'Ii-my nL-l‘, I I. " “'1‘ 1'" li.-~ I I ‘4‘ x"... . .I. .;':;..I.,\, . - I‘- ' - .5'. '. < J.‘_ ‘-_ Quixaqfw I?" L" I I’m W 3%? ‘3: '51-'43 .l' 'I' «11...; 1'”: I I “f . y I %:"‘.V '3“:sz “" \n‘. '; Ag.” .v ‘0.“ ‘ Mw’gfiy I _\ Ms ~73. “55$ .§:'| 4‘ 0 ', 133:4: WY ."t'ly': ' HI I”. ',.:{."‘.Ix 5:: -'v. "3+" ,' ' 'o"'.‘ ..I§;.f\£9_.."~ ”:3“ I ' C ‘I ' ”its 33L 1‘ M; llvqii¢3| '!'..‘.I:o. 1 “4.x“, "“1.‘ "1\ ~" KG". '. ‘I‘w‘v’fug¢‘).‘.:\ 3‘ fi.. vvfifé, " w- n... . ‘Yl.c"" :6th ‘1’55 1‘ '.‘-' '-\ , ,2‘1" .:I:I ‘\ n .- ‘I‘ . (1 . 1" AL? '33‘33‘? ."‘ I :35: . I.. £13,: 32-. w 3‘ a: 148:3.“ "5:13;? , :0 1:. ‘5‘1'.’ 3 ' ,’ 3*.“ w I"I""£~‘-" ’ ' ., «59‘8"? "\~.' ‘1'." ..—~ - V Illllll ll“: 312 310816 7838 ll'lllll’lllllll LIB RA R Y Michigan State University This is to certify that the thesis entitled Pre-Retirement Exit of Farm Operators: Conceptual Framework and Empirical Study presented by Claude Falgon has been accepted towards fulfillment of the requirements for Ph.D. d . Agricultural Economics egree 1n % flifla/de/{e’lé/ Major professor Date fig /é//Z/ 0-7 539 111+ t... . PRE-RETIREMENT EXIT OF FARM OPERATORS: CONCEPTUAL FRAMEWORK AND EMPIRICAL STUDY By Claude Falgon A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1978 z i?¢:> 39‘ ABSTRACT PRE-RETIREMENT EXIT OF FARM OPERATORS: CONCEPTUAL FRAMEWORK AND EMPIRICAL STUDY By Claude Falgon The number of farm operators has declined drastically in most industrialized countries during recent decades. This phenomenon has often been considered necessary to maintain or improve incomes of farm operators who remained in farming. The number of farm operators is the aggregate and cumulative result of individuals' entry and exit decisions. Causes affecting these decisions will, therefore, bear on farm demography. In order to have the capability of influ- encing the evolution of farm demography to fulfill some pre-determined social goals, one must know the factors which affect the entry into farming, the pre-retirement exit, and the retirement of farm operators. Three main objectives were set for this study: 1. To provide a conceptual framework for the analysis of the decision to leave farming before retirement. 2. To appraise the ability of the Canadian Census of Agricul- ture Match to identify entrants and exiters, and to evaluate its usefulness as a major data source for analytical studies of entry and exit from farming. 3. To test as many hypotheses concerning factors affecting off-farm movement, as the available data would permit. Claude Falgon A review of literature on off-farm movement and migration sum- marizes theories which have been proposed to explain off-farm move- ment and migration, empirical studies conducted at either the macro- level or the micro-level, and policy recommendations which have been formulated. A theoretical framework for the pre-retirement decision to leave farming is developed. The standard economic model of off—farm movement, based on a maximizing behavior, is critically reviewed. Elements for an expanded framework, which are drawn from the economic, psychological, and sociological literatures, are presented. Thus, farming is seen as a form of habitual behavior whereas pre-retirement decision to leave farming is considered as a genuine decision. Farm operators' behavior is looked upon as being of a satisficing nature. The decision to leave farming before retirement is considered as a group (family) decision, where family members often hold conflicting goals or aspirations. These goals are constantly adjusted upwards or downwards according to successes or failures in meeting past goals. Farm operators' decisions are based on reality as it is perceived. Perception of reality is both a screening process, by which some elements are known and some remain unknown, and the organizing of known elements into a meaningful whole. Attachments to the community and to farming as an occupation are important factors affecting pre- retirement decision to leave farming. A newly available longitudinal data base, the Canadian Census of Agriculture Match, is presented and assessed in relation to its use for this study. Methodological considerations on inference and Claude Falgon data analysis are discussed and hypotheses to be confronted to empirical evidence are stated. In