UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1981_A1 K47.pdf [ 8.01MB ]
Metadata
JSON: 831-1.0095470.json
JSON-LD: 831-1.0095470-ld.json
RDF/XML (Pretty): 831-1.0095470-rdf.xml
RDF/JSON: 831-1.0095470-rdf.json
Turtle: 831-1.0095470-turtle.txt
N-Triples: 831-1.0095470-rdf-ntriples.txt
Original Record: 831-1.0095470-source.json
Full Text
831-1.0095470-fulltext.txt
Citation
831-1.0095470.ris

Full Text

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 University of B r i t i s h Columbia, 1969 M.A., Simon Fraser University, 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 this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1981 (c) William A. Kerr In presenting th is thes is in pa r t i a l fu l f i lment o f the r e q u i r e m e n t s f o r an advanced degree at the Univers i ty of B r i t i s h C o lumbia, I agree t h a t the L ibrary sha l l make it f ree ly ava i lab le for r e f e r e n c e and study . I fur ther agree that permission for extensive copying o f t h i s t h e s i s for scho lar ly purposes may be granted by the Head o f my Department or by his representat ives. It i s understood that c o p y i n g o r p u b l i c a t i o n o f th is thes is for f inanc ia l gain sha l l not be allowed w i t h o u t my writ ten permission. Department of C ^ ^ ^ ^ ^ ^ 3 The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 i v 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 dissertation investigates the process of genetic-based technical change in the Canadian beef cattle industry. S p e c i f i c a l l y , I analyze the effect of market forces on three processes necessary for genetic-based technological change: expansion of the genetic pool, inbreeding of divergent genetic strains to increase the probability of desired heritable properties in a pure breeding s t r a i n , and crossing of pure breeding strains to take advantage of hybrid vigour. This i s accomplished through two studi es. The f i r s t study, examines the expansion of the genetic pool through the establishment of purebred breeders of cattle breeds imported since 1965. A model i s developed to explain the location of breeders within a time framework. The model was tested across breeds and over time. The process of breeder location appears consistent for 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 of c a t t l e in different 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 "characteristics" approach to production i i i with the phenotypic characteristics of breeding bulls as arguments in a production function. Prices of individual bulls and values for the characteristics were collected at bull sales and shadow values for the characteristics estimated. These shadow values were used to predict characteristics which should be emphasized in herd improvement, and the prediction was compared to observed practices. The use of the characteristic: approach led to the i d e n t i f i c a t i o n of a different production function for the t r a d i t i o n a l straightbred technology and the new crossbred technology. Market forces seem to regulate the process of technological change and promote breed improvement. 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 biological l i m i t s to increasing the stock of purebred females. i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS iv LIST OF TABLES vi LIST OF DIAGRAMS v i i ACKNOWLEDGEMENTS v i i i CHAPTER I INTRODUCTION 1 i Foreword 1 i i Background 2 i i i I n s t i t u t i o n a l Considerations 5 iv Economic Analysis of Technological Change 7 CHAPTER II STUDY I THE SUPPLY OF A NEW TECHNIQUE 11 i Background 11 i i Institutions 13 i i a Importation 14 i i b Registration of Animals 17 i i c Evaluation of Genetic Potential 18 i i d Promotion and Sale of Cattle 19 i i i Review of Literature 20 iv Hypotheses 23 v The Model 24 vi Variables and Data 27 vi a The Dependent Variable 27 vi b Independent Variables 29 vi b 1 Potential Market 29 vi b 2 The Expected Rate of Acceptance 30 vi b 3 Market Costs 31 vi b 4 Cost of Introduction 32 v i i S t a t i s t i c a l Methods and Results 34 v i i a Five Year Estimates 35 v i i b Seven Year Estimates 47 v i i c Nine Year Estimates 53 v i i d Eleven Year Estimates 57 v i i e Nineteen Year Estimates for Charolais Breed 59 v i i i Tests for Consistency of Pattern 60 ix Discussion 69 V Page CHAPTER III STUDY II CONTINUING TECHNICAL PROGRESS - GENETIC IMPROVEMENT IN THE CANADIAN CATTLE INDUSTRY 82 i Background 82 i i Review of Literature 84 i i i Hypotheses 88 iv The Model 88 v Data 98 vi S t a t i s t i c a l Analysis and Results 101 v i i Discussion 119 CHAPTER IV SUMMARY AND CONCLUSIONS 128 FOOTNOTES 138 REFERENCES 143 APPENDIX I EXAMPLE OF DETAILED CALCULATIONS FOR TABLE III 3 AND TABLE III 4 149 APPENDIX II SUMMARY OF DATA USED IN STUDY I 151 APPENDIX III 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 of Location by Breed . . . . 38 11.2 Estimates of F i r s t Seven Years of Location by Breed . . . 48 11.3 Estimates of F i r s t Nine Years of 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 for . , the Charolais Breed 59 116 Coefficient Values and Variance of the Estimate as Truncation i s Increased from 5 to 9 Years 68 11.7 Average Number of Census Areas Entered by Breed with Different F i r s t Dates of Entry 70 11.8 Number of Females Imported by Breed in the F i r s t Five Years 71 11.9 Percent of Market Penetration by Breed 74 11.10 Summary of Market Penetration by Province, 18 Exotic Breeds, 1978 , .75 11.11 , Market Penetration by Province, 18 Exotic Breeds, 1978 77 111.1 Li s t of Bull Sales 99 111.2 Number of Bulls by Breed 99 111.3 Expected Value of Improving Weaning Weight and Average Daily Gain - Saskatchewan Bull Test Station Bulls I . 11.1 111.4 Expected Value of Improving Weaning Weight and Average Daily Gain - National R.O.P. Averages 1970-1978 . . . . 115 V I1 LIST OF DIAGRAMS DIAGRAM Page II.1 66 v i i i ACKNOWLEDGEMENTS It i s a pleasure to acknowledge my debt to the many people who have helped me with ideas in the course of the present investigation. Thanks are due f i r s t of a l l to the members of my dissertation committee, Professors Chris Archibald, Jim MacMillan, Bob Allen and Dave Stapleton. My debt to Professor Archibald i s a la s t i n g one for he provided the insights 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 Allen 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 to Professor G. Rosenbluth of the Economics Department and Professor R. Barichello of the Department of Agricultural Economics. Professor Rosenbluth got me started on the right track and l e t me c a l l upon his time and ideas without reservation. Professor Barichello always had..an ;open door and an::interest in 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 co l l e c t i n g and organizing the large amounts of data u t i l i z e d in the project, and to Brenda MacDonald who spent many hours on the phone checking and double checking the data. A special thanks must also go to Anne 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 for the innumerable hours spent editing and typing the various manuscripts, and more importantly for the years of continual encouragement and support. This thesis i s dedicated to them. W.A. Kerr Vancouver, B.C. September, 1980 CHAPTER I: INTRODUCTION I i Foreword One of the necessary conditions for the existence of modern industrial society has been the production revolution which the agricultural sector has experienced during the past four centuries. This "revolution" i s dependent upon two positive actions, the development of new production processes and the u t i l i z a t i o n of such processes by producers. These actions are generally termed "innovation" and "adoption". During this century improvements in the productivity of agricultural operations due to technological change have been manifest primarily in three ways: 1) improvements to inputs of production resulting-from the development of the internal 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 resulting from advances in pure science ( f e r t i l i z e r , herbicides, pesticides); and 3) improvements to the inputs of production through theoretical and, subsequently, applied advances in genetics (hybrid corn, hybrid sugar, and miracle rice and wheat, Holsteins). Of course, these new processes may often act in conjunction with each other. The majority of genetic-based improvements have been in plant science. More recently, however, the techniques developed in modern genetics have been applied in the animal industry. The basis of genetic improvement in animals i s selective breeding. The process of genetic improvement i s identical to that which i s used in plant breeding, and i t i s a function of three d i s t i n c t processes: expansion of the genetic pool, inbreeding of divergent genetic strains to increase the probability of desired heritable properties in a pure breeding s t r a i n , and crossing of the pure breeding strains to take advantage of hybrid vigour. Z. The beef cattle industry i s the last major segment of primary agriculture to experience the production revolution resulting from advances in applied genetics. The potential exists for increasing percentage yields from animals an amount equal to, or greater than, that manifest in 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 diffusion 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 particular relevance to the beef cat t l e case are changes in the di s t r i b u t i o n of income between firms which results from unequal use of innovations over time and those alte r i n g the innovation i t s e l f , which result from imperfections in the genetic mix or changes in the environment, both physical and economic. The Canadian cattle industry operates within an i n s t i t u t i o n a l structure which i s unique in terms of major genetic technical change, while the biological parameters of cattle 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 in the Canadian beef cat t l e industry hopefully provides additional insight into the more general process of technical change and the approach to i t s study by economists. I i i Background Improvement of livestock by selective breeding has been practiced since antiquity. Modern beef cattle breeding has i t s origin in the development of purebred strains in B r i t a i n during the 17th and 18th centuries. As there are no cat t l e indigenous to North America, the foundation herds were the result of importations to Mexico by the Spanish, and importations to the United States and Canada by, for the most part, B r i t i s h s e t t l e r s . 3. It was not long before interest in catt l e improvement led to the importation of purebreds into North America. The f i r s t Shorthorns imported to America were brought to Vir g i n i a in 1783; Herefords were f i r s t imported in 1817, Galloways in 1837 and Aberdeen Angus in 1873 (Plumb, 1920). These animals, and subsequent importations, provided the basis for the genetic upgrading of the North American cattle herd. Under the constraint of a straight-bred philosophy these animals evolved into stock adapted to local production conditions and consumer preferences (Hunsley, 1975). However, through the 1950's and 60's, improvement in genetic knowledge and changes in consumer preferences provided incentive for changes in the catt l e breeding industry. \; Pressure from applied geneticists ( P h i l l i p s , 1961) and evidence from the poultry and swine industry (Carman, 1960) led to an interest in cross-breeding by commercial cattlemen (Ackerson, 1967). At the same time, consumer preferences (and eventually the grading systems) were changing to require higher yields of lean of acceptable eating quality from beef carcasses (Warwick, 1973). The development of the cattle industry in continental Europe had paralleled that in B r i t a i n and North America with the establishment of breeds and breed standards. The F.A.O. publication European Breeds of  Cattle (French, 1966), delineates some 150 different breeds or strains of ca t t l e . 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 in Europe an ideal set of germ plasm with the genetic diver s i t y necessary for effective crossbreeding and developed characteristics which would complement the so called B r i t i s h ^ breeds in North America. However, expansion of the genetic pool by the importation of catt l e from Europe was prohibited by the quarantine regulations of the Canadian 4. and American governments. Thus, rapid genetic-based technological change in the beef c a t t l e industry was e f f e c t i v e l y thwarted. In 1966, effe c t i v e lobbying (Trenkle and Will ham, 1977) induced the Health of Animals Branch of Agriculture Canada to open a quarantine station on Grosse l i e in the St. Lawrence, accommodating 240 head once a year and, subsequently, a second station on St. Pierre 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, Italy and a number of other European countries, as well as Australia and New Zealand, were added to the l i s t . The response by the cat t l e industry was dramatic. In 1966, the set of pure strains with desirable properties available to Canadian cattlemen was limited almost exclusively to three breeds, the Hereford, the Aberdeen Angus and the Shorthorn. In 1976, a decade after 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 sixty-eight 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 exotic animals increased rapidly 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. Clearly, the p o s s i b i l i t y of rapid genetic-based technological change exists in the Canadian c a t t l e industry. However, the re a l i z a t i o n of genetic-based technological change and the effects of the transiti 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 structure of the Canadian beef c a t t l e industry to expand the genetic pool, improve the divergent genetic strains and cross the purebred strains to take advantage of hybrid vigour. 5. I i i i I n s t i t u t i o n a l Considerations The process of genetic improvement in the Canadian beef cattle 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 station (or private research f a c i l i t y ) , where a wide variety of species are i n i t i a l l y collected and then the inbreeding and crossbreeding are conducted by geneticists using the principles of theoretical and applied genetics (Evenson and Kislev, 1975). Only when the hybrid has been tested i s i t released to the market. There i s no market operating within the i n s t i t u t i o n i t s e l f . In the poultry industry, the development of superior breeding strains takes place largely in a few large private breeding establishments which are similar to those found in plant breeding. Only the,basis of the hybrid strains is.released to regional commercial chick suppliers 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, selection and crossing i t s e l f (Warren, 1974). Rapid genetic improvement in swine has followed the establishment of i n s t i t u t i o n a l arrangements sim i l a r to the poultry industry with specialized breeding operations, although the system i s not yet as universal. Genetic improvement in the dairy industry l i e s primarily in the hands of a r t i f i c i a l insemination (A.I.) units. Extensive records are kept and bulls are selected on the basis of progeny testing. 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 selecting which semen to purchase. Again, i t 6. i s the extensive collection of physical data which determines the selection of genetic material to be released and not the market. A.I. exists for beef cat t l e but i t has not been widely accepted. In the Canadian beef c a t t l e industry the processes of genetic im-provement 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 strains 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 cattle operator. Both these industries are composed of thousands of individual operators, few of whom have any formal t r a i n i n g in genetics. The p r o f i t a b i l i t y of individual breeding enterprises determines the extent of expansion of the genetic pool, while the market operating between pure-bred breeders and commercial operators should regulate the process of genetic improvement through the price mechanism. The question therefore becomes, how does the market affect 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 thesis presents two studies. The f i r s t examines the process of expanding the genetic pool and the second examines the market between pure-bred breeders and commercial cat t l e operators. As the potential exists for s h i f t i n g the aggregate production function in the beef cat t l e industry approximately 20 percent (Willham, 1976), a greater understanding of the factors affecting the realization of this technical improvement could be of considerable economic significance, given the size and re l a t i v e importance of the beef industry. Next to f i e l d grains, ca t t l e and calves constitute the second most important single commodity, by value, providing income from cash receipts for primary production in the agricultural sector (Canada Year  Book , 1978-79). Approximately 3.5 m i l l i o n beef animals are slaughtered each year. 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 for growth in the agricultural 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 Agriculture, 1971). In the past, s h i f t s in the production function for other commodities have created si g n i f i c a n t adjustment problems for the rural community. Further, there i s evidence that cattle breeders have not responded to the production needs of the industry in the past, and that considerable waste of resources was the result. The box-like Hereford of the 19401 s and 50's is the most notable example (Marlow and Bower, 1 978). Ex-ante knowledge of what may be expected from any process of diffusion may indicate areas where adjustment problems can be expected, while an under-standing of the process of the improvement in innovations may reduce some waste of resources. Certainly, there i s l i t t l e reason to suspect that genetic-based technological change in the beef cat t l e industry i s near completion. New synthetic breeds are continually being developed and the diverse germ plasm in Europe i s far from exhausted. Unfortunately, existing studies provide l i t t l e in the way of insights into the ongoing process of technological change. I iv Economic Analysis of Technical Change The vast majority of empirical studies concerned with technological change have been ex-post in nature (Peterson and Hayami, 1977). Econometric studies of genetic-based technical change have generally followed either a diffusion approach or a production function approach. The diffusion approach attempts to explain the lag in the introduction of new v a r i e t i e s , the rate of 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 lag in the 8. introduction of new techniques (G r i l i c h e s , 1957) (Cordrey, 1968) examine problems similar to the expansions of the genetic pool in the cat t l e industry and have been adapted to our problem. These studies of the introduction of new techniques have been limited to one innovation in a single time period. Our study provides an improvement to these studies by examining a number of breeds which entered Canada at different time periods. We can therefore examine the consistency of the diffusion process across commodities and over time. Other studies of new varieties generally follow the approach of 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 varieties over time as s h i f t parameters, usually in the form of dummy variables or investment expenditures (Hertford, et a l . , 1977) (Nagy and Furtan, 1978) (Evenson and Kislev, 1975). Output i s measured in y i e l d per acre. Such studies provide information on the existence of technological change and may be useful in establishing the return on investment in genetic-based technological change, but they do not provide insights into the process of genetic improvement i t s e l f . Although studies of both types discuss the characteristic improvements in v a r i e t i e s , the actual process of determining which characteristics researchers improve upon i s ignored. Evenson and Kislev (1975, 1976) investigate the returns to the process of genetic experimentation i t s e l f , but do not analyse the process of interaction between those who are to u t i l i z e the new v a r i e t i e s and those who select the characteristics of the new v a r i e t i e s . Kislev (1 979), in his study of genetic change in the dairy industry, i s spared this discussion by assuming a selection process concentrating on a single c h a r a c t e r i s t i c , milk production. Non genetic-based technical change in the agricultural sector has 9. been analysed using models similar to those used for genetic-based technical change (Peterson and Hayami, 1977) and, as a r e s u l t , we know there are new models of tractors, corn harvesters and milking equipment, new f e r t i l i z e r s , feed mixes and herbicides, and new growth stimulants, estrus syncronizers and veterinary aids, a l l of which increase productivity. But we have no information on how or why a tractor of a certain vintage d i f f e r s , in the pa r t i c u l a r manner that i t does, from a tractor of the previous vintage. Induced innovation theorists (Fellner, 1961) (Hayami and Ruttan, 1971) suggest that the key may l i e with changes in r e l a t i v e factor prices which provide the incentive for the development of new products which have reduced technical requirements for the now r e l a t i v e l y expensive input. However, the model may be too r e s t r i c t i v e in i t s application. The theory assumes that there must be an ex-ante equilibrium and that a change in r e l a t i v e prices must be observed. In our case of genetic-based technological change, the potential exists for slow but continuing dynamic change (un 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 in r e l a t i v e factor prices. Secondly, capital and labour are always selected as the inputs against which this substitution takes place and changes in the prices of other inputs are ignored. The work of Berndt and Wood (1975) in production theory indicates this 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 less intensive r e l a t i v e to the new higher cost input. In our case, this would t e l l us that a new input w i l l appear and that i t w i l l be the input with the highest additional value over the feasible interval of im-provement but i t cannot provide any descriptive information regarding the 10. inherent q u a l i t i e s of the new good. Clearly, this i s the Lancastrian (1966) problem in production space. The problem is one of heterogeneous inputs to production. As Archibald and Rosenbluth (1978) have indicated, the characteristic approach has been i m p l i c i t l y used in much of the recent work on production functions. Traditional production theory, based on the assumption of homogeneous inputs to production, does not provide the tools to analyse the problem of genetic improvement in the context of the selection procedures of breeders and commercial cattlemen. I f the process of technological change in the beef cat t l e industry i s to be evaluated, then further incursions into the use of the characteristic approach seems necessary. To summarize, the major contributions of these studies are threefold. F i r s t , they provide an examination of how the market system regulates the three processes of genetic-based technological change; expansion of the genetic pool, inbreeding of divergent genetic strains to increase the probability of desired heritable properties in a pure breeding strain and the crossing of the pure breeding strains to take advantage of hybrid vigour. Other genetic innovations have had some or a l l of these processes regulated (at least in part) by the s c i e n t i f i c community rather than the market. Secondly, the study of the diffusion of new breeds provides a stronger examination of the economic forces influencing the a v a i l a b i l i t y of innovations than previous studies through the comparison of different 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 characteristic 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 characteristics approach, they have not developed t h e i r theoretical models in the context of characteristics. Chapter II STUDY I THE SUPPLY OF A NEW TECHNIQUE II i Background The process of adoption of any new technique i s i n i t i a l l y determined by i t s a v a i l a b i l i t y . Unless an innovation i s available 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 existing technology, large scale adoption w i l l not take place. ^ The majority of innovations developed for the North American market have usually been available in adequate quantities within extremely short periods. Mechanical equipment, f e r t i l i z e r , pesticides, etc., 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 restraints do not appear as constraints to the process of technical change, except in the extremely short run. Cattle, as a species, are not p r o l i f i c , nor do they have a short gestation period. Purebred cattle move to market through local auctions and, although cattle are readily transportable, expense (especially when the opportunity cost of a cattleman's time i s considered) and risk 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 localized breeders. Casual examination of the geographic location of Hereford breeders (or one of the other tr a d i t i o n a l breeds) corroborates this 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" cattle were imported into Canada by cattlemen. 12. These suppliers of the innovation were extremely adept at u t i l i z i n g the available foundation stock, as herd numbers seem to have increased at very close to the biological maximum. At the close of the decade, the number of calves registered for the various breeds was 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 established Hereford. Exotic ca t t l e cannot, however, be supposed to have been equally available to a l l commercial c a t t l e -men at the same time. 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 individuals imported a limited number of superior stock and within a few years a nucleus of interested breeders formed a breed association. It i s these breeders, and those who subsequently joined the industry, who provided the means of technological change. The industry, of course, operates en 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 pro f i t s would be greatest, those who were to follow 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 supplier, the location of breeders w i l l determine those ranches which can profitably u t i l i z e the breed. The effect on the rate of adoption w i l l , however, not be solely related to the cost of physically acquiring a b u l l . As i t would appear that the willingness to adopt a new technology i s , in part, 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 in 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 for 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 in the area. As with innovations such as hybrid corn, i t would be unfair to blame a commercial operator for not adopting a new technique when the product was not competitively available (Gril.iches, I960)'.' Cattlemen in B.C., for example, are often cited for 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 this apparent lack of adoption may be a result of the non-a v a i l a b i l i t y of exotic c a t t l e . In the short run, the early establishment of a local breeder i s l i k e l y to provide a considerable advantage to those who would be inclined to adopt the new technology. In addition, the longer the herd i s in being, the more valuable i t w i l l become as a source of commercial germ plasm, as breeders are able to establish mating and c u l l i n g strategies which can be ta i l o r e d to local demand. In order to gain some insight into the process of technological change in the cattle industry, i t may be useful to map the spread of breeders of exotic cattle through space and over time and, subsequently, to investigate those economic forces which appear to influence the location of breeders. It i s probably safe to suggest that the stock of the world's germ plasm has not been exhausted and that, as knowledge of genetics improves, additional breeds of cattle (either synthetic or imported) w i l l be diffused within the Canadian cattle industry. I f there i s any consistency in the locational patterns of various breeds, this may provide some insight 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 early access to improvements to the technology in the future. II i i Institutions The i n s t i t u t i o n s which regulate the purebred cattle industry have an important role in the diffusion 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, Agriculture Canada); 2) the registration of animals (national breed organizations, Canadian National Livestock Records), 3) evaluation of genetic potential (Federal-Provincial Record-of-Performance-for-Beef-program, provincial government, national and provincial breed organizations); and 4) promotion and sale of cattle (provincial breed organizations, the auction system). Of course, individual breeders are involved in each function. In addition, the federal government and other i n s t i t u t i o n s conduct research into various aspects of beef breeding. II i i a Importation Since 1966, European cat t l e have been able to enter Canada under a maximum security quarantine policy devised by the Health of Animals Branch of Agriculture Canada. In order to minimize the ris k of introducing new diseases into Canada, the importation procedures are complicated and costly. In most years there i s a demand to import more catt l e than can be accomodated in the quarantine f a c i l i t i e s and the Department allocates the limited number by issuing importation permits. Applications are received up to a certain deadline date, and then each applicant i s required to. submit information about his background and experience in the cat t l e business, and his plans for 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 allocated on their "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 policy involves four levels of i s o l a t i o n and inspection. The f i r s t i s on the farm of origin where calves, designated for export to Canada, must be kept separate from a l l other cat t l e and undergo a series of te 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 is supervised by local 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, after which animals passing a l l the tests may proceed to the Canadian quarantine station. Two are now in use - one on Grosse He accepting 240 head once a year entering in October, and another at St. Pierre accomodating 250 twice a year entering in November and May. These stations are supervised by Canadian veterinary o f f i c e r s and the quarantine period lasts for a minimum of 90 days, or u n t i l a l l the tests are completed. I f any animal f a i l s a test or contracts a disease during the quarantine period, the Veterinary Director General of Canada may require that a l l animals in the station be slaughtered, without compensation to the owners. I f foot and mouth disease or contageous pleuropneumonia i s diagnosed in any animal at t h i s point, the Canadian Veterinary Director must order a l l animals in the station slaughtered, and again there i s no provision for compensation to the owners. I f , at this stage, a l l animals pass the tests successfully, they may be transported to the owner's premises, but s t i l l they must undergo an on-farm quarantine period in which they are penned with a group of contact animals and, at le a s t , double fenced away from any other animals for a period of three months. During this period, 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 is s i x for the f i r s t import and one additional animal for.each additional import. It takes about a year from the time the animal i s purchased un t i l i t i s free to move in Canada. 16. At a l l stages of the quarantine program except the on-farm quarantine, tests are done for foot and mouth disease, rinderpest, contagious pleuropneumonia, tuberculosis, b r u c e l l o s i s , trichomoniasis, leukosis, lept o s p i r o s i s , Johne's disease and blue tongue. During the station quarantine in the country of origin and in Canada temperatures are taken d a i l y , and during the f i r s t fourteen days in the Canadian quarantine stations temperatures are taken twice d a i l y . From the time the animal begins the tests on the farm of origin u n t i l the time i t i s released from on-farm quarantine in Canada, i t i s isolated from a l l c a t t l e outside the import program (except the contact animals in the on-farm quarantine). A l l vehicles and ships used for transportation must be thoroughly d i s -infected before and after use. A l l feed and bedding must be brought to the quarantine station from Canada, or a country with equivalent health standards. A l l costs of the maximum security importation program are borne by the importers, except the salaries of the Canadian veterinary o f f i c e r s who inspect the c a t t l e . The Canadian quarantine stations were b u i l t with public funds, but this cost i s being repaid by a quarantine charge l a i d on each animal imported. The cost of importing one animal, exclusive of purchase price, includes a $600 charge for the care and feeding throughout the station quarantine period, a $900 quarantine charge, and charges for transportation, administration and special tests, which increases the total cost to somewhat more than $2,000. Over time, the number of countries from which importation may be made has increased and in each instance a number of new breeds has been imported. F i r s t importations were from France in 1968, Switzerland 1971, 17. I t a l y 1971, Australia 1972, West Germany 1972 and Netherlands 1975. The importance of the import regulations to the spread of technological change is twofold. F i r s t , the issuance of 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 ca t t l e herd and establishes 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 in the importation of c a t t l e , plus the personal dossier, excludes the majority of cattlemen from being importers. II i i b Registration of Animals The task of registration i s undertaken either by the Canadian National Livestock Records division of Agriculture Canada, or the various national breed organizations themselves (The Registration of Animals in Canada, 1975). No animal can be sold as a purebred without registration papers. The registration 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 particular breed organizations. I t further provides information on the pedigree of registered animals to help the purchaser in his selection. The economic significance of registration is that such regulations can be used as barriers to entry into the industry. However, the regulations of the various exotic breed organizations have, as yet, been extremely l i b e r a l in an ef f o r t to expand the breed organizations rather than to r e s t r i c t entry. The breed organizations have sanctioned the process of "upgrading". Upgrading allows for percentage animals (those whose antecedents are not a l l of the same breed) to be included in the herd (registration) 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 in question, and a l l generations back to one half recorded in the herdbook ( i . e . , approximately 4 or 5 generations, 1/2, 3/4, 7/8, 15/16, 31/32). Older, more established breeds allow no upgrading, requiring that a l l the antecedents of the animals be purebred. Further, membership fees of the breed organizations have been r e l a t i v e l y low and do not constitute a barrier to entry. Thus, the registration regulations of the "exotic" breeds have not acted as a retarding influence on the spread of technology. II i i c Evaluation of Genetic Potential In addition to the registration of animals to ensure thei r pedigree, information regarding the genetic potential of individual animals i s also collected. A number of organizations are involved in 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 testing" of potential breeding stock. R.O.P. beef provides a system whereby ranchers record weaning weights and average daily gain on feed (the most heritable of the major phenotypic indicators of genetic per formance) and, since 1977, incidents of calving 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 additional information to potential purchasers. Certain of the "exotic" breed organizations require that a l l registered animals must be evaluated. In addition, the various provincial governments and some breed organizations run bull "test" Stations, where breeders can have t h e i r animals evaluated in conditions of controlled environment and management, which aids in the i d e n t i f i c a t i o n of purely genetic performance. In some cases additional information on fat cover and carcass quality i s collected. The programs provide information to the potential buyers on the merit of the animals to be purchased. They have provided extensive quantitative 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 Cattle 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 agricultural ex-h i b i t i o n s , their primary function remains the registration of animals. Provincial level breed organizations conduct promotional campaigns and help to organize local sales. There are three major types of auctions at which purebred c a t t l e are purchased by the commercial sector: 1 ) breed organized sales; 2 ) consignment sales; 3 ) production sales. Breed organized sales are usually conducted at local auction f a c i l i t i e s but organized by the provincial breed association of the par t i c u l a r breed. Animals are drawn from a number of herds and the events are well publicized. These sales require that there be a considerable number of breeders in the v i c i n i t y , so that s u f f i c i e n t animals are available for a profitable sale. Costs of such sales are borne by the part i c i p a t i n g breeders through a percentage levy on the i r gross sales at the auction. Consignment sales are those in which a breeder consigns a certain 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 single breed but, in 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 their gross sales at the auction. 20. These sales are well publicized by the organizers. Ranch production sales are held on the premises of the individual breeder and the year's production i s sold at auction. The costs of publicizing the sale, providing the sale f a c i l i t i e s and hiring the auctioneer are a l l borne by the individual 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 in attracting s u f f i c i e n t customers for a "successful" sale (enough bidders to ensure active bidding for animals), and a volume of sal e s x t o cover the fixed costs of the auction. New breeders, or small operators, may have d i f f i c u l t y in attracting 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 transferred between the breeder and the commercial cattleman through "private treaty". Of limited importance, also, are dispersal sales when an owner i s s e l l i n g his entire herd and leaving the industry. These represent the major i n s t i t u t i o n s of the purebred cat t l e industry. II i i i Review of Literature Only a limited number of studies have been conducted which have examined what could be termed the supply side of the spread of tech-nological change. G r i l i c h e s , for example, in his study of hybrid corn, observed marked differences in the date at which adoption in a particular state began. He set out his problem as: "The actual breeding of adoptable hybrids had to be done separately for each area. Hence, besides the difference in 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". (Gr i l i c h e s , 1957, p. 502). 21. Griliches assumed that seed producers were p r o f i t maximizers and suggested that; "The date at which adoptable hybrids become available in an area i s viewed as the result of seed producers ranking different areas according to expected pro-f i t a b i l i t y of entry and deciding t h e i r actions on that basis. The re l a t i v e p r o f i t a b i l i t y of entry into an area w i l l depend upon the size of the eventual market in that area, marketing costs, the cost of innovating for that area, and . . . the expected rate of acceptance". (Gr 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 affecting 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 si 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 in being and available to potential suppliers of any area regardless of time. In the case of hybrid corn, seed companies were forced to develop area-specific hybrids which entailed considerable e f f o r t and time. This represents a factor in the a v a i l a b i l i t y problem which i s not present in either Cordrey's study or our own. Further, the AI establishment i s r e l a t i v e l y limited in i t s effective range of . operation. Thus, the diffusion of the innovation required the establishment of a large number of small local AI units which i s similar to the cattle breeder case. In addition, hybrid corn was marketed by large seed companies who could draw on professional marketing expertise. I t i s unlikely that the local AI unit, or the individual c a t t l e breeder, would have such market information. Cordrey's hypothesis was that: "The year in which AI organizations would be es-tablished in any given state would depend on the expected p r o f i t a b i l i t y of entry. In turn, 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 size of the potential breeding market; (2) AI service costs; (3) the innovation or introduction cost; and (4) the expected rate at which AI service would be adopted". (Cordrey, 1968, p. 14). Cordrey specified a simple line a r model with four independent variables and used the method of least squares regression analysis to test his model. In general, his model was confirmed. "The economic interpretation of the results . . . would indicate that AI organizations were es-tablished early in states having large potential markets and low AI service and introduction costs and expanded into 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 local AI establishments". (Cordrey, 1968, p. 31). _ Both these studies are typical of ex-post examinations of technological innovations. In the exotic cattle case, however, the process of diffusion i s not complete. Further, the innovation i s comprised of a variety of commodities (breeds) in various stages of diffusion. It 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 essent i a l l y one of disequilibrium. 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 reward of his services to the society". This "reward" i s essent i a l l y the same as Schumpter's (1934) "entrepreneural" p r o f i t . As Schumpter states; "The size 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 in the c i r c u l a r flow. In particular i t cannot be said of i t , as of elements of costs in the l a t t e r , that i t just suffices to c a l l forth precisely the 'quantity of entre-preneurial 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 actually obtained in a given time, as well as the p r o f i t realized by an individual entrepreneur, may be much greater than that necessary to c a l l forth the entrepreneurial services which were actually operative". Clearly, one of the factors which w i l l affect the size of "entrepreneurial" p r o f i t i s the characteristics of the market which the new firm would expect to serve. I f , as in the case of "exotic" c a t t l e , the supply of new inputs to production i s r e s t r i c t e d in the short run (by the import licenses and subsequently by the biological rate of reproduction), then entrepreneurs are faced with a choice of markets in which to locate. 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 later 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 iv Hypotheses Following Griliches and Cordrey, we postulate that the entry of a firm into a new market area in any year i s dependent upon the r e l a t i v e "entrepreneurial" p r o f i t expected in that area. The hypothesis i s that the rel a t i v e p r o f i t a b i l i t y of entry into an area w i l l depend upon the size of the market in that area, marketing costs, expected rate of acceptance and the cost of innovating. A further hypothesis i s that the pattern of entry of new firms i s consistent across breeds and over time. 24. II v The Model Although there i s evidence regarding the unequal dates of a v a i l a b i l i t y of "exotic" cattle in different areas of the country at the provincial level (Annual Reports of Canadian Livestock Records), i t seems unlikely 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 this study, the basic unit of measurement of the market area i s the census division used for the Census of Agriculture. Although census divisions do vary considerably in area and shape, they can, in most cases, represent what might be regarded as a reasonable market area for a breeder. Census divisions vary from about 35 to 60 miles in width, with those in the western provinces being on average larger, those in the Maritimes smaller, and those in central Canada being about average. Of course, there are some obvious exceptions in the far northern areas of the central and western provinces. One of the basic r e a l i t i e s of animal production i s the need for constant attention and care of livestock. Therefore, the cow-calf operator i s , to a large degree, bound to his 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 in the morning after checking the stock, spending the afternoon at the auction and returning to the farm or ranch in the evening. In central and eastern Canada, where fewer animals are ranged and must be fed, the distance of such excursions would probably be reduced. The importance of mixed dairy-beef enterprises in the east would further reduce the convenient period of absence. In addition, 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 in the central or eastern part of the country. Therefore, an average census division seems to be a reasonable unit of measure. The theoretical basis for 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 location i s r e l a t i v e l y straight forward. Ceteris paribus, the size of 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 in areas where the continuing volume of sales would be greatest. This hypothesis i s supported by the empirical work of Griliches and Cordrey.for agricultural innovations, as well as a number of studies from the in d u s t r i a l sector ( M i l l s , 1964) (Urban, 1970). An existing and e f f i c i e n t l y functioning marketing system for the sale of a firm's product w i l l reduce the costs of disposing of product and i t s storage. It would be expected, therefore, that the date of entry of a firm into an area would be affected by the existing marketing i n s t i t u t i o n s of the area. The size of market and the costs of marketing are relevant to the location 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 additional factors. The rate at which an innovation i s u t i l i z e d by firms in the market w i l l affect the short term pr o f i t s of the supplying firm. In other words, even though the size of the market may be such that i t w i l l allow for 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" p r o f i t s . The factors affecting the rate of adoption can be divided into two categories, those which are related 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 relate to the amount of information available and u t i l i z e d by potential adopters. In the cow-calf industry the size 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 risk involved in experimenting with a new breed. For example, using the usual ra t i o of one bull to 25 cows, the use of one exotic 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 related to the size 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 for any firm w i l l be related to the knowledge potential adopters have regarding the innovation. In other words, the introduction of an innovation by an individual firm w i l l force that firm to incur some costs of education. The higher the level of information, the lower the cost w i l l be to the firm. 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 2, Z 3, Z 4) (2.1) where D i s the year in which the f i r s t registered breeder of a particular breed was established in an area, Z-| i s the expected size of the market (the number of cows in 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 participating in the R.O.P. beef program). Each independent variable was expected to be pos 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 this examination are twofold, to determine the factors influencing the date of entry of a breeder into a market area, and to investigate the consistency of the locational pattern over time and between breeds. It 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, largely as a result of the expanding number of countries from which imports were allowed, the number of years of data available on the location of breeders d i f f e r s between breeds. Data were collected for 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 in each case. Thus, there are data available for eighteen breeds for five years, nine breeds for seven years, six breeds for nine years, two breeds for eleven years and Charolais for nineteen years. II vi a The Dependent Variable The dependent variable (D) i s defined as the year in which the f i r s t breeding enterprise of a particular breed was established in the census d i v i s i o n . 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 in any area. Of course, actual a v a i l a b i l i t y of the breed for u t i l i z a t i o n by the local commercial operator would be l a t e r than the date of introduction in 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 lag 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 into production. To acquire the date-of-location for individual breeders I asked each national breed association for a l i s t of members, th e i r addresses and the date when they joined the organization. In some cases the information was provided immediately. In other instances l i s t s of members were provided without the date of entry. As these organizations usually cited 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 retrieve the information myself. In some cases such permission was granted. I f an on-site inspection of the national records was denied, I phoned the various provincial organizations and requested the information over the phone. F i n a l l y , those breeders for whom the date-of-location was lacking were contacted d i r e c t l y . Checks on the accuracy of these colle c t i o n methods for the breeds where national information was not provided were then conducted. The technical publications of the industry had to be searched for data on auction markets and advertisements of breeders. This information was then matched against the l i s t s compiled from provincial organizations and contact with individual breeders. Although not a l l breeders advertised, no breeder was found who was not included in the l i s t s , and no breeder who advertised did so in a period in excess of three years from the date obtained from the breed organization. In addition, to coll e c t data for 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 original 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 add-i 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 into the 252 census divisions of the 1971 Cansus of Agriculture. As no complete l i s t of postal locations by census division i s available, this was accomplished by f i r s t consulting the two incomplete l i s t s of locations to census divisions (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) in conjunction with census maps. As the Gazetteer provides coordinates of latitude and long-itude for a l l place names in Canada, i t was possible to map a l l breeders into census divisions. The date-of-location of the f i r s t breeder in a census division was thus obtained. II vi b Independent Variables As was suggested above, relative p r o f i t a b i l i t y would be expected to depend upon (1) the expected size of the market; (2) the expected rate of acceptance; (3) marketing costs; (4) what Griliches termed the cost of innovating. Of course, data pertaining to each independent variable are not available. Instead, the tota l number of cows, the average herd size of commercial operations, the number of functioning cattle auctions in the year previous to establishment, and the number of ranchers par-t i c i p a t i n g in the R.O.P. beef program in the year previous to establishment were used as proxies. II vi b 1 Potential Market The number of cows or heifers, two years old and older, u t i l i z e d in beef production w i l l be used to approximate the size of the potential market (Z-j). This represents the number of female animals used for the production of beef. Although there does exist a figure for the number of bulls kept in each census d i v i s i o n , this figure includes dairy as well as beef bulls and would therefore bias the result. In a l l cases, data were drawn from the 1971 Census of Agriculture. This was done for reasons of consistency. For each of the possible years, 1961 , 1966, 1 971 , 1976, the agriculture census divisions in some provinces were altered. I t was therefore impossible to c o l l e c t a consistent set of data. However, for those census divisions 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 relative 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 establish a breeding herd, and the r e l a t i v e l y long gestation period un 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 their product. It would therefore be advantageous for them to locate in areas where potential early adopters were greatest. As the use of any innovation w i l l entail some risk ( i f not actual, 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 size (Z^) was chosen to proxy early adopters for the reasons indicated above. The hypothesis therefore i s that the breeders would enter e a r l i e r those areas where the average herd size was largest. Observation on the average size of herd was collected from the 1971 Census of Agriculture. 