank, Washington, 1975, mimeo.

Sch lu te r , M.G.G., and T.D. Mount. "Management Objec t ives of t h e Peasant

Farmer: An Analys is of Risk Aversion i n t h e Choice of Cropping

P a t t e r n , Su ra t D i s t r i c t , India". J. Dev. Stud. 1 2 (1976): ( i n

p re s s ) .

Simmons, R . L . , and C. Pomareda. "Equilibrium Quant i ty and Timing of

Mexican Vegetable Exports". h e r . J. Agr. Econ. 57 (1975): i

472-9.

- - Whnr ;on, C.R. "Risk, Uncertainty and the Subs is tence Farmer"'. Dev. Diges t

.$ 7 (1969)'' 3-10.

* - - 4

Wiens, T.B. "Uncertainty and Factor A l loca t ion i n a Peasant E c ~ n o g y ' ~ . D

Univers i ty 3f Oregon Working Papers i n Economics No. 2 , 1973.

Wiens, T.B. "Peasant Risk Aversion and A l l o c a t i v e Behavior: A Programming

~xper imen t " , Univers i ty of Oregon Working Papers i n Economics No.

8, 1974.

Wolgin, J . M . "Resource Al loca t ion and Risk: A Case Study of Smallholder

Agr i cu l tu re i n Kenya". h e r . J . Agr. Econ. 57 (1975:): 622-30.

The a u t h o r s a r e g r a t e f u l t o EMBRAPA (The ~ r a z - i l i a n n a t i o n a l a g r i -

c u l t u r a l r e sea rch agency) , FIPE ( t h e economics r e s e a r c h i n s t i t u t e of t h e

Un ive r s i t y of S3o Paulo) and t h e Department of A g r i c u l t u r a l Economics of

t he Un ive r s i t y of Cear6 f o r t h e oppor tun t iy of under tak ing the p r e s e n t

s tudy . Jock Anderson, a e l a Balassa and C l ive B e l l a s s i s t e d lwith c r i t i c a l

comments. Opinions expressed a r e s o l e l y t h e r e s p o n s i b i l i t y (of t h e au tho r s .

1 The a c t u a l ques t ions asked followed t h e same b a s i c p a t t e r n f o r

each sample group and each r i s k s i t u a t i o n ; and though h y p o t h e t i c a l , t h e

r i s k y p rospec t s posed were not of t h e "pure game" type bu t were r e a l i s t i c

i n t h e sense of involv ing p o s t u l a t e d p r o b a b i l i t i e s and consequences

regarded as no t unreasonable f o r t h e r eg i cn . With s u b s i s t e n c e a s su red ,

t h e i n i t i a l ques t ion t o owners was: "Which would you p r e f e r - (A) a farm

which gave you every year your family food requirements p l u s a n e t cash

r e t u r n of CrS3500; o r (B) a farm which i n t h r e e y e a r s o u t of fou r gave

you your fami ly food requirements p l u s a n e t cash r e t u r n of ~ r $ 4 2 0 0 and i n

one yea r ou t of f o u r gave you your f ami ly food requi rements p l u s a n e t cash

r I t

r e t u r n of Cr$1400?" I f A was p r e f e r r e d t o B , t h e cash r e t u r n i n A was

reduced by decrements of CrS500 u n t i l i n d i f f e r e n c e o r a swi tch t o B was - - e s t n b l i s h c d . I f B wasgpreferred t o A , t h e same procedure was repea ted bu t - wi th the cash r e t u r n i & A increased by increments of Cr$250. For share-

D

c roppe r s , w i th s u b s i s t e n c e assured , t h e i n i t i a l cash sum i n A was s e t a t

Cr$2000 and those i n B a t Cr$2400 and Cr$800, and increments of CrS200

were used both up and down. With s u b s i s t e n c e a t r i s k , t h e i n i t i a l ques t ion

t o owners was: "Which would you p r e f e r - (A) 3 farm which gave you every

a a .

y e a r your family food requlrements and no a d d i t i o n a l n e t cash r e t u r n ; o r

( B ) a farm which i n t h r e e y e a r s out of f o u r gave you your fami1.y food

requlrements p lus a ne t cash r e t u r n of CrS5000 and i n one year out o f ' fou r

gave you j u s t h a l f your family food requirements and no n e t cash r e t u r n ?"

I f A was p re fe r r ed t o B, t h e b e t t e r outcome i n B was increased by increments

of Cr$1000 u n t i l i n d i f f e r e n c e o r a swi tch t o B was e s t a b l i s h e d . I f B w a s

p r e f e r r e d t o A , t h e s u r e prospect was increased by increments of CrS1000

u n t i l i n d i f f e r e n c e o r a swi tch t o A was e s t ab l i shed . For sharecroppers ,

wi th subs i s t ence a t r i s k , t h e i n i t i a l b e t t e r outcome i n B was s e t a t CrS2500.

