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Micro economic approaches to technical change in the Canadian beef cattle industry: two studies of crossbreeding… Kerr, William Alexander 1981

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MICRO ECONOMIC APPROACHES TO TECHNICAL CHANGE IN THE CANADIAN BEEF CATTLE INDUSTRY:  TWO STUDIES OF  CROSSBREEDING AS AN INNOVATION by WILLIAM A. KERR B.A., The U n i v e r s i t y of B r i t i s h Columbia, 1969 M.A., Simon Fraser U n i v e r s i t y , 1973  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Economics  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA January 1981 (c) William A. Kerr  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I for  the U n i v e r s i t y  s h a l l make i t  freely  fulfilment o f the requirements f o r of B r i t i s h  available  for  Columbia,  I agree  that  r e f e r e n c e and s t u d y .  f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s  thesis  s c h o l a r l y purposes may be granted by the Head o f my D e p a r t m e n t o r  by  his  of  this  written  representatives. thesis for  It  financial  i s understood that c o p y i n g gain shall  permission.  Department o f The  in p a r t i a l  University  C ^ ^ ^ ^ ^ ^ of B r i t i s h  2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  3  Columbia  or publication  not be allowed w i t h o u t  my  iv MICRO ECONOMIC APPROACHES TO TECHNICAL CHANGE IN THE CANADIAN BEEF CATTLE INDUSTRY:  TWO STUDIES OF CROSSBREEDING AS  AN INNOVATION  William Alexander Kerr  Chairman:  Professor G. C. Archibald  ABSTRACT This d i s s e r t a t i o n investigates the process of genetic-based technical change i n the Canadian beef c a t t l e industry.  S p e c i f i c a l l y , I analyze the  e f f e c t o f market forces on three processes necessary f o r genetic-based technological change:  expansion of the genetic pool, inbreeding of  divergent genetic s t r a i n s to increase the p r o b a b i l i t y of desired h e r i t a b l e properties i n a pure breeding s t r a i n , and crossing o f pure breeding s t r a i n s to take advantage of hybrid vigour.  This i s accomplished through two  studi es. The f i r s t study, examines the expansion o f the genetic pool through the establishment of purebred breeders of c a t t l e breeds imported since 1965. A model i s developed t o explain the l o c a t i o n o f breeders w i t h i n a time framework.  The model was tested across breeds and over time.  The process  of breeder l o c a t i o n appears consistent f o r the various breeds and can help explain the dates of a v a i l a b i l i t y of new breeds o f c a t t l e i n d i f f e r e n t areas of the country. The second study examines the ongoing process of genetic technical change through the improvement and sale of breeding stock.  A model i s  developed e x p l i c i t l y using the " c h a r a c t e r i s t i c s " approach to production  i i i  with the phenotypic c h a r a c t e r i s t i c s of breeding bulls as arguments in a production  function.  Prices of i n d i v i d u a l b u l l s and values f o r the c h a r a c t e r i s t i c s were c o l l e c t e d at b u l l sales and shadow values f o r the c h a r a c t e r i s t i c s estimated.  These shadow values were used to predict  characteristics  which should be emphasized i n herd improvement, and the prediction compared to observed practices.  The use of the c h a r a c t e r i s t i c : approach  led to the i d e n t i f i c a t i o n of a d i f f e r e n t production function t r a d i t i o n a l straightbred  was  f o r the  technology and the new crossbred technology.  Market forces seem to regulate the process of technological and promote breed improvement.  change  The major constraint to a v a i l a b i l i t y  appears to be the l i m i t a t i o n on imports and the b i o l o g i c a l l i m i t s to increasing  the stock of purebred  females.  iv TABLE OF CONTENTS Page ABSTRACT  i i  TABLE OF CONTENTS  iv  LIST OF TABLES  vi  LIST OF DIAGRAMS  vii  ACKNOWLEDGEMENTS  viii  CHAPTER I  INTRODUCTION  i ii iii iv  Foreword Background I n s t i t u t i o n a l Considerations Economic Analysis of Technological Change STUDY I  CHAPTER II i ii ii ii ii ii iii iv v vi vi vi vi vi vi vi vii vii vii vii vii vii viii ix  a b c d  a b b b b b a b c d e  1 2 3 4  1 1 2 5 7  THE SUPPLY OF A NEW TECHNIQUE  11  Background Institutions Importation Registration o f Animals Evaluation of Genetic Potential Promotion and Sale of Cattle Review of L i t e r a t u r e Hypotheses The Model Variables and Data The Dependent Variable Independent Variables Potential Market The Expected Rate o f Acceptance Market Costs Cost o f Introduction S t a t i s t i c a l Methods and Results Five Year Estimates Seven Year Estimates Nine Year Estimates Eleven Year Estimates Nineteen Year Estimates f o r Charolais Breed Tests f o r Consistency o f Pattern Discussion  11 13 14 17 18 19 20 23 24 27 27 29 29 30 31 32 34 35 47 53 57 59 60 69  V  Page CHAPTER I I I i ii iii iv v vi vii CHAPTER IV  STUDY II CONTINUING TECHNICAL PROGRESS - GENETIC IMPROVEMENT IN THE CANADIAN CATTLE INDUSTRY Background Review o f L i t e r a t u r e Hypotheses The Model Data S t a t i s t i c a l Analysis and Results Discussion SUMMARY AND CONCLUSIONS  82 82 84 88 88 98 101 119 128  FOOTNOTES  138  REFERENCES  143  APPENDIX I  EXAMPLE OF DETAILED CALCULATIONS FOR TABLE I I I 3 AND TABLE I I I 4  149  APPENDIX I I  SUMMARY OF DATA USED IN STUDY I  151  APPENDIX I I I  SUMMARY OF DATA USED IN STUDY II  170  vi LIST OF TABLES TABLE  Page  11.1  Estimates of F i r s t Five Years o f Location by Breed . . . .  38  11.2  Estimates o f F i r s t Seven Years of Location by Breed  ...  48  11.3  Estimates of F i r s t Nine Years o f Location by Breed . . . .  54  11.4  Estimates of F i r s t Eleven Years of Location by Breed . . .  58  II 5  Estimates of F i r s t Nineteen Years of Location f o r . the Charolais Breed  59  116 11.7 11.8  ,  C o e f f i c i e n t Values and Variance o f the Estimate as Truncation i s Increased from 5 t o 9 Years  68  Average Number o f Census Areas Entered by Breed with D i f f e r e n t F i r s t Dates of Entry  70  Number of Females Imported by Breed i n the F i r s t Five Years  11.9  Percent of Market Penetration by Breed  Summary of Market Penetration by Province, 18 Exotic Breeds, 1978 11.11 , Market Penetration by Province, 18 Exotic  71 74  11.10  , .75  Breeds, 1978  77  111.1  L i s t o f Bull Sales  99  111.2  Number o f B u l l s by Breed  99  111.3  Expected Daily Expected Daily  111.4  Value o f Improving Weaning Weight and Average Gain - Saskatchewan Bull Test Station Bulls I . Value o f Improving Weaning Weight and Average Gain - National R.O.P. Averages 1970-1978 . . . .  11.1 115  VI1  LIST OF DIAGRAMS  DIAGRAM II.1  Page 66  viii ACKNOWLEDGEMENTS I t i s a pleasure to acknowledge my debt to the many people who have helped me with ideas i n the course of the present i n v e s t i g a t i o n .  Thanks  are due f i r s t of a l l to the members of my d i s s e r t a t i o n committee, Professors Chris A r c h i b a l d , Jim MacMillan, Bob A l l e n and Dave Stapleton. My debt t o Professor Archibald i s a l a s t i n g one f o r he provided the i n s i g h t s and breadth necessary to overcome the l i m i t s of my knowledge and provide a wider scope for the study.  Professors MacMillan and A l l e n made  many helpful suggestions, while my discussions with Professor Stapleton during the estimation stage were extremely valuable. I should also l i k e to extend my deepest thanks t o Professor G. Rosenbluth of the Economics Department and Professor R. B a r i c h e l l o of the Department of A g r i c u l t u r a l Economics.  Professor Rosenbluth got me s t a r t e d  on the r i g h t track and l e t me c a l l upon his time and ideas without reservation.  Professor B a r i c h e l l o always had..an ;open door and an::interest  i n the project which provided a great deal of encouragement. I also wish to thank Sharon Chestnutt and Margot Boyle who worked f a i t h f u l l y at c o l l e c t i n g and organizing the large amounts of data u t i l i z e d i n the p r o j e c t , and to Brenda MacDonald who spent many hours on the phone checking and double checking the data. must also go to Anne  A s p e c i a l thanks  McClelland of the Department of Animal Science  who answered without complaint my many questions regarding genetics.  1  x  F i n a l l y , I express deep gratitude to my parents f o r the innumerable hours spent e d i t i n g and typing the various manuscripts, and more importantly f o r the years of continual encouragement and support. thesis i s dedicated to them. W.A. Kerr Vancouver, B.C. September, 1980  This  CHAPTER I : INTRODUCTION  I i  Foreword One of the necessary conditions for the existence of modern i n d u s t r i a l  society has been the production revolution which the a g r i c u l t u r a l sector has experienced  during the past four centuries.  This " r e v o l u t i o n " i s dependent  upon two p o s i t i v e a c t i o n s , the development of new production processes and the u t i l i z a t i o n of such processes by producers. termed "innovation" and "adoption".  These actions are generally  During t h i s century improvements i n the  p r o d u c t i v i t y of a g r i c u l t u r a l operations due to technological change have been manifest p r i m a r i l y i n three ways:  1) improvements to inputs of  production resulting-from the development o f the i n t e r n a l combustion or e l e c t r i c a l engines (the movement from animal power to motor driven machinery);  2) improvements to inputs to, production r e s u l t i n g from advances  in pure science ( f e r t i l i z e r , herbicides, p e s t i c i d e s ) ; and 3) improvements to the inputs of production through t h e o r e t i c a l and, subsequently,  applied  advances i n genetics (hybrid corn, hybrid sugar, and miracle r i c e and wheat, H o l s t e i n s ) . Of course, these new processes may often act i n conjunction with each other.  The majority of genetic-based  More r e c e n t l y , however, the techniques applied i n the animal industry. i s s e l e c t i v e breeding.  improvements have been i n plant science. developed i n modern genetics have been  The basis of genetic improvement i n animals  The process of genetic improvement i s i d e n t i c a l to  that which i s used i n plant breeding, and i t i s a function o f three d i s t i n c t processes:  expansion of the genetic pool, inbreeding of divergent  genetic  s t r a i n s to increase the p r o b a b i l i t y of desired h e r i t a b l e properties i n a pure breeding s t r a i n , and crossing o f the pure breeding s t r a i n s to take advantage of hybrid vigour.  Z. The beef c a t t l e industry i s the l a s t major segment of primary a g r i c u l t u r e to experience the production revolution r e s u l t i n g from advances in applied genetics. The potential e x i s t s f o r increasing percentage  yields  from animals an amount equal t o , or greater than, that manifest i n f i e l d crops.  At present, the innovation i s not u t i l i z e d by a l l members of the  industry as the process of d i f f u s i o n i s not complete.  Ex post examination  of previous genetic-based innovations have yielded some rather consistent conclusions about what may be expected from the process of genetic-based technical change.  Of p a r t i c u l a r relevance to the beef c a t t l e case are  changes in the d i s t r i b u t i o n of income between firms which r e s u l t s from unequal use of innovations over time and those a l t e r i n g the innovation i t s e l f , which r e s u l t from imperfections i n the genetic mix or changes i n the environment, both physical and economic. The Canadian c a t t l e industry operates within an i n s t i t u t i o n a l structure which i s unique i n terms of major genetic technical change, while the b i o l o g i c a l parameters of c a t t l e breeding demands an extension of economic analysis into an area of production theory which has not been well explored. This study of genetic-based technical change i n the Canadian beef c a t t l e industry hopefully provides additional i n s i g h t i n t o the more general process of technical change and the approach to i t s study by economists. I i i Background Improvement of l i v e s t o c k by s e l e c t i v e breeding has been practiced since antiquity.  Modern beef c a t t l e breeding has i t s o r i g i n i n the development  of purebred strains i n B r i t a i n during the 17th and 18th centuries.  As  there are no c a t t l e indigenous to North America, the foundation herds were the r e s u l t of importations to Mexico by the Spanish, and importations to the United States and Canada by, f o r the most p a r t , B r i t i s h s e t t l e r s .  3. I t was not long before i n t e r e s t i n c a t t l e improvement led t o the importation of purebreds into North America.  The f i r s t Shorthorns imported to America  were brought t o V i r g i n i a i n 1783; Herefords were f i r s t imported i n 1817, Galloways i n 1837 and Aberdeen Angus i n 1873 (Plumb, 1920).  These animals,  and subsequent importations, provided the basis f o r the genetic upgrading of the North American c a t t l e herd.  Under the constraint o f a straight-bred  philosophy these animals evolved i n t o stock adapted to l o c a l production conditions and consumer preferences (Hunsley, 1975).  However, through the  1950's and 60's, improvement i n genetic knowledge and changes i n consumer preferences provided incentive f o r changes i n the c a t t l e breeding industry. \; Pressure from applied g e n e t i c i s t s ( P h i l l i p s , 1961) and evidence from the poultry and swine industry (Carman, 1960) l e d to an i n t e r e s t i n crossbreeding by commercial cattlemen (Ackerson, 1967).  At the same time,  consumer preferences (and eventually the grading systems) were changing to require higher y i e l d s of lean of acceptable eating q u a l i t y from beef carcasses (Warwick, 1973). The development of the c a t t l e industry i n continental Europe had p a r a l l e l e d that i n B r i t a i n and North America with the establishment of breeds and breed standards. The F.A.O. p u b l i c a t i o n European Breeds of Cattle (French, 1966), delineates some 150 d i f f e r e n t breeds or s t r a i n s o f cattle.  Some of these European breeds had concentrated on heavy muscling  for draught purposes which i n d i r e c t l y produced animals with larger leaner carcasses.  Therefore, there seemed to be i n Europe an ideal set of germ  plasm with the genetic d i v e r s i t y necessary f o r e f f e c t i v e crossbreeding and developed c h a r a c t e r i s t i c s which would complement the so c a l l e d B r i t i s h ^ breeds i n North America. However, expansion of the genetic pool by the importation of c a t t l e from Europe was prohibited by the quarantine regulations of the Canadian  4. and American governments.  Thus, rapid genetic-based technological change i n  the beef c a t t l e industry was e f f e c t i v e l y thwarted.  In 1966, e f f e c t i v e  lobbying (Trenkle and W i l l ham, 1977) induced the Health o f Animals Branch of A g r i c u l t u r e Canada to open a quarantine s t a t i o n on Grosse l i e in the St. Lawrence, accommodating 240 head once a year and, subsequently, a second s t a t i o n on St. P i e r r e accepting 250 animals twice a year (Newman n.d.). I n i t i a l l y , imports were r e s t r i c t e d to animals coming from France, but in subsequent years Switzerland, Germany, I t a l y and a number of other European c o u n t r i e s , as well as A u s t r a l i a and New Zealand, were added to the l i s t . The response by the c a t t l e industry was dramatic.  In 1966, the set of  pure s t r a i n s with d e s i r a b l e properties a v a i l a b l e to Canadian cattlemen was l i m i t e d almost e x c l u s i v e l y to three breeds, the Hereford, the Aberdeen Angus and the Shorthorn.  In 1976, a decade a f t e r the opening of the quarantine  f a c i l i t i e s , the National Association of Animal Breeders l i s t e d s i x t y - e i g h t c a t t l e breeds which they considered important, while Cattlemen (1976) could provide a l i s t of Canada's twenty-six "most popular breeds".  Breed  organizations were formed to regulate and promote the various breeds. Registrations of e x o t i c animals increased r a p i d l y and at the end of the decade were running in excess of 60,000 per year, c o l l e c t i v e l y r i v a l l i n g the long standing Hereford.  C l e a r l y , the p o s s i b i l i t y of rapid genetic-based  technological change e x i s t s i n the Canadian c a t t l e industry.  However, the  r e a l i z a t i o n of genetic-based technological change and the e f f e c t s of the t r a n s i t i o n a l period depends on the a b i l i t y of the i n s t i t u t i o n a l s t r u c t u r e of the Canadian beef c a t t l e industry to expand the genetic p o o l , improve the divergent genetic s t r a i n s and cross the purebred s t r a i n s to take advantage of hybrid vigour.  5. I i i i Institutional  Considerations  The process of genetic improvement i n the Canadian beef c a t t l e industry takes place within an i n s t i t u t i o n a l structure which d i f f e r s considerably from those under which other genetic improvements are conducted.  In plant  science, the three processes are subsumed under one i n s t i t u t i o n , the research s t a t i o n (or p r i v a t e research f a c i l i t y ) , where a wide v a r i e t y of species are i n i t i a l l y c o l l e c t e d and then the inbreeding and crossbreeding are conducted by g e n e t i c i s t s using the p r i n c i p l e s of t h e o r e t i c a l and applied genetics (Evenson and K i s l e v , 1975). i s i t released to the market. institution  Only when the hybrid has been tested  There i s no market operating within the  itself.  In the p o u l t r y industry, the development of superior breeding s t r a i n s takes place l a r g e l y i n a few large p r i v a t e breeding establishments which are s i m i l a r to those found i n plant breeding.  Only the,basis of the hybrid  s t r a i n s i s . r e l e a s e d to regional commercial chick s u p p l i e r s who, themselves, do not improve the breed.  Commercial growers purchase chicks from such  suppliers and seldom do any breeding of t h e i r own.. Again, no market operated on the process of expansion, s e l e c t i o n and crossing i t s e l f (Warren, 1974). Rapid genetic improvement i n swine has followed the establishment of i n s t i t u t i o n a l arrangements s i m i l a r to the poultry industry with s p e c i a l i z e d breeding operations, although the system i s not yet as u n i v e r s a l . Genetic improvement i n the d a i r y industry l i e s p r i m a r i l y i n the hands of a r t i f i c i a l insemination (A.I.) u n i t s .  Extensive records are kept and  bulls are selected on the basis of progeny t e s t i n g .  Semen i s sold only  from the highest rated animals and the farmer r e l i e s on an extensive set' of genetic s t a t i s t i c s when s e l e c t i n g which semen to purchase.  Again, i t  6. i s the extensive c o l l e c t i o n of physical data which determines the s e l e c t i o n of genetic material to be released and not the market. beef c a t t l e but i t has not been widely  A.I. e x i s t s for  accepted.  In the Canadian beef c a t t l e industry the processes of genetic improvement are shared between two i n s t i t u t i o n s ; the expansion of the genetic pool and the improvement of the pure s t r a i n s are the r e s p o n s i b i l i t y of the purebred breeders, while crossbreeding i s the r e s p o n s i b i l i t y of the commercial c a t t l e operator.  Both these i n d u s t r i e s are composed of thousands  of i n d i v i d u a l operators, few of whom have any formal t r a i n i n g i n genetics. The p r o f i t a b i l i t y of i n d i v i d u a l breeding enterprises determines the extent of expansion of the genetic pool, while the market operating between purebred breeders and commercial operators should regulate the process genetic improvement through the price mechanism.  of  The question therefore  becomes, how does the market a f f e c t the t r a n s i t i o n a l stage of technological change and regulate the ongoing process of genetic improvement? This t h e s i s presents two studies.  The f i r s t examines the process of  expanding the genetic pool and the second examines the market between purebred breeders and  commercial c a t t l e operators.  As the p o t e n t i a l e x i s t s  for s h i f t i n g the aggregate production function i n the beef c a t t l e industry approximately  20 percent (Willham, 1976), a greater understanding  of the  factors a f f e c t i n g the r e a l i z a t i o n of t h i s technical improvement could be of considerable economic s i g n i f i c a n c e , given the s i z e and r e l a t i v e importance of the beef industry.  Next to f i e l d grains, c a t t l e and calves c o n s t i t u t e  the second most important s i n g l e commodity, by value, providing income from cash receipts for primary production i n the a g r i c u l t u r a l sector (Canada Year Book , 1978-79). year.  Approximately  3.5 m i l l i o n beef animals are slaughtered each  Per capita consumption i s approximately  90 pounds a year and  7. increasing.  Further, given an income e l a s t i c i t y of .5 (Hassan and Johnson,  1976), beef has one of the highest prospects f o r growth i n the a g r i c u l t u r a l sector.  In the 1971 census, beef animals were reported on 64% of the farms  in Manitoba, 60% in Saskatchewan, 71% in Alberta and 56% in B r i t i s h Columbia (Census of A g r i c u l t u r e , 1971).  In the past, s h i f t s i n the production  function f o r other commodities have created s i g n i f i c a n t adjustment problems for  the rural community.  Further, there i s evidence that c a t t l e breeders  have not responded to the production needs of the industry i n the past, and that considerable waste of resources was the r e s u l t . of  The box-like Hereford  the 1940 s and 50's i s the most notable example (Marlow and Bower, 1 978). 1  Ex-ante knowledge of what may be expected from any process of d i f f u s i o n  may  i n d i c a t e areas where adjustment problems can be expected, while an understanding of the process of the improvement i n innovations may reduce some waste of resources. C e r t a i n l y , there i s l i t t l e reason to suspect that genetic-based technological change i n the beef c a t t l e industry i s near completion.  New synthetic breeds are c o n t i n u a l l y being developed and the  diverse germ plasm i n Europe i s f a r from exhausted.  Unfortunately,  e x i s t i n g studies provide l i t t l e i n the way of i n s i g h t s i n t o the ongoing process of technological I iv  change.  Economic Analysis of Technical Change The vast majority of empirical studies concerned with technological  change have been ex-post i n nature (Peterson and Hayami, 1977).  Econometric  studies of genetic-based technical change have generally followed e i t h e r a d i f f u s i o n approach or a production function approach.  The d i f f u s i o n  approach attempts to explain the l a g i n the introduction of new v a r i e t i e s , the  rate o f adoption and the f i n a l proportion of use by expectations of  p r o f i t a b i l i t y ( G r i l i c h e s , 1960).  Models used to explain the l a g in the  8. introduction of new techniques ( G r i l i c h e s , 1957) (Cordrey, 1968) examine problems s i m i l a r to the expansions o f the genetic pool i n the c a t t l e industry and have been adapted to our problem.  These studies of the  introduction of new techniques have been l i m i t e d to one innovation i n a s i n g l e time period.  Our study provides an improvement to these studies by  examining a number of breeds which entered Canada at d i f f e r e n t time periods. We can therefore examine the consistency of the d i f f u s i o n process across commodities and over time. Other studies of new v a r i e t i e s generally follow the approach o f defining a production function ( i m p l i c i t l y or e x p l i c i t l y ) and then adding new plant v a r i e t i e s over time as s h i f t parameters, usually in the form of dummy variables or investment expenditures (Hertford, et a l . , (Nagy and Furtan, 1978) (Evenson and K i s l e v , 1975). y i e l d per acre.  1977)  Output i s measured i n  Such studies provide information on the existence of  technological change and may be useful i n e s t a b l i s h i n g the return on investment i n genetic-based technological change, but they do not provide i n s i g h t s into the process of genetic improvement i t s e l f .  Although studies  of both types discuss the c h a r a c t e r i s t i c improvements i n v a r i e t i e s , the actual process of determining which c h a r a c t e r i s t i c s researchers improve upon i s ignored.  Evenson and K i s l e v (1975, 1976) investigate the returns  to the process of genetic experimentation i t s e l f , but do not analyse the process of i n t e r a c t i o n between those who are to u t i l i z e the new  varieties  and those who s e l e c t the c h a r a c t e r i s t i c s of the new v a r i e t i e s .  Kislev  (1 979), i n his study of genetic change i n the dairy i n d u s t r y , i s spared t h i s discussion by assuming a s e l e c t i o n process concentrating on a s i n g l e c h a r a c t e r i s t i c , milk production. Non genetic-based technical change i n the a g r i c u l t u r a l sector has  9. been analysed using models s i m i l a r to those used f o r genetic-based technical change (Peterson and Hayami, 1977) and, as a r e s u l t , we know there are new models of t r a c t o r s , corn harvesters and m i l k i n g equipment, new f e r t i l i z e r s , feed mixes and h e r b i c i d e s , and new growth s t i m u l a n t s , estrus syncronizers and v e t e r i n a r y a i d s , a l l of which increase p r o d u c t i v i t y . But we have no information on how or why a t r a c t o r of a c e r t a i n vintage d i f f e r s , i n the p a r t i c u l a r manner that i t does, from a t r a c t o r of the previous vintage. Induced innovation t h e o r i s t s ( F e l l n e r , 1961) suggest that the key may  (Hayami and Ruttan,  1971)  l i e with changes i n r e l a t i v e f a c t o r p r i c e s which  provide the i n c e n t i v e f o r the development of new products which have reduced technical requirements f o r the now r e l a t i v e l y expensive model may  input.  However, the  be too r e s t r i c t i v e in i t s a p p l i c a t i o n . The theory assumes that  there must be an ex-ante e q u i l i b r i u m and that a change i n r e l a t i v e p r i c e s must be observed.  In our case of genetic-based  technological change, the  p o t e n t i a l e x i s t s f o r slow but continuing dynamic change ( u n t i l a l l the genetic v a r i a b i l i t y i s exhausted), whether or not there are changes i n relative factor prices.  Secondly, c a p i t a l and labour are always selected as  the inputs against which t h i s s u b s t i t u t i o n takes place and changes in the prices o f other inputs are ignored.  The work of Berndt and Wood (1975) i n  production theory i n d i c a t e s t h i s may  be misleading.  Further, the theory  of induced innovation suggests only that new goods w i l l appear, but provide no information on the composition of such goods except they w i l l be l e s s intensive r e l a t i v e to the new higher cost input. t e l l us that a new  In our case, t h i s would  input w i l l appear and that i t w i l l be the input  with the highest a d d i t i o n a l value over the f e a s i b l e i n t e r v a l of improvement but i t cannot provide any d e s c r i p t i v e information regarding the  10. inherent q u a l i t i e s of the new good. problem i n production space. production.  C l e a r l y , t h i s i s the Lancastrian (1966)  The problem i s one of heterogeneous inputs to  As Archibald and Rosenbluth (1978) have i n d i c a t e d , the  c h a r a c t e r i s t i c approach has been i m p l i c i t l y used i n much of the recent work on production functions.  T r a d i t i o n a l production theory, based on the  assumption of homogeneous inputs to production, does not provide the t o o l s to analyse the problem of genetic improvement i n the context of the s e l e c t i o n procedures of breeders and commercial cattlemen.  I f the process  of  technological change in the beef c a t t l e industry i s to be evaluated, then further incursions i n t o the use of the c h a r a c t e r i s t i c approach seems necessary. To summarize, the major contributions of these studies are t h r e e f o l d . F i r s t , they provide an examination three processes of genetic-based  of how the market system regulates the technological change; expansion of the  genetic pool, inbreeding of divergent genetic s t r a i n s to increase the p r o b a b i l i t y of desired h e r i t a b l e properties i n a pure breeding s t r a i n and the crossing of the pure breeding s t r a i n s to take advantage of hybrid vigour. Other genetic innovations have had some or a l l of these processes  regulated  (at least i n part) by the s c i e n t i f i c community rather than the market. Secondly, the study of the d i f f u s i o n of new breeds provides a stronger examination  of the economic forces i n f l u e n c i n g the a v a i l a b i l i t y of  innovations than previous studies through the comparison of d i f f e r e n t breeds over time.  F i n a l l y , the study of ongoing genetic improvement  e x p l i c i t l y uses the c h a r a c t e r i s t i c approach to production to examine the process of technological change.  Although other studies may  have made  i m p l i c i t use of the c h a r a c t e r i s t i c s approach, they have not developed t h e i r t h e o r e t i c a l models i n the context of c h a r a c t e r i s t i c s .  Chapter II STUDY I  II i  THE SUPPLY OF A NEW TECHNIQUE  Background The process of adoption of any new technique i s i n i t i a l l y  by i t s a v a i l a b i l i t y .  determined  Unless an innovation i s a v a i l a b l e at a cost to the  producer (where cost i s defined to include the cost of v i s i t i n g the market, the cost of transportation to the farm and the cost of acquiring information, as well as the purchase price of the a r t i c l e ) , which i s competitive with the e x i s t i n g technology, large scale adoption w i l l not take place. ^  The  majority of innovations developed f o r the North American market have usually been a v a i l a b l e i n adequate q u a n t i t i e s within extremely short periods. Mechanical equipment, f e r t i l i z e r , p e s t i c i d e s , e t c . , move through established marketing channels, although there may be short term bottlenecks in the manufacturing process.  Given that crops and poultry are very p r o l i f i c , or  blessed with short gestation periods, supply r e s t r a i n t s do not appear as constraints to the process of technical change, except i n the extremely short run.  C a t t l e , as a s p e c i e s , are not p r o l i f i c , nor do they have a  short gestation period.  Purebred c a t t l e move to market through l o c a l  auctions and, although c a t t l e are r e a d i l y transportable, expense ( e s p e c i a l l y when the opportunity cost of a cattleman's time i s considered) and r i s k increase with distance. An e f f i c i e n t purebred industry therefore would seem to require the establishment of a large number of l o c a l i z e d breeders. Casual examination of the geographic location of Hereford breeders (or one of the other t r a d i t i o n a l breeds) corroborates t h i s suggestion. In 1965, there were, to a l l intents and purposes, no "exotic" breeders in Canada.  With the opening of quarantine stations in the next few years,  large numbers of "exotic" c a t t l e were imported i n t o Canada by cattlemen.  12. These suppliers of the innovation were extremely adept at u t i l i z i n g the a v a i l a b l e foundation stock, as herd numbers seem to have increased at very close to the b i o l o g i c a l maximum.  At the close of the decade, the number of  calves registered f o r the various breeds was running i n excess of 60,000 per year, c o l l e c t i v e l y r i v a l l i n g the established Hereford.  Exotic c a t t l e cannot,  however, be supposed to have been equally a v a i l a b l e to a l l commercial men at the same time.  cattle-  The expansion of the industry required the  establishment of a large number of purebred enterprises.  In the case of each  new breed, a few interested i n d i v i d u a l s imported a l i m i t e d number of superior stock and within a few years a nucleus of i n t e r e s t e d breeders formed a breed association.  I t i s these breeders, and those who subsequently joined the  industry, who provided the means of technological change. The i n d u s t r y , of course, operates e n t i r e l y within the private sector. I f one assumes that breeders are p r o f i t maximizers, one would expect them to enter e a r l i e s t those areas where expected p r o f i t s would be greatest, those who were to f o l l o w the next best area, and so on ( G r i l i c h e s , 1957).  This.however,  suggests that the benefits of technological change would accrue to adopters of technology unevenly.  Given that cost of acquiring the new technology  increases with distance from the s u p p l i e r , the l o c a t i o n of breeders w i l l determine those ranches which can p r o f i t a b l y u t i l i z e the breed.  The e f f e c t  on the rate of adoption w i l l , however, not be s o l e l y related to the cost of p h y s i c a l l y acquiring a b u l l .  As i t would appear that the willingness to adopt  a new technology i s , i n p a r t , a function of the a v a i l a b i l i t y of information (Kennedy, 1977), the existence of a breeder i n proximity to a rancher s i g n i f i c a n t l y reduces the cost of information.  The cost of acquiring  information w i l l be reduced not only through the reduction of the time and expense necessary f o r acquiring f i r s t hand knowledge from attending sales and  13.  v i s i t s to the breeder, but also from the a b i l i t y to observe or communicate with previous adopters i n the area.  As with innovations such as hybrid corn,  i t would be unfair to blame a commercial operator f o r not adopting a new technique when the product was not competitively a v a i l a b l e (Gril.iches, I960)'.' Cattlemen i n B.C., for example, are often c i t e d f o r being "conservative" and "unprogressive" because the rate of adoption appears to have been r e l a t i v e l y slow, but t h i s apparent lack of adoption may be a r e s u l t of the nona v a i l a b i l i t y of exotic c a t t l e . In the short run, the e a r l y establishment of a l o c a l breeder i s l i k e l y to provide a considerable advantage t o those who would be i n c l i n e d to adopt the new technology.  In a d d i t i o n , the longer the herd i s i n being, the more  valuable i t w i l l become as a source o f commercial germ plasm, as breeders are able to e s t a b l i s h mating and c u l l i n g strategies which can be t a i l o r e d to l o c a l demand. In order to gain some i n s i g h t i n t o the process of technological change in the c a t t l e industry, i t may be useful to map the spread of breeders o f e x o t i c c a t t l e through space and over time and, subsequently, to investigate those economic forces which appear to influence the l o c a t i o n of breeders. I t i s probably safe to suggest that the stock of the world's germ plasm has not been exhausted and t h a t , as knowledge of genetics improves, additional breeds of c a t t l e ( e i t h e r synthetic or imported) w i l l be d i f f u s e d within the Canadian c a t t l e industry.  I f there i s any consistency i n the l o c a t i o n a l  patterns of various breeds, t h i s may provide some i n s i g h t into the expected patterns of d i f f u s i o n , and thus suggest those areas that are l i k e l y to have the advantage of e a r l y access to improvements to the technology i n the future. II i i I n s t i t u t i o n s The i n s t i t u t i o n s which regulate the purebred c a t t l e industry have an  important role i n the d i f f u s i o n of genetic-based technological change and therefore merit some explanation.  The functions of these i n s t i t u t i o n s can  be divided into four major categories: 1) the regulation of importation (Health of Animals Branch, A g r i c u l t u r e Canada);  2) the r e g i s t r a t i o n of  animals (national breed o r g a n i z a t i o n s , Canadian National Livestock Records), 3) evaluation of genetic potential (Federal-Provincial Performance-for-Beef-program, breed o r g a n i z a t i o n s ) ;  Record-of-  p r o v i n c i a l government, national and p r o v i n c i a l  and 4) promotion  organizations, the auction system).  and sale of c a t t l e ( p r o v i n c i a l  breed  Of course, i n d i v i d u a l breeders are  involved in each f u n c t i o n . In a d d i t i o n , the federal government and other i n s t i t u t i o n s conduct research i n t o various aspects of beef breeding. II i i a  Importation  Since 1966, European c a t t l e have been able to enter Canada under a maximum s e c u r i t y quarantine p o l i c y devised by the Health of Animals Branch of A g r i c u l t u r e Canada.  In order to minimize the r i s k of i n t r o d u c i n g new  diseases i n t o Canada, the importation procedures are complicated and c o s t l y . In most years  there i s a demand to import more c a t t l e than can be  accomodated i n the quarantine f a c i l i t i e s and the Department a l l o c a t e s the l i m i t e d number by i s s u i n g importation permits.  A p p l i c a t i o n s are received  up to a c e r t a i n deadline date, and then each applicant i s required to. submit information about his background and experience i n the c a t t l e business, and his  plans f o r using the imported stock.  These submissions, i d e n t i f i e d only  by code number, are considered by a panel of experts, and permits are a l l o c a t e d on t h e i r "merit" plus a report prepared on the prospective importer's f a c i l i t i e s by an inspector of the Health of Animals  branch.  Only those receiving permits are able to import c a t t l e . The quarantine p o l i c y involves four l e v e l s of i s o l a t i o n and i n s p e c t i o n .  The f i r s t i s on the farm of o r i g i n where calves, designated f o r export to Canada, must be kept separate from a l l other c a t t l e and undergo a s e r i e s of t e s t s , a l l within f o r t y - f i v e days of entering the next stage which i s quarantine in country of o r i g i n .  This period of segregation i s supervised  by l o c a l veterinarians and Canadian veterinary o f f i c e r s .  The quarantine i s  for a minimum of t h i r t y days, a f t e r which animals passing a l l the tests proceed to the Canadian quarantine s t a t i o n . Grosse H e  may  Two are now i n use - one on  accepting 240 head once a year entering i n October, and another  at St. Pierre accomodating 250 twice a year entering in November and  May.  These s t a t i o n s are supervised by Canadian veterinary o f f i c e r s and the quarantine period l a s t s f o r a minimum of 90 days, or u n t i l a l l the t e s t s are completed.  I f any animal f a i l s a t e s t or contracts a disease during  the quarantine period, the Veterinary Director General of Canada may require that a l l animals i n the s t a t i o n be slaughtered, without compensation owners.  I f foot and mouth disease or contageous  pleuropneumonia  to the  i s diagnosed  in any animal at t h i s point, the Canadian Veterinary Director must order a l l animals i n the s t a t i o n slaughtered, and again there i s no provision f o r compensation  to the owners.  I f , at t h i s stage, a l l animals pass the tests  s u c c e s s f u l l y , they may be transported to the owner's premises, but s t i l l they must undergo an on-farm quarantine period i n which they are penned with a group of contact animals and, at l e a s t , double fenced away from any other animals f o r a period of three months.  During t h i s p e r i o d , the animals are  inspected at least everv two weeks by an o f f i c e r of the Canadian Health of Animals branch.  The number of contact animals required i s s i x f o r the f i r s t  import and one additional animal for.each additional import.  I t takes about  a year from the time the animal i s purchased u n t i l i t i s free to move i n Canada.  16. At a l l stages of the quarantine program except the on-farm quarantine, tests are done f o r foot and mouth disease, r i n d e r p e s t , contagious pleuropneumonia, t u b e r c u l o s i s , b r u c e l l o s i s , trichomoniasis, l e u k o s i s , l e p t o s p i r o s i s , Johne's disease and blue tongue.  During the s t a t i o n  quarantine i n the country of o r i g i n and i n Canada temperatures are taken d a i l y , and during the f i r s t fourteen days i n the Canadian quarantine stations temperatures are taken twice d a i l y .  From the time the animal  begins the t e s t s on the farm of o r i g i n u n t i l the time i t i s released from on-farm quarantine i n Canada, i t i s i s o l a t e d from a l l c a t t l e outside the import program (except the contact animals i n the on-farm quarantine). A l l v e h i c l e s and ships used f o r transportation must be thoroughly infected before and a f t e r use.  dis-  A l l feed and bedding must be brought to  the quarantine s t a t i o n from Canada, or a country with equivalent health standards. A l l costs o f the maximum s e c u r i t y importation program are borne by the importers, except the s a l a r i e s of the Canadian v e t e r i n a r y o f f i c e r s who inspect the c a t t l e .  The Canadian quarantine s t a t i o n s were b u i l t with p u b l i c  funds, but t h i s cost i s being repaid by a quarantine charge l a i d on each animal  imported.  The cost o f importing one animal, e x c l u s i v e of purchase p r i c e , includes a $600 charge f o r the care and feeding throughout the s t a t i o n quarantine period, a $900 quarantine charge, and charges f o r t r a n s p o r t a t i o n , administration and s p e c i a l t e s t s , which increases the t o t a l cost to somewhat more than $2,000. Over time, the number of countries from which importation may be made has increased and i n each instance a number of new breeds has been imported.  F i r s t importations were from France i n 1968, Switzerland 1971,  17. I t a l y 1971, A u s t r a l i a 1972, West Germany 1972 and Netherlands 1975. The importance of the import regulations to the spread o f technological change i s twofold.  F i r s t , the issuance o f permits by f i a t provides a means  of regulating the number of animals of each breed admitted to Canada and, therefore, determines the composition of the national c a t t l e herd and e s t a b l i s h e s l i m i t s to the rate of spread of each breed.  Secondly, the  r i s k , expense and additional f a c i l i t i e s required i n the importation o f c a t t l e , plus the personal dossier, excludes the majority o f cattlemen from being importers. II i i b  Registration of Animals  The task of r e g i s t r a t i o n i s undertaken e i t h e r by the Canadian National Livestock Records d i v i s i o n of A g r i c u l t u r e Canada, or the various national breed organizations themselves (The Registration of Animals i n Canada, 1975). No animal can be sold as a purebred without r e g i s t r a t i o n papers. The r e g i s t r a t i o n of animals provides the purchaser of a registered animal with the assurance that he i s acquiring an animal which conforms to the regulations established by the p a r t i c u l a r breed organizations.  It  further provides information on the pedigree of registered animals to help the purchaser i n his s e l e c t i o n .  The economic s i g n i f i c a n c e of r e g i s t r a t i o n  is that such regulations can be used as barriers to entry i n t o the industry. However, the regulations of the various exotic breed organizations have, as y e t , been extremely l i b e r a l i n an e f f o r t to expand the breed organizations rather than to r e s t r i c t entry. process of "upgrading".  The breed organizations have sanctioned the  Upgrading allows f o r percentage animals (those  whose antecedents are not a l l of the same breed) to be included i n the herd ( r e g i s t r a t i o n ) book, so that over a few generations of breeding to purebred s i r e s , the herd animals can become purebreds.  The usual  18. requirement i s 15/16 or 31/32 of the animal's pedigree must be,from registered animals of the breed i n question, and a l l generations one h a l f recorded i n the herdbook ( i . e . , approximately 1/2,  3/4, 7/8, 15/16, 31/32).  back to  4 or 5 generations,  Older, more established breeds allow no  upgrading, r e q u i r i n g that a l l the antecedents of the animals be purebred. Further, membership fees o f the breed organizations have been r e l a t i v e l y low and do not constitute a b a r r i e r to entry.  Thus, the r e g i s t r a t i o n  regulations o f the " e x o t i c " breeds have not acted as a retarding influence on the spread of technology. II i i c Evaluation o f Genetic P o t e n t i a l In addition t o the r e g i s t r a t i o n of animals t o ensure t h e i r  pedigree,  information regarding the genetic p o t e n t i a l o f i n d i v i d u a l animals i s also collected.  A number of organizations are involved i n the evaluation  programs.  The largest of these i s the Federal-Provincial Record-of-  Performance (R.O.P.)-for Beef program for on-farm evaluation or "home t e s t i n g " of p o t e n t i a l breeding stock.  R.O.P. beef provides a system  whereby ranchers record weaning weights and average d a i l y gain on feed (the most h e r i t a b l e of the major phenotypic i n d i c a t o r s o f genetic per formance) and, since 1977, incidents of c a l v i n g d i f f i c u l t y on a breed basis.  Such information i s useful for the management of the breeder's own  stock improvement program, as well as providing a d d i t i o n a l information to potential purchasers.  Certain of the " e x o t i c " breed organizations require  that a l l registered animals must be evaluated.  In a d d i t i o n , the various  p r o v i n c i a l governments and some breed organizations run bull " t e s t " S t a t i o n s , where breeders can have t h e i r animals evaluated i n conditions o f c o n t r o l l e d environment and management, which aids i n the i d e n t i f i c a t i o n o f purely genetic performance.  In some cases a d d i t i o n a l information on fat  cover and carcass q u a l i t y i s c o l l e c t e d . The programs provide information to the potential buyers on the merit of the animals to be purchased.  They have provided extensive q u a n t i t a t i v e  information on the genetic performance of the various breeds and, therefore, reduced the cost of information to entrants to the beef breeding business. II i i d  Promotion and Sale of C a t t l e  Although the national breed organizations do undertake some promotional work in the form of l i t e r a t u r e and a c t i v i t i e s at major a g r i c u l t u r a l exh i b i t i o n s , t h e i r primary function remains the r e g i s t r a t i o n of animals. P r o v i n c i a l l e v e l breed organizations conduct promotional campaigns and help to organize l o c a l sales. There are three major types of auctions a t which purebred c a t t l e are purchased by the commercial sector:  1 ) breed organized s a l e s ; 2 ) consignment  s a l e s ; 3 ) production sales. Breed organized sales are usually conducted a t l o c a l auction  facilities  but organized by the p r o v i n c i a l breed association of the p a r t i c u l a r breed. Animals are drawn from a number of herds and the events are well p u b l i c i z e d . These sales require that there be a considerable number of breeders i n the v i c i n i t y , so that s u f f i c i e n t animals are a v a i l a b l e f o r a p r o f i t a b l e s a l e . Costs of such sales are borne by the p a r t i c i p a t i n g breeders through a percentage levy on t h e i r gross sales a t the auction. Consignment sales are those in which a breeder consigns a c e r t a i n number of animals to be sold at one time.  These sales are usually  organized by c a t t l e brokers or the operators of auction f a c i l i t i e s .  They  can be made up of animals from a s i n g l e breed but, i n most cases, a number of breeds are represented. Again, the cost of the sale i s borne by the consignors through a percentage levy on t h e i r gross sales a t the auction.  20. These sales are well p u b l i c i z e d by the organizers. Ranch production sales are held on the premises of the i n d i v i d u a l breeder and the year's production i s sold at auction.  The costs of  p u b l i c i z i n g the s a l e , providing the sale f a c i l i t i e s and h i r i n g the auctioneer are a l l borne by the i n d i v i d u a l breeder.  Such sales are  favoured by breeders with established reputations and large annual outputs. Such breeders have l i t t l e d i f f i c u l t y i n a t t r a c t i n g s u f f i c i e n t  customers  for a "successful" sale (enough bidders to ensure active bidding f o r animals), and a volume of s a l e s t o cover the fixed costs of the auction. x  New breeders, or small operators, may have d i f f i c u l t y i n a t t r a c t i n g interested buyers to ranch sales.  In areas where breeder-organized, or consignment  sales are not conducted, i t may, however, be the only market mechanism at the disposal of the breeders.  Some animals, of course, are t r a n s f e r r e d  between the breeder and the commercial cattleman through "private t r e a t y " . Of l i m i t e d importance, a l s o , are dispersal sales when an owner i s s e l l i n g his e n t i r e herd and leaving the industry. These represent the major i n s t i t u t i o n s of the purebred c a t t l e industry. II i i i  Review of L i t e r a t u r e  Only a l i m i t e d number of studies have been conducted which have examined what could be termed the supply side of the spread of technological change.  G r i l i c h e s , f o r example, i n his study of hybrid corn,  observed marked differences i n the date at which adoption i n a p a r t i c u l a r state began.  He set out his problem as:  "The actual breeding of adoptable hybrids had to be done separately f o r each area. Hence, besides the difference i n the rate of adoption of hybrids by farmers - the acceptance problem - we also have to explain the lag in development of adoptable hybrids for s p e c i f i c areas - the a v a i l a b i l i t y problem". ( G r i l i c h e s , 1957, p. 502).  21. G r i l i c h e s assumed that seed producers were p r o f i t maximizers and suggested t h a t ; "The date at which adoptable hybrids become a v a i l a b l e i n an area i s viewed as the r e s u l t of seed producers ranking d i f f e r e n t areas according to expected prof i t a b i l i t y of entry and deciding t h e i r actions on that basis. The r e l a t i v e p r o f i t a b i l i t y of entry i n t o an area w i l l depend upon the size of the eventual market i n that area, marketing costs, the cost of innovating f o r that area, and . . . the expected rate of acceptance". ( G r i l i c h e s , 1957, p. 502) He found that his model was generally borne out although there were some measurement d i f f i c u l t i e s . A further study of the factors a f f e c t i n g the a v a i l a b i l i t y of an innovation i s Cordrey's (1968) examination of the spread of a r t i f i c i a l insemination.  This innovation i s s i m i l a r to ours, not only because i t  applies to the animal industry, but also because the technology, that i s to say the actual technique, was i n being and a v a i l a b l e to potential s u p p l i e r s of any area regardless of time.  In the case of hybrid corn,  seed companies were forced to develop a r e a - s p e c i f i c hybrids which e n t a i l e d considerable e f f o r t and time.  This represents a factor i n the a v a i l a b i l i t y  problem which i s not present i n e i t h e r Cordrey's study or our own.  Further,  the AI establishment i s r e l a t i v e l y l i m i t e d i n i t s e f f e c t i v e range of . operation.  Thus, the d i f f u s i o n of the innovation required the establishment  of a large number of small local AI units which i s s i m i l a r to the c a t t l e breeder case.  In a d d i t i o n , hybrid corn was marketed by large seed companies  who could draw on professional marketing expertise.  I t i s u n l i k e l y that  the l o c a l AI u n i t , or the i n d i v i d u a l c a t t l e breeder, would have such market information.  Cordrey's hypothesis was t h a t : "The year i n which AI organizations would be est a b l i s h e d i n any given state would depend on the expected p r o f i t a b i l i t y of entry. In t u r n , r e l a t i v e p r o f i t a b i l i t y would depend on (1) the expected s i z e of the potential breeding market; (2) AI service costs; (3) the innovation or introduction c o s t ; and (4) the expected rate at which AI service would be adopted". (Cordrey, 1968, p. 14). Cordrey s p e c i f i e d a simple l i n e a r model with four independent variables and used the method of least squares regression analysis to t e s t his model.  In general, his model was confirmed. "The economic i n t e r p r e t a t i o n of the r e s u l t s . . . would i n d i c a t e that AI organizations were established e a r l y i n states having large potential markets and low AI service and introduction costs and expanded i n t o states having smaller potential markets and higher costs. Moreover, one of the basic conclusions of t h i s study was that areas of highest cow density were areas of e a r l i e s t l o c a l AI establishments". (Cordrey, 1968, p. 31).  _ Both these studies are t y p i c a l of ex-post examinations of technological innovations.  In the e x o t i c c a t t l e case, however, the process of d i f f u s i o n  i s not complete. commodities  Further, the innovation i s comprised of a variety of  (breeds) i n various stages of d i f f u s i o n .  I t would provide a  stronger test of the model's v a l i d i t y i f i t s consistency could be established across breeds and over time. The problem of the a v a i l a b i l i t y of new innovations i s e s s e n t i a l l y one of d i s e q u i l i b r i u m .  Marshall (1920) suggested that there were two types  of employers, "those who open out new and improved methods of business, and those who follow beaten tracks" (p. 597).  The former, he suggested,  should receive an extra-normal p r o f i t so that "he w i l l earn the f u l l of his services to the s o c i e t y " .  reward  This "reward" i s e s s e n t i a l l y the same as  Schumpter's (1934) "entrepreneural" p r o f i t .  As Schumpter states;  "The s i z e of p r o f i t i s not d e f i n i t e l y determined as the magnitude of incomes i n the c i r c u l a r flow. In p a r t i c u l a r i t cannot be s a i d of i t , as of elements of costs i n the l a t t e r , that i t j u s t s u f f i c e s to c a l l forth p r e c i s e l y the 'quantity of entrepreneurial services required'. Such a quantity t h e o r e t i c a l l y determinable, does not e x i s t . And the t o t a l amount of p r o f i t a c t u a l l y obtained i n a given time, as well as the p r o f i t r e a l i z e d by an i n d i v i d u a l entrepreneur, may be much greater than that necessary to c a l l forth the entrepreneurial services which were a c t u a l l y operative". C l e a r l y , one of the factors which w i l l a f f e c t the s i z e of "entrepreneurial" p r o f i t i s the c h a r a c t e r i s t i c s of the market which the new  firm would expect to serve.  the supply of new  I f , as i n the case of " e x o t i c " c a t t l e ,  inputs to production i s r e s t r i c t e d i n the short run  (by the import licenses and subsequently by the b i o l o g i c a l rate of reproduction), then entrepreneurs which to l o c a t e .  are faced with a choice of markets i n  I f we assume that entrepreneurs  are p r o f i t maximizers,  then they would tend to locate e a r l i e s t where expected p r o f i t s are greatest, and to enter l a t e r areas where expected p r o f i t i s lower.  This process  would continue u n t i l a l l areas where the market would be expected to support entrepreneurial p r o f i t were exhausted. II i v  Hypotheses Following G r i l i c h e s and Cordrey, we postulate that the entry of a  firm i n t o a new market area i n any year i s dependent upon the r e l a t i v e "entrepreneurial" p r o f i t expected i n that area.  The hypothesis  i s that the  r e l a t i v e p r o f i t a b i l i t y of entry i n t o an area w i l l depend upon the s i z e of the market i n that area, marketing costs, expected rate of acceptance and the cost of innovating. entry of new  A f u r t h e r hypothesis  i s that the pattern of  firms i s consistent across breeds and over time.  24.  II v  The Model Although there i s evidence regarding the unequal dates o f  a v a i l a b i l i t y of "exotic" c a t t l e i n d i f f e r e n t areas o f the country at the p r o v i n c i a l level (Annual Reports o f Canadian Livestock Records), i t seems u n l i k e l y that any worthwhile information could be obtained from such an aggregate measure.  The market area of a breeder i s much smaller than a  province, which suggests that a less aggregate measure would be appropriate. In t h i s study, the basic unit o f measurement of the market area i s the census d i v i s i o n used f o r the Census of A g r i c u l t u r e .  Although census  d i v i s i o n s do vary considerably i n area and shape, they can, i n most cases, represent what might be regarded as a reasonable market area f o r a breeder. Census d i v i s i o n s vary from about 35 to 60 miles i n width, with those in the western provinces being on average l a r g e r , those i n the Maritimes smaller, and those i n central Canada being about average. are  Of course, there  some obvious exceptions i n the f a r northern areas of the central and  western provinces. One of the basic r e a l i t i e s o f animal production i s the need f o r constant attention and care o f l i v e s t o c k .  Therefore, the  cow-calf operator i s , t o a large degree, bound to h i s operation, and one would expect absences to be confined to a period of less than one day on average.  In other words, a convenient period of absence to acquire an  animal (or information about an animal) would be defined by t r a v e l l i n g to an auction i n the morning a f t e r checking the stock, spending the afternoon at the auction and returning to the farm or ranch i n the evening.  In  central and eastern Canada, where fewer animals are ranged and must be f e d , the distance of such excursions would probably be reduced.  The importance  of mixed dairy-beef enterprises i n the east would further reduce the convenient period of absence.  In a d d i t i o n , t r a d i t i o n a l patterns of rural  25.  movement seem to suggest that western farmers are accustomed to t r a v e l l i n g greater distances than those i n the central or eastern part of the country. Therefore,  an average census d i v i s i o n seems to be a reasonable unit of  measure. The t h e o r e t i c a l basis f o r the choice of variables which are expected to influence the p r o f i t a b i l i t y of a l o c a t i o n i s r e l a t i v e l y s t r a i g h t forward. Ceteris paribus, the s i z e o f the market to be served determines the p r o f i t a b i l i t y of a s i t e .  Firms would be expected to locate f i r s t i n areas  where the continuing volume of sales would be greatest.  This hypothesis i s  supported by the empirical work of G r i l i c h e s and Cordrey.for  agricultural  innovations, as well as a number of studies from the i n d u s t r i a l sector ( M i l l s , 1964) (Urban, 1970).  An e x i s t i n g and e f f i c i e n t l y functioning  marketing system f o r the sale of a firm's product w i l l reduce the costs o f disposing of product and i t s storage.  I t would be expected, t h e r e f o r e ,  that the date of entry of a firm i n t o an area would be affected by the e x i s t i n g marketing i n s t i t u t i o n s of the area.  The s i z e o f market and the  costs of marketing are relevant to the l o c a t i o n of a firm s e l l i n g any product.  The introduction of a new product or an innovation, on the other  hand, may be affected by a d d i t i o n a l f a c t o r s .  The rate at which an  innovation i s u t i l i z e d by firms i n the market w i l l a f f e c t the short term p r o f i t s of the supplying firm.  In other words, even though the s i z e of  the market may be such that i t w i l l allow f o r non-negative long term p r o f i t s , i f the process of adoption i s extremely slow, then the supplying firm may not receive s u f f i c i e n t "entrepreneural"  profits.  The factors a f f e c t i n g the rate of adoption can be divided i n t o two categories, those which are r e l a t e d to the a b i l i t y of the u t i l i z i n g firm  26. to bear r i s k , and those which r e l a t e to the amount of information a v a i l a b l e and u t i l i z e d by potential adopters.  In the cow-calf industry the  s i z e of the cow herd w i l l determine, to some extent, the a b i l i t y of the firm to assume the r i s k involved i n experimenting with a new breed.  For example,  using the usual r a t i o of one bull to 25 cows, the use of one e x o t i c bull would represent an experiment with 50% of a 50 cow herd's output, but only 8% of the output of a 300 cow firm.  Thus, the rate of acceptance could be  expected to be r e l a t e d to the s i z e d i s t r i b u t i o n of firms.  Areas with  concentrations of large firms would be expected to have higher rates of acceptance.  F i n a l l y , the cost of entry f o r any f i r m w i l l be r e l a t e d to the  knowledge potential adopters have regarding the innovation.  In other words,  the introduction of an innovation by an i n d i v i d u a l firm w i l l  force that firm  to incur some costs of education. lower the cost w i l l be to the firm.  The higher the level o f information, the Thus, one would expect firms to enter  areas with lower expected costs at an e a r l i e r date than areas with higher expected costs. ^ Thus, we represent the date-of-location equation as D = F(Z  r  Z, Z, Z) 2  3  4  (2.1)  where D i s the year i n which the f i r s t registered breeder of a p a r t i c u l a r breed was established i n an area, Z-| i s the expected s i z e of the market (the  number of cows i n the area), 1^ i s the expected rate of acceptance  (the  average size of buyer's herds), Z^ i s the cost of marketing (the  number of bull auctions) and Z^ i s the cost of introduction (the percent of herds p a r t i c i p a t i n g in the R.O.P. beef program).  Each independent  variable was expected to be p o s i t i v e l y related to the date-of-location. No a p r i o r i r e s t r i c t i o n s were imposed on the form of the date-of-location equation.  II vi  Variables and Data  The objectives of t h i s examination are twofold, to determine the factors i n f l u e n c i n g the date of entry of a breeder i n t o a market area, and to investigate the consistency of the l o c a t i o n a l pattern over time and between breeds.  I t was therefore necessary to c o l l e c t information on  a number of breeds over time.  As the dates when breed organizations were  formed vary, l a r g e l y as a r e s u l t of the expanding number of countries from which imports were allowed, the number of years of data a v a i l a b l e on the l o c a t i o n of breeders d i f f e r s between breeds.  Data were c o l l e c t e d f o r  3  eighteen breeds, Charolais (1960),  Simmental (1969), Limousin (1969),  Maine Anjou (1970), Murray Grey (1970), Brown Swiss (1970),  4  Welsh Black  (1970), Chianina (1971), South Devon (1971), Blonde d'Aquitaine (1972), Gelbveih (1972), Tarentaise (1972), Pinzgauer (1973), Salers (1973), Normande (1973), Romagnola (1973), MRI (1974), Marchigiana (1974).  The  date above indicates the year of the f i r s t observation i n each case. Thus, there are data a v a i l a b l e f o r eighteen breeds f o r f i v e years, nine breeds f o r seven years, s i x breeds f o r nine years, two breeds f o r eleven years and Charolais f o r nineteen years. II vi a The Dependent Variable The dependent v a r i a b l e (D) i s defined as the year i n which the f i r s t breeding enterprise of a p a r t i c u l a r breed was established i n the census division.  This would represent the e a r l i e s t " a v a i l a b i l i t y " of the  innovation i n any area.  Of course, actual a v a i l a b i l i t y of the breed f o r  u t i l i z a t i o n by the l o c a l commercial operator would be l a t e r than the date of introduction i n any area.  The chance to adopt the innovation would be  delayed, but the observing and learning process could begin immediately. Further, one would expect that the l a g between the date of entry and the  date of commercial a v a i l a b i l i t y would be r e l a t i v e l y constant, as i t depends only on the time necessary to bring the herd i n t o production. To acquire the date-of-location f o r i n d i v i d u a l breeders I asked each national breed association f o r a l i s t o f members, t h e i r addresses and the date when they joined the organization. provided immediately.  In some cases the information was  In other instances l i s t s of members were provided  without the date o f entry.  As these organizations usually c i t e d time and  resource constraints to providing such information, I inquired i f I could inspect the records at the national headquarters of the breeds and r e t r i e v e the information myself.  In some cases such permission was granted.  I f an on-site inspection o f the national records was denied, I phoned the various p r o v i n c i a l organizations and requested the information over the phone.  F i n a l l y , those breeders f o r whom the date-of-location was l a c k i n g  were contacted d i r e c t l y .  Checks on the accuracy of these c o l l e c t i o n  methods f o r the breeds where national information was not provided were then conducted.  The technical publications of the i n d u s t r y had to be  searched f o r data on auction markets and advertisements o f breeders.  This  information was then matched against the l i s t s compiled from p r o v i n c i a l organizations and contact with i n d i v i d u a l breeders.  Although not a l l  breeders advertised, no breeder was found who was not included i n the l i s t s , and no breeder who advertised d i d so i n a period i n excess o f three years from the date obtained from the breed organization. In a d d i t i o n , t o c o l l e c t data f o r another independent variable ( Z ^ ) , l i s t s of the ranches on R.O.P. had to be obtained.  These are divided by breed.  Again, these were checked against the o r i g i n a l l i s t s .  As R.O.P. i s  voluntary, not a l l breeders on the l i s t s were represented, but no addi t i o n a l breeders were found.  No breeder was found on R.O.P. before the  dates suggested on the l i s t s . Once complete membership l i s t s for a l l breeds had been acquired, they were mapped by date i n t o the 252 census d i v i s i o n s of the 1971 Cansus of Agriculture.  As no complete l i s t of postal locations by census d i v i s i o n  i s a v a i l a b l e , t h i s was accomplished by f i r s t consulting the two incomplete l i s t s of locations to census d i v i s i o n s (Census of Canada, 1971, Table 21A, Table 24A) provided by the census.  In the case of those observations which  were not found on the l i s t s , the o f f i c i a l  Gazetteer of the various  provinces was used (Gazetteer of Canada, various dates) i n conjunction with census maps.  As the Gazetteer provides coordinates of l a t i t u d e and long-  itude f o r a l l place names i n Canada, i t was possible to map a l l breeders i n t o census d i v i s i o n s .  The date-of-location of the f i r s t breeder i n a  census d i v i s i o n was thus obtained. II vi b  Independent  Variables  As was suggested above, r e l a t i v e p r o f i t a b i l i t y would be expected to depend upon (1) the expected s i z e of the market; (2) the expected rate of acceptance; (3) marketing costs; (4) what G r i l i c h e s termed the cost o f innovating.  Of course, data pertaining to each independent variable are  not a v a i l a b l e .  Instead, the t o t a l number of cows, the average herd s i z e  of commercial operations, the number of functioning c a t t l e auctions i n the year previous to establishment, and the number of ranchers part i c i p a t i n g i n the R.O.P. beef program i n the year previous to establishment were used as proxies. II vi b 1  Potential  Market  The number of cows or h e i f e r s , two years o l d and older, u t i l i z e d i n beef production w i l l be used to approximate the s i z e of the potential  market (Z-j).  This represents the number of female animals used f o r the  production of beef.  Although there does e x i s t a figure f o r the number  of b u l l s kept i n each census d i v i s i o n , t h i s figure includes dairy as well as beef b u l l s and would therefore bias the r e s u l t . drawn from the 1971 Census of A g r i c u l t u r e . consistency.  In a l l cases, data were  This was done f o r reasons of  For each of the possible years, 1961 , 1966, 1 971 , 1976, the  a g r i c u l t u r e census d i v i s i o n s i n some provinces were a l t e r e d . therefore impossible to c o l l e c t a consistent set of data.  I t was  However, f o r  those census d i v i s i o n s which remained unchanged over the period, the data were compared against the 1971 census.  Although the absolute numbers of  cows fluctuated to some extent, the r e l a t i v e numbers remain approximately constant.  There would not seem to be any great loss of information by  using the central 1971 census. II vi b 2  The Expected Rate of Acceptance  Given the considerable investment necessary to e s t a b l i s h a breeding herd, and the r e l a t i v e l y long gestation period u n t i l the enterprise could reach i t s f u l l potential production, i t i s important that firms have a market conducive to acceptance of t h e i r product. advantageous  I t would therefore be  f o r them to locate i n areas where potential e a r l y adopters  were greatest.  As the use of any innovation w i l l e n t a i l some r i s k ( i f  not a c t u a l , at least perceived), the rate of adoption w i l l be a function of the a b i l i t y of firms to absorb r i s k .  Average herd s i z e (Z^) was  to proxy e a r l y adopters f o r the reasons indicated above.  chosen  The hypothesis  therefore i s that the breeders would enter e a r l i e r those areas where the average herd s i z e was l a r g e s t .  Observation on the average size of herd  was c o l l e c t e d from the 1971 Census of A g r i c u l t u r e .  31. II v i b 3  Market Costs  There i s no adequate method of estimating the costs of marketing. It would seem, however, that the greater the number of o u t l e t s f o r a producer's b u l l s , the less marketing costs he must incur himself. This i s postulated f o r three reasons.  F i r s t , as bull markets are dispersed, the  l i k e l i h o o d of a market being i n proximity to a breeder increases, and thus reduces h i s cost o f t r a n s p o r t a t i o n . his  Secondly, the more l o c a l outlets f o r  product, the better known the breeder i s l i k e l y to become, and the less  he must r e l y on conventional (and cash cost) forms of a d v e r t i s i n g .  Third,  the greater the number of sales the less i s the time between them, thereby reducing the time a bull must be fed and cared f o r . Of course, the d i s advantages r e s u l t i n g from the absence of "breed organized" sales i n the area are obvious.  E i t h e r the breeder w i l l be faced with larger trans-  portation costs, or with the costs of construction and promotion of his own auction f a c i l i t i e s .  I t would therefore be expected that breeders would  f i r s t enter those areas where the number of functioning outlets was greatest. Although there i s no central data source f o r s a l e s , they are well advertised i n the l i m i t e d number of technical journals of the industry. Therefore, f o r the years 1 959-1978 the major trade journals were examined for advertised sales.  The publications consulted were, Cattlemen (national  coverage), Focus on Beef (national coverage), Country Guide ( l i m i t e d national coverage - Ontario - Quebec covered e x t e n s i v e l y ) , Free Press Weekly Report on Farming, Western Edition (Four Western Provinces),  Beef  Today (Four Western Provinces), Farm Focus (Maritimes), Country L i f e in B r i t i s h Columbia (B.C.).  The exact observations c o l l e c t e d were references  to auction f a c i l i t i e s where purebred sales were conducted.  These  observations were tabulated from advertisements f o r sales or reports of completed s a l e s .  In a few cases i n d i v i d u a l auction f a c i l i t i e s were used  more than once a year.  Such f a c i l i t i e s were only counted once.  Once a l i s t of f a c i l i t i e s was c o l l e c t e d f o r each year, they were mapped i n t o the census d i v i s i o n s by the same method described f o r the dependent variable i n section II v i a.  Variation between years was not  large and no noticeable trends i n the number of sales over time were observed. II vi b 4  Cost of Introduction  Both Cordrey and G r i l i c h e s suggested that the introduction of any new innovations would e n t a i l considerable educational e f f o r t . to  According  Cordrey, "This e f f o r t was helped by Dairy Herd Improvement Associations, state and country extension personnel, registered dairy c a t t l e associations and other farm organizations interested i n improving d a i r y farmers' incomes, as well as the National Association o f Animal Breeders and the central and l o c a l AI organizations. The educational e f f o r t s of these farmer groups would have reduced the t o t a l cost of introducing AI service to area farmers". (Cordrey, 1968, p. 24).  As d i r e c t measures of these expenditures were not a v a i l a b l e , Cordrey used the proportion of cow herds p a r t i c i p a t i n g i n the programs of Dairy Herd Improvement Associations (DHIA) as an approximation of t h i s educational effort.  The Record-of-Performance-for Beef program f o r beef animals plays  a s i m i l a r role to DHIA i n the dairy industry.  We therefore chose the  percentage of herds p a r t i c i p a t i n g i n the R.O.P. beef program the year previous to the establishment of a breeder i n a census d i v i s i o n as the appropriate measure. Other measures may have been a v a i l a b l e f o r use as proxies f o r Z„.  For example, information on average years o f schooling by type o f operation i s a v a i l a b l e from the census.  As education i s often used as a proxy f o r  the a b i l i t y o f farmers to assimilate information, years of schooling might have been an appropriate measure.  However, the data does not e x h i b i t  as great a v a r i a b i l i t y across census d i v i s i o n s as the R.O.P. data, and therefore may be a less precise measure.  Secondly, as years o f education  would not take i n t o account the differences i n expenditures on extension programs, the ex post accurate.  R.O.P. measure was judged l i k e l y to be more  F i n a l l y , as information about crossbreeding and e x o t i c c a t t l e  was being disseminated over the p e r i o d , the yearly R.O.P. data were deemed superior t o ten year census averages.  Data may also have been a v a i l a b l e  on extension expenditures but obtaining an accurate breakdown by commodities seemed u n l i k e l y .  The ex post measure o f R.O.P. p a r t i c i p a t i o n also seemed  a better measure as i t should, i n p a r t , mirror the effectiveness o f extension programs i n the beef industry as well as the expenditures. L i s t s o f p a r t i c i p a t i n g herds were obtained from both the federal o f f i c e and the p r o v i n c i a l representatives of the R.O.P. beef program f o r various years.  Data f o r the years 1959-1963 proved t o be inadequate, as  p a r t i c i p a t i o n i n the R.O.P. program by the provinces o f Ontario and Quebec was not f u l l y organized.  Thus, the 1964 figure was used f o r a l l years of  t h i s period. As t h i s only affected estimates f o r the Charolais breed, i t does not appear to be a serious handicap. Again, the l i s t s of p a r t i c i p a t i n g herds were mapped from t h e i r addresses i n t o census d i v i s i o n s by the method o u t l i n e d i n I I i i  a. Thus,  the number of p a r t i c i p a t i n g herds i n each census d i v i s i o n was a r r i v e d a t for each year 1964-1978.  Although membership i n the R.O.P. beef program  has increased considerably over the twenty year p e r i o d , from approximately  300 to 3,000 p a r t i c i p a t i n g herds, i t was found that the r e l a t i v e numbers of p a r t i c i p a t i n g herds across census d i v i s i o n s d i d not greatly change over time.  This suggests that the progressive areas o f a decade ago  remain the progressive areas today.  As i t was a measure of r e l a t i v e  progressiveness which was desired, the absolute number o f p a r t i c i p a t i n g herds i n each census d i v i s i o n was converted to percentages o f herds on R.O.P. f o r that year by d i v i d i n g the number o f herds i n each census d i v i s i o n by the t o t a l number o f p a r t i c i p a t i n g herds.  As areas where more  c a t t l e are located would be expected to have l a r g e r numbers o f R.O.P. herds, t h i s figure was then divided by the percentage of the national cow herd (Census of A g r i c u l t u r e , 1971) found i n the census d i v i s i o n , i . e . , % TOTAL HERDS ON R.O.P. % TOTAL COW HERD for each census d i v i s i o n .  Therefore, a value of 1 would i n d i c a t e an area  which had the same percentage o f herds on R.O.P. as there were cows i n the  national c a t t l e herd; a value o f greater than 1 would i n d i c a t e an area  which had more herds on R.O.P. r e l a t i v e to the national cow herd, and might be considered more progressive.  A value less than 1 would i n d i c a t e  a less progressive area. II v i i S t a t i s t i c a l Methods and Results As there were no a p r i o r i r e s t r i c t i o n s imposed on the form o f the date-of-location function, s t a t i s t i c a l estimates were undertaken to e s t a b l i s h the form o f the r e l a t i o n s h i p .  The independent v a r i a b l e s , as  defined, were a l l expected to have a net p o s i t i v e effect' on the date-oflocation.  As the object of the exercise was to examine the d i f f u s i o n o f  e x o t i c c a t t l e across breeds and over time, estimates were made f o r each  breed f o r varying periods determined by the number p f years the breed organization had e x i s t e d . breeds.  Five years of data existed f o r a l l eighteen  Separate estimates f o r the date-of-location function of each  breed were undertaken f o r the f i r s t f i v e years of breeder establishment. S i m i l a r l y , there was information f o r nine breeds f o r the f i r s t seven years of breeder establishment; f o r s i x breeds f o r nine years o f breeder establishment; f o r two breeds f o r eleven years o f establishment. Separate breed by breed estimates were undertaken f o r each period.  In a d d i t i o n ,  an equation was estimated f o r the Charolais breed over nineteen years. A l l estimates were conducted using the ordinary least squares (OLS) algorithm programmed into the SHAZAM (White, 1977) econometrics package on the University of B r i t i s h Columbia computer. II v i i a  Five Year Estimates  I n i t i a l p l o t t i n g o f the data suggested a l i n e a r r e l a t i o n s h i p between each of the independent variables and the dependent v a r i a b l e .  However,  i n i t i a l estimates, conducted i n the simple l i n e a r form f o r the four independent v a r i a b l e s , while y i e l d i n g r e l a t i v e l y consistent equations across breeds, d i d not provide encouraging r e s u l t s . characterized by low R  The estimates were  values and the c o e f f i c i e n t s f o r Z^ (size o f market)  were i n c o n s i s t e n t and not s i g n i f i c a n t .  The c o e f f i c i e n t  introduction) c o n s i s t e n t l y had the wrong sign. functional form were then undertaken.  f o r Z^ (costs of  Estimates of a f l e x i b l e  A Generalized Leontief (Diewert,  1973a) of the form  4  D = b  oo  +  E  .  = 1  4 I  • •^ b..l. l. , 2  2  iJ i  j,  J  b. . = b..  iJ  Ji  (2.2)  36.  was estimated, but again the sign on  ( Z ^ Z^ ) 2  2  was i n c o n s i s t e n t .  Further, there was a high degree of m u l t i c o l i n e a r i t y between the i n t e r active terms and the arguments themselves. was  A re-examination of the data  undertaken. The apparent inconsistency of the sign of the c o e f f i c i e n t s of Z^  appeared to be related to the expected s i z e of the market.  In e a r l y  periods breeder location was observed in areas where expected s i z e of the market was l a r g e s t , even where the areas were less progressive.  In  subsequent years, however, two types of i n t e r a c t i o n were observed.  As  one would expect, breeders located i n areas with smaller expected s i z e of market and s l i g h t l y lower indexes of progressiveness.  In a d d i t i o n ,  however, areas with dramatically smaller expected market s i z e and very high indexes of progressiveness were observed as areas where breeders located. sign.  I t i s these observations which tended to give Z^ an i n c o n s i s t e n t  Further, i n l a t e r years, some areas with large market areas, but  very low values f o r the indexes of progressiveness, became areas of location. market).  This tended to weaken the s i g n i f i c a n c e of Z^ (expected s i z e of These observations suggested that there was an i n t e r a c t i o n between  the two v a r i a b l e s .  Therefore, a new v a r i a b l e , Zg, was constructed by  m u l t i p l y i n g Z^ by Z^.  The new variable could be described as the expected  s i z e of the market weighted by the index of progressiveness.  In other words,  the date-of-location would be expected to be p o s i t i v e l y related to the s i z e of the market adjusted for the progressiveness of the area.  As the above  procedure i s e n t i r e l y data dependent, the B estimators are biased (Wallace and Ashar, 1972).  The use of t - s t a t i s t i c s for hypothesis t e s t i n g i s  technically invalid.  37. Estimates were conducted i n the simple l i n e a r form o f , D = b  o  + brlc  5 5  + b Z  2 2 9  9  +  b.Z,  3 3  for a l l eighteen breeds and reasonable r e s u l t s obtained. on c o e f f i c i e n t s Z,-,  Note the signs  and Z^ would be expected negative as D i s indexed  from 1 to 5, from e a r l y locations to l a t e l o c a t i o n s . presented i n Table II 1 below.  The breeds are l i s t e d i n order, beginning  with the most recent importations to Canada. expected signs are underlined.  The r e s u l t s are  C o e f f i c i e n t s with un-  TABLE II 1 ESTIMATES OF FIRST FIVE YEARS OF LOCATION BY BREED BREED  : MARCH IGlANA  PERIOD  1974 - 1978  Variable name  n = 52 Estimated coefficient  t ratio 40 df  Z o c  -0.58414E-05  - 1.9738  Z  2  -0.19995E-01  -1.7035  Z  3  -0.29593  - 2.0156  3.7561  13.763  Intercept  R  BREED  2  = .4697  : MEUSE - RHINE - IJSSEL (MRI)  PERIOD : 1974 - 1978 Variable name  n = 17 Estimated coefficient  t ratio 13 df  Z 5 c  -0.45160E-O5  - 4.2502  Z  2  -0.45981E-02  - 0.50665  Z  3  -0.26324  - 3.7015  3.2817  12.953  Intercept  R  2  = .9715  TABLE I I 1 (continued) BREED  : ROMAGNOLA  PERIOD : 1973 - 1977 Variable name  n = 22 Estimated coefficient  t ratio 18 df  Z o c  -0.57922E-06  -0.16580  Z  2  -0.19234E-01  -1.1949  Z  3  -0.37862  -2.6260  4.2035  7.2031  Intercept  R = .4593 2  BREED  : NORMANDE  PERIOD : 1973 - 1977 Variable name  n = 13 Estimated coefficient  t ratio 9 df  Z o  -0.61827E-05  -1.6582  Z  2  -0.40847E-01  -2.1567  Z  3  -0.60279E-01  -0.34762  c  Intercept  4.4746  8.1016 R = .6255 2  TABLE I I 1 (continued) BREED  : SALERS  PERIOD : 1973 - 1977 Variable name  n = 17 Estimated coefficient  t ratio 13 df  Z  5  -0.13449E-05  - 0.37802  Z  2  -0.34787E-01  - 1.8432  Z  3  -0.23117  - 1.4646  Intercept  3.9302  5.4205 R  BREED  2  = .4667  : PINZGAUER  PERIOD : 1974 - 1978 Variable name  n = 41 Estimated coefficient  t ratio 37 df  Z o c  -0.70653E-05  - 2.5320  Z  2  -0.20261E-01  -2.0995  Z  3  Intercept  0.61026E-01 3.3285  0.41586 11.347 R  2  = .3713  TABLE I I 1 (continued) BREED  : TARENTAISE  PERIOD : 1972 - 1976 Variable name  Intercept  n = 16 Estimated c o e f f i cient  t ratio 12 df  -0.28315E-05  -0.87820  -0.39477E-01  -2.3902  -0.13230  -0.64988  4.3475  8.0333 R  BREED  2  = .4999  : GELBVEIH  PERIOD : 1972 - 1976 Variable name  n - 32 Estimated coefficient  t ratio 28 df  Z  g  -0.37421E-05  -2.3487  Z  2  -0.39061E-01  -4.7697  -0.17253  -1.9083  4.1980  9.0894  Z3  Intercept  R  2  = .7788  TABLE I I 1 (continued) BREED  : BLONDE D'AQUITAINE n = 43  PERIOD I 1972 - 1976 Variable name  Intercept  Estimated coefficient  t ratio 39 df  -0.72134E-05  - 3.4764  -0.65956E-02  - 0.78741  -0.11388  - 0.94034  3.6564  17.511 R  BREED  2  = .5507  : SOUTH DEVON  PERIOD : 1971 - 1975 Variable name  n -9 Estimated coefficient  t ratio 5 df  -0.65367E-05  - 1.4213  Z  g  Z  2  0.91182E-02  0.30231  Z  3  0.66755  0.70699  1.9711  2.9198  Intercept  R  2  = .2054  TABLE I I 1 (continued)  BREED  : CHIANINA  PERIOD : 1971 - 1975 Variable name  n = 67 Estimated coefficient  t ratio 63 df  Z  5  -0.45465E-05  - 2.3636  Z  £  -0.11355E-01  - 2.0473  Z  3  -0.13706  - 1.4028  3.8266  19.815  Intercept  R  BREED  2  = .3731  : WELSH BLACK  PERIOD : 1970 - 1974 Variable name  n = 13 Estimated coefficient  t ratio 9 df  Z  5  -0.10640E-05  - 0.19288  Z  2  -0.36734E-01  - 1.2636  Z  3  -0.50048E-01  - 0.23606  Intercept  4.0142  4.2269 R  2  = .0783  TABLE I I 1 (continued)  BREED  : BROWN SWISS  PERIOD : 1970 - 1974 Variable name  n = 49 Estimated coefficient  t ratio 45 df  Z b c  -0.79625E-05  - 4.2154  Z  2  -0.26186E-01  - 3.4554  Z  3  -0.54987E-01  - 0.57413  Intercept  5.1467  21.201 R  BREED  2  = .6293  : MURRAY GREY  PERIOD : 1970 - 1974 Variable name  n = 47 Estimated coefficient  t ratio 43 df  Z  c  -0.74677E-05  - 4.6896  Z  2  -0.58618E-02  - 1.2069  Z  3  -0.19131  - 2.3453  5.0702  28.416  Intercept  R  2  = .6850  TABLE II 1 (continued)  BREED  : MAINE ANJOU  PERIOD : 1970 - 1974 Vari able name  Intercept  n = 49 Estimated c o e f f i cient  t ratio 45 df  •0.49919E-05  - 2.1907  •0.69335E-02  - 2.6359  -0.36703  - 2.6024  5.0246  20.968 R  BREED  2  = .5425  : LIMOUSIN  PERIOD : 1969 - 1973 Vari able name  Intercept  n = 40 Estimated coefficient  t ratio 36 df  -0.70945E-05  - 2.8050  -0.16235E-01  - .2.1827  -0.14562  - 0.88887  4.5383  18.746 R  2  = .5410  TABLE II 1 (continued)  BREED  : SIMMENTAL  PERIOD : 1969 - 1973 Variable name  n = 87 Estimated coefficient  t ratio 83 df  Z  5  -0.54515E-05  - 2.0745  Z  2  -0.17496E-01  - 2.5145  Z  3  -0.31581  - 2.0909  3.8845  21.584  Intercept  R  BREED  2  = .4377  : CHAROLAIS  PERIOD : 1960 - 1964 Variable name  n = 91 Estimated coefficient  t ratio 87 df  Z  g  -0.12453E-04  - 6.89298  Z  2  -0.12418E-01  -2.0220  Z  3  -0.13460  - 0.78563  Intercept  4.1142  26.004 R  2  = .5701  In only two cases, Pinzgauer and South Devon,, were c o e f f i c i e n t s with t h e o r e t i c a l l y i n c o r r e c t signs found.  In the case of South Devon  there i s an extremely small number of observations. _2  The values of the  R 's are acceptable, given that the estimates use cross-sectional data. Although a l l independent variables were not s i g n i f i c a n t (at the .05 percent l e v e l ) i n every e s t i m a t i o n , they were a l l s i g n i f i c a n t i n some. The r e l a t i v e magnitudes of the c o e f f i c i e n t s appear to be I r e l a t i v e l y consistent across breeds. II v i i b  Seven Year Estimates  The same independent v a r i a b l e s , Z , c  o  Z  0  c  and Z. were used f o r the J  estimates of the seven year date-of-location equations.  Again, i n i t i a l  p l o t t i n g of the data suggested a l i n e a r r e l a t i o n s h i p between each variable.  Therefore, estimates of the form  D * b  Q  +  b Z 5  5  +  b Z 2  2  were made f o r each breed. a v a i l a b l e f o r nine breeds.  + b Z 3  3  Data f o r seven years of breeder locations  was  The r e s u l t s are presented below i n Table II  Again, breeds are presented i n order s t a r t i n g from the newest imports to Canada.  As before, negative signs are expected f o r the c o e f f i c i e n t s .  TABLE II 2 ESTIMATES OF FIRST SEVEN YEARS OF LOCATION BY BREED BREED  : SOUTH DEVON  PERIOD : 1971 - 1977 Variable name Z  n = 15 Estimated coefficient  c  0.65995E-05  b  ZZZZZZZZIZZZI  t ratio 11 df 0.98936  Z  2  -0.17855E-01  - 0.83082  Z  3  -0.36697  - 0.89713  4.4021  2.9631 R = .1123  Intercept  2  BREED  : CHIANINA  PERIOD : 1971 - 1977 Variable name  n = 71 Estimated coefficient  t ratio 67 df  Z o c  -0.58291E-05  - 2.5318  Z  2  -0.14269E-01  - 2.1486  Z  3  -0.11944  -1.0178  4.1189  18.358  Intercept  R  2  = .3567  TABLE II 2 (continued) BREED  : WELSH BLACK n = 15  PERIOD : 1970 - 1976 Vari able name  Intercept  Estimated coef f i c i e n t  t ratio 11 df  -0.55385E-05  - 0.66033  -0.19041E-01  - 0.42758  -0.34315E-01  - 0.10528  4.7177  3.2494 R  BREED  = .0132  : BROWN SWISS n = 76  PERIOD : 1970 - 1976 Variable name  Intercept  Estimated coefficient  t ratio 72 df  -0.10078E-04  - 3.7153  -0.34480E-01  - 3.4164  -0.15978  - 1.1547  6.2878  26.310 R  2  = .5561  TABLE II 2 (continued) BREED  : MURRAY GREY  PERIOD : 1970 - 1976 Variable name  n = 71 Estimated coefficient  t ratio 74 df  Z b c  -0.11810E-04  - 6.6659  Z  2  -0.67873E-02  - 1.2634  Z  3  -0.99465E-01  - 1.0600  Intercept  5.8066  37.748 R  BREED  2  = .6535  : MAINE ANJOU  PERIOD : 1970 - 1976 Variable name  n = 78 Estimated coefficient  t ratio 74 df  Z  g  -0.10287E-04  - 3.7859  Z  2  -0.17634E-01  -2.1804  Z  3  -0.36255  - 2.1117  6.1 913  20.968  Intercept  R  2  = .5061  TABLE II 2 (continued)  BREED  : LIMOUSIN n = 59  PERIOD : 1969 - 1975 Vari able name  Intercept  Estimated coef f i cient  t ratio 55 df  -0.10293E-04  - 2.9918  -0.11585E-01  - 1.1180  -0.16049  - 0.76937  5.4549  18.908 R  BREED  2  = .3986  : SIMMENTAL  PERIOD : 1969 - 1975 Variable name  Intercept  n = 116 Estimated c o e f f i cient  t ratio 112 df  -0.10844E-04  - 2.9805  -0.16177E-01  -,1.7863  -0.34671  - 1.6400  4.9103  23.014 R  2  = .3897  TABLE I I 2 (continued)  BREED  : CHAROLAIS  PERIOD : 1960 - 1966 Variable name  n = 127 Estimated coefficient  t ratio 123 df  Z 5 c  -0.18849E-04  - 6.2089  Z  2  -0.17737E-01  - 1.75 95  Z  3  -0.18535  - 0.63379  5.4853  26.527 R = .4476  Intercept  2  Only i n the case of the South Devon was a c o e f f i c i e n t with an inconsistent sign found.  Again, there i s an extremely small number of  observations f o r t h i s breed.  A l l c o e f f i c i e n t s were not s i g n i f i c a n t (at  the .05 percent l e v e l ) i n every equation, but each was s i g n i f i c a n t i n some equations.  The value of the c o e f f i c i e n t s remains r e l a t i v e l y stable  across breeds and s i m i l a r to those observed i n the 5 year date-of-location estimates. II v i i c  Nine Year Estimates  The same independent v a r i a b l e s , Z , Z„ and Z_ were used i n the nine c  b  year estimates.  l  3  P l o t s of the independent variables against the dependent  variable suggested that the r e l a t i o n s h i p might be changing as more years were added.  The r e l a t i o n s h i p showed some curvature, t a i l i n g o f f as the  majority of favoured c a t t l e areas had already.been entered. r e l a t i o n s h i p was suggested.  A logarithmic  Therefore, two estimates were conducted.  One was of the l i n e a r form used above, D = b + bcZ + b Z + b-Z. 0 0 5 2 2 3 3 K  9  9  and one with the independent variables converted to logs;  D  =  c  o  +  c  5  1 o g  Z  5  +  c  2  l o g  Z  2  +  c  3  l o g  Z  3  The model which i s l i n e a r i n a l l variables provided the estimate with the _2 highest R  and therefore was judged to provide the best f i t .  estimates are presented below i n Table II breeds f o r nine years of breeder l o c a t i o n s .  3.  These  Data were a v a i l a b l e for s i x  Again, negative signs should  be expected f o r c o e f f i c i e n t s and the breeds are ordered from the most recent import.  TABLE I I 3 ESTIMATES OF FIRST NINE YEARS OF LOCATION BY BREED BREED  : BROWN SWISS  PERIOD : 1970 - 1978 Variable name  n = 91 Estimated coefficient  t ratio 87 df  Z 5 c  -0.12110E-04  - 3.9461  Z  2  -0.39940E-01  - 3.6572  Z  3  -0.20490  - 1.2999  6.9176  30.278  Intercept  R  BREED  2  = .5679  : MURRAY GREY  PERIOD : 1970 - 1978 Variable name  n = 74 Estimated coefficient  t ratio 70 df  Z  5  -0.13084E-04  - 6.1957  Z  2  -0.52692E-02  - 0.84142  Z  3  -0.98573E-01  - 0.87407  Intercept  5.9847  33.859 R  2  = .5954  TABLE II 3 (continued) BREED  : MAINE ANJOU  PERIOD : 1970 - 1978 Variable name  n = 105 Estimated coefficient  t ratio 101 df  Z  c  -0.14244E-04  - 4.4933  Z  2  -0.35408E-01  -;3.7453  Z  3  -0.33644  - 1.6908  7.4279  32.969  Intercept  R  BREED  2  = .5436  : LIMOUSIN  PERIOD : 1969 - 1977 Variable name  n = 67 Estimated coefficient  t ratio 63 df  Z b c  -0.12434E-04  - 3.2411  Z  2  -0.19908E-01  - 1.6196  Z  3  -0.81896E-01  - 0.35980  Intercept V  6.0716  20.806 R  2  = .3771  56.  