preparation for the empirical study, a review of statistical methods for the analysis of qualitative dependent variables is per- formed. It covers the standard linear model, logit/probit-type models, discriminant analysis, measures of association in contingency tables and a multivariate log-linear model with exogenous variables. The empirical study consists of an exploratory and confirmatory analysis of data drawn from the Census of Agriculture Match for the province of Saskatchewan. Pre-retirement exit of farm operators is shown to be positively related to age, value of land and buildings (expressed as a percentage of total capital value) and negatively related to residence on the farm. Inconclusive results are obtained concerning the hypothesized negative relationship of pre-retirement exit to total acreage and total capital value of the farm. Pre- retirement exit of farm operators is shown to be unrelated to involve- ment in off-farm work, degree of ownership of farm land, total sales of agricultural products, productivity of land and of capital, degree of mechanization, and distance to towns. These results prompted a proposal for a longitudinal survey which would fruitfully continue this study. ACKNOWLEDGMENTS A number of pe0ple contributed to the development and fulfillment of this study. I express my appreciation to all. Professor Manderscheid provided, despite the distance between us, the necessary guidance and encouragement during this study. Professor Obst, by remaining critical of my ideas, helped me in making them more precise. Drs. N. V. Candler, K. J. McKenzie, D. McClatchy, J. Nash, G. T. MacAulay, and Mr. M. Mouelhi, all of Agriculture Canada at some time or another, contributed in different ways and at different stages to this study. Statistics Canada and R. D. Bollman made available to me the data used in this study. Professors M. Nerlove and H. H. Stokes provided me with one of the computer programs used in the empirical analysis. Finally, I would like to express my gratitude to Agriculture Canada, for granting educational leave to undertake graduate studies. ii TABLE OF CONTENTS Page List of Tables ....................... List of Figures ...................... CHAPTER I INTRODUCTION .................. l Farm Demography in Canada in the Recent Decades ................... 1 Low Income in Farming ............ 3 Programs Bearing on Farm Demography ..... 6 Small Farm Development Program (S.F.D.P.) 7 Farm Development Loan Board and Capital Assistance Program, Newfoundland ..... 8 Land Development Corporation, Prince Edward Island .............. 8 Establishment of New Farmers--Interest Foregiveness, Nova Scotia ........ 8 Farm Enlargement and Consolidation Program, Ontario ............. 9 Junior Agriculturalist Program, Ontario . 9 Land Lease Program, Manitoba ...... 9 Farmstart, Saskatchewan ......... 9 Green Certificate Program, Alberta . lO Beginning Farmer's Program, Alberta . . . lO Land Use and Farm Adjustment--ARDA, British Columbia ............ l0 Conclusion ................ l0 Definition of the Problem .......... lO Objectives of the Study . . . J ....... ll Relevance of the Study ........... 12 Area Chosen for the Empirical Study ..... 13 Definition of Terms ............. 13 Organization of the Thesis ......... 15 II A REVIEW OF LITERATURE ON OFF-FARM MOVEMENT AND MIGRATION .................. 17 General Scope of the Literature ....... l7 Theories Explaining Off-Farm Movement and Migration ................ 20 iii CHAPTER III IV The Treadmill Theory .......... The Career Theory ............ The "Push-Pull" Theory ......... A Benefit-Cost Model .......... Empirical Studies at a Macro-Level ..... Empirical Studies at a Micro-Level ..... Policy Recommendations ........... Conclusion ................. AN EXPANDED THEORETICAL FRAMEWORK FOR THE PRE-RETIREMENT DECISION TO LEAVE FARMING The Standard Economic Model of Off-Farm Movement .................. The Model ................ A Critical Review of the Behavioral Assumptions ............... The Standard Economic Model and Off-Farm Movement ................ Elements for an Expanded Framework . . . . . Single-Motive and Multiple-Motives Theor- ies of Action .............. A General Model of Individual Behavior Habitual Behavior and Genuine Decisions . Level of Aspiration and Satisficing Behavior . ._ .............. Cognitive Aspects of Behavior ...... Social Aspects of Behavior ....... Summary and Implications .......... DATA, DATA ANALYSIS AND HYPOTHESES ....... The Data Base ................ The Census of Agriculture ........ The Matching Procedure ......... Suitability of the Census of Agriculture Match for a Study of Off-Farm Movement. . Content of the Data-Base ........ Conclusion ............... Inference and Data Analysis ......... Types of Inference ........... Inductive Inference and Hypotheses iv 57 57 59 66 69 7O 74 77 94 97 101 101 101 103 107 111 113 113 113 115 CHAPTER V VI Hypotheses Conclusion One Qualitative Variable Conclusion Reductive Inference and Hypotheses . . . Exploratory and Confirmatory Data Analysis ................ Implication for this Research ..... Age of Operator ............ Off-Farm Work ............. Tenure ................. Size of the Farm ............ Productivity of Land and Capital . . . . Mechanization ............. Distance to Towns ........... Residence ............... Conclusion ............... UNIVARIATE AND MULTIVARIATE MODELS FOR THE ANALYSIS OF QUALITATIVE DEPENDENT VARIABLES One Dichotomous Variable ........ One Polytomous Variable ........ Several Qualitative Variables ........ Measures of Association in Contingency Tables ................. Log-Linear Models of Contingency Tables. Multivariate Log-Linear Models with Exogenous Variables .......... Joint Estimation Using Generalized Least Squares ............. EMPIRICAL FINDINGS ................ Extent of Exit and Pre-retirement Exit from Farming Contingency Tables ........... Discriminant Analyses ......... A Multivariate Log-Linear Model of Pre-retirement Exit from Farming V Exploratory Results from Cross-Tabulations and Discriminant Analyses .......... Page 118 120 121 123 124 127 129 129 130 131 131 142 151 151 163 177 183 186 188 188 191 191 193 Choice of a Model ............ 205 Testing the Model ............ 218 Conclusion .................. 225 VII PROPOSAL FOR FURTHER EMPIRICAL RESEARCH: A LONGITUDINAL SURVEY ................ 227 Assessment of the Analysis of Secondary Data . 227 Highlights of the Conceptual Framework . 227 Shortcomings of Available Secondary Data. 231 A Longitudinal Survey ............ 233 Objectives of the Survey ........ 233 Desirable Features of the Survey . . . . 234 Informational Content .......... 235 Data Analysis .............. 233 Conclusion .................. 233 VIII SUMMARY, CONCLUSIONS, AND METHODOLOGICAL CONSIDERATIONS .................. 239 Sumary and Conclusions ........... 239 Methodological Considerations ........ 247 A Behavioral Approach .......... 247 Statistical Methods and Inference . . . . 248 APPENDICES A NAMES AND DESCRIPTIONS OF VARIABLES ........ 252 B CROSS-TABULATIONS ................. 259 BIBLIOGRAPHY ......................... 274 vi TABLE 10 11 12 13 LIST OF TABLES Farm Holdings in Canada and Saskatchewan ..... Percentage of Farmers by Age Class, 1951 to 1971, Saskatchewan ................... Percentage of Farmers by Age Class, 1951 to 1971 Canada ...................... Comparison of Census Totals and Agriculture Quality Check, 1966, 1971, Prairie Provinces . . . Number of Stayers, Entrants, and Exiters Classi- fied by Age in 1966 and 1971, Saskatchewan . . . . Measures of Association Between Pre-retirement Exit and Some Selected Variables ......... Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Standardized Coefficients Of Discriminant Function for Exiters and Stayers, 64 or Less, Census Divi- sion 7, Saskatchewan ............... Maximum Liklihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate and Trivariate Effects, Comparison with Conditional Estimates, Census Division 7 ........... vii Page 189 193 195 196 197 198 200 201 206 TABLE 14 15 16 17 18 19 20 21 22 23 24 Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate and Trivariate Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate and Trivariate Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate and Trivariate Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate and Trivariate Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables, Comparison with Condi- tional Estimates, Census Division 7 ......... Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Comparison with Conditional Estimates, Census Division 7 ............ Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Census Division 7 ....... Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Census Division 1 ....... viii Page 208 209 210 212 213 214 215 216 217 219 220 ’ph If'lu n) TABLE 25 26 27 Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Census Division 11 ...... Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Census Division 15 ...... Maximum Likelihood Estimates of Main Effects Depen- dent on Exogenous Variables and Constant Bivariate Interaction Effects, Census Division 17 ...... ix Page 221 222 223 LIST OF FIGURES FIGURE Page 1 Constrained and Unconstrained Linear Probability Function, and True Probability Function ...... 134 CHAPTER I INTRODUCTION Farm Demography_in Canada in the Recent Decades In Canada, as in most other industrialized countries, the number of farmers has rapidly decreased during recent decades. Table 1 dis- plays the changes in the number of farm holdings in Canada and Saskatchewan from 1951 to 1976. Table 1. Farm Holdings in Canada and Saskatchewan Year Canada Saskatchewan 1951 617,722 111,586 1961 476,125 93,924 1966 428,794 85,686 1971 366,128 76,970 1976 338,578 70,958 Source: Census of Agriculture, Statistics Canada. For Canada, the average annual rate of decrease in the number of farms was 2.3 percent between 1951 and 1961, 2.0 percent between 1961 and 1966, 2.9 percent between 1966 and 1971, and 1.5 percent between 1971 and 1976. For Saskatchewan, this rate was 1.6 percent between 1951 and 1961, 1.8 percent between 1961 and 1966, 2.0 percent between 1966 and 1971, and 1.6 between 1971 and 1976. The number of farms (and farmers) has been declining at an increasing rate from 1951 to 1971 and thereafter at a lower rate. age (1". farrer vintee I .2" ll 9:: ‘11 (’1 L” J":- (‘1 f\’ —_ n Decreasing numbers of farmers have been accompanied by changing age distributions. Tables 2 and 3 display the age distributions of farmers from 1951 to 1976, for Saskatchewan and Canada. In most pro- vinces the mean age of farmers had been increasing slightly until 1971. In Saskatchewan the mean age of farmers increased from 45.1 in 1951 to 47.2 in 1961, 47.4 in 1966, 48.6 in 1971, and decreased to 47.0 in 1976. In Canada the mean age of farmers increased from 46.9 in 1951 to 48.3 in 1961, 48.8 in 1966, 48.8 in 1971, and declined to 48.4 in 1976. Table 2. Percentage of Farmers by Age Class, 1951 to 1971, Saskatchewan Age Class 1951 1961 1966 1971 1976 Under 25 5.5 3.6 3.1 3.5 6.8 25 - 34 22.2 15.7 13.9 12.6 16.0 35 - 44 25.4 25.9 24.0 21.6 19.3 45 - 54 19.9 25.8' 28.1 29.0 25.9 55 - 50 9.1 12.5 60 - 64 1 17.8 19.5 22.8 9.7 65 - 69 J 14.3 5.4 70 and over 3.6 11.2 10.4 10.5 4.4 Source: Census of Agriculture, Statistics Canada. Table 3. Percentage of Farmers by Age Class, 1951 to 1971, Canada Age Class 1951 1961 1966 1971 1976 Under 25 3.5 2.6 2.2 2.4 3.8 24 - 34 18.3 14.2 13.1 12.8 15.3 35 - 44 25.3 24.7 23.8 22.8 19.9 45 - 54 23.4 . 26.6 27.7 29.1 27.3 55 - 59 10.1 1 1 12.0 60 - 64 ] 20.2 21.5 22.1 9.3 65 — 69 14.4 1 5.4 70 and over 5.0 11.7 J 11.7 10.8 5.0 Source: Census of Agriculture, Statistics Canada. labor I estim‘ farm W1 nearl y farmer farmer CC‘iTJ' The decrease in the number of farmers implies that the amount of labor expended in agriculture has decreased. This, however, under- estimates the decrease in farm labor since, concurrently, the number of farm workers has declined similarly. The decrease in the number of farms and farmers used to be seen nearly unanimously as a necessity by the main parties, including farmers' organizations. External effects of the decreasing number Of farmers, mainly as increased cost of providing public services in rural communities with dwindling population came to be recognized only recently. Since then, it has been realized that the two objectives, healthy rural communities and an efficient agriculture, have become in direct conflict. ‘ Low Income in Farming Low rates of return on farm resources have been considered by most agricultural economists and in many different countries as the major "farm problem.