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When an image on the film is obliterated w ith a round black m ark, it is an indication o f eith er blurred copy because o f m ovem ent during exposure, duplicate copy, o r copyrighted m aterials th a t should n o t have been filmed. F o r blurred pages, a good image o f the page can be found in the adjacent frame. If copyrighted m aterials were deleted, a target n o te will appear listing the pages in the adjacent frame. 3. When a m ap, drawing or ch art, etc., is p art o f th e m aterial being photographed, a definite m ethod o f “ sectioning” th e m aterial has been followed. It is custom ary to begin filming at the up p er left hand corner o f a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until com plete. 4. F or illustrations th a t can n o t be satisfactorily reproduced by xerographic means, photographic p rints can be purchased at additional cost and inserted into y o u r xerographic copy. These prints are available upon request from the D issertations C ustom er Services D epartm ent. 5. Some pages in any docum ent may have indistinct print. In all cases the best available copy has been film ed. Uni international 300 N. Z eeb Road Ann Arbor, Ml 48106 8308911 Carman, Garth Alan AN APPLICATION O F STOCHASTIC DOMINANCE WITH RESPECT TO A FUNCTION: MEASURING T H E RELATIONSHIP O F PRODUCER ATTRIBUTES TO RISK PREFERENCES Ph.D . Michigan Stale University University Microfilms International 300 N. Zeeb Road, Ann Arbor, MI 48106 1982 AN APPLICATION OF STOCHASTIC DOMINANCE WITH RESPECT TO A FUNCTION: MEASURING THE RELATIONSHIP OF PRODUCER ATTRIBUTES TO RISK PREFERENCES By Garth A. Carman A DISSERTATION Submitted to Michigan S t a t e U n iv e rs ity in p a r t i a l f u l f i l l m e n t o f the requirements f o r the degree of DOCTOR OF PHILOSOPHY 1982 ABSTRACT AN APPLICATION OF STOCHASTIC DOMINANCE WITH RESPECT TO A FUNCTION: MEASURING THE RELATIONSHIP OF PRODUCER ATTRIBUTES TO RISK PREFERENCES By Garth A. Carman S t o c h a s t i c dominance with r e s p e c t to a fu nction i s used to develop confidence i n t e r v a l s around r i s k prefe renc e measures f o r 30 farmers in South Central Michigan. The p r e d i c t i v e power r e s u l t i n g from t h es e i n t e r ­ val measures a r e compared with th e accuracy o f a s i n g le - v a lu e d u t i l i t y f u n c t i o n and f i r s t and second degree s t o c h a s t i c dominance e f f i c i e n c y c r i ­ teria. The r e l a t i v e m e r i ts o f each d e cisio n tool a re disc usse d. A f t e r a j u s t i f i c a t i o n f o r the use o f t h i s technique an empirical a p p l i c a t i o n i s p res en te d . In comparison with a si n g l e - v a lu e d u t i l i t y fu n c t i o n and f i r s t and second s t o c h a s t i c dominance, the i n t e r v a l measure o f r i s k p refe ren c e has a c l e a r advantage because i t allows f o r t r a d e - o f f s between accuracy o f p r e d i c t i v e c a p a b i l i t i e s and ordering o f a c t io n c h o ic es . The i n t e r v a l measures o f r i s k prefe ren c e f u n c t i o n s , are then used to e s t a b l i s h a r e l a t i o n s h i p between the r i s k preferences and producer attrib utes. Using d i s c r i m i n a n t a n a l y s i s , producers can be c l a s s i f i e d i n to r i s k pre f e r e n c e c a t e g o r i e s by t h e i r a t t r i b u t e s a t s p e c i f i c po ints on the r i s k p refe ren c e i n t e r v a l . However, th es e a t t r i b u t e s do not Garth A. Carman remain c o n s i s t e n t as movement occurs along the f u n c t i o n . F i n a l l y , p ro ­ ducer a t t r i b u t e s a re used to p r e d i c t r i s k p refe ren c es and those r i s k p r e ­ feren ces are used to p r e d i c t a c t io n choices . ACKNOWLEDGEMENTS The auth or wishes to g r a t e f u l l y acknowledge the valuable a s s i s t a n c e received from my t h e s i s committee: Robison, and Steve Harsh. Drs. L este r Manderscheid, Lindon I am e s p e c i a l l y thankful to Dr. Lindon Robison, my t h e s i s s u p e r v i s o r , whose c o n stan t support and encouragement provided the impetus f o r conducting the study and re p o r t i n g the r e s u l t s . Parti­ c u l a r thanks are extended to Dr. L es te r Manderscheid who served as major p r o f e s s o r throughout my gradua te s t u d i e s . Funding f o r t h i s stud y was provided by the Michigan A g r ic u ltu r a l Experiment S t a t i o n t o which I extend my a p p r e c i a ti o n . I am a l s o indebted to my pare nts and family f o r teaching me the value o f an education and providing a p o s i t i v e environment which e l i m i ­ nated b a r r i e r s which I encountered throughout my educational experi ence. F i n a l l y , and most im p o r t a n t l y , I wish to thank my w ife, Sherry. Her comfort and encouragement through the hard times and enthusiasm and companionship through th e good times will always be remembered. The f a c t t h a t she gave so much and asked so l i t t l e in r e t u r n was res p o n s i b l e f o r my accomplishments. TABLE OF CONTENTS Page ACKNOWLEDGEMENTS...................................................................................................... ii LIST OF TABLES.......................................................................................................... v LIST OF FIGURES...................................................................................................... vi CHAPTER I. INTRODUCTION................................................................................................... 1.1 Study Background and Purpose .................................................. 1.2 Problem S e t t i n g and Sta te m en t.................................................. 1 1 7 II. LITERATURE REVIEW ...................................................................................... 11 III. THEORETICAL APPROACH AND METHODOLOGY................................................ 3.1 The Interv al Method....................................................................... 3.2 Empirical Test o f I n t e r v a l Approach...................................... 3.3 Experimental Design........................................................................ 3.4 A n a l y s i s ............................................................................................ 20 20 29 29 33 IV. QUESTIONNAIRE AND SAMPLE DESIGN ......................................................... 4.1 Que stionnaire Design ................................................................... 4.2 P r e - T e s t ............................................................................................. 4.3 Sample S e l e c ti o n ............................................................................ 4.4 S a m p l e ................................................................................................. 4.5 Data A c q u i s i t i o n ............................................................................ 40 40 50 50 51 52 V. ANALYSIS OF DATA......................................................................... 5.1 Response R ate..................................................................................... 5.2 Ordering Based on Risk I n t e r v a l .............................................. 5.3 Discriminant A n a l y s i s .................................................................... 5.4 Results a t $0..................................................................................... 5.5 Results a t $10,000 ......................................................................... 5.6 Results a t $25,000 ......................................................................... 5.7 Results a t $45,000 ......................................................................... 5.8 I n t e r p r e t a t i o n o f R e s u l t s ........................................................... 5.9 Summary o f Resu lts ........................................................................ 5.10 Using A t t r i b u t e s t o P r e d i c t Action Choices ..................... 53 53 54 56 58 60 60 64 64 69 70 VI. CONCLUSIONS AND FUTURE RESEARCH............................... 6.1 Conclusions......................................................................................... 6.2 Areas o f F u rth e r Research........................................................... 74 74 75 iii Page APPENDICES A Cover L e t t e r .................................................................................................. B Question naire .............................................................................................. C Follow-Up L e t t e r .......................................................................................... 77 78 93 BIBLIOGRAPHY.............................................................................................................. 97 iv LIST OF TABLES TABLE 3.1 Page Absolute Risk Aversion Levels Defining Measurement G rid .......................................................................................................... 31 Empirical Resu lts o f Action Choice P r e d i c t io n s Using Interv al Risk Measures and a U t i l i t y Function ................. 34 Accuracy o f I n terva l Compared to U t i l i t y Function Approach................................................................................................. 38 Absolute Risk Aversion Levels Defining Measurement G ri d.......................................................................................................... 44 Correspondence Between Questions Asked and Risk I n t e r v a l s I d e n t i f i e d ........................................................................ 48 5.1 Ordering and Accuracy o f I n te r v a l Approach................................ 55 5.2 Discriminant Function a t Zero Income L ev e l.............................. 59 5.3 Discriminant F u n c tio n 's P r e d i c t i v e A b i l i t y , Zero Income L e v e l . ..................................................................................... 61 5.4 Discriminant Function a t $10,000 Income Level ....................... 62 5.5 Discriminant F u n c t io n 's P r e d i c t i v e A b i l i t y , $10,000 Income L evel......................................................................................... 63 3.2 3.3 4.1 4.2 5.6 Discriminant Function a t $25,000 Income Level ...................... 65 5.7 Discriminant F u n c tio n 's P r e d i c t i v e A b i l i t y , $25,000 Income L evel......................................................................................... 66 5.8 Discriminant Function a t $45,000 Income Level ...................... 67 5.9 Discriminant Fun c tio n 's P r e d i c t i v e A b i l i t y , $45,000 Income L ev e l......................................................................................... 68 5.10 Most I n f l u e n t i a l Va riables in C l a s s i f i c a t i o n Proces s. . . 71 V LIST OF FIGURES FIGURE 1.1 Page A Schematic Describing Relationships Between Producer A t t r i b u t e s , Risk P r e f e r e n c e s, and Responses to Risk. . . 9 3.1 F i r s t Degree S t o c h a s ti c Dominance o f G(y) by F ( y ) .................. 23 3.2 I n t e r s e c t i n g Cumulative D i s t r i b u t i o n s Which Vio late F i r s t Degree S t o c h a s ti c Dominance Requirements ................. 24 3 .3 Reduction o f I n t e r v a l S i z e ................................................................ 28 4.1 Iterative 46 Process Used in Questionnaire Design....................... Vi CHAPTER I INTRODUCTION 1.1 Study Background and Purpose All a g r i c u l t u r a l producers must decide how to a l l o c a t e t h e i r r e ­ sources in a manner c o n s i s t e n t with both t h e i r monetary and nonmonetary g o a ls . The resources a v a i l a b l e to the o p e r a t o r a re numerous and often a re c l a s s i f i e d as e i t h e r l a n d , l a b o r , o r c a p i t a l . The s e t o f resource a l l o c a t i o n a l t e r n a t i v e s a v a i l a b l e a r e de fined as a c tio n choic es. c a l l y , economists assume a c e r t a i n t y model. Typi­ Within t h i s model th e pro­ duction f u n c t i o n , c o s t , and revenue curves a re known. This assumption and the assumption o f p o s i t i v e marginal u t i l i t y f o r money allows f o r a c t i o n choices to be accepted o r r e j e c t e d on the b a s i s o f a p r o f i t maxi­ mization model s u b j e c t t o res our ce c o n s t r a i n t s . Management's d e c i s i o n ­ making s e r v i c e s no useful purpose under th ese assumptions o f c e r t a i n t y . The economist could simply t e l l the producer what to produce and how to produce i t . Consequently, the f a c t o r s in flu e n cin g the d e cision pro cess, as well as the d e c i s i o n process i t s e l f , are not s i g n i f i c a n t . However, when th e u n c e r t a i n t y , which e x i s t s in the "real world," i s introduced non-uniqueness o f d e c i s i o n s comes i n to e x is te n c e . Resource p r i c e , and c o s t data a r e no lo n ger th e s o l e f a c t o r s in solving f o r unique decisions. I n s t e a d , management and t h e manner in which i t responds to an u n c e r t a i n environment become c r u c i a l f a c t o r s in the resource a l l o c a t i o n and production process. 2 Within t h i s framework two are as deserve a t t e n t i o n . The f i r s t area i s an a n a l y s i s o f the f a c t o r s t h a t in flu e n ce the actual decision-making p rocess. The second area de als with the decision-making process i t s e l f . While a g r e a t deal o f a t t e n t i o n has been focused on the l a t t e r , th e form­ e r has received much l e s s a t t e n t i o n . These two a r e a s , f a c t o r s t h a t i n ­ flu ence the decision-making process and the actual process i t s e l f , a l l u d e a g r i c u l t u r a l economists in ach iev ing a complete understanding. This i s f o r t u n a t e sin ce a b e t t e r understanding in these a re as could lead to more complete knowledge o f t h e i r im p l i c a ti o n s on both a micro and macro level. More s p e c i f i c a l l y , in an u n c e r t a i n world producers possess c e r t a i n attributes. The a t t r i b u t e s t h a t may a f f e c t the d e cisio n-m a ker's s e l e c ­ t i o n o f an a c t io n choice includ e: age, e d u c a tio n , t e n u r e , business s i z e , w ealth, income p o t e n t i a l and a c t io n ch oic e, e t c . f lu en ce the r i s k prefe renc es o f producers. These a t t r i b u t e s i n ­ For example, an o l d e r o p e r a t o r nearing r e t i r e m e n t may wish to "play i t s a f e " and t h e r e f o r e may not de­ s i r e to tak e r i s k s t h a t a r e necessary t o ge nerate a d d it i o n a l income r e ­ q uired f o r growth. different On the o t h e r hand, a younger producer may have q u i t e r i s k preferen ces f o r j u s t the o p p o site reasons . Sim ilarly, a producer with a l a r g e r family and l i m i t e d wealth may not be able to w ithstand f l u c t u a t i n g incomes as e a s i l y as a producer with a sm aller family o f g r e a t e r wealth. As a r e s u l t o f such a t t r i b u t e s , t h es e i n d i v i ­ duals could very well possess d i f f e r e n t r i s k p r e f e r e n c e s . The r i s k p references o f an in d iv id u a l may in flu e n ce the manner in which he manages the pro du ction , marketing, and f i n a n c i a l r i s k s t h a t e x i s t in his p a r t i c u l a r environment. For example, given two producers, one r i s k - a v e r s e and one r i s k - l o v i n g , one might f i n d t h a t the r i s k - a v e r s e 3 producer might u t i l i z e forward marketing, in su r a n c e , c a p i t a l r e s e r v e s , excess machinery c a p a c i t y , e t c . , in a manner which e i t h e r reduces or t r a n s f e r s marketing r i s k s ; while a more r i s k - l o v i n g o p e ra t o r may choose to c a r r y t h es e r i s k s . The success or f a i l u r e of these management te c h n iq u e s, along with economies of s c a l e , may influ ence the s t r u c t u r a l c h a r a c t e r i s t i c s of the a g r i c u l t u r a l production s e c t o r . The t r a d i t i o n a l a n a l y s i s of farm s i z e changes has focused on econo­ mies and diseconomies of s i z e r e ly in g p r i m a r il y on c o s t curve a n a l y s i s . This has been done with hopes t h a t changes in farm numbers and t h e i r a s s o c i a t e d s i z e s could be explained and p r e d i c te d a c c u r a t e l y in th e f u t u r e . For th ose who b e li e v e farming i s a de creasing c o s t i n d u s t r y , concern i s generated over the f u t u r e of the small family farm o p e ra tio n in the coming years. However, Madden (1967) found a f t e r reviewing a number of s t u d i e s of crop farming s i t u a t i o n s in various s t a t e s t h a t : "In most of t h es e s i t u a t i o n s a l l o f the economies of s i z e could be achieved by modern and f u l l y mechanized one-man or two-man farms." The r e l a t i v e importance of r i s k and u n c e r t a i n t y in determining s t r u c t u r a l changes is not known. I t i s , however, recognized. French (1977) r e f e r r e d to r i s k and u n c e r t a i n t y in hi s summary of economies of scale. Heady (1952) perhaps b e s t recognized t h e importance of r i s k and u n c e r t a i n t y in s t a t i n g : 4 "Continuance o f the s o - c a l l e d family farm as the main s t r u c t u r e o f a g r i c u l t u r e su g g e s ts , on the one hand t h a t i f s i z e economies e x i s t , they soon give way to diseconomies. Concurrently, th e con­ tin uance o f small farms suggest th e hypothesis t h a t economic dynamics of r i s k and u n c e r t a i n t y may be the f i n a l de te rm inant o f farm s i z e in agriculture." The s t r u c t u r a l changes t h a t occur then in flu e n ce the aggregate a t t r i b u t e makeup in subsequent p e r i o d s . For example, suppose t h a t small producers a re more r i s k - l o v i n g and as a r e s u l t do not u t i l i z e c e r t a i n r i s k management t o o l s . Given an unfavorable environment, i t i s p o s s ib l e t h a t thes e sm all, r i s k - l o v i n g producers would be e li m in a te d from the market plac e. Thus t h e next period would r e f l e c t an aggregate farm population o f fewer small farm ers. S i m i l a r l y , t h i s type o f an example holds f o r o t h e r a t t r i b u t e s . At t h i s time, i t i s unknown whether t h i s dynamic framework or p a r t s o f i t a re v a l i d . The t e s t i n g o f the p o s s i b l e r e l a t i o n s h