31. II vi 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 outlets for a producer's b u l l s , the less marketing costs he must incur himself. This i s postulated for three reasons. F i r s t , as bull markets are dispersed, the likel i h o o d of a market being in proximity to a breeder increases, and thus reduces his cost of transportation. Secondly, the more local outlets for his product, the better known the breeder i s l i k e l y to become, and the less he must rely on conventional (and cash cost) forms of advertising. 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 for. Of course, the d i s -advantages resulting from the absence of "breed organized" sales in the area are obvious. Either 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 . It 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 for sales, they are well advertised in the limited number of technical journals of the industry. Therefore, for 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 (limited national coverage - Ontario - Quebec covered extensively), Free Press  Weekly Report on Farming, Western Edition (Four Western Provinces), Beef  Today (Four Western Provinces), Farm Focus (Maritimes), Country Life in  B r i t i s h Columbia (B.C.). The exact observations collected 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 for sales or reports of completed sales. In a few cases individual 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 collected for each year, they were mapped into the census divisions by the same method described for the dependent variable in section II vi a. Variation between years was not large and no noticeable trends in the number of sales over time were observed. II vi b 4 Cost of Introduction Both Cordrey and Griliches suggested that the introduction of any new innovations would entail considerable educational e f f o r t . According to Cordrey, "This e f f o r t was helped by Dairy Herd Improvement Associations, state and country extension personnel, registered dairy cattle associations and other farm organizations interested in improving dairy farmers' incomes, as well as the National Association of Animal Breeders and the central and local AI organizations. The educational efforts of these farmer groups would have reduced the total cost of introducing AI service to area farmers". (Cordrey, 1968, p. 24). As direct measures of these expenditures were not available, Cordrey used the proportion of cow herds participating in the programs of Dairy Herd Improvement Associations (DHIA) as an approximation of this educational e f f o r t . The Record-of-Performance-for Beef program for beef animals plays a similar role to DHIA in the dairy industry. We therefore chose the percentage of herds participating in the R.O.P. beef program the year previous to the establishment of a breeder in a census division as the appropriate measure. Other measures may have been available for use as proxies for Z„. For example, information on average years of schooling by type of operation i s available from the census. As education i s often used as a proxy for the a b i l i t y of farmers to assimilate information, years of schooling might have been an appropriate measure. However, the data does not exhibit as great a v a r i a b i l i t y across census divisions as the R.O.P. data, and therefore may be a less precise measure. Secondly, as years of education would not take into account the differences in expenditures on extension programs, the ex post R.O.P. measure was judged l i k e l y to be more accurate. F i n a l l y , as information about crossbreeding and exotic cattle was being disseminated over the period, the yearly R.O.P. data were deemed superior to ten year census averages. Data may also have been available on extension expenditures but obtaining an accurate breakdown by commodities seemed unlikely. The ex post measure of R.O.P. participation also seemed a better measure as i t should, in part, mirror the effectiveness of extension programs in the beef industry as well as the expenditures. Lists of participating herds were obtained from both the federal o f f i c e and the provincial representatives of the R.O.P. beef program for various years. Data for the years 1959-1963 proved to be inadequate, as participation in the R.O.P. program by the provinces of Ontario and Quebec was not f u l l y organized. Thus, the 1964 figure was used for a l l years of this period. As t h i s only affected estimates for the Charolais breed, i t does not appear to be a serious handicap. Again, the l i s t s of participating herds were mapped from the i r addresses into census divisions by the method outlined in II i i a. Thus, the number of participating herds in each census division was arrived at for each year 1964-1978. Although membership in the R.O.P. beef program has increased considerably over the twenty year period, from approximately 300 to 3,000 participating herds, i t was found that the rela t i v e numbers of participating herds across census divisions did not greatly change over time. This suggests that the progressive areas of a decade ago remain the progressive areas today. As i t was a measure of relative progressiveness which was desired, the absolute number of partic i p a t i n g herds in each census division was converted to percentages of herds on R.O.P. for that year by dividing the number of herds in each census division by the total number of partic i p a t i n g herds. As areas where more cattle are located would be expected to have larger numbers of R.O.P. herds, this figure was then divided by the percentage of the national cow herd (Census of Agriculture, 1971) found in 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 indicate an area which had the same percentage of herds on R.O.P. as there were cows in the national cattle herd; a value of greater than 1 would indicate an area which had more herds on R.O.P. rela t i v e to the national cow herd, and might be considered more progressive. A value less than 1 would indicate 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 of the date-of-location function, s t a t i s t i c a l estimates were undertaken to establish the form of the relationship. The independent variables, as defined, were a l l expected to have a net positive effect' on the date-of-location. As the object of the exercise was to examine the diffusion of exotic cattle across breeds and over time, estimates were made for each breed for varying periods determined by the number pf years the breed organization had existed. Five years of data existed for a l l eighteen breeds. Separate estimates for the date-of-location function of each breed were undertaken for the f i r s t five years of breeder establishment. S i m i l a r l y , there was information for nine breeds for the f i r s t seven years of breeder establishment; for si x breeds for nine years of breeder establishment; for two breeds for eleven years of establishment. Separate breed by breed estimates were undertaken for each period. In addition, an equation was estimated for 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 plotting of the data suggested a linear relationship between each of the independent variables and the dependent variable. However, i n i t i a l estimates, conducted in the simple linear form for the four independent variables, while y i e l d i n g r e l a t i v e l y consistent equations across breeds, did not provide encouraging results. The estimates were characterized by low R values and the coefficients for Z^  (size of market) were inconsistent and not s i g n i f i c a n t . The coefficient for Z^  (costs of introduction) consistently had the wrong sign. Estimates of a f l e x i b l e functional form were then undertaken. A Generalized Leontief (Diewert, 1973a) of the form 4 4 • • ^  j, D = b + E I b..l.2l.2, b. . = b.. (2.2) oo . = 1 i J i J i J J i 36. was estimated, but again the sign on (Z^ 2 Z^2) was inconsistent. Further, there was a high degree of multicolinearity between the i n t e r -active terms and the arguments themselves. A re-examination of the data was undertaken. The apparent inconsistency of the sign of the coefficients of Z^  appeared to be related to the expected size of the market. In early periods breeder location was observed in areas where expected size of the market was largest, even where the areas were less progressive. In subsequent years, however, two types of interaction were observed. As one would expect, breeders located in areas with smaller expected size of market and s l i g h t l y lower indexes of progressiveness. In addition, however, areas with dramatically smaller expected market size and very high indexes of progressiveness were observed as areas where breeders located. It i s these observations which tended to give Z^  an inconsistent sign. Further, in l a t e r years, some areas with large market areas, but very low values for the indexes of progressiveness, became areas of location. This tended to weaken the significance of Z^  (expected size of market). These observations suggested that there was an interaction between the two variables. Therefore, a new variable, Zg, was constructed by multiplying Z^  by Z^ . The new variable could be described as the expected size 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 size 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 testing i s technically i n v a l i d . 37. Estimates were conducted i n the simple linear form of, D = b + brlc + b 9Z 9 + b.Z, o 5 5 2 2 3 3 for a l l eighteen breeds and reasonable results obtained. Note the signs on coefficients Z,-, and Z^  would be expected negative as D i s indexed from 1 to 5, from early locations to late locations. The results are presented in Table II 1 below. The breeds are l i s t e d in order, beginning with the most recent importations to Canada. Coefficients with un-expected signs are underlined. TABLE II 1 ESTIMATES OF FIRST FIVE YEARS OF LOCATION BY BREED BREED : MARCH IGlANA PERIOD 1974 - 1978 n = 52 Variable Estimated t r a t i o name coefficient 40 df Zc -0.58414E-05 - 1.9738 o Z 2 -0.19995E-01 -1.7035 Z 3 -0.29593 - 2.0156 Intercept 3.7561 13.763 R2 = .4697 BREED : MEUSE - RHINE - IJSSEL (MRI) PERIOD : 1974 - 1978 n = 17 Variable Estimated t rat i o name coe f f i c i e n t 13 df Zc -0.45160E-O5 - 4.2502 5 Z2 -0.45981E-02 - 0.50665 Z 3 -0.26324 - 3.7015 Intercept 3.2817 12.953 R2 = .9715 TABLE II 1 (continued) BREED : ROMAGNOLA PERIOD : 1973 - 1977 n = 22 Variable Estimated t r a t i o name coe f f i c i e n t 18 df Z c -0.57922E-06 -0.16580 o Z 2 -0.19234E-01 -1.1949 Z 3 -0.37862 -2.6260 Intercept 4.2035 7.2031 R2 = .4593 BREED : NORMANDE PERIOD : 1973 - 1977 n = 13 Variable Estimated t rati o name coeffic i e n t 9 df Zc -0.61827E-05 -1.6582 o Z 2 -0.40847E-01 -2.1567 Z 3 -0.60279E-01 -0.34762 Intercept 4.4746 8.1016 R2 = .6255 TABLE II 1 (continued) BREED : SALERS PERIOD : 1973 - 1977 n = 17 Variable Estimated t ra t i o name coe f f i c i e n t 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 R2 = .4667 BREED : PINZGAUER PERIOD : 1974 - 1978 n = 41 Variable Estimated t ra t i o name coefficient 37 df Zc -0.70653E-05 - 2.5320 o Z 2 -0.20261E-01 -2.0995 Z 3 0.61026E-01 0.41586 Intercept 3.3285 11.347 R2 = .3713 TABLE II 1 (continued) BREED : TARENTAISE PERIOD : 1972 - 1976 Variable name Estimated coeffi cient n = 16 t rat i o 12 df Intercept -0.28315E-05 -0.39477E-01 -0.13230 4.3475 -0.87820 -2.3902 -0.64988 8.0333 R2 = .4999 BREED : GELBVEIH PERIOD : 1972 - 1976 n - 32 Variable Estimated t rat i o name coefficient 28 df Zg -0.37421E-05 -2.3487 Z 2 -0.39061E-01 -4.7697 Z3- -0.17253 -1.9083 Intercept 4.1980 9.0894 R2 = .7788 TABLE II 1 (continued) BREED : BLONDE D'AQUITAINE PERIOD I 1972 - 1976 Variable name Estimated coefficient n = 43 t ratio 39 df Intercept -0.72134E-05 -0.65956E-02 -0.11388 3.6564 - 3.4764 - 0.78741 - 0.94034 17.511 R2 = .5507 BREED : SOUTH DEVON PERIOD : 1971 - 1975 n - 9 Variable Estimated t ra t i o name coefficient 5 df Z g -0.65367E-05 - 1.4213 Z 2 0.91182E-02 0.30231 Z 3 0.66755 0.70699 Intercept 1.9711 2.9198 R2 = .2054 TABLE II 1 (continued) BREED : CHIANINA PERIOD : 1971 - 1975 n = 67 Variable Estimated t ra t i o name coe f f i c i e n t 63 df Z 5 -0.45465E-05 - 2.3636 Z £ -0.11355E-01 - 2.0473 Z 3 -0.13706 - 1.4028 Intercept 3.8266 19.815 R2 = .3731 BREED : WELSH BLACK PERIOD : 1970 - 1974 n = 13 Variable Estimated t rat i o name coefficient 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 R2 = .0783 TABLE II 1 (continued) BREED : BROWN SWISS PERIOD : 1970 - 1974 n = 49 Variable Estimated t rat i o name coeffic i e n t 45 df Zc -0.79625E-05 - 4.2154 b Z 2 -0.26186E-01 - 3.4554 Z 3 -0.54987E-01 - 0.57413 Intercept 5.1467 21.201 R2 = .6293 BREED : MURRAY GREY PERIOD : 1970 - 1974 n = 47 Variable Estimated t r a t i o name coefficient 43 df Zc -0.74677E-05 - 4.6896 Z 2 -0.58618E-02 - 1.2069 Z 3 -0.19131 - 2.3453 Intercept 5.0702 28.416 R2 = .6850 TABLE II 1 (continued) BREED : MAINE ANJOU PERIOD : 1970 - 1974 Vari able name Estimated coeffi cient n = 49 t ratio 45 df Intercept •0.49919E-05 •0.69335E-02 -0.36703 5.0246 - 2.1907 - 2.6359 - 2.6024 20.968 R2 = .5425 BREED : LIMOUSIN PERIOD : 1969 - 1973 Vari able name Estimated coefficient n = 40 t r a t i o 36 df Intercept -0.70945E-05 -0.16235E-01 -0.14562 4.5383 - 2.8050 - .2.1827 - 0.88887 18.746 R2 = .5410 TABLE II 1 (continued) BREED : SIMMENTAL PERIOD : 1969 - 1973 n = 87 Variable Estimated t rat i o name co e f f i c i e n t 83 df Z 5 -0.54515E-05 - 2.0745 Z 2 -0.17496E-01 - 2.5145 Z 3 -0.31581 - 2.0909 Intercept 3.8845 21.584 R2 = .4377 BREED : CHAROLAIS PERIOD : 1960 - 1964 n = 91 Variable Estimated t rat i o name coe f f i c i e n t 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 R2 = .5701 In only two cases, Pinzgauer and South Devon,, were coeff i c i e n t s with theore t i c a l l y incorrect signs found. In the case of South Devon there i s an extremely small number of observations. The values of the _2 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 level) in every estimation, they were a l l s i g n i f i c a n t in some. The relative magnitudes of the coefficients 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 variables, Zc, Z 0 and Z. were used for the o c 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 relationship between each variable. Therefore, estimates of the form D * b Q + b 5Z 5 + b 2Z 2 + b 3Z 3 were made for each breed. Data for seven years of breeder locations was available for nine breeds. The results are presented below in Table II Again, breeds are presented in order starting from the newest imports to Canada. As before, negative signs are expected for 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 n = 15 Variable Estimated t r a t i o name coe f f i c i e n t 11 df Z c 0.65995E-05 0.98936 b ZZZZZZZZIZZZI Z 2 -0.17855E-01 - 0.83082 Z 3 -0.36697 - 0.89713 Intercept 4.4021 2.9631 R2 = .1123 BREED : CHIANINA PERIOD : 1971 - 1977 n = 71 Variable Estimated t rat i o name coeffic i e n t 67 df Zc -0.58291E-05 - 2.5318 o Z 2 -0.14269E-01 - 2.1486 Z 3 -0.11944 -1.0178 Intercept 4.1189 18.358 R2 = .3567 TABLE II 2 (continued) BREED : WELSH BLACK PERIOD : 1970 - 1976 Vari able name Estimated coef f i cient n = 15 t ra t i o 11 df Intercept -0.55385E-05 -0.19041E-01 -0.34315E-01 4.7177 - 0.66033 - 0.42758 - 0.10528 3.2494 R = .0132 BREED : BROWN SWISS PERIOD : 1970 - 1976 Variable name Estimated coe f f i c i e n t n = 76 t r a t i o 72 df Intercept -0.10078E-04 -0.34480E-01 -0.15978 6.2878 - 3.7153 - 3.4164 - 1.1547 26.310 R2 = .5561 TABLE II 2 (continued) BREED : MURRAY GREY PERIOD : 1970 - 1976 n = 71 Variable Estimated t rat i o name coeffic i e n t 74 df Zc -0.11810E-04 - 6.6659 b Z2 -0.67873E-02 - 1.2634 Z 3 -0.99465E-01 - 1.0600 Intercept 5.8066 37.748 R2 = .6535 BREED : MAINE ANJOU PERIOD : 1970 - 1976 n = 78 Variable Estimated t ratio name coefficient 74 df Zg -0.10287E-04 - 3.7859 Z 2 -0.17634E-01 -2.1804 Z 3 -0.36255 - 2.1117 Intercept 6.1 913 20.968 R2 = .5061 TABLE II 2 (continued) BREED : LIMOUSIN PERIOD : 1969 - 1975 Vari able name Estimated coef f i cient n = 59 t ra t i o 55 df Intercept -0.10293E-04 -0.11585E-01 -0.16049 5.4549 - 2.9918 - 1.1180 - 0.76937 18.908 R2 = .3986 BREED : SIMMENTAL PERIOD : 1969 - 1975 Variable name Estimated coeffi cient n = 116 t ra t i o 112 df Intercept -0.10844E-04 -0.16177E-01 -0.34671 4.9103 - 2.9805 -,1.7863 - 1.6400 23.014 R2 = .3897 TABLE II 2 (continued) BREED : CHAROLAIS PERIOD : 1960 - 1966 n = 127 Variable Estimated t r a t i o name coefficient 123 df Zc -0.18849E-04 - 6.2089 5 Z 2 -0.17737E-01 - 1.75 95 Z 3 -0.18535 - 0.63379 Intercept 5.4853 26.527 R2 = .4476 Only in the case of the South Devon was a coe f f i c i e n t with an inconsistent sign found. Again, there i s an extremely small number of observations for this breed. A l l coefficients were not s i g n i f i c a n t (at the .05 percent level) in every equation, but each was s i g n i f i c a n t in some equations. The value of the coefficients remains r e l a t i v e l y stable across breeds and si m i l a r to those observed in the 5 year date-of-location estimates. II v i i c Nine Year Estimates The same independent variables, Z c, Z„ and Z_ were used in the nine b l 3 year estimates. Plots of the independent variables against the dependent variable suggested that the relationship might be changing as more years were added. The relationship showed some curvature, t a i l i n g o f f as the majority of favoured cattle areas had already.been entered. A logarithmic relationship was suggested. Therefore, two estimates were conducted. One was of the linear form used above, D = b + bcZ K + b 9Z 9 + b-Z. 0 0 5 2 2 3 3 and one with the independent variables converted to logs; D = co + c5 1 o g Z5 + c2 l o g Z2 + c3 l o g Z3 The model which i s linea r in a l l variables provided the estimate with the _2 highest R and therefore was judged to provide the best f i t . These estimates are presented below in Table II 3. Data were available for s i x breeds for nine years of breeder locations. Again, negative signs should be expected for coefficients and the breeds are ordered from the most recent import. TABLE II 3 ESTIMATES OF FIRST NINE YEARS OF LOCATION BY BREED BREED : BROWN SWISS PERIOD : 1970 - 1978 n = 91 Variable Estimated t ratio name coefficient 87 df Z c -0.12110E-04 - 3.9461 5 Z 2 -0.39940E-01 - 3.6572 Z 3 -0.20490 - 1.2999 Intercept 6.9176 30.278 R2 = .5679 BREED : MURRAY GREY PERIOD : 1970 - 1978 n = 74 Variable Estimated t r a t i o name coeffic i e n t 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 R2 = .5954 TABLE II 3 (continued) BREED : MAINE ANJOU PERIOD : 1970 - 1978 n = 105 Variable Estimated t rat i o name coefficient 101 df Zc -0.14244E-04 - 4.4933 Z 2 -0.35408E-01 -;3.7453 Z 3 -0.33644 - 1.6908 Intercept 7.4279 32.969 R2 = .5436 BREED : LIMOUSIN PERIOD : 1969 - 1977 n = 67 Variable Estimated t rat i o name coefficient 63 df Zc -0.12434E-04 - 3.2411 b Z 2 -0.19908E-01 - 1.6196 Z 3 -0.81896E-01 - 0.35980 Intercept 6.0716 20.806 V R2 = .3771 TABLE II 3 (continued) 56. BREED : SIMMENTAL PERIOD : 1969 - 1977 . n = 131 Variable Estimated t r a t i o name coefficient 127 df lc -0.13494E-04 - 3.0852 b Z 2 -0.26221E-01 - 2.4068 Z 3 -0.36325 - 1.4248 Intercept 5.6606 23.914 R2 = .3914 BREED : CHAROLAIS PERIOD : 1960 - 1968 n = 139 Variable Estimated t rat i o name coefficient 135 df Zc -0.20150E-04 - 6.1923 b Z 2 -0.27046E-01 - 2.4054 Z 3 -0.12331 - 0.37426 Intercept 6.0472 26.204 R2 = .4467 No coeff i c i e n t had an unexpected sign. The value of the coefficients remained r e l a t i v e l y stable across breeds, and si m i l a r to those observed in the five 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 linear model f i t s f a i r l y well for the early years of breeder location, but as the better market areas are entered the values of the independent variables in the remaining areas show less variation between years. The choice of areas for new locations becomes less d i s t i n c t when only this set of independent variables i s considered. II v i i d Eleven Year Estimates Eleven years of data was available for 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 + bK.ZK + b 9Z 9 + b,Z_ o 5 5 2 2 3 3 and D = c Q + c 5 log Z 5 + c 2 log Z 2 + c 3 log Z 3 In this case the equation in logs provided the better estimate. The results are presented below in Table II 4. Negative signs should be expected for the coefficients 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 Estimated t rat i o name coeffic i e n t 141 df Log Z 5 - -0.81599 -5.3743 Log Z 2 -0.44314 -1.6610 Log Z 3 -1.2811 -2.1254 Intercept 14.107 8.6035 R2 = .4191 BREED : CHAROLAIS PERIOD : 1960 -1970 n = 160 Variable Estimated t rat i o name coeffic i e n t 156 df Log Z 5 -0 . 92 4 87 -6 . 831 9 Log Z 2 -0.752 92 -2.8450 Log Z 3 -0.70561 -0.72207 Intercept 15.810 7.1309 *2 4842 II v i i e Nineteen Year Estimation for Charolais Breed For the Charolais breed data for 19 years of breeder locations were available. 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 3 The result i s presented in Table II 5 below. Negative signs were expected for the coe f f i c i e n t s . TABLE II 5 ESTIMATE OF FIRST NINETEEN YEARS OF LOCATION • FOR THE CHAROLAIS BREED BREED : CHAROLAIS i PERIOD : 1960 - 1 978 Variable 1 name Esti mated coeffi cient n = 199 t ra t i o 195 df Log Z 5 Log Z 2 Log Z 3 Intercept -0.84696 -1.4931 -1.2254 18.102 -4.3931 -3.9247 -0.77314 6.4643 R2 = .3403 II v i i Tests for Consistency of Pattern To examine the hypothesis that the pattern of breeder location was consistent across breeds and over time, a number of tests were conducted. These tests were carried out using the algorithms programmed into the Equality of Slope Test (Le, 1976) computer package on the computer of the University of B r i t i s h Columbia. Tests were conducted for each group of 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 linear regression equations in m independent variables, * i = b o + b l 1 x l + bJ*J> i=1'2 k the f i r s t hypothesis to be tested i s H : b.1 = b. 2 = b. k, j = l , 2 m o J J J That i s , once a regression equation y = b„ + b. x. + + b x J o i I m m is computed for each of k sets of data, F tests are conducted to determine whether the differences in the regression coefficients between groups may be ascribed to sampling errors, or must be attributed to differences between groups. The theory for the F tests for the hypothesis of common coefficients i s presented in Rao (1970, p. 239). The algorithm in the Equality of Slope Test computer package i s a simple generalization of th 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 coefficients are equal, the hypothesis * 1 2 H = b = b o o o i s tested. That i s , the hypothesis that the intercepts with the Y axis are equal i s tested. I f H q i s not rejected, then a common equation i s computed by the Equality of Slopes Test algorithm. Tests of common slope * H q and common intercepts H q were conducted at a . 0 5 level of significance I f H Q i s rejected, then a Scheffe ( 1 9 7 0 , pp. 6 6 - 7 0 ) test of multiple coefficients of 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 ; 1 , ^ 2 ) , ^ 1 , ^ 3 ) ( b / . b ^ ) , ^ 2 , ^ 3 ) ( b ^ ^ . b ^ ) (b2\bz2),(bz\bz3) ( b 2 \ b 2 k ) , ( b 2 2 , b 2 3 ) ( b 2 k _ 1 , b 2 k ) (b \ b 2 ) , ( b \ b 3) v m m ' v m m 1 (b b k ) , ( b 2 m ' v m b3 ) m ' (b k _ 1,b k) m m In other words, the hypotheses are ( H S : b. h = b.1 o J j h, i = 1, h f. i , k j=l ... m This test i d e n t i f i e s the spec i f i c coefficients which d i f f e r between equations. These Scheffe tests were conducted at the . 1 0 level of significance recommended by Le (1970, p. 3). Identifying which co-e f f i c i e n t s d i f f e r between equations would be useful in establishing whether any pattern existed for changing c o e f f i c i e n t values over time. I f differences in coefficients can be i d e n t i f i e d for equations from data sets progressing through time, e.g., 1 960-1964, 1969-1973, 1 973-1977, then the changing importance of the independent variables in the location decision of breeders may be i d e n t i f i e d . Grouping of equations with similar time periods might then be suggested. The hypothesis H Q for the eighteen equations estimated for the f i r s t five years of breeder locations was rejected at the .05 level of significance; g 3 4 =1.78 (FPROB = .00103 < .05). The Scheffe test was then conducted for a l l coefficients 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 signs, Pinzgauer and South Devon (see Table II 1)., and the equation for Tarentaise and Salers with their small number of observations (n = 16 and n = 17 respectively), were dropped from the test. The hypothesis H Q was not rejected for the fourteen remaining equations; F 3 g 5 5 2 = 1.41 (FPROB = .05417 > .05). In this case, differences among a l l the coefficients of each independent variable may be attributed to sampling errors (at .05 level of * significance). The test of hypothesis for the common equations H q was then conducted. The hypothesis was rejected at the .05 level of significance, F 1 3 g g l = 13.51 (FPROB = 0.0 < .05). The tests were then conducted for the nine equations of the f i r s t seven years of breeder location. The hypothesis, H 0 > was rejected at the .05 level of significance; F 2 4 5 7 7 = 2.36 (FPROB = .00033 < .05). The Scheffe test was then conducted for a l l coefficients of the nine equati ons. H S : b. h = b. 1, h, i = 1, 9 o J O h t i j r 1, 2, 3 None of the 135 hypotheses were rejected. Therefore, following the procedure used in the five year t e s t s , the equation for South Devon was removed because of the unexpected sign on variable (see Table II 2), and the equation for Welsh Black because of the small number of observations (n = 15). The hypothesis, H q , was tested again for the seven remaining breeds. Although the F value was considerably reduced, F18 555 = 1 - 6 5 ( F P R 0 B = - 0 4 4 8 3 < - 0 5)> t h e hypothesis was again rejected at the .05 level of significance. The differences in the seven year equations cannot be considered as resulting from sampling errors. Unfortunately, Scheffe's test provided no insights into the cause of the differences. The tests were then conducted for the six breeds for which nine years of data on breeder location were available. H Q was not rejected at .05 percent level of significance; F 1 5 5 4 4 = 1.58 (FPROB = .07474 > .05). Therefore, the differences in the values of coefficients in the nine year estimates may be attributed to sampling error. As H q was not rejected, hypothesis H was tested. The hypothesis was rejected at the .05 level of significance; F g 5 g g = 15.82 (FPROB = .00036 < .-05). Therefore, even though the coefficients cannot be considered d i f f e r e n t , the hypothesis of a common equation i s rejected due to differences in the intercepts. The tests were f i n a l l y conducted for the two equations estimated from eleven years of data. H q was not rejected at .05 percent level of significance; F 3 2 g y = 0.79 (FPROB = 0.50172 > .05). The test for hypothesis H Q was then conducted and was not rejected at the .05 level of significance; F^  3 0 Q = .02 (FPROB = 0.88039 > .05). A common equation for eleven years of breeder establishment was therefore estimated. This equation i s , D = 15.12 - .8857 log 1^ - .5996 log Z 2 - .9830 log Z 3 This was the only common equation generated. It must be recognized that the use of Ordinary Least Squares (0LS) may not be s t r i c t l y appropriate for these estimations. As the diffusion process i s not complete, the model truncates the dist r i b u t i o n of dates for each span of estimation conducted. In other words, the use of data for only the f i r s t arbitrary t ( i . e . , 5, 7, 9, 11 or 19) years of diffusion r e s t r i c t s the value of D. for a given level of Z. to < t. The truncation of 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 li 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. To use this method, information i s required on the probability of 's being < t . To calculate this probability observations are required for a l l values of the Z.1s. This means we need information on the observations for the Z^'s for a l l periods t+1, t+2, t T , where T i s the date of location of the last breeder of the particular breed in a new location (the completion of the diffusion process). As the process of diffusion i s not complete for any breed, information on t T does not exist (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 in areas where breeders have not yet located do not exi s t . It would be possible to use current values but they would be subject to error. Of course, for some breeds in the 5, 7, 9 and 11 year estimations, some information regarding values of Z..1 s for t's > t do e x i s t , but using this information would not remove the bias in 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 available. Given the nature of the Z^1 s used in this model, correct specification equations to predict, for example, the average size of herd, seems unlikely. Such methods, therefore, did not seem promising. Information on the nature of the bias can, however, be discerned. In truncation models additional observations can be added with or without moving the l i m i t point. In our example, only the former case i s possible. When the l i m i t point i s expanded certain changes in the bias can be expected. These can be i l l u s t r a t e d in 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 1 1 to t 1 to t T , t 1 1 < t 1 < tj, for values of D. Line E{D/Z, D < t^ .) represents the regression for the completed process of diffusion. From the diagram, i t can be seen that for any estimates where t < t ^ the coefficients 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 of the truncated disturbance. Further, the variance of the truncated disturbance w i l l increase as the 67. truncation point increases. For example, as the truncation point i s moved from t 1 1 to t 1 the range of observations at increases from ab to ac. Table II 6 presents comparisons of the values of the coefficients of Z„ and Z_ for s i x breeds as the truncation point i s increased from 0 L O five 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 Z5 Z2 Z3 INT VE R^  5 -.00007 -.026 -.054 5.1 0.68 .62 7 -.00010 -.034 -.159 6.2 1.42 .55 9 -.00012 -.039 -.205 6.9 1.79 .56 MURRAY GREY * ** _2 YEARS h Z3 Z3 INT VE R^  5 -.00007 -.005 -.191 5.0 0.42 .68 7 -.00012 -.007 -.099 5.8 0.61 .65 9 -.00013 -.005 -.099 5.9 0.86 .59 MAINE ANJOU * ** _2 YEARS Z5 Z2 Z3 INT VE R^  5 -.00005 -.007 -.367 5.02 0.89 .54 7 -.00010 -.018 -.362 6.19 0.89 .51 9 -.00014 -.035 -.336 7.42 2.25 .54 LIMOUSIN * ** „? YEARS Z5 Z2 Z3 INT VE R 5 -.00007 -.016 -.145 4.53 0.86 .54 7 -.00010 -.012 -.160 5.45 2.04 .40 9 -.00012 -.019 -.081 6.07 2.86 .38 SIMMENTAL * ** _o YEARS Z5 Z2 Z3 INT VE IT 5 -.00005 -.017 T.315 3.88 1.14 .44 7 -.00011 -.016 ,am 4.91 2.32 .40 9 -.00013 -.026 -.363 5.66 3.42 .39 CHAROLAIS * ** _2 YEARS Z5 Z2 Z3 INT VE R^  5 -.00012 -.012 -.134 4.11 0.96 .57 7 -.00019 -.017 -.185 5.48 1.79 .45 9 -.00020 -.027 -.123 6.04 3.66 .45 Intercept Variance of the estimate In most cases, as expected, the value of the coefficients diverged from zero as the number of years increased. Further, the variance of the estimate consistently increases as the sample period i s extended. 69. II i x Discussion The results of this study indicate that breeders located e a r l i e r in 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 variables. There i s no evidence, however, to suggest that the influence of the independent variables upon the decisions of breeders has followed any discernible pattern over time. The results do, however, suggest that the differences in the locational patterns of breeders might, in part, be explained by the absolute number of areas entered. In the case of the five year estimates, removal of three breeds with very low degrees of diffusion helped to decrease the degree of sampling error. For the seven year estimates, removal of the two breeds with a poor degree of diffusion (n = 15 in both cases, mean of remaining breeds i s 85 locations) reduced the F s t a t i s t i c considerably. Where there were no breeds with poor diffusion records, as in the nine year estimates, the differences in the coefficient were not s i g n i f i c a n t . A small number of observations means that, over time the locational choices of breeders are not as restricted as for faster diffusing breeds. It i s not surprising, therefore, that breeders of those breeds whose degree of diffusion i s very small do not appear to be as responsive to market forces. This brings up the question of why breeds diffuse at different rates. At f i r s t glance, i t would appear that the rate of diffusion i s a function of the date of importation. Table II 7 presents the mean values for the number of areas entered for 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 FIRST 5 FIRST 7 FIRST 9 FIRST 11 ENTRY YEARS YEARS YEARS 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, Salers, 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 diffusion as those imported in e a r l i e r periods. One possible explanation for these differences i s that the diffusion process i s constrained by the purebred stock available - primarily females. To be an active purebred breeder requires that at least some of the breeder's cows must be purebreds. Although bulls may be mated to a large number of non-purebred females (the number of matings may be greatly expanded through the use of a r t i f i c i a l insemination), a purebred heifer must come from a purebred cow. Therefore, the rate of diffusion i s constrained by the number of purebred cows of a particular breed availa In the early years of any breed's existence, this i s a function of the number of females imported. Table II 8 presents a l i s t of the number of females imported by breed in the f i r s t five years and the number of census divisions entered. TABLE II 8 NUMBER OF FEMALES IMPORTED BY BREED IN THE FIRST FIVE YEARS BREED NUMBER OF NUMBER OF FEMALES * CENSUS DIVISIONS IMPORTED ENTERED SIMMENTAL 1375 87 MAINE ANJOU 242 67 MURRAY GREY 127 47 CHIANINA 246 67 SOUTH DEVON 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 *Source: Annual Reports: Canadian National Livestock Records. The coeffi c i e n t of correlation between the number of imports and the number of areas entered i s .77. As space in the quarantine stations is limited, breeds imported in early periods would be at an advantage. In 1969, only breeds from France competed for space, Charolais, Simmental, Maine Anjou and Limousin. By 1974, eighteen breeds were competing for the same number of spaces in the quarantine stations. The number of imports per breed was bound to decline. In addition, the license granting authority appeared to follow no clear set of p r i o r i t i e s , favouring certain breeds in some years (Slessor, 1979). The extreme prices received for individual cows (up to $200,000 in some cases, but $50 to $60,000 were not uncommon) in the early years of breed importations corroborate the hypothesis that females provided the major constraint on di 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 transplants, which would indicate that a l l e v i a t i n g the shortage of females was a major concern. It may be that the increased number of locations for breeds imported in 1974 Table II 7 results from the use 5 of ova transplants on a commercial basis. Thus, the importation policy of Agriculture Canada may have d i r e c t l y affected the diffusion of the new technology. By sanctioning an importation policy which allowed for great divers i t y of genetic material, the general spread of the new technology was probably retarded, as each new breed followed a diffusion process in which breeders entered the same areas. A smaller number of breeds imported would have meant an increased number of importations for the remaining breeds and a more rapid rate of diffusion. Of course, over time, the spread of breeds becomes less dependent on the number of imports, especially when upgrading programs are completed. 73. I f we define the market for genetic material as the to t a l number of cows in a census d i v i s i o n , and define penetration of a market as the establishment of one breeder of a particular breed in that market, then we can define the percent of market penetration in terms of the national cow herd. The percent of market penetration by breed i s presented in Table II 9 for the f i r s t 5, 7, 9, 11 and 19 years of existence for breed organizations. TABLE II 9 PERCENT OF MARKET PENETRATION BY BREED FIRST . . . i . 5 YEARS, ,7 YEARS, , 9 YEARS, 11 YEARS, 19 YEARS 93.40 97.83 93.90 BREED CHAROLAIS 84.03 87. 57 91 .60 SIMMENTAL 83.87 91 . ,31 92.38 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 II 9 when the total market i s considered in eleven of the eighteen breeds examined, over 50% of the potential market was penetrated in the f i r s t five years. For the breeds imported before 1972, most had penetrated 70% of the market in the f i r s t seven years of thei r existence. Thus, the means of technical change had been 75. made available to the majority of the Canadian cattle industry within an extremely short period. The process of diffusion i s also continuing. Although the absolute number of breeders has declined (Canadian National Livestock Records) as the prices in the commercial cattle market moved through the trough of the beef cycle (1975 - 1977), in a l l of the eighteen breeds examined establishment of breeders in new areas i s continuing. In the two decades of i t s existence, breeders belonging to the Canadian Charolais Association have established themselves in 199 of the possible 256 d i v i s i o n s , and have penetrated almost 98 percent of the market. Yet, through 1 978, new Charolais enterprises were s t i l l being established in unpenetrated census divisions. There seems, to this date, no area with a market potential too small to warrant the establishment of a local breeder. Although, when the total 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 II 10 provides a summary of market penetration by province. TABLE II 10 SUMMARY OF MARKET PENETRATION BY PROVINCE 18 EXOTIC BREEDS, 1978 NUMBER OF ALTA SASK MAN B.C. ONT PEI NS PQ NB NFLD BREEDS AVAILABLE 10 4 2 2 2 1 0 0 0 0 TO 90% OF THE MARKET NUMBER OF BREEDS AVAILABLE 18 12 5 6 6 2 1 1 1 0 TO 50% OF THE MARKET The establishment of breeders takes place e a r l i e s t in Alberta, 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, in that order. Of course, t h i s reflects the size and importance of the cattle industry in 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, 18 EXOTIC BREEDS, 1978 Years of Breed Prov. Organization 3 to >> cu ra o to o tu o cu sz c to •r> •r- S- > to •r— S- rt) ra <0 c s 1 CJ3 cu (13 cu cu i — • to +-> •r— < 0 0 CQ Q c res *i— -o 3 O a> J c CO >> CU T - CU to c res c o CU (1) res c > S- to c n D l J C S- E o c 2 to u +-> cu c c r cu E N fO U E E •r- o 1—' s_ s_ o «a; i— 1—• s_ c ' 5= i—i CC i . • r ~ •r— (0 S- 3 o ro r — — CD o •1— 6 re) 0 0 s: 0 0 c_> I— CQ Q CD 00 s: 18 10 10 9 9 9 9 8 8 7 7 7 6 6 6 6 5 5 Years t i l l Available to 90% of Potential Market 10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 B.C. Years t i l l Available to 50% of Potential Market 10 7 8 >9 >6 >8 >4 >7 >7 >7 >6 >6 >6 >(> >5 >5 % of Market Covered 1978 .99 ,99 .48 .86 .55 .09 .78 .32 .83 .12 .33 ,09 .06 .00 .13 .03 .04 .08 90% 5 2 7 5 5 >9 4 >8 3 >7 3 >7 >6 >6 2 >5 >5 2 Alta. 50% 1 1 2 3 2 3 3 6 3 2 2 2 3 2 T 3 2 1 % 1978 .99 .99 .92 .99 .99 .70 .99 .63 .99 .66 .92 .86 .81 .61 .98 .79 .61 .94 90% 3 3 >10 >6 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 5 >6 >^5 >5 Sask. 50% 1 2 5 4 5 >9 4 >8 3 >7 3 4 >6 >6 2 5 >5 2 % 1978 .99 .99 .81 .99 .84 .23 .90 128 .85 .19 .68 .53 .17 .22, . .93 .55 .20 .84 90% 14 6 >io >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 Man. 50% 3 . 3. >10 7 6 . >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 4 % 1978 .91 .99 .35 .65 .67 .10 .41 .00 .35 .19 .44 .30 .13 .07 .19 .07 .07 .55 90% 14 10 >10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 Ont. 50% 5 5 10 8 6 >9 >6 >8 >8 >7 >7 >7 >6 >6 >6 >5 >5 >5 % 1978 .91 .90 .50 .64 .73 .00 .64 .01 .45 .00 .13 .04 .01 .01 .08 .01 .04 .23 9 0 % >18 >10 >10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 Que. . 50 % • 10 >10 >10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 % 1978 83 .26 .09 .17 .13 .00 .00 .00 .01 .00 .04 .01 .01 .00 .05 .00 .00 .01 9.0% >18 >.10 >10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 N.S. . 50% . 10 >10 >10 >9 >9 >9 >9 >8 >8 >7 >7 >7 >6 >6 >6 >6 >5 >5 % 1978 .83 .41 .26 .37 .17 .00 .00 .00 .01 .00 .00 .00 .00 .00 .11 .08 .00 .00 NFLD. P.E.I. N.B. % 1978 o vo O S« % 1978 cn O s« vo O 6^  % 1978 cn o &s CO o \ CO V 0 0 >18 vo vo ro 0 0 CTl oo cn V 0 0 Charolais ro oo OK OK cn cn V o VO OK V o Simmental b o OK >10 ro vo >10 OK o o OK OK Limousin o o V CO V vo rx> vo V VO V VO -pa cn V vo V vo Maine Anjou o o V VO V vo no CTl V VO V VO 0 0 V vo V co Brown Swiss o o V VO V VO IN5 CT) V vo V vo o o V vo V VO Welsh Black o o V VO V VO o o V CO V VO vo V CO V VO Murray Grey o o V oo V oo o o V 0 0 V oo o o V oo V oo South Devon o o V oo V oo l>o vo V 0 0 V oo o VO V oo V oo Chianina o o V V b o V •--1 V o o V \ i V Tarentaise o o V •^J V •~J f>0 CO V V o o V V Blonde D1 Aquitaine o o V —J V ~J ro vo V V - d o o V ^1 V —1 Gelbvei h o o V CTl V cn o o V CTl V CTl o o V CTl V cn Salers o o V CTl V CTl o o V CTl V CTl o o V CTl V vn Normande o o V en V cn o o V CTl V CTl o o V cn V vn Pinzgauer o o V cn V VT> o o V OS V CTl o o V CTl V vn Romagnola o o V cn V cn o o V cn V cn o o V cn V cn MRI o o V cn V cn ro vo V cn V cn o o V cn V cn Marchi gi ana Although differences in the dates of a v a i l a b i l i t y of 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 cattle economy which i s located in areas of late a v a i l a b i l i t y , the absence of the new technology may s t i l l have important ramifications for have-not areas. As the market for beef in Canada i s a national market, the competitive position of areas where new technology i s not u t i l i z e d can only deteriorate. H i s t o r i c a l l y , Canadian agricultural policy has favoured the geographical diver s i t y of beef production through freight rates, t a r i f f s , feed freight assistance for feed grains, etc. The geographic diffusion of exotic cattle i s not consistent with this policy objective. In addition, certain provincial governments have been promoting greater s e l f sufficiency in food s t u f f s . As most of the areas of the country where exotic cattle w i l l be available l a t e r are net beef importing areas, the promotion of s e l f sufficiency w i l l be more d i f f i c u l t . F i n a l l y , the deteriorating competitive position of cattlemen in areas of non-availability may increase the rela t i v e poverty in areas with few alternative opportunities, especially in rural Quebec and the Maritimes. The measurement of such possible effects i s beyond the scope of this study. The information provided regarding the diffusion of herds does suggest there may be such a problem. Further, the estimates of the date-of-location functions should help to identify those areas where non-availability may be expected. Although i t i s not possible to derive a common equation for the date of-location function for each period of 5, 7, 9 and 11 years, t h i s i s primarily a problem of the rejection of the hypothesis H that the intercept values are equal. Fourteen, equations of the f i r s t 5 years of location do, however, have a common value for the coefficients of the 80. independent variables; -0.555E-05 for Zg, -0.016 for 1^ and -0.144 for l y These values could be used with a f a i r degree of confidence for breeds which were not subject to severe importation constraints. The s i x breeds, for which nine years of data are available, have common slopes of -0.1487E-04, -0.025 and -0.139 for Z^, Z^  and Z^  respectively. ^ 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 of diffusion. At present, the total stock of animals with superior genetic potential seems inadequate to meet the demands of the cattle industry, even with a doubling of purebred registrations since the opening of 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 exist for that breed. In the long run, as the national cattle herd improves, the base upon which bulls are judged superior w i l l r i s e , but the process by which a new breed diffuses should not be affected 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 cattle cycle and other changes to the industry since 1960. The importation of additional breeds seems to have halted temporarily, probably as a result of the poor cat t l e prices and, subsequently, purebred prices in the 1970's. A large number of breeds, however, remain in Europe and other parts of the world which have not yet been imported into Canada. The improving prices for cattle in 1978 and 1 979 may stimulate a new demand for imports. Further, a number of so-called synthetic breeds, 7 such as Hay's Converter, Beefmaster and Alberta Hybrid, are being developed. I f the market does develop for such synthetics, they w i l l begin the more general diffusion process. In either 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 this study. Chapter III STUDY II - CONTINUING TECHNICAL PROGRESS - GENETIC IMPROVEMENT IN THE CANADIAN CATTLE INDUSTRY III i Background The importation of "exotic" ca t t l e over the last decade provides the increased diver s i t y of germ plasm necessary for more rapid genetic im-provement in the Canadian cattle industry. This, however, i s only the f i r s t step in the process of technological change. Although s i g n i f i c a n t short term gains can be realized from crossbreeding the available stock of germ plasm (Willham, 1976), long term progress w i l l arise through the selection process in pure strains. Breeding programs should provide animals which embody increasing amounts of innate productive capacity. As in plant breeding and other sectors of the livestock industry, breeding the optimal genetic mix i s a long term project.inv.olving an interaction between those who use the genetic material commercially and those who provide the genetic inputs to production. Genetic progress in the livestock industry may be based on the same principles of selection as those in plant science, but there are two major differences in the practice of animal breeding. The f i r s t i s that the breeding programs are conducted largely within the commercial sector. The second major difference i s that livestock improvement i s a longer term and continuous process, while advances in plant science have been discrete improvements from controlled experimental designs combined with extensive testing and evaluation (Evenson and Kislev, 1975). Economic studies have, to a large extent, ignored the interactive process between the breeders of improved genetic material and those who u t i l i z e i t in 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 of crossbred cat t l e (Jeffery, 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 in the f i e l d s of induced innovation suggests that new processes arise in response to changes in 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 relative prices and th e i r changes. Such improvements in the Canadian cattle industry are being undertaken within the commercial sector. Instead of the breeding process being internalized within 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 cattle operations) with a market mechanism operating between them. Thus, market forces should d i r e c t l y affect the process of genetic improvement. Genetic progress in the animal industry i s , in r e a l i t y , the provision of additional quantities of existing inputs to production. In other words, just as hybrid plant varieties are bred because they combine certain production characteristics such as "short term", "rust resistance", "drought resistance", etc., so livestock can be bred for "disease resistance", "feed conversion", "egg laying a b i l i t y " , "backfat". etc. The expected quantities of these characteristics vary from breed to breed. In the cattle industry (as well as other branches of the livestock sector), there i s no market for s p e c i f i c genetic characteristics. The char-a c t e r i s t i c s are subsumed under one purchasable commodity, a b u l l . The value of a bull in commercial production i s related to the genetic 84. characteristics which the animal carries. 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 this value. Economists have paid scant attention to the market for genetic factors of 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 of Literature In the majority of economic research (both theoretical and applied), i t i s assumed that the inputs to production are homogeneous. Of course, bulls are not a homogeneous commodity. There i s no single price for b u l l s . The value of a bull i s determined by the genetic characteristics embodied in the individual animal and, of course, represents a combination of the innate properties of the animal and the cumulative breeding a b i l i t y of the owners of a l l the bull's ancestors. In this way bulls are very similar to land in 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 "original and indestructible properties of the s o i l " plus, presumably, the myriad of improvements or degradations carried out by a l l the previous owners. There has, as yet, been l i t t l e study of inputs to production which are not homogeneous. I m p l i c i t l y , however, the computation and comparison of rates of return to alternate investment.possibilities .within :firmsi could be viewed as a recognition that the inputs of production are not homogeneous. Comparisons of improvements to, 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 different potentials for improvement, given limited c a p i t a l . Similar arguments can be made in terms of the individual's decision regarding his investment in human ca p i t a l . In fact, an entire "testing industry" has been developed to 85. ide n t i f y characteristics of educational potential to help individuals maximize the return to t h e i r investment in education. In general, in would seem that there has been no systematic study of the process of production in terms of characteristics when inputs are heterogeneous. This may be one of the reasons why technical change i s portrayed as a s h i f t in the production function due to the use of a new input, when, in fact, in many cases the "new input" simply provided greater amounts of existing characteristics of production. Genetic improvements in crops provide a good example. Miracle rice may be viewed as a new product, but i t i s s t i l l r i c e . The difference i s that i t internalized a superior mix of production characteristics (rust resistance, response to f e r t i l i z e r , shorter growing season . . .) than previously existing natural v a r i e t i e s . The process of selecting the mix of characteristics has not been subject to investigation 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 called "characteristic approach". This e f f o r t stems from two sources: 1) an attempt to overcome the obvious weakness of existing demand theory (Lancaster, 1966) (Lipsey and Rosenbluth, 1971), and 2) a serious attempt to deal with the problem of constructing price indexes in the face of changing quality of goods (Gri l i c h e s , 1971) (Terleckyj, 1975). These theoretical developments and empirical investigations have not been paralleled in production economics. The paper by Archibald and Rosenbluth (1978) provides a new and notable exception. Two elements of th i s paper suggest t h e i r relevance to this study. F i r s t , "The characteristic approach i s well adapted to deal with the observed heterogeneity of inputs" (p. 1). Second, they suggest that the characteristic approach could be helpful in analyzing the source of technological change. Further, Archibald and Rosenbluth suggest that: 86. "We do not need to suppose that producers compute them formally, but i t i s natural to assume that 'good management1 has an appropriate rule of thumb or i n t u i t i v e understanding of the shadow prices of important characteristics required to select the cost minimizing input mix", (p. 16) In the case of exotic c a t t l e , we seem to have both situations, 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 characteristics. In the attempt to establish 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 application of regression analysis to price measurement rests on the hypothesis that price differences among variants of a product in a particular market can be accounted for by i d -e n t i f i a b l e characteristics of these variants . . . By f i t t i n g a regression equation to observations on the price and characteristics of commodity variants, t y p i c a l l y in a cross section for a market at a given time, we can learn which characteristics are associated with the price of a commodity, and what that relationship 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 co-e f f i c i e n t s of the equation can be interpreted as prices for the characteristics", (pp. 151-152). However, much of the empirical research on'hedonic pricing suffers from serious theoretical deficiencies (Lucas, 1975) (Muellbauer, 1974) (Muellbauer, 1975). 