Otherwise t h e quest5uas were t h e same a s f o r owners wi th subs i s~ tence a t 'b

r i s k .

2 I n 1973, a World Bank-SUDENE team working on a nuch I.arger survey

(8,000 farms) i n t h e same geographical a r e a , reached t h e same conclusion

a f t e r ( f a i l e d ) a t tempts a t applying a q u e s t i o n n a i r e on r i s k a t t i t u d e s based

on ques t ions of t h e "pure game" type which made no a t tempt t o mimic r e a l i t y .

It i s perhaps worth no t ing t h a t f i r s t impressions i n p i l o t d i s c l s s i o n s wi th

some of our farmers ind ica t ed a f a t a l i s t i c r a t h e r than p r o b a b i l i s t i c

approach t o unce r t a in ty . Fu r the r d i scuss ion , however, i nd ica t ed t h a t pro-- , * r

b a b i l i t i e s could be e l i c i t e d though no t a s e a s i l y a s , i n our experience,

wi th non-peasant farmers. - i

.! 3 ~ i t h d u t r e f e r r i n g t o a s p e c i f i c model, here we cons ider a s - - -

," wi l l ing t o t ake r i s k s" those s u b j e c t s who w e r e a n d i f f e r e n t between a m

I

random prospect X and a c e r t a i n t y equ iva len t C.E. such t h a t E(X) < C.E.

For the S .R. case , t h i s assessment involves v a l u a t i o n of each farmer ' s

s u b s i s t e n c e a t market va lue .

4 W e could a l s o have es t imated t h e r i s k parameter a i n t h e u t i l i t y

f u n c t i o n U = -exp(aX) b u t , u n l i k e t h e ( E , a ) and ( 9 , K) models, t h e

exponen t i a l is no t convenient f o r l i n e a r p r o g r a m i n g a n a l y s i s .

5 We used l i n e a r d i s c r iminan t f u n c t i o n ininimizing Mahalanobis

g e n e r a l i z e d d i s t a n c e between t h e two groups. The hypo thes i s t h a t t h e two

groups a r e indeed d i f f e r e n t can be r e j e c t e d a t any computable degree of

s i g n i f i c a n c e . When d i f f e r e n c e s due t o o t h e r f a c t o r s a r e taken i n t o account

i t appea r s t h a t t h e r i s k behavior of t h e two groups i s n o t s i g n i f i c a n t l y

d i f f e r e n t a t r ea sonab le conf idence l e v e l s . A d i s c u s s i o n of t h e method

and t h e tests used is g iven by E i s e n t e i s and Avery.

6 A n o t e of c a u t i o n is i n o r d e r t o e v a l u a t e t h e s e r e s u l t s . A s

s t a t e d i n t h e t e x t , s u b s i s t e n c e was measured a s t h e v a l u e of t h e home

produced household consumption. T h i s measure is n o t s a t i s f a c t o r y a s t h e

s h a r e of s e l f p roduct ion tends t o s h i f t from y e a r t o yea r due t o change

i n c rops . S ince d a t a f o r t he e n t i r e survey per iod were a v a i l a b l e , however,

a s imple average of t h e two yea r (1973-74) pe r iod was used t o approximate

t h e s u b s i s t e n c e v a r i a b l e . The r e s u l t s ob ta ined f o r s u b s i s t e n c e a t r i s k i

a r e r e l i a b l e only t o t h e e x t e n t t h a t " r u r a l" househo1.d~ i n t h e survey a r e a

"tend" t o produce a c o n s t a n t minin\rlm amount ( t h e s u b s i s t e n c e l e v e l ) of - '2

food f o r fami ly consumption. Not ice ' a l s o t h a t 1973 i s regarded a s a Aormal - year i n Canind6 b u t p74 was a bad y e a r due t o f l oods .

-1 -1 7 These c a s e s a r i s e when s i g n (( - 1 s i g n (R1 - R2 1 and 1

-1 - 1 I el - m 2 1 > I R1 - R2 1 . For t h e s e c a s e s t h e $ - K model is no t

a p p r o p r i a t e s i n c e t h e s r ~ b j e c t s e i t h e r e x h i b i t p o s i t i v e r i s k p r e f e r e n c e i n

only one of t h e a l t e r n a t i v e s o r they a r e less r i s k a v e r s e when t h e

p rospec t i s r i s k i e r .