i p s o f f e r s r e ­ wards f o r policy-makers a t both the firm and aggregate l e v e l . This res ea rch does n o t attem pt to e s t a b l i s h a l l o f the previous ly discusse d r e l a t i o n s h i p s . R ather, i t proposes to study the r e l a t i o n s h i p s between p ro d u ce r's a t t r i b u t e s and r i s k p r e f e r e n c e s . Currently, l i t t l e i s known about th e r e l a t i o n s h i p o f producer a t t r i b u t e s to r i s k p refe ren c es. I f r e l a t i o n s h i p s can be e s t a b l i s h e d , f u r t h e r work can be suggested. If no r e l a t i o n s h i p e x i s t s , t h i s area o f r e s e a r c h can be e li m in a te d in the future. The need to recognize p e rs o n a l , b u s i n e s s , and economic a t t r i b u t e s has o f t e n been suggested. Barry and Baker (1977) s t a t e t h a t "the need t o t e s t hypotheses on r i s k behavior i s one area needing f u r t h e r study. For example, how do r i s k premiums re q u ir e d by primary producers vary 5 with s e l e c t e d p e rs o n al, b u s in e ss, and economic a t t r i b u t e s . " The Western Regional Research Committee (W-149) considered measuring u t i l i t y fun ctio n s f o r a l a r g e number o f producers d i f f e r e n t i a t e d by s e l e c t e d a t t r i b u t e s , Robison and King (1978). While c r i t i c a l of the methodology proposed by W-149, n o n e th e le ss , they recognized t h e need to c o n s i d e r th e a t t r i b u t e s . Although the Western Regional Committee r e c e n tly r e j e c t e d t h e i d e a , the r e j e c t i o n was based on the methodology proposed r a t h e r than the need to e stab lish existing relationships. The need to i d e n t i f y t h es e r e l a t i o n ­ s h i p s , or lack t h e r e o f , between producer a t t r i b u t e s and r i s k prefe re nces i s recognized. This res ea rch e f f o r t focuses on accomplishing t h i s t a s k . A t t r i b u t e s o f a g r i c u l t u r a l producers a re o f t e n broken down i n to various c a t e g o r i e s . Barry and Baker (1977) c l a s s i f y a t t r i b u t e s as e i t h e r being p e rs o n al, b u sin e ss, o r economic. The a t t r i b u t e s o f c h a r a c t e r i s t i c s o f the general a g r i c u l t u r a l pro­ duction s e c t o r population have undergone many changes over t h e p a s t cen­ tury. Some o f t h es e changes have generated l i t t l e concern, while o th ers have been the focus o f a g r e a t deal o f a t t e n t i o n . French and Carman (1979) note t h a t between 1945 and 1974 the average age o f a l l farm o p e ra to r s increased from 48.7 to 51.7 y e a r s o f age; mean­ w hile, the average age o f o p e ra t o r s f o r the l a r g e s t farms was somewhat lower. S i m i l a r l y , they note t h a t the education lev e l o f farm o p e ra t o r s has increas ed as i t has f o r the general po pulation as a whole. Changes have als o taken plac e with regard to o t h e r a t t r i b u t e s . Changes in tenure have occurred over the past two decades. In 1954, 44.8 p ercen t o f the farms with over $2,500 o f s a les were ope rated by f u l l owners. In 1974 t h i s number increased to 53.3 p e r c e n t . For t h i s same time period part-owners increased from 25.2 p e rc e n t to 33.4 p e rc e n t . 6 Tenants decreased from 29.1 p ercen t in 1954 t o 13.3 percent in 1974. The value o f s a l e s group d i s t r i b u t i o n by ten u re shows 45 p ercen t of pa rt-o w ne rs, 32 p e rc en t o f t e n a n t farms, and 17 percent o f fu ll- ow n er farmers had s a l e s o f over $40,000. In o t h e r words, full- o w ners tended to o pe ra te sm a ll e r farms than e i t h e r t e n a n t o r part-owners. Quite p o s s i b l y , th e most o f t e n disc ussed a t t r i b u t e r e l a t e d to the a g r i c u l t u r a l pro duction s e c t o r i s t h a t of busin ess s i z e . The s t r u c t u r e o f the United S t a t e s a g r i c u l t u r a l production s e c t o r has long been of i n t e r e s t to producers, policy-makers, and r e s e a r c h e r s . During the past t h r e e decades the U.S. a g r i c u l t u r a l s e c t o r has undergone tremendous growth in p r o d u c t i v i t y and e xte n sive s t r u c t u r a l change, both l a r g e l y a t t r i b u t a b l e to r a p id technolo gical change and the in c r e a s in g degree of s p e c i a l i z a t i o n t h a t has accompanied i t . In 1940 farm p r o d u c t i v i t y , measured by th e index o f ou tpu t per u n i t o f in p u t with 1960 as a base, was 60. In 1950, 1960, and 1970 t h i s index in cre ased to 73, 100, and 101, r e s p e c t i v e l y . In 1974 t h i s index had in cre ased to 104. During t h i s tim e, and e s p e c i a l l y in th e p a s t decade, a g r e a t deal o f i n t e r e s t has been focused on who w ill control a g r i c u l t u r e , and, pos­ s i b l y more im po rtant, who should control a g r i c u l t u r e . In h is 1978 p re ­ s i d e n t i a l a d d r e s s , B. F. Stanton discussed farm s i z e . Stanton (1978) o u t l i n e d f o u r reasons why farm s i z e i s s u e s have been the focus of con­ cern f o r so many f o r so long. One reason i s t h e poverty a s s o c i a t e d with r u r a l incomes and the a s s o c i a t e d welfare i m p l i c a t i o n s . A second i s r e ­ l a t e d t o business management aspects o f an o p e r a t i o n , i . e . , f in d in g pro­ d uction res ource combinations and then tak in g t h i s knowledge and applying i t to in d iv id u al farms. Closely r e l a t e d , the t h i r d has to do with 7 r e a l i z i n g the most e f f i c i e n t combination o f resources f o r in d iv id u al farms and farms in g e n e r a l . F i n a l l y , the fourth i s concerned with d i s t r i b u ­ t i o n a l i s s u e s , i . e . , who c o n tr o l s the resources and how broadly o r narrow­ ly t h e s e resources are d i s t r i b u t e d among farmers and o t h e r s . In 1850 t h e r e were 1,449,073 farms in the United S t a t e s averaging 202.6 a cres in s i z e . Farm numbers in creased to 6,812,350 in 1935 while the average farm s i z e decreased to 154.8 a c r e s . Since t h a t time the tr en d has r e v e r s e d —the number of farms has declined while the average farm s i z e has in cre as ed . 389.5 a c r e s . In 1969 t h e r e were 2,730,250 farms averaging S i m i l a r l y , the land devoted to a g r i c u l t u r a l production was 393,560,614 a cres in 1850, in cre asin g and reaching a peak in the 1950's and then d e c l in i n g to 1,063,346,489 acres in 1969. the number o f sm aller farms has As t h i s data su g ge sts, declined as l a r g e r farm numbers have in cre ased. Conc urrently, t h e r e have been s i g n i f i c a n t changes in economic a t t r i ­ butes o f farm producers. Leverage, as measured by the r a t i o o f t o t a l debts to t o t a l a s s e t s o f farms in the United S t a t e s , has been changing. In 1960 th e lev erag e r a t i o was 11.8, i n cre as in g t o a peak o f 16.8 in 1970 and 1972, and then decreasing to 15.6 in 1974. le v e r a g e , has s i m i l a r l y increased sin ce 1960. Net income, l i k e In 1960 average n e t i n ­ come was $16,195, in c r e a s in g to $47,510 in 1973, and d e c l in i n g t o $37,857 in 1977. 1.2 Problem S e t t i n g and Statement Risk and u n c e r t a i n t y permeate almost every a s p e c t o f the U.S, a g r i ­ c u l t u r a l production s e c t o r . The degree o f r i s k and u n c e r t a i n t y and the a s s o c i a t e d response have a g r e a t impact on a l l market p a r t i c i p a n t s . A 8 model o f the r e l a t i o n s h i p between r i s k , producer a t t r i b u t e s and responses to r i s k may be u s e f u l . The r e p r e s e n t a t i o n in Figure 1, although highly s i m p l i f i e d , d e s c r i b e s one view o f the r e l a t i o n s h i p s . In th e i n i t i a l s t a g e s t h e r e are a group o f a g r i c u l t u r a l producers w h o a l l possess c e r t a i n a t t r i b u t e s such as those l i s t e d e a r l i e r . I t is commonly recognized t h a t these a t t r i b u t e s have an in flu e n ce on the pro­ d u c e r 's r i s k p r e f e r e n c e . The r i s k pre ference o f an individual o p e ra tin g in a s t o c h a s t i c environment in tu rn has an in flu e n ce on the manner in which producers manage or otherwise t r a n s f e r production, f i n a n c i a l , or marketing r i s k s . These r i s k management s t r a t e g i e s may, along with econo­ mies o f s c a l e , in f lu e n c e s t r u c t u r a l c h a r a c t e r i s t i c s in the farming s e c ­ tor. Furthermore, s t r u c t u r a l c h a r a c t e r i s t i c s i n f lu e n c e what r i s k manage­ ment s t r a t e g i e s a re a v a i l a b l e t o the farm. Given the success or f a i l u r e of th es e s t r a t e g i e s , s t r u c t u r a l changes will impact upon the f u t u r e a t ­ t r i b u t e s of t h e a g r i c u l t u r a l production s e c t o r and thus the process con­ tinues. This research i s concerned with measuring the r e l a t i o n s h i p between producer a t t r i b u t e s and r i s k p r e f e r e n c e s . As s t a t e d e a r l i e r , t h i s r e l a ­ t i o n s h i p must be e s t a b l i s h e d be fore r e l a t i o n s h i p s between a t t r i b u t e s and r i s k responses can be e s t a b l i s h e d . This research should provide some i n s i g h t s into the f e a s i b i l i t y o f f u r t h e r work in t h i s a re a. With t h e s e o b j e c t i v e s in mind, t h i s research will focus on two in te r r e la te d research areas. The f i r s t area will be an attempt t o id en ­ t i f y any sy ste m atic r e l a t i o n s h i p s t h a t e x i s t between p e rs o n al, b u s i n e s s , and economic a t t r i b u t e s and r i s k p r e f e r e n c e s . a versio n vary by producer a t t r i b u t e s ? That i s , how does r i s k As will be discussed l a t e r , some work has been done in t h i s area but t h i s work needs improvement in two Producer A t t r i b u t e s — personal — business --econom ic Producer Risk Preferences Risk Management Strategies Economies S t r u c tu r a l C haracteristics Scale FIGURE 1.1 A Schematic Describing R ela tio n ship s Between Producer A t t r i b u t e s , Risk P r e f er e n ce s, and Responses to Risk 10 areas. F i r s t , more a t t r i b u t e s deserve c o n s i d e r a t i o n . Second, the p a s t e f f o r t s have r e l i e d on a methodology t h a t i s open to much c r i t i c i s m since th e procedures used could have a l t e r e d the r e s u l t s . Consequently, a new methodology i s proposed, defended, and used f o r t h i s a n a l y s i s . The second i n t e r r e l a t e d r es ea r ch area i s to use the a t t r i b u t e - p r e f ere nce r e l a t i o n s h i p to determine how a c c u r a t e l y actio n choices can be predicted. In accomplishing t h e s e goals t h i s d i s s e r t a t i o n i s divided into six chapters. This c h a p te r has provided a b r i e f i n t r o d u c t i o n , a problem state m ent and framework o f a n a l y s i s . Chapter II reviews the l i t e r a t u r e and c r i t i q u e s work t h a t has been performed in t h i s a r e a . In l i g h t o f t h e d e f i c i e n c i e s o f previous r e s e a r c h , Chapter I I I p r e s e n ts a newlydeveloped t h e o r e t i c a l approach and methodology. Empirical evidence of t h i s methodology's s u p e r i o r i t y i s a ls o pre sented and disc usse d . Chapter IV p res en ts t h e q u e s t i o n n a i r e , survey d esign , and background on the sample chosen f o r o b s e r v a t i o n . Chapter V presen ts th e a n a l y s i s of the da ta while Chapter VI focuses on the summary and conclusions o f the dissertation. CHAPTER II LITERATURE REVIEW We need a c l e a r e r understanding o f how personal b u s i n e s s , and econo­ mic a t t r i b u t e s in flu e n ce r i s k p r e f e r e n c e s . In o t h e r words, a r e t h e r e s i m i l a r i t i e s in r i s k a t t i t u d e s f o r d e c i s i o n makers who possess s i m i l a r p e rs o n a l , business and economic a t t r i b u t e s ? By studying the c o r r e l a t i o n between producer a t t r i b u t e s and r i s k p r e f e r e n c e , we can improve our a b i l ­ i t y to design p o l i c i e s and make,, recommendations f o r s p e c i f i c groups. Some previous s t u d i e s have d e a l t with the t o p ic o f t h i s d i s s e r t a t i o n . The e a r l i e s t work was by H a l t e r (1956) as p a r t of th e i n t e r s t a t e mana­ g e r i a l study. and l o s s e s . He posed q u e s t io n s to producers about hy p o th etica l gains In each case a producer was o ffere d a p o s s i b i l i t y o f a c e r ­ t a i n gain o r l o s s and the p o s s i b i l i t y o f g e t t i n g ou t o f th e group (th e one f o r which a p o s s i b i l i t y o f a l o s s e x is te d ) or g e t t i n g i n to a group ( t h e one f o r which a p o s s i b i l i t y o f a gain e x is te d ) f o r a cash payment. They found t h a t the type o f in d iv id u a l who answered yes ( i . e . , to get i n t o o r out o f the group who faced t h e p o s s i b i l i t y o f a gain o r lo ss r e s p e c t i v e l y ) to a l l l o s s o r gain q u e s t io n s had c e r t a i n d i s t i n g u i s h i n g characteristics. On the average t h i s group were the o l d e s t , had fewer dependents and more farming e x p erien c e. debt p o s i t i o n s . They had high n e t worth and low These r e s u l t s su gg est t h e i n d iv i d u a ls were both r i s k - a v e r s e and r i s k - l o v i n g which i s c o n s i s t e n t with a Friedman-Savage 11 12 u t i l i t y function. However, t h i s was as f a r as the res e a r c h went. No e f f o r t was made to measure r i s k aversion over more a re a s o f incomes and sin c e gains and l o s s e s as well as p r o b a b i l i t i e s were not v a r i e d , r e l a ­ t i v e r i s k preferences were only e s t a b l i s h e d above and below two points (one a t a l o ss and one a t a g a i n ) . C e r ta in l y a more d e t a i l e d examination would have been required to focus in on a p o i n t o r area o f r i s k aversion over several are as o f income and then r e l a t e t h i s to th e disc ussed attribu tes. As i t was, t h i s r i s k prefe re nce was composed to two d i s ­ c r e t e r i s k aversion points (one above and one below) and then r e l a t e d to d i s c r e t e a t t r i b u t e s ( e . g . , o l d e r and younger). While t h i s was perhaps a p p r o p r i a t e given the s t a t e o f th e a r t a t t h a t time i t i s c e r t a i n l y l a c k ­ ing in p r e c i s i o n given the s t a t e o f the a r t today. H a l t e r a ls o found t h a t t h i s group was w i l l i n g to accept a l l u n f a i r insurance schemes and u n f a i r r i s k s i t u a t i o n s - - a s u r p r i s i n g conclusion. However H a lte r went on to s t a t e t h a t t h i s f a c t was more a r e f l e c t i o n of th e s t u d y ' s technique r a t h e r than the d i s p o s i t i o n s of the i n d i v i d u a l s . Interview ing procedures were a ls o blamed. More r e c e n t l y Dillon and Scandizzo (1978) recognized the need to examine socioeconomic c h a r a c t e r i s t i c s as they r e l a t e to r i s k pr e f e r e n c e s . They used a sample o f 130 small farmers who e i t h e r owned o r sharecropped in n o r t h e a s t B r a z i l . Using the expected u t i l i t y approach they e l i c i t e d the u t i l i t y f u n c tio n s o f t h e s e farmers in two c a se s. The f i r s t involved payoffs above s u b s is te n c e l e v e l s , thus i n s u r in g s u b s i s t e n c e ; and the second included the p o s s i b i l i t y o f not reaching s u b s is t e n c e l e v e l s o f income. Each farmer was given a choice between a r i s k y and s a f e p r o j e c t and t h e cash r e t u r n was va ried u n t i l , in most c a s e s , the po in t of i n d i f ­ fe r e n c e was achieved. In th e o t h e r cases assumptions were necessary to 13 determine the c e r t a i n t y e q u iv a le n t . On t h i s basis th e farmers were c l a s ­ s i f i e d as r i s k - a v e r s e , r i s k - l o v i n g or r i s k - n e u t r a l . They then used l i n e a r , q u a d ra tic and exponential u t i l i t y models to e stim ate r i s k a t t i ­ tude c o e f f i c i e n t s . With t h e exception o f the exponential model, they found t h a t on the average both owners and sharecroppers were more than r i s k - a v e r s e when s u b s is t e n c e was a t r i s k than when i t was assu red . When s u b s is t e n c e was assured a g a i n , with the exception o f the exponential model, owners appeared to be more r i s k - a v e r s e than sh a recroppers. They a ls o s t a t e with r e s p e c t to the exponential u t i l i t y model t h a t no strong d i f f e r e n c e s in r i s k a t t i t u d e s e x i s t . They go on to poin t out the need to co n sid er the magnitudes o f r i s k p references r a t h e r than re l y i n g on c l a s s i f i c a t i o n o f producers as e i t h e r r i s k - a v e r t e r s o r r i s k - p r e f e r e r s . They a ls o note t h a t conclusions about r i s k a t t i t u d e s a re highly c o n t i n ­ gent upon the type o f fun ction al form t h a t i s f i t t e d to the u t i l i t y func­ tion. Further a n a l y s i s by Dillon and Scandizzo suggests t h a t socioeconomic c h a r a c t e r i s t i c s may account f o r some o f the v a r i a t i o n s in r i s k a t t i t u d e s . They examined farm ers' age, income, household s i z e and e t h i c a l a t t i t u d e toward b e t t i n g . Using l i n e a r and qua d ra tic models they estimate d equa­ t i o n s to determine th e impact t h a t th es e socioeconomic v a r i a b le s have on risk attitudes. Again c o n f l i c t s arose between the l i n e a r and q u a d ra tic models, f u r t h e r evidence o f the importance o f s e l e c t i n g fun ctio n al forms. They conclude t h a t income level and perhaps o t h e r socioeconomic v a r i a b le s in flu e n ce farmers' r i s k p r e f e r e n c e s . While an attempt was made to examine th e impact o f a t t r i b u t e s on r i s k p r e f e r e n c e s , Dillon and Scandizzo 's e f f o r t did l i t t l e t o p o in t out 14 th e c r i t i c a l natu re o f the assumptions of t h e f u nction al forms o f the u t i l i t y fu n ctio n . Also o f i n t e r e s t i s t h a t s e l e c t i o n o f socioeconomic v a r i a b l e s was based p r i m a r il y on easy a c c e s s i b i l i t y . The e x -p o s t natu re o f the a n a ly sis precluded th e use o f o t h e r a t t r i b u t e s t h a t could and pos­ s i b l y should have been used in the a n a l y s i s . Again i t i s worth noting t h a t a u t i l i t y fu n c tio n approach was used in t h i s study. H a l te r and Mason (1978) provided one o f the most r e c e n t s t u d i e s on a t t r i b u t e prefe re nce r e l a t i o n s h i p s . They d e sc r ib e t h e i r recommended method o f e l i c i t i n g a u t i l i t y fu n ctio n as such. By holding p r o b a b i l i t i e s c o n s t a n t and varying income, p oin ts o f i n d i f f e r e n c e were o b tain ed . Then, through subsequent q u e s t i o n s , u t i l i t y f u n c tio n s were c o n s t r u c t e d . A f te r they pres ented t h e i r s i n g le - v a lu e d u t i l i t y fun ction approach, they attempted to demonstrate t h a t estim ated decision-makers u t i l i t y f u n c t i o n s could be used to determine i f r i s k a t t i t u d e s a re r e l a t e d to farm and producer c h a r a c t e r i s t i c s . Their sample c o n s i s t e d o f 11 grass seed farmers who opera ted farms in Willamette Valley, Oregon. They s t a t e t h a t due to lack o f precedence, t h e r e is l i t t l e t h e o r e t i c a l b a s i s upon which to hypothesize r e l a t i o n s h i p s . Consequently they r e l i e d on r e g r e s ­ sion models to s o r t ou t important c h a r a c t e r i s t i c s in both a step-wise add and d e l e t e manner. The dependent v a r i a b le used was the c o e f f i c i e n t of a b s o l u te r i s k aversio n which i s defined as th e ne gativ e r a t i o o f the second d e r i v a t i v e to the f i r s t d e r i v a t i v e o f the u t i l i t y f u n ctio n e v a l u ­ a te d a t the respondents income l e v e l . A f t e r st e p -w ise add and d e l e t e r e ­ g r e s s i o n , the s i g n i f i c a n t v a r i a b l e s l e f t were: education l e v e l , and age. p e rc ent of land owned, No mention is made o f the o t h e r v a r i a b l e s analyzed, so l i t t l e i s known about the comprehensiveness o f the study. 