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 arise in the bull case due to the passive role of the s e l l e r in the setting of price determined by auction). Further, i f the problem i s presented in terms of a representative consumer, then the specification of the hedonic function must be linear (Lucas, 1975, p. 175). 87. Most of the empirical studies, however, have reported estimates in a non-linear form which forces the abandonment of the representative consumer. Abandonment of the representative consumer implies that any welfare state-ments resulting from quality adjusted price indexes necessitate interpersonal comparisons of u t i l i t y . In production space this problem does not arise, 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 in a limited 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 calculate shadow prices. The problem, however, i s e n t i r e l y data related and could be overcome when using, for example, biological 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 linear 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 in swine production; backfat, feed eff i c i e n c y and average daily gain. They use t h e i r model to discern "the amount by which maximum pr o f i t may be expected to increase for each unit of improvement in that animal". This, 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 (1976) developed a si m i l a r linear programming model among ten breeding characteristics for integrated b r o i l e r operations. In the beef industry s i m i l a r studies have, as yet, not been conducted. Further, there has been no examination of the interaction between those who use purebred cattle and those who improve them. I l l i i i Hypotheses The basic premise of t h i s study i s that the mix of production characteristics produced by the suppliers of genetic materials (the registered breeders) w i l l be determined by the production process used in the cow-calf industry. The s p e c i f i c hypothesis i s that the prices paid for bulls 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 , internalized by bulls which are phenotypic proxies for the genetic components of the production function. Implicit values for these characteristics may then be determined. A further hypothesis i s that the process of genetic selection followed by purebred breeders conforms to the market forces indicated in the commercial cattle operations' selection of b u l l s . I l l i v The Model Given the i r biological nature, processes in primary agriculture 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 m, G r G2, Gn) (3.1) where Y stands for units of output, the X.'s are non-genetic components of the production function, and the G^ 's are the underlying genetic components of the production function. Of course, in most cases, the G^ 's are assumed fixed and are omitted from the production function (Heady and D i l l o n , 1961). For the purpose of our study of the cat t l e industry, we shall assume 89. that a l l genetic components of the production function are subsumed under the b u l l . 2 The production enterprise w i l l be defined in terms of individual b u l l s . In other words, the commercial cow-calf producer i s assumed to treat each set of cows which a bull can service as a separate enterprise in terms of the decision to purchase a b u l l . Therefore, the production function can be reduced t o , Y B = F B(g, x) (3.2) where Yg = the output per b u l l , pounds of calf/bull/year g = the bull component of the production function which i s a vector of genetic-based characteristics - i . e . , g = (G-|, Gg, Gn) internalized in one b u l l , x = the vector of non-genetic inputs associated with the production expected from the number of cows one bull i s expected to service. The p r o f i t maximizing firm w i l l be expected to u t i l i z e each non-genetic input of production to the point where, assuming perfect'competition W j = PY ( 9 YB 1 8 V ' (3>3) in equilibrium where W. = the price of input j Xi = the quantity of input j Py = the price of output (the price of calves) Under the assumption of perfect competition, the value of a bull 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 solution values for (3.3) and Z W. X. include 0 j = 1 J J "normal" returns to the rancher's labour and c a p i t a l . Of course, a bull i s used as the herd s i r e for a number of years (approximately 8 years on average). Hence, the bull's contribution 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 bull i s used in production. What one would be w i l l i n g to pay for a bull would therefore be Wa2 W 3 + V _ (3.5) B g 1 (1+r) (1+r) 2 ( l + r ) T _ 1 where the W . are the quasi-rents expected from the bull 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 bulls are heterogeneous, each bull's price i s determined i n -di v i d u a l l y . The market for breeding stock i s of the tr 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 relationship, then the price of a b u l l , Pg, should r e f l e c t i t s expected value in production (Wilson, 1977). Certainly, no one would pay more for a bull than i t s expected value in production and, given the assumptions regarding the technical knowledge of producers, low prices would be bid away (Vickrey, 1961). Of course, this argument i s very similar- to that used in determining the rental price of land, the admission of heterogeneity is 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 cattle i s the supplier of genetic improvement to the commercial cow-calf enterprise. Once established, the purebred breeder i s r e l a t i v e l y constrained in the amount of genetic improvement which he can expect to produce. The expected phenotypic change in any characteristic for one generation i s described by Lasley (1978, p. 163); A G.j = the expected increment in the characteristic over a generation i n t e r v a l . G.j£ = the measurable quantity of characteristic G^  of the s i r e selected for breeding. G^ = the mean quantity of characteristic G^  of the selected sire's male contemporaries within a herd. Hgi = the h e r i t a b i l i t y of characteristic Gi (%). I = the generation interval which i s defined as the average age of the parents when thei r f i r s t offspring are born (Pirchner, 1969). This i s the rate of improvement in the next generation of sires which the breeder can expect to r e a l i z e , on average, for any one cha r a c t e r i s t i c . For example, l e t us choose the characteristic "weaning weight". I f the average weaning weight of the sire's in-herd contemporaries i s 500 l b s . , and the weaning weight of the bull to be mated i s 560 l b s . , then we have H Gi A G i z = ( G i s - G i S) 2 (3.6) where G i S = 500 lbs. 560 lbs. 92. HGi f o r w e a n l n 9 w e i 9 n t is<^.35 (Lasley, 1978) so AG.j = (560 - 500) (.35/2) = (60) (.175) = 10.5 lbs. or that the expected mean weaning weight of the bull's progeny w i l l be 510.5 lbs. Bulls to be used for breeding in the next season are chosen by ranking a l l the bulls in a herd, and then s u f f i c i e n t numbers (relative to the size of the cow herd) of those highest ranked are retained (Lasley, 1978), Bulls v not retained for use by the purebred breeder are, depending on t h e i r rank, sold to commercial cow-calf enterprises or culled. What i s extremely important to the selection process for 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 correlations (Lasley, 1978) (Jeffery, 1971). Genetic progress i s reduced as the number of characteristics selected for emphasis at any breeding increases. It i s suggested, for example, that "The progress one can make when selecting for 4 characters that are unrelated i s I/V4 or % of that which i s possible when selecting 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 selection process designed to provide 3 improvement primarily on one chara c t e r i s t i c . " H e r i t a b i l i t y and rela t i v e economic importance determine the attention each t r a i t should receive in selection. The greater the number of t r a i t s selected, the less progress can be made for any one t r a i t " . (Davis, 1972). The problem for the purebred breeder thus becomes, in any time period, to choose that which w i l l maximize the value of the bulls he w i l l s e l l in the next generation - i . e . , to improve upon that characteristic which would maximize the expected increase in the price of the progeny produced in the next generation. As the cost of raising and maintaining bulls with various mixes of characteristics are not s i g n i f i c a n t l y different (Slessor, 1979), the decision .-should depend, on the absolute level of the G.'s, the A G.-j's and the i m p l i c i t values of the characteristics. The G..'s and the expected A G..1 s should be known by the purebred breeder. Although diminishing returns may eventually be reached for some characteristics, as the physiological 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 for the characteristics in beef c a t t l e . The G^j's can therefore be assumed constant in succeeding I's. The value to the purebred breeder of additional units of characteristics should be reflected in the prices received for bulls 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 of important char a c t e r i s t i c s , and thus, through the market, establish t h e i r value to the purebred breeder. Then i t would be possible to establish whether purebred breeders are following the market forces indicated (given that information of G\'s and A G^'s i s generally available). Of course, the actual genetic components of the production function are not readily observable. Instead, the purebred breeder and the cow-c a l f operator must rely on phenotypic (observable) t r a i t s , or char-t e r i s t i c s which are known to correlate with genetic improvement. Data for 94. individual animals i s usually collected 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 addition, s t a t i s t i c s are collected by herd on the incidents of dystocia and breed-by-breed indexes of calving d i f f i c u l t y , G^ , are published and well known. These characteristics 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 relationship between these char-a c t e r i s t i c s and the production of pounds of c a l f per bull in commercial herds i s not e x p l i c i t l y known as the relationship i s complex, involving the interaction of the factors of h e r i t a b i l i t y , heterosis and additive gene action (Willham, 1976). I t i s possible, however, to discern some general indications of the form of the r e l a t i o n . I t i s well known (Woodland, 1 978) (Lasley, 1978) that, 3 Y B / 3 G] > 0 3 YB / 3 G2 > 0 3 Yg / 3 G3 < 0 It 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 characteristics suggested above. In essence, estimation of the value of the genetic-based charac-t e r i s t i c s manifest in bulls i s equivalent to estimating a value added 95. production function. Under constant returns, value added in money terms i s defined as (Arrow, 1975), n m V = i = PY Y " (3.7) where V = value added in money terms = price of output Y = quantity of output Z.'s = quantities of inputs contributing to value added R^'s = prices of inputs contributing to value added X.'s - quantities of inputs not contributing to value added 3 W.'s = prices of inputs not contributing to value added Clearly, the right hand expression of (3.7) i s equivalent to (3.4) The production function (3.2) was defined as, where the G^ 's are the genetic-based inputs suggested above. Assuming that the G.j 's are weakly separable from the elements of x (Berndt and Christensen, g 1972), the function F can be represented by for some suitable chosen functions M and K. This assumption i s equivalent Y R = F (g, x) (3.8) and we now define g = ( G r G2, G3) F B (g, x) = H [K(g), x j (3.9) 96. to the statement that the marginal rates of substitution between the genetic based characteristics are independent of the quantities of the non=genetic inputs. It has been shown by Arrow (1975) that as long as F i s homogeneous of degree one and concave in i t s arguments, K can be id e n t i f i e d with a value added production function, and that K has " a l l the properties of a neoclassical production function" (Arrow, 1975, p. 18). We can therefore write, Qv = K (g) (3.10) where Qy i s the quantity (real) value added. Thus, (3.8) can be written as, Y B = H (Q v, x) (3.11) but from (3.7) Qv = or from (3.4) in our case where Wy i s defined as the price of a unit of real value added Q v = ^ - (3-12) Therefore, Wg = Wy Qy = Wv • K (g) (3.13) I f Wy i s the same for 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 principle of duality (Diewert, 1973b), i t can be shown that there w i l l be a unit cost function P Y = C (Wv, w) (3.14) where w i s a v e c t o r o f p r i c e s o f n o n - g e n e t i c i n p u t s . As P v and a l l t he e l e m e n t s o f w a r e assumed c o n s t a n t , W y must be c o n s t a n t , so t h a t U = W • K (g) ( 3 . 1 5 ) g V Under p e r f e c t c o m p e t i t i o n , we assume t h a t a l l g e n e t i c - b a s e d c h a r a c t e r i s t i c s a re d i s c o u n t e d a t t h e same r a t e and t h a t f u t u r e Py and Y ^ ' s and m Z W. X . - ' s a re p e r c e i v e d and d i s c o u n t e d a t t he same r a t e by a l l p r o d u c e r s , j - 1 J J whence f rom ( 3 . 5 ) we can w r i t e , P 3 = W v * • K* (g) ( 3 . 1 6 ) * where K i s t he v a l u e added p r o d u c t i o n f u n c t i o n d e f i n e d o v e r the b r e e d i n g * l i f e o f a b u l l , and W i s d e f i n e d o v e r t he same p e r i o d . I f ( 3 . 1 6 ) can be e s t i m a t e d , t h e n 3 P f i / 3 G. . 1 s can be d e r i v e d f o r e a c h g e n e t i c - b a s e d c h a r a c t e r i s t i c . 3 Pg / 3 G | r e p r e s e n t s the m a r g i n a l p r o d u c t i n money terms o f a d d i t i o n a l u n i t s o f G. . . G i v e n a v e c t o r o f G ^ ' s , i t i s t h e r e f o r e p o s s i b l e t o c a l c u l a t e t he m a r g i n a l p r o d u c t i n money t e r m s o f i m p r o v i n g each G ^ . T h e n , g i v e n i n f o r m a t i o n on the e x p e c t e d r a t e o f i m -provement f o r each G ^ , i . e . , A G ^ j , the a p p r o p r i a t e G^ t o be i m p r o v e d can be d i s c e r n e d , s i n c e the c o s t s 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 w i t h d i f f e r e n t mixes o f c h a r a c t e r i s t i c s do n o t v a r y s i g n i f i c a n t l y ( S l e s s o r , 1 9 7 9 ) . As measures o f t h e mean v a l u e s f o r t h e G ^ ' s and t h e i r s t a n d a r d d e v i a t i o n s a re a v a i l a b l e f rom p u b l i s h e d s o u r c e s , a l o n g w i t h e s t i m a t e s o f H Q . J f o r each c h a r a c t e r i s t i c , e s t i m a t e s o f A G^j can be made. C o m b i n i n g t h i s i n f o r m a t i o n w i t h t h e e s t i m a t e s o f m a r g i n a l p r o d u c t i n v a l u e t e r m s f o r each G. j , one can d e t e r m i n e the c h a r a c t e r i s t i c upon w h i c h improvement s h o u l d be made f o r a g i v e n v e c t o r g . These e s t i m a t e s w i l l t hen be compared t o a c t u a l o b s e r v e d t r e n d s i n b r e e d improvement o v e r t i m e . T h i s s h o u l d p r o v i d e 98. an indication 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 characteristics. I l l v Data Much of the transfer of genetic material between purebred breeders and commercial cow-calf operators i s carried out at bull auctions. To c o l l e c t a set of observations on the genetic characteristics and prices of individual b u l l s , a large number of bull auctions were attended during late March, April and May of 1979. Auctions were attended in the four western provinces of Canada. A subset of sales, which provided a consistent set of charac-t e r i s t i c s and other relevant information, was selected for s t a t i s t i c a l analysis. This subset i s composed of twenty-one individual sales at nine locations in the four western provinces. A l i s t of sales i s provided in TABLE III 1. TABLE III 1 99. LIST OF BULL SALES 1. Alberta Bull Test Station Sale 2. Simmental - Monte Creek Test Sale (B.C.) 3. Manitoba Shorthorn Bull Test Sale 4. Alberta Murray Grey Association Sale 5. Saskatchewan Angus Bull Test Sale 6. Saskatchewan Shorthorn Bull Test Sale 7. Alberta Hereford Test Centre Sale 8. Syrinx Angus Ranch Sale (B.C.) 9. Manitoba Maine Anjou Bull Test Sale 10. Blonde d'Aquitaine Bull Test Sale (Alta.) 11. Saskatchewan Charolais Bull Test Sale 12. Saskatchewan Simmental Bull Test Sale 13. B r i t i s h Columbia Simmental Bull Test Sale 14. Manitoba Limousin Bull Test Sale 15. Manitoba Aberdeen Angus Bull Test Sale. 16. Saskatchewan Hereford Bull Test Sale 17. Manitoba Hereford Bull Test Sale 18. National Limousin Bull Test Sale (Alta.) 19. Duffield Test Station Sale (Alta.) 20. Willbar Bull Test Station Sale (Alta.) 21. Saskatchewan Maine Anjou Bull Test Sale These sales provide observations on 616 individual bulls from 15 breeds. A detailed breakdown i s provided in TABLE III 2. TABLE III 2 NUMBER OF BULLS BY BREED BREED # OF BULLS 1. Hereford 2. Aberdeen Angus 207 88 86 67 47 33 22 21 19 9 9 3 3 3. Charolais 4. Simmental 5. Limousin 6. Maine Anjou 7. Blonde d'Aquitaine 8. Shorthorn 9. Murray Grey 10. Brown Swiss 11. Salers 12. Chianina 13. Pinzgauer 14. Welsh Black 15. Red Angus TOTAL 616 100. A l l bulls 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 available 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 characteristics (weaning weight and average daily 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, in most cases, some information on the animal's pedigree. The information for average daily gain on feed i s d i r e c t l y comparable for a l l bulls in the sample. Data on weaning weights, on the other hand, demanded conversion to a standard measure. The term weaning weight i s somewhat of a misnomer i t s e l f . The s t a t i s t i c actually computed i s either a 200 or a 205 day weight and therefore only approximates weaning weight. Weaning i t s e l f i s usually carried out at one common time for a l l calves in the herd, regardless of whether they are early or late born calves. Weighing of calves i s usually conducted at approximately 200 days from the middle of the calving 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 this study, the 200 day weight i s used and the formula employed for conversion i s that u t i l i z e d by the Federal-Provincial Record of Performance for Beef Program, i . e . , WEIGHT AT WEIGHIN -BIRTHWEIGHT Y 9 n n . R T D T U I I | : T r u T  A G E I N D A Y S X 2 0 0 + BIRTHWEIGHT The information provided in the catalogues and sale sheets i s in various forms, ranging from those already standardized to 200 day weights, 205 day weights, unadjusted weaning weights, and weights at the commencement of average daily gain t r i a l s . As the birth dates and date of weighing were l i s t e d for each b u l l , i t was possible to standardize a l l 101. bulls to a 200 day weight. Incidents of dystocia, of course, are an ex-post measure of any individual b u l l . In other words, such information must come from the births of the progeny of the individual b u l l . No such information exists for bulls which have not yet been bred. 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 into the price a potential purchaser is w i l l i n g to pay for a b u l l . An index of calving d i f f i c u l t y i s calculated for each breed by province by the Federal-Provincial Record of 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 in 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 provincial departments of Agriculture annually publish information on G^ 's and t h e i r standard deviation for each breed. H 's are available for the phenotypic characteristics from a number of sources (Lasley, 1978) (Willham, 1976). I l l vi S t a t i s t i c a l Analysis and Results As a value added production function has been shown to have a l l the usual properties of a neoclassical production function, s i m i l a r methods may be used in their estimation. Assuming constant returns to scale, Diewert, (1973a) has shown that a generalized lin e a r transformation function of the form k k 1 , = t(y:x) = t(z) = a Q 0 + ^ ^ a ^ z^ 2 a i j = a j i where z i s a k dimensional vector of non-negative outputs [y^ y m) and an "n" dimensional vector of non-negative inputs (x-j 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 regularity 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 coefficients a^. . . . be non-negative". (Diewert, 1973a, p. 287). Further, Diewert (1973a, p. 299) suggests that this particular functional form would be best suited for the direct estimation of production functions. As the function i s line a r in 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 i j = a j i ( 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 calving d i f f i c u l t y could be considered weakly separable from weaning weights and average daily gain. The index of calving d i f f i c u l t y i s a measure of dystocia, and i s an indication of the number of l i v e calves one can expect from the number of cows one bull i s expected to service. Increases or decreases in the number of l i v e calves should not affect the marginal rate of substitution between weaning weights and average daily gains for 103. those calves which are successfully dropped. I n i t i a l l y , however, estimation was done without the assumption of weak separability and no meaningful results could be obtained. Subsequently, the cross product terms 2 G^2 and G^2 G 3 2 were omitted. Prices for bulls ranged from $700 to $24,000, with a mean of $2,250. A cursory examination of the characteristics data made i t clear that the prices realized for certain bulls 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 clearly, beyond the price a commercial producer would be w i l l i n g to pay. It was thereforeedecided that a closer examination of the market was necessary. For some sales, information on the purchaser as well as the consignor was collected. Taking an arbitrary price of $3,000 for a bull as the suspected maximum commercial price, bulls purchased at prices over $3,000 were investigated. From the diffusion study, the names of registered breeders of the various exotic breeds were available. These were checked against the buyers of bulls over the price of $3,000, and i t was found that a disproportionate number of purebred breeders purchased such animals. A further check on animals purchased for less than $3,000 revealed that there were very few bought by members of purebred organizations. This suggested there were two markets at the auctions, one for transfers from purebred breeders to commercial cow-calf operators, and one for transfers between purebred breeders, each with i t s own pricing c r i t e r i a . Cattlemen who raise cattle which w i l l be used solely for the production of meat w i l l be interested, in a set of characteristics in breeding bulls which w i l l d i r e c t l y affect the number, quality and growth;, eff i c i e n c y of the dressed carcasses produced. Breeders of purebred bulls and cows are interested in a set of characteristics in the sires they 104. purchase which w i l l produce superior breeding stock for 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 sires may be selected to a l l e v i a t e a particular deficiency 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 characteristics desired by purebred breeders i s unlikely to coincide with those of the commercial operator. Further, as the returns from the acquisition of a "superior" s i r e can be far greater for the purebred breeder, the price he w i l l be w i l l i n g to pay for such a sire 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 primarily for breeder to breeder transfers, purebred breeders are in attendance at commercial auctions in thei r role as consignors. As bull 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 primarily commercial sales, they participate along with commercial cattlemen. In most cases, the high prices received for bull s purchased by purebred breeders suggest that there i s a common recognition of suitable animals by purebred breeders. Otherwise, i t would only be necessary for the purebred breeders to outbid commercial cattlemen and lead to only marginal price increases. In addition, i t i s well known that purebred Breeders use collusive bidding tactics in attempts to effect the "mood" of the sale. The removal of bulls purchased by purebred breeders therefore seemed a reasonable procedure. As a check, however, estimates with the entire sample were undertaken and meaningless results obtained. It was therefore decided to remove a l l bulls transferred between purebred breeders from the sample. The organizations which sponsored 105. sales for which information on buyers had not i n i t i a l l y been collected were therefore contacted and the l i s t s of buyers obtained for each sale. The purchasers of bulls were checked against l i s t s of purebred breeders of exotic ca t t l e in the diffusion study. In the case of Herefords, Aberdeen Angus and Shorthorns, which were not'included in the diffusion study, the provincial breed organizations were contacted by phone and asked i f their buyers were members of thei r organizations. In the f i n a l result 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. The 99 bulls were removed from the sample. Hence, the f i n a l data set used for estimation i s 517 bulls with prices., ranging from $700 to $4,000. For the realization of genetic-based technological change, i . e . , a B B change in the form of the production function from F to G . crossbreeding must be undertaken. The biological phenomenon upon which genetic-based technological change i s founded is heterosis, 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 plants, as compared with those resulting from inbreeding" (Webster's, 1965). Although the majority of breeds imported from continental Europe are larger than those developed from stocks in Britain and North America before the opening of the quarantine stations, in 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 action. In other words, straightbred commercial herds of exotic c a t t l e would exhibit genetic performance similar to that which i s realized in herds,; of existing B r i t i s h c a t t l e , excepting differences between breeds. Technological change in the cattle industry w i l l not be accomplished 106. through the replacement of commercial herds of straightbred Hereford or Shorthorn cattle with straightbred Simmental or Chianina c a t t l e . I t i s the crossbreeding of such herds which generates the technological change in the industry. At present, the basis of the commercial cow herd in Canada i s B r i t i s h , and countinues :to be so to take advantage of the hybrid vigour which results from the mating with cattle from continental Europe. As yet, purebred exotic 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 this 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 bulls are s t i l l mated with inbred lines of commercial B r i t i s h cattle and l i t t l e heterosis should be expected. On the other hand, European cat t l e are mated with the same inbred lines of commercial B r i t i s h cows to take advantage of hybrid vigour. One would expect, therefore, that the production function from the two mating schemes would d i f f e r . Hence, a separate regression was specified for large breeds (Charolais, Si mmental^ Maine Anjou, Blonde d'Aquitaine, Brown Swiss, Salers, Chianina and Pinzgauer) using 209 bulls 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 bu l l s . The index of calving d i f f i c u l t y was removed from the estimation equation for small breeds. As a result of t h e i r generally smaller frames, the index of calving d i f f i c u l t y ranged from 1.03 to 1.10 which did not provide s u f f i c i e n t v a r i a b i l i t y . These figures representino appreciable calving d i f f i c u l t y and r e f l e c t individual rather than breed related 107 . problems. In the case of small breeds, i t was found that at one sale, the National Limousin Bull Test Sale in Alberta, bulls brought considerably higher prices than the i r merit suggested. This was not the case.with animals of the Limousin breed auctioned at other sales. No explanation of this apparent enthusiasm at the National Limousin Sale i s offered. A dummy variable (NLBTS) is included in the equation for small breeds. The crossproduct term (G^ 2 G^2) i s denoted CP in the estimating equations. The results of the regression are presented below. \ DEPENDENT VARIABLE = PRICE OF EULLS 108. LARGE BREEDS n = 209 Variable name Estimated coeffi cient t r a t i o ( s i g n i f i c a n t at) 204 df .05** .10 * WEAN ING WEIGHT LBS. (G^) AVERAGE DAILY GAIN LBS/DAY (G 2) G1 2 G2 2 INDEX OF CALVING DIFFICULTY (G 3) INTERCEPT 5.0249 1159.4 65.427 • 246.04 -7550.1 2.7649 3.4304 1.2194 - 4.6848 -10.605 ** R^  = .5156 (3.18a) SMALL BREEDS n = 308 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 Estimated coefficient 4.9941 547.42 52.358 754.15 -4372.0 t ra t i o (significant at) 303 df .05** 3.8839 2.2696' 1.4827 ** ** ** 7.4791 ** -10.911 .10 R-2 = .4738 (3.18b) 109. These estimates appear consistent with theoretical analysis. The larger values for the coefficients of weaning weight and average daily gain (over the relevant range), indicated in the equation for large breeds, suggest an awareness of hybrid vigour among purchasers of such c a t t l e , and the s h i f t in the production function expected from technological change. Although the estimates presented would not allow a breeder to predict, with any accuracy, the price of an individual b u l l , given the _2 low R , the results do indicate 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 of b u l l s . Further, the estimates should indicate to the breeder (with a given characteristics mix for his herd) which characteristics w i l l be most valuable for him to improve. I t i s to this problem that we now turn. To estimate whether breeders, in thei r selection process, emphasize the characteristics which would maximize the expected value of bulls in the next generation (as indicated by the bull price equations estimated above), i t i s f i r s t necessary to establish an expected increase for the phenotypic characteristics in physical terms using equation (3.6), or G i w = G n + — r — — <3-19' where ^ i l + l = ^ e e x P e c t e u " m e a n v a ^ u e °f characteristic for bulls in generation 1+1. G.T = the value of G. for the s i r e to be bred in qeneration I. G.jj - the mean value of characteristic G^  of the selected sire's male contemporaries within a herd. Hg^ = the h e r i t a b i l i t y of characteristic G.. Once estimates for each are obtained from (3.19), these values can be no. u t i l i z e d in the estimating equations (3.18a, 3.18b) for the relevant breed and the expected increase in value for improvement on each characteristic 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 in his selection program, can then be i d e n t i f i e d . The estimates can then be compared to the actual characteristics emphasized by breeders over a generation. As actual data on the intensity of selection (G.^- G^j) i s not available, some assumptions w i l l have to be made regarding this parameter. These w i l l be made e x p l i c i t for the particular data sets u t i l i z e d below. Ideally, one would l i k e to have data on individual herds over time. Such data i s , however, not generally available. Fortunately, some data on groups of individual bulls are available. The Saskatchewan Bull Test program publishes the results of i t s t r i a l s for individual animals i d e n t i f i e d by herd (approximately ten animals from each herd on test each 1 year). Assuming that bulls on test are representative of the sample, herd';s genetic material, an estimate of the mean values G^'s, and the range for '. each characteristic can be obtained. Then, assuming the animal which ranked highest for each G. would be used for rebreeding, an estimate of * G - j + i can be made for each characteristic. These can be substituted into (3.18a) or (3.18b) and the expected increase in dollar value calculated. The characteristic which the breeder would be expected to emphasize can then be i d e n t i f i e d . These results can be compared to the actual improvements observed in bulls of the same herd in the next generation - in t h i s case, bulls on test two years l a t e r . For the 1 975-76 & 1977^78 and the 1 976-77 & 1 978-79 te s t s , fifty-seven herds with representative bulls have been i d e n t i f i e d . The results of the comparisons are presented below in TABLE III 3. For the calculation of h e r i t a b i l i t y , a value of .35 was used for G-| and .50 for G2 (Lasley, 1978, p. 330). TABLE III 3 EXPECTED VALUE OF IMPROVING WEANING WEIGHT AND AVERAGE DAILY GAIN SASKATCHEWAN BULL TEST STATION BULLS HERD BREED WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED CHANGE IN PREDICTED PREDICTED MEAN BEST MEAN MEAN BEST MEAN (1975) (1 975) (1 977) (1 975) (1 975) (1 977) CHANGE IN VALUE {$) WW ADG VALUE FROM OBSERVED PHENOTYPIC CHANGE WW ADG EQUALS OBSERVED EMPHASIS DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS BLACKLOCK ANGUS 569 617 595 2 .49 2. 79 2. 72 $ 54 $ 70 $ 175 $ 215 ** COOK ANGUS 473 553 542 2 .72 2. 92 2. 68 $ 97 $ 62 $ 476 $• •177 ** MCCALL ANGUS 522 557 499 2 .92 3. 39 2. 71 $ 42 $115 $-189 $--160 ** MCNINCH C ANGUS 522 608 545 3 .03 3. 09 3. 15 $104 $ 13 $ 160 $ 106 ** MCNINCH J ANGUS 517 543 624 2 .94 3. 24 3. 09 $ 31 $ 66 $ 48 $ 133 ** PERRYVILLS ANGUS 621 657 602 3 .08 3. 1 9 2. 74 $ 40 $ 28 $-130 $--316 ** STABLES ANGUS 514 581 557 2 .93 3.22 2. 74 $ 79 $ 67 $ 297 $--173 ** TONER ANGUS 454 505 520 2 .80 2. 90 2. 91 $ 49 $ 22 $ 390 $ 96 ** WILLMOT ANGUS 495 52 9 5 91 2 .63 2. 75 2. 99 $ 37 $ 27 $ 654 $ 322 ** SPARROW CHARILAIS 588 644 657 3 .40 3. ,70 3. 22 $ 71 $118 $ 513 $--287 BARDICK HEREFORD 540 607 549 2 .77 3. 03 2. 79 $ 78 $ 59 $ 61 $ 18 ** DECOR BY HEREFORD 4 94 521 558 2 .84 3. 01 3. 02 $ 42 $ 39 $T521 $ 159 ** FERGUSON HEREFORD 527 557 587 2 .72 2. 97 3. 01 $ 34 $ 58 $ 409 $ 261 HORKOFF HEREFORD 494 522 564 2 .85 3. 12 2. 78 $ 31 $ 62 $ 483 $-- 62 HOUGHAM HEREFORD 428 479 466 2 .48 2. 67 2. 83 $ 59 $ 44 $ 290 $ 279 ** JENSON HEREFORD 431 46 9 457 2 .76 3. 05 2. 70 $ 46 $ 65 $ 183 $ 52 JOHNSON HEREFORD 586 619 592 3 .13 3. 61 3. 19 $ 38 $107 $ 41 $ 54 ** KAEDING HEREFORD 499 535 574 3 .10 3. 20 3. 14 $ 42 $ 37 $ 521 $ 114 ** KONSCHUH HEREFORD 484 565 506 2 .64 2. 93 2. 87 $ 73 $ 76 $ 134 $ 205 ** MCKENZIE HEREFORD 452 497 522 2 .72 2. 96 2. 73 $ 52 $ 47 $ 485 $ 35 ** MCTAGGART HEREFORD 516 580 533 2 .70 3. 06 2. 92 $ 75 $ 81 $ 116 $ 198 ** MILLHAM HEREFORD 523 539 569 2 .77 3. 12 3. 21 $ 17 $ 63 $ 315 $ 393 ** NOBS HEREFORD 479 509 511 2 .71 3. 03 3. 10 $ 34 $ 71 $ 221 $ 344 ** $ 47 $ 24 $ 31 $ 19 TABLE III 3 (continued) HERD BREED WEANING WEIGHT AVERAGE DAILY GAIN MEAN BEST MEAN MEAN BEST MEAN (1 975) (1 975) (1 977) (1 975) (1 975) (1 977) PREDICTED CHANGE IN PREDICTED PREDICTED CHANGE IN VALUE FROM EQUALS DIFFERENCE VALUE ($) OBSERVED OBSERVED IN VALUE WW ADG PHENOTYPIC EMPHASIS OF IMPROVED CHANGE CHARACTERISTICS WW ADG PALASCHUK HEREFORD 509 525 565 2.87 3.01 3.06 $ 21 $ 31 $ 385 $ 186 ** SPENCER HEREFORD 431 457 462 2.59 2.78 2.57 $ 31 $ 44 $ 216 $- 17 $ 13 WAINMAN HEREFORD 549 581 509 2.47 2.95 2.87 $ 37 $111 $-271 $ 369 ** BROWN SHORTHORN 458 485 465 2.67 2.94 2.81 $ 17 $ 62 $- 20 $ 124 ** CAMPBELL SHORTHORN 465 498 557 2.91 3.13 3.11 $ 39 $ 48 $ 640 $ 174 $ :9 COOPER SHORTHORN 494 540 515 3.20 3.24 2.94 $ 56 $ 9 $ 148 $-228 ** MORTON SHORTHORN 540 580 671 2.76 3.11 2.88 $ 48 $ 81 $ 885 $ 109 $ 33 MCLEOD SIMMENTAL 637 753 747 3.09 3.35 3.10 $145 $105 $ 792 $ 16 ** kkkkk kkkkk kkkkk kkkkk kkkkk ***** ***** ***** ***** ***** ***** ***** ***** ***** kkkkk (1 976)(1976)(1 978) (1 976)(1 976)(1 97 8) ANAKA ANGUS 522 643 592 2.78 3.17 2.66 $105 $ 90 $ 272 $-110 ** DRYLAND ANGUS 498 513 597 2.85 3.12 2.81 $ 17 $ 62 $ 681 $- 36 $ 45 MCCALL ANGUS 508 545 578 3.28 3.51 2.84 $ 64 $ 52 $ 490 $-388 ** MCNINCH ANGUS 574 62 9 601 3.11 3.17 3.18 $ 65 $ 13 $ 186 $ 63 ** SAUDER ANGUS 5 94 649 605 3.00 3.53 2.87 $105 $102 $ 74 $-119 ** STABLES ANGUS 510 541 547 2.85 2.94 2.78 $ 34 $ 22 $ 255 $- 62 ** WILLMS ANGUS 533 547 592 2.85 2.97 2.84 $ 24 $ 22 $ 370 $- 18 ** BEGRAND CHAROLAIS 683 750 653 3.29 3.72 3.54 $ 84 $178 $-219 $ 405 ** HOWE CHAROLAIS 650 712 649 3.18 3.63 3.11 $ 65 $186 $- 80 $-114 $121 MCKENZIE CHAROLAIS 540 623 6 97 3.66 4.02 3.70 $126 $119 $1183 $ 62 ** PLEWIS CHAROLAIS 743 792 629 3.51 4.02 3.68 $ 61 $211 $-939 $ 277 ** SIMPSON CHAROLAIS 672 713 618 3.62 3.92 3.49 $ 51 $121 $-403 $-209 $ 70 WIENS CHAROLAIS 575 594 551 3.51 3.97 3.84 $ 22 $180 $-182 $ 517 ** BARDICK HEREFORD 493 517 570 2.62 2.77 3.03 $ 27 $ 36 $ 525 $ 366 $ 9 DECORBY HEREFORD 484 537 554 2.78 3.19 3.04 $ 63 $ 93 $ 483 $ 230 $ 30 GAMBLE HEREFORD 533 543 555 2.76 3.06 3.02 $ 10 $ 67 $ 150. $ 234 ** GRESS HEREFORD 472 527 456 2.92 3.15 2.92 $ 60 $ 65 $-113 $ 00 ** JENSON HEREFORD 429 461 484 2.72 2.95 2.80 $ 39 $ 52 $ 385 $ 69 $ 13 TABLE III 3 (continued) HERD BREED WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED CHANGE IN PREDICTED PREDI CTED MEAN BEST MEAN MEAN BEST MEAN CHANGE I.N VALUE FROM EQUALS DIFFERENCE (1976)(1976)(1978) (1 976) (1 976) (1 978) VALUE ($) OBSERVED OBSERVED IN VALUE WW ADG PHENOTYPIC EMPHASIS OF IMPROVED CHANGE CHARACTERISTICS WW ADG JONES HEREFORD 509 565 481 2.62 2.85 2.94 $ 58 $ 59 $-193 $ 288 ** MILLHAM HEREFORD 532 573 563 '2.88 2,96 2,76 $48 $ 18 $ 213 $-108 ** MISTY MDS HEREFORD 509 537 506 3.16 3.38 3.12 $ 31 $ 48 $- 21 $- 35 $ 17 WAINMAN HEREFORD 542 585 535 2.61 2.89 2,84 $ 50 $ 64 $- 47 $ 210 ** COOPER SHORTHORN 500 542 522 2.94 3.39 3.27 $ 49 $101 $ 153 $ 290 ** MANN SIMMENTAL 609 652 661 3,47 4,02 3.38 $ 56 $221 $ 396 $-143 $165 MCLEOD SIMMENTAL 5 90 670 637 3.41 3.55 3.00 $104 $ 55 $ 350 $-657 ** For details of calculations see Appendix I 1_ ** Denote those cases where the ch 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 for improvement, coincided with the characteristic actually emphasized for improvement. 2_ Values in this column denote, for those cases where the characteristic predicted for emphasis did not coincide with the characteristic actually emphasized, the difference in the predicted value of improvement between the former and the l a t t e r . 114. The characteristic actually selected for emphasis in improvement coincided with the characteristic predicted from equations (3.18a) and (3.18b) seventy-two percent of the time. Further, in only three cases when the characteristic actually emphasized for improvement did not agree with the predicted characteristic to be emphasized, did the difference in the predicted additional dollar value of alternative improvements to characteristics exceed $50. The average differences in predicted value of improvement to alternative characteristics for inconsistent predictions i s $43. This compares to an average of $34 in the case of correct predictions. This would suggest that the market i s not precise and that either breeders are i n -different about the characteristics which they select for improvement, or that random elements are s u f f i c i e n t to distort the perception of breeders as to the correct choice of emphasis in improvement. On the other hand, in only three cases of fourteen where the difference exceeded $50, did the predicted and actual characteristic emphasized d i f f e r . On a more aggregate scale, the Federal Record of Performance for Beef program publishes annual summaries on weaning weight and average da 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 distributed among herds, then the characteristic to be selected for emphasis can be i d e n t i f i e d by a procedure similar to that out-lined above for individual animals. As the intensity of selection i s not known, i t w i l l be assumed at one standard deviation from the mean for each cha r a c t e r i s t i c . These values were again substituted into equation (3.19) for the intervals 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 in equations (3.18a) and (3.18b) and values for predicted and actual improvements derived. The results were presented in TABLE III 4. TABLE III 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 B 473 66 475 1.88 .49 1.83 $ 76 $109 HEREFORD B 479 73 459 2.02 .51 1.97 $ 83 $121 SHORTHORN B 473 66 460 1 .94 .52 1.93 $ 76 $122 CHAROLAIS B 586 100 545 2.36 .64 2.30 $123 $265 RED ANGUS B 467 103 449 2.12 .30 2.03 $120 $ 69 SIMMENTAL B 560 59 568 2.96 .84 2.62 $ 73 $334 ANGUS B/C 494 75 498 1 .98 .47 1.98 $100 $ 99 HEREFORD B/C 509 81 478 2.05 .52 1.98 $ 92 $123 SHORTHORN B/C 481 60 488 1.97 .46 2.03 $ 69 $108 SIMMENTAL B/C 613 43 513 3.10 .64 2.90 $ 54 $257 kkkkk kkkkk kkkkk ***** ***** ***** ***** ***** ***** ***** (1 971)(1971 )(1973) (1971)(1971)(1973) ANGUS 3 473 67 481 1.89 .50 1.87 $ 76 $118 HEREFORD B 483 76 460 1 .98 .52 1.98 $ 86 $122 SHORTHORN B 473 70 45 9 1 .92 .54 1.93 $ 79 $127 CHAROLAIS B 589 98 546 2.28 .62 2.46 $119 $258 RED ANGUS B 458 68 452 1.65 .39 1.92 $ 75 $ 97 SIMMENTAL B 544 88 499 2.55 .27 2.08 $115 $114 ANGUS B/C 495 64 499 1 .88 .47 2.08 $ 72 $115 HEREFORD B/C 507 77 479 2.13 .46 2.09 $ 86 $108 SHORTHORN B/C 467 65 475 2.01 .38 2.02 $ 87 $ 84 ***** ***** ***** kkkkk ***** ***** ***** ***** ***** ***** CHANGE IN PREDICTED PREDICTED VALUE FROM EQUALS DIFFERENCE OBSERVED OBSERVED IN VALUE PHENOTYPIC EMPHASIS OF IMPROVED CHANGE CHARACTERISTICS WW ADG _2_ $ 13 $- 48 $ 33 $-134 $- 47 ** $- 86 $-. 9 ** $-292 $-100 ** $- 90 $-107 ** $ 59 $-551 $261 $ 26 $ 00 ** $-206 $- 67 ** $ 46 $ 57 ** $-744 $ 325 ** ***** ***** ***** ***** kkkkk $ 53 $- 19 $ 42 $-153 $ 00 ** $- 93 $ 9 ** $-305 $ 301 ** $-3 9 $ 260 ** $-328 $-780 ** $ 26 $ 192 ** $=187 $- 38 ** $ 53 $ 9 ** ***** ***** ***** ***** ***** TABLE III 4 (continued) BREED CLASS WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED CHANGE IN PREDICTED PREDICTED MEAN SD MEAN MEAN SD MEAN CHANGE IN VALUE FROM EQUALS DIFFERENCE (1972)(1 972)(1 974) (1972)(1972)(1 974) VALUE ($) OBSERVED OBSERVED IN VALUE WW ADG PHENOTYPIC EMPHASIS OF IMPROVED CHANGE CHARACTERISTICS WW ADG ANGUS B 475 91 463 1.83 .51 1.75 $102 $124 $- 79 $- 77 ** HEREFORD B 459 95 454 1.97 .51 1.83 $120 $111 $- 33 $- 133 ** SHORTHORN B 460 90 459 1 .93 .49 1.72 $108 $102 $- 7 $- 202 ** CHAROLAIS B 545 118 550 2.30 .72 2.36 $145 $2 95 $ 35 $ 99 ** RED ANGUS B 449 84 492 2.03 .56 1.87 $ 97 $129 $ 288 $- 151 $ 32 SIMMENTAL B 568 94 542 2.62 .59 2.27 $115 $244 $-188 $ 580 $129 ANGUS B/C 498 93 479 1.98 .37 1.80 $105 $ 90 $-126 $- 174 ** HEREFORD B/C 478 99 484 1.98 .58 1.84 $122 $120 $ 40 $- 134 ** SHORTHORN B/C 488 81 485 2.03 ;36 2.00 $ 93 $ 84 $- 20 $- 28 ** CHAROLAIS B/C 587 122 565 2.51 .66 2.40 $149 $271 $-175 $- 167 ** SIMMENTAL B/C 513 95 55 9 2.90 .40 2.44 $126 $158 $ 341 $- 741 ** ***** ***** ***** ***** •kk'k'k'k ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** (1973)(1973)(1975) (1973)(1 973)(1 975) ANGUS B 481 88 468 1.87 .57 1.67 $ 99 $138 $- 86 $- 1 95 $ 39 HEREFORD B 460 96 463 1.98 .51 1.75 $110 $113 $ 20 $- 220 ** SHORTHORN 3 45 9 94 462 1.93 .55 1.72 $119 $111 $ 20 $- 202 ** CHAROLAIS B 456 111 540 2.46 .62 2.02 $1 40 $246 $ 614 $- 715 $106 RED ANGUS B 452 85 537 1.92 .45 1.84 $106 $102 $ 582 $- 76 ** SIMMENTAL 3 500 104 553 2.61 .74 1.93 $132 $295 $ 388 $-1119 $163 ANGUS B/C 499 93 465 2.08 .45 2.10 $106 $108 $-228 $ 19 ** HEREFORD B/C- 479 102 467 2.09 .48 2.03 $112 $118 $- 80 $- 56 ** SHORTHORN B/C 475 87 447 2.02 .44 1.84 $100 $103 $-188 $- 172 ** CHAROLAIS B/C 587 107 557 2.61 .57 2.28 $132 $237 $-216 $- 549 $105 SIMMENTAL B/C 492 95 533 2.41 .44 2.28 $134 $177 $ 297 $- 212 $ 43 MURRAY GTEY B/C 473 56 445 1 .39 .44 1.31 $ 60 $111 $-180 $- 82 ** LIMOUSIN B/C 457 106 520 2.81 .63 1.82 $139 $129 $ 439 $- 907 ** WELSH BLACK B/C 551 112 506 2.41 .38 1 .24 $130 $ 88 $-304 $-1179 ** ***** ***** ***** •kickick ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** CTl TABLE III 4 (continued) BREED CLASS WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED CHANGE IN PREDI CTED PREDI CTED MEAN SD 1 MEAN MEAN SD MEAN CHANGE IN VALUE FROM EQUALS DIFFERENCE (1974)(1974)(1976) (1974)(1974)(1976) VALUE ($) OBSERVED OBSERVED IN VALUE WW ADG PHENOTYPIC EMPHASIS OF IMPROVED CHANGE CHARACTERISTICS WW ADG ANGUS B 463 74 481 1.75 .57 1.91 $ 82 $138 $ 118 $ 154 ** HEREFORD B 454 78 466 1 .83 .58 1.94 $ 89 $136 $ 79 $ 104 ** SHORTHORN B 459 76 460 1 .72 .64 2.03 $ 85 $153 $ 6 $ 296 ** CHAROLAIS B 550 117 567 2.16 .66 2.15 $140 $274 $ 119 $- 16 $1 34 SIMMENTAL B 542 107 640 2.27 .68 2.41 $131 $279 $ 690 $ 231 $148 LIMOUSIN B 523 62 559 2.64 .73 2.48 $ 71 $167 $ 245 $- 147 $ 96 ANGUS B/C 472 74 441 1 .90 .50 1.68 $ 81 $121 $-204 $- 19 ** HEREFORD B/C 484 81 479 1 .84 .56 2.23 $ 92 $133 $- 33 $ 370 ** SHORTHORN B/C 482 77 452 2.00 .44 2.28 $ 86 $103 $-201 $ 263 ** CHAROLAIS B/C 573 108 594 2.30 .85 2.42 $130 $351 $ 148 $ 200 ** SIMMENTAL B/C 559 76 632 2.44 .60 2.39 $ 93 $245 $ 51 9 $- 82 $152 ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** (1 975) (1 975) (1977) (1975)(1 975)(1977) ANGUS B 468 74 501 1.67 .61 1.90 $ 81 $149J $ 215 $ 223 ** HEREFORD B 463 59 479 1 .75 .65 2.00 $ 65 $157 $ 105 $ 239 ** SHORTHORN B 462 79 475 1.72 .61 2.06 $ 88 $148 $ 85 $ 325 ** CHAROLAIS B 540 102 585 2.02 .67 2.25 $122 $286 $ 314 $ 386 ** RED ANGUS B 537 52 523 1.84 .36 2.00 $ 58 $ 58 $- 91 $ 157 ** SIMMENTAL B 552 100 676 1 .93 .67 2.48 $121 $287 $ 843 $ 922 ** LIMOUSIN B 520 78 552 1.82 .70 2.08 $ 88 $169 $ 208 $ 253 ** MAINE ANJOU B 506 99 638 1.24 '.94 2.56 $112 $415 $ 864 $ 2245 ** ANGUS B/C 465 83 510 2.10 .66 1.96 $102 $152 $ 301 $- 132 $ 50 HEREFORD B/C 467 81 487 2.03 .64 2.35 $ 93 $148 $ 133 $ 137 ** SHORTHORN B/C 447 61 512 1 .84 .66 2.11 $ 69 $154 $ 429 $ 254 $ 85 CHAROLAIS B/C 557 104 579 2.28 .71 2.57 $127 $297 $ 156 $ 479 ** SIMMENTAL B/C 533 89 575 2.28 .54 2.64 $110 $222 $ 298 $ 590 ** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** TABLE III 4 (continued) BREED CLASS WEANING WEIGHT AVERAGE DAILY GAIN PREDICTED CHANGE IN PREDICTED PREDICTED MEAN SD MEAN MEAN SD MEAN CHANGE IN VALUE FROM EQUALS (1 976) (1 976) (1 978) (1 976) (1 976) (1978) VALUE ($) OBSERVED OBSERVED WW ADG PHENOTYPIC EMPHASIS CHANGE DIFFERENCE IN VALUE OF IMPROVED CHARACTERISTICS WW ADG ANGUS B 481 40 506 1 .91 ,56 1 , .97 $ 92 $1 32 $ 165 $ 57 $ 80 RED ANGUS B 483 68 521 1 .80 .40 1 .77 $ 75 $ 96 $ 249 $-- 29 $.21 BROWN SWISS B 573 171 614 2 .40 .72 2, .58 $209 $296 $ 291 $ 297 ** CHAROLAIS B 567 97 595 2 .15 .64 2, .35 $115 $498 $ 196 $ 335 ** HEREFORD B 466 80 486 1 .94 .53 2, ,03 $ 93 $126 $ 133 $ 85 $ 33 LIMOUSIN B 559 94 552 2 .48 .68 2, .22 $109 $157 $-- 47 $• -247 $ 48 MAINE ANJOU B 597 130 632 2 .57 .69 2, .37 $160 $287 $ 249 $--333 $127 SIMMENTAL B 640 119 661 2 .41 .53 2, .48 $128 $226 $ 127 $ 138 ** SHORTHORN B 460 77 491 2 .03 .62 2, .06 $ 87 $143 $ 207 $ 28 $ 56 WELSH BLACK B 487 113 563 1 .65 1.07 1, .68 $126 $260 $ 490 $ 29 $134 ANGUS B/C 441 101 536 1 .68 .75 2, .19 $115 $180 $ 620 $ 480 $ 65 CHAROLAIS B/C 5 94 97 616 2 .42 .73 2, .46 $116 $305 $ 155 $ 66 $189 HEREFORD B/C 479 78 509 2 .23 .46 2, .20 $100 $ 95 $ 202 $• - 27 ** LIMOUSIN B/C 560 141 555 2 .59 .36 2, .31 $164 $ 83 $-• 33 $--246 ** SIMMENTAL B/C 632 156 62 9 2 .39 .75 2. .22 $188 $335 $-- 35 $ 253 $147 SHORTHORN B/C 452 75 493 2 .28 .55 2, .39 $ 88 $126 $ 279 $ 100 $ 38 For details of calculations see Appendix I 1_ ** Denote those cases where the cha r a c t e r i s t i c , which the estimating equation (3.18a or 3.18b) indicated should be emphasized for improvement, coincided with the characteristic actually emphasized for improvement 2_ Values in t h i s column denote, for those cases where the characteristic predicted for emphasis did not coincide with the characteristic actually emphasized, the difference in the predicted value of improvement between the former and the l a t t e r . oo 119. The actual characteristic emphasized in improvement was predicted correctly 68% of the time for the 85 observations. In twenty-eight of the forty-four cases, where the difference in predicted values of alternate characteristics exceeded $50, the predicted emphasis was consistent with the observed emphasis. Again, this 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 in section III vi suggest three conclusions: 1) commercial cattlemen recognize the important genetic inputs to t h e i r production process and this i s reflected in the prices they are w i l l i n g to pay for b u l l s ; 2) the prices of bulls r e f l e c t the change in the production process expected from the hybrid vigour associated with crossbreeding; 3) the selection of characteristics emphasized in 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 characteristics. Taken together, they indicate 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 under-standing of the shadow values of important characteristics for the market to regulate the process of genetic improvement. Such conclusions are not surprising. I t would seem highly unlikely that commercial cattlemen would take the time and trouble to purchase a particular s i r e for 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 unlikely that purebred enterprises, whose sole purpose and income i s derived from providing bulls with additional genetic potential, would devise t h e i r breeding strategy without some understanding of the relative value of the alternative f i n a l products. Probably the most t e l l i n g indication of the importance of genetic parameters to cattlemen i s t h e i r willingness to assume the high cost of obtaining information on the genetic characteristics of t h e i r herds. Over 2,500 breeders and commercial cattlemen voluntarily participate in the Federal-Provincial R.O.P. Beef program each year. On this program the operator must weigh and record his animals two or three times a year. This entails con-siderable time, e f f o r t and labour. Yet, information i s collected on over 100,000 animals a year. Approximately 50% of a l l purebred calves are R.O.P. tested on this program (Annual Report 1974-75). In addition, many breed organizations and provincial governments operate bull test stations, where breeders can have their 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 in 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. It would seem unlikely that such information would be collected unless i t s worth to the operator was i d e n t i f i e d . 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 of genetic improvement is poorly regulated. The most obvious distorter of perception i s the market situation i t s e l f - the auction. The author, in his discussions with provincial agriculture o f f i c e r s , found that many had calculated the correlations between the prices of bulls and their genetic characteristics. Most of them found low values for.the correlation c o e f f i c i e n t , which led them to discount the a b i l i t i e s of purchasers. Most, however, recognized the fact that purebred breeders attempt to , distort the market through collusive bidding. In addition, most admitted that purebred breeders based thei r purchases, in part, upon the pedigree of the animals in addition to t h e i r apparent genetic worth. None had removed such observations from th e i r calculations of correlations. As suggested above, no meaningful results 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 in operation, one for transfers from purebred breeder to pure-bred breeder, and one for transfers from purebred breeders to commercial cattle operations. Each has i t s own pricing 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 pricing of bulls i s a largely random exercise. The second feature of the bull market, which contributes to the impression that the pricing of bulls bears l i t t l e relation to t h e i r genetic merit, i s that each individual animal may have physiological t r a i t s which are not heritable 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 "size and depth of the scrotum" may indicate physical rather than genetic breeding a b i l i t y , while general conformation and apparent _2 temperament may affect the price of any individual animal. The low R in equations (3.18a) and (3.18b) tends to provide corroboration of t h i s . At any individual sale of 20 to 30 animals, the relation of the prices to the genetic characteristics may therefore be obscured by such random fluctuations. Thirdly, i t seems clear that any evaluation of genetic characteristics must be made within the context of the breeding system employed. The value of a vector of genetic characteristics to be used in a straightbred system w i l l d i f f e r from those to be employed in a crossbreeding system. In sales at which a selection of breeds i s auctioned, correlations between the price of the animals and thei r characteristics w i l l be low unless the 122. type of breeding system expected is taken into account. It may also appear that breeders follow no systematic .improvement program for the i r herds. In addition to the well known biological and environmental factors which can affect the physical manifestations of a herd's characteristics at any point in time, there also appear to be economic factors which can give the outward impression of lack of direction and consistency. F i r s t , i t becomes obvious from a close examination of TABLES 3 and 4 that, in many cases, the difference in the expected value of improving one characteristic relative to another i s marginal at best. For the . Saskatchewan Bull Test sample, in 42 of the 56 cases examined, the difference between the expected value of improving alternative charac-t e r i s t i c s was $50 or less per animal. For the annual R.O.P. Beef case this was true 50 out of 84 times. In many cases, therefore, the breeder may be indifferent about the characteristic he may choose to improve or, indeed, from the information received from the pricesrat any one sale, he may not be able to discern any clear pattern. On the other hand, breeders may also be so responsive to changes, in the relative value of improving alternative characteristics:that no: clear direction can be discerned from t h e i r breeding program. For example, from TABLE III 4, i t would appear that Hereford breeders changed the emphasis of t h e i r breeding program three times in the seven periods between 1 970 and 1973, following d i r e c t l y the relative values suggested from equation (3.18b). In two cases, Mi 11 ham and McLeod, where a change of emphasis was indicated from predicted relative values in the Sask-atchewan Bull Test, sample breeders appear to have altered t h e i r breeding emphasis in the one year period. To the collec t o r of physical data, such a 123. change in emphasis may make i t appear that the breeder has "no-clear objectives" for his herd when, in fa c t , the decisions are based on rational economic assessments. The equations estimated from bull price data and characteristics corroborate the evidence from research by geneticists regarding the increased productivity expected from hybrid vigour. It i s , however, equally-clear 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 led to i t s inclusion in the R.O.P. Beef,program for the f i r s t time in 1976 (Annual Report 1976-77). The importance attached to this variable by cattlemen i s indicated by the significance of the index of calving d i f f i c u l t y variable in equation (3.18b). Although i t may be too early to speculate, i t would seem that the next l o g i c a l step in the production revolution w i l l be the development of specialized females which w i l l possess a genetic make up which w i l l retain the level of hybrid vigour in crossbreeding, yet w i l l not suffer from calving problems. Such breeding systems have been proposed by animal sc i e n t i s t s (Cartwright, 1975) (Cunningham, 1974) but, as yet, few producers have been w i l l i n g to i n i t i a t e such sophisticated systems. The conclusions also lend support to the induced innovation hypothesis. At least improvements to the existing technologies, both the new and the old, appear to follow the prices indicated by the market. I f the marginal changes in prices predicted for bulls can " i n i t i a t e changes in breeding programs, then the more dramatic change in prices, 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. The characteristic approach to change in technology u t i l i z e d in this study may also suggest that more meaningful results could be obtained by those who study technological change, i f t h e i r analysis were conducted in characteristics space rather than goods space. One of the problems', of studying induced innovations in 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 of ongoing adjustments.;, to existing inputs, 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 characteristics. It would, however, be an error to suggest that they represent the same input. The usual approach to this problem in goods space i s to define the input', in terms of vintages, but vintages:, carry no quantitative information and cannot explain how vintage t i s different from vintage t+1. It i s no more help in production space than i t would be for those who attempt to construct price indexes to include a 1976 Buick in 1976 and a 1977' Buick in 1977, without defining them in terms of characteristics. It would therefore seem that i f a better understanding of the economics of technical change i s desired, i t might be more rewarding to define production in terms of characteristics and more thoroughly examine the effects of changing prices. This may not provide any new insights into the process by which "true innovations" are produced, but i t w i l l remove the necessity* imposed by defining production in goods space, of analysing technical change in 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 that, i n i t i a l l y , one must decide whether one i s dealing with a fixed l i s t of inputs and outputs. Although calving d i f f i c u l t y i s included in the equation for large breeds and not'included in the equation for small breeds, this does not mean that calving problems represent a new argument in the vector of input characteristics. H i s t o r i c a l l y , calving percentages have been increasing and the low levels observed for Herefords, Aberdeen:, Angus and Shorthorns are a r e l a t i v e l y new phenomenon. It 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 fixed l i s t of cha 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 either, 1) the introduction of a new production function, or 2) "the introduction of an altered input which combines additional quantities of existing input characteristics. In our case, i t would appear that we have been discussing technological change of both kinds. A change in the production function implies that there i s a new way of producing an existing good. The new production function in beef cattle results from the discoveries of applied geneticists who i d e n t i f i e d the increased production expected from cross-breeding. 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 genetic material. The change in the production process i s indicated by the different production function implied from the estimation of (3.18a) and (3.18b). On the other hand, genetic improvement in existing populations, whether they are used in a straightbred system or a crossbreeding system, represent new inputs combining ^additional quantities of existing;; characteristics. Improvements to the characteristics mix of bulls appear to be determined by the prices imputed to the characteristics.; The f u l l r e a l i z a tion of the genetic potential, internalized in the co l l e c t i v e available germ plasm, w i l l depend upon the selective breeding of pure strains. As the purebred breeders would appear to be responsive to short term changes in the expected value of alternative breeding strategies, the maximum attainable genetic improvement may not be achieved. I f there are costs in terms of sustained genetic progress associated with the switching of selection emphasis, as some suggest (Johnson, 196$):, then the breeder response to "spot prices" 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 additional research into such costs should be conducted by economists, and animal s c i e n t i s t s . We s t i l l have not, of course, found any insights into the forces which bring about an innovation that changes the production function. In the beef cattle industry, the crossbreeding innovation i s clearly one externality derived from pure genetic research and i t s subsequent application in other agricultural sectors. In one sense the discovery of hybrid vigour was an accident. S c i e n t i s t s , attempting to find better combinations of characteristics in the existing (straightbred) technology, discovered the technology of crossbreeding. A further case might therefore be made for the funding of basic and applied research. F i n a l l y , in the case of the Canadian cattle industry, the question as to whether the new technology w i l l replace the old cannot, as yet, be answered. It w i l l depend on the relative prices and the rates of genetic progress. Crossbreeding, as a production process, has only been available 127. since the opening of the quarantine stations just over a decade ago, and i s therefore hardly five generations old in the areas of the country where imported cattle were available very early. In terms of most genetic evaluations, five generations i s an i n s i g n i f i c a n t period. In any case, the straightbred technology must remain to provide replacement females for crossbreeding un t i l breeding systems are introduced to provide specialized females. Chapter IV SUMMARY AND CONCLUSIONS An examination of genetic-based technological change in the Canadian beef cattle industry has provided the focus of th i s study. The primary interest 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 agricultural production have been engineered by applied geneticists. The f i r s t step was to iden t i f y the processes necessary for the rea l i z a t i o n of any genetic-based technological .change. These are: 1) expansion of the genetic pool, 2) inbreeding of divergent genetic strains to increase the probability of desired heritable properties in a pure breeding s t r a i n , and 3) crossing of the pure breeding strains 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 cattle 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 far from complete, considerable insights have been gained into the a b i l i t y of market forces to direct the process of genetic improvement. Expansion of the genetic pool in the Canadian beef c a t t l e industry is being accomplished through the formation of breed organizations, the importation of purebred cattle and the establishment of individual breeders. As space in the quarantine stations i s l i m i t e d , s u f f i c i e n t cattle cannot be imported at one time to provide breeding stock for the entire 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 allocation of breeding stock, with breeders locating 129. e a r l i e s t , in areas with favourable market potential. Over time, as the numbers of breeding stock increase through local production and additional 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 cattle and the more progressive ranchers, the present allocation mechanism allows for e f f i c i e n t use of a resource which i s limited in the short term. There w i l l be some loss in e f f i c i e n t allocation of breeding stock because individual commercial operators, located in less favourable market areas, w i l l be unable to obtain the innovation at competitive cost, while favourably located but potentially 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 in certain areas of the country. In other words, an Alberta cattleman, who li v e s in 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 available, 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 in Alberta. The magnitude of the effect on the re l a t i v e income of commercial operators, which w i l l result from some areas benefitting from a s h i f t in the production function while others do not, can not be ascertained at present. Certainly, experience from several green revolution crops and some grains in 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 thing does appear clear, 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 within 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 diffusion of c a t t l e has been the quarantine stations. Given that demand has exceeded the supply of spaces in the quarantine stations, given that domestic prices for some females of new breeds reached $200,000, given that importers pay both the operating and capital costs of the stations, why additional f a c i l i t i e s have not been constructed or private firms have not been licenced to operate s i m i l a r stations i s unclear. Additional quarantine f a c i l i t i e s would not result in a decline in health standards, the maintenance of which should be the sole purpose of quarantine stations. Additional importations would increase the speed with which the diffusion of new breeds could be accomplished by reducing the slow task of expanding the herd of purebred females. The system, as now constituted, provides windfall gains for those who obtain import licences. The policy of allowing the importation of a large number of different breeds through the limited f a c i l i t i e s has also affected the diffusion of new genetic stock. Certain areas of the country, therefore, have access to a wide range of breeds in the i r early states of d i f f u s i o n , while other areas have access to none. In general, the policies of Agriculture Canada which deal with breed importation should be reviewed. The processes of inbreeding and crossbreeding were examined by estimating shadow values for genetic characteristics using price and characteristics information collected at bull sales. The characteristics selected reflected the information about genetically controlled factors which is generally available to the purchasers of bulls. I t was found that the characteristics i d e n t i f i e d were s i g n i f i c a n t in determining the price of b u l l s . The importance of this result should not be ignored. I f the price of bulls did not ref l e c t their genetic ch a r a c t e r i s t i c s , three possible 131. situations would be suggested: 1) that the characteristics selected for measurement by animal s c i e n t i s t s and subsequently ranchers are unimportant; 2) that the purchasers of bulls are ignorant of genetic processes; or 3) that the production process i s heterogeneous. Each of these situations would have particular ramifications for the process of genetic-based technological change. I f the characteristics are unimportant, then relevant alternative characteristics which are important should be i d e n t i f i e d by animal s c i e n t i s t s . Otherwise, there is no method whereby genetic progress can be monitored and ranchers engaged in the collection of the existing set of characteristics 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 for 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. If the production at the farm level proved to be heterogeneous, then the problem would be more severe. Heterogeneous production i s taken here to mean that each farm would derive different r e l a t i v e shadow values for genetic characteristics. In this case, even i f each farm could maximize i t s potential in the short run, the prices received for bulls would not provide consistent information on the shadow value of characteristics and purebred breeders would not be able to determine the appropriate breeding strategy for 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 alternative mechanism would have to be found. The results of Study I I , however, indicate that none of the cases above exist. Bull sales provide s u f f i c i e n t information to influence the direction of genetic progress. The results of Study II also show that commercial producers recognize the change in production relationship when crossbreeding i s i n s t i t u t e d . This i s observable in the prices received for bulls and reflected in the different r e l a t i v e shadow values of characteristics of breeding stock used in the crossbred and straightbred technologies. The significance of the index of calving d i f f i c u l t y in the determination of the price of bulls to be used for crossbreeding indicates that the increase in productivity from the use of the innovation is not as dramatic as o r i g i n a l l y envisioned by many. As calving d i f f i c u l t y can only be measured ex-post for any i n -dividual animal, research into characteristics which are measureable, inexpensive to col l e c t and highly correlated to the expected calving performance of individual s i r e s , should be undertaken by geneticists. One f i n a l question can also be addressed. The most common question asked of those involved in the study of cattle breeding i s , "What i s the best breed?" The results of Study II indicate that the "merit" of particular breeds i s not reflected in the shadow values of characteristics. The commercial cattleman may express his breed preferences by selecting which sales to attend, but the prices he i s w i l l i n g to pay for the genetic characteristics selected in this study do not appear to d i f f e r between breeds. A move to the characteristics 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 catt l e breeding i s conducted (by both economists and physical s c i e n t i s t s ) within the framework of inter-breed comparisons. The majority of empirical analysis conducted attempts to determine whether there are si g n i f i c a n t differences between breeds. Within each breed, however, the animals have a range of values for. characteristics. Market competition w i l l determine whether there are s u f f i c i e n t numbers of 133. cattle-of a particular breed which have the superior genetic potential to ensure that the breed survives. Providing information on inter-breed differences detracts from the e f f o r t of identifying those ch a r a c t e r i s t i c s , across breeds, which affect the production expected from any individual s i r e . The labour of research scie n t i s t s might better be spent developing and expanding the set of relevant measureable characteristics than designing and conducting experiments which attempt to ide n t i f y inter-breed differences. Thinking in terms of goods rather than characteristics is not confined to those conducting economic analysis. Study II also provides evidence to j u s t i f y the use of the characteristics approach when studying technological change. It i s d i f f i c u l t to conceive how any meaningful analysis of technological change in the Canadian cat t l e industry could have been conducted in 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 in terms of the value of i t s chara c t e r i s t i c s , i t does not represent a unique case in production. There are a large number of examples which come to mind where the inputs to production are heterogeneous and unique. It i s more prevalent when the inputs have a biological rather than an ind u s t r i a l o r i g i n . In addition to genetic-based inputs to production in other sectors of the livestock and poultry industry, a number of other examples may be cited. Each deposit of coal, for example, has unique chemical properties which can be expressed in continuous measures. As the chemical analysis must be conducted to establish grades, i t seems that pricing might better be established on a continuous scale rather than for arbitrary grades. Estimation of the shadow values for characteristics could be used to identify deposits which should be selected for future extraction. As with c a t t l e , 134. trees used both for lumber or pulp are graded on the basis of characteristics which are continuous rather than discrete. Information on the shadow values of those characteristics which can be influenced genetically could provide valuable information to forest geneticists attempting to select the characteristics 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 collection of characteristics such as s o i l f e r t i l i t y , r a i n f a l l , aspect, location, improvement, etc., which for the most part can be measured quantitatively. Evaluating land through the use of shadow values for characteristics could provide information on where the most valuable improvements should be undertaken. Studies of labour have tended to assume homogeneity or, at best, a few arbitrary categories. Each i n d i v i d u a l , however, is a unique combination of education, experience and innate a b i l i t y , most of which can be measured as continuous characteristics. By establishing shadow values for such cha r a c t e r i s t i c s , individuals could better determine which characteristics they could improve to maximize t h e i r u t i l i t y . The state could also establish where the highest returns to educational expenditures might l i e . The development of the characteristics 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 inputs, where heterogeneity of inputs i s r e a l i s t i c a l l y reduced to a limited number of standardized combinations of characteristics which can be reproduced in quantity, then a "best" input choice i s possible and analysis similar to Lancaster's applies. The emphasis for improvements to the technology in this case w i l l also be indicated by the relative shadow prices of the characteristics. The use of the characteristic approach in production f a c i l i t a t e s the examination of improvements to existing technology. In the "exotic" cattle case i t would be impossible to identify new goods. 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 characteristics. Improvements to the technology can, however, be examined by studying the changing quantities of characteristics over time. Defining inputs in terms of characteristics would allow the monitoring of marginal improvements to technology over time. The characteristics approach does not improve upon the goods approach in providing explanations of the creation of e n t i r e l y new processes. Neither the characteristics approach nor the goods approach can explain the discovery of crossbreeding. The use of the characteristics approach in production, however, can help identify technical changes which are a true s h i f t in a production function, rather than new good with additional quantities of existing characteristics. A s h i f t in the production function can be i d e n t i f i e d in two ways, either from an addition to the set of characteristics and/or a radical change in the shadow prices of existing characteristics. In goods space such changes in the production function would be covered up by identifying only a new good. Although the s h i f t in * the production function, which results from the introduction of cross-breeding, might have been anticipated in goods space analysis, i t could not be differentiated from additional units of the same input added to the original production function. The change in the shadow value for char-a c t e r i s t i c s of bulls to be used in crossbreeding indicates a s h i f t in the production function. In short, although this study has focused on genetic improvement in the Canadian beef cat 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 characteristics rather than goods may provide. The study has also indicated the limitations of such analysis, p a r t i c u l a r l y delineating what forms of technological improvement might be predicted from the characteristics approach. A great deal of care should be taken to identify a l l the participants in the market when applying the characteristics approach. The same good may be used as an input to a number of productive processes and the shadow prices of characteristics may vary between alternate uses. In the bull example, alternative uses :(sires for commercial herds and purebred herds) were easily i d e n t i f i e d and the auction system allows the price of bulls for alternative uses to ref 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, alternative uses of inputs w i l l s t i l l have different shadow prices for characteristics. I t would seem that in such cases great care would be needed to discern the effects of multiple 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 rela t i n g the price of bulls to characteristics have met with l i t t l e success, primarily, 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 for 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, therefore, 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 in the regulation of the breeding process. I t may also have instigated a considerable waste of e f f o r t in a search for characteristics 137. which would re f l e c t the values cattlemen place on bu l l s . The general conclusion i s that market forces, especially i f unfettered by regulations, can provide the means to expand the genetic pool and influence the inbreeding and crossbreeding process, so that genetic-based technological change in the Canadian beef cattle industry can be attained. The efficiency 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 catt l e and crossbreeding systems has resulted in a large expenditure of resources for experimentation by commercial cattlemen. Some of the breeds'.imported in the last decade may not prove viable and w i l l disappear. This i s also a waste of resources which must be written off as experimentation. One cannot determine whether an alternative mechanism for the regulation of technological change in the beef industry could accomplish the change with less waste of resources. What i s clear i s that sixty 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 British will be used to denote Aberdeen Angus, Hereford and Shorthorn catt le. Although i t is a controversial term, "Exotic" will be used to denote Charolais and al l breeds imported since 1966. 139. Footnotes - Chapter II 1. Of course, one may observe limited adoption by producers who are i d e n t i f i e d as, for example, "Innovators: Venturesome", by rural sociologists (Rogers, 1962) and who presumably receive some consumption benefit from the use of innovations. 2. In one of the few studies of the purebred battle industry, Wendland (1972) shows that transportation costs and advertising costs remain approximately constant per animal unit, until the very largest of enterprises i s reached. As there are, as far as I have been able to ascertain, no purebred operations in Canada with more than 750 brood cows, costs of transportation and advertising might be approximately constant in 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 in the 1930's. Sub-sequently, there were a few breeders established in Canada during the 1950's. However, until the interest in crossbreeding, such breeders remained essent i a l l y hobbyists with l i t t l e commercial market for t h e i r product. About 1960, the Charolais breed began i t s rapid expansion. 4. Brown Swiss cattle have existed in Canada for a long time, but as a dairy breed. However, with the opening of the quarantine stations, animals of the beef type were imported and breeders established in primarily beef cattle areas. 5. Whereby multiple f e r t i l i z a t i o n s are induced in purebred females and then the embryo are sur g i c a l l y removed and implanted into any host cow. This procedure greatly increases the number of heifers produced by each purebred cow. C 140. 6. By changing the level of significance 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 respectively for Zg, 1^, and Z^ . These values are sim i l a r to those of the 5 and 9 year case. 7. Synthetic breeds result from the multiple crossing of established breeds whose offspring are inbred to attempt to establish a new breed with certain desired characteristics. The f i r s t synthetic, Hay's Convertor, was given o f f i c i a l breed status by Agriculture Canada in 1978. 141. Footnotes - Chapter III 1. Presumably, i f a l l land were homogeneous (had the same ch a r a c t e r i s t i c s ) , then such calculations would only have to be conducted for a single piece of land (until the relative prices of making the improvements changed). 2. Of course, some genetic progress can be made through the judicious selection of cows. Further, i t i s obvious that in any mating scheme cows have 50% of the genes. The assumption i s made because, in terms of management, the genetic factors over which a rancher has the most direct control i s the selection of b u l l s . Hence, "Over 90% of the selection advance w i l l come from s i r e selection, with the remainder coming from heifer selection. This results because the sex ratio i s 50 to 50, while only 1 male to 20 females i s required under natural service" (Willham, 1 978, p. 132). Therefore, just as in the tra d i t i o n a l production function s t y l i z a t i o n , Y = F ( X r X 0, X m) where the genetic inputs to production are deleted because they cannot be controlled, the genetic inputs to production which are not internalized 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 heifers, i t i s unlikely that commercial female stock w i l l d i f f e r greatly from the average for those purchasing purebred bull s . - for example, "In U.S. beef production, no such ready source of cross-bred replacements e x i s t s , and i t appears rather unlikely that a segment of the industry w i l l find such production lucrative enough. The design of 142. simple crossbreeding schemes, u t i l i z i n g the crossbred cow in 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 selection of superior bulls i s made on a particular c h a r a c t e r i s t i c , subject to the condition that some minimum level i s retained on a l l other t r a i t s . Geneticists are cognizant that this i s not an optimum selection process and are attempting to develop indexes for selection which take into account the rel a t i v e economic importance of characteristics. As yet these indexes remain in the development stage and are not in general use. These indexes w i l l , however, s t i l l suggest a single most important t r a i t that would have a weighted value. 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 in Terms of  Characteristics: Some Preliminary Considerations, Discussion Paper No. 78-19, (Department of Economics, University of B r i t i s h Columbia). Arrow, K. J. (1975), "The Measurement of Real Value Added", in David, P. A. and M. W. Reder, Nations and Households in Economic Growth, (New York, 1975). Berndt, E. R. and L. R. Christensen (1973), "The Internal Structure of Functional Relationships: Separability, Substitution and Aggregation," Review of Economic Studies, 40 (123), pp. 403-410. Berndt, E. R. and D. 0. Wood (1975), "Technology, .Prices and the Derived Demand for Energy", Review of Economics and S t a t i s t i c s , 57, pp. 259-68. Boykin, C. C. and T. C. Cartwright (1967), Beef Cattle Production Techniques which may have Major Economic Implications for the South, Department Information Report, (Agricultural Economics and Sociology, Texas Agricultural Experiment Station). Burkholder, E. R. (1976), "Breed Decision' Making for Integrated B r o i l e r Operations", Feedstuffs 44 (4), pp. 18-23. Canada Year Book (1978-79), ( S t a t i s t i c s Canada). Carman, J. L. (1960), A Comparison of Several Crossbreeding Systems and the  Prediction of Crossbred Performance, Technical B u l l e t i n , N.S. 19, (Georgia Agriculture Experiment Station). Cartwright, T. C. (1975), "Crossbreeding Systems" in Beef Cattle Science  Handbook (12), (Clovis, Agriservices Foundation). Cattlemen (1976), "28, 68 or more", 39 (12), p. 23. Census of Agriculture (1971). Cordrey, J. (1968), An Economic Study of an Agricultural Innovation: A r t i f i c i a l Insemination, Unpublished Ph.D. Dissertation, (North Carolina State University at Raleigh). Cunningham, E. P. (1974), "Crossbreeding Strategies in Cattle Populations", in Proceedings of the working Symposium on Breed Evaluation and Crossing  Experiments with Farm Animals, (Zeist, Research Institute for Animal ~~ Husbandry). Davis, W. A. (1972), Beef Cattle Performance Selection in Canada, (Agriculture Canada Publication 1480). Dietz, W. (1973), What Size. Beef Cows?, (Edmonton, Alberta Agriculture). 1 4 4-Diewert, W. E. (:1973a), "Functional Forms for P r o f i t and Transformation Functions", Journal of Economic Theory 6, pp. 284-316. Diewert, W. E. (1973b), Applications of Duality Theory, Ottawa, Department of Manpower and Immigration. Evenson, R. E. and Y. Kislev (1975), Agricultural Research and  Productivity, (New Haven, Yale University Press). Evenson, R. E. and Y. Kislev (1976), "A Stochastic Model of Applied Research", Journal of P o l i t i c a l Economy, 84 (2), pp. 265-81. Fellner, W. (1961), "Two Propositions on the Theory of Induced Innovations", Economic Journal , (71), pp. 305-310. French, M. H. (1966), European Breeds of Cattle, F.A.O. Agriculture Study, No. 67, 2 Vol. (Rome, F.A.O.). Gazatteer of Canada, (various dates), Canadian Permanent Committee on Geographic Names, (Geographical Branch, Department of Energy, Mines and Resources). G r i l i c h e s , Z. (1957), "Hybrid Corn: An Exploration into the Economics of Technological Change", Econometrica, 25 (4), pp. 501-522. Gr i l i c h e s , Z. (1960), "Hybrid Corn and the Economics of Innovation", Science, 132 (3422), pp. 275-280. G r i l i c h e s , Z. (ed) (1971), Price Indexes and Quality Change, (Cambridge, Harvard University Press). Hassan, Z. A. and S. R. Johnson (1976), Consumer Demand for Major Foods in  Canada , (Economics Branch, Agriculture Canada 76/2). Hayami, Y. and V. Ruttan (1971), Agricultural Development: An International  Perspective, (Baltimore, Johns Hopkins Press). Heady, E. 0. and J. L. Dillon (1961), Agricultural Production Functions, (Ames, Iowa State University Press!"! Hertford, R., A r d i l a , J . , Rocha, A., T r u j i l l o , C. (1977), "Productivity of Agricultural Research in Columbia", in Arndt, T. M., Dalrymple, D. G. and Ruttan, V. W., Resource Allocation and Productivity, (Minneapolis, University of Minnesota Press). " H i l l , W. G. (1971), "Investment Appraisal for National Breeding Programs", Animal Production, 13, pp. 37-42. Hunsley, R. E. (1 975), Livestock Judging and Evaluation, (Lafayette, Purdue University). Jeffery, H. B. (1971), Biometrical and Economic Analysis of Cow and Calf Variables as Related to Preweaning and Postweaning Performance of Calf, (Unpublished Ph.D. Dissertation, University of Alberta). Johnson, L. E. (1966), "A Breeding Program and Record System for Seedstock Producers", Beef Cattle Science Handbook, Vol. 3, (Clovis, Agriservices Foundati on). Kennedy, L. (1977), "Evaluation of a Model Building Approach to the Adoption of Agricultural Innovations", Journal of Agricultural Economics, 27 (1) pp. 55-61. Kisl e v , Y. (197 9), An Analysis of the Dynamics of Technological Change in  Agriculture, paper presented at the Seventeenth International Conference of Agricultural Economists, Banff, Alberta, Sept. 3-12. ' Kravis, I. B. and R. E. Lipsey (1971), "International Price Comparisons by Regression Methods", in G r i l i c h e s , Z. (ed), Price Indexes and Quality  Change, (Cambridge, Harvard University PressJ^ Ladd, G. W. and C. Gibson (1978), "Microeconomics of Technical Change: What's a Better Animal Worth?", American Journal of Agricultural  Economics, (60) 2, pp. 236-240 Lancaster, K. J. (1966), "A New Approach to Consumer Theory", Journal of  P o l i t i c a l Economy, (74) , p p 132-157. Lasley, J. F. (1978), Genetics of Livestock Improvement, (New Jersey, Prenti ce Hal 1). Le, C. (1976), Equality of Slope Test; Vancouver, University of B r i t i s h Columbia. Leigh, A. E. (1972), Choice of Crossbreeding Systems for Commercial Cattle  Production, (Unpublished Ph.D. Dissertation, University of Guelph). Lipsey, R. G. and G. Rosenbluth (1971), "A Contribution to the New Theory of Demand", Canadian Journal of Economics, (4) 2, pp. 131-163. Lucas, R. E. B. (1975), "Hedonic Price Functions", Economic Inquiry,(13)^2 pp. 157-178 McCarthy, W. 0. (1970), "Factors Affecting Beef. Breed P r o f i t a b i l i t y in Central Queensland", Proceedings of the Australian Society of Animal  Production, 8, pp. 97-108. Marlowe, T. J. and D. E. Bower (1978), "Relationship of the Commercial Cow-c a l f Producer to the Purebred Cattle Breeder", in 0'Mary, C. C. and I. A. Dyer, Commercial Beef Cattle Production, (Philadelphia, Lea and Febriger). Marshall, A. (1920), Principles of Economics, Eighth Edition, (London, MacMillan and CoT] p. 858. 146. M i l l s , H. P. (1964), "The Dynamics of New Products Campaigns", Journal of  Marketing, (28) 4, pp. 60-63. Meullbauer, J. (1974), "Household Production Theory: Quality and the Hedonic Approach", American Economic Review, (64) 6, pp. 977-995. Meullbauer, J. (1975), "The Cost of Living and Taste and Quality Change", Journal of Economic Theory, (10) 3, pp. 269-283. Nagy, J. G. and H. Furtan (1978), "Economic Costs and Returns from Crop Development Research: The Case of Rapeseed Breeding in Canada", Canadian Journal of Agricultural Economics, 26 (1), pp. 1-14. Newman, J. A. (n.d.), Foreign Cattle Breeds for Beef Production, (Alberta Department of Agriculture, Mimeo). Peterson, W. and Y. Hayami (1977), "Technical Change in Agriculture", in Martin, R. (ed), A Survey of Agricultural Economics Literature, (Minneapolis, University of Minnesota Press). P h i l i p s , R. W. (1959), "Untapped Sources of Germ Plasm", in Hodgeson, R. E. (ed), Germ Plasm Resources, (Washington, American Association of Animal Science), pp. 43-75. Pirchner, F. (1969), Population Genetics in Animal Breeding, (San Francisco, W. H. Freeman Co.). Plumb, C. S. (1920), Types and Breeds of Farm Animals, (Boston, Ginn and Co.). Rao, G. R. (1970), Linear S t a t i s t i c a l Inference and Its Application, (New York, John Wiley). The Registration of Animals in Canada, (1975), (Agriculture Canada, 1557). Ricardo, D. (1817), Principles of P o l i t i c a l Economy and Taxation, (London, G. Bell and Sons, 1911). Rogers, E. M. (1962), Diffusion of Innovations, (New York, The Free Press of Glencoe). Rogers, L. F. (1969), Economics of A r t i f i c i a l Insemination and Crossbreeding  on Commercial Cattle Ranches in Washington, Circular 507, (Pullman, Washington State Agricultural Experiment Station). Scheffe, H. (1970), The Analysis of Variance, (New York, John Wiley) Schumpter, J. A. (1934), The Theory of Economic Development, (New York, Oxford University Press, 1961). Shumway, C. R. and E. Bentley, (1974a), "Analysis of Innovations: Dairy and Exotic Crossbreds for Beef Producion", Southern Journal of  Agricultural Economics, 6 (1), pp. 235-239. 147. Shumway, C. R., Bentley, E., Barrick, E. R. (1974b), Economic Analysis of  a Beef Production Innovation: Dairy Beef Crossbreeding, Economic Research Report No. 26, (Department of Economics, North Carolina State University). Slen, S. B. and M. A. Cameron (1969), "Prospects and Potentials in Canadian Beef Production", Canadian Journal of Agricultural Economics, 17 (3), pp. 80-89. Slessor, R. (1979), Personal Communication, Mr. Slessor worked on importation policy for the Canadian Simmental Association. Smith, G. M. (1976), "Sire Breed Effects on Economic Efficiency of a Terminal Cross Beef Production System", Journal of Animal Science, 43 (6), pp. 261-267. Terleckyj, W. E. (1975), Household Production and Consumption, (New York, Columbia University Press). Tobin, J. "Estimation of Relationships for Limited Dependent Variables", Econometrica, 26 (1958) pp.. 24-36. Trenkle, A. and R. L. Willham (1977), "Beef Production Ef f i c i e n c y " , Science, 198 (4321), pp. 1009-1015. Twenty-first Annual Report, Federal-Provincial Record of Performance for Beef Cattle, 1974-75, (1975), (Production and Marketing Branch, Agriculture Canada). Urban, G. L. (1970), "A Model for Analysis of New Frequently Purchased Consumer Products", Operations Research, 18 (5), pp. 805-811. Vickrey, W. (1961), "Counterspeculation, Auctions and Competitive Sealed Tenders", Journal of Finance, (14) 1, pp. 8-37. Wales, T. J. and A. D. Woodland (1980), Sample S e l e c t i v i t y and the Estimation of Labour Supply Functions, Dept. of Economics, U.B.C. mimeo. Wallace, T. D. and V. G. Ashar (1972), "Sequential Methods in Model Construction", Review of Economics and S t a t i s t i c s , (54) 2, pp. 172-178. Warren, D. C. (1974), "Breeding", in Skinner, J. L. American Poultry History, 1823-1973, (Madison, American Poultry H i s t o r i c a l Society). Warwick, E. J. (1973), "Future Role of Simmental, Limousin and Other New Breeds in United States Beef Production", Crossbred Beef Cattle  Series Vol. 2, (Florida University). Webster's Third New International Dictionary, (Springfield, C & G Merrian Co.) 1965. 148. Wendland, K. H. (1972), An Economic Analysis of the Registered Beef Cattle  Industry of South Texas, (Unpublished Ph.D. Dissertation, Texas A & M University). White, K. J. (1977), Shazam - An Econometrics Computer Program, (Vancouver, University of B r i t i s h Columbia). Will ham, R. L. (1976), "Practical Beef Cattle Improvement", in Swan, H. W. and W. H. Broster, Principles of Cattle Production, (London, Butter-worths), pp. 387-404. Will ham, R. L. (1 978), "Beef Cattle Breeding Programs", in O'Mary, C. C. and I. A. Dyer, Commercial Beef Cattle Production, (Philadelphia, Lea and Gebiger). Wilson, R. (1977), "A Bidding Model of Perfect Competition", Review of  Economic Studies, (44) 3, pp. 194-198. Woodland, R. R. (1978) "Sire Selection", in O'Mary, C. C. and I. A. Dyer, Commercial Beef Cattle Production, (Philadelphia, Lea and Gebiger). 149. APPENDIX I EXAMPLE OF DETAILED CALCULATIONS FOR TABLE III 3 AND TABLE III 4 The f i r s t l i n e of Table III reads; BLACKLOCK ANGUS 569 617 595 2.49 2.79 2.72 $54 $71 $175 $215 ** 569 represents the mean weaning weight for bulls of the Angus breed from the Blacklock ranch which were tested in the Saskatchewan Bull Test Station in 1975; 617 represents the bull with the best weaning weight for bulls of the Angus' breed from the Blacklock ranch which were tested in the Saskatchewan Bull Test Station in 1975; 595 represents the mean weaning weight for bulls of the Angus breed from the Blacklock ranch which were tested in the Saskatchewan Bull Test Station in 1977; 2.49, 2.79 and 2.72 represent sim i l a r observations for average daily gain; These values were then substituted into equation (3.19), e.g., r* - r + H r i ( G n T " ^ T ) Gi I + 1 " GfI + _ J ] l l l l _ where for i = weaning weight = G-j G i l = 6 1 7 G i : = 569 Hg. for weaning weight i s estimated at .35 (Lasley, 1978, p. 330) Substituting one gets a predicted value of G.T ,, of 150. G* = 569 + 35 ( 6 1 7 - 5 6 9> i l + l 2 = 577 As Angus are a small breed these values are substituted into the small breeds equation (3.18b), e.g., P D = 4.99(569) + 547.42(2.49) + 52.35(23.85)(1.58) + 754.15(0) - 4372 D = $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 in value of $1853 - 1799 = $54 A s i m i l a r calculation was conducted for average daily gain which yielded an expected change of $71. This suggests that average daily gain should be selected for emphasis in the next breeding period. The values 595 for weaning weight and 2.72 average daily gain represent the observed values for the mean weaning weight and average daily gain of bulls in generation 1+1. Substituting these values into equation (3.18b) gives the change in value which would be expected from the actual improvement, $175 and $215 respectively. Average daily gain received a greater value in improvement as predicted. This i s denoted by ** Where the predicted and the actual deviate i n apparent emphasis, the difference in the predicted values of emphasizing weaning weight or average daily gain are noted - e.g., $47 for the Sparrow ranch. Similar calculations were conducted for Table III 4. APPENDIX II SUMMARY OF DATA USED IN STUDY I FIVE YEAR ESTIMATES BREED MARCH IGIANA Variable Dependent Z l Mean 2.5556 44495. 22.348 1.0926 1.1133 51199. Standard Deviation 1.3827 37848. 16.253 1.2629 0.62918 55560. BREED : MEUSE Variable Dependent RHINE - IJSSEL (MRI) Mean 2.1176 61397. 28.639 1.9412 1.3494 85539. Standard Deviation 1.1663 49007. 18.678 1.8531 0.72689 82074. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : ROMAGNOLA Variable Mean Standard Deviation Dependent Z l 2.8182 71697. 28.037 2.0000 1.2218 90109. 1.2960 40050. 15.471 2.0702 0.42839 63475. BREED : NORMANDE Variable Mean Standard Deviation Dependent 2.0000 1.4720 Z1 82257. 43792. Z 2 29.458 15.648 Z 3 2.3846 2.3288 Z 4 1.1 975 0.45813 Zc 0.102 95E+06 73927. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : SALERS Vari able Mean Standard Deviation Dependent Z l 2.2353 70572. 27.752 2.2353 1.2066 90515. 1.2515 46308.. 14.431 2.2508 0.56740 72399. BREED : PINZGAUER Vari able Mean Standard Deviation Dependent Z l 2.0732 56367. 27.404 1.2439 1.1025 61338. 1.1914 39298. 17.149 1.5777 0.56074 57224. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : TARENTAISE Variable Mean Standard Deviation Dependent 2.5000 1.1547 Z1 69399. 48162. Z 2 28.826 14.058 Z 3 2.0625 1.7689 Z 4 1.3054 0.55728 lr 85122. 64066. BREED : GELBVEIH Variable Mean Standard Deviation Dependent 2.5294 0.99195 Z] 52783. 43776. Z 2 22.772 15.653 Z 3 1.5882 1.6536 Z 4 1.2743 1.2403 lr 63626. 62139. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : BLONDE D'AQUITAINE Variable Mean Standard Deviation Dependent 2.6279 1.1957 Z] 47948. 41598. Z 2 23.238 17.560 Z 3 1.3023 1.5203 Z 4 1.3552 1.6268 Z c 57849. 61067. BREED : SOUTH DEVON Variable Mean Standard Deviation Dependent Z l 2.8889 73284. 37.984 2.4444 1.3341 0.11363E+06 1.2693 46594. 34.677 1.8782 0.66258 90786. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : CHIANINA Variable Mean Standard Deviation Dependent 3.0735 38723. 23.440 1.1176 1.2829 46931. 0.96686 37855. 21.081 1.4815 1.0298 54604. BREED : WELSH BLACK Variable Mean Standard Deviation Dependent Z l 2.6154 75201. 29.581 2.6923 1.0909 95865. 1.3253 44578. 16.119 2.6263 0.54247 85063. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : BROWN SWISS Variable Mean Standard Deviation Dependent 3.6531 48050. 24.760 1.2857 1.2225 53864. 1.2674 37887. 16.272 1.6330 0.87891 56244. BREED : MURRAY GREY Variable Mean Standard Deviation Dependent 3.8723 1(.1538 Z1 52114. 38164. Z 2 27.059 21.263 Z 3 1.3191 1.6564 Z 4 1.1685 0.74680 Zc 60308. 59510. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : MAINE ANJOU Variable Mean Standard Deviation Dependent 3.6735 1.4052 Z1 48732. 40116. Z 2 25.926 21.477 Z 3 1.0816 1.3515 Z 4 1.2056 0.81360 Zr 60161. 60166. BREED LIMOUSIN Variable Mean Standard Deviation Dependent Z l 3.2750 48285. 23.460 1.2500 1.2209 57838. 1.3395 42337. 21.676 1.3540 0.72732 60434. APPENDIX II (continued) FIVE YEAR ESTIMATES BREED : SIMMENTAL Variable Mean Standard Deviation Dependent '2.8736 1.4044 Z1 34351. 35701. Z 2 20.580 18.638 Z 3 0.88506 1.2335 Z 4 1.3249 1.4427 lr 39115. 49000. BREED : CHAROLAIS Variable Mean Standard Deviation Dependent 2.9780 1.4905 Z ] 33230. 35415. Z2 20.778 19.320 Z 3 0.39560 0.78711 Z 4 1.1189 1.5069 Z r 37398. . 57545. APPENDIX II (continued) SEVEN YEAR ESTIMATES 160. BREED : SOUTH DEVON Variable Mean Standard Deviation Dependent 4.2000 1.9346 Z] 81259. 42413. Z 2 34.811 26.820 Z 3 1.9333 1.7512 Z 4 1.1977 0.60480 Zc 0.10521E+06 78748. 5 BREED : CHIANINA Variable Mean Standard Deviation Dependent 3.2500 ' 1.1956 Z] 36914. 37543. Z2 22.658 20.774 Z 3 1.0694 1.4567 Z 4 1.2705 ' 1.0126 Zc 44624. 53910. APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED : WELSH BLACK Variable Mean Standard Deviation Dependent Z l 3.2000 71468. 29.433 2.5333 1.0726 90752. 1.9712 43005. 15.225 2.4746 0.56541 82065. BREED : BROWN SWISS Variable Mean Standard Deviation Dependent 4.6842 1.7528 Z ] 36255. 35716. Z 2 20.563 / 15.611 Z 3 0.94737 1.4132 Z 4 1.1951 0.82180 Z c 41013. 50950. APPENDIX II (continued) SEVEN YEAR ESTIMATES BREED : MURRAY GREY Variable Mean Standard Deviation Dependent 4.6056 1.3988 Z1 39161. 36899. Z 2 23.183 20.386 Z 3 1.0986 1.4457 Z 4 1.1217 0.72820 Zr 44690. 54181. BREED > MAINE ANJOU Variable Mean Standard Deviation Dependent 3.6735 1.4052 Z1 48732. 40116. Z 2 25.926 21.477 Z 3 1.0816 1.3515 Z 4 1.2056 0.81360 2r 60161. 60166. APPENDIX II (continued) SEVEN YEAR ESTIMATES 163. BREED : LIMOUSIN Variable Mean Standard Deviation Dependent 4.2203 1.7818 Z1 39961. 40006. Z 2 20.808 20.421 Z 3 , 1.0339 1.2726 Z 4 1.3047 0.92197 Zr 47007. 55190. BREED : SIMMENTAL Vari able Mean Standard Deviation Dependent Z l 3.7500 28049. 18.964 0.71552 1 .3974 31750. 1.9644 33197. 18.010 1 .1253 1.6853 44545. ) APPENDIX II (continued) SEVEN YEAR ESTIMATES 164. BREED : CHAROLAIS Vari able Mean Standard Deviation Dependent Z l 3.6339 28127. 18.613 0.33036 1.1666 32201. 1.9312 33794. 18.415 0.72768 1.5687 53351. APPENDIX II (continued) NINE YEAR ESTIMATES BREED : BROWN SWISS Variable Mean Standard Deviation Dependent Z l 5 . 2 4 1 8 3 0 9 1 6 . 1 8 . 6 4 9 0 .80220 1 .1589 35046 . 2 . 0 4 0 4 34793 . 1 5 . 4 5 8 1.3352 0 . 8 7 1 2 9 48536 . BREED MURRAY GREY Variable Mean Standard Deviation Dependent Z l 4 . 7 5 6 8 37704 . 2 3 . 1 2 5 1.0676 1 .1858 4 3 2 3 2 . 1 .5599 36830 . 2 0 . 5 1 6 1 .4270 0 .93316 5 3 5 6 1 . APPENDIX II (continued) NINE YEAR ESTIMATES BREED : MAINE ANJOU Variable Mean Standard Deviation Dependent Z l 5.6952 29129. 19.062 0.68571 1 .2057 33888. 2.2750 34408. 18.241 1.0590 1 0142 48325. BREED : LIMOUSIN Vari able Mean Standard Deviation Dependent Z l 4.7500 35658. 19.113 1.0000 1 .2212 41547. 2.1536 38893. 19.552 1.2339 0.89406 53275. APPENDIX II (continued) NINE YEAR ESTIMATES BREED : SIMMENTAL Variable Mean Standard Deviation Dependent 4.2901 2.3907 Z ] 25128. 32280. Z 2 17.55V 17.419 Z 3 0.64122 1.0818 Z 4 1.3346 1.6437 lr 28366. 42958. BREED : CHAROLAIS Variable Mean Standard Deviation Dependent 4.5683 2.5877 Z] 23695. 31821. Z 2 16.789 17.344 Z 3 0.26619 0.66568 Z 4 1.0773 1.4808 Z c 27145. 49291. APPENDIX II (continued) ELEVEN YEAR ESTIMATES BREED : SIMMENTAL Variable Mean Standard Deviation Dependent 4.8690 2.8874 Z ] 23075. 31343. Z 2 17.010 17.294 Z 3 0.57931 1.0453 Z 4 1.3688 1.6775 lc 26285. 41415. BREED : CHAROLAIS Variable Mean Standard Deviation Dependent Z l 5.3438 20987. 15.483 0.23125 1.0623 23896. 3.1384 30484. 16.639 0.62668 1.5628 46716. APPENDIX II [continued) NINETEEN YEAR ESTIMATES BREED : CHAROLAIS Vari able Mean Standard Deviation Dependent Z l 7.0302 17668. 13.744 0.18593 0.99416 20096. 4.5360 28342. 15.516 0.56907 1.4472 43046. APPENDIX III SUMMARY OF DATA USED IN STUDY II * LARGE BREEDS (Equation 3.18a) Variable Mean Standard Deviation Price Weaning Weight Average Daily Gain Index of Calving D i f f i c u l t y 1727.4 569.05 3.3856 1.4491 586.35 83.034 0.41111 0.55675 * Charolais, Simmental, Maine Anjou, Blonde d'Aquitaine, Brown Swiss Salers, Chianina, Pinzgauer. Variable ** SMALL BREEDS (Equation 3.18b) Mean Standard Deviation Price , Weaning Weight Average Daily Gain 1821.4 492.02 3.1244 532 .67 92.012 0.53341 ** Hereford, Aberdeen Angus, Limousin, Shorthorn, Murray Grey, Welsh Black Red Angus. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0095470/manifest

Comment

Related Items