“ Low rates of returns are generally considered to be the direct consequence of a farm resources disequilibrium: resources are not properly allocated between the farm and nonfarm sectors nor are they within the farm sector itself. Low rates of return on farm resources (including farm labor) translate into low income for farm families. The emergence and wide development of multiple job-holding imply, however, that low income from farming does not necessarily mean low income for farm families. Hhen low farm family income is studied, nonfarm sources of income must be considered. Resources disequilibrium is thought to be generated by three fa factors: (1) economic growth,(2) inflation, and(3) output increasing technology.1 Tweeten reviewed critically three theories which have purported to explain the persistence of this resource disequilibrium. These three theories, namely, the fixed resource theory, the decreas- ing cost theory, and the imperfect competition theory lead to contra- dictory conclusions as to the persistency and permanency of low rates of return on farm resources. The fixed resource theory implies that low rates of return are temporary. The increasing returns to size theory implies that low returns will last as long as a majority of farms operate under an economic size. The imperfect competition theory yields the conclusion that low rates of returns are permanent. A minority of economists have argued that in fact there is no resources disequilibrium and no low rates of returns on farm resources: the opportunity cost of farm resources (especially labor) has been overestimated by simply equating it to the rates of returns on nonfarm resources. Perkins,2 for example, maintains that low income in farm- ing is a marginal phenomenon reflecting less the labor market dis- equilibrium than poor career decisions, 1ack of resources when starting farming, and preference for farm life. The income problem appears, then, to be one of low absolute income rather than low relative income. The general viewpoint has been, however, that low returns pre- vail; in the short run, these can be alleviated' by transfer payments 1See Luther G. Tweeten, "Theories Explaining the Persistence of Low Resource Returns in a Growing Farm Economy," American Journal of Agricultural Economics 51 (November 1969): 799-801. 2Brian B. Perkins, “Farm Income and Labour Mobility," American Journal of Agricultural Economics 55 (December 1973): 914-916. or A sive ECOF or high support prices but a long run solution must be found in mas- sive transfer of labor out of agriculture. Some leading agricultural economists strongly expressed such a view: Since agriculture obviously has a surplus labor force, it would seem that returns on resources in agriculture in the long run can be best put on a part with those in other industries by maintaining a growing number of non- farm employment opportunities and by reduging the total farm input and population in agriculture. If farm people are to share in the fruits of technical progress and economic growth in the next decade or two, it appears that the rate of labor transfer from agricul- ture must be increased or the rate of technical advance must be decreased. There is no satisfactory alternative to greater mobility of labor if agricultural incomes are to be increased relative to nonagricultural. Labor must be made more expensive by making it scarce.5 As mentioned previously, transfer of labor out of the farm sector implies, but is not equivalent to, a decrease in the number of farm operators. It was shown in the preceding section that the number of farmers decreased rapidly in recent decades, according to the forecasts and wishes of most economists. This phenomenon does not seem, however, to have alleviated the farm income problem. Darcovich et al. have attempted to estimate the extent of low income in the farm sector in Canada, drawing on newly available income 3Earl O. Heady, "Adjusting the Labor Force to Agriculture," Agricultural Adjustment Problems in a Growing Economy, eds. Earl O. Heady et a1. (Ames: Iowa State College Press, 1958), p. 145. 4Karl A. Fox, "Guiding Agricultural Adjustments," Journal of Farm Economics 34 (December 1957): 1099. 