15 Once the t h r e e s i g n i f i c a n t v a r i a b l e s were i d e n t i f i e d , l i n e a r and quadra­ t i c a n a l y s i s were performed. They found g r e a t e r r i s k preference among higher educated farmers as p e rc en t of ownership in c r e a s e d . Lower educated farmers demonstrated g r e a t e r r i s k aversion with i n c r e a s in g l e v e l s o f ownership. They a ls o found r i s k aversion i n c r e a s e s with i n c r e a s in g age f o r higher educated farmers and decrease s with lower education l e v e l s . When age and percent ownership a r e analyzed j o i n t l y , i t was found t h a t r i s k pre ferences i n ­ c re as e with age f o r a l l l e v e l s o f p ercen t ownership with the exception o f o l d e r farmers. In e f f e c t the Halter-Mason study found t h a t age, edu­ c a t i o n , and percentage of land owned, e i t h e r s e p a r a t e l y or j o i n t l y , were s t a t i s t i c a l l y s i g n i f i c a n t v a r i a b l e s r e l a t e d to r i s k a t t i t u d e s . concluded t h a t : They " F i n a l l y , f u r t h e r empirical work needs t o be done with r e s p e c t to monetary l o s s e s and how to o b t a i n the u t i l i t y fu nction and i t s im p l i c a ti o n s across both gains and l o s s e s . " I t i s worth noting t h a t the a b solu te r i s k aversion c o e f f i c i e n t u t i l i z e d as the dependent v a r i a b l e in t h e i r a n a l y s i s was a t only one l e v e l , t h a t being the farmers' level o f income. No comparisons were made f o r negativ e income o r l o s s e s nor was r i s k aversion examined a t o t h e r l e v e l s o f income, which given the s t o c h a s t i c n a tu r e o f p r i c e s and production could e a s i l y be a p p l i c a b l e . In o t h e r words, they used a r i s k aversion p o in t r a t h e r than a r i s k a v e r ­ sion f u n c tio n . Moscardi and de Janvry (1977) have a ls o r e l a t e d behavior to r i s k with socioeconomic and s t r u c t u r a l v a r i a b l e s by studying a sample of pe asant households in Mexico. Rather than using the d i r e c t approach of d i r e c t l y e l i c i t i n g u t i l i t y f u n c t i o n s , they p r e s e n t and u t i l i z e an i n d i ­ r e c t approach. This approach i n v o lv e s, given a production fu n ctio n and 16 a s s o c i a t e d marginal value pro du cts, the comparison of actual f e r t i l i z e r a p p l i c a t i o n s with those t h a t a r e a t an economic optimum. They then r e ­ l a t e r i s k aversion to socioeconomic c h a r a c t e r i s t i c s o f peasant households. By using d i s c r im i n a n t a n a l y s i s and re g r e ss io n a n a l y s i s they found t h a t t h e i r r e s u l t s generated support f o r the hypothesis t h a t r i s k bearing c ap a city o f peasants could be explained by c e r t a i n c h a r a c t e r i s t i c s . They found land under c o n t r o l , o f f - f a r m income, and membership in a s o l i d a r i t y group were s i g n i f i c a n t ; however, age, sc hoolin g, and family s i z e were not significant. The signs o f the estim ated r e l a t i o n s h i p g e n e r a l l y agreed with t h e i r hypotheses. The ne gativ e r e l a t i o n s h i p between r i s k aversion and land under control and o f f - f a r m income a re c o n s i s t e n t with the hypo­ t h e s i s o f decreasi ng a b so lu te r i s k aversion with r e s p e c t t o wealth. They a ls o found a negative r e l a t i o n with r e s p e c t to r i s k and group membership. A s i m i l a r study by Binswanger (1978) examined the r e l a t i o n s h i p o f c h a r a c t e r i s t i c s with r i s k preferences using a sample of peasant farmers in ru ral In d ia. These r e s u l t s found t h a t wealth had l i t t l e e f f e c t on r i s k aversion while sc hooling tended to reduce a v er sio n . Sex, p r o g r e s­ s i v e n e s s , dependency r a t i o , amount of land r e n t e d , and age had a l e s s c l e a r impact, i f any, on r i s k p r e f e r e n c e s . While t h e s e s t u d i e s are i n t e r e s t i n g , several c r i t i c i s m s seem j u s t i ­ fied. F i r s t the work o f Scandizzo and Dillon (1978), Moscardi and de Janvry (1977), and Binswanger (1978) were a l l performed in l e s s developed c o u n tr i e s with peasants comprising the samples. Given the v a s t d i f f e r e n c e s t h a t e x i s t between th e p e a s a n t s ' environment and t h a t p res en t in the U.S commercial a g r i c u l t u r a l s e c t o r , any g e n e r a l i z a t i o n s between these e n v ir on ­ ments would c e r t a i n l y r e q u i r e a g r e a t leap o f f a i t h . 17 The second c r i t i c i s m i s t h a t given the work necessary f o r each study, i t would seem a p p r o p r i a t e t h a t as many a t t r i b u t e s as p o s s i b l e should be recognized and analyzed. As d isc u sse d , some cases based s e l e c t i o n of a t t r i b u t e s t o be considered on e x i s t i n g d a ta . The t h i r d and most important c r i t i c i s m i s methodology employed. Previous r e s e a r c h f o r the most p a r t has r e l i e d on measuring u t i l i t y func­ t i o n s and then d e r i v i n g r i s k aversion measurements from the u t i l i t y func­ tion. art. This tec hnique was c e r t a i n l y j u s t i f i a b l e given the s t a t e o f the However, many r e s e a r c h e r s have noted the need to r e f i n e techniques in t h i s a r e a , and t h e i r concerns a r e q u i t e v a l i d . Hypothetical questio n s used to e l i c i t u t i l i t y functions q u i t e p o ssib ly y i e l d responses t h a t w ill not agre e with a ctu al d e c i s i o n s . As d i s c u s s e d , d i r e c t e l i c i t a t i o n o f u t i l i t y fu n ctio n s by inte rv ie w procedures a r e designed to determine p o in ts of i n d i f f e r e n c e between a r i s k y and a c e r t a i n outcome. Once t h e s e poin ts o f i n d i f f e r e n c e a r e d e t e r ­ mined the u t i l i t y f u n ctio n i s f i t t e d by means o f r e g r e s s i o n . The methodology i s c r i t i c i z e d as a source o f bias f o r several r e a ­ sons. Some people have a real aversion to gambling. In o t h e r words, people, when given an op tio n o f a gamble and a su re income, may avoid the gamble in a hy p o th etica l s e t t i n g when, in f a c t , they undertake many gambles in real l i f e . The von Neumann-Morgenstern model i s such an example sin c e i t has a bias f o r the u t i l i t y and d i s u t i l i t y o f gambling. Dillon and S can d iz zo 's work (1978) f u r t h e r emphasizes th e need f o r c o r­ r e c t i n g t h i s shortcoming. In t h e i r sample o f Brazil farmers 30 percent believed t h a t gambling was immoral and 80 perc ent had never gambled. 18 With several methods the problems a ss o c i a t e d with d i s t i n g u i s h i n g between p r o b a b i l i t i e s e x i s t . In o t h e r words, does a decision-maker change choices when p r o b a b i l i t i e s a r e changed by small increments and, i f so, a t what point? S e le c tio n o f the proper f u n ctio n al form i s a ls o an area to open to c r i t i c i s m and o f t e n leads to u n d e sirab le im p licatio n s (Lin and Chang , 1978). In some i n s t a n c e s d i f f e r e n t f u nction al forms lead to i n c o n s i s t e n t results. F i n a l l y , the d i r e c t e l i c i t a t i o n o f u t i l i t y fun ction approach i s not only u n i n t e r e s t i n g f o r th e respondent but i t i s d i f f i c u l t to conduct. Consequently many r e s e a r c h e r s use i n te r v ie w teams to e l i c i t the informa­ t i o n from the samples. As a r e s u l t se vere in te rv ie w e r r o r s and i n t e r ­ viewer bias may occur. Most methods o f e l i c i t i n g u t i l i t y fun ctio n s from decision-makers have one o r more o f the p rev io u s ly mentioned weaknesses. O f f i c e r and H a l te r (1968) analyzed t h e von Neumann-Morgenstern model, a modified von Neumann-Morgenstern model and the Ramsey model. They compared each f o r i t s a p p l i c a b i l i t y to th e real world and discu ss the a s s o c i a t e d weaknesses o f each model. They conclude t h a t c u r r e n t c r i t i c i s m s will n o t be a l l e v i a t e d by generatin g new t h e o r i e s o f u t i l i t y a n a l y s i s , but r a t h e r the more pro ductive mode o f o p e ra tio n i s to f u r t h e r t e s t e x i s t i n g theories, Regardless o f t h i s f a t a l i s t i c philosophy, t h e r e e x i s t s a need to develop a new technique in de riv ing r i s k p r e f e r e n c e s . The shortcomings o f d i r e c t l y e l i c i t i n g u t i l i t y fu n c t i o n s a r e too g r e a t to ig nore. Given t h a t few o t h e r methods e x i s t e d as p r e c e d e n ts, i t i s not d i f f i c u l t to understand why s i n g l e - v a lu e d u t i l i t y f u n c tio n s were used even in s p i t e 19 of c r i t i c i s m s . I t a ls o suggests a p o s s ib l e reason why a d d it i o n a l work has n o t been conducted in the a t t r i b u t e - p r e f e r e n c e r e l a t i o n s h i p . Re­ se arc h ers in t h i s area were cognizant o f the weaknesses and were apolo­ g e t i c regarding t h e i r methodology choice. C e r ta in ly o th e r s recognized the shortcomings o f t h i s approach and t h e r e f o r e s h i f t e d t h e i r research e f f o r t s to o t h e r a r e a s . As suggested e a r l i e r , t h e r e appears to be an a l t e r n a t i v e to th e d i r e c t e l i c i t a t i o n o f u t i l i t y fun ctio n methodology. That a l t e r n a t i v e methodology, as well as empirical evidence o f i t s super­ i o r i t y , will be disc ussed in Chapter I I I . CHAPTER I I I THEORETICAL APPROACH AND METHODOLOGY 3.1 The I n t e r v a l Method As discu ssed in Chapter I I , previous research in the a t t r i b u t e - p r e ­ f e r e n c e area has ignored severa l a t t r i b u t e s as well as r e l i e d upon e s ­ t a b l i s h i n g a u t i l i t y functio n from which r i s k aversion was determined. Several c r i t i c i s m s a r e j u s t i f i e d when d ealin g with a d i r e c t l y e l i c i t e d , s i n g l e - v a lu e d u t i l i t y f u n c t i o n . To a l l e v i a t e t h es e problems a new metho­ dological approach was developed which d i r e c t l y measures the r i s k a v e r ­ sion f u n c t i o n . This d i r e c t measurement o f r i s k aversion f u n c tio n s was developed by King and Robison (1979). Not only does t h i s approach have t h e advantage o f d i r e c t l y measuring r i s k p r e f e r e n c e s , i t a ls o does so in a manner which c o n s t r u c t s an i n t e r v a l f o r the range o f r i s k aversion functions. When u t i l i t y f u n c t i o n s a re used the r i s k aversio n fun ction i s si n g l e - v a lu e d j u s t as the u t i l i t y fun ctio n from which i t i s de rived is. There seldom i s a p e r f e c t f i t when e stim a tin g a u t i l i t y f u n c t i o n ; however, the a s s o c i a t e d r i s k av ersion f u n ctio n a c t s as i f t h e r e i s . The methodology used here allows f o r assig n in g an i n t e r v a l to the range o f r i s k aversion f u n c t i o n s . King and Robison (1979) u t i l i z e s t o c h a s t i c dominance with r e s p e c t to a fun ction to o r d e r a c t io n choices o f decision-makers. 20 Rather than 21 r e l y i n g on u t i l i t y f u n c t i o n s , an e f f i c i e n c y c r i t e r i o n i s used. The e f ­ f i c i e n c y c r i t e r i o n t h a t i s used i s s t o c h a s t i c dominance. There a re t h r e e degrees of s t o c h a s t i c dominance. F i r s t degree s t o ­ c h a s t i c dominance implies second degree s t o c h a s t i c dominance and t h i r d degree s t o c h a s t i c dominance. Second degree s t o c h a s t i c dominance implies t h i r d degree s t o c h a s t i c dominance. F i r s t degree s t o c h a s t i c dominance (FSD) implies the p r o b a b i l i t y fu n ctio n f(y) dominates (o r i s p r e f e r r e d to) g(y) by FSD i f , and only i f : F.|(y) i G - , ( y ) f o r a l l y e [ a , b ] with F](y) < G-j(y) f o r a t l e a s t one value o f y. FSD r e q u i r e s t h a t th e marginal u t i l i t y o f income plus wealth U(y) be p o s i t i v e . U'(y) > 0. Second degree s t o c h a s t i c dominance implies the p r o b a b i l i t y function f( y ) dominates (or i s p r e f e r r e d to) g(y) by SSD i f and only i f : ' y* F2(y)dy <_ *y * G2 (y)dy I y *d Fo(y)dy < a /5* d a G9(y)dy f o r a l l y* e [ a , b ] with f o r a t l e a s t one value ofy. SSD r e q u i r e s the decision-maker to be everywhere r i s k a v erse , t h a t is: U'(y) > 0 and U"(y) < 0. Third degree s t o c h a s t i c dominance (TSD) r e q u ir e s t h a t UI M (y) > 0; i . e . , decreasing r i s k a v er sio n . TSD i s not u t i l i z e d in King's (1979) methodology as he fin d s FSD and SSD s u f f i c i e n t f o r h i s purposes. FSD and SSD can be demonstrated g r a p h i c a l l y . FSD means t h a t the cumulative d e n sity f u n ctio n o f the p r e f e r r e d s t r a t e g y l i e in p a r t to the r i g h t and no where to th e l e f t o f the cumulative d e n sity fu nction f o r th e dominated prosp ect (Figure 3 . 1 ) . When the cumulative d e n s i ty fu nctions f o r prospects i n t e r s e c t then SSD must be examined. For example, Figure 3.2 e x h i b i t s no FSD. Since FSD c o nd itio n f a i l e d we now t e s t f o r SSD ' y*F(y)dy - ^y *G(y)dy <_ 0 o r in t h i s case [ ' CF(y)dy - ' cG(y)dy] + 1 F(y)dy - ' YlG(y)dy] <_0. With r es p ec t to Figure 3 . 2 , the f i r s t term i s the negative o f area A with th e second term equal to area B. In t h i s i n s t a n c e , F(y.) dominates G(y) by SSD since are a A i s g r e a t e r than are a B. Above y ^ , F(y) is always below G(y), so th e accumulated area under F(y) continues to be l e s s than t h a t under G(y). Since SSD r e q u i r e s diminishing marginal u t i l i t y [U"(y) < 0] the u t i l i t y gain from the reduced p r o b a b i l i t y of low payoffs rep resente d by area A must be l e s s than the u t i l i t y loss a s s o c i a t e d with the higher p r o b a b i l i t y o f in te rm e d iate outcomes r e p r e ­ sented by area B s i n c e A >^B and the marginal u t i l i t y o f y i s g r e a t e r in the i n t e r v a l [ a , c ] than the i n t e r v a l [ c , y ] . Two c r i t i c i s m s can be made a g a i n s t SSD (King, 1979). The f i r s t is t h a t i t requ ire s decision-makers to be everywhere r i s k - a v e r s e , and second SSD i s not always a d i s c r im i n a t o r y t o o l . With t h i s in mind King (1979) attempted to e li m in a te th es e c r i t i c i s m s by u t i l i z i n g s t o c h a s t i c dominance with r e s p e c t to a f u n c t i o n . With t h i s technique lower and upper bounds a r e put on the r i s k aversi on fu nction r( y ) defined as: 23 1 F(y); G(y) G(y) ^ FIGURE 3.1 F i r s t Degree S t o c h a s t i c Dominance o f G(y) by F(y) G(y) a c y FIGURE 3.2 I n t e r s e c t i n g Cumulative D i s t r i b u t i o n s Which Violate F i r s t Degree S t o c h a s ti c Dominance Requirements b 25 FSD and SSD then become two sp e cia l cases with r^(y) = -°° and ^ ( y ) = 00 f o r FSD and r-j(y) = 0 and r 2(y) = °° f o r SSD. By allowing the i n t e r v a l to take any shape th e c r i t i c i s m s o f the sp e cia l cases a r e e li m in a te d . S t o c h a s t i c dominance with r e s p e c t to a f u n c t i o n , as developed by Meyer (1977), i s a much more powerful tool in o r d in a r y a c t i o n choices than e i t h e r FSD o r SSD. This technique ord ers u n c e r ta in a c tio n choices f o r a decision-maker who possesses a c e r t a i n lower and upper bound, r^ (y ) and ^ ( y ) * on his a b s o l u te r i s k aversion f u n c t i o n . These upper and lower bounds then d e f i n e an i n t e r v a l measurement o f r i s k p r e f e r e n c e s . The appea ling f e a t u r e o f t h i s i n t e r v a l measurement once obtained is t h a t i t allows us to o r d e r a c t i o n cho ices . shape o f the f u n c t i o n . I t imposes no assumptions on the Consequently i t can be as narrow ( p r e c i s e ) or wide (imprecise) as d e s i r e d . Furthermore, t h i s i n t e r v a l can take any shape and thus no r e s t r i c t i v e assumptions about r i s k aversion a r e neces­ sa r y . In o t h e r words, r a t h e r than assuming the shape o f the f u n c t i o n , the shape i s determined by the decisio n -m a ker's p r e f e r e n c e s . As a r e s u l t r i s k - l o v i n g [n eg a tiv e r ( y )] as well as r i s k - a v e r s e [ p o s i t i v e r ( y ) ] be­ havio r is accounted f o r . This i s done by i d e n t i f y i n g a u t i l i t y fun ction U(y) which minimizes g 1CG(y) - F(y)] U'(y)dy s u b j e c t to t h e c o n s t r a i n t ^(y) ± U"(y) / U'(y) < r 2( y ) ; y e [ 0 , 1 ] . In e f f e c t the d i f f e r e n c e in the expected u t i l i t i e s between F(y) and G(y) i s minimized. I f the minimum i s z e r o , then F(y) and G(y) cannot be ordered and i n d i f f e r e n c e i s e s t a b l i s h e d . then prefe ren c e cannot be e s t a b l i s h e d and When the minimum i s ne gativ e 26 £ [F(y) - G(y)] U1(y)dy i s minimized s u b j e c t to the same c o n s t r a i n t a lre ad y mentioned. d i f f e r e n c e i s p o s i t i v e , G(y) i s p r e f e r r e d to F(y). If this I f the d i f f e r e n c e is n e g a t iv e , o r d e r in g i s not p o s s ib l e given the de c isio n - m a k e r 's p r e f e r e n c e s . By u t i l i z i n g optimal control techniques Meyer developed a program to o r d e r a c t i o n choices .^ However, t h i s assumed t h a t decision-makers' i n t e r v a l s were known which i s not the case . a l i z e d Meyer's program f o r h i s own needs. King (1979) then o p e r a t i o n ­ Given t h a t a r i s k aversion i n t e r v a l will enable one to o r d e r a c tio n c h o ic e s , King r e a l i z e d t h a t comparisons and p r e f e r e n c e o f a c t io n choices allow one to e s t a b l i s h a r i s k a versio n i n t e r v a l . programs. With t h i s in mind he developed several computer The f i r s t program, NORGEN, generates a s e t o f normal random sample d i s t r i b u t i o n s with a predetermined mean, v a r i a n c e , and number o f elements. The second program, INTID, then tak es t h e s e d i s t r i b u t i o n s and determines what s p e c i f i e d s e t o f i n t e r v a l s s e p a r a t e th es e plans. These two programs are nece ssary to e s t a b l i s h th e q u e s t i o n n a i r e t h a t w ill be used to e l i c i t the r i s k i n t e r v a l . Once t h i s t a s k i s accomplished and th e r i s k i n t e r v a l i s known, t h i s i n t e r v a l can be fed i n t o the t h i r d pro­ gram, UFUNC, which g e n erate s the u t i l i t y fu nctio n o f the decision-maker. Using t h i s fun ctio n in th e f o u r t h program, NSTDO, th e a c t io n choices under c o n s i d e r a t i o n can be o rd ere d . Consequently, g e n e r a tio n o f sample d i s t r i b u t i o n s i s the f i r s t s t e p . The u se r o f NORGEN must s p e c i f y th e mean, stan d ard e r r o r , number o f V o r a complete e x p la n a t i o n , see King (1979). 27 d i s t r i b u t i o n s d e s i r e d , and number o f elements in each d i s t r i b u t i o n . The second s t e p , which involves the se p a r a tio n o f d i s t r i b u t i o n s by r i s k i n ­ t e r v a l s , r e q u i r e s the s p e c i f i c a t i o n o f i n t e r v a l measurements. surement g r id used w ill be disc ussed l a t e r . The mea­ A f te r t h i s task i s accomplished the c o n s t r u c t io n o f the q u e s t io n n a ir e can proceed. The approach i s an i t e r a t i v e one. By using an i t e r a t i v e approach the r i s k aversion i n t e r v a l can be c o n str u cted by comparisons o f those carefully selected pairs of d is trib u tio n s . Construction o f the i n te r v a l measurements o f decision- makers' a bso lute r i s k aversion fu nction i s based on t h e premise t h a t a choice between d i s t r i b u t i o n s divid es r i s k aversion between two spaces: with i t . one c o n s i s t e n t with the choice and one i n c o n s i s t e n t Since the p r o p e r t i e s o f the d i s t r i b u t i o n s d e fin e the two r eg io n s , the level o f r i s k aversion depends s o l e l y on the two d i s t r i b u t i o n s being compared. By re p e a t e d ly comparing d i s t r i b u t i o n s the s i z e o f the i n t e r ­ val can be reduced. With each choice a po rtio n o f the a b so lu te r i s k aversion i n t e r v a l e s t a b l i s h e d in the previous comparison i s e li m in a te d , since i t i s i n c o n s i s t e n t with the d ecisio n-m aker's revealed p r e f e r e n c e s . This procedure continues u n t i l the d e s i r e d level o f p r e c i s i o n i s a t t a i n e d . This i s done a t each o f the r e l e v a n t income l e v e l s and then by connecting known portio n s o f the upper and lower bounds the e n t i r e r i s k aversion fun ctio n can be c o n s t r u c t e d . This procedure i s demonstrated in Figure 3.3. Suppose an indiv idual was given a choice between D i s t r i b u t i o n A and D i s t r i b u t i o n B. s e l e c t e d than r( y ) l i e s below p o i n t x. I f A is Depending on the f i r s t response the individua l i s asked to choose between two more d i s t r i b u t i o n s , C and D. I f C i s chosen, then r ( y ) upper and lower a re po ints x and s r es p ec ­ tively. I f D i s chosen t becomes the new upper bound and the process 28 r(y) +00 B .X .y A c .t .s D —oc FIGURE 3. 3 Reduction o f In te r v a l Size 29 continues to e s t a b l i s h the bounds. Then by changing the values o f the d i s t r i b u t i o n and thus moving along the h orizon tal axis the process con­ tinues. By connecting the po ints on the upper and lower bounds horizon­ t a l l y th e a b so lu te r i s k i n t e r v a l fu n ctio n i s e s t a b l i s h e d . Once th es e bounds have been e s t a b l i s h e d they can then be used to p r e d i c t which a c t io n choices w ill be followed. Each indiv idual i s assigned a range and t h e s e ranges u su a lly d i f f e r from one indiv idual t o th e next. The d e cisio n -m a k er's prefe renc es determine the level and shape o f t h i s i n t e r v a l function and thus no assumptions about decision-maker p r e f e r ­ ences a re r eq u ire d . 3.2 Empirical Test of I n t e r v a l Approach In th e previous c hap ter a l i t e r a t u r e review was provided summarizing work done in the p r e f e r e n c e - a t t r i b u t e r e l a t i o n s h i p a r e a . The major c r i ­ t i c i s m o f th es e s t u d i e s was the use o f a s i n g l e - v a lu e d u t i l i t y function approach. The need f o r a new methodology was recognized and disc usse d and the i n t e r v a l methods j u s t pres ented was o f f e r e d as a s u p e r i o r t e c h ­ nique. In l i g h t o f the c r i t i c i s m s le v e le d a t the methodologies employed in previous s t u d i e s and the development o f the i n t e r v a l method as a s u p e r i o r a l t e r n a t i v e , i t seems only reasonable t h a t an empirical j u s t i ­ f i c a t i o n follow. 3.3 Experimental Design Ten gradua te stu d e n ts from the Department o f A g r ic u ltu r a l Economics a t Michigan S t a t e U n ivers ity (MSU) were sampled. These stu d e n ts were chosen on the b a sis o f t h e i r knowledge o f the th eo ry. Since several courses tau g h t a t MSU deal with r i s k and u n c e r t a i n t y and s t o c h a s t i c 30 dominance, an attempt was made to s e l e c t stu d e n ts with l i t t l e o r no ex­ posure to th ese concepts. In s e t t i n g up t h i s experiment two tasks were necessary. The f i r s t was to determine the income range over which r i s k aversion should be measured. While any number o f income ranges can be s e l e c t e d , i t was found t h a t t h r e e income l e v e l s were s u f f i c i e n t . Since the sample was composed o f graduate s t u d e n t s , the income ranges were: $ 9 ,0 0 0 - $ l1,000, and $16,000-$18,000. $2,000-$4,000, The f i r s t two l e v e l s were chosen sin c e they r e p r e s e n t a o n e - q u a r t e r , o n e - h a l f , or t h r e e - q u a r t e r time gradua te a s s i s t a n t appointment. one form o f t h i s funding. All people in the sample were r e c e i v i n g The t h i r d level was s e l e c t e d to r e p r e s e n t the income level o f t h e s e i n d i v i d u a l s i f they were t o e n t e r the job market, i . e . , t h e i r o p p o r tu n ity c o s t , Consequently, t h e s e t h r e e l e v e l s o f an- naul income r e f l e c t e d income most c o n s i s t e n t with the i n d i v i d u a l s ' l i f e ­ s t y l e s and thus were easy f o r them to r e l a t e t o . The second t a s k to be accomplished p r i o r to conducting t h i s e x p e r i ­ ment was to s e t up the measurement g r i d . This g r id e s t a b l i s h e s the r i s k av ersion i n t e r v a l to be determined f o r each indiv idual a t each o f the t h r e e income l e v e l s . The g r i d t h a t was s e l e c t e d is presented in Table 3.1. This g r i d i s both p r e c i s e and complete in t h a t the extreme values a r e very r i s k - l o v i n g and r i s k - a v e r s e - - s o much so t h a t the r i s k premium as approximated by tt _ - a 2 X F becomes u n r e a l i s t i c a l l y h ig h, sugge sting t h a t few i f any would f a l l out o f t h i s range. 31 TABLE 3.1 Absolute Risk Aversion Levels Defining Measurement Grid .010000 .005000 .002500 .001500 .001000 .000800 .000600 .000400 .000300 .000200 .000100 0.000000 -.000100 -.000250 -.000500 -.001000 32 Once t h i s t a s k was completed 40 Monte Carlo d i s t r i b u t i o n s were _ ? g e n e r a te d , with x = 0 and o = 500. Then, by u t i l i z i n g the pr eviously d iscu ssed s t o c h a s t i c dominance with r e s p e c t to a f u n c t i o n , each o f th es e d i s t r i b u t i o n s were s e p a r a te d from one anoth er by an i n t e r v a l . In o t h e r words a decision-maker, making p a ir - w i s e comparisons, who p r e f e r r e d one d i s t r i b u t i o n would l i e above the lower bound o f the i n t e r v a l while a decision-maker who s e l e c t e d th e o t h e r d i s t r i b u t i o n would l i e below the upper bound. Using the previo usly discussed i t e r a t i v e approach t h i s allowed a narrowing o f t h i s i n t e r v a l , thus achieving any d e sir e d level o f preciseness. P r i o r to making any comparisons a l l t h a t i s known i s t h a t the r i s k av ersio n c o e f f i c i e n t i s bounded by negativ e o r p o s i t i v e i n f i n i t y . A f te r t h e f i r s t comparison a new upper or. lower bound can be e s t a b l i s h e d . a f t e r one q u e stion decision-makers f a l l i n to one o f two i n t e r v a l s . Thus, Sub­ sequent questio n s allow placement o f the i n t e r v a l in one o f f o u r , e i g h t , or sixteen in te rv a ls. Each respondent was asked to complete a f i v e - p a r t q u e s t io n n a ir e . The f i r s t t h r e e s e c t i o n s contained f i f t e e n qu e stio n s each, and respondents were i n s t r u c t e d to respond to f ou r q u e stio n s in each s e c t i o n . In an i t e r a t i v e process t h es e t h r e e p a r t s narrowed in on th e r i s k aversion i n ­ t e r v a l a t each o f the t h r e e prev io u s ly disc ussed income l e v e l s . The f o u r t h s e c t i o n o f the q u e s t i o n n a i r e was a d i r e c t e l i c i t a t i o n o f the i n ­ d i v i d u a l ' s u t i l i t y f u n c t i o n , a methodology s i m i l a r to previous s t u d i e s in the are a o f p r e f e r e n c e - a t t r i b u t e r e l a t i o n s h i p s . The f i f t h p a r t asked each respondent to make s i x p a ir - w i s e comparisons o f income l e v e l s over the e n t i r e range of incomes, i . e . , $2,000-$18,000, This was done in 33 such a way t h a t each respondent chose the one income d i s t r i b u t i o n level t h a t they most p r e f e r r e d . An attempt was made to g e t the respondents to r e l a t e t h i s to t h e i r own circumstances. In each p a ir - w i s e comparison the d i s t r i b u t i o n con­ ta i n e d s i x elements r e p r e s e n t i n g s i x d i f f e r e n t income l e v e l s . Each e l e ­ ment was e qu ally l i k e l y to occur; thus i t was e q u iv a le n t to r o l l i n g a d ie to determine an i n d i v i d u a l ' s annual income l e v e l . In completing th e s e q u e s t io n n a ir e s each respondent was informed t h a t one element o f th e chosen d i s t r i b u t i o n would be h i s / h e r income level f o r a y e a r . They were asked to c on sider what they would do i f they received a ."good" or "bad" outcome. "Bad" outcomes would n e c e s s i t a t e borrowing, l i q u i d a t i n g a s s e t s , o r drawing on savin gs. "Good" outcomes would allow f o r the pur­ chase o f a d d it i o n a l a s s e t s , savin g, o r l i q u i d a t i o n d e b ts . In o t h e r words each respondent was asked to c on sider what they would do, thus drawing a r e l a t i o n s h i p between t h i s experiment and the i n d i v i d u a l ' s own circumstances. 3.4 Analysis Of the ten q u e s t i o n n a i r e s , nine were properly completed and return e d . This allowed the p r e d i c t i o n o f 54 a c t i o n choices with both the r i s k i n ­ t e r v a l method and the s i n g l e - v a lu e d u t i l i t y f u n c t i o n . The f i r s t p a r t o f the a n a l y s i s was to use the i n t e r v a l e s t a b l i s h e d e a r l i e r to p r e d i c t which a c t i o n choices would be s e l e c t e d over the e n t i r e income range. S i m i l a r l y , the same t a s k was completed with the s i n g l e ­ valued u t i l i t y f u n c tio n . te re stin g insights. The r e s u l t s shown in Table 3.2 o f f e r some i n ­ 34 TABLE 3.2 Empirical Results o f Action Choice P r e d i c t io n s Using I n terva l Risk Measures and a U t i l i t y Function Nurtiber o f Questions Percent of I n c o r r e c t P re d ictio n s Percent Un-Ordered Percent Ordered U ti1i ty Function 1 2 3 4 2% 12% 22% 28% 90.735 50% 16.7% 9.3% 0% 9.3% 50% 83.3% 90.7% 100% 35% As seen in Table 3 . 2 , the u t i l i t y fu n ctio n i s 65 p ercen t a c c u ra te in i t s p r e d i c t i v e power while i t i s able to o rder a l l d i s t r i b u t i o n s . The i n t e r v a l method i s 98, 88, 78 and 72 perc ent acc u ra te in i t s p r e d i c ­ t i v e power a f t e r one, two, t h r e e and f ou r q u e s t io n s , r e s p e c t i v e l y . In o t h e r words as we narrowed the i n t e r v a l s t o a higher level o f p r e c i s i o n , accuracy was given up in t h e p r e d i c t i v e c a p a b i l i t i e s . Also o f i n t e r e s t i s t h a t as th e number o f q u e stio n s used to d efin e the i n t e r v a l i n c r e a s e d , thus decreasing the width o f the i n t e r v a l , the number o f d i s t r i b u t i o n s t h a t could be ordered in c r e a s e d . As discussed e a r l i e r , the i n t e r v a l allows us to s e p a r a t e d i s t r i b u t i o n s i n to t h r e e groups: those unanimously p r e f e r r e d , th ose dominated, and those which f a l l within th e i n t e r v a l and thus cannot be o rd ered. The perc ent o f a c t io n choices unordered decreases as the i n t e r v a l i s narrowed. Several p oin ts a r e worth no tin g . F i r s t , the d i s t r i b u t i o n s used f o r p r e d i c t i o n s were very s i m i l a r and thus choices between d i s t r i b u t i o n s were very d i f f i c u l t f o r many. None o f the seven d i s t r i b u t i o n s could be e l i ­ minated with f i r s t degree s t o c h a s t i c dominance. Also, second degree s t o ­ c h a s t i c dominance which assumes an i n t e r v a l between zero and i n f i n i t y could o r d e r only 7.4 p e rc en t. Fu rther comparisons o f the i n t e r v a l method with second degree s t o ­ c h a s t i c dominance y i e l d e d i n t e r e s t i n g i n s i g h t s . SSD y i e l d e d a 98 perc ent accuracy r a t e while only o rd erin g 7.4 p ercen t o f th ese d i s t r i b u t i o n s — i n f e r i o r r e s u l t s to those obt ained a f t e r only one question with the i n ­ t e r v a l method. Of those d i s t r i b u t i o n s ord ere d , SSD was in e r r o r 25 p e r ­ c ent o f the time while the e r r o r percentage f o r one and two q ue stio ns f o r the same comparisons was 20 and 19 p e r c e n t , r e s p e c t i v e l y . Obviously t h i s 36 i s an example o f the problem confronted when making the assumption t h a t t h e r e i s decreasing a b so lu te r i s k aversion over wealth. With regard to t h i s p o i n t i t was found t h a t the i n d i v i d u a l ' s r i s k av ersio n i n t e r v a l s took no p a r t i c u l a r shape. As s t a t e d SSD assumes de­ c re as in g a b s o l u te r i s k a versio n over wealth and d i f f e r e n t functional forms o f u t i l i t y fu n c t i o n s suggest c o n stan t in c r e a s in g o r decreasing a b s o l u te r i s k a v er sio n . Our r e s u l t s do not demonstrate t h i s . Every i n t e r v a l was d i f f e r e n t and t h e r e was no c o n s i s t e n t shape--some had i n ­ c r e a s i n g then d e c r e a sin g , decre asing then i n c r e a s i n g , i n c r e a s i n g , de­ c r e a s i n g , and c o n s t a n t a b s o l u te r i s k aversion over wealth. Obviously one o f the a t t r a c t i v e f e a t u r e s o f th e i n t e r v a l method i s t h a t i t does no t make any assumptions about the shape o f the i n t e r v a l ; r a t h e r , i t l e t s the i n t e r v a l take whatever shape i s c o n s i s t e n t with the d e c i s i o n ­ makers' p r e f e r e n c e s . Robison and King (1978) d isc ussed the s i m i l a r i t i e s between s i n g l e ­ valued u t i l i t y and production f u n c t i o n s . J u s t and Pope (1978) suggested an unwillingness to assume t h a t production responses a re de sc ri bed by a s i n g l e - v a lu e d f u n c t i o n . Robison and King made s i m i l a r inf e r e n c e s to u t i l i t y fu n c t i o n s and suggested the i n t e r v a l method as a s u p e r i o r t e c h ­ nique. They j u s t i f i e d t h i s i n t e r v a l method s u p e r i o r i t y on th e b a s i s o f the h igh er degree o f r e a lis m a s s o c i a t e d with an i n t e r v a l as opposed to a s i n g l e - v a lu e d fu n ctio n , One would hypothesize t h a t as the level o f p r e c i s i o n in measuring p refe ren c es i n c r e a s e s , thus decreasing the width o f the i n t e r v a l , t h a t the accuracy de crea se s. Also, as the p r e c i s i o n i s i n c r e a s e d , the number o f o r d e r in g s would i n c r e a s e s in c e th e d i s t r i b u t i o n s are l e s s l i k e l y to f a l l within the i n t e r v a l . These empirical r e s u l t s support th e s e hypotheses. 37 At t h i s po int i t should be c l e a r t h a t the i n te r v a l method i s a more r e a l is ti c tool. However i t i s u ncle ar whether i t i s a s u p e r i o r tool to s i n g l e - v a lu e d u t i l i t y fu n c t i o n s where complete orderings a re d e s i r e d . In o t h e r words, the u t i l i t y fu nctio n was l e s s a c c u r a t e , but i t ordered every choice. To t e s t which tool was b e t t e r given i d e n t i c a l c o n d i t i o n s , a comparison was made o f th e accuracy r a t e f o r the d i s t r i b u t i o n s t h a t were ordered. To accomplish t h i s goal the p a i r s t h a t were ordered a f t e r each question were examined and then compared with the r e s u l t s obtained using the u t i l i t y f u n c t i o n . The r e s u l t s o f placing the i n t e r v a l and u t i l i t y f u n ctio n on the same level a r e presen ted in Table 3 .3 . In fou r o f the f i v e case s t e s t e d , the i n t e r v a l approach was s u p e r i o r in accuracy with r e s p e c t t o choosing among a c tio n cho ices . A f t e r one question both the u t i l i t y functio n and i n t e r v a l method were e q u iv a le n t . Consequently, th ese empirical r e s u l t s suggest the i n t e r v a l method i s not only a more r e a l i s t i c tool f o r e l i c i t a t i o n o f r i s k p r e f e r e n c e s , but a s u p e r i o r tool as well. This c o n s i d e r a ti o n i s magnified when one considers t h e e l i c i t a t i o n process i t s e l f . To e s t a b l i s h th e u t i l i t y fu nctio n the respondents had to complete nine q u e s t io n s . Three, s i x , nine and twelve q u e stio n s were nece ssary f o r the i n t e r v a l method f o r one, two, t h r e e and fou r q u e s t i o n s , respectively. Most respondents complained about the d i f f i c u l t y o f com­ p l e t i n g t h e u t i l i t y q u e s t i o n n a i r e while they enjoyed the i n t e r v a l method s i n c e they perceived i t as more r e a l i s t i c . As demonstrated, t h e r e e x i s t s a t r a d e - o f f between accuracy and the number o f o rd erin g s t h a t e x i s t . This t r a d e - o f f needs f u r t h e r i n v e s t i g a ­ t i o n , but i t i s s i m i l a r to recognizing th e t r a d e - o f f s between type I and type II e r r o r s in s t a t i s t i c a l a n a l y s i s . As Manderscheid (1965) suggested, 38 TABLE 3.3 Accuracy o f I n te r v a l Compared to U t i l i t y Function Approach Question 1 2 3 4 (P ercen t Correct) In te r v a l 80% 81.5% 73.3% 67.4% U t i l i t y Function 80% 74.0% 60.0% 61.0% 39 the l o s s e s a s s o c i a t e d with those e r r o r s , as well as t h e i r p r o b a b i l i t i e s , need to be recognized when determining where to s e t s i g n i f i c a n c e l e v e l s . A s i m i l a r type o f a n a l y s i s i s a p p r o p r i a te here. In o t h e r words, i f a high level o f o rderin g i s d e s i r e d and th e c o sts a s s o c i a t e d with e l i m i n a t ­ ing a p r e f e r r e d choice i s . s m a l l , then a very p r e c i s e measurement i s called for. On the o t h e r hand, i f accuracy i s very important and o r d e r ­ ing i s n o t , then a l e s s p r e c i s e i n t e r v a l measurement i s nece ssary. The i n t e r v a l method allows a g r e a t deal of f l e x i b i l i t y . Regardless o f the level o f accuracy d e s i r e d t h i s method g r e a t l y reduces t h e number o r a c t i o n choices c o n s i s t e n t with decision-makers p refe ren c es.. Given the design o f t h i s experiment, a low ord erin g occurred with high accuracy. In a p r a c t i c a l s e t t i n g i t i s very l i k e l y t h a t a higher percentage of o r d e r in g s will occur with the same level o f accuracy. CHAPTER IV QUESTIONNAIRE AND SAMPLE DESIGN In an attem pt to e s t a b l i s h r e l a t i o n s h i p s t h a t might e x i s t between producer a t t r i b u t e s and r i s k prefe ren c es and then to use t h a t r e l a t i o n ­ sh ip in p r e d i c t i n g a c t i o n c h o ic e s , two p r i o r s t e p s must be accomplished. The f i r s t i s c o n s t r u c t i n g the q u e s t i o n n a i r e . The second i s s e l e c t i n g and qu estio ning the sample. 4.1 Questionnaire Design Designing a q u e s t i o n n a i r e r e q u i r e s much time and planning. While an example was given in th e previous c h a p t e r , i t should prove b e n e f i c i a l to o u t l i n e the q u e s t i o n n a i r e design procedure si n c e the q u e s t io n n a ir e is the primary b a s i s f o r t h i s resea rch e f f o r t . The f i r s t s t e p i s the gen eration o f sample d i s t r i b u t i o n s to be used. In o r d e r to do t h i s , one must f i r s t decide on f i v e f a c t o r s and then e n t e r t h es e f i v e f a c t o r s i n to th e program NORGENJ The program NORGEN generates sample d i s t r i b u t i o n s from an underlying normal d i s t r i b u t i o n . The f i r s t f a c t o r s p e c i f i e d i s NE, which- i s th e number o f d i s t r i b u ­ t i o n s to be generated. While t h i s number can vary g r e a t l y , depending on the make-up o f the q u e s t i o n n a i r e , f o r t h i s s t u d y ' s purpose 40 d i s t r i ­ butio ns proved s u f f i c i e n t . Generation of l e s s than 40, given the V o r a l i s t i n g o f NORGEN and INTIDPROG, see King and Robison (1981). 40 measurement g r i d to be used, runs the r i s k o f not having d i s t r i b u t i o n s se p ara ted by a l l o f the s p e c i f i e d r i s k av ersion l e v e l s on the measurement scale. Any more than 40 i s redundant. The second v a r i a b l e t h a t must be s p e c i f i e d is ND, which i s ber o f elements in each d i s t r i b u t i o n . pears a c c e p t a b l e . Any number from t h r e e to the num­ s i x ap­ More than s i x makes comparisons between d i s t r i b u t i o n s both l e s s r e a l i s t i c and more u n i n t e r e s t i n g . Also, s e l e c t i o n o f th e num­ ber o f d i s t r i b u t i o n s should be guided by a b i l i t y o f the r e s e a r c h e r to r e ­ l a t e d i s t r i b u t i o n s to real world events as well as p r o b a b i l i t i e s . For the purpose o f t h i s a n a l y s i s , the number of d i s t r i b u t i o n s was s e t a t s i x . This was done p r i m a r il y to r e f l e c t the p r o b a b i l i t y o f outcomes s i m i l a r to the t o s s i n g o f a d ie. In o t h e r words, farmers could be t o l d t h a t the s i x elements o f a d i s t r i b u t i o n was p r i n te d on one o f the s i x sid e s o f a die. When making comparisons between d i s t r i b u t i o n s a farmer could be t o l d t h a t he must choose which o f the two di ce to r o l l with the outcome being r e a l i z e d income. The t h i r d v a r i a b l e t h a t must be determined i s YMEAN, which i s the mean o f th e underlying d i s t r i b u t i o n s . To do t h i s i t must be decided over what income range one wishes to measure r i s k a v e r s i o n , and a t how many points. Since each element o f the d i s t r i b u t i o n was to r e p r e s e n t a f t e r ­ tax farm p r o f i t , the range o f income used f o r t h i s a n a l y s i s was $-1,000 t o $50,000. sampled. This range seems r e a l i s t i c f o r the farmers who would be In deciding how many l e v e l s to measure r i s k a v e r s i o n , a t r a d e ­ off exists. N a tu ra lly i t i s p r e f e r a b l e t o measure r i s k aversion a t as many p o in ts as p o s s i b l e ; however, the more po ints chosen i n c r e a s e s the number o f comparisons t h a t must be made by a m u l t i p l i c a t i v e f a c t o r . t h i s case fo u r po in ts seemed optim al. In Consequently YMEAN was s e t a t $0, 42 $10,000, $25,000, and $45,000 f o r the fo ur d i f f e r e n t runs t h a t were ne­ cessary. This , in conjunction with s e t t i n g the standard d e v ia tio n of d i s t r i b u t i o n s , made the range o f income over which r i s k aversion was measured $-1,000 to $50,000. The f o u r t h v a r i a b l e t h a t needs t o be s p e c i f i e d i s STD, which i s the standard d e v ia tio n o f each o f the underlying d i s t r i b u t i o n s . In doing t h i s care must be taken not to assume t h a t r i s k aversio n i s c o n sta n t over too l a r g e an income range. o f income. This i s e s p e c i a l l y c r i t i c a l with low l e v e l s P r i o r to t h i s a n a l y s i s STD was u su a lly s e t a t 500, as was the case with the example given in the previous c h a p t e r . However, as income g e ts g r e a t e r , one could argue t h a t r i s k av ersio n i s c o n s t a n t over longer ranges. Also comparisons between d i s t r i b u t i o n s becomes l e s s i n ­ t e r e s t i n g when th e mean o f d i s t r i b u t i o n s a re in creased and the standard d e v ia tio n remains small. In o t h e r words, the d i f f e r e n c e o f $500 means much l e s s when comparing hundreds o f thousands o f d o l l a r s than i t does when comparing thousands o f d o l l a r s . Consequently i t was assumed t h a t c o n stan t a b so lu te r i s k aversion held f o r g r e a t e r d o l l a r increments as the mean o f th e d i s t r i b u t i o n s i n c r e a s e . As a r e s u l t f o r YMEAN equal to $-5,000, $10,000, $25,000, and $45,000, STD was s e t a t 500, 500, 2500, and 2500, r e s p e c tiv e ly .' In e f f e c t , c o n s t a n t a b so lu te r i s k aversion was assumed between $-1,000 and $1,000; $9,000 and $11,000; $22,000 and $28,000; and $40,000 and $50,000. This method i s both more i n t e r e s t i n g and v a l i d than previous work. I t should be noted, however, t h a t by in c r e a s in g the width as income in c r e a s e s d i f f e r e n c e s in the d is c r im i n a n t a n a l y s i s r e s u l t s a t various income l e v e l s cannot be a t t r i b u t e d s o l e l y to changes in r i s k p r e f e r e n c e s . 43 I t may be t h a t the assumption o f c o n s t a n t r i s k aversion in f lu e n c e s the r e s u l t s and b ias es the t e s t o f the h y po thesis . Fu rther r e s e a r c h i s ne­ c ess ary to determine i f t h i s i s a problem and i f so how s i g n i f i c a n t is the problem. F i n a l l y , i t i s necessary to s p e c i f y IROUND, which i s a rounding f a c ­ t o r f o r each element o f each d i s t r i b u t i o n . Many numbers have been used but exp erience suggests t h a t IROUND = 100 i s the most i d e a l . Using a sm aller rounding f a c t o r makes comparisons t e d i o u s , while using a l a r g e r f a c t o r i s not r e a l i s t i c in t h i s given case . Using t h es e values NORGEN was run f ou r tim e s, once f o r each income level. This data was then sto r e d and used f o r input on the next program, INTID. INTID i s a program which takes the d i s t r i b u t i o n s and i d e n t i f i e s a boundary i n t e r v a l f o r p a i r s o f d i s t r i b u t i o n s . Inputs necessary f o r t h i s program includ e NE and ND as disc ussed in Chapter I I I . S i m i la r ly NAME and R, which a re th e a rr a y s used to d e scr ib e sample d i s t r i b u t i o n s , a re read from catalogued NORGEN output so t h i s i n p u t involves very l i t t l e effort. Factors t h a t must be determined a re NG, which i s the number o f l e v e l s on the measurement g r i d , and RA, which i s the a rr a y o f values th em self. As s t a t e d e a r l i e r , a very good g r i d was found. values o f RA a re l i s t e d in Table 4 . 1 . tailed. NG i s equal to 16 and the This g r i d i s both complete and de­ I t i s complete in t h a t i t c o n ta in s a range o f r i s k a v e r sio n co­ e f f i c i e n t s t h a t most a r e l i k e l y to f a l l w i t h in . I t i s d e t a i l e d in t h a t the 16 values allow f o r small incremental changes. 44 TABLE 4.1 Absolute Risk Aversion Levels Defining Measurement Grid .010000 .005000 .002500 .001000 .000800 .000600 .000400 .000200 .000100 0.000000 -.0 0 0 1 0 0 -.000250 -.000500 -.001000 45 The o utp u t o f t h i s program d e t a i l s which plans a r e p r e f e r r e d above and below s p e c i f i e d r i s k aversion p o i n ts . With t h i s information the pro­ cess o f completing the q u e s t i o n n a i r e could continue. The next s t e p necessary i s t h a t o f sequencing q u e s t io n s . As d i s ­ cussed e a r l i e r , the upper and lower bounds o f the r i s k aversion fu nction a re n e c e s s a r i l y assumed p o s i t i v e and ne gativ e i n f i n i t y p r i o r to q u e s t io n ­ ing. By using an i t e r a t i v e process t h i s space can be reduced to as n a r ­ row an i n t e r v a l as d e s i r e d o r deemed nece ssary. The same question design was used here as in the p r e v io u s ly discusse d example s in c e th e measure­ ment g r i d was the same. However, in reviewing the q u e s t io n n a ir e i t was decided to use only t h r e e q uestio ns r a t h e r than four. The l o ss o f accur­ acy and o rd erin g c a p a b i l i t y were o f f s e t by the b e n e f i t s received by r e ­ ducing the q u e s t io n n a ir e s i z e . As can be seen by examining the q u e s t io n n a ir e (see Appendix), t h e r e a re seven qu e stio n s to a s e c t i o n , to which each person responded to t h r e e . With fo ur q u e stio n s the t o t a l number in each s e c t i o n in c r e a s e s to f i f t e e n even though each respondent makes only one a d d itio n a l comparison. I t was believ ed t h a t t h i s added len gth might reduce the response r a t e and t h e r e ­ f o r e not be worth i t . Also, the a n a l y s i s in the previous c h ap ter had low o r d e r in g because the comparison between those d i s t r i b u t i o n s was so d ifficu lt. As will be d i s c u s s e d , an attempt t o a l l e v i a t e t h i s problem was made so t h a t th e l o s s o f ord ering power and accuracy by moving to only t h r e e q u e stio n s would no t be r e a l i z e d . The qu e stio ning sequence scheme i s presented in Figure 4.1. S t a r t i n g a t the t o p , the f i r s t q u e stio n s compare two d i s t r i b u t i o n s t h a t a r e s e ­ p arated by the measurement l e v e l s o f .0003 and .0004. Depending on ( .0 0 0 3 , .0004) (.001 , .0015) ( - . 0001, 0 ) (-.0 0 0 5 , •.00035) (.0001 , .0002) (.0 006, .0008) FIGURE 4.1 I t e r a t i v e Process Used in Questionnaire Design (.0025, .005) CT> 47 which d i s t r i b u t i o n i s s e l e c t e d , the decision-maker w ill e i t h e r e s t a b l i s h a new upper bound o f .0004 o r a lower bound o f .0003. Thus the new i n ­ t e r v a l w ill be ( - « , .0004) o r (.0 003, +») depending on th e choice o f the comparison. A s i m i l a r a n a l y s i s tak es place f o r any subsequent number o f q u e stio n s d e s i r e d . Consequently f o r t h i s work t h r e e q u e stio n s y i e l d e d e i g h t i n t e r v a l s i n to which a p a r t i c u l a r decision-maker could f a l l . The i n t e r v a l s i n to which a decision-maker could f a l l f o r each qu estio n are l i s t e d in Table 4 .2 . The f i r s t number in the brackets r e p r e s e n ts the lower bound, while the second r e p r e s e n t s the upper bound f o r the a b solu te r i s k aversion i n t e r v a l . The above de sc ribed procedure was followed fo u r tim es, once f o r each income l e v e l . The r e s u l t s o f t h i s work a re Sections I , I I , I I I , and IV o f the q u e s t io n n a ir e as shown in the Appendix. As i s a p p a r e n t , t h i s i s both th e most complex and time-consuming p o rtion o f the q u e s t io n n a ir e construction. The f i r s t four s e c t i o n s o f the q u e s t io n n a ir e e s t a b l i s h a r i s k a v e r ­ sion i n t e r v a l f o r each d e cisio n maker. Using t h a t i n t e r v a l i t i s p o s s ib le to p r e d i c t which a c t io n choices w ill be s e l e c t e d and Section V i s used f o r such p r e d i c t i v e purposes. The d i s t r i b u t i o n s used should span the range over which the f u n ctio n has been e s t a b l i s h e d . Care should be taken t o i n s u r e t h a t no d i s t r i b u t i o n i s dominated by f i r s t degree s t o c h a s t i c dominance s i n c e th ese comparisons are not i n t e r e s t i n g , In o t h e r words, no one who has p o s i t i v e u t i l i t y f o r wealth would s e l e c t a plan dominated by f i r s t degree s t o c h a s t i c dominance. TABLE 4 .? Correspondence Between Questions Asked and Risk I n t e r v a l s I d e n t i f i e d Number o f Questions 0 P o s sib le In te r va ls +») 1 ( - » , .0004) (.0 0 0 3 , +*) 2 (-»» o) ( - . 0 0 0 1 , .0004) ( .0 0 0 3 , .0015) 3 ( — , -.00 025 ) (.0 0 0 5 , 0) ( .0 0 1 , ») ( - .0 0 0 1 , .0002) (.0 0 0 1 , .0004) (.0 0 0 3 , .0008) ( .0 0 0 6 , .0015) (.0 0 0 1 , .005) ( .0 0 2 5 , - ) 00 49 The manner in which d i s t r i b u t i o n s a re compared i s i n n ov ative. Other s t u d i e s have not allowed f o r c o n t r a d i c t i o n o f th e t r a n s i t i v i t y axiom; how­ e v e r , t h i s procedure will allow f o r t e s t i n g the e x t e n t o f t h i s oc currence. F i n a l l y , s e c t i o n VI i s used to e l i c i t information about p e rs o n a l , b u s i n e s s , and economic a t t r i b u t e s . This information was not r e a d i l y a v a i l a b l e by o t h e r sources and w ill be disc ussed l a t e r . Also contained in t h i s s e c t i o n a re s i x qu e stio n s used to determine p e r s o n a l i t y t r a i t s . Work has been done to examine t h e r e l a t i o n s h i p o f p e r s o n a l i t y t r a i t s to job p r e f e r e n c e , grade p o i n t average, as well as many o t h e r f a c t o r s (Roberts and Lee, 1977; Myers, 1962). With t h i s in mind s i x f a c u l t y members in the A g r i c u l t u r a l Economics Department a t MSU were asked to f i l l out the i n t e r v a l measurement ques­ t i o n n a i r e and provide t h e i r Myers-Briggs s c o r e s . Then an a n a l y s i s was done to see which, i f any, f a c t o r s were r e l a t e d to t h e i r r i s k a v ersio n . Of the f o ur p e r s o n a l i t y t r a i t s two showed promise; i n t r o v e r t - e x t r o v e r t and judgement-perception. Obviously the small sample s i z e precludes r e p o r t i n g r e s u l t s sin c e any conclusions cannot provide a st rong b a s i s f o r including the Myers-Briggs q u e s t io n s . However, t h e a d d it i o n a l informa­ t i o n was obtained a t a low c o s t and might prove worthwhile in th e f u t u r e . The s i x questions used were based on q u e stion s in the Myers-Briggs t e s t s (Briggs and Myers, 1976). The f i r s t t h r e e q u e stio n s c l a s s i f y d e c i s i o n ­ makers as e i t h e r an i n t r o v e r t o r e x t r o v e r t , while the last, t h r e e seek t o e s t a b l i s h whether judgement o r pe rc eption i s p r e s e n t . B a s i c a ll y an i n t r o ­ v e r t e x i s t s and r e l a t e s to his own inner-world while an e x t r o v e r t works in th e o u ter-w orld. The j u d g e r s l i k e to or ganize and plan while the p e r c e p t e r s are l e s s organized and have t r o u b l e making d e c i s i o n s . 50 I t i s a ls o worth noting t h a t composing the q u e s t io n n a ir e i n s t r u c t i o n s r eq u ir e d much work. C l e a r , concise i n s t r u c t i o n s are necessary f o r c o r ­ r e c t completion o f the q u e s t i o n n a i r e ; however, they must a ls o be s h o r t so as t o avoid reducing the response r a t e . A f t e r several d r a f t s and r e ­ views the f i n a l wording o f the i n s t r u c t i o n s was s e l e c t e d . 4 .2 Pre-Test Seven farmers were sent, the q u e s t i o n n a i r e as a p r e - t e s t . Five ques­ t i o n n a i r e s were r e t u r n e d , but one o f t h es e q u e s t io n n a ir e s was not com­ p l e t e d s i n c e the respondent i n d ic a t e d concerns about th e purpose o f the study. Once th e q u e s t io n n a ir e s were r e t u r n e d , the f i v e respondents were con­ t a c t e d by telephone in an attem pt to d isc ern whether they understood th e instructions. For t h e most p a r t the i n s t r u c t i o n s were c l e a r ; however, the farmer who r etu r n e d the blank q u e s t io n n a ir e i n d ic a t e d a statement o f the s t u d y ' s purpose would f a c i l i t a t e a higher response r a t e . These sug­ g e s t io n s and c r i t i c i s m s were acknowledged and several changes were made to a l l e v i a t e perceived problems. The p r e - t e s t was c e r t a i n l y a worthwhile t a s k which improved the f i n a l r e s u l t . 4 .3 Sample S e le c tio n In any study the s e l e c t i o n o f a sample i s a d i f f i c u l t t a s k . Obvious­ ly the way in which th e r e s u l t s a r e to be used should guide the s e l e c t i o n process . Factors such as r e p r e s e n t a t i v e n e s s , ease o f a cq u irin g d a t a , response r a t e , e t c . , must a l l be examined. For t h i s study i t was d e t e r ­ mined t h a t th e sample population should come from Telfarm p a r t i c i p a n t s a t Michigan S t a t e U n iv e rs ity . Telfarm i s a volu n ta ry record-keeping 51 system t h a t the A g r i c u l t u r a l Economics Department provides to i n t e r e s t e d Michigan farmers f o r a s p e c i f i e d f e e . The disadvantages o f using th ese p a r t i c i p a n t s as a sample include lack o f r e p r e s e n t a t i v e n e s s , i n a b i l i t y t o g e t wide d i s p e r s i o n o f s i z e , as well as o t h e r shortcomings o f a non­ random sample. Obviously the r e s u l t s will be only g e n e r a l i z a b l e to the sample i t s e l f . While the disadvantages are s i g n i f i c a n t , t h e advantages appear to dominate. Given t h a t p e rs o n a l , b u s i n e s s , and economic a t t r i b u t e s will be used in the a n a l y s i s , the use o f Telfarm records w ill provide s i g n i ­ f i c a n t amounts o f d e t a i l e d and s e n s i t i v e information a t a low c o s t . Not only will exclusion o f t h i s information from a q u e s t io n n a ir e reduce the s i z e o f the q u e s t i o n n a i r e , thus p o ss ib ly in c r e a s in g the response r a t e , but i t will a l s o be much e a s i e r and l e s s time-consuming to c o l l e c t . Also, Telfarm p a r t i c i p a n t s h i s t o r i c a l l y have been c oo pera tive study p a r t i c i ­ p a n ts , again i n c r e a s in g th e response r a t e . Of the Telfarm p a r t i c i p a n t s , i t was decided t o examine t h r e e e n t e r ­ p r i s e types: d a i r y , c a t t l e f ee d in g , and cash crop. This s e l e c t i o n was made to determine i f any rec ognizable d i f f e r e n c e s e x i s t e d in r i s k p re ­ ferences. In a d d i t i o n to Telfarm membership, the p a r t i c i p a n t s had to be included in the 1979 Business a n a l y s i s . This f u r t h e r requirement had two p u r p o s e s - - f i r s t , i t in su red t h a t t h e s e i n d i v i d u a l s were s p e c i a l i z e d in each p a r t i c u l a r e n t e r p r i s e , and second, i t insured complete reco rds. 4.4 Sample The sample used f o r t h i s study c o n siste d o f 37 d a ir y farm ers , 17 c a t t l e f e e d e r s , and 26 Saginaw Valley cash crop produce rs, f o r a sample 52 t o t a l o f 80. Since Telfarm c l a s s i f i e d by county, i n d iv i d u a ls were s e l e c t e d p r i m a r il y by c o u n ties with a l a r g e number o f q u a l i f i e r s in each county. 4.5 Data A c q uisitio n Once the q u e s t i o n n a i r e and sample s e l e c t i o n had been completed, i t was necessary to determine th e b e st s t r a t e g y f o r q u e s t io n n a ir e completion. The two methods con sidered were: campaign. a mail survey o r a personal in te rv ie w A mail survey had the disadvantages o f lower response r a t e s and p o s s ib l y l e s s accuracy; however, t h i s method was both l e s s c o s t l y and time-consuming. Given the l a r g e sample s i z e and t h e i r geographical d i s t r i b u t i o n s around the s t a t e o f Michigan, th e time and c o s t f a c t o r s a s s o c i a t e d with personal in te rv ie w s made t h a t a l t e r n a t i v e p r o h i b i t i v e . Thus th e q u e s t io n n a ir e s were mailed to the sample population. Two weeks a f t e r the f i r s t m a i l in g , non-respondents were s e n t a follow-up l e t t e r . A f t e r an a d d it i o n a l two weeks, non-respondents were co ntacted by t e l e ­ phone in an attem pt to i n c r e a s e the response r a t e . CHAPTER V ANALYSIS OF DATA 5.1 Response Rate Of the 80 q u e s t io n n a ir e s t h a t were mailed to Michigan farmers, a t o t a l of 39 were retu rn ed f o r a response r a t e o f 48.75%. By using the postmark da te s i t was determined t h a t 17 or 44% o f the retu rn ed ques­ t i o n n a i r e s were retu rne d a f t e r the f i r s t m ailing. An a d d it i o n a l 9, or 23%, were retu rned a f t e r the follow-up l e t t e r while 13, o r 33%, o f the r etu r n e d q u e s t io n n a ir e s followed t h e phone c a l l . While a 49% response r a t e is a c c e p t a b l e , i t would l i k e l y have been higher i f the mailing had not occurred when farmers were t r y i n g to get t h e i r crops plan ted . In the telephone follow-up many of the producers mentioned how busy they were and s t a t e d t h a t the q u e s t io n n a ir e would rec eiv e a t t e n t i o n i f t h e i r time c o n s t r a i n t s allowed. In several cases they could not f in d the time to complete the q u e s t io n n a ir e . The response r a t e s between d a i r y , cash crop, and beef feed ers were reasonably c o n s i s t e n t with 49% o f the d a ir y produ cers, 42% o f the cash c ro p s, and 59% o f t h e c a t t l e fee d ers responding to the survey. Only 31 o f the 39 r etu r n e d q u e s t io n n a ir e s were accep tab le f o r use in t h e a n a l y s i s . P r i o r t o d i s t r i b u t i o n o f the surveys i t was hoped t h a t t h e r e would be a t l e a s t 30 q u e s t io n n a ir e s to analyze and t h i s hope was satisfied. 53 54 5.2 Ordering Based on Risk In terv al Once the q u e s t io n n a ir e s had been r e t u r n e d , each was analyzed to determine the a p p r o p r i a t e r i s k aversi on fu nction f o r each i n d i v i d u a l . The r i s k aversion fu n c t i o n was determined a f t e r one, two, and t h r e e q u e s t io n s . This information was then used to p r e d i c t the a c t i o n choices s e l e c t e d in Section V o f the q u e s t io n n a ir e in the same manner as was done e a r l i e r . Again th e r e s u l t s were encouraging as can be seen in Table 5.1. As can be seen th es e r e s u l t s a r e s i m i l a r to th ose obt ained e a r l i e r . Again, t h e r e e x i s t s a t r a d e - o f f between t h e accuracy o f ord erin g and the level o f ord erin g t h a t o c cu rs. As sugg ested, the t r a d e - o f f s between accuracy and f a i l u r e to p r e d i c t an a c t i o n choice must be c a r e f u l l y weighed. Also the need to tak e i n to c o n s i d e r a ti o n t h e d i f f i c u l t y o f comparing ac­ t i o n choices i s the primary determinant o f choosing th e c o r r e c t number o f qu e stio n s to be used in t h i s a n a l y s i s . In o t h e r words, when choices a r e r e l a t i v e l y easy a wider i n t e r v a l will s u f f i c e while with more d i f f i ­ c u l t choices i t i s necessary to ob tain a narrower i n t e r v a l . Again we emphasize t h a t the r i s k p reference i n t e r v a l s which were e l i c i t e d from the producers were a l l unique. In o t h e r words, any general assumption about r i s k p refe ren c es f o r a l l producers i s not supported by th is study's findings. B a s i c a l l y , t h e r e appears to be two key f a c t o r s t h a t should become e vide n t from t h i s work. The f i r s t i s t h a t t h e r e e x i s t s a t r a d e - o f f between accuracy o f ord erin g and th e ord ering o f a c t io n ch oic es. I f a high level of ord erin g i s d e s i r e d then a higher e r r o r r a t e in ord erin g will occur. I f a small e r r o r r a t e in ordering is d e sir e d then a sm a ller level o f 55 TABLE 5.1 Ordering and Accuracy o f I n t e r v a l Approach Number of Questions Incorrect P r e d i c t io n s (p erc en t) Corr ect Predictions (p erc en t) Choices Unordered (p e r c e n t) Choices Ordered (p erc en t) 0 0 100 100 0 1 0 100 97 3 2 6.5 93.5 78.1 21.9 3 16 84 52 48 FSD 0 100 100 0 SSD 11 89 70 30 56 o r d e r in g must be accepted. C e r ta in l y the a p p r o p r i a t e t r a d e - o f f must be determined when using th e i n t e r v a l method as an actual a id to producers f o r decision-making. The c o s t s and p r o b a b i l i t i e s o f e r r o r a re o f p r i ­ mary importance in t h i s r e s p e c t . While no work has been done in t h i s are a i t i s only because o f the newness o f the tec h niqu e , r a t h e r than i t s lack o f importance. Future research should address t h e s e t r a d e - o f f s . The second lesso n worth r e i t e r a t i n g i s t h a t the i n t e r v a l method o f f e r s a s u p e r i o r technique to any a r b i t r a r y assumption about r i s k p r e ­ ference f u n c t i o n s . In the p a s t , assumptions have been made and analyses have been completed based on th es e assumptions. This res ea rch has de­ monstrated t h a t i n d i v i d u a l s possess a l l d i f f e r e n t shapes o f r i s k aversion fu n ctio n s and as a r e s u l t i f the i n t e r v a l i s p r a c t i c a l , th e r e s u l t s o f any res ea rch p r e d i c t i n g a c t i o n choices would l i k e l y be s u p e r i o r to those where the i n t e r v a l o r r i s k prefe ren c e i s assumed. 5.3 Discriminant Analysis A f te r the o rderin g p o r tio n o f the a n a l y s i s was completed, i t was then necessary to determine i f any syste m atic r e l a t i o n s h i p e x i s t e d between r i s k p references and producer a t t r i b u t e s . To do t h i s d i s c r im i n a n t a n a l y ­ s i s was performed a t each o f the fo u r l e v e l s o f income t h a t r i s k p re ­ f ere nce s were measured. At each level o f income the producers were se p ara ted in to t h r e e near evenly di vided groups based on r i s k p r e f e r e n c e s . A d i s c r im i n a n t f u n ctio n was then derived to s e p a r a t e as many o f the pro­ ducers i n to t h e i r c o r r e c t c l a s s i f i c a t i o n s as p o s s i b l e . Variables were e lim in a te d i f they added nothing to the c o r r e c t n e s s o f t h i s c l a s s i f i c a t i o n scheme. follows: The v a r i a b l e s used in t h i s a n a l y s i s were f o r 1978 and a re as 57 V1 = m arita l s t a t u s (0 = s i n g l e , 1 = married) V2 = age (years) Vg = number o f c h ild r e n = education level (number o f grades completed) Vg = y e ars l i v i n g on farm Vg = y e ars managing farm Vy = p e rc en t o f income from farm Vg = p ercen t o f farm income yours Vg = acres owned V^q = a c r e s rented V-jp = i n t r o v e r t - e x t r o v e r t (Measured +3 to -3 with higher value i n d i c a t i n g hi gher degree o f i n t r o ­ v e r t and lower value e x t r o v e r t . Zero i n d i c a t e s n e u t r a l i t y . ) V-jg = p e rc ep tio n -ju d g in g (Measured the same with higher value f o r jud g in g, lower f o r p e r c e p t i o n .) V ^ = net worth ( d o l l a r s ) V-jg = n e t cash income ( d o l l a r s ) V^g = n e t w o r t h / a s s e t s (p ercent) Where necessary the u n i t s o f measurement a r e included. To a s s i s t in providing information on the general c h a r a c t e r i s t i c s o f the sample, th e v a r i a b l e s , t h e i r means, standard d e v ia tio ns and ranges a re a ls o provided as follows: 58 Variables High Value Standard Deviation 0 .93 .24 61 20 45.26 11.71 09 0 3.29 2.23 16 10 12.39 1.66 61 20 44.00 12.34 40 1 22.52 11.94 100 50 .90 .15 100 33 .75 .25 1,100 0 321.77 241.03 700 0 239.84 188.82 3 -3 1.35 2.04 3 -3 -1.06 1.72 1,002,800 -415,157 366,803.00 283,867.00 136,368 -197,454 43,335.20 57,839.70 .66 .68 V2 V3 V4 V5 V6 V7 V8 V9 V10 V12 V13 V15 100.00 v1R 5.4 Mean 1 V1 V14 Low Value 24. 53 Results a t $0 For r i s k prefe re nces measured a t zero income l e v e l s , respondents were separated i n to t h r e e groups. ( - . 0 1 , -.00025). The f i r s t group had an i n t e r v a l o f The second group had an i n t e r v a l o f ( - .0 0 0 5 , 0) and the t h i r d group had an i n t e r v a l o f ( - . 0 0 0 1 , .0002) c r l a r g e r . The r e s u l t s o f the s ta n d ard ize d d is c r im i n a n t f u n ctio n can be seen in Table 5.2, Those v a r i a b l e s with th e l a r g e s t a b so lu te values a r e the ones which a re th e most important in the c l a s s i f i c a t i o n scheme. Conse­ quently age, y e ars on farm, y e a r s managing farm, and n e t worth were o f primary importance in c l a s s i f i c a t i o n . 59 TABLE 5.2 D is c r im in a n t F u n c tio n a t Zero Income Level Standardized Discriminant Function C o e f f i c ie n t s 1 2 .85028 2.19746 V3 - .88473 - .16746 V4 .08774 - .49067 V5 -2.04446 .03079 V6 2.14624 -2.12725 - .11255 - .03732 .90806 - .21596 - .67952 - .22689 .26481 - .44742 .48395 .51225 .79638 .03752 V14 1.22467 .15993 V15 - .14345 - .37445 -1.06328 - .65862 Group 1 -2.19848 .03311 Group 2 1.00343 -1.22477 Group 3 1.26060 .28343 V2 V7 V8 V9 V10 V12 V13 V16 Centroids o f Groups in Reduced Space 60 The p r e d i c t i v e a b i l i t y o f the d isc r im in a n t fun ctio n was a ls o g ener­ ate d and the r e s u l t s a re presented in Table 5.3. As can be seen t h i s fun ction c o r r e c t l y c l a s s i f i e d 84% o f the producers. Also worth noting i s t h a t only two people were i n c o r r e c t l y c l a s s i f i e d i n to an extreme group. In o t h e r words, only two i n d i v i d u a l s were s e l e c t e d f o r a group t h a t was two groups away from where they a c t u a l l y belonged. 5.5 Results a t $10,000 A s i m i l a r a n a l y s i s was conducted a t the $10,000 level o f income. Here Groups 1, 2 and 3 were those with i n t e r v a l s o f ( 0 .0 1 , 0 ) , (- .0 0 0 1 , .0004), and (.0003, .0008) and l a r g e r r e s p e c t i v e l y . Again an attem pt was made to s e p a r a t e producers in to t h r e e evenly di vided groups based on r i s k p r e f e r e n c e s . This was done f o r e f f i c i e n c y s in c e no obvious clustering pattern existed. The r e s u l t s o f t h i s a n a l y s i s can be seen in Tables 5.4 and 5.5 . At t h i s income level number o f c h i l d r e n , acres owned, net worth, and n e t cash income were the most important v a r i a b l e s in the c l a s s i f i c a ­ t i o n scheme. Again t h i s f u n ctio n c l a s s i f i e d 84% o f the producers into the c o r r e c t group, only t h i s time no one was m i s - c l a s s i f i e d to an extreme. Also t h i s fu nction u t i l i z e d a l l 15 v a r i a b l e s where the previous fu nction e lim in a te d m arita l s t a t u s as a n o n - co n tr ib u tin g f a c t o r . 5.6 Resu lts a t $25,000 Producers were c l a s s i f i e d here in to t h r e e groups a l s o . Those with an i n t e r v a l o f ( - . 0 1 , -.00025) formed Group 1 while th ose with an i n t e r ­ val o f e i t h e r ( - .0 0 0 3 , 0.0) o r ( - .0 0 0 1 , .0002) formed Group 2. Anyone 61 TABLE 5 .3 Discriminant F u n c t io n 's P r e d i c t i v e A b i l i t y , Zero Income Level Actual Group Name Code Number o f Cases Pre d icted Group Membership Group 1 Group 2 Group 3 Group 1 2 11 10. 90.9% 0. 0% Group 2 3 4 0. 0% 4. 100.0% 0. 0% Group 3 4 16 3. 18.8% 12. 75.0% 1. 6.3% 83.9% o f Known Cases C o r r e c t l y C l a s s i f i e d C hi-Square = 35.629 S ig n if ic a n c e = .000 1. 9.1% 62 TABLE 5.4 D is c r im in a n t F u n c tio n a t $10,000 Income Level Standardized Discriminant Function C o e f f i c i e n t s 1 2 V1 -1.25845 .12082 V2 .19637 -1.00134 V3 1.62285 - .41860 V4 - .45847 - .15178 V5 .17034 .65933 V6 - .80688 1.27414 1.32675 .01316 -1.37030 - .71373 1.69500 - .20420 - .80147 - .49913 1.14935 .16294 - .34766 .28638 -1.53637 - .00809 -1.44442 - .30078 .78975 - .56384 Group 1 -1.73775 .58390 Group 2 - .24506 - .80137 Group 3 2.75699 .39920 V7 V8 V9 V10 V12 V13 V14 V15 V16 Centroids o f Groups in Reduced Space 63 TABLE 5 .5 Discriminant F u n c t io n 's P r e d i c t i v e A b i l i t y , $10,000 Income Level Actual Group Code Name Number o f Cases Pre d icted Group Membership Group 1 Group 2 Group Group 1 2 11 9. 81.8% 2. 18.2% 0. 0% Group 2 3 12 3. 25.0% 9. 75.0% 0. 0% Group 3 4 8 0. 0% 0. 0% 8. 100.0% 83.9% o f Known Cases C o r r e c t l y C l a s s i f i e d C hi-Square = 35.629 S ig n i f i c a n c e = .000 64 with an i n t e r v a l o f (.0 001, .0004) formed Group 3. Results o f the d i s ­ crim inant a n a l y s i s can be seen in Tables 5.6 and 5.7. At t h i s income level age, perc ent o f farm income y o u r s, a c r e s r e n t e d , and n e t worth were the most important v a r i a b l e s in the c l a s s i f i c a t i o n scheme. Here c l a s s i f i c a t i o n was 77.4 pe rc ent a c c u r a t e . were included in the a n a l y s i s . Again a l l v a r i a b l e s Also, no extreme m i s c l a s s i f i c a t i o n took place. 5.7 Results a t $45,000 Producers were c l a s s i f i e d i n to t h r e e groups here a l s o . The f i r s t had a r i s k i n t e r v a l o f ( - . 0 1 , 0.00025) o r ( - . 0 0 0 5 , .00) while the second had an i n t e r v a l o f ( - .0 0 0 1 , .0002) o r (.0001, .0004). F i n a l l y the t h i r d group c o n s i s t e d o f those producers with an i n t e r v a l o f (.000 3, .0008) or l a r g e r . The same a n a l y s i s was conducted here with the r e s u l t s r e ­ ported in Tables 5.8 and 5.9 . In t h i s case ye ars managing a farm, acres r e n t e d , age, and years l i v i n g on a farm were the most important v a r i a b l e s in the c l a s s i f i c a t i o n scheme. In t h i s case 74 p erc ent o f the producers were c o r r e c t l y c l a s s i f i e d by t h e i r a t t r i b u t e s . categories. 5.8 Here t h r e e producers were m i s c l a s s i f i e d to extreme Again, a l l v a r i a b l e s were included. I n t e r p r e t a t i o n o f Results There a re two i n t e r r e l a t e d s t a t i s t i c s provided with the d i s c r im i n a n t a n a l y s i s r e s u l t s t h a t are worth d i s c u s s i o n , th ose being the c h i- s q u a r e s t a t i s t i c and the s i g n i f i c a n c e l e v e l . These s t a t i s t i c s answer th e ques­ t i o n could t h e s e r e s u l t s have been obt ained i f the groupings were in f a c t 65 TABLE 5.6 D is c r im in a n t F u n c tio n a t $25,000 Income Level Standardized Discriminant Function C o e f f i c ie n t s 1 2 - .22988 .19375 -1.63521 .58505 .68701 .58228 - .44701 .44583 .38311 .91488 .21969 .10659 - .12150 .21414 -1.40130 .10541 .50581 .78900 -1.51630 .14400 .50259 .09913 .85489 .65913 .92993 .03030 - .89838 .02147 - .73326 .59558 Group 1 -1.13733 .75454 Group 2 - .66602 .61140 Group 3 2.09935 .12860 V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V12 V13 VH V15 V!6 Centroids o f Groups in Reduced Space 66 TABLE 5.7 Discriminant F u nc tio n 's P r e d i c t i v e A b i l i t y , $25,000 Income Level Name Code Cases Group 1 2 Group 2 3 Group 3 4 Group 1 Group 2 9 7. 77.8% 2. 22.2% 0 0% 13 3. 23.1% 9. 69.2% 1. 0 0% 1. 11.1% 9 77.4 Percent o f Known Cases. C o rrec tly C l a s s i f i e d Chi-Square = 27.113 S ig n if ic a n c e = .000 Group 3 7.7% 8. 88.9% 67 TABLE 5.8 Discriminant Function a t $45,000 Income Level Standardized Discriminant Function C o e f f i c ie n t s 1 2 vi .16772 - .23096 V2 - .40000 1.20345 - .58839 .42323 - .24545 .13167 - .19480 -2.36374 .84495 .99286 V3 V4 h V6 h .38387 . - .13944 .78077 .17677 - .45983 .59130 1.09601 - .19480 - .32667 .06263 .19436 .49412 - .22369 .22091 V15 .40643 .47012 V16 .20904 - .47189 Group 1 .26761 - .66118 Group 2 -1.27620 .32080 Group 3 .96741 .79617 V8 V9 V10 V12 V13 V14 Ce ntroids o f Groups in Reduced Space 68 TABLE 5.9 Discriminant F u n c t io n 's P r e d i c t i v e A b i l i t y , $45,000 Income Level Name Code Cases Group 1 Group 2 Group 3 Group 1 2 14 10. 71.4% 3. 21.4% 1. 7.1% Group 2 3 9 1. 11.1% 8. 88.9% 0 0% Group 3 4 6 2. 25.0% 1. 12.5% 5. 52.5% 74.2 Percent o f Known Cases C orrec tly C l a s s i f i e d Chi-Square = 23.290 S ig n i f ic a n c e = ,000 69 a random occurrence? At each income l e v e l , given the c h i- s q u a r e s t a t i s ­ t i c , th e s i g n i f i c a n c e level o f zero i n d i c a t e s t h a t t h e r e i s a zero p r o ­ b a b i l i t y o f th es e groupings oc cu rrin g randomly. When examining the sta n d ard ize d d i s c r im i n a n t fu nctio n i t i s worth noting t h a t th e a b s o l u te values o f the c o e f f i c i e n t s t e l l s us how impor­ t a n t each v a r i a b l e is in th e c l a s s i f i c a t i o n pro cess. a b s o l u te value the more important t h a t v a r i a b l e i s . The g r e a t e r the As can be seen from the r e s u l t s a p a r t i c u l a r v a r i a b l e may be very important in se p a r a tin g group 1 from group 2 while of l i t t l e importance in d iv id i n g group 2 from group 3. S t r u c t u r a l c o e f f i c i e n t s were not obtained in t h i s a n a l y s i s . These c o e f f i c i e n t s have an advantage over the sta n d ard ize d c o e f f i c i e n t in t h a t they a r e not a f f e c t e d by r e l a t i o n s h i p s with o t h e r v a r i a b l e s . Standardized c o e f f i c i e n t s u t i l i z e the simultaneous c o n t r i b u t i o n s o f a l l the o t h e r v a r i a b l e s in the a n a l y s i s . Consequently, the sta n d ard ize d c o e f f i c i e n t s may not r e f l e c t the a p p r o p r i a t e weight o f a p a r t i c u l a r v a r i a b l e due to a high c o r r e l a t i o n with anoth er v a r i a b l e . However, t h i s does not appear to pose a problem in t h i s a n a l y s i s sin ce each v a r i a b l e u t i l i z e d is not highly c o r r e l a t e d with t h e remaining v a r i a b l e s . I f high c o r r e l a t i o n e x i s t s , s t r u c t u r a l c o e f f i c i e n t s should be included in the a n a l y s i s . 5.9 Summary o f Results A f t e r completing the d i s c r im i n a n t a n a l y s i s , r e g r e s s io n a n a l y s i s was performed on the same d a t a . The dependent v a r i a b l e s were th e upper and lower bounds o f the r i s k a v ersio n f u n c tio n s a t each income level with th e independent v a r i a b l e s being those a t t r i b u t e s used in the d i s c r im i n a n t analysis. Since t h e primary d i f f e r e n c e in the two methodologies i s t h a t 70 the r e g r e s s io n a n a l y s i s r e l i e s on a continuous r i s k v a r i a b l e and the d is c r im i n a n t a n a l y s i s u t i l i z e s d i s c r e t e r i s k v a r i a b l e s , i t can be ex­ pected t h a t th e r e s u l t s would be q u i t e s i m i l a r . As expected, they were. Several f a c t o r s appear worth noting based on the previous a n a l y s i s . Based on a t t r i b u t e s , d i s c r i m i n a n t a n a l y s i s did a reasonably good job o f c l a s s i f y i n g producers by r i s k p ref e r e n c e s a t a l l f o u r income l e v e l s . However, no s e t o f v a r i a b l e s was c o n s i s t e n t l y th e most i n f l u e n t i a l in t h a t c l a s s i f i c a t i o n process . Using th e r e s u l t s o f t h e d isc r im in a n t analy­ s i s which a re c l o s e l y repeated with the r e g r e s s io n r e s u l t s , a comparison o f the most i n f l u e n t i a l v a r i a b l e s in the c l a s s i f i c a t i o n scheme can be seen and compared in Table 5.10. Also contained in t h i s t a b l e i s the most i n f l u e n t i a l v a r i a b l e s over a l l income l e v e l s based on r e g r e s s io n analysis. While t h e s e r e s u l t s demonstrate t h a t i t is p o s s ib l e to c l a s s i f y producers i n to r i s k p re f e r e n c e groups by a t t r i b u t e s with a reasonable degree o f accuracy a t p a r t i c u l a r income l e v e l s , c l a s s i f i c a t i o n over the complete r i s k aversion fu n c t i o n measured over a l l income l e v e l s was much less successful. The following s e c t i o n will devote a t t e n t i o n to r i s k i n t e r v a l s over a l l income l e v e l s and use t h e s e r e s u l t s to p r e d i c t a c t io n choic es. 5.10 Using A t t r i b u t e s to P r e d i c t Action Choices A f t e r completing the d is c r im i n a n t a n a l y s i s f u r t h e r work was done to see how well r i s k p refe ren c e fu n ctio n s over a l l l e v e l s o f r e l e v a n t income could be p r e d i c t e d . To accomplish t h i s , th e upper and lower bounds o f the r i s k a v ersion f u n ctio n were used s e p a r a t e l y as the dependent v a r i a b l e , with th e a t t r i b u t e s p rev io u s ly mentioned, serving as independent 71 TABLE 5.10 Most I n f l u e n t i a l Variables in C l a s s i f i c a t i o n Process Income Level V A n aly sis'1 Discriminant Analysis 0-45,000 0 10,000 25,000 45,000 V0 V2 V3 V2 V6 A R V2 V5 V9 ' V8 V10 I V4 V6 V14 V10 V2 V9 V14 V 15 V14 V5 A B L E S V10 72 variables. Since the fun ctio n was measured a t fou r l e v e l s t h e r e were fou r o b se rv atio n s per in d iv id u al producer. not as good as hoped f o r . Unfortunately the r e s u l t s were A f t e r using a step-w ise process f o r adding and d e l e t i n g v a r i a b l e s , two equations remained. Equation 5.1 i s the estim ated equation f o r the lower bound on a b so lu te r i s k a v e r sio n , and Equation 5.2 i s the equation f o r th e upper bound. (5.1 ) Rl = -.00005158 V2 + .00000512 Vg - .000155 V4 ( -1.8 1) (3.048) (-.1598) R2 = .08 (5.2 ) Ry= .00157 + .000000012 VQ- .0000262 (2.88) (1.68) ( - 2 .5 5 ) V2 - .00000099 V]0 (-1.5 5 ) R2 = .08 Where: VQ = income V2 = age V4 = education Vg = acre s owned V*| q — acres rented R^ = lower bound on r i s k aversion Ry = upper bound on r i s k aversio n and t values a re under th e c o e f f i c i e n t s . Obviously only a small percentage o f the v a r i a t i o n i s explained p (R = .08). The v a r i a b l e s a re s i g n i f i c a n t and the signs f o r th e most p a r t follow accepted t h e o r i e s . The negativ e r e l a t i o n s h i p between age and r i s k aversion i s c o n s i s t e n t with de creasing a b so lu te r i s k a v ersion with r e s p e c t to wealth. r i s k a v erse . As you ge t o l d e r , you ge t more wealthy and l e s s Decreasing a b s o l u te r i s k av ersio n with education i s a ls o 73 expected. However, th e signs on Vq and V g , income and a cres owned a re the re v e r se o f what we would expect. N a t u ra l ly a b e t t e r s e t o f equatio ns would have been describ ed in p r e d i c t i n g a c t i o n choices based on a t t r i b u t e s . However, sin ce t h e s e were the b e s t t h a t were o b t a i n e d , they must s u f f i c e . In o r d e r to p r e d i c t a c t io n c h o ic e s , f i v e producers were se parated from the r e s t . The f i v e pro ducers' c h a r a c t e r i s t i c s were then plugged in to the above equation to p r e d i c t an upper and lower bound on t h e i r r i s k aversion i n t e r v a l . These estim ated i n t e r v a l s were then run to p r e d i c t a c t i o n choices o f each o f the producers. then compared with th e a ctual c h oic es. These p r e d i c ti o n s were This model was able to p r e d i c t e i g h t r i g h t , t h r e e wrong, while not ordering 39. Consequently, 22 p e r ­ cent were ordered and the e r r o r r a t e was 6 perc ent. While t h es e r e s u l t s appear good, cautio n i s advised. a re only as good as the model t h a t generates them. The i n t e r v a l s Obviously the r e g r e s ­ sion model generated here i s lackin g in most r e s p e c t s . The f a c t i t worked well in f i v e cases c e r t a i n l y d o e s n 't in su r e i t w ill do so in 20 o r 50 c a se s. CHAPTER VI CONCLUSIONS AND FUTURE RESEARCH 6.1 Conclusions The o b j e c t i v e s o f t h i s research can be c l a s s i f i e d i n to t h r e e a r e a s . Those t h r e e are as and the r e s u l t s obtained will now be summarized. The f i r s t o b j e c t i v e was to examine the i n t e r v a l method and i t s use­ f u l n e s s in p r e d i c t i n g a c t i o n choic es. As d i s c u s s e d , th e previous methods o f analyzing and u t i l i z i n g r i s k preferences have shortcomings. The i n ­ t e r v a l method i s a new tool and i t s s u p e r i o r i t y has n o t , u n t i l now, been demonstrated. C e r t a i n l y t h i s work has shown t h a t producers possess d i f f e r e n t r i s k prefe ren c e fu n c t i o n s and th ese fu n ctio n s take a l l d i f f e r e n t shapes. The i n t e r v a l method, when i t s use i s j u s t i f i e d , allows f o r t h a t to be taken i n t o c o n s i d e r a t i o n . The i n t e r v a l method a ls o demonstrated i t s g r e a t e r f l e x i b i l i t y and accuracy than a s i n g le - v a lu e d fu n ctio n . F i n a l l y , th e use o f the i n t e r v a l method to p r e d i c t a c tio n choices pro­ vided r e s u l t s t h a t a re very encouraging f o r f u r t h e r work in t h i s a re a. Not only does the i n t e r v a l method provide f o r a higher degree o f accuracy than a s i n g l e - v a lu e d f u n c t i o n , i t has the added f e a t u r e o f allowing f o r t r a d e - o f f s o f accuracy and o r d ering a c tio n choic es. The second o b j e c t i v e o f t h i s research was to e s t a b l i s h a r e l a t i o n ­ ship between the r i s k i n t e r v a l and producer a t t r i b u t e s . The r e s u l t s showed t h a t i t i s p o s s i b l e t o use producer a t t r i b u t e s to c o r r e c t l y 74 75 c l a s s i f y a l a r g e p e rc ent o f producers i n to t h e i r c o r r e c t r i s k preference category a t a p a r t i c u l a r income l e v e l . However, when using the e n t i r e r i s k p refe ren c e f u n c t i o n s , the r e l a t i o n s h i p between r i s k prefe renc e and a t t r i b u t e s i s much l e s s s u c c e s s f u l . This i s a r e s u l t o f th e f a c t t h a t a t t r i b u t e s t h a t c l a s s i f y a t each income level follow no c o n s i s t e n t p a t ­ t e r n over a l l income l e v e l s . F i n a l l y , the t h i r d o b j e c t i v e was to examine whether the a t t r i b u t e s could be used to p r e d i c t t h e p r o d u c e r 's r i s k p refere nce and then use t h i s i n t e r v a l to p r e d i c t a c t i o n c ho ic es . a p p o in tin g . The r e s u l t s in t h i s are a were d i s ­ This was a r e s u l t o f th e f a c t t h a t no s e t o f c o n s i s t e n t a t ­ t r i b u t e s were found ove r a l l income l e v e l s . 6.2 Areas of Further Research While t h i s res e a r c h has answered many q u e s t i o n s , i t ha s, in the pr o c e ss , c r e a t e d many more unanswered qu estio ns t h a t deserve f u r t h e r attention. In regards to the i n t e r v a l method, probably th e one area t h a t needs f u r t h e r a n a l y s i s i s th e t r a d e - o f f s between o rd ering o f a c t i o n choices and the accuracy a s s o c i a t e d with t h a t o r d e r in g . As was demonstrated with both the graduate s t u d e n ts and the farmers, an obvious t r a d e - o f f e x i s t s . Additional r e s e a r c h i s needed on what e x a c tly t h i s t r a d e - o f f i s and how, given the c o s t s and p r o b a b i l i t i e s o f e r r o r s , to make t h e c o r r e c t t r a d e ­ offs. Before the i n t e r v a l method i s a v ia b le decision-making t o o l , t h i s quest io n must be r eso lved, Other are as o f r e s e a r c h deserving a t t e n t i o n a re numerous. a re mentioned here. Several Does the r i s k i n t e r v a l o f a producer change over time and i f so, i s i t r e l a t e d to producer a t t r i b u t e s . This research was 76 c r o s s - s e c t i o n a l over producers. Time-series research over a p a r t i c u l a r s e t of producers would be very i n t e r e s t i n g . F i n a l l y , how well does the i n t e r v a l method perform when used in the actual decision-making environment r a t h e r than the hyp oth etica l example used in t h e q u e s t io n n i a r e ? I s i t p o s s ib l e to o b t a i n a r i s k i n t e r v a l based on a ctual marketing, management, and o t h e r bu siness d e cision s? Obviously the l i s t goes on. Obviously many q u e s t io n s are l e f t unanswered, some which a r e men­ tion ed here. Further e f f o r t s a re needed befo re th e p o t e n t i a l o f the r i s k p ref e r e n c e i n t e r v a l method as a new a n a l y t i c a l tool even begins to be exploited. APPENDICES APPENDIX A COVER LETTER 77 APPENDIX A COVER LETTER October 10, 1979 Dear S i r : You, o f cours e, know t h a t fanners d i f f e r in the amount o f r i s k they a re w i l l i n g to bear. This w i l li n g n e s s t o bear r i s k i n flu e n ce s the farm management decisi ons they make. C u rren tly , l i t t l e i s known about what determines p a r t i c u l a r r i s k a t t i t u d e s . I t i s because o f t h i s lack of knowledge t h a t the Department o f A g r i c u l t u r a l Economics a t Michigan S t a t e i s sponsoring research to determine what f a c t o r s i n f lu e n c e pro­ ducer a t t i t u d e s toward r i s k . A b e t t e r understanding in t h i s area should enable the U n ivers ity to provide b e t t e r farm management advice to you and farm managers l i k e you in the f u t u r e . Would you be w i l l i n g to p a r t i c i p a t e in t h i s study by completing the enclosed q u e s t io n n a ir e which should take l e s s than 45 minutes. Although the q u e s t io n n a ir e appears long, you a re only asked to complete a portio n of i t . To help you complete the q u e s t io n n a ir e each s e c t i o n begins with a s e t o f i n s t r u c t i o n s . The person who has primary r e s p o n s i b i l i t y f o r managing the farm should answer th e q u e s t i o n s , completing each se c t i o n as a c c u r a t e l y as p o s s ib l e . Once you have completed the q u e s t i o n n a i r e , please r e t u r n i t in the enclosed envelope as soon as p o s s ib l e . Naturally, a l l information t h a t you provide i s kept c o n f i d e n t i a l . Let me thank you in advance f o r your coopera tion. Your p a r t i c i p a ­ t i o n w ill assure you a copy o f th e research r e s u l t s once they are completed. S i n c e r e ly , Garth Carman Research A s s i s t a n t in A g r i c u l t u r a l Economics /law Enc. APPENDIX B QUESTIONNAIRE 78 APPENDIX B QUESTIONNAIRE INSTRUCTIONS FOR COMPLETING SECTIONS I - IV This p a r t o f the q u e s t i o n n a i r e i s designed to measure your a t t i t u d e towards r i s k . Each q u e s tio n asks you to make a comparison between two pl an s. Below each plan a r e l i s t e d s i x numbers, which r e p r e s e n t l e v e l s of a f t e r - t a x farm p r o f i t . One of th e s i x income l e v e l s w i l l be r e a l i z e d but assume you d o n ' t know which one a t th e time you s e l e c t a farm plan. To i l l u s t r a t e , assume each o f the farm income l e v e l s were p r i n t e d on the face of th e d i e . Each plan would be p r i n t e d on a d i f f e r e n t die so t h a t you would choose the d i e , then r o l l i t with the outcome being your r e a l i z e d farm income. This i s s i m i l a r to choosing between two crops knowing t h a t s i x d i f ­ f e r e n t p r i c e s and weather s i t u a t i o n s would occur. Suppose you could p l a n t Crop A and Crop B and your a f t e r - t a x farm p r o f i t i s t h a t l i s t e d under each s t a t e of n a tu re . STATE OF NATURE (1) (2) (3) (4) (5) (6) Poor p r i c e s , poor weather Poor p r i c e s , average weather Average p r i c e s , poor weather Average p r i c e s , good weather Good p r i c e s , average weather Good p r i c e s , good weather CROP A CROP B -5,000 5,000 6,000 15,000 20,000 25,000 5,000 10,000 12,000 13,000 14,000 15,000 You d o n ' t know what the weather w ill be l i k e nor do you know what p r ic e s will be, but you s t i l l must decide which crop you a r e going to produce. Again, you must decide i f you are w i l l i n g to p l a n t Crop A with lower l e v e l s o f income f o r bad outcomes so t h a t you could r e a l i z e higher income l e v e l s i f good outcomes occurred or whether you would produce Crop B giving up a chance o f high income l e v e l s so you w on't have to take a chance with low income l e v e l s . More importan tly t h i s d e cisio n i s based on the d i f f e r e n c e in income l e v e l s between the two crops f o r each s t a t e o f n a ture . In o t h e r words how much a r e you w i l l i n g to give up f o r a chance of being b e t t e r o f f to avoid a chance o f being worse o f f ? This i s the a n a l y s i s you should make. There a re several f a c t o r s to keep in mind as you complete t h i s questionnaire. (1) There a re no r i g h t o r wrong answers. Everyone has d i f f e r e n t a t t i t u d e s towards tak in g chances as opposed to playing i t s a f e . (2) Try to r e l a t e t h i s experiment to your own s i t u a t i o n . Assume t h a t a t the beginning o f the y e a r t h e r e were the two farm plans a v a i l a b l e t o you and t h a t you had to choose one f o r t h a t y e ar. 79 (3) Assume each income level r e p r e s e n ts your a f t e r - t a x farm p r o f i t f o r the e n t i r e y e a r . With t h i s in mind th in k about what you would do i f a good outcome occurred (good p r ic e s and weather) and you took the plan with the h ig h er income l e v e l . On the o t h e r hand, think about what you would do i f a bad outcome occurred (poor p r i c e s and weather) and you took the plan with t h e lower income l e v e l . (4) The si gn preceding the income level means income l o s s e s . In each s e c t i o n you are asked to make a comparison and based on which plan you s e l e c t , you a re asked to go to another q u e stio n . As a r e s u l t , you are only asked to respond to t h r e e o f the seven q u e stio n s in each section. Each s e c t i o n examines d i f f e r e n t income l e v e l s . In the f i r s t s e c t i o n t h e r e are negativ e income l e v e l s ( o r l o s s e s ) . Assume t h a t i f you d i d n ' t take one of th es e plans your l o sse s would be even g r e a t e r . In each of the following s e c t i o n s the income l e v e l s i n c r e a s e . With t h es e i n s t r u c t i o n s in mind, please complete Sections I , I I , I I I , and IV. 80 SECTI ON 1. I I f you were r e q u ir e d t o choose between PLAN 17 and PLAN 3, p u t a check i n th e box t o th e r i g h t o f th e one you would s e le c t . PLAN 17 | $$$$$ $ 1 950 550 100 50 50 450 PLAN 3 $$$$$ $ 650 550 450 300 150 300 I f you p r e f e r PLAN 17, go to Question 3. I f you p r e f e r PLAN 3, go to Question 2. 2. I f you were re qu ire d to choose between PLAN 7 and PLAN 3, put a check in the box to th e r i g h t o f the one you would s e l e c t . PLAN 7 | 1 $-1 ,000 $- 450 $- 150 400 $ 450 $ ,100 $ 1 PLAN 3 $$$$$ $ □ 650 550 450 300 150 300 I f you p r e f e r PLAN 7, go to Question 5. I f you p r e f e r PLAN 3, go to Question 4. I f you were requ ire d to choose between PLAN 8 and PLAN 4 r put a check in the box to th e r i g h t o f the one you would s e l e c t . PLAN 8 | $$$ $ $ $ 950 50 0 50 150 200 1 PLAN 4 $$$$ $ $ 450 300 200 50 100 200 I f you p r e f e r PLAN 8 , go t o Q uestion 7. I f you p r e f e r PLAN 4, go t o Q uestion 6. I f you were r e q u ir e d t o choose between PLAN 2 and PLAN 12, p u t a check i n th e box t o th e r i g h t o f th e one you would s e l e c t . PLAN 2 PLAN 12 j $- 550 $ 0 $ 0 $ 400 $ 650 $ 1,100 $$$$ $ $ 1 350 150 150 100 250 500 Stop and go to Section I I . I f you were req u ired t o choose between PLAN 7 and PLAN 4, put a check in the box to the r i g h t of the one you would s e l e c t . PLAN 7 1 | PLAN 4 $- 1,000 $- 450 $- 150 400 $ 450 $ $ 1,100 Stop and go t o Section I I . $$$$ $ $ 450 300 200 50 100 200 I f you were r eq u ire d t o choose between PLAN 26 and PLAN 5, put a check in the box to th e r i g h t of the one you would s e l e c t . PLAN 26 | | $- 950 $- 500 $- 150 250 $ 250 $ 450 $ Stop and go to Section I I . PLAN 5 $$$$$ $ 600 150 100 100 50 150 I f you were r eq u ir e d t o choose between PLAN 29 and PLAN 1, put a check in the box to t h e r i g h t of the one you would s e l e c t . PLAN 29 | | $-1,000 $- 200 $ 0 $ 100 $ 600 $ 1,050 Stop and go to Section I I . PLAN 1 [ $$$$ $ $ 300 250 100 450 450 600 | 82 SECTI ON 1. II I f you were r e q u ir e d t o choose between PLAN 3 and PLAN 17, p u t a check i n th e box t o th e r i g h t o f th e one you would s e l e c t . PLAN 17 | 1 $ 9,000 $ 9,050 $ 9,150 $10,000 $10,700 $11,100 PLAN 3 $ 9,350 $ 9,450 $ 9,550 $ 9,700 $10,150 $10,300 p r e f e r PLAN 17, go to Question 2. I f you p r e f e r PLAN 3, go to Question 3. 2. I f you were r eq u ire d to choose between PLAN 8 and PLAN 4, put a check in th e box to the r i g h t of the one you would s e l e c t . PLAN 8 1 I $ 9,050 $ 9,950 $10,000 $10,050 $10,150 $10,200 PLAN 4 $ 9,550 $ 9,700 $ 9,800 $10,050 $10,100 $10,200 I f you p r e f e r PLAN 8, go to Question 4. I f you p r e f e r PLAN 4, go to Question 5. I f you were r eq u ire d to choose between PLAN 2 and PLAN 13, put a check in the box t o the r i g h t o f the one you would s e l e c t . PLAN 2 | $ 9,450 $10,000 $10,000 $10,400 $10,650 $11,100 | PLAN 13 | $ 9,700 $ 9,850 $ 9,950 $10,350 $10,400 $10,800 I f you p r e f e r PLAN 2 , go t o Q uestio n 6. I f you p r e f e r PLAN 13, t o t o Q uestion 7. | 83 4. I f you were r e q u ir e d t o choose between PLAN 29 and PLAN 1, p u t a the box to the r i g h t o f the one you would s e l e c t . PLAN 29 1 I $ 9,000 $ 9,800 $10,000 $10,100 $10,600 $11,050 PLAN 1 □ $ 9,700 $ 9,750 $ 9,900 $10,450 $10,450 $10,600 go to Section I I I . 5. I f you were req uired to choose between PLAN 6 and PLAN 40, put a the box to the r i g h t o f th e one you would s e l e c t . PLAN 40 | | $ 9,150 $ 9,400 $ 9,750 $10,200 $10,600 $10,600 PLAN 6 □ $ 9,350 $ 9,550 $ 9,650 $ 9,950 $10,550 $10,600 go to Section I I I . I f you were req uire d to choose between PLAN 7 and PLAN 4, put a check in the box to the r i g h t o f the one you would s e l e c t . PLAN 7 | | PLAN 4 | $ 9,000 $ 9,550 $ 9,850 $10,400 $10,450 $ 9,550 $ 9,700 $ 9,800 $10,050 $10,100 $11,1 0 0 $10,200 Stop and go t o S e c tio n I I I . [ 84 7. I f you were r e q u ir e d to choose between PLAN 1 and PLAN 38, put a check in th e box t o th e r i g h t o f the one you would s e l e c t . PLAN 1 | 1 $ 9,700 $ 9,750 $ 9,900 $10,450 $10,450 $10,600 Stop and go t o S e c tio n I I I . PLAN 38 | $ 9,700 $ 9,900 $10,000 $10,050 $10,250 $10,450 | 85 SECTI ON 1. III I f you were r e q u ir e d t o choose between PLAN 29 and PLAN 4 , p u t a check in th e box t o th e r i g h t o f the one you would s e l e c t . PLAN 29 | 1 $21,900 $24,350 $24,900 $25,350 $26,850 $28,250 PLAN 4 [~~] $23,650 $24,100 $24,300 $25,150 $25,350 $25,700 I f you p r e f e r PLAN 29, go to Question 3. I f you p r e f e r PLAN 4, go to Question 2. 2. I f you were req u ired to choose between PLAN 2 and PLAN 11, put a check in the box to th e r i g h t o f th e one you would s e l e c t . PLAN 2 1 | PLAN 11 $23,600 $24,250 $24,500 $25,800 $25,950 $27,700 $23,300 $24,900 $25,100 $26,250 $26,950 $28,300 I f you p r e f e r PLAN 2, go to Question 5. I f you p r e f e r PLAN 11, go to Question 4. 3. I f you were r eq u ir e d to choose between PLAN 17 and PLAN 4, put a check in the box to t h e r i g h t o f the one you would s e l e c t . PLAN 17 $21,900 $22,150 $22,450 $25,000 $27,200 $28,400 [ | PLAN 4 | $23,650 $24,100 $24,300 $25,150 $25,350 $25,700 I f you p r e f e r PLAN 17, go t o Q uestio n 7. I f you p r e f e r PLAN 4 , go to Q uestion 6. | 86 4. I f you were r e q u ir e d t o choose between PLAN 6 and PLAN 3, p u t a check in the box t o th e r i g h t o f th e one you would s e le c t , PLAN 6 | | PLAN 3 f $22,950 $23,650 $23,850 $24,800. $26,700 $26,850 | $23,000 $23,350 $23,600 $24,100 $25,500 $26,000 Stop and go to Section IV. I f you were r eq u ire d to choose between PLAN 2 and PLAN 1, put a check in the box to t h e r i g h t o f the one you would s e l e c t . PLAN 2 | | PLAN 1 | $23,300 $24,900 $25,100 $26,250 $26,950 $28,300 Stop and | $24,050 $24,200 $24,700 $26,450 $26,450 $26,850 go to Section IV. I f you were r eq u ire d to choose between PLAN 6 and PLAN 4, put a check in the box to the r i g h t o f the one you would s e l e c t . PLAN 6 | | $22,950 $23,650 $23,850 $24,800 $26,700 $26,850 Stop and go t o S e c tio n IV. PLAN 4 | $23,650 $24,100 $24,300 $25,150 $25,350 $25,700 | 87 I f you were r e q u ir e d t o choose between PLAN 17 and PLAN 1, p u t a check in the box to th e r i g h t o f th e one you would s e l e c t . PLAN 17 | | $21,900 $22,150 $22,450 $25,000 $27,200 $28,400 Stop and go t o S e c tio n IV. PLAN 1 | $24,050 $24,200 $24,700 $26,450 $26,450 $26,850 | 88 SECTI ON IV I f you were r e q u ir e d t o choose between PLAN 2 and PLAN 1, p u t a check in th e box t o th e r i g h t o f th e one you would s e l e c t . PLAN 2 | L $42,100 $44,850 $45,200 $47,100 $48,250 $50,550 PLAN 1 [ j $43,450 $43,650 $44,500 $47,450 $47,450 $48,100 I f you p r e f e r PLAN 2, go to Question 2. I f you p r e f e r PLAN 1, go to Question 3. I f you were r eq u ire d to choose between PLAN 19 and PLAN 1, put a check in the box to th e r i g h t o f the one you would s e l e c t . PLAN 19 | $41,250 $44,500 $45,500 $45,800 $46,350 $50,450 | PLAN 1 I I $43,450 $43,650 $44,500 $47,450 $47,450 $48,100 I f you p r e f e r PLAN 19, go to Question 5. I f you p r e f e r PLAN 1, go to Question 4. 3. I f you were req u ire d to choose between PLAN 14 and PLAN 3, put a check in the box to th e r i g h t o f the one you would s e l e c t . PLAN 14 □ PLAN 3 I $41,350 $42,200 $44,400 $44,700 $47,250 $47,500 $41,650 $42,250 $42,650 $43,500 $45,850 $46,700 I f you p r e f e r PLAN 14, go t o Q uestion 6. I f you p r e f e r PLAN 3, go to Q uestion 7. 1 89 I f you were r e q u ir e d t o choose between PLAN 28 and PLAN 1, p u t a check in th e box to th e r i g h t o f th e one you would s e l e c t . PLAN 28 | | PLAN 1 | $41,250 $44,500 $44,550 $48,700 $49,150 $49,400 Stop and 5. | $43,450 $43,650 $44,500 $47,450 $47,450 $48,100 go to Section V. I f you were req uired to choose between PLAN 9 and PLAN 1, put a the box to th e r i g h t o f the one you would s e l e c t . PLAN 9 | 1 $41,200 $42,900 $43,250 $45,400 $45,850 $50,000 PLAN 1 | | $43,450 $43,650 $44,500 $47,450 $47,450 $48,100 go to Section V. 6. I f you were require d to choose between PLAN 2 and PLAN 11, put a check in the box to the r i g h t o f the one you would s e l e c t . PLAN 2 | 1 $42,100 $44,850 $45,200 $47,100 $48,250 $50,550 Stop and go t o S e c tio n V. PLAN 11 ( 1 $42,700 $43,750 $44,100 $46,300 $46,550 $49,500 90 S E C T I O N V In t h i s s e c t i o n you a r e asked to make the same type o f comparisons you j u s t made in Sections I - IV only ove r a wider range o f p o s s ib l e income l e v e l s . L is te d below are f i v e plans: PLAN 1 PLAN 2 PLAN 3 PLAN 4 PLAN 5 $-1,100 $ 3,000 $18,000 $35,000 $45,000 $50,000 $ 5,000 $11,000 $19,000 $26,000 $32,000 $37,000 $10,000 $15,000 $20,000 $25,000 $28,000 $30,000 $- ,800 $ 2,000 $11,000 $25,000 $40,000 $48,000 $- ,200 $10,000 $22,000 $25,000 $35,000 $40,000 Compare each s e t o f plans l i s t e d below and put a check in the e r i g h t o f the one you p r e f e r : PLAN 1 □ OR PLAN 2 □ PLAN 1 n OR PLAN 3 □ PLAN 1 □ OR PLAN 4 □ PLAN 1 □ OR PLAN 5 □ PLAN 2 □ OR PLAN 3 □ PLAN 2 □ OR PLAN 4 □ PLAN 2 □ OR PLAN 5 □ PLAN 3 □ OR PLAN 4 □ PLAN 3 □ OR PLAN 5 □ PLAN 4 OR PLAN 5 □ Go to se c t i o n VI. □ 91 SECTI ON VI In t h i s s e c tio n we w ish t o f i n d o u t some o f th e c h a r a c t e r i s t i c s ab ou t you and y o u r f a m il y o p e r a t io n . The in f o r m a t io n t h a t i s needed i s l i s t e d below. Please check o r f i l l i n th e a p p r o p r ia te b la n k s : (1) Marital s t a t u s (2) Age (3) Number o f c h il d r e n (4) Last grade o f school you completed (5) How many ye ars have you spent ] Married j 1 Single l i v i n g on a farm? managing a farm? (6) What % o f your t o t a l family income i s from the farm? % (7) What %o f your farm income i s your share? % (8) How many acres do you own? I (9) (10) ren t? How many cows do you own? I f you had an important farm management decisio n t o make, would you: 1 Feel more c o n fid e n t about i t i f you have o t h e r p e o p le 's advice; OR I Feel t h a t nobody e l s e i s in as good a p o s i t i o n to judge as you a re . 92 (11) For en te rta in m e n t would you r a t h e r 1 Be around f r i e n d s ( l i k e going to a p a rty ) OR 1 Be more to y o u r s e l f ( l i k e going to a movie). (12) Are you u s u a l ly a I | Good mixer OR 1 Quiet and re served. (13) When you make a de cision do you u su a lly I | Make i t r i g h t away OR 1 Wait as long as you reasonably can before deciding. (14) Do you p r e f e r to 1 | Organize your schedule well in advance OR | Be f r e e to do whatever looks b e st when the time comes. (15) When you make a d e cisio n do you | Tend to be s a t i s f i e d OR 1 Tend to be curious and look f o r new l i g h t on the subject. You have now completed the q u e s t i o n n a i r e . cooperation. Thank you f o r your APPENDIX C FOLLOW-UP LETTER 93 APPENCIX C FOLLOW-UP LETTER October 22, 1979 Dear S i r : Curr ently l i t t l e i s known about pro ducers' a t t i t u d e s toward r i s k . These a t t i t u d e s toward r i s k a re important in determining both farm and nonfarm investment d ecisio n s t h a t farmers make. Furthermore, even le s s i s known about how th ese r i s k a t t i t u d e s a re r e l a t e d to the c h a r a c t e r ­ i s t i c s of the farmer and his farming o p e ra tio n . This lack o f knowledge l i m i t s the e f f e c t i v e n e s s of the farm management advice t h a t the Univer­ s i t y provides t o decision-makers such as y o u r s e l f . About two weeks ago you received a q u e s t io n n a ir e in th e mail which was designed t o gain a b e t t e r understanding about the r e l a t i o n s h i p between your r i s k a t t i t u d e and the c h a r a c t e r i s t i c s of your farm opera­ t i o n . The r e s u l t s of your q u e s t io n n a ir e w ill be used, along with o th er farmers who received the q u e s t i o n n a i r e , to gain a b e t t e r understanding about farmers' a t t i t u d e s toward r i s k and th e manner in which these a t t i t u d e s are r e l a t e d to c h a r a c t e r i s t i c s of the farming o p e ra tio n . I f you have a lr ead y re tu r n e d the completed q u e s t i o n n a i r e , please accept my thanks. I f you have not y e t done so, please r e t u r n the com­ p l e t e d q u e s t io n n a ir e as soon as p o s s ib l e . A f t e r the q u e s t i o n n a i r e s are r e t u r n e d , they w ill be analyzed and you w ill r eceiv e a copy o f the research r e s u l t s . S i n c e r e ly , Garth Carman Research A s s i s t a n t in A g r i c u l t u r a l Economics GC/law BIBLIOGRAPHY BIBLIOGRAPHY Altman, Edward I. "Financial R a t i o s , Disc riminan t Analysis and the P r e d i c t i o n o f Corporate Bankruptcy." Journal o f Finance, 23 (September 1968), pp. 589-609. Barry, P e t e r J . and Baker, C. B. "Management o f Firm Level Financial S t r u c t u r e . " A g r i c u l t u r a l Finance Review, E .R .S ., U.S.D.A., 37 (February 1977). Barry, P e t e r J . and F r a s e r , Donald R. "Risk Management in Primary A g r i c u l t u r a l Production: Methods, D i s t r i b u t i o n s , Rewards, and S t r u c t u r a l I m p l i c a t i o n s . 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" A g r i c u l t u r a l Econo­ mics S t a f f Paper No. 79-10, Department o f A g r i c u l t u r a l Economics, Michigan S t a t e U n i v e r s i t y , 1979. King, Robert P. and Robison, Lindon J . "Implementation o f the I n t e r v a l Approach to the Measurement o f Decision Maker P r e f e r e n c e s . " Michigan S t a t e U n i v e rs i ty A g r i c u l t u r a l Experiment S t a t i o n Research Report #418, November 1981. Lin, William W. and Chang, Hui S. " S p e c i f i c a t i o n of B ern o ullian U t i l i t y Functions in Decision A n a l y s i s . " A g r i c u l t u r a l Economics Re se arch, 30 (1978), pp. 30-36. Lin, W.; Dean, 6. W.; and Moore, C. V. "An Empirical Test o f U t i l i t y vs. P r o f i t Maximization in A g r i c u l t u r a l P r o d u c tio n ." American Journal o f A g r i c u l t u r a l Economics, 56 (1974), pp. 497-508. Madden, J . P a t r i c k Economics o f Size in Farming. United S t a t e s Depart­ ment of A g r i c u l t u r e , A g r i c u l t u r a l Economics Report No. 107, February 1967. Manderscheid, L e s t e r V. " S i g n i f i c a n t Levels - - 0 .0 5 , 0 . 0 1 , or ?" Journal o f Farm Economics 47 (December 1965), pp. 1381-1385. McKinnon, Ronald I. "Future Markets, Buffer Stocks, and Income S t a b i l ­ i t y f o r Primary Producers." The Journal o f P o l i t i c a l Economy 75 (December 1967), pp. 844-861. Meyer, Jack "Choice Among D i s t r i b u t i o n s . " J . Ecpn. Theory 14(1977): 96 M o sc a rd i, Edgardo and de J a n v r y , A l a i n " A t t i t u d e s Toward R isk Among Peasants: An E conom etric A p p ro a c h ." American J o u rn a l o f A g r i ­ c u l t u r a l Economics, 50 (November 1 9 7 7 ), pp. 710-716. Myers, Isabel Briggs The r-fyers-Briggs Type I n d i c a t o r . P sychologists P r e s s , Palo A l t o , C a l i f o r n i a , 1962. Consulting O f f i c e r , R. R. and H a l t e r , A. W. " U t i l i t y Analysis in a P r a c t i c a l S e t t i n g . " American Journal o f A g r i c u l t u r a l Economics, 50 (May 1968). Roberts, Dayton Young and Lee, Hong Yong " P e r s o n a li z in g Learning Responses in A g r i c u l t u r a l Economics." American Journal o f Agri­ c u l t u r a l Economics, 59 (December 1977). Robison, Lindon J . and King, Robert P. " S p e c i f i c a t i o n o f Micro Risk Models f o r Farm Management and P olicy Research." A g r i c u l t u r a l Economics Report No. 349, Department o f A g r i c u l t u r a l Economics, Michigan S t a t e U n i v e r s i t y , December 1978. Stanto n, B. F. " P e r s p e c t i v e o f Farm S i z e . " American Journal o f Ag ri­ c u l t u r a l Economics, 60 (December 1978). T i n t n e r , Gerhard Econometrics. (1952), pp. 96-102. New York: John Wiley and Sons, U.S. Bureau o f Census, Census o f A g r i c u l t u r e , 1969, Vol. I I . 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