TABLE II 3 (continued) BREED  : SIMMENTAL  PERIOD : 1969 - 1977 Variable name l  b  c  .  n = 131  Estimated coefficient  t ratio 127 df  -0.13494E-04  - 3.0852  Z  2  -0.26221E-01  - 2.4068  Z  3  -0.36325  - 1.4248  5.6606  23.914  Intercept  R  BREED  2  = .3914  : CHAROLAIS  PERIOD : 1960 - 1968 Variable name  n = 139 Estimated coefficient  t ratio 135 df  Z b c  -0.20150E-04  - 6.1923  Z  2  -0.27046E-01  - 2.4054  Z  3  -0.12331  - 0.37426  Intercept  6.0472  26.204 R  2  = .4467  No c o e f f i c i e n t had an unexpected sign.  The value of the c o e f f i c i e n t s  remained r e l a t i v e l y stable across breeds, and s i m i l a r to those observed i n the f i v e year and seven year date-of-location  estimates.  The f i t , however,  in l a t e r years i s very poor as i s evidenced by the values of the intercepts.  The l i n e a r model f i t s f a i r l y well f o r the e a r l y years of  breeder l o c a t i o n , but as the better market areas are entered the values of the independent variables i n the remaining areas show less v a r i a t i o n between years.  The choice of areas f o r new locations becomes less d i s t i n c t  when only t h i s set of independent variables i s considered. II v i i d  Eleven Year Estimates  Eleven years of data was a v a i l a b l e f o r two breeds, Simmental and Charolais.  P l o t t i n g of the independent variables against the dependent  variable showed a d i s t i n c t curvature.  Again, two forms of the date-of-  location function were estimated, D = b + b .Z + b Z + b,Z_ o 5 5 2 2 3 3 K  K  9  9  and D = c  Q  + c  5  log Z  5  + c  2  log Z  2  + c  3  log Z  3  In t h i s case the equation i n logs provided the better estimate. r e s u l t s are presented below i n Table II 4.  The  Negative signs should be  expected f o r the c o e f f i c i e n t s and the breeds are ordered from the most recent import.  TABLE II 4 ESTIMATES OF FIRST ELEVEN YEARS OF LOCATION BY BREED BREED  :. SIMMENTAL  PERIOD : 1969 - 1979  n = 145  Variable name -  Estimated coefficient  t ratio 141 df  -0.81599  -5.3743  Log Z  5  Log Z  2  -0.44314  -1.6610  Log Z  3  -1.2811  -2.1254  14.107  8.6035  Intercept  R  BREED  2  = .4191  : CHAROLAIS  PERIOD : 1960 -1970 Variable name  n = 160 Estimated coefficient  t ratio 156 df  Log Z  5  -0 . 92 4 87  Log Z  2  -0.752 92  -2.8450  Log Z  3  -0.70561  -0.72207  Intercept  15.810  -6 . 831 9  7.1309 *2  4842  II v i i e  Nineteen Year Estimation  For the Charolais available.  f o r Charolais  Breed  breed data f o r 19 years of breeder locations were  The function was estimated with the independent  variables  transferred to logarithmic measure, i . e . , D = c  Q  + c  5  log Z  5  + c  2  log Z  £  + c  3  log Z  The r e s u l t i s presented i n Table II 5 below.  3  Negative signs were expected  for the c o e f f i c i e n t s .  TABLE II 5 ESTIMATE OF FIRST NINETEEN YEARS OF LOCATION • BREED  FOR THE CHAROLAIS BREED  : CHAROLAIS  i  PERIOD : 1960 - 1 978 Variable name 1  n = 199 E s t i mated coeffi cient  t ratio 195 df  Log Z  5  -0.84696  -4.3931  Log Z  2  -1.4931  -3.9247  Log Z  3  -1.2254  -0.77314  Intercept  18.102  6.4643 R  2  = .3403  II v i i Tests for Consistency o f Pattern To examine the hypothesis that the pattern o f breeder l o c a t i o n was consistent across breeds and over time, a number o f t e s t s were conducted. These tests were c a r r i e d out using the algorithms programmed into the E q u a l i t y o f Slope Test  (Le, 1976) computer package on the computer o f the  University o f B r i t i s h Columbia.  Tests were conducted f o r each group o f  equations separately, i . e . , 5 year date-of-location equations, seven year date-of-location equations, nine year date-of-location equations and eleven year date-of-location equations. Given that one has k l i n e a r regression equations i n m independent variables,  *  i  =  b  o  +  b  l  1  x  l  +  J*J> '  b  i=1 2  k  the f i r s t hypothesis to be tested i s H : b. = b. = o J J 1  2  b. , J k  j=l, 2  m  That i s , once a regression equation y = b„ + b. x. + o i I J  + b x mm  i s computed f o r each o f k sets o f data, F tests are conducted to determine whether the differences i n the regression c o e f f i c i e n t s between groups may be ascribed to sampling e r r o r s , or must be a t t r i b u t e d t o differences between groups.  The theory f o r the F t e s t s f o r the hypothesis o f common  c o e f f i c i e n t s i s presented i n Rao (1970, p. 239).  The algorithm i n the  Equality o f Slope Test computer package i s a simple g e n e r a l i z a t i o n o f t h i s method (Le, 1976, p. 2 ) . I f hypothesis H  n  i s not rejected, the hypothesis that a common equation  can be used for a l l samples can be tested.  S p e c i f i c a l l y , given that the  regression c o e f f i c i e n t s are equal, the hypothesis H o  *  1  2  = b =b o o  i s tested.  That i s , the hypothesis that the intercepts with the Y axis If H  are equal i s tested.  q  i s not rejected, then a common equation i s  computed by the Equality o f Slopes Test algorithm. * H  q  and common intercepts H If  H  Q  q  Tests o f common slope  were conducted at a . 0 5 level o f s i g n i f i c a n c e  i s r e j e c t e d , then a Scheffe  pp.  (1970,  66-70)  t e s t o f multiple  c o e f f i c i e n t s o f regression i s conducted for a l l pairs of c o e f f i c i e n t s , i . e (b; ,^ ),^ ,^ )  (b/.b^),^ ,^ )  (b^^.b^)  (b \b ),(b \b )  (b \b ),(b ,b )  (b  1  2  1  2  2  3  3  z  z  k  z  2  (b \ b ) , ( b \ b ) m m ' m m 2  3  v  2  v  1  In other words, the hypotheses are H  S  o  : b. = b. J j h  1  2  2  2  b ),(b m ' m  (b  3  k  2  v  3  2  b ) 3  m '  (b  k _ 1 2  ,b )  ,b ) m m k _ 1  (  h, i = 1,  , k  h f. i j=l ... m  This test i d e n t i f i e s the s p e c i f i c c o e f f i c i e n t s which d i f f e r between equations.  k  2  These Scheffe t e s t s were conducted at the . 1 0 l e v e l of  k  s i g n i f i c a n c e recommended by Le (1970, p. 3).  I d e n t i f y i n g which co-  e f f i c i e n t s d i f f e r between equations would be useful i n e s t a b l i s h i n g whether any pattern existed f o r changing c o e f f i c i e n t values over time. I f d i f f e r e n c e s i n c o e f f i c i e n t s can be i d e n t i f i e d f o r equations from data sets progressing through time, e.g., 1 960-1964, 1969-1973, 1 973-1977, then the changing importance of the independent v a r i a b l e s i n the l o c a t i o n decision of breeders may be i d e n t i f i e d .  Grouping of equations with  s i m i l a r time periods might then be suggested. The hypothesis H  Q  for the eighteen equations estimated f o r the  f i r s t f i v e years of breeder locations was rejected at the .05 l e v e l of significance;  g 3 4  =1.78  (FPROB = .00103 < .05).  The Scheffe t e s t  was then conducted f o r a l l c o e f f i c i e n t s of the eighteen equations. H  q  S  :  b.  h  =  b.\  h, i = 1,  18  h f i j = 1, 2, 3 None of the 480 hypotheses, however,.were rejected.  This suggested that  there was no s i g n i f i c a n t difference between any pair of c o e f f i c i e n t s . Therefore, the two equations with unexpected s i g n s , Pinzgauer and South Devon (see Table II  1)., and the equation f o r Tarentaise and Salers  with t h e i r small number of observations (n = 16 and n = 17 r e s p e c t i v e l y ) , were dropped from the t e s t . fourteen remaining equations;  The hypothesis H F  3 g  5 5 2  = 1.41  Q  was not rejected f o r the  (FPROB = .05417 > .05).  t h i s case, d i f f e r e n c e s among a l l the c o e f f i c i e n t s of each  In  independent  v a r i a b l e may be a t t r i b u t e d to sampling e r r o r s (at .05 l e v e l of  * significance).  The t e s t of hypothesis f o r the common equations H  then conducted.  The hypothesis was rejected at the .05 l e v e l of  q  was  significance, F  1 3  = 13.51 (FPROB = 0.0 < .05).  g g l  The tests were then conducted f o r the nine equations o f the f i r s t The hypothesis, H  seven years o f breeder l o c a t i o n . .05 level of s i g n i f i c a n c e ;  F  2 4  0 >  was rejected at the  = 2.36 (FPROB = .00033 < .05).  5 7 7  The Scheffe test was then conducted f o r a l l c o e f f i c i e n t s o f the nine equati ons. H  S  o  : b. = b. , h  h, i = 1,  1  J  O  9  h t i j r 1, 2, 3 None of the 135 hypotheses were rejected.  Therefore, following the  procedure used i n the f i v e year t e s t s , the equation f o r South Devon was removed because of the unexpected  sign on variable  (see Table II 2 ) ,  and the equation f o r Welsh Black because o f the small number of observations (n = 15). The hypothesis, H , was tested again f o r the seven q  remaining breeds. F  18 555  =  1 - 6 5  (  Although the F value was considerably reduced,  F P R 0 B =  -  0 4 4 8 3  <  - )> 05  at the .05 l e v e l of s i g n i f i c a n c e .  t h e  hypothesis was again  The differences  rejected  i n the seven year  equations cannot be considered as r e s u l t i n g from sampling e r r o r s . Unfortunately, Scheffe's t e s t provided no i n s i g h t s i n t o the cause o f the differences. The t e s t s were  then conducted f o r the s i x breeds f o r which nine  years of data on breeder location were a v a i l a b l e . .05 percent level o f s i g n i f i c a n c e ; Therefore, the differences  F  1 5  5 4 4  was tested.  Q  = 1.58 (FPROB = .07474 > .05).  i n the values of c o e f f i c i e n t s i n the nine year  estimates may be a t t r i b u t e d to sampling e r r o r . hypothesis H  H was not rejected at  As H was not rejected, q  The hypothesis was rejected at the .05 l e v e l  of s i g n i f i c a n c e ; F  g 5 g g  = 15.82 (FPROB = .00036 < .-05).  Therefore, even  though the c o e f f i c i e n t s cannot be considered d i f f e r e n t , the hypothesis o f a common equation i s rejected due to differences i n the i n t e r c e p t s . The tests were f i n a l l y conducted eleven years o f data. significance; hypothesis H significance;  F Q  3 2 g y  for the two equations estimated from  H was not rejected at .05 percent l e v e l o f q  = 0.79 (FPROB = 0.50172 > .05).  The t e s t f o r  was then conducted and was not rejected at the .05 level o f F^  3 0 Q  = .02 (FPROB = 0.88039 > .05).  A common equation  for eleven years o f breeder establishment was therefore estimated.  This  equation i s , D = 15.12 - .8857 log 1^ - .5996 log Z This was the only common equation  2  - .9830 log Z  3  generated.  It must be recognized that the use o f Ordinary Least Squares (0LS) may not be s t r i c t l y appropriate for these estimations.  As the d i f f u s i o n  process i s not complete, the model truncates the d i s t r i b u t i o n o f dates for each span o f estimation conducted.  In other words, the use o f data  for only the f i r s t a r b i t r a r y t ( i . e . , 5, 7, 9, 11 or 19) years o f d i f f u s i o n r e s t r i c t s the value o f D. for a given l e v e l o f Z. to < t . The truncation o f the dependent variable implies that the disturbances do not have zero mean and the estimates w i l l be biased (Wales and Woodland, 1980). The use of the single equation maximum l i k e l i h o o d (ML) method (Tobin, 1958) to overcome these d i f f i c u l t i e s does not seem appropriate. method, information i s required on the p r o b a b i l i t y o f  To use t h i s  's being < t .  To c a l c u l a t e t h i s p r o b a b i l i t y observations are required f o r a l l values o f the Z. s. This means we need information on the observations for the Z^'s 1  for a l l periods t+1, t+2,  t , where T i s the date of l o c a t i o n o f T  the l a s t breeder o f the p a r t i c u l a r breed i n a new l o c a t i o n (the completion  of the d i f f u s i o n process).  As the process of d i f f u s i o n i s  not complete for any breed, information on t  T  does not e x i s t  (except  tj > t ) . We do not have information on the Z^'s for events that have not taken place.  In other words, the values of l.'s i n areas where  breeders have not yet located do not e x i s t .  I t would be possible t o  use current values but they would be subject to e r r o r .  Of course, f o r  some breeds i n the 5, 7, 9 and 11 year estimations, some information regarding values of Z.. s for t's > t do e x i s t , but using t h i s information 1  would not remove the bias i n the absence of information regarding tj. Wales and Woodland (1980) suggest that multiple equation methods could be appropriate to overcome the problem when complete information on independent variables i s not a v a i l a b l e . Given the nature of the Z^ s 1  used in t h i s model, correct s p e c i f i c a t i o n equations to p r e d i c t , f o r example, the average s i z e o f herd, seems u n l i k e l y .  Such methods, therefore,  did not seem promising. Information on the nature of the bias can, however, be discerned. In truncation models a d d i t i o n a l observations can be added with or without moving the l i m i t point. possible.  In our example, only the former case i s  When the l i m i t point i s expanded c e r t a i n changes i n the bias  can be expected.  These can be i l l u s t r a t e d i n Diagram II 1.  66.  DIAGRAM II 1  In the simple example above with one independent variable Z, the truncation point i s increased from t values of D.  1  1  to t  1  to t , t T  1  1  < t  1  < tj, f o r  Line E{D/Z, D < t^.) represents the regression f o r the  completed process o f d i f f u s i o n .  From the diagram, i t can be seen that  for any estimates where t < t ^ the c o e f f i c i e n t s w i l l be biased toward zero and that the bias w i l l diminish as the truncation point increases. Secondly, the variance of the truncated disturbance at any Z, e.g., Z^ w i l l be less than or equal to the variance o f the truncated disturbance. Further, the variance of the truncated disturbance w i l l increase as the  67. truncation point increases. moved from t  1  1  to t  1  For example, as the truncation point i s  the range of observations at  increases from  ab to ac. Table II of  6 presents comparisons of the values of the c o e f f i c i e n t s  Z„ and Z_ f o r s i x breeds as the truncation point i s increased from 0 L O f i v e to nine years.  68. TABLE II 6 COEFFICIENT VALUES AND VARIANCE OF THE ESTIMATE AS TRUNCATI ON IS INCREASED FROM 5 TO 9 YEARS BROWN SWISS YEARS 5 7 9 MURRAY GREY YEARS 5 7 9 MAINE ANJOU YEARS 5 7 9 LIMOUSIN YEARS 5 7 9 SIMMENTAL YEARS 5 7 9 CHAROLAIS YEARS 5 7 9  5 -.00007 -.00010 -.00012  2 -.026 -.034 -.039  3 -.054 -.159 -.205  -.00007 -.00012 -.00013  3 -.005 -.007 -.005  3 -.191 -.099 -.099  5 -.00005 -.00010 -.00014  2 -.007 -.018 -.035  3 -.367 -.362 -.336  5 -.00007 -.00010 -.00012  2 -.016 -.012 -.019  3 -.145 -.160 -.081  5 -.00005 -.00011 -.00013  2 -.017 -.016 -.026  Z  -.363  5 -.00012 -.00019 -.00020  2 -.012 -.017 -.027  3 -.134 -.185 -.123  Z  h  Z  Z  Z  Z  Z  Z  Z  Z  Z  Z  Z  Z  Z  Z  3  T.315  ,am Z  INT  *  5.1 6.2 6.9 INT  *  5.0 5.8 5.9 INT  *  5.02 6.19 7.42 INT  *  4.53 5.45 6.07 INT  *  3.88 4.91 5.66 INT  *  4.11 5.48 6.04  **  VE  R^  0.68 1.42 1.79  .62 .55 .56  VE  **  0.42 0.61 0.86  **  _2 R^ .68 .65 .59  VE  _2 R^  0.89 0.89 2.25  .54 .51 .54  **  VE  R  0.86 2.04 2.86 VE  „?  **  1.14 2.32 3.42  **  .54 .40 .38 _o  IT  .44 .40 .39  VE  _2 R^  0.96 1.79 3.66  .57 .45 .45  Intercept Variance of the estimate In most cases, as expected, the value of the c o e f f i c i e n t s diverged from zero as the number o f years increased.  Further, the variance o f the estimate  c o n s i s t e n t l y increases as the sample period i s extended.  69.  II i x Discussion The r e s u l t s of t h i s study i n d i c a t e that breeders located e a r l i e r i n areas having low marketing costs, higher expected rates of acceptance and larger expected markets, then expanded into areas with smaller markets and higher costs.  Such firms conform to p r o f i t maximizing behaviour.  The  members of a l l breed organizations cannot be assumed to have been influenced to the same degree by the independent v a r i a b l e s .  There i s no  evidence, however, to suggest that the influence of the independent variables upon the decisions of breeders has followed any d i s c e r n i b l e pattern over time. The results do, however, suggest that the differences i n the l o c a t i o n a l patterns of breeders might, i n part, be explained by the absolute number of areas entered.  In the case of the f i v e year estimates,  removal of three breeds with very low degrees of d i f f u s i o n helped to decrease the degree of sampling e r r o r .  For the seven year estimates,  removal of the two breeds w i t h a poor degree of d i f f u s i o n (n = 15 i n both cases, mean o f remaining breeds i s 85 l o c a t i o n s ) reduced the F s t a t i s t i c considerably.  Where there were no breeds with poor d i f f u s i o n records,  as i n the nine year estimates, the differences in the c o e f f i c i e n t were not s i g n i f i c a n t .  A small number of observations means t h a t , over time  the l o c a t i o n a l choices of breeders are not as r e s t r i c t e d as f o r f a s t e r d i f f u s i n g breeds.  I t i s not s u r p r i s i n g , therefore, that breeders of those  breeds whose degree of d i f f u s i o n i s very small do not appear to be as responsive to market forces. This brings up the question of why breeds d i f f u s e at d i f f e r e n t rates.  At f i r s t glance, i t would appear that the rate of d i f f u s i o n i s  a function of the date of importation.  Table II  7  presents the mean  values f o r the number of areas entered f o r the various i n i t i a l dates.  TABLE II 7 AVERAGE NUMBER OF CENSUS AREAS ENTERED BY BREEDS WITH DIFFERENT FIRST DATES OF ENTRY DATE OF FIRST ENTRY  FIRST 5 YEARS  FIRST 7 YEARS  FIRST 9 YEARS  FIRST 11 YEARS  1 960 (a)  91.0  127.0  139.0  160.0  1969 (b)  64.3  87.5  99.3  145.0  1970 (c)  39.5  75.0  90.2  1971 (d)  38.0  33.6  1 972 (e)  30.3  1 973 ( f )  17.3  1 974 (g)  36.6  (a) Charolais; (b) Simmental, Limousin; (c) Maine Anjou, Murray Grey, Brown Swiss, Welsh Black; (d) Chianina, South Devon; (e) Blonde d'Aquitaine, Gelbveih, Tarentaise; ( f ) Pinzgauer, S a l e r s , Normande, Romagnola; (g) MRI, Marchigiana.  It would seem that breeds which were imported at l a t e r dates did not have as great a rate of d i f f u s i o n as those imported i n e a r l i e r periods. One possible explanation f o r these differences i s that the d i f f u s i o n process i s constrained by the purebred stock a v a i l a b l e - p r i m a r i l y females.  To be an active purebred breeder requires that at least some of  the breeder's cows must be purebreds. large number of non-purebred  Although bulls may be mated to a  females (the number of matings may be g r e a t l y  expanded through the use of a r t i f i c i a l  insemination), a purebred h e i f e r  must come from a purebred cow. Therefore, the rate of d i f f u s i o n i s constrained by the number of purebred cows of a p a r t i c u l a r breed a v a i l a In the early years of any breed's existence, t h i s i s a function of the number of females imported.  Table I I 8 presents a l i s t of the number  of females imported by breed i n the f i r s t f i v e years and the number of census d i v i s i o n s entered. TABLE II 8 NUMBER OF FEMALES IMPORTED BY BREED IN THE FIRST FIVE YEARS BREED  SIMMENTAL  NUMBER OF FEMALES * IMPORTED  NUMBER OF CENSUS DIVISIONS ENTERED  1375  87  MAINE ANJOU  242  67  MURRAY GREY  127  47  CHIANINA  246  67  4  9  BLONDE D'AQUITAINE  17  43  GELBVEIH  40  32  TARENTAISE  33  16  PINZGAUER  19  41  SALERS  32  17  ROMAGNOLA  49  22  MRI  98  17  SOUTH DEVON  *Source: Annual Reports: Canadian National Livestock Records.  The c o e f f i c i e n t of c o r r e l a t i o n between the number of imports and the number of areas entered i s .77.  As space in the quarantine s t a t i o n s  i s l i m i t e d , breeds imported i n early periods would be at an advantage. In 1969, only breeds from France competed f o r space, Charolais, Simmental, Maine Anjou and Limousin. the  By 1974, eighteen breeds were competing f o r  same number o f spaces i n the quarantine s t a t i o n s .  imports per breed was bound to decline.  The number o f  In a d d i t i o n , the l i c e n s e granting  a u t h o r i t y appeared to follow no c l e a r set of p r i o r i t i e s , favouring c e r t a i n breeds i n some years (Slessor, 1979).  The extreme prices received f o r  i n d i v i d u a l cows (up to $200,000 i n some cases, but $50 to $60,000 were not uncommon) i n the e a r l y years of breed importations corroborate the hypothesis that females provided the major constraint on d i f f u s i o n . Further, a great deal of e f f o r t was spent developing the technology of ova t r a n s p l a n t s , which would i n d i c a t e that a l l e v i a t i n g the shortage of females was a major concern.  I t may be that the increased number of  locations f o r breeds imported i n 1974 5 of ova transplants  Table II  7  r e s u l t s from the use  on a commercial basis.  Thus, the importation p o l i c y of A g r i c u l t u r e Canada may have d i r e c t l y affected the d i f f u s i o n of the new technology.  By sanctioning an  importation p o l i c y which allowed f o r great d i v e r s i t y of genetic m a t e r i a l , the  general spread of the new technology was probably retarded, as each  new breed followed a d i f f u s i o n process i n which breeders entered the same areas.  A smaller number of breeds imported would have meant an increased  number of importations f o r the remaining breeds and a more rapid rate o f diffusion.  Of course, over time, the spread of breeds becomes less  dependent on the number of imports, e s p e c i a l l y when upgrading programs are  completed.  73. I f we define the market f o r genetic material as the t o t a l number o f cows i n a census d i v i s i o n , and define penetration of a market as the establishment o f one breeder of a p a r t i c u l a r  breed i n that market, then  we can define the percent of market penetration i n terms of the national cow herd.  The percent of market penetration by breed i s presented i n  Table II 9  f o r the f i r s t 5, 7, 9, 11 and 19 years o f existence f o r  breed organizations.  TABLE II 9 PERCENT OF MARKET PENETRATION BY BREED FIRST . . . i . 5 YEARS,  ,7 YEARS, , 9 YEARS,  11 YEARS,  19 YEARS  BREED CHAROLAIS  84.03  87. 57  91 .60  93.40  SIMMENTAL  83.87  91 ,31 .  92.38  93.90  LIMOUSIN  54.22  66. 18  69.74  MAINE ANJOU  67.02  81. 62  85.84  MURRAY GREY  68.87  78. 03  78.30  BROWN SWISS  66.08  77. 47  79.10  WELSH BLACK  27.44  32. 78  CHIANINA  73.90  74. 59  SOUTH DEVON  18.51  34. 24  BLONDE D'AQUITAINE  57.88  GELBVEIH  50.34  TARENTAISE  31 .16  PINZGAUER  64.86  SALERS  33.46  NORMANDE  30.12  ROMAGNOLA  45.47  MRI  29.29  MARCHIGlANA  67.43  As can be seen from Table I I 9  97.83  when the t o t a l market i s considered  in eleven o f the eighteen breeds examined, over 50% of the potential market was penetrated i n the f i r s t f i v e years.  For the breeds imported  before 1972, most had penetrated 70% o f the market i n the f i r s t seven years of t h e i r existence.  Thus, the means of technical change had been  75. made a v a i l a b l e t o the majority o f the Canadian c a t t l e industry w i t h i n an extremely short period.  The process o f d i f f u s i o n i s also continuing.  Although the absolute number of breeders has declined (Canadian National Livestock Records) as the prices i n the commercial c a t t l e market moved through the trough o f the beef cycle (1975 - 1977), i n a l l o f the eighteen breeds examined establishment  of breeders i n new areas i s continuing.  the two decades o f i t s existence, breeders belonging  In  to the Canadian  Charolais Association have established themselves i n 199 o f the possible 256 d i v i s i o n s , and have penetrated  almost 98 percent o f the market. Yet,  through 1 978, new Charolais enterprises were s t i l l unpenetrated census d i v i s i o n s .  being e s t a b l i s h e d i n  There seems, to t h i s date, no area with a  market potential too small to warrant the establishment  o f a l o c a l breeder.  Although, when the t o t a l market i s examined, the record of breed penetration appears quite impressive, i f the record i s examined on a regional basis some d i s t i n c t patterns emerge. TABLE I I 10  provides a  summary o f market penetration by province. TABLE II 10 SUMMARY OF MARKET PENETRATION BY PROVINCE 18 EXOTIC BREEDS, 1978 NUMBER OF BREEDS AVAILABLE TO 90% OF THE MARKET NUMBER OF BREEDS AVAILABLE TO 50% OF THE MARKET  ALTA  SASK  MAN  B.C.  ONT  10  4  2  2  2  18  12  5  6  6  PEI  NS  1  PQ 0  2  1  NB 0  1  0  1  NFLD 0  0  The establishment of breeders takes place e a r l i e s t i n A l b e r t a , followed by the remainder of the p r a i r i e s , B r i t i s h Columbia, Ontario and Quebec, and the Maritimes, i n that order.  Of course, t h i s r e f l e c t s  the s i z e and importance of the c a t t l e industry i n the various regions of the country.  Table II  11 provides a complete breakdown of market  penetration by breed for each province.  TABLE II 11) MARKET PENETRATION BY:PROVINCE,  to J  to  o S-  Years of Breed Prov. Organization Years t i l l Available to 90% of Potential Market Years t i l l Available B.C. to 50% of P o t e n t i a l Market % of Market Covered 1978 90% Alta. 50% % 1978 90% Sask. 50% % 1978 90% Man. 50% % 1978 90% Ont. 50% % 1978 90% Que. . 50 % • % 1978 9.0% N.S. . 50% . % 1978  <0 +-> c CU  E E •r~ 00  18  10  3 o •r>  •r-  •r— CO  <  00  o E •r—  c •r-  10  c  (1)  to to  o  s  1 CQ  to  (0  2 o S-  1—'  9  9  10 >9 10 .99 ,99 .48 5 2 7 1 2 1 .99 .99 .92 3 >10 3 1 2 5 .99 .99 .81 14 6 >io 3 . 3. >10 .91 .99 .35 14 10 >10 5 5 10 .91 .90 .50 >18 >10 >10 10 >10 >10 83 .26 .09 >18 >.10 >10 10 >10 >10 .83 .41 .26  7 .86 5 3 .99 >6 4 .99 >9 7 .65 >9 8 .64 >9 >9 .17 >9 >9 .37  18 EXOTIC BREEDS, 1978 >> tu S-  CJ3 >> res u  o  cu  Q  cu sz  cu to  >  c  res  ccu  •r—  (13 CU T -  to  i—CD CD  00  7  7  6  6  >7  >7  >7  >6  >4  >7  >7  >7  .83 3 3 .99 >8 3 .85 >8 >8 .35 >8 >8 .45 >8 >8 .01 >8 >8 .01  .12 >7 2 .66 >7 >7 .19 >7 >7 .19 >7 >7 .00 >7 >7 .00 >7 >7 .00  .33 3 2 .92 >7 3 .68 >7 >7 .44 >7 >7 .13 >7 >7 .04 >7 >7 .00  ,09 >7 2 .86 >7 4 .53 >7 >7 .30 >7 >7 .04 >7 >7 .01 >7 >7 .00  00  c_>  ro — I  CQ  9  9  8  8  7  >9  >9  >9  >8  >8  8  >9  >6  >8  .78 4 3 .99 >9 4 .90 >9 >9 .41 >9 >6 .64 >9 >9 .00 >9 >9 .00  .32 >8 6 .63 >8 >8 128 >8 >8 .00 >8 >8 .01 >8 >8 .00 >8 >8 .00  .55 .09 5 >9 2 3 .99 .70 >9 >9 5 >9 .84 .23 >9 >9 6 . >9 .67 .10 >9 >9 6 >9 .73 .00 >9 >9 >9 >9 .13 .00 >9 >9 >9 >9 .17 .00  -co  E s_ o  s_ 3 s:  o  >  cu  to Scu  1—•  +->  s_  c cr «a; ro — —  *i— CU  Q  S-  cu 3 res cn N  c' •1—  ra c ra a>  rt) i—• O c Dl fO  5=  JC U i.  6  i—i CC  6  6  5  5  >6  >6  >6  >5  >5  >6  >6  >6  >(> >5  >5  .06 >6 3 .81 >6 >6 .17 >6 >6 .13 >6 >6 .01 >6 >6 .01 >6 >6 .00  .00 .13 .03 .04 >6 2 >5 >5 2 T 2 3 .61 .98 .79 .61 >6 5 >6 ^>5 >6 2 5 >5 .22,. .93 .55 .20 >6 >6 >6 >5 >6 >6 >6 >5 .07 .19 .07 .07 >6 >6 >6 >5 >6 >6 >5 >5 .01 .08 .01 .04 >6 >6 >6 >5 >6 >6 >6 >5 .00 .05 .00 .00 >6 >6 >6 >5 >6 >6 >6 >5 .00 .11 .08 .00  re) s:  .08 2 1 .94 >5 2 .84 >5 4 .55 >5 >5 .23 >5 >5 .01 >5 >5 .00  N.B.  P.E.I.  NFLD.  1978  1978  1978  cn vo O O s« 6^  %  %  %  vo o O S«  cn o  &s  CO  o  \  VO  o o  00  V o  Simmental Limousin  V V V V V V rx> VO VO -pa o CO vo vo vo vo o cn V V V V V V no VO VO o VO vo CTl o 0 0 vo co o  o o o  V V VO  VO  V V  VO  VO  IN5 CT)  o o  V V o o o oo oo o V V l>o o o oo oo vo V V o b  o  o  V V  o o  •^J  o  —J  o  o  o o  o o  o o  o o  o o o  •~J  V V ~J  f>0  ro  vo  cn o  V V  CTl CTl  o o  o V V o en cn o V V VT> o cn o V V cn o cn o  vo  C O VO  Maine Anjou Brown Swiss Welsh Black Murray Grey  V V 00 o oo o V V o 00 oo VO V V o •--1  V V oo oo  \i  Tarentaise  V V  V V  Blonde D Aquitaine  o  CO  V V  CTl  V V V V vo o VO vo o vo V V V V C O VO  Charolais  OK  oo  V cn  OK  OK  CTl  OK  ro vo  OK  OK  cn cn  V o  OK  00  >10  b o  vo vo ro  >10  ro oo  >18  V CO 0 0  V V -d  o o  V V oo oo V V  V V —1 o ^1 o  South Devon Chianina  1  Gelbvei h  V V  V V CTl CTl o CTl cn o V V V V CTl CTl o CTl vn o V V V V CTl CTl o o cn vn  Salers Normande Pinzgauer  V V  V V OS CTl o CTl vn o V V V V o cn cn o cn cn V V V V V V cn ro cn cn o cn cn vo o cn  Romagnola MRI Marchi gi ana  Although differences i n the dates o f a v a i l a b i l i t y o f the new technology may not appear as a serious problem, given the r e l a t i v e l y small percentage of the Canadian c a t t l e economy which i s located i n areas o f l a t e a v a i l a b i l i t y , the absence o f the new technology may s t i l l have important ramifications f o r have-not areas.  As the market f o r beef  in Canada i s a national market, the competitive p o s i t i o n o f areas where new technology i s not u t i l i z e d can only d e t e r i o r a t e . H i s t o r i c a l l y , Canadian a g r i c u l t u r a l p o l i c y has favoured the geographical d i v e r s i t y o f beef production through f r e i g h t rates, t a r i f f s , feed f r e i g h t assistance for  feed g r a i n s , e t c .  The geographic d i f f u s i o n o f e x o t i c c a t t l e i s not  consistent with t h i s p o l i c y o b j e c t i v e . In a d d i t i o n , certain p r o v i n c i a l governments have been promoting greater s e l f s u f f i c i e n c y i n food s t u f f s . As most o f the areas o f the country where e x o t i c c a t t l e w i l l be a v a i l a b l e l a t e r are net beef importing areas, the promotion will  be more d i f f i c u l t .  of s e l f s u f f i c i e n c y  F i n a l l y , the d e t e r i o r a t i n g competitive p o s i t i o n  of cattlemen i n areas of n o n - a v a i l a b i l i t y may increase the r e l a t i v e poverty i n areas with few a l t e r n a t i v e o p p o r t u n i t i e s , e s p e c i a l l y i n rural Quebec and the Maritimes.  The measurement o f such possible e f f e c t s i s  beyond the scope of t h i s study.  The information provided regarding the  d i f f u s i o n of herds does suggest there may be such a problem.  Further,  the estimates o f the date-of-location functions should help to i d e n t i f y those areas where n o n - a v a i l a b i l i t y may be expected. Although i t i s not possible t o derive a common equation for the date o f - l o c a t i o n function for each period o f 5, 7, 9 and 11 years, t h i s i s p r i m a r i l y a problem o f the r e j e c t i o n of the hypothesis H intercept values are equal.  that the  Fourteen, equations o f the f i r s t 5 years  of location do, however, have a common value for the c o e f f i c i e n t s o f the  80. independent v a r i a b l e s ; -0.555E-05 f o r Zg, -0.016 f o r 1^ and -0.144 f o r ly  These values could be used with a f a i r degree of confidence f o r breeds  which were not subject to severe importation c o n s t r a i n t s .  The s i x breeds,  for which nine years o f data are a v a i l a b l e , have common slopes o f -0.1487E-04, -0.025 and -0.139 f o r Z^, Z^ and Z^ r e s p e c t i v e l y . ^  Of course, for eleven  years of breeder establishment a common equation was generated. The consistency of the estimates over time suggests that one might expect any future breeds to follow s i m i l a r patterns o f d i f f u s i o n .  At  present, the t o t a l stock o f animals with superior genetic potential seems inadequate to meet the demands o f the c a t t l e industry, even with a doubling o f purebred r e g i s t r a t i o n s since the opening o f the quarantine stations.  As long as a new breed has s u f f i c i e n t animals with superior  genetic p o t e n t i a l , then markets w i l l e x i s t f o r that breed. run,  In the long  as the national c a t t l e herd improves, the base upon which b u l l s are  judged superior w i l l r i s e , but the process by which a new breed diffuses should not be a f f e c t e d as long as the breed can provide superior stock. The process of breeder establishment seems r e l a t i v e l y unaffected by phases of c a t t l e cycle and other changes to the industry since 1960.  The  importation o f additional breeds seems t o have halted temporarily, probably as a r e s u l t of the poor c a t t l e prices and, subsequently, purebred prices in the 1970's.  A large number o f breeds, however, remain i n Europe and  other parts o f the world which have not yet been imported i n t o Canada. The improving p r i c e s f o r c a t t l e i n 1978 and 1 979 may stimulate a new demand f o r imports.  Further, a number o f so-called synthetic breeds,  7  such as Hay's  Converter, Beefmaster and Alberta Hybrid, are being developed.  I f the  market does develop f o r such s y n t h e t i c s , they w i l l begin the more general  d i f f u s i o n process.  In e i t h e r case, the s t a b i l i t y of the date-of-  location function might suggest that the pattern of establishment for future breeders would follow the general pattern established t h i s study.  Chapter III STUDY II - CONTINUING TECHNICAL PROGRESS - GENETIC IMPROVEMENT IN THE CANADIAN CATTLE INDUSTRY  III  i  Background  The importation of " e x o t i c " c a t t l e over the l a s t decade provides the increased d i v e r s i t y of germ plasm necessary for more rapid genetic improvement i n the Canadian c a t t l e industry.  This, however, i s only the  f i r s t step i n the process o f technological change.  Although  significant  short term gains can be r e a l i z e d from crossbreeding the a v a i l a b l e stock of germ plasm (Willham, 1976), long term progress w i l l a r i s e through the selection process i n pure s t r a i n s .  Breeding programs should provide  animals which embody increasing amounts of innate productive capacity.  As  in plant breeding and other sectors of the l i v e s t o c k i n d u s t r y , breeding the optimal genetic mix i s a long term project.inv.olving an i n t e r a c t i o n between those who use the genetic material commercially  and those who provide the  genetic inputs to production. Genetic progress i n the l i v e s t o c k industry may be based on the same p r i n c i p l e s of s e l e c t i o n as those i n plant science, but there are two major differences i n the p r a c t i c e of animal breeding.  The f i r s t i s that the  breeding programs are conducted l a r g e l y within the commercial sector.  The  second major difference i s that l i v e s t o c k improvement i s a longer term and continuous  process, while advances i n plant science have been d i s c r e t e  improvements from c o n t r o l l e d experimental  designs combined with extensive  t e s t i n g and evaluation (Evenson and K i s l e v , 1975).  Economic studies have,  to a large extent, ignored the i n t e r a c t i v e process between the breeders of improved genetic material and those who u t i l i z e  i t i n production.  Studies  83. of "exotic" c a t t l e and breeding systems have concentrated on the p r o f i t a b i l i t y o f crossbred c a t t l e ( J e f f e r y , 1971) (Leigh, 1972) (Smith, 1976) (Shumway et a l . , 1974) (Slen and Cameron, 1969) (Rogers, 1969) (McCarthy, 1970)  ( H i l l , 1971) (Dietz, 1973) (Shumway and Bentley, 1974) (Boykin and  Cartwright, 1967). Work i n the f i e l d s o f induced innovation suggests that new processes a r i s e i n response to changes i n the price of output or the prices of inputs (Hayami and Ruttan, 1971).  I t i s reasonable, one can suggest,  that an ongoing or continuous process of technical improvement would also respond both to r e l a t i v e p r i c e s and t h e i r changes.  Such improvements i n the  Canadian c a t t l e industry are being undertaken w i t h i n the commercial sector. Instead of the breeding process being i n t e r n a l i z e d w i t h i n one i n s t i t u t i o n a l structure (such as a research s t a t i o n ) , there are two i n s t i t u t i o n s involved (registered breeders and commercial c a t t l e operations) with a market mechanism operating between them.  Thus, market forces should d i r e c t l y  a f f e c t the process of genetic improvement. Genetic progress i n the animal industry i s , i n r e a l i t y , the provision of additional q u a n t i t i e s of e x i s t i n g inputs to production.  In other words,  j u s t as hybrid plant v a r i e t i e s are bred because they combine certain production c h a r a c t e r i s t i c s such as "short term", "rust r e s i s t a n c e " , "drought r e s i s t a n c e " , e t c . , so  livestock can be bred f o r "disease  r e s i s t a n c e " , "feed conversion", "egg l a y i n g a b i l i t y " , "backfat". e t c . The expected q u a n t i t i e s of these c h a r a c t e r i s t i c s vary from breed to breed. In the c a t t l e industry (as well as other branches of the l i v e s t o c k s e c t o r ) , there i s no market f o r s p e c i f i c genetic c h a r a c t e r i s t i c s .  The char-  a c t e r i s t i c s are subsumed under one purchasable commodity, a b u l l . value of a b u l l i n commercial production i s related to the genetic  The  84. c h a r a c t e r i s t i c s which the animal c a r r i e s .  I f the market i s working  e f f i c i e n t l y , improvements to the genetic mix should r e f l e c t t h i s value. Economists have paid scant attention to the market f o r genetic factors o f production.  Yet, i t provides the key to an e f f i c i e n t process of genetic  progress. I l l i i Review o f L i t e r a t u r e In the majority of economic research (both t h e o r e t i c a l and a p p l i e d ) , i t i s assumed that the inputs to production are homogeneous. bulls are not a homogeneous commodity.  Of course,  There i s no s i n g l e price f o r b u l l s .  The value of a bull i s determined by the genetic c h a r a c t e r i s t i c s embodied in the i n d i v i d u a l animal and, of course, represents a combination  of the  innate properties o f the animal and the cumulative breeding a b i l i t y of the owners of a l l the b u l l ' s ancestors.  In t h i s way b u l l s are very s i m i l a r to  land i n t r a d i t i o n a l analysis (Ricardo, 1817), where the rental price of land was a product of the " o r i g i n a l and i n d e s t r u c t i b l e properties of the s o i l " plus, presumably, the myriad of improvements or degradations out by a l l the previous owners.  carried  There has, as y e t , been l i t t l e study o f  inputs t o production which are not homogeneous. I m p l i c i t l y , however, the computation and comparison o f rates of return to alternate i n v e s t m e n t . p o s s i b i l i t i e s .within :firmsi could be viewed as a recognition that the inputs of production are not homogeneous. Comparisons of improvements t o , for example, farm land (e.g., improved drainage vs. removal of stones) can be viewed as a recognition that the various components of the land base contain d i f f e r e n t p o t e n t i a l s f o r improvement, given l i m i t e d c a p i t a l .  S i m i l a r arguments can be made i n  terms of the i n d i v i d u a l ' s decision regarding his investment i n human capital.  In f a c t , an e n t i r e " t e s t i n g industry" has been developed to  85. i d e n t i f y c h a r a c t e r i s t i c s of educational p o t e n t i a l to help i n d i v i d u a l s maximize the return to t h e i r investment i n education.  In general, i n would  seem that there has been no systematic study of the process o f production in terms of c h a r a c t e r i s t i c s when inputs are heterogeneous.  This may be one  of the reasons why t e c h n i c a l change i s portrayed as a s h i f t i n the production function due to the use of a new input, when, i n f a c t , i n many cases the "new input" simply provided greater amounts of e x i s t i n g c h a r a c t e r i s t i c s of production.  Genetic improvements i n crops provide a good example.  r i c e may be viewed as a new product, but i t i s s t i l l  rice.  Miracle  The difference  i s that i t i n t e r n a l i z e d a superior mix of production c h a r a c t e r i s t i c s (rust r e s i s t a n c e , response to f e r t i l i z e r , shorter growing season . . .) than previously e x i s t i n g natural v a r i e t i e s .  The process of s e l e c t i n g the mix  of c h a r a c t e r i s t i c s has not been subject to i n v e s t i g a t i o n by economists. In consumption theory, however, over the l a s t two decades there has been considerable e f f o r t directed to the so c a l l e d " c h a r a c t e r i s t i c approach".  This e f f o r t stems from two sources: 1) an attempt to overcome  the obvious weakness of e x i s t i n g demand theory (Lancaster, 1966) (Lipsey and Rosenbluth, 1971), and 2) a serious attempt  to deal with the problem  of constructing price indexes i n the face o f changing q u a l i t y of goods ( G r i l i c h e s , 1971) ( T e r l e c k y j , 1975).  These t h e o r e t i c a l developments and  empirical i n v e s t i g a t i o n s have not been p a r a l l e l e d i n production economics. The paper by Archibald and Rosenbluth (1978) provides a new and notable exception. study.  Two elements of t h i s paper suggest t h e i r relevance to t h i s  F i r s t , "The c h a r a c t e r i s t i c approach i s well adapted to deal with the  observed heterogeneity of inputs" (p. 1). Second, they suggest that the c h a r a c t e r i s t i c approach could be h e l p f u l i n analyzing the source of technological change.  Further, Archibald and Rosenbluth suggest t h a t :  86. "We do not need to suppose that producers compute them formally, but i t i s natural to assume that 'good management has an appropriate rule of thumb or i n t u i t i v e understanding of the shadow prices of important c h a r a c t e r i s t i c s required to s e l e c t the cost minimizing input mix", (p. 16) 1  In the case of e x o t i c c a t t l e , we seem to have both s i t u a t i o n s , heterogeneity  of inputs based on production  c h a r a c t e r i s t i c s , and a process  of technological change which should be responsive to the shadow prices of those c h a r a c t e r i s t i c s . In the attempt to e s t a b l i s h price indexes for various products, based on observable c h a r a c t e r i s t i c s , the method of estimating hedonic prices has been heavily u t i l i z e d .  According to Kravis and Lipsey (1971),  "The a p p l i c a t i o n of regression analysis to price measurement rests on the hypothesis that price differences among variants of a product i n a p a r t i c u l a r market can be accounted for by i d e n t i f i a b l e c h a r a c t e r i s t i c s of these variants . . . By f i t t i n g a regression equation to observations on the price and c h a r a c t e r i s t i c s of commodity v a r i a n t s , t y p i c a l l y i n a cross section f o r a market at a given time, we can learn which c h a r a c t e r i s t i c s are associated with the price of a commodity, and what that r e l a t i o n s h i p i s , and, i f we have properly i d e n t i f i e d the relevant c h a r a c t e r i s t i c s , the coe f f i c i e n t s of the equation can be interpreted as prices for the c h a r a c t e r i s t i c s " , (pp. 151-152). However, much of the empirical research on'hedonic p r i c i n g suffers from serious t h e o r e t i c a l d e f i c i e n c i e s (Lucas, 1975) (Muellbauer, 1975).  (Muellbauer,  1974)  when hedonic estimates for new consumer goods are  undertaken, i t i s often questioned whether the i m p l i c i t prices derived from the hedonic function are estimates of consumer valuations or producer costs (a problem which does not a r i s e i n the b u l l case due to the passive role of the s e l l e r i n the s e t t i n g of price determined by auction). problem i s presented in terms of a representative  Further, i f the  consumer, then the  s p e c i f i c a t i o n of the hedonic function must be l i n e a r (Lucas, 1975,  p.  175).  87. Most of the empirical s t u d i e s , however, have reported estimates i n a nonl i n e a r form which forces the abandonment of the representative consumer. Abandonment of the representative consumer implies that any welfare s t a t e ments r e s u l t i n g from q u a l i t y adjusted price indexes necessitate interpersonal comparisons of u t i l i t y .  In production space t h i s problem does not a r i s e ,  although assumptions must be made about the nature of the production  process.  F i n a l l y , most hedonic studies have used i n d u s t r i a l l y produced goods which come i n a l i m i t e d number of "packages".  The a r i s i n g d i s c o n t i n u i t i e s must be  assumed away i f the t r a d i t i o n a l calculus methods are used to c a l c u l a t e shadow prices.  The problem, however, i s e n t i r e l y data r e l a t e d and could be overcome  when using, f o r example, b i o l o g i c a l data with a large number of observations. In such a case, continuous  functions can be approached.  Only recently have economists turned t h e i r attention to d i s aggregating the genetic components of production.  They have used the  method of l i n e a r programming to estimate the value of genetic inputs.  Ladd  and Gibson (1978), for example, attempt to derive the value of three genetic-based economic t r a i t s i n swine production; backfat, feed e f f i c i e n c y and average d a i l y gain. maximum p r o f i t may that animal".  They use t h e i r model to discern "the amount by which  be expected to increase for each unit of improvement i n  T h i s , they suggest, determines the price one should be w i l l i n g  to pay for a herd s i r e .  What goes unstated i s that such information should  also be valuable to the breeder.  In other words, such information should  help the purebred breeder choose which t r a i t to improve upon, i f he knows the rate at which he can expect to improve such t r a i t s .  Burkholder  developed a s i m i l a r l i n e a r programming model among ten breeding c h a r a c t e r i s t i c s f o r integrated b r o i l e r operations.  (1976)  In the beef industry s i m i l a r studies have, as y e t , not been conducted. Further, there has been no examination of the i n t e r a c t i o n between those who use purebred c a t t l e and those who improve them. Ill iii  Hypotheses  The basic premise of t h i s study i s that the mix of production c h a r a c t e r i s t i c s produced by the suppliers of genetic materials (the registered breeders) w i l l be determined by the production process used i n the cow-calf industry.  The s p e c i f i c hypothesis i s that the prices paid  for b u l l s are a function of' i d e n t i f i a b l e c h a r a c t e r i s t i c s , i n t e r n a l i z e d by b u l l s which are phenotypic proxies f o r the genetic components of the production function. be determined.  I m p l i c i t values f o r these c h a r a c t e r i s t i c s may then  A further hypothesis i s that the process of genetic  s e l e c t i o n followed by purebred breeders conforms to the market forces indicated i n the commercial c a t t l e operations' s e l e c t i o n of b u l l s . Ill  iv  The Model  Given t h e i r b i o l o g i c a l nature, processes i n primary a g r i c u l t u r e can be portrayed with a s t y l i z e d production function of the form Y = F( X  ]5  X, 2  X, G m  r  G, 2  G) n  (3.1)  where Y stands f o r units of output, the X.'s are non-genetic components of the production f u n c t i o n , and the G^'s components of the production function. G^'s  are the underlying genetic Of course, in most cases, the  are assumed f i x e d and are omitted from the production function  (Heady and D i l l o n , 1961). For the purpose of our study of the c a t t l e industry, we s h a l l assume  89.  that a l l genetic components o f the production function are subsumed under the b u l l .  2  The production enterprise w i l l be defined i n terms of i n d i v i d u a l bulls. treat  In other words, the commercial cow-calf producer i s assumed to each set of cows which a b u l l can service as a separate e n t e r p r i s e  in terms of the decision to purchase a b u l l .  Therefore, the production  function can be reduced t o , Y  = F ( g , x)  (3.2)  B  B  where Yg = the output per b u l l , pounds o f c a l f / b u l l / y e a r g  = the b u l l component of the production function which i s a vector of genetic-based  c h a r a c t e r i s t i c s - i . e . , g = (G-|, Gg,  G) n  i n t e r n a l i z e d i n one b u l l , x  = the vector of non-genetic  inputs associated with the production  expected from the number of cows one b u l l i s expected to s e r v i c e . The p r o f i t maximizing firm w i l l be expected to u t i l i z e each nongenetic input of production to the point where, assuming perfect'competition W  j  =  P  Y  ( 9  Y  B  8 1  V  '  (3>3)  in e q u i l i b r i u m where W. = the price of input j X  i  = the quantity of input j  Py = the price of output (the price of calves) Under the assumption o f perfect competition, the value of a b u l l w i l l be determined by what i t i s expected to add to the value of production,  90. m *  m  where the X. 's are the s o l u t i o n values f o r (3.3) and Z 0 j = 1  W. X. include J J  "normal" returns to the rancher's labour and c a p i t a l . Of course, a b u l l i s used as the herd s i r e f o r a number of years (approximately 8 years on average).  Hence, the b u l l ' s c o n t r i b u t i o n to  production would be expected to continue over i t s useful breeding l i f e , so that there would be a W^  t  for each year (t) the b u l l i s used i n production.  What one would be w i l l i n g to pay f o r a b u l l would therefore be W2  W  (1+r)  (1+r)  a  B  g 1  3  V  +  _  (l+r)  2  (3.5)  T _ 1  where the W . are the quasi-rents expected from the b u l l from (3.4), T i s Qt i t s expected productive l i f e and r i s the purchaser's perceived discount rate. As b u l l s are heterogeneous, each b u l l ' s price i s determined i n dividually.  The market f o r breeding stock i s of the t r a d i t i o n a l auction  form, with the price determined by competitive bidding.  I f the commercial  cattleman has an i n t u i t i v e understanding of the production r e l a t i o n s h i p , then the price o f a b u l l , Pg, should r e f l e c t i t s expected value i n production (Wilson, 1977).  C e r t a i n l y , no one would pay more f o r a b u l l  than i t s expected value i n production and, given the assumptions regarding the technical knowledge o f producers, low prices would be bid away (Vickrey, 1961).  Of course, t h i s argument i s very similar- to that used i n  determining the rental price of land,  the admission  of heterogeneity  i s t r i v i a l unless the process of price determination and technical change through genetic improvement are examined.  The importance of the heterogeneity of the genetic inputs becomes more obvious when the actual process of genetic improvement i s examined. The breeder of purebred c a t t l e i s the s u p p l i e r of genetic improvement to the commercial cow-calf enterprise.  Once e s t a b l i s h e d , the purebred breeder  i s r e l a t i v e l y constrained i n the amount o f genetic improvement which he can expect to produce.  The expected phenotypic change i n any c h a r a c t e r i s t i c  for one generation i s described by Lasley (1978, p. 163);  A G  iz  = (G  i s  - G )  H  Gi  (3.6)  iS  2  where A G.j = the expected increment i n the c h a r a c t e r i s t i c  over a  generation i n t e r v a l . G.j£  = the measurable quantity of c h a r a c t e r i s t i c G^ o f the s i r e selected f o r breeding.  G^  = the mean quantity of c h a r a c t e r i s t i c G^ o f the selected s i r e ' s male contemporaries within a herd.  Hg  = the h e r i t a b i l i t y of c h a r a c t e r i s t i c G (%).  i  i  I  = the generation i n t e r v a l which i s defined as the average age of the parents when t h e i r f i r s t o f f s p r i n g are born (Pirchner, 1969). This i s the rate o f improvement i n the next generation of s i r e s which  the breeder can expect to r e a l i z e , on average, f o r any one c h a r a c t e r i s t i c . For example, l e t us choose the c h a r a c t e r i s t i c "weaning weight".  I f the  average weaning weight of the s i r e ' s in-herd contemporaries i s 500 l b s . , and the weaning weight of the b u l l to be mated i s 560 l b s . , then we have  G  i S = 500 l b s . 560 l b s .  92. H  Gi  f o r  w e a n l n  9  w e  i9  n t  i s < ^ . 3 5 (Lasley, 1978)  so AG.j  = (560 - 500) (.35/2) = (60) (.175) = 10.5 l b s .  or that the expected mean weaning weight of the b u l l ' s progeny w i l l be 510.5 l b s . Bulls to be used f o r breeding i n the next season are chosen by ranking a l l the bulls i n a herd, and then s u f f i c i e n t numbers ( r e l a t i v e to the s i z e of the cow herd) of those highest ranked are retained (Lasley, 1978),  Bulls  not retained f o r use by the purebred breeder are, depending on t h e i r rank, sold to commercial cow-calf enterprises or c u l l e d . What i s extremely important to the s e l e c t i o n process f o r genetic improvement i s that the various economically important genetic t r a i t s have low (or s l i g h t l y negative) simple c o r r e l a t i o n s (Lasley, 1978) ( J e f f e r y , 1971).  Genetic progress i s reduced as the number o f c h a r a c t e r i s t i c s  selected f o r emphasis at any breeding increases.  I t i s suggested, f o r  example, that "The progress one can make when s e l e c t i n g f o r 4 characters that are unrelated i s I/V4 or % of that which i s possible when s e l e c t i n g for one character. I f the characters are negatively correlated to any degree, progress soon goes to zero" (Johnson, 1966).  In general, therefore,  the purebred breeder w i l l use a s e l e c t i o n process designed to provide 3 improvement p r i m a r i l y on one c h a r a c t e r i s t i c . " H e r i t a b i l i t y and r e l a t i v e economic importance determine the attention each t r a i t should receive in s e l e c t i o n . The greater the number of t r a i t s s e l e c t e d , the less progress can be made f o r any one t r a i t " . (Davis, 1972).  v  The problem f o r the purebred breeder thus becomes, i n any time period, to choose that  which w i l l maximize the value of the b u l l s he w i l l  sell  in the next generation - i . e . , to improve upon that c h a r a c t e r i s t i c which would maximize the expected increase in the price of the progeny  produced  in the next generation. As the cost of r a i s i n g and maintaining bulls with various mixes of c h a r a c t e r i s t i c s are not s i g n i f i c a n t l y d i f f e r e n t (Slessor, 1979), the decision .-should depend, on the absolute l e v e l o f the G.'s, the A G.-j's and the i m p l i c i t values of the c h a r a c t e r i s t i c s . expected A G.. s should be known by the purebred breeder. 1  The G..'s and the Although  diminishing returns may eventually be reached for some c h a r a c t e r i s t i c s , as the p h y s i o l o g i c a l l i m i t s to genetic improvement are approached, i t can be assumed that no such l i m i t has yet been reached f o r the c h a r a c t e r i s t i c s i n beef c a t t l e .  The G^j's can therefore be assumed constant i n succeeding I's.  The value to the purebred breeder of a d d i t i o n a l units of c h a r a c t e r i s t i c s should be r e f l e c t e d i n the prices received f o r b u l l s sold to commercial cow-calf enterprises.  I f the commercial cattleman i s to make the breeding  decision which w i l l maximize his p r o f i t s , he must have an appropriate r u l e of-thumb, or i n t u i t i v e understanding, of the shadow prices o f important c h a r a c t e r i s t i c s , and thus, through the market, e s t a b l i s h t h e i r value to the purebred breeder.  Then i t would be possible to e s t a b l i s h whether purebred  breeders are following the market of G\'s  and A G^'s  forces indicated (given that information  i s generally a v a i l a b l e ) .  Of course, the actual genetic components of the production function are  not r e a d i l y observable.  Instead, the purebred breeder and the cow-  c a l f operator must r e l y on phenotypic (observable) t r a i t s , or chart e r i s t i c s which are known to c o r r e l a t e with genetic improvement.  Data f o r  94. i n d i v i d u a l animals i s usually c o l l e c t e d on 2 phenotypic c h a r a c t e r i s t i c s : 1) the weaning weight, G-j 2) the average d a i l y gain on feed post weaning, G^ In a d d i t i o n , s t a t i s t i c s are c o l l e c t e d by herd on the incidents of dystocia and breed-by-breed indexes of c a l v i n g d i f f i c u l t y , G^, are published and well known. These c h a r a c t e r i s t i c s represent surrogates for the major contribution of a bull to the process of herd production - the rate of growth while sucking, the rate of growth and conversion of feed post weaning, and the number of calves expected per b u l l i The exact functional form of the r e l a t i o n s h i p between these chara c t e r i s t i c s and the production of pounds of c a l f per bull i n commercial herds i s not e x p l i c i t l y known as the r e l a t i o n s h i p i s complex, i n v o l v i n g the i n t e r a c t i o n of the factors of h e r i t a b i l i t y , heterosis and additive gene action (Willham, 1976).  It is  possible, however, to discern some general  i n d i c a t i o n s of the form of the r e l a t i o n . (Lasley, 1978)  I t i s well  known (Woodland, 1 978)  that,  3  Y  B  / 3 G  ]  > 0  3  Y  B  / 3 G  2  > 0  3  Yg / 3 G  3  < 0  I t would seem that i t would be useful to be able to estimate the i m p l i c i t price of additional units of phenotypic c h a r a c t e r i s t i c s suggested above. In essence, estimation of the value of the genetic-based charact e r i s t i c s manifest i n b u l l s i s equivalent to estimating a value added  95.  production function.  Under constant returns, value added i n money terms  i s defined as (Arrow, 1975),  V=  n  m i  =  P  Y  Y  (3.7)  "  where = value added i n money terms  V  = price o f output Y  = quantity of output  Z.'s  = q u a n t i t i e s of inputs c o n t r i b u t i n g to value added  R^'s  = prices o f inputs c o n t r i b u t i n g to value added  X.'s  - q u a n t i t i e s o f inputs not c o n t r i b u t i n g to value added  3  W.'s  = prices of inputs not c o n t r i b u t i n g to value added  C l e a r l y , the r i g h t hand expression of (3.7) i s equivalent to (3.4) The production function (3.2) was Y  R  = F  defined as, (3.8)  (g, x)  and we now define g = (G  r  G, G) 2  3  where the G^'s are the genetic-based  inputs suggested above.  Assuming that  the G.j 's are weakly separable from the elements o f x (Berndt and Christensen, g 1972), the function F can be represented by F  B  (g, x) = H [K(g), x j  for some s u i t a b l e chosen functions M and K.  (3.9) This assumption i s equivalent  96. to the statement that the marginal rates of s u b s t i t u t i o n between the genetic based c h a r a c t e r i s t i c s are independent of the quantities of the non=genetic inputs.  I t has been shown by Arrow (1975) that as long as F  i s homogeneous of degree one and concave i n i t s arguments, K can be i d e n t i f i e d with a value added production f u n c t i o n , and that K has " a l l the properties of a neoclassical production function" (Arrow, 1975, p. 18). We can therefore w r i t e , Q where Q  = K (g)  v  (3.10)  i s the quantity ( r e a l ) value added.  y  Y  Thus, (3.8) can be written as,  = H (Q , x)  B  (3.11)  v  but from (3.7) Q  =  v  where W  or from (3.4) i n our case  i s defined as the price of a unit o f real value added  y  Q  v  = ^ -  (3-12)  Therefore, W  g  If W  y  = W  y  Q  = W  y  v  • K (g)  (3.13)  i s the same f o r a l l b u l l s , then we can estimate (3.13) d i r e c t l y .  From  equation (3.11), using the p r i n c i p l e of d u a l i t y (Diewert, 1973b), i t can be shown that there w i l l be a unit cost function P  Y  = C (W , w) v  (3.14)  where w i s a v e c t o r o f p r i c e s elements  U  o f w are  constant,  W must  inputs.  As P  be c o n s t a n t ,  y  and a l l  v  so  the  that  = W • K (g) V  g  Under p e r f e c t are  assumed  of non-genetic  (3.15)  c o m p e t i t i o n , we assume t h a t  discounted  at  the  same r a t e  and t h a t  all  genetic-based  future  characteristics  Py and Y ^ ' s a n d  m W. X . - ' s a r e  Z j-1  J  p e r c e i v e d and d i s c o u n t e d  at  the  same r a t e  by a l l  producers,  J  whence  from ( 3 . 5 )  P  we can  write,  = W * • K* ( g )  3  (3.16)  v  * K  where  is  the  value  added p r o d u c t i o n  function  d e f i n e d o v e r the  breeding  * life  of a bull, If  (3.16)  genetic-based money t e r m s therefore  and W can  be e s t i m a t e d ,  of additional  i m p r o v i n g each  discerned,  to  G^.  f o r each since  HQ.J  f o r each  units  the  costs  /  3 G.. s can 1  Given  marginal  characteristic,  G . j , one can d e t e r m i n e for a given vector  marginal  a vector of G^'s, i t product  appropriate  f o r the  estimates  estimates  expected G^ t o  product  characteristic  g.  These e s t i m a t e s w i l l  in  is  rate o f im-  with  upon w h i c h then  improvement over t i m e .  be  different  1979). standard  along with estimates  the  observed t r e n d s i n breed  product  be i m p r o v e d can  o f A G ^ j can be made.  of marginal  each  i n money t e r m s o f  G ^ ' s and t h e i r  from p u b l i s h e d s o u r c e s ,  each  the  vary s i g n i f i c a n t l y (Slessor,  mean v a l u e s  available  be d e r i v e d f o r  o f d e v e l o p i n g and m a i n t a i n i n g b u l l s  do n o t  i n f o r m a t i o n with the  actual  o f G... the  f i  3 G| represents  G ^ , i . e . , A G ^ j , the  this  be made  3 P  same p e r i o d .  T h e n , g i v e n i n f o r m a t i o n on t h e  As m e a s u r e s o f t h e are  then  3 Pg /  calculate  mixes o f c h a r a c t e r i s t i c s  deviations  d e f i n e d over the  characteristic.  possible  provement  is  of  Combining  i n value terms  for  improvement  should  be c o m p a r e d  to  This should  provide  98. an i n d i c a t i o n of whether registered breeders respond to the demands of the commercial sector when making breeding decisions and, therefore, do have an appropriate rule-of-thumb or i n t u i t i v e understanding  of the shadow prices  of important c h a r a c t e r i s t i c s . Ill v  Data Much of the t r a n s f e r of genetic material between purebred breeders and  commercial cow-calf operators i s c a r r i e d out at b u l l auctions. To c o l l e c t a set of observations on the genetic c h a r a c t e r i s t i c s and prices of i n d i v i d u a l b u l l s , a large number of bull auctions were attended during l a t e March, A p r i l and May of 1979. Canada.  Auctions were attended i n the four western provinces of  A subset of s a l e s , which provided a consistent set of charac-  t e r i s t i c s and other relevant information, was selected f o r s t a t i s t i c a l analysis.  This subset i s composed of twenty-one i n d i v i d u a l sales at nine  locations i n the four western provinces. TABLE I I I  1.  A l i s t of sales i s provided i n  99. TABLE I I I 1 LIST OF BULL SALES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.  Alberta Bull Test Station Sale Simmental - Monte Creek Test Sale (B.C.) Manitoba Shorthorn Bull Test Sale Alberta Murray Grey Association Sale Saskatchewan Angus Bull Test Sale Saskatchewan Shorthorn Bull Test Sale Alberta Hereford Test Centre Sale Syrinx Angus Ranch Sale (B.C.) Manitoba Maine Anjou Bull Test Sale Blonde d'Aquitaine Bull Test Sale (Alta.) Saskatchewan Charolais Bull Test Sale Saskatchewan Simmental Bull Test Sale B r i t i s h Columbia Simmental Bull Test Sale Manitoba Limousin Bull Test Sale Manitoba Aberdeen Angus Bull Test Sale. Saskatchewan Hereford Bull Test Sale Manitoba Hereford Bull Test Sale National Limousin Bull Test Sale (Alta.) D u f f i e l d Test Station Sale (Alta.) W i l l b a r Bull Test Station Sale (Alta.)  21. Saskatchewan Maine Anjou Bull Test Sale These sales provide observations on 616 i n d i v i d u a l breeds.  b u l l s from 15  A d e t a i l e d breakdown i s provided i n TABLE I I I 2. TABLE I I I 2 NUMBER OF BULLS BY BREED BREED  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.  # OF BULLS  Hereford Aberdeen Angus Charolais Simmental Limousin Maine Anjou Blonde d'Aquitaine Shorthorn Murray Grey Brown Swiss Salers Chianina Pinzgauer Welsh Black Red Angus  207 88 86 67 47 33 22 21 19 9 9 3 3  TOTAL  616  100. A l l b u l l s auctioned at these sales are o f f i c i a l l y classed as 1 year olds (born between December 1977 and June 1978), and no information would therefore be a v a i l a b l e on t h e i r progeny, but a l l animals carry a guarantee of f e r t i l i t y . In addition to the performance c h a r a c t e r i s t i c s  (weaning  weight and average d a i l y gain on feed), a l l catalogues or sale sheets. provide information on the b i r t h date of b u l l s , the name of the consignor and, i n most cases, some information on the animal's pedigree. The information f o r average d a i l y gain on feed i s d i r e c t l y for a l l b u l l s i n the sample.  Data on weaning weights, on the other hand,  demanded conversion t o a standard measure. somewhat o f a misnomer i t s e l f .  comparable  The term weaning weight i s  The s t a t i s t i c a c t u a l l y computed i s e i t h e r  a 200 or a 205 day weight and therefore only approximates weaning weight. Weaning i t s e l f i s usually c a r r i e d out at one common time f o r a l l calves i n the herd, regardless o f whether they are e a r l y or late born calves. Weighing of calves i s usually conducted at approximately 200 days from the middle of the c a l v i n g period, and then the weight of each c a l f i s . converted to a 200 or 205 day weight by a standard formula.  In t h i s study,  the 200 day weight i s used and the formula employed f o r conversion i s that u t i l i z e d by the Federal-Provincial Record of Performance f o r Beef Program, i.e., WEIGHT AT WEIGHIN -BIRTHWEIGHT A G E  I N  X  2Y 0 9 0 n +n  D A Y S  . BIRTHWEIGHT  R T D T U I I | : T r u T  The information provided i n the catalogues and sale sheets i s i n various forms, ranging from those already standardized to 200 day weights, 205 day weights, unadjusted weaning weights, and weights at the commencement o f average d a i l y gain t r i a l s .  As the b i r t h dates and date o f  weighing were l i s t e d f o r each b u l l , i t was possible t o standardize a l l  101. b u l l s to a 200 day weight. Incidents of d y s t o c i a , of course, are an ex-post measure of any individual b u l l .  In other words, such information must come from the  b i r t h s of the progeny of the i n d i v i d u a l b u l l . for b u l l s which have not yet been bred.  No such information e x i s t s  There are, however, s i g n i f i c a n t  differences between breeds, and such information should s t i l l enter i n t o the price a p o t e n t i a l purchaser i s w i l l i n g to pay f o r a b u l l .  An index o f  c a l v i n g d i f f i c u l t y i s c a l c u l a t e d f o r each breed by province by the FederalP r o v i n c i a l Record o f Performance Beef Program (R.O.P.), based on the records made on approximately  100,000 animals each year.  These are published  annually and the summaries reprinted i n the various trade journals as a matter of course. To estimate the A G^'s, i t i s necessary to have information on the G.'s and estimates of H  's. The federal R.O.P. program and various  p r o v i n c i a l departments of A g r i c u l t u r e annually publish information on G^'s and t h e i r standard deviation f o r each breed.  H  's are a v a i l a b l e f o r the  phenotypic c h a r a c t e r i s t i c s from a number of sources (Lasley, 1978) (Willham, 1976). I l l v i S t a t i s t i c a l Analysis and Results As a value added production function has been shown t o have a l l the usual properties o f a n e o c l a s s i c a l production f u n c t i o n , s i m i l a r methods may be used i n t h e i r estimation.  Assuming constant returns to s c a l e , Diewert,  (1973a) has shown that a generalized  l i n e a r transformation function of  the form k = t(y:x) = t ( z ) = a  a  ij  = a  j i  Q 0+  ^  k ^  ,  1  a ^ z^  2  where z i s a k  dimensional vector of non-negative outputs [y^  and an "n" dimensional vector of non-negative inputs (x-j  y ) m  x ), n  k = m - 1 + n provides a second order approximation to a twice di f f erentiable transformation function  which s a t i s f i e s desired non-negati.vity,  monotonicity and convexity and/or concavity properties.  This i s . subject to  the c o e f f i c i e n t s , a.., being consistent with the r e s t r i c t i o n s necessary to s a t i s f y the suggested r e g u l a r i t y conditions.  In the production function  case (one output), i t i s s u f f i c i e n t that " a l l the c o e f f i c i e n t s a^. . . . be non-negative".  (Diewert, 1973a, p. 287).  Further, Diewert (1973a, p. 299) suggests that t h i s p a r t i c u l a r functional form would be best suited f o r the d i r e c t estimation of production functions.  As the function i s l i n e a r i n i t s unknown parameters,  i t i s amenable to estimation by l i n e a r regression.  In our case, from (3.16).  the function to be estimated would be:  '  j ,  j,  «1J  6  1  %  6  j %  a  ij = ji a  ( 3  -  1 7 )  Estimates were conducted by Ordinary Least Squares (OLS) using the algorithm programmed into the SHAZAM (White, 1977) econometrics package on the computer of the University of B r i t i s h  Columbia.  A p r i o r i , however, i t seemed reasonable that the index of c a l v i n g d i f f i c u l t y could be considered weakly separable from weaning weights and average d a i l y gain.  The index of c a l v i n g d i f f i c u l t y i s a measure of  d y s t o c i a , and i s an i n d i c a t i o n of the number of l i v e calves one can expect from the number of cows one bull i s expected to s e r v i c e .  Increases  or decreases i n the number of l i v e calves should not a f f e c t the marginal rate of s u b s t i t u t i o n between weaning weights and average d a i l y gains f o r  103. those calves which are s u c c e s s f u l l y dropped.  I n i t i a l l y , however,  estimation was done without the assumption of weak s e p a r a b i l i t y and no meaningful results could be obtained. terms  2  G^  2  and G^  2  G  2 3  Subsequently, the cross product  were omitted.  Prices f o r b u l l s ranged from $700 to $24,000, with a mean of $2,250. A cursory examination of the c h a r a c t e r i s t i c s data made i t clear that the prices r e a l i z e d f o r certain b u l l s were s i g n i f i c a n t l y greater than t h e i r indicators of genetic merit suggested, and were c l e a r l y , beyond the price a commercial producer would be w i l l i n g to pay.  I t was thereforeedecided that  a closer examination of the market was necessary.  For some s a l e s ,  information on the purchaser as well as the consignor was c o l l e c t e d . Taking an a r b i t r a r y price of $3,000 f o r a bull as the suspected maximum commercial p r i c e , b u l l s purchased at prices over $3,000 were  investigated.  From the d i f f u s i o n study, the names of registered breeders of the various exotic breeds were a v a i l a b l e .  These were checked against the buyers of  b u l l s over the price of $3,000, and i t was found that a disproportionate number o f purebred breeders purchased such animals.  A further check on  animals purchased f o r less than $3,000 revealed that there were very few bought by members o f purebred organizations.  This suggested there were  two markets at the auctions, one f o r transfers from purebred breeders to commercial cow-calf operators, and one f o r transfers between purebred breeders, each with i t s own p r i c i n g c r i t e r i a . Cattlemen who raise c a t t l e which w i l l be used s o l e l y f o r the production of meat w i l l be interested,  i n a set of c h a r a c t e r i s t i c s i n  breeding b u l l s which w i l l d i r e c t l y a f f e c t the number, q u a l i t y and growth;, e f f i c i e n c y o f the dressed carcasses produced.  Breeders o f purebred b u l l s  and cows are interested i n a set of c h a r a c t e r i s t i c s i n the s i r e s they  104.  purchase which w i l l produce superior breeding stock f o r commercial use, and superior breeding stock which can be used to continue t h e i r own herd improvement, or be sold to other purebred breeders.  Such s i r e s may  be  selected to a l l e v i a t e a p a r t i c u l a r d e f i c i e n c y in the purebred breeder's herd, or on the basis of h i s t o r i c information in the form of pedigree. In short, the set of c h a r a c t e r i s t i c s desired by purebred breeders i s u n l i k e l y to coincide with those of the commercial operator.  Further, as  the returns from the a c q u i s i t i o n of a "superior" s i r e can be f a r greater for the purebred breeder, the price he w i l l be w i l l i n g to pay f o r such a s i r e w i l l be greater than the commercial cattleman.  The shadow value of  the c h a r a c t e r i s t i c s , of course, would not be expected to coincide with those perceived by the commercial cattlemen. Although there are auctions organized p r i m a r i l y f o r breeder to breeder t r a n s f e r s , purebred breeders are i n attendance at commercial auctions i n t h e i r role as consignors.  As b u l l s which s u i t t h e i r p a r t i c u l a r needs may  be auctioned at p r i m a r i l y commercial s a l e s , they p a r t i c i p a t e along with commercial cattlemen.  In most cases, the high prices received f o r b u l l s  purchased by purebred breeders suggest that there i s a common recognition of s u i t a b l e animals by purebred breeders.  Otherwise, i t would only be  necessary f o r the purebred breeders to outbid commercial cattlemen and lead to only marginal price increases.  In a d d i t i o n , i t i s well known  that purebred Breeders use c o l l u s i v e bidding t a c t i c s i n attempts to e f f e c t the "mood" of the sale.  The removal of b u l l s purchased by purebred breeders  therefore seemed a reasonable procedure.  As a check, however, estimates  with the e n t i r e sample were undertaken and meaningless r e s u l t s obtained. I t was therefore decided to remove a l l b u l l s transferred between purebred breeders from the sample.  The organizations which sponsored  105. sales f o r which information on buyers had not i n i t i a l l y been c o l l e c t e d were therefore contacted and the l i s t s of buyers obtained f o r each s a l e . The purchasers of bulls were checked against l i s t s of purebred breeders of e x o t i c c a t t l e in the d i f f u s i o n study.  In the case of Herefords, Aberdeen  Angus and Shorthorns, which were not'included in the d i f f u s i o n study, the p r o v i n c i a l breed organizations were contacted by phone and asked i f t h e i r buyers were members of t h e i r organizations.  In the f i n a l r e s u l t i t  was  found that 99 of the 616 sample bulls were purchased by purebred breeders. Further, the highest price paid by a commercial producer was $4,000. 99 b u l l s were removed from the sample.  The  Hence, the f i n a l data set used f o r  estimation i s 517 bulls with prices., ranging from $700 to $4,000. For  the r e a l i z a t i o n of genetic-based technological change, i . e . , B  change i n the form of the production function from F must be undertaken.  a  B to G . crossbreeding  The b i o l o g i c a l phenomenon upon which genetic-based  technological change i s founded i s h e t e r o s i s , commonly observed as the physical expression of hybrid vigour.  Heterosis i s defined as "the  greater vigour or capacity for growth frequently displayed by crossbred animals or p l a n t s , as compared with those r e s u l t i n g from inbreeding" (Webster's, 1965).  Although the majority of breeds imported from  continental Europe are larger than those  developed from stocks i n B r i t a i n  and North America before the opening of the quarantine s t a t i o n s , i n breeding of such animals would y i e l d only the progress which can be obtained from h e r i t a b i l i t y and additive gene a c t i o n .  In other words, straightbred  commercial herds of exotic c a t t l e would e x h i b i t genetic performance s i m i l a r to that which i s r e a l i z e d i n herds,; of e x i s t i n g B r i t i s h c a t t l e , excepting differences between breeds. Technological change i n the c a t t l e industry w i l l not be accomplished  106. through the replacement of commercial herds of straightbred Hereford or Shorthorn c a t t l e with straightbred Simmental or Chianina c a t t l e . the  It is  crossbreeding of such herds which generates the technological change  in the industry.  At present, the basis o f the commercial cow herd i n  Canada i s B r i t i s h , and countinues to be so to take advantage of the hybrid :  vigour which r e s u l t s from the mating with c a t t l e from continental Europe. As y e t , purebred e x o t i c females are s t i l l too valuable as inputs to the production of purebred exotics to be used as commercial cows with B r i t i s h bulls.  Evidence of t h i s i s provided from the Federal R.O.P. program's  annual reports.  For example, in 1977, of the. over 36,500 matings of  Hereford bulls reported, less than 100 were crosses with continental females (Twenty-Second Annual Report, 1977-1978).  Thus, purebred B r i t i s h  b u l l s are s t i l l mated with inbred l i n e s of commercial B r i t i s h c a t t l e and l i t t l e heterosis should be expected. are  On the other hand, European c a t t l e  mated with the same inbred l i n e s of commercial B r i t i s h cows to take  advantage of hybrid vigour.  One would expect, t h e r e f o r e , that the production  function from the two mating schemes would d i f f e r .  Hence, a separate  regression was s p e c i f i e d f o r large breeds (Charolais, Si mmental^ Maine Anjou, Blonde d'Aquitaine, Brown Swiss, S a l e r s , Chianina and Pinzgauer) using 209 b u l l s from which hybrid vigour would be expected, and another for  small and mainly B r i t i s h derived breeds (Hereford, Aberdeen Angus,  Limousin, Shorthorn, Murray Grey, Welsh Black and Red Angus) using 308 bulls.  The index of c a l v i n g d i f f i c u l t y was removed from the estimation  equation f o r small breeds. the  As a r e s u l t of t h e i r generally smaller frames,  index of c a l v i n g d i f f i c u l t y ranged from 1.03 to 1.10 which  provide s u f f i c i e n t v a r i a b i l i t y .  d i d not  These figures representino appreciable  c a l v i n g d i f f i c u l t y and r e f l e c t i n d i v i d u a l rather than breed r e l a t e d  107.  problems.  In the case of small breeds, i t was found that at one s a l e , the  National Limousin B u l l Test Sale i n A l b e r t a , b u l l s brought considerably higher prices than t h e i r merit suggested.  This was not the case.with  animals of the Limousin breed auctioned at other sales.  No explanation of  t h i s apparent enthusiasm at the National Limousin Sale i s offered. variable (NLBTS) i s included i n the equation f o r small breeds. crossproduct term (G^ G^ ) 2  2  The  i s denoted CP i n the estimating equations.  The results of the regression are presented below.  \  A dummy  108. DEPENDENT VARIABLE = PRICE OF EULLS n = 209  LARGE BREEDS Variable name  Estimated c o e f f i cient  WEANING WEIGHT LBS. (G^) AVERAGE DAILY GAIN LBS/DAY (G ) 2  G  1  2  G  5.0249 1159.4 65.427  2 2  t ratio (significant at) 204 df .05** .10 * 2.7649 3.4304 1.2194  INDEX OF CALVING DIFFICULTY (G )  • 246.04  - 4.6848  INTERCEPT  -7550.1  -10.605  3  ** R^ = .5156 (3.18a)  SMALL BREEDS Estimated coefficient  Vari able name WEANING WEIGHT LBS. (G-,) AVERAGE DAILY GAIN LBS/DAY (G ) 2  G^G  2 2  (CP)  NATIONAL LIMOUSIN BULL TEST SALE DUMMY (NLBTS) INTERCEPT  n = 308  4.9941 547.42 52.358  754.15 -4372.0  t ratio (significant at) 303 df .05** .10 3.8839 ** 2.2696'** 1.4827 7.4791 ** ** -10.911 R- = .4738 2  (3.18b)  109. These estimates appear consistent with t h e o r e t i c a l a n a l y s i s .  The  l a r g e r values f o r the c o e f f i c i e n t s of weaning weight and average d a i l y gain (over the relevant range), indicated i n the equation f o r large breeds, suggest an awareness o f hybrid vigour among purchasers of such c a t t l e , and the s h i f t i n the production function expected from technological change.  Although the estimates presented would not allow a breeder to  p r e d i c t , with any accuracy, the p r i c e o f an i n d i v i d u a l b u l l , given the _2 low R , the r e s u l t s do i n d i c a t e that the i d e n t i f i a b l e genetic factors of production, in most cases, s i g n i f i c a n t l y a f f e c t the price o f b u l l s . Further, the estimates should i n d i c a t e to the breeder (with a given c h a r a c t e r i s t i c s mix f o r his herd) which c h a r a c t e r i s t i c s w i l l be most valuable f o r him to improve.  I t i s to t h i s problem that we now turn.  To estimate whether breeders, i n t h e i r s e l e c t i o n process, emphasize the c h a r a c t e r i s t i c s which would maximize the expected value o f b u l l s in the next generation (as indicated by the bull p r i c e equations estimated above), i t i s f i r s t necessary to e s t a b l i s h an expected increase f o r the phenotypic c h a r a c t e r i s t i c s i n physical terms using equation (3.6), or  G  iw n — r — — =G  +  <-' 3 1 9  where ^il+l  =  ^  e  e x  P  e c t e u  "  m e a n  v a  ^  u e  °f c h a r a c t e r i s t i c  for bulls in  generation 1+1. G.  = the value of G. f o r the s i r e to be bred i n qeneration I.  G.jj  - the mean value of c h a r a c t e r i s t i c G^ of the selected s i r e ' s  T  male contemporaries w i t h i n a herd. Hg^  = the h e r i t a b i l i t y of c h a r a c t e r i s t i c G..  Once estimates f o r each  are obtained from (3.19), these values can be  no. u t i l i z e d i n the estimating equations (3.18a, 3.18b) for the relevant breed and the expected increase in value f o r improvement on each c h a r a c t e r i s t i c obtained.  The c h a r a c t e r i s t i c , which the breeder would be expected to em-  phasize i n h i s selection program, can then be i d e n t i f i e d .  The estimates can  then be compared to the actual c h a r a c t e r i s t i c s emphasized by breeders over a generation.  As actual  data on the i n t e n s i t y of selection  (G.^- G^j) i s not  a v a i l a b l e , some assumptions w i l l have to be made regarding t h i s parameter. These w i l l be made e x p l i c i t f o r the p a r t i c u l a r data sets u t i l i z e d below. I d e a l l y , one would l i k e to have data on i n d i v i d u a l herds over time. Such data i s , however, not generally  available.  groups of i n d i v i d u a l b u l l s are a v a i l a b l e .  Fortunately, some data on  The Saskatchewan Bull Test  program publishes the r e s u l t s of i t s t r i a l s f o r i n d i v i d u a l animals i d e n t i f i e d by herd (approximately ten animals from each herd on t e s t each year).  1  Assuming that b u l l s on t e s t are representative of the sample, herd';s  genetic m a t e r i a l , an estimate of the mean values G^'s, and the range f o r '. each c h a r a c t e r i s t i c can be obtained.  Then, assuming the animal which  ranked highest f o r each G. would be used f o r rebreeding, an estimate of * G - j i can be made f o r each c h a r a c t e r i s t i c . +  These can be substituted  into  (3.18a) or (3.18b) and the expected increase i n d o l l a r value calculated. The c h a r a c t e r i s t i c which the breeder would be expected to emphasize can then be i d e n t i f i e d .  These r e s u l t s can be compared to the actual  improvements  observed i n b u l l s of the same herd i n the next generation - i n t h i s case, bulls on t e s t two years l a t e r . For the 1 975-76 & 1977^78 and the 1 976-77 & 1 978-79 t e s t s , f i f t y - s e v e n herds with representative b u l l s have been i d e n t i f i e d . comparisons are presented below i n TABLE I I I  3.  The r e s u l t s of the  For the c a l c u l a t i o n of  h e r i t a b i l i t y , a value o f .35 was used f o r G-| and .50 f o r G 1978, p. 330).  2  (Lasley,  TABLE I I I  3  EXPECTED VALUE OF IMPROVING WEANING WEIGHT AND AVERAGE DAILY GAIN SASKATCHEWAN BULL TEST STATION BULLS  HERD  BLACKLOCK COOK MCCALL MCNINCH C MCNINCH J PERRYVILLS STABLES TONER WILLMOT SPARROW BARDICK DECOR BY FERGUSON HORKOFF HOUGHAM JENSON JOHNSON KAEDING KONSCHUH MCKENZIE MCTAGGART MILLHAM NOBS  BREED  ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS CHARILAIS HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD  WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED MEAN BEST MEAN MEAN BEST MEAN CHANGE IN VALUE {$) (1975) (1 975) (1 977) (1 975) (1 975) (1 977) WW ADG  569 473 522 522 517 621 514 454 495 588 540 4 94 527 494 428 431 586 499 484 452 516 523 479  617 553 557 608 543 657 581 505 52 9 644 607 521 557 522 479 46 9 619 535 565 497 580 539 509  595 542 499 545 624 602 557 520 5 91 657 549 558 587 564 466 457 592 574 506 522 533 569 511  2 .49 2 .72 2 .92 3 .03 2 .94 3 .08 2 .93 2 .80 2 .63 3.40 2 .77 2 .84 2 .72 2 .85 2 .48 2 .76 3.13 3.10 2 .64 2 .72 2 .70 2 .77 2 .71  2.79 2.92 3.39 3.09 3.24 3.1 9 3.22 2.90 2. 75 3.,70 3.03 3.01 2.97 3.12 2.67 3.05 3.61 3.20 2.93 2.96 3.06 3.12 3.03  2. 72 2.68 2. 71 3.15 3.09 2. 74 2. 74 2.91 2.99 3.22 2. 79 3.02 3.01 2. 78 2.83 2.70 3.19 3.14 2.87 2. 73 2. 92 3.21 3.10  $ 54 $ 97 $ 42 $104 $ 31 $ 40 $ 79 $ 49 $ 37 $ 71 $ 78 $ 42 $ 34 $ 31 $ 59 $ 46 $ 38 $ 42 $ 73 $ 52 $ 75 $ 17 $ 34  $ 70 $ 62 $115 $ 13 $ 66 $ 28 $ 67 $ 22 $ 27 $118 $ 59 $ 39 $ 58 $ 62 $ 44 $ 65 $107 $ 37 $ 76 $ 47 $ 81 $ 63 $ 71  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG $ 175 $ 476 $-189 $ 160 $ 48 $-130 $ 297 $ 390 $ 654 $ 513 $ 61 $ 521 $ 409 $ 483 $ 290 $ 183 $ 41 $ 521 $ 134 $ 485 $ 116 $ 315 $ 221 T  PREDICTED EQUALS OBSERVED EMPHASIS  $ 215 $••177 $--160 $ 106 $ 133 $--316 $--173 $ 96 $ 322  ** ** ** ** ** ** ** ** **  $ 18 $ 159 $ 261 $-- 62 $ 279 $ 52 $ 54 $ 114 $ 205 $ 35 $ 198 $ 393 $ 344  ** **  $- -287  ** ** ** ** ** ** ** **  PREDICTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS  $ 47 $ 24 $ 31 $ 19  TABLE I I I HERD  PALASCHUK SPENCER WAINMAN BROWN CAMPBELL COOPER MORTON MCLEOD kkkkk  kkkkk  BREED  HEREFORD HEREFORD HEREFORD SHORTHORN SHORTHORN SHORTHORN SHORTHORN SIMMENTAL kkkkk  3 (continued)  WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED MEAN BEST MEAN MEAN BEST MEAN CHANGE IN (1 975) (1 975) (1 977) (1 975) (1 975) (1 977) VALUE ($) WW ADG  509 431 549 458 465 494 540 637 kkkkk  525 457 581 485 498 540 580 753 kkkkk  565 462 509 465 557 515 671 747 *****  2.87 3.01 3.06 $ 21 $ 31 2.59 2.78 2.57 $ 31 $ 44 2.47 2.95 2.87 $ 37 $111 2.67 2.94 2.81 $ 17 $ 62 2.91 3.13 3.11 $ 39 $ 48 3.20 3.24 2.94 $ 56 $ 9 2.76 3.11 2.88 $ 48 $ 81 3.09 3.35 3.10 $145 $105 ***** ***** ***** *****  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG $ 385 $ 216 $-271 $- 20 $ 640 $ 148 $ 885 $ 792 *****  $ 186 $- 17 $ 369 $ 124 $ 174 $-228 $ 109 $ 16 *****  PREDICTED PREDICTED EQUALS DIFFERENCE OBSERVED IN VALUE EMPHASIS OF IMPROVED CHARACTERISTICS  ** ** ** ** ** ***** *****  $ 13 $ :9 $ 33 kkkkk  (1 976)(1976)(1 978) (1 976)(1 976)(1 97 8) ANAKA DRYLAND MCCALL MCNINCH SAUDER STABLES WILLMS BEGRAND HOWE MCKENZIE PLEWIS SIMPSON WIENS BARDICK DECORBY GAMBLE GRESS JENSON  ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS ANGUS CHAROLAIS CHAROLAIS CHAROLAIS CHAROLAIS CHAROLAIS CHAROLAIS HEREFORD HEREFORD HEREFORD HEREFORD HEREFORD  522 498 508 574 5 94 510 533 683 650 540 743 672 575 493 484 533 472 429  643 513 545 62 9 649 541 547 750 712 623 792 713 594 517 537 543 527 461  592 597 578 601 605 547 592 653 649 6 97 629 618 551 570 554 555 456 484  2.78 3.17 2.85 3.12 3.28 3.51 3.11 3.17 3.00 3.53 2.85 2.94 2.85 2.97 3.29 3.72 3.18 3.63 3.66 4.02 3.51 4.02 3.62 3.92 3.51 3.97 2.62 2.77 2.78 3.19 2.76 3.06 2.92 3.15 2.72 2.95  2.66 2.81 2.84 3.18 2.87 2.78 2.84 3.54 3.11 3.70 3.68 3.49 3.84 3.03 3.04 3.02 2.92 2.80  $105 $ 17 $ 64 $ 65 $105 $ 34 $ 24 $ 84 $ 65 $126 $ 61 $ 51 $ 22 $ 27 $ 63 $ 10 $ 60 $ 39  $ 90 $ 62 $ 52 $ 13 $102 $ 22 $ 22 $178 $186 $119 $211 $121 $180 $ 36 $ 93 $ 67 $ 65 $ 52  $ 272 $-110 $ 681 $- 36 $ 490 $-388 $ 186 $ 63 $ 74 $-119 $ 255 $- 62 $ 370 $- 18 $-219 $ 405 $- 80 $-114 $1183 $ 62 $-939 $ 277 $-403 $-209 $-182 $ 517 $ 525 $ 366 $ 483 $ 230 $ 150.$ 234 $-113 $ 00 $ 385 $ 69  ** ** ** ** ** ** ** ** ** ** ** **  $ 45  $121 $ 70 $ 9 $ 30 $ 13  TABLE I I I 3 (continued) HERD  JONES MILLHAM MISTY MDS WAINMAN COOPER MANN MCLEOD  BREED  HEREFORD HEREFORD HEREFORD HEREFORD SHORTHORN SIMMENTAL SIMMENTAL  AVERAGE DAILY GAIN PREDICTED WEANING WEIGHT MEAN BEST MEAN MEAN BEST MEAN CHANGE I.N (1 976) (1 976) (1 978) VALUE ($) (1976)(1976)(1978) WW ADG  509 532 509 542 500 609 5 90  565 573 537 585 542 652 670  481 563 506 535 522 661 637  2.62 2.85 2.94 '2.88 2,96 2,76 3.16 3.38 3.12 2.61 2.89 2,84 2.94 3.39 3.27 3,47 4,02 3.38 3.41 3.55 3.00  $ 58 $48 $ 31 $ 50 $ 49 $ 56 $104  $ 59 $ 18 $ 48 $ 64 $101 $221 $ 55  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG $-193 $ 288 $ 213 $-108 $- 21 $- 35 $- 47 $ 210 $ 153 $ 290 $ 396 $-143 $ 350 $-657  PREDICTED EQUALS OBSERVED EMPHASIS  PREDI CTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS  ** ** ** ** **  $ 17 $165  For d e t a i l s of c a l c u l a t i o n s see Appendix I 1_ ** Denote those cases where the c h a r a c t e r i s t i c , which the estimating equation (3.18a or 3.18b) indicated should be emphasized f o r improvement, coincided with the c h a r a c t e r i s t i c a c t u a l l y emphasized f o r improvement. 2_  Values i n t h i s column denote, f o r those cases where the c h a r a c t e r i s t i c predicted f o r emphasis did not coincide with the c h a r a c t e r i s t i c a c t u a l l y emphasized, the difference i n the predicted value of improvement between the former and the l a t t e r .  114. The c h a r a c t e r i s t i c a c t u a l l y selected f o r emphasis i n improvement coincided with the c h a r a c t e r i s t i c predicted from equations (3.18a) and (3.18b) seventy-two percent of the time.  Further, i n only three cases when the  c h a r a c t e r i s t i c a c t u a l l y emphasized f o r improvement d i d not agree with the predicted c h a r a c t e r i s t i c to be emphasized, did the difference i n the predicted additional d o l l a r value of a l t e r n a t i v e improvements to c h a r a c t e r i s t i c s exceed $50.  The average differences i n predicted value of improvement to  a l t e r n a t i v e c h a r a c t e r i s t i c s f o r inconsistent predictions i s $43. compares to an average of $34 i n the case of correct p r e d i c t i o n s .  This This would  suggest that the market i s not precise and that e i t h e r breeders are i n d i f f e r e n t about the c h a r a c t e r i s t i c s which they s e l e c t f o r improvement, or that random elements are s u f f i c i e n t to d i s t o r t the perception of breeders as to the correct choice of emphasis i n improvement.  On the other hand, i n only  three cases of fourteen where the difference exceeded $50, did the predicted and actual c h a r a c t e r i s t i c emphasized d i f f e r . On a more aggregate s c a l e , the Federal Record o f Performance f o r Beef program publishes annual summaries on weaning weight and average d a i l y gain, along with t h e i r standard deviation by breed.  I f we assume that the genetic  material i s randomly d i s t r i b u t e d among herds, then the c h a r a c t e r i s t i c to be selected f o r emphasis can be i d e n t i f i e d by a procedure s i m i l a r to that outl i n e d above f o r i n d i v i d u a l animals. known, i t w i l l characteristic.  As the i n t e n s i t y of s e l e c t i o n i s not  be assumed at one standard deviation from the mean f o r each These values were again substituted i n t o equation (3.19)  for the i n t e r v a l s 1 970 & 1972 , 1 971 & 1 973, 1 972 & 1974, 1973 $ 1975, 1974 $ 1 976, 1 975 & 1 977 and 1976 & 1 978.  The values thus obtained were again  substituted i n equations (3.18a) and (3.18b) and values f o r predicted and actual improvements derived.  The r e s u l t s were presented i n TABLE I I I 4.  TABLE I I I 4 EXPECTED VALUE OF IMPROVING WEANING WEIGHT AND AVERAGE DAILY GAIN NATIONAL R.O.P. AVERAGES 1970 - 1978  BREED  CLASS  WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED MEAN SD MEAN MEAN SD MEAN CHANGE IN (1 970)(1970) (1 972) (1 970)(1 970)(1 972) VALUE ($) WW ADG  ANGUS HEREFORD SHORTHORN CHAROLAIS RED ANGUS SIMMENTAL ANGUS HEREFORD SHORTHORN SIMMENTAL  B B B B B B B/C B/C B/C B/C  473 479 473 586 467 560 494 509 481 613  kkkkk  kkkkk  *****  kkkkk  66 73 66 100 103 59 75 81 60 43  *****  475 459 460 545 449 568 498 478 488 513  *****  1.88 2.02 1 .94 2.36 2.12 2.96 1 .98 2.05 1.97 3.10  .49 .51 .52 .64 .30 .84 .47 .52 .46 .64  1.83 1.97 1.93 2.30 2.03 2.62 1.98 1.98 2.03 2.90  $ 76 $109 $ 83 $121 $ 76 $122 $123 $265 $120 $ 69 $ 73 $334 $100 $ 99 $ 92 $123 $ 69 $108 $ 54 $257  ***** ***** *****  *****  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG  PREDICTED EQUALS OBSERVED EMPHASIS  PREDICTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS _2_  $ 13 $-134 $- 86 $-292 $- 90 $ 59 $ 26 $-206 $ 46 $-744 *****  $- 48 $- 47 $-. 9 $-100 $-107 $-551 $ 00 $- 67 $ 57 $ 325 *****  ** ** ** ** ***** *****  $ 53 $-153 $- 93 $-305 $-3 9 $-328 $ 26 $=187 $ 53 *****  $- 19 $ 00 $ 9 $ 301 $ 260 $-780 $ 192 $- 38 $ 9 *****  ** ** ** ** ** ** ** ** ***** *****  ** ** ** **  $ 33  $261  kkkkk  (1 971)(1971 )(1973) (1971)(1971)(1973) ANGUS HEREFORD SHORTHORN CHAROLAIS RED ANGUS SIMMENTAL ANGUS HEREFORD SHORTHORN  *****  3 B B B B B B/C B/C B/C  ***** *****  473 483 473 589 458 544 495 507 467 kkkkk  67 76 70 98 68 88 64 77 65  *****  481 460 45 9 546 452 499 499 479 475  *****  1.89 1 .98 1 .92 2.28 1.65 2.55 1 .88 2.13 2.01  .50 .52 .54 .62 .39 .27 .47 .46 .38  1.87 1.98 1.93 2.46 1.92 2.08 2.08 2.09 2.02  $ 76 $118 $ 86 $122 $ 79 $127 $119 $258 $ 75 $ 97 $115 $114 $ 72 $115 $ 86 $108 $ 87 $ 84  ***** ***** *****  *****  $ 42  *****  TABLE I I I 4 (continued) BREED  ANGUS HEREFORD SHORTHORN CHAROLAIS RED ANGUS SIMMENTAL ANGUS HEREFORD SHORTHORN CHAROLAIS SIMMENTAL ***** *****  CLASS  B B B B B B B/C B/C B/C B/C B/C *****  WEANING WEIGHT AVERAGE DAILY GAIN MEAN SD MEAN MEAN SD MEAN (1972)(1 972)(1 974) (1972)(1972)(1 974)  475 459 460 545 449 568 498 478 488 587 513 *****  91 95 90 118 84 94 93 99 81 122 95 •kk'k'k'k  463 454 459 550 492 542 479 484 485 565 55 9 *****  1.83 1.97 1 .93 2.30 2.03 2.62 1.98 1.98 2.03 2.51 2.90 *****  PREDICTED CHANGE IN VALUE ($) WW ADG  .51 1.75 $102 $124 .51 1.83 $120 $111 .49 1.72 $108 $102 .72 2.36 $145 $2 95 .56 1.87 $ 97 $129 .59 2.27 $115 $244 .37 1.80 $105 $ 90 .58 1.84 $122 $120 ;36 2.00 $ 93 $ 84 .66 2.40 $149 $271 .40 2.44 $126 $158 ***** ***** *****  CHANGE IN PREDICTED VALUE FROM EQUALS OBSERVED OBSERVED PHENOTYPIC EMPHASIS CHANGE WW ADG  PREDICTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS  $- 79 $- 33 $- 7 $ 35 $ 288 $-188 $-126 $ 40 $- 20 $-175 $ 341 *****  ** $- 77 ** $- 133 ** $- 202 ** $ 99 $- 151 $ 580 ** $- 174 ** $- 134 ** $- 28 ** $- 167 ** $- 741 ***** ***** *****  $- 86 $ 20 $ 20 $ 614 $ 582 $ 388 $-228 $- 80 $-188 $-216 $ 297 $-180 $ 439 $-304 *****  $- 1 95 ** $- 220 ** $- 202 $- 715 ** $- 76 $-1119 ** $ 19 ** $- 56 ** $- 172 $- 549 $- 212 ** $- 82 ** $- 907 ** $-1179 ***** ***** *****  $ 32 $129  *****  (1973)(1973)(1975) (1973)(1 973)(1 975) ANGUS HEREFORD SHORTHORN CHAROLAIS RED ANGUS SIMMENTAL ANGUS HEREFORD SHORTHORN CHAROLAIS SIMMENTAL MURRAY GTEY LIMOUSIN WELSH BLACK ***** *****  B B 3 B B 3 B/C B/CB/C B/C B/C B/C B/C B/C *****  481 460 45 9 456 452 500 499 479 475 587 492 473 457 551 •kickick  88 96 94 111 85 104 93 102 87 107 95 56 106 112 *****  468 463 462 540 537 553 465 467 447 557 533 445 520 506 *****  1.87 1.98 1.93 2.46 1.92 2.61 2.08 2.09 2.02 2.61 2.41 1 .39 2.81 2.41 *****  .57 1.67 $ 99 $138 .51 1.75 $110 $113 .55 1.72 $119 $111 .62 2.02 $1 40 $246 .45 1.84 $106 $102 .74 1.93 $132 $295 .45 2.10 $106 $108 $112 $118 .48 2.03 .44 1.84 $100 $103 .57 2.28 $132 $237 .44 2.28 $134 $177 .44 1.31 $ 60 $111 .63 1.82 $139 $129 .38 1 .24 $130 $ 88 ***** ***** *****  $ 39 $106 $163  $105 $ 43  ***** CTl  TABLE I I I 4 (continued) CLASS  BREED  WEANING WEIGHT MEAN SD 1MEAN  AVERAGE DAILY GAIN MEAN MEAN SD  (1974)(1974)(1976) (1974)(1974)(1976)  ANGUS HEREFORD SHORTHORN CHAROLAIS SIMMENTAL LIMOUSIN ANGUS HEREFORD SHORTHORN CHAROLAIS SIMMENTAL  B B B B B B B/C B/C B/C B/C B/C  *****  *****  *****  463 454 459 550 542 523 472 484 482 573 559  74 78 76 117 107 62 74 81 77 108 76  *****  481 466 460 567 640 559 441 479 452 594 632  *****  1.75 1 .83 1 .72 2.16 2.27 2.64 1 .90 1 .84 2.00 2.30 2.44  *****  .57 .58 .64 .66 .68 .73 .50 .56 .44 .85 .60  1.91 1.94 2.03 2.15 2.41 2.48 1.68 2.23 2.28 2.42 2.39  *****  PREDICTED CHANGE IN VALUE ($) WW ADG  $ 82 $ 89 $ 85 $140 $131 $ 71 $ 81 $ 92 $ 86 $130 $ 93  *****  $138 $136 $153 $274 $279 $167 $121 $133 $103 $351 $245  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG  PREDI CTED EQUALS OBSERVED EMPHASIS  $ 118 $ 154 $ 79 $ 104 $ 6 $ 296 $ 119 $- 16 $ 690 $ 231 $ 245 $- 147 $-204 $- 19 $- 33 $ 370 $-201 $ 263 $ 148 $ 200 $ 51 9 $- 82  *****  PREDI CTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS  ** ** **  $1 34 $148 $ 96  ** ** ** ** *****  $152  *****  *****  (1 975) (1 975) (1977) (1975)(1 975)(1977)  ANGUS HEREFORD SHORTHORN CHAROLAIS RED ANGUS SIMMENTAL LIMOUSIN MAINE ANJOU ANGUS HEREFORD SHORTHORN CHAROLAIS SIMMENTAL  B B B B B B B B B/C B/C B/C B/C B/C  *****  *****  *****  468 463 462 540 537 552 520 506 465 467 447 557 533  *****  74 59 79 102 52 100 78 99 83 81 61 104 89  *****  501 479 475 585 523 676 552 638 510 487 512 579 575  *****  1.67 1 .75 1.72 2.02 1.84 1 .93 1.82 1.24 2.10 2.03 1 .84 2.28 2.28  *****  .61 .65 .61 .67 .36 .67 .70 '.94 .66 .64 .66 .71 .54  1.90 2.00 2.06 2.25 2.00 2.48 2.08 2.56 1.96 2.35 2.11 2.57 2.64  *****  $ 81 $ 65 $ 88 $122 $ 58 $121 $ 88 $112 $102 $ 93 $ 69 $127 $110  *****  $149J $157 $148 $286 $ 58 $287 $169 $415 $152 $148 $154 $297 $222  *****  $ 215 $ 223 $ 105 $ 239 $ 85 $ 325 $ 314 $ 386 $- 91 $ 157 $ 843 $ 922 $ 208 $ 253 $ 864 $ 2245 $ 301 $- 132 $ 133 $ 137 $ 429 $ 254 $ 156 $ 479 $ 298 $ 590  *****  *****  ** ** ** ** ** ** ** ** ** ** ** ***** *****  $ 50 $ 85  *****  TABLE I I I BREED  ANGUS RED ANGUS BROWN SWISS CHAROLAIS HEREFORD LIMOUSIN MAINE ANJOU SIMMENTAL SHORTHORN WELSH BLACK ANGUS CHAROLAIS HEREFORD LIMOUSIN SIMMENTAL SHORTHORN  CLASS  B B B B B B B B B B B/C B/C B/C B/C B/C B/C  WEANING WEIGHT MEAN SD MEAN (1 976) (1 976) (1 978)  481 483 573 567 466 559 597 640 460 487 441 5 94 479 560 632 452  40 68 171 97 80 94 130 119 77 113 101 97 78 141 156 75  506 521 614 595 486 552 632 661 491 563 536 616 509 555 62 9 493  4 (continued)  AVERAGE DAILY GAIN MEAN SD MEAN (1 976) (1 976) (1978)  1 .91 1 .80 2 .40 2 .15 1 .94 2 .48 2 .57 2 .41 2 .03 1 .65 1 .68 2 .42 2 .23 2 .59 2 .39 2 .28  ,56 .40 .72 .64 .53 .68 .69 .53 .62 1.07 .75 .73 .46 .36 .75 .55  1 .97 , 1 .77 2,.58 2,.35 2,,03 2,.22 2,.37 2,.48 2,.06 1,.68 2,.19 2,.46 2,.20 2,.31 2..22 2,.39  PREDICTED CHANGE IN VALUE ($) WW ADG  $ 92 $ 75 $209 $115 $ 93 $109 $160 $128 $ 87 $126 $115 $116 $100 $164 $188 $ 88  $1 32 $ 96 $296 $498 $126 $157 $287 $226 $143 $260 $180 $305 $ 95 $ 83 $335 $126  CHANGE IN VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG $ 165 $ 249 $ 291 $ 196 $ 133 $-- 47 $ 249 $ 127 $ 207 $ 490 $ 620 $ 155 $ 202 $-• 33 $-- 35 $ 279  $ 57 $-- 29 $ 297 $ 335 $ 85 $•-247 $--333 $ 138 $ 28 $ 29 $ 480 $ 66 $•-  27 $--246 $ 253 $ 100  PREDICTED EQUALS OBSERVED EMPHASIS  PREDICTED DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS  ** **  **  ** **  $ 80 $.21 $ 33 $ 48 $127 $ 56 $134 $ 65 $189 $147 $ 38  For d e t a i l s o f c a l c u l a t i o n s see Appendix I 1_  2_  ** Denote those cases where the c h a r a c t e r i s t i c , which the estimating equation (3.18a or 3.18b) i n d i c a t e d should be emphasized for improvement, coincided with the c h a r a c t e r i s t i c a c t u a l l y emphasized for improvement Values i n t h i s column denote, for those cases where the c h a r a c t e r i s t i c predicted for emphasis did not coincide with the c h a r a c t e r i s t i c actually emphasized, the difference i n the predicted value o f improvement between the former and the l a t t e r .  oo  119. The actual c h a r a c t e r i s t i c emphasized i n improvement was predicted c o r r e c t l y 68% of the time f o r the 85 observations.  In twenty-eight of the  f o r t y - f o u r cases, where the difference i n predicted values of alternate c h a r a c t e r i s t i c s exceeded $50, the predicted emphasis was consistent with the observed emphasis.  Again, t h i s suggests that the market i s not precise.  The results are consistent with those from the Saskatchewan Bull Test animals presented above. I l l v i i Discussion The results presented i n section I I I vi suggest three conclusions: 1) commercial  cattlemen recognize the important genetic inputs to t h e i r  production process and t h i s i s r e f l e c t e d i n the prices they are w i l l i n g to pay f o r b u l l s ;  2) the prices of b u l l s r e f l e c t the change i n the production  process expected from the hybrid vigour associated with crossbreeding; 3) the s e l e c t i o n of c h a r a c t e r i s t i c s emphasized i n the breeding programs of purebred breeders corresponds, in general, to the choices indicated by the estimated i m p l i c i t values of c h a r a c t e r i s t i c s .  Taken together, they  i n d i c a t e that both producers and breeders have s u f f i c i e n t i n t u i t i v e understanding of the shadow values of important c h a r a c t e r i s t i c s f o r the market to regulate the process of genetic improvement. Such conclusions are not s u r p r i s i n g . that commercial  I t would seem h i g h l y u n l i k e l y  cattlemen would take the time and trouble to purchase a  p a r t i c u l a r s i r e f o r his breeding a c t i v i t y without some genetic c r i t e r i a upon which to evaluate, however i n t u i t i v e l y , the value of that s i r e . Further, i t i s u n l i k e l y that purebred e n t e r p r i s e s , whose sole purpose and income i s derived from providing b u l l s with additional genetic p o t e n t i a l , would devise t h e i r breeding strategy without some understanding of the r e l a t i v e value of the a l t e r n a t i v e f i n a l products.  Probably the most  t e l l i n g i n d i c a t i o n of the importance of genetic parameters to cattlemen i s t h e i r w i l l i n g n e s s to assume the high cost of obtaining information on the genetic c h a r a c t e r i s t i c s of t h e i r herds.  Over 2,500 breeders and  commercial cattlemen v o l u n t a r i l y p a r t i c i p a t e i n the Federal-Provincial R.O.P. Beef program each year.  On t h i s program the operator must weigh  and record his animals two or three times a year. siderable time, e f f o r t and labour. 100,000 animals a year.  This e n t a i l s con-  Yet, information i s c o l l e c t e d on over  Approximately 50% o f a l l purebred calves are R.O.P.  tested on t h i s program (Annual Report 1974-75).  In a d d i t i o n , many breed  organizations and p r o v i n c i a l governments operate bull t e s t s t a t i o n s , where breeders can have t h e i r animals evaluated at t h e i r own expense.  The  f a c i l i t i e s provide better control over the physical environment and management than i s possible i n the on-farm s i t u a t i o n , and therefore allow a more precise i d e n t i f i c a t i o n of genetic merit.  I t would seem u n l i k e l y  that such information would be c o l l e c t e d unless i t s worth to the operator was  identified. There are, however, a number of factors which may make i t appear  as i f the market i s chaotic and that the process o f genetic improvement i s poorly regulated. The most obvious d i s t o r t e r of perception i s the market s i t u a t i o n i t s e l f - the auction.  The author, i n his discussions  with p r o v i n c i a l a g r i c u l t u r e o f f i c e r s , found that many had c a l c u l a t e d the c o r r e l a t i o n s between the prices o f b u l l s and t h e i r genetic c h a r a c t e r i s t i c s . Most of them found low values for.the c o r r e l a t i o n c o e f f i c i e n t , which l e d them to discount the a b i l i t i e s o f purchasers.  Most, however, recognized  the fact that purebred breeders attempt t o , d i s t o r t the market through c o l l u s i v e bidding.  In a d d i t i o n , most admitted that purebred breeders based  t h e i r purchases, i n p a r t , upon the pedigree o f the animals i n addition to  t h e i r apparent genetic worth.  None had removed such observations from  their calculations of correlations.  As suggested above, no meaningful  r e s u l t s could be obtained u n t i l these observations were i d e n t i f i e d and removed from the sample.  This suggests that at any bull sale there are  two markets i n operation, one f o r transfers from purebred breeder to purebred breeder, and one f o r transfers from purebred breeders to commercial c a t t l e operations.  Each has i t s own p r i c i n g c r i t e r i a .  The .-.combination of  the two markets at the same time and place however may give the. impression that the p r i c i n g of b u l l s i s a l a r g e l y random exercise. The second feature of the b u l l market, which contributes to the impression that the p r i c i n g of b u l l s bears l i t t l e r e l a t i o n to t h e i r genetic merit, i s that each i n d i v i d u a l animal may have p h y s i o l o g i c a l t r a i t s which are not h e r i t a b l e  but s t i l l  determine, to some extent, the  animal's a b i l i t y as a breeder.  For example, the "set of the legs" and  the " s i z e and depth of the scrotum" may i n d i c a t e physical rather than genetic breeding a b i l i t y , while general conformation and apparent _2  temperament may a f f e c t the price of any i n d i v i d u a l animal.  The low R  in equations (3.18a) and (3.18b) tends to provide corroboration of t h i s . At any i n d i v i d u a l sale of 20 to 30 animals, the r e l a t i o n of the prices to the genetic c h a r a c t e r i s t i c s may therefore be obscured by such random fluctuations. T h i r d l y , i t seems c l e a r that any evaluation of genetic c h a r a c t e r i s t i c s must be made within the context of the breeding system employed.  The  value of a vector of genetic c h a r a c t e r i s t i c s to be used i n a straightbred system w i l l d i f f e r from those to be employed i n a crossbreeding system. In sales at which a s e l e c t i o n of breeds i s auctioned, c o r r e l a t i o n s between the price of the animals and t h e i r c h a r a c t e r i s t i c s w i l l be low unless the  122. type of breeding system expected i s taken into account. I t may also appear that breeders follow no systematic .improvement program f o r t h e i r herds.  In addition to the well known b i o l o g i c a l and  environmental factors which can a f f e c t the physical manifestations of a herd's c h a r a c t e r i s t i c s at any point i n time, there also appear to be economic factors which can give the outward impression o f lack of d i r e c t i o n and consistency. F i r s t , i t becomes obvious from a close examination o f TABLES 3 and 4 that, i n many cases, the difference i n the expected value of improving one c h a r a c t e r i s t i c r e l a t i v e to another i s marginal at best.  For the .  Saskatchewan Bull Test sample, i n 42 of the 56 cases examined, the difference between the expected value of improving a l t e r n a t i v e charact e r i s t i c s was $50 or less per animal. t h i s was true 50 out of 84 times.  For the annual R.O.P. Beef case  In many cases, t h e r e f o r e , the breeder  may be i n d i f f e r e n t about the c h a r a c t e r i s t i c he may choose to improve o r , indeed, from the information received from the p r i c e s r a t any one s a l e , he may not be able t o discern any c l e a r pattern. On the other hand, breeders may also be so responsive t o changes, in the r e l a t i v e value of improving a l t e r n a t i v e c h a r a c t e r i s t i c s : t h a t no: c l e a r d i r e c t i o n can be discerned from t h e i r breeding program.  For example,  from TABLE I I I 4, i t would appear that Hereford breeders changed the emphasis o f t h e i r breeding program three times i n the seven periods between 1 970 and 1973, following d i r e c t l y the r e l a t i v e values suggested from equation (3.18b).  In two cases, Mi 11 ham and McLeod, where a change  of emphasis was indicated from predicted r e l a t i v e values i n the Saskatchewan Bull Test, sample breeders appear to have emphasis i n the one year period.  a l t e r e d t h e i r breeding  To the c o l l e c t o r o f physical data, such a  123. change i n emphasis may make i t appear that the breeder has "no-clear objectives" f o r his herd when, i n f a c t , the decisions are based on r a t i o n a l economic assessments. The equations estimated from b u l l price data and c h a r a c t e r i s t i c s corroborate the evidence from research by g e n e t i c i s t s regarding the increased p r o d u c t i v i t y expected from hybrid vigour.  I t i s , however,  e q u a l l y - c l e a r that the calving problem associated with the larger animals can counteract, to some extent, the gains from crossbreeding. Thus, the technical advantage of the imported breeds i s not as s i g n i f i c a n t as may have been i n i t i a l l y believed.  The desire by ranchers to. have information  on dystocia l e d to i t s i n c l u s i o n i n the R.O.P. Beef,program time i n 1976 (Annual Report 1976-77).  f o r the f i r s t  The importance attached to t h i s  v a r i a b l e by cattlemen i s indicated by the s i g n i f i c a n c e of the index of c a l v i n g d i f f i c u l t y variable i n equation (3.18b).  Although i t may be too  e a r l y to speculate, i t would seem that the next l o g i c a l step i n the production revolution w i l l be the development of s p e c i a l i z e d females which w i l l possess a genetic make up which w i l l retain the level of hybrid vigour i n crossbreeding, yet w i l l not s u f f e r from c a l v i n g problems.  Such  breeding systems have been proposed by animal s c i e n t i s t s (Cartwright, 1975) (Cunningham, 1974) but, as y e t , few producers have been w i l l i n g to i n i t i a t e such s o p h i s t i c a t e d systems. The conclusions also lend support to the induced innovation hypothesis.  At l e a s t improvements to the e x i s t i n g technologies, both the  new and the o l d , appear to follow the prices indicated by the  market.  I f the marginal changes i n prices predicted f o r bulls can " i n i t i a t e changes in breeding programs, then the more dramatic change i n p r i c e s , usually observed by those conducting empirical research on induced innovation,  would also be expected to e l i c i t a response from the input sector. c h a r a c t e r i s t i c approach to change i n technology  The  u t i l i z e d i n t h i s study  may  also suggest that more meaningful r e s u l t s  could be obtained by those  who  study technological change, i f t h e i r analysis were conducted i n  c h a r a c t e r i s t i c s space rather than goods space.  One of the problems', of  studying induced innovations i n goods space i s that there must be a new good i d e n t i f i e d .  Most changes i n the technology  of production are  probably  in the form o f ongoing adjustments.;, to e x i s t i n g i n p u t s , rather than the creation of a t o t a l l y new input or process.  In our case, a Charolais of  1972 would probably be hard to t e l l from a Charolais of 1978  unless  one  defines the animal in terms of i t s genetic c h a r a c t e r i s t i c s .  I t would,  however, be an e r r o r to suggest that they represent the same input. The usual approach to t h i s problem i n goods space i s to define the input', in terms of vintages, but vintages:, carry no q u a n t i t a t i v e information cannot explain how vintage t i s d i f f e r e n t from vintage t+1.  and  I t i s no  more help i n production space than i t would be for those who attempt to construct price indexes to include a 1976  Buick i n 1976 and a 1977' Buick  in 1977, without defining them i n terms of c h a r a c t e r i s t i c s . therefore seem that i f a better understanding  I t would  of the economics of technical  change i s desired, i t might be more rewarding to define production i n terms of c h a r a c t e r i s t i c s and more thoroughly examine the e f f e c t s of changing prices.  This may not provide any new i n s i g h t s i n t o the process by which  "true innovations" are produced, but i t w i l l  remove the necessity*  imposed by d e f i n i n g production i n goods space, of analysing t e c h n i c a l change i n terms of i d e n t i f i a b l e innovations. F i n a l l y , the type of technological" change with which we have been dealing must be i d e n t i f i e d .  In the sector of t h e i r paper, dealing with  125. technological change, Archibald and Rosenbluth (1978) suggest t h a t , i n i t i a l l y , one must decide whether one i s dealing with a f i x e d l i s t of inputs and outputs. equation  Although calving d i f f i c u l t y i s included in the  f o r large breeds and not'included in the equation  f o r small  breeds, t h i s does not mean that c a l v i n g problems represent a new argument in the vector of input c h a r a c t e r i s t i c s .  H i s t o r i c a l l y , c a l v i n g percentages  have been increasing and the low l e v e l s observed f o r Herefords, Aberdeen:, Angus and Shorthorns are a r e l a t i v e l y new phenomenon.  I t i s the lack of  v a r i a b i l i t y , rather than i t s lack of importance, which leads to i t s omission from equation  (3.18b).  I f we can therefore assume that we are dealing with a f i x e d l i s t of c h a r a c t e r i s t i c s , thus following Archibald and Rosenbluth, the possible types of technological change can be i d e n t i f i e d as e i t h e r , 1) the introduction of a new production  f u n c t i o n , or 2) "the introduction of an  a l t e r e d input which combines additional q u a n t i t i e s of e x i s t i n g input characteristics.  In our case, i t would appear that we have been discussing  technological change of both kinds.  A change in the production  implies that there i s a new way of producing an e x i s t i n g good. production  The  i d e n t i f i e d the increased production expected from cross-  The innovation, i f i t can be defined as such, i s the change of  regulations which allowed the importation of animals with diverse material.  new  function in beef c a t t l e r e s u l t s from the discoveries of applied  g e n e t i c i s t s who breeding.  function  genetic  The change i n the production process i s indicated by the  d i f f e r e n t production  function implied from the estimation of (3.18a) and  (3.18b). On the other hand, genetic improvement in e x i s t i n g populations, whether they are used in a straightbred system or a crossbreeding  system,  represent new inputs combining ^ a d d i t i o n a l q u a n t i t i e s of existing;; characteristics.  Improvements to the c h a r a c t e r i s t i c s mix o f b u l l s appear  to be determined by the prices imputed to the characteristics.;  The f u l l  r e a l i z a t i o n of the genetic p o t e n t i a l , i n t e r n a l i z e d i n the c o l l e c t i v e a v a i l a b l e germ plasm, w i l l depend upon the s e l e c t i v e breeding of pure strains.  As the purebred breeders would appear to be responsive t o short  term changes i n the expected value of a l t e r n a t i v e breeding s t r a t e g i e s , the maximum a t t a i n a b l e genetic improvement may not be achieved.  I f there  are costs i n terms o f sustained genetic progress associated with the switching of s e l e c t i o n emphasis, as some suggest (Johnson, 196$):, then the breeder response t o "spot p r i c e s " may not be the ideal monitor of genetic progress.  This, however, i s a problem of information, rather  than of the market i t s e l f and suggests that a d d i t i o n a l research i n t o such costs should be conducted by economists, and animal  scientists.  We s t i l l have not, of course, found any i n s i g h t s i n t o the forces which bring about an innovation that changes the production f u n c t i o n . In the beef c a t t l e i n d u s t r y , the crossbreeding innovation i s c l e a r l y one e x t e r n a l i t y derived from pure genetic research and i t s subsequent a p p l i c a t i o n i n other a g r i c u l t u r a l sectors. hybrid vigour was an accident.  In one sense the discovery o f  S c i e n t i s t s , attempting to f i n d better  combinations of c h a r a c t e r i s t i c s i n the e x i s t i n g (straightbred) technology, discovered the technology of crossbreeding.  A f u r t h e r case might therefore  be made for the funding of basic and applied research. F i n a l l y , i n the case of the Canadian c a t t l e i n d u s t r y , the question as to whether the new technology w i l l replace the o l d cannot, as y e t , be answered.  I t w i l l depend on the r e l a t i v e prices and the rates o f genetic  progress.  Crossbreeding,  as a production process, has only been a v a i l a b l e  127.  since the opening o f the quarantine stations  j u s t over a decade ago,  and i s therefore hardly f i v e generations o l d i n the areas of the country where imported c a t t l e were a v a i l a b l e very e a r l y .  In terms o f most genetic  evaluations, f i v e generations i s an i n s i g n i f i c a n t period.  In any case,  the s t r a i g h t b r e d technology must remain to provide replacement  females  for crossbreeding u n t i l breeding systems are introduced to provide specialized  females.  Chapter IV SUMMARY AND CONCLUSIONS  An examination of genetic-based technological change i n the Canadian beef c a t t l e industry has provided the focus of t h i s study.  The primary  i n t e r e s t was to evaluate the a b i l i t y of market forces to regulate the process of genetic improvement when h i s t o r i c a l l y major genetic improvements in a g r i c u l t u r a l production have been engineered by applied g e n e t i c i s t s .  The  f i r s t step was to i d e n t i f y the processes necessary f o r the r e a l i z a t i o n o f any genetic-based technological .change.  These are:  1) expansion of the  genetic p o o l , 2) inbreeding of divergent genetic s t r a i n s to increase the p r o b a b i l i t y of desired h e r i t a b l e properties i n a pure breeding s t r a i n , and 3) crossing of the pure breeding s t r a i n s to take advantage of hybrid vigour. Two studies were then conducted; the f i r s t examining the expansion of the genetic pool within the i n s t i t u t i o n a l context of the Canadian c a t t l e industry; the second examining the process of inbreeding and/Crossbreeding through the market i n s t i t u t i o n of bull auctions.  Although adoption of the  crossbreeding innovation by the industry i s f a r from complete, considerable i n s i g h t s have been gained into the a b i l i t y of market forces to d i r e c t the process of genetic improvement. Expansion of the genetic pool i n the Canadian beef c a t t l e industry i s being accomplished through the formation of breed o r g a n i z a t i o n s , the importation of purebred c a t t l e and the establishment of i n d i v i d u a l breeders. As space i n the quarantine stations i s l i m i t e d , s u f f i c i e n t c a t t l e cannot be imported at one time to provide breeding stock f o r the e n t i r e industry. The a v a i l a b i l i t y of new breeds therefore takes on time and geographic  dimensions  as the scarce commodity i s rationed. Market forces appear to be s i g n i f i c a n t in determining the a l l o c a t i o n of breeding stock, with breeders l o c a t i n g  129.  e a r l i e s t , i n areas with favourable market p o t e n t i a l .  Over time, as the  numbers of breeding stock increase through l o c a l production and a d d i t i o n a l imports, less favourable areas are entered.  This pattern has been consistent  across breeds and over time. As the market areas entered e a r l i e s t are those with the largest number of c a t t l e and the more progressive ranchers, the present a l l o c a t i o n mechanism allows for e f f i c i e n t use of a resource which i s l i m i t e d i n the short term. There w i l l be some loss i n e f f i c i e n t a l l o c a t i o n of breeding stock because i n d i v i d u a l commercial operators, located i n less favourable market areas, w i l l be unable to obtain the innovation at competitive c o s t , while favourably located  but p o t e n t i a l l y less e f f i c i e n t ranchers w i l l have access to the  innovation.  These time d i f f i c u l t i e s are compounded because areas of s i m i l a r  market potential are geographically concentrated i n certain areas of the country.  In other words, an A l b e r t a cattleman, who l i v e s i n an area with no  breeder, may be able to assume the cost of obtaining a bull from a nearby area where the breed i s a v a i l a b l e , while a s i m i l a r cattleman from  Quebec  or the Maritimes would not be able to assume the cost of t r a v e l l i n g to the same area i n A l b e r t a . The magnitude of the e f f e c t on the r e l a t i v e income of commercial operators, which w i l l r e s u l t from some areas b e n e f i t t i n g from a s h i f t i n the production function while others do not, can not be ascertained at present.  C e r t a i n l y , experience from several green r e v o l u t i o n crops and  some grains i n the United States would suggest f a l l i n g incomes for areas of late a v a i l a b i l i t y .  One t h i n g does appear c l e a r , the lag for some areas w i l l  be greater than twenty years.  As ninety percent of the national cow  herd  w i l l , i t appears, have access to a breed w i t h i n the f i r s t ten years of i t s importation, such d i f f i c u l t i e s are not l i k e l y to be too severe.  130. One of the major constraints to the d i f f u s i o n of c a t t l e has been the quarantine s t a t i o n s . Given that demand has exceeded the supply of spaces i n the quarantine s t a t i o n s , given that domestic prices for some females of new breeds reached $200,000, given that importers pay both the operating and c a p i t a l costs of the s t a t i o n s , why  a d d i t i o n a l f a c i l i t i e s have not been  constructed or private firms have not been licenced to operate stations i s unclear.  similar  Additional quarantine f a c i l i t i e s would not r e s u l t i n a  decline i n health standards, the maintenance of which should be the sole purpose of quarantine s t a t i o n s . Additional importations would increase the speed with which the d i f f u s i o n of new breeds could be accomplished by reducing the slow task of expanding the herd of purebred females.  The  system, as now c o n s t i t u t e d , provides w i n d f a l l gains for those who obtain import l i c e n c e s . The p o l i c y of allowing the importation of a large number of d i f f e r e n t breeds through the l i m i t e d f a c i l i t i e s has also a f f e c t e d the d i f f u s i o n of new  genetic stock.  Certain areas of the country, t h e r e f o r e , have access to  a wide range of breeds i n t h e i r e a r l y states of d i f f u s i o n , while other areas have access to none.  In general, the p o l i c i e s of A g r i c u l t u r e Canada which  deal with breed importation should be  reviewed.  The processes of inbreeding and crossbreeding were examined by estimating shadow values for genetic c h a r a c t e r i s t i c s using price and c h a r a c t e r i s t i c s information c o l l e c t e d at b u l l s a l e s .  The  characteristics  selected r e f l e c t e d the information about g e n e t i c a l l y c o n t r o l l e d factors which i s generally a v a i l a b l e to the purchasers  of b u l l s .  I t was found that  the c h a r a c t e r i s t i c s i d e n t i f i e d were s i g n i f i c a n t i n determining the price of bulls.  The importance of t h i s r e s u l t should not be ignored.  I f the price  of b u l l s did not r e f l e c t t h e i r genetic c h a r a c t e r i s t i c s , three possible  131. s i t u a t i o n s would be suggested:  1) that the c h a r a c t e r i s t i c s selected f o r  measurement by animal s c i e n t i s t s and  subsequently ranchers are unimportant;  2) that the purchasers of b u l l s are ignorant of genetic processes; or 3) that the production process i s heterogeneous. p a r t i c u l a r ramifications change.  Each of these s i t u a t i o n s would have  f o r the process of genetic-based technological  I f the c h a r a c t e r i s t i c s are unimportant, then relevant a l t e r n a t i v e  characteristics scientists.  which are important should be i d e n t i f i e d by animal  Otherwise, there i s no method whereby genetic progress can be  monitored and ranchers engaged i n the c o l l e c t i o n of the e x i s t i n g set of c h a r a c t e r i s t i c s are expending a great deal of e f f o r t to no a v a i l . I f ranchers are ignorant of the genetic process, then one would expect that l i t t l e genetic progress could be made.  A case might then be made f o r  increased expenditure on education and/or the i n s t i t u t i o n of a s i r e monitoring and regulated breeding program where the decision process was removed from the operator. I f the production at the farm l e v e l proved to be heterogeneous, then the problem would be more severe.  Heterogeneous  production i s taken here  to mean that each farm would derive d i f f e r e n t r e l a t i v e shadow values f o r genetic c h a r a c t e r i s t i c s .  In t h i s case, even i f each farm could maximize  i t s potential i n the short run, the p r i c e s received f o r bulls would not provide consistent information on the shadow value of c h a r a c t e r i s t i c s  and  purebred breeders would not be able to determine the appropriate breeding strategy f o r the future.  The market system would not be able to regulate  e f f e c t i v e l y the process of genetic improvement and some a l t e r n a t i v e mechanism would have to be found.  The r e s u l t s of Study I I , however,  indicate that none of the cases above e x i s t .  Bull s a l e s provide s u f f i c i e n t  information to influence the d i r e c t i o n of genetic progress.  The r e s u l t s of Study II also show that commercial producers  recognize  the change i n production r e l a t i o n s h i p when crossbreeding i s i n s t i t u t e d . This i s observable i n the p r i c e s received for bulls and r e f l e c t e d i n the d i f f e r e n t r e l a t i v e shadow values of c h a r a c t e r i s t i c s of breeding stock used in the crossbred and s t r a i g h t b r e d technologies.  The s i g n i f i c a n c e of the  index of c a l v i n g d i f f i c u l t y i n the determination of the price o f b u l l s to be used for crossbreeding i n d i c a t e s that the increase i n p r o d u c t i v i t y from the use of the innovation i s not as dramatic as o r i g i n a l l y envisioned by many.  As c a l v i n g d i f f i c u l t y can only be measured ex-post for any i n -  dividual animal, research i n t o c h a r a c t e r i s t i c s which are measureable, inexpensive t o c o l l e c t and highly c o r r e l a t e d to the expected c a l v i n g performance o f i n d i v i d u a l s i r e s , should be undertaken by g e n e t i c i s t s . One f i n a l question can also be addressed.  The most common question  asked of those involved i n the study o f c a t t l e breeding i s , "What i s the best breed?"  The results of Study I I i n d i c a t e that the "merit" of  p a r t i c u l a r breeds i s not r e f l e c t e d i n the shadow values of c h a r a c t e r i s t i c s . The commercial cattleman may express h i s breed preferences by s e l e c t i n g which sales to attend, but the prices he i s w i l l i n g t o pay f o r the genetic c h a r a c t e r i s t i c s selected i n t h i s study do not appear to d i f f e r between breeds.  A move to the c h a r a c t e r i s t i c s approach to production may therefore  be appropriate for both economists and physical s c i e n t i s t s .  At present,  v i r t u a l l y a l l of the research on c a t t l e breeding i s conducted (by both economists and physical s c i e n t i s t s ) within the framework o f inter-breed comparisons.  The majority o f empirical analysis conducted attempts to  determine whether there are s i g n i f i c a n t d i f f e r e n c e s between breeds.  Within  each breed, however, the animals have a range of values for. c h a r a c t e r i s t i c s . Market competition w i l l determine whether there are s u f f i c i e n t numbers of  133.  c a t t l e - o f a p a r t i c u l a r breed which have the superior genetic p o t e n t i a l to ensure that the breed survives.  Providing information on inter-breed  differences detracts from the e f f o r t of i d e n t i f y i n g those c h a r a c t e r i s t i c s , across breeds, which a f f e c t the production expected from any i n d i v i d u a l  sire.  The labour of research s c i e n t i s t s might better be spent developing and expanding the set of relevant measureable c h a r a c t e r i s t i c s than designing and conducting experiments which attempt to i d e n t i f y inter-breed differences. Thinking i n terms of goods rather than c h a r a c t e r i s t i c s i s not confined to those conducting economic a n a l y s i s . Study II also provides evidence to j u s t i f y the use of the c h a r a c t e r i s t i c s approach when studying technological change.  I t i s d i f f i c u l t to conceive how  any meaningful analysis of technological change i n the Canadian c a t t l e industry could have been conducted i n goods space.  Although the heter-  ogeneous nature of the input to production studied may represent the extreme case where each goods input i s unique i n terms of the value of i t s c h a r a c t e r i s t i c s , i t does not represent a unique case i n production.  There  are a large number of examples which come to mind where the inputs to production are heterogeneous and unique.  I t i s more prevalent when the  inputs have a b i o l o g i c a l rather than an i n d u s t r i a l o r i g i n . In addition to genetic-based inputs to production i n other sectors of the l i v e s t o c k and poultry industry, a number of other examples may be c i t e d . Each deposit of c o a l , for example, has unique chemical properties which can be expressed i n continuous measures.  As the chemical analysis must be  conducted to e s t a b l i s h grades, i t seems that p r i c i n g might better be established on a continuous scale rather than for a r b i t r a r y grades. Estimation of the shadow values f o r c h a r a c t e r i s t i c s could be used to i d e n t i f y deposits which should be selected f o r future e x t r a c t i o n .  As with c a t t l e ,  134.  trees used both f o r lumber or pulp are graded on the basis of c h a r a c t e r i s t i c s which are continuous  rather than d i s c r e t e .  Information on the shadow values  of those c h a r a c t e r i s t i c s which can be influenced g e n e t i c a l l y could provide valuable information to forest geneticists attempting to select the c h a r a c t e r i s t i c s which should be emphasized for improvement. The economic study of land as an input has suffered from the goods approach.  Individual  pieces of farm land are not homogeneous inputs.  Each  represents a c o l l e c t i o n of c h a r a c t e r i s t i c s such as s o i l f e r t i l i t y , r a i n f a l l , aspect, l o c a t i o n , improvement, e t c . , which for the most part can be measured quantitatively.  Evaluating land through the use of shadow values f o r  c h a r a c t e r i s t i c s could provide information on where the most valuable improvements should be undertaken. Studies of labour have tended to assume homogeneity o r , at best, a few a r b i t r a r y categories.  Each i n d i v i d u a l , however, i s a unique combination  of  education, experience and innate a b i l i t y , most of which can be measured as continuous c h a r a c t e r i s t i c s .  By e s t a b l i s h i n g shadow values for such  c h a r a c t e r i s t i c s , i n d i v i d u a l s could better determine which c h a r a c t e r i s t i c s they could improve to maximize t h e i r u t i l i t y .  The state could also  e s t a b l i s h where the highest returns to educational expenditures might l i e . The development of the c h a r a c t e r i s t i c s approach by economists would demand con siderable e f f o r t both t h e o r e t i c a l l y and  empirically.  In the case of i n d u s t r i a l l y produced i n p u t s , where heterogeneity of inputs i s r e a l i s t i c a l l y reduced to a l i m i t e d number of standardized combinations of c h a r a c t e r i s t i c s which can be reproduced i n quantity, then a "best" input choice i s possible and analysis s i m i l a r to Lancaster's applies.  The emphasis f o r improvements to the technology i n t h i s case w i l l  also be indicated  by the r e l a t i v e shadow prices of the c h a r a c t e r i s t i c s .  The  use of the c h a r a c t e r i s t i c approach in production f a c i l i t a t e s  examination of improvements to e x i s t i n g technology. case i t would be impossible to i d e n t i f y new  goods.  In the "exotic"  the cattle  Each bull i s an i n -  dividual good i d e n t i f i e d by i t s combination of genetic c h a r a c t e r i s t i c s . Improvements to the technology can, however, be examined by studying the changing quantities of c h a r a c t e r i s t i c s over time.  Defining inputs in terms  of c h a r a c t e r i s t i c s would allow the monitoring of marginal improvements to technology over time.  The  c h a r a c t e r i s t i c s approach does not improve upon  the goods approach in providing explanations of the creation processes.  new  Neither the c h a r a c t e r i s t i c s approach nor the goods approach can  explain the discovery of crossbreeding.  The  use of the  characteristics  approach in production, however, can help i d e n t i f y technical are a true s h i f t in a production function, rather than new additional q u a n t i t i e s of e x i s t i n g c h a r a c t e r i s t i c s . function  of e n t i r e l y  changes which  good with  A s h i f t i n the production  can be i d e n t i f i e d i n two ways, e i t h e r from an addition  to the set of  c h a r a c t e r i s t i c s and/or a r a d i c a l change i n the shadow prices of e x i s t i n g characteristics.  In goods space such changes in the production  would be covered up by i d e n t i f y i n g only a new  good.  Although the s h i f t i n  * the production function, which r e s u l t s from the introduction breeding, might have been anticipated be d i f f e r e n t i a t e d from additional o r i g i n a l production function.  The  function  of c r o s s -  i n goods space a n a l y s i s , i t could not  units of the same input added to the change in the shadow value for char-  a c t e r i s t i c s of b u l l s to be used in crossbreeding indicates a s h i f t in the production  function.  In short, although t h i s study has  focused on genetic improvement i n  the Canadian beef c a t t l e industry, i t has also provided an example of the information concerning the form of technological  change which  defining  136.  production in terms of c h a r a c t e r i s t i c s rather than goods may provide.  The  study has also indicated the l i m i t a t i o n s of such a n a l y s i s , p a r t i c u l a r l y d e l i n e a t i n g what forms of technological improvement might be predicted from the c h a r a c t e r i s t i c s approach. A great deal of care should be taken to i d e n t i f y a l l the p a r t i c i p a n t s in the market when applying the c h a r a c t e r i s t i c s approach. may  The same good  be used as an input to a number of productive processes and the shadow  prices of c h a r a c t e r i s t i c s may vary between alternate uses.  In the b u l l  example, a l t e r n a t i v e u s e s ( s i r e s for commercial herds and purebred herds) :  were e a s i l y i d e n t i f i e d and the auction system allows the price of b u l l s for a l t e r n a t i v e uses to r e f l e c t t h e i r value as inputs.  In the more conventional  case, where a standard price i s reached by some tatonnement process, a l t e r n a t i v e uses of inputs w i l l s t i l l have d i f f e r e n t shadow p r i c e s for characteristics.  I t would seem that i n such cases great care would be  needed to discern the e f f e c t s of  m u l t i p l e demands upon the tatonnement  process and, i n d i r e c t l y , on the improvements which might be expected for the product.  In our case, researchers r e l a t i n g the p r i c e of b u l l s to  c h a r a c t e r i s t i c s have met with l i t t l e success, p r i m a r i l y , i t would seem, because they have not separated the sample by the use to which the bull i s put.  Not separating b u l l s , both by whether they were to be used for pure-  bred or commercial breeding, and whether they were to used f o r commercial straightbreeding or commercial crossbreeding, has led to the b e l i e f that the bull market does not r e f l e c t genetic values and, t h e r e f o r e , that cattlemen do not understand the process of genetic improvement.  Such conclusions  could lead to expenditures on unnecessary educational programs or i n t e r ference i n the regulation of the breeding process.  I t may a l s o have  i n s t i g a t e d a considerable waste of e f f o r t i n a search for c h a r a c t e r i s t i c s  137.  which would r e f l e c t the values cattlemen place on b u l l s . The general conclusion i s that market f o r c e s , e s p e c i a l l y i f unfettered by r e g u l a t i o n s , can provide the means to expand the genetic pool and influence the inbreeding and crossbreeding process, so that genetic-based technological change i n the Canadian beef c a t t l e industry can be a t t a i n e d . The e f f i c i e n c y with which the change w i l l be accomplished  cannot be judged.  The u t i l i z a t i o n of new breeds of c a t t l e and crossbreeding systems has resulted i n a large expenditure o f resources for experimentation by commercial cattlemen.  Some of the breeds'.imported  not prove v i a b l e and w i l l disappear.  i n the l a s t decade may  This i s also a waste of resources  which must be written o f f as experimentation.  One cannot determine  whether  an a l t e r n a t i v e mechanism f o r the regulation of technological change in the beef industry could accomplish the change with less waste of resources. What i s c l e a r i s that s i x t y thousand more purebred animals are produced and u t i l i z e d each year than was the case a l i t t l e over a decade ago, and that the process of technological change i s well advanced.  FOOTNOTES  Footnotes - Chapter I 1.  For the remainder of this discussion, the term B r i t i s h w i l l be used to denote Aberdeen Angus, Hereford and Shorthorn  cattle.  Although i t is a controversial term, "Exotic" w i l l be used to denote Charolais and a l l breeds imported since 1966.  139. Footnotes - Chapter II 1.  Of course, one may observe l i m i t e d adoption by producers who are i d e n t i f i e d as, f o r example, "Innovators: Venturesome", by rural s o c i o l o g i s t s (Rogers, 1962) and who presumably receive some consumption  2.  benefit from the use of innovations.  In one of the few studies of the purebred b a t t l e industry, Wendland (1972) shows that transportation costs and a d v e r t i s i n g costs remain approximately constant per animal u n i t , u n t i l the very largest of enterprises i s reached.  As there are, as f a r as I have been able to  a s c e r t a i n , no purebred operations i n Canada with more than 750 brood cows, costs of transportation and a d v e r t i s i n g might be approximately constant i n animal units. 3.  The Charolais breed was introduced to North America through Mexico, and a few found t h e i r way to United States i n the 1930's.  Sub-  sequently, there were a few breeders established i n Canada during the 1950's.  However, u n t i l the i n t e r e s t i n crossbreeding, such breeders  remained e s s e n t i a l l y hobbyists with l i t t l e commercial market f o r t h e i r product. 4.  About 1960, the Charolais breed began i t s rapid expansion.  Brown Swiss c a t t l e have existed i n Canada f o r a long time, but as a dairy breed.  However, with the opening o f the quarantine s t a t i o n s ,  animals of the beef type were imported and breeders established i n p r i m a r i l y beef c a t t l e areas. 5.  Whereby multiple f e r t i l i z a t i o n s are induced i n purebred females and then the embryo are s u r g i c a l l y removed and implanted i n t o any host cow.  This procedure greatly increases the number o f heifers produced  by each purebred  cow.  C  140. 6.  By changing the level of s i g n i f i c a n c e to .10 for? the seven equations of the seven year date-of-location functions, common slopes were also calculated.  They are -0.1076E-04, -0.016, and -.141 r e s p e c t i v e l y  for Zg, 1^, and Z^.  These values are s i m i l a r to those of the 5 and  9 year case. 7.  Synthetic breeds r e s u l t from the multiple crossing of established breeds whose o f f s p r i n g are inbred to attempt to e s t a b l i s h a new breed with certain desired c h a r a c t e r i s t i c s . The f i r s t s y n t h e t i c , Hay's Convertor, was given o f f i c i a l in 1978.  breed status by A g r i c u l t u r e Canada  141. Footnotes - Chapter I I I 1. Presumably, i f a l l land were homogeneous (had the same c h a r a c t e r i s t i c s ) , then such c a l c u l a t i o n s would only have t o be conducted f o r a s i n g l e piece o f land ( u n t i l the r e l a t i v e prices of making the improvements changed). 2. Of course, some genetic progress can be made through the j u d i c i o u s s e l e c t i o n of cows.  Further, i t i s obvious that i n any mating scheme  cows have 50% of the genes.  The assumption i s made because, i n terms of  management, the genetic factors over which a rancher has the most d i r e c t control i s the s e l e c t i o n o f b u l l s .  Hence, "Over 90% of the s e l e c t i o n  advance w i l l come from s i r e s e l e c t i o n , with the remainder coming from heifer selection.  This results because the sex r a t i o i s 50 to 50, while  only 1 male to 20 females i s required under natural s e r v i c e " (Willham, 1 978, p. 132).  Therefore, j u s t as i n the t r a d i t i o n a l production  function s t y l i z a t i o n , Y = F(X X , r  0  X) m  where the genetic inputs to production are deleted because they cannot be c o n t r o l l e d , the genetic inputs to production which are not i n t e r n a l i z e d in the bull w i l l be deleted. Further, the assumption w i l l  be made throughout that cows are  constant, i . e . , that there i s an average female.  Without a supply of  special crossbred replacement h e i f e r s , i t i s u n l i k e l y that commercial female stock w i l l d i f f e r greatly from the average f o r those purchasing purebred b u l l s . - for example, "In U.S. beef production, no such ready source of crossbred replacements e x i s t s , and i t appears rather u n l i k e l y that a segment of the  industry w i l l f i n d such production l u c r a t i v e enough.  The design o f  142. simple crossbreeding schemes, u t i l i z i n g the crossbred cow i n a small commercial  herd, i s impossible without a source of replacement females"  (Will ham, 1 976, p. 396). 3. This i s not s t r i c t l y true.  In most cases, the s e l e c t i o n of superior b u l l s  i s made on a p a r t i c u l a r c h a r a c t e r i s t i c , subject to the condition that some minimum l e v e l i s retained on a l l other t r a i t s .  Geneticists  are cognizant that t h i s i s not an optimum s e l e c t i o n process and are attempting to develop indexes f o r s e l e c t i o n which take i n t o account the r e l a t i v e economic importance of c h a r a c t e r i s t i c s .  As yet these indexes  remain i n the development stage and are not i n general use. indexes w i l l , however, s t i l l would have a weighted value.  These  suggest a s i n g l e most important t r a i t that See Lasley (1978, pp. 367-368).  143. REFERENCES Ackerson, C. W. (1967), "Hybrid Vigor and the Beef Cattle Industry", Feeds I l l u s t r a t e d , 18 (10), pp. 42-47. Archibald, G. C. and G. Rosenbluth (1 978), Production Theory i n Terms o f C h a r a c t e r i s t i c s : Some Preliminary Considerations, Discussion Paper No. 78-19, (Department o f Economics, University o f B r i t i s h Columbia). Arrow, K. J . (1975), "The Measurement o f Real Value Added", i n David, P. A. and M. W. 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(1977), "A Bidding Model of Perfect Competition", Review o f Economic Studies, (44) 3, pp. 194-198. Woodland, R. R. (1978) "Sire S e l e c t i o n " , i n O'Mary, C. C. and I. A. Dyer, Commercial Beef Cattle Production, ( P h i l a d e l p h i a , Lea and Gebiger).  149. APPENDIX I EXAMPLE OF DETAILED CALCULATIONS FOR TABLE I I I 3 AND TABLE I I I 4 The f i r s t l i n e of Table I I I reads;  BLACKLOCK ANGUS  569 617 595 2.49  2.79 2.72  $54  $71  $175 $215 **  569 represents the mean weaning weight f o r b u l l s of the Angus breed from the Blacklock ranch which were tested i n the Saskatchewan B u l l Test Station i n 1975; 617 represents the b u l l with the best weaning weight f o r bulls of the Angus' breed from the Blacklock ranch which were tested i n the Saskatchewan  Bull  Test Station i n 1975; 595 represents the mean weaning weight f o r b u l l s of the Angus breed from the  Blacklock ranch which were tested i n the Saskatchewan  Bull Test  Station i n 1977; 2.49, 2.79 and 2.72 represent s i m i l a r observations f o r average d a i l y gain;  These values were then s u b s t i t u t e d i n t o equation (3.19), e.g.,  r* G  i I + 1  -" rG  + + _ Jr ]i ( n Tl "l H  fI  G  ^  T  )  l l _  where f o r i = weaning weight = G-j G  il  G  i:  =  6 1 7  = 569  Hg. for weaning weight i s estimated at .35 (Lasley, 1978, p. 330) S u b s t i t u t i n g one gets a predicted value of G.  T  ,, of  150. G* = 569 + il+l  35 (  6 1 7  2  5 6 9  >  = 577 As Angus are a small breed these values are substituted i n t o the small breeds equation (3.18b), e.g., P  D  D  = 4.99(569) + 547.42(2.49) + 52.35(23.85)(1.58) + 754.15(0) - 4372 = $1 799.27  and P  D  = 4.99(577) + 547.42(2.49) + 52.35(24.39)(1.58) + 754.15(0) - 4372 .= $1853.39  Giving an expected change i n value of $1853 - 1799 = $54 A s i m i l a r c a l c u l a t i o n was conducted f o r average d a i l y gain which y i e l d e d an expected change of $71. This suggests that average d a i l y gain should be selected f o r emphasis i n the next breeding period.  The values 595 f o r weaning weight and  2.72  average d a i l y gain represent the observed values f o r the mean weaning weight and average d a i l y gain of b u l l s i n generation 1+1.  Substituting  these values i n t o equation (3.18b) gives the change i n value which would be expected from the actual improvement, $175 and $215 r e s p e c t i v e l y . d a i l y gain received a greater value i n improvement as predicted.  Average This i s  denoted by ** Where the predicted and the actual deviate i n apparent emphasis, the difference i n the predicted values of emphasizing weaning weight or average d a i l y gain are noted - e.g., $47 f o r the Sparrow ranch. c a l c u l a t i o n s were conducted f o r Table I I I 4.  Similar  APPENDIX I I SUMMARY OF DATA USED IN STUDY I FIVE YEAR ESTIMATES BREED  MARCH IGIANA  Variable Dependent Z  Mean 2.5556 44495.  l  22.348  : MEUSE  Variable Dependent  1.3827 37848. 16.253  1.0926  1.2629  1.1133  0.62918  51199.  BREED  Standard Deviation  55560.  RHINE - IJSSEL (MRI) Mean 2.1176 61397. 28.639  Standard Deviation 1.1663 49007. 18.678  1.9412  1.8531  1.3494  0.72689  85539.  82074.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED  : ROMAGNOLA  Variable Dependent Z  Mean 2.8182 71697.  l  28.037  1.2960 40050. 15.471  2.0000  2.0702  1.2218  0.42839  90109.  BREED  Standard Deviation  63475.  : NORMANDE  Variable  Mean  Dependent  2.0000 82257.  Standard Deviation 1.4720  Z  1  Z  2  Z  3  2.3846  2.3288  Z  4  1.1 975  0.45813  Z  c  0.102 95E+06  29.458  43792. 15.648  73927.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED  : SALERS  Vari able Dependent Z  Mean 2.2353 70572.  l  27.752  1.2515 46308.. 14.431  2.2353  2.2508  1.2066  0.56740  90515.  BREED  Standard Deviation  72399.  : PINZGAUER  Vari able Dependent Z  l  Mean 2.0732 56367. 27.404  Standard Deviation 1.1914 39298. 17.149  1.2439  1.5777  1.1025  0.56074  61338.  57224.  APPENDIX I I (continued) FIVE YEAR ESTIMATES BREED  : TARENTAISE  Variable Dependent  Mean 2.5000 69399.  Standard Deviation 1.1547  Z  1  Z  2  Z  3  2.0625  1.7689  Z  4  1.3054  0.55728  28.826  l  85122.  r  BREED  48162. 14.058  64066.  : GELBVEIH  Variable Dependent  Mean 2.5294  0.99195  Z  ]  Z  2  Z  3  1.5882  1.6536  Z  4  1.2743  1.2403  l  r  52783.  Standard Deviation  22.772  63626.  43776. 15.653  62139.  APPENDIX I I (continued) FIVE YEAR ESTIMATES BREED  : BLONDE D'AQUITAINE  Variable  Mean  Dependent  2.6279  ]  Z  2  Z  3  1.3023  1.5203  Z  4  1.3552  1.6268  Z  c  23.238  57849.  41598. 17.560  61067.  : SOUTH DEVON  Variable  Mean  Dependent  2.8889  Z  1.1957  Z  BREED  47948.  Standard Deviation  l  73284. 37.984  Standard Deviation 1.2693 46594. 34.677  2.4444  1.8782  1.3341  0.66258  0.11363E+06  90786.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED  : CHIANINA Mean  Variable  3.0735  Dependent  38723. 23.440  0.96686 37855. 21.081  1.1176  1.4815  1.2829  1.0298  46931.  BREED  Standard Deviation  54604.  : WELSH BLACK  Variable Dependent Z  l  Mean 2.6154 75201. 29.581  Standard Deviation 1.3253 44578. 16.119  2.6923  2.6263  1.0909  0.54247  95865.  85063.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : BROWN SWISS Mean  Variable  3.6531  Dependent  48050. 24.760  1.2674 37887. 16.272  1.2857  1.6330  1.2225  0.87891  53864.  BREED  Standard Deviation  56244.  : MURRAY GREY  Variable Dependent  Mean 3.8723 52114.  Standard Deviation 1 .1538 (  Z  1  Z  2  Z  3  1.3191  1.6564  Z  4  1.1685  0.74680  Z  c  27.059  60308.  38164. 21.263  59510.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED  : MAINE ANJOU  Variable  Mean  Dependent  3.6735 48732.  Standard Deviation 1.4052  Z  1  Z  2  Z  3  1.0816  1.3515  Z  4  1.2056  0.81360  Z  r  25.926  60161.  40116. 21.477  60166.  LIMOUSIN  BREED  Variable Dependent Z  l  Mean 3.2750 48285. 23.460  Standard Deviation 1.3395 42337. 21.676  1.2500  1.3540  1.2209  0.72732  57838.  60434.  APPENDIX II (continued) FIVE YEAR ESTIMATES BREED  : SIMMENTAL  Variable Dependent  Mean '2.8736 34351.  Standard Deviation 1.4044  Z  1  35701.  Z  2  Z  3  0.88506  1.2335  Z  4  1.3249  1.4427  20.580  lr  39115.  BREED  18.638  49000.  : CHAROLAIS  Variable Dependent  Mean 2.9780 33230.  Standard Deviation 1.4905  Z  ]  35415.  Z  2  Z  3  0.39560  0.78711  Z  4  1.1189  1.5069  Z  r  20.778  37398.  .  19.320  57545.  160.  APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED  : SOUTH DEVON  Variable Dependent  Mean  Standard Deviation  4.2000  1.9346  Z  ]  81259.  Z  2  Z  3  1.9333  1.7512  Z  4  1.1977  0.60480  34.811  Z 5  26.820  0.10521E+06  c  BREED  42413.  78748.  : CHIANINA  Variable Dependent  Mean 3.2500  Z  ]  36914.  Z  2  Z  3  1.0694  Z  4  1.2705  Z  c  Standard Deviation '  1.1956 37543.  22.658  44624.  20.774 1.4567 '  1.0126  53910.  APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED  : WELSH BLACK Mean  Variable Dependent Z  Standard Deviation  3.2000  1.9712 43005.  71468.  l  15.225  29.433 2.5333  2.4746  1.0726  0.56541  90752.  BREED  : BROWN SWISS  Variable Dependent Z  82065.  Mean  Standard Deviation  4.6842  1.7528  36255.  ]  Z  2  Z  3  0.94737  1.4132  Z  4  1.1951  0.82180  Z  c  20.563  35716.  41013.  /  15.611  50950.  APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED  : MURRAY GREY  Variable  Mean  Dependent  4.6056  1.3988  Z  1  Z  2  Z  3  1.0986  1.4457  Z  4  1.1217  0.72820  Z  r  BREED  39161.  Standard Deviation  23.183  44690.  36899. 20.386  54181.  > MAINE ANJOU  Variable Dependent  Mean 3.6735  1.4052  Z  1  Z  2  Z  3  1.0816  1.3515  Z  4  1.2056  0.81360  2  r  48732.  Standard Deviation  25.926  60161.  40116. 21.477  60166.  163.  APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED  : LIMOUSIN  Variable  Mean  Dependent Z  1  Z  2  Z  3  Z  4  Z  r  BREED  4.2203 39961. 20.808 ,  Standard Deviation 1.7818 40006. 20.421  1.0339  1.2726  1.3047  0.92197  47007.  55190.  : SIMMENTAL  Vari able  Mean  Dependent  3.7500  Z  28049.  l  18.964  1.9644 33197. 18.010  0.71552  1 .1253  1 .3974  1.6853  31750.  )  Standard Deviation  44545.  APPENDIX I I (continued)  164.  SEVEN YEAR ESTIMATES BREED  : CHAROLAIS  Vari able  Mean  Dependent  3.6339  Z  l  28127. 18.613  Standard Deviation 1.9312 33794. 18.415  0.33036  0.72768  1.1666  1.5687  32201.  53351.  APPENDIX II (continued) NINE YEAR ESTIMATES BREED  : BROWN SWISS  Variable  Mean  Dependent Z  5.2418 30916.  l  18.649  2.0404 34793. 15.458  0.80220  1.3352  1.1589  0.87129  35046.  48536.  MURRAY GREY  BREED  Variable Dependent Z  Standard Deviation  l  Mean 4.7568 37704. 23.125  Standard Deviation 1.5599 36830. 20.516  1.0676  1.4270  1.1858  0.93316  43232.  53561.  APPENDIX II (continued) NINE YEAR ESTIMATES BREED  : MAINE ANJOU  Variable  Mean  Dependent  5.6952  Z  29129.  l  19.062  2.2750 34408. 18.241  0.68571  1.0590  1 .2057  1 0142  33888.  BREED  Standard Deviation  48325.  : LIMOUSIN  Vari able  Mean  Dependent  4.7500  Z  l  35658. 19.113  Standard Deviation 2.1536 38893. 19.552  1.0000  1.2339  1 .2212  0.89406  41547.  53275.  APPENDIX I I (continued) NINE YEAR ESTIMATES BREED  : SIMMENTAL  Variable Dependent  Mean 4.2901 25128.  Standard Deviation 2.3907  Z  ]  Z  2  Z  3  0.64122  1.0818  Z  4  1.3346  1.6437  17.55V  l  28366.  r  BREED  32280. 17.419  42958.  : CHAROLAIS  Variable Dependent  Mean 4.5683 23695.  Standard Deviation 2.5877  Z  ]  Z  2  Z  3  0.26619  0.66568  Z  4  1.0773  1.4808  Z  c  16.789  27145.  31821. 17.344  49291.  APPENDIX II (continued) ELEVEN YEAR ESTIMATES BREED  : SIMMENTAL  Variable Dependent  Mean 4.8690 23075.  Standard Deviation 2.8874  Z  ]  Z  2  Z  3  0.57931  1.0453  Z  4  1.3688  1.6775  17.010  l  26285.  c  BREED  17.294  41415.  : CHAROLAIS  Variable Dependent Z  31343.  l  Mean 5.3438 20987. 15.483  Standard Deviation 3.1384 30484. 16.639  0.23125  0.62668  1.0623  1.5628  23896.  46716.  APPENDIX II [continued) NINETEEN YEAR ESTIMATES BREED  : CHAROLAIS  Vari able Dependent Z  l  Mean 7.0302 17668. 13.744  Standard Deviation 4.5360 28342. 15.516  0.18593  0.56907  0.99416  1.4472  20096.  43046.  APPENDIX I I I SUMMARY OF DATA USED IN STUDY II  *  LARGE BREEDS (Equation 3.18a)  Variable  Mean  Price  1727.4  Weaning Weight  569.05  Standard  Deviation  586.35 83.034  Average Daily Gain  3.3856  0.41111  Index of Calving D i f f i c u l t y  1.4491  0.55675  *  Charolais, Simmental, Maine Anjou, Blonde d'Aquitaine, Brown Swiss S a l e r s , Chianina, Pinzgauer.  SMALL BREEDS ** (Equation 3.18b) Variable Price , Weaning Weight Average Daily Gain  Mean 1821.4 492.02 3.1244  Standard Deviation 532  .67  92.012 0.53341  ** Hereford, Aberdeen Angus, Limousin, Shorthorn, Murray Grey, Welsh Black Red Angus.  

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