5D. Gale Johnson, "Labor Mobility and Agricultural Adjustment," Aggicultural Adjustment Problems in a Growing Economy, eds. Earl O. Heady et al. (Ames: Iowa State College Press, 1958), p. 171. Irv-I tax data.6 They found that 29 percent of farm taxfilers families in Canada in 1974 were in the low income category, with a high of 52 percent in Newfoundland and a low of 22 percent in Saskatchewan. Con- ceptual difficulties related to the definition of low income cut-offs and the questionable reliability of the data prohibit the consideration of these figures as definitive estimates. These findings support the hypothesis that low income in farming is a real problem, even after nonfarm income has been considered. In conclusion, it must be said that despite its failure to alle- viate low income in farming, massive transfer of labor out of agricul- ture is still considered as the solution provided one forgets the external effects on rural communities: This solution is still advanced as the most obvious one, even though the high exodus rates of the past apparently have not resulted in changing either the income distribu- tion within agriculture or the relative income position of farm and nonfarm people.7 Prggrams Bearing on Farm Demography In this section programs bearing in some way on farm demography are presented. Direct increase or decrease in the number of entries or exits may not be the main objectives of these programs but they all make reference to changing these flows. 6N. Darcovich, J. Gellner and Z. Piracha, "Estimates of Low Income in the Farm Sector, 1974," Working Paper, Agriculture Canada, November 1977. 7Dale E. Hathaway and Brian B. Perkins, "Farm Mobility, Migra- tion and Income Distribution," American Journal of Agricultural Economics 50 (May 1968): 342. Small Farm Development Program (S.F.D.PL) The S.F.D.P. is a joint federal/provincial program, operated, with some variations, in all provinces of Canada. It consists of two major parts: first, a Land Transfer Program (L.T.P.) and, second, Rural Counselling and Farm Management Services. The objectives of the L.T.P. is to enable small farm owners to purchase additional land and to financially assist those who want to enter nonfarm occupations or retire. In other words, the goals are to incite some farm operators to leave farming, either to retire or take up nonfarm occupations, thereby freeing land to enable other farms to reach an economic size. The L.T.P. is thus perfectly consistent with, first, the hypothesis that there is redundant labor in agricul- ture and, second, the decreasing cost theory according to which the majority of farms operate at a size below the optimal economic size. Under the L.T.P., grants are offered to farmers leaving farming, with certain conditions restraining the eligibility. Do these grants constitute a sufficient incentive? It seems this question was not considered at the outset of the program. The objectives of the Rural Counselling Service are to help the individual farmer obtain information and do the analysis required to enable him to decide his future and to assist him in the adjustment to nonfarm employment or retirement. These activities constitute a lever of a different kind from the grant under the L.T.P. These counselling activities have, however, been very limited. It seems that the S.F.D.P. will put more emphasis in the future on counselling services as opposed to grants. An evaluation of the S.F.D.P. is in rh.A..._ 85 ”E 56 E u 0U F progress and should shed some light on the respective effectiveness of grants and services. The objective of theFfirNIManagement Service is to help small farmers who remain in agriculture to develop a commercially viable farm business by providing them with farm management advice. Farm Development Loan Board and Capital Assistance Program, Newfoundland The objectives are to "provide low interest loans for the establishment or improvement of farms"8 and to "increase producti- vity and efficiency throughout the agricultural sector by encouraging individuals to enter the farming profession and assist existing farmers in becoming more productive.”9 Lgnd Development Corporation, Prince Edward Island The Land Development Corporation assists existing farmers and new farmers who want to acquire agricultural land, by buying and selling land and making land improvements. §§tablishment of New Farmers--Interest Forgiveness, Nova Scotia The objectives of this program are to "assist new farmers in purchasing and establishing a farm operation by eliminating the interest payable on borrowed capital over the first two years."m 8A. R. Jones, Policies and Programs for Agriculture--At1antic Provinces, Publication No. 76/13_(Ottawa: Agriculture Canada, 1976), program Nfld.-37. 91bid., program Nfld-38. 10Ibid., program N.S.-41. Farm Enlarggment and Consolidation Program, Ontario One of the objectives of this program is to "enable farmers wishing to retire, relocate or adjust out of agriculture the oppor- tunity to do so."]] Junior Agriculturalist Program, Ontario The objective is to "provide a practical learning experience during the summer for young people from nonfarm homes who are inter- ested in agriculture."12 Lgpd Lease Program, Manitoba The objective is to “purchase farm land and lease it to eligible farm operators who do not have the necessary security to establish or maintain a viable farm unit."13 Farmstart, Saskatchewan One of the objectives of Farmstart is to "assist farmers and potential farmers who face difficulties in developing economic farm units."14 1]A. R. Jones, Policies and Programs for Agriculture--Ontario-- Quebec, Publication No. 76/14 (Ottawa: Agriculture Canada, 1976), program 0-86. 12Ibid., program 0-89. 13A. R. Jones, Policies and Programs for Agriculture-~Nestern Provinces, Publication No. 76/12 (Ottawa: Agriculture Canada, 1976), program M- 63. 14Ibid., program S-51. 10 Green Certificate Program, Alberta This is a joint federal/provincial program whose objective is to “provide a necessary on-farm and institutional training to young people choosing farming as a vocation."15 Beginning Farmer's Program, Alberta A provincial program whose objective is to "assist young potential "16 farmers to become established in farming operations through loans for land, machinery, and improvements. Land Use and Farm Adjustment--ARDA, British Columbia A partial objective is to assist in the withdrawal from agricul- ture of low agricultural capability land by buying land from farmers operating nonviable farms who are willing to sell. Conclusion From the brief foregoing review one can realize that objectives of these programs can be seen as contradictory: some programs tend to accelerate the rate of exit and others to encourage entry. This can only be reconciled if the clients of these programs differ in some relevant way (e.g., age, education, progressiveness, etc.). Recon- ciliation of these programs is certainly a task remaining to be done. Definition of the Problem Different theories purporting to explain low income in farming have been mentioned earlier in this chapter; they stress in different 15 16 Ibid., program A-06. Ibid., program A-57. 11 ways the importance of redundant labor. The resource fixity and the imperfect competition theories identify causes which would influence the decision of a farm operator with respect to leaving farming and would induce him to stay. In doing so, these theories rely on the conventional model of individual behavior; thus, they look for "external" causes of the failure of farmers to adjust out of farming. It is postulated here, that the failure of farmers to leave farming as they are expected according to standard theory has "internal" causes, or more precisely, that the behavioral model commonly used in economic theory does not describe adequately the decision making process actually taking place. Several programs aiming at modifying flows of farm operators into and out of agriculture were briefly presented. These programs have been developed in reaction to political concerns and were designed with little study of their possible effects which depend largely on how each individual farm operator reacts to the different stimuli. Without a clear knowledge of how the decision to enter farming or to leave farm- ing is made, it is impossible to forecast with precision the effects of these programs. This research attempts to shed some light on one of these decisions, namely the decision to leave farming before retire- ment. Objectives of the Study The first objective of this study was to provide a conceptual framework for the analysis of the decision to leave farming before retirement. Because of the many theoretical difficulties, mainly due to the efforts in bringing together elements and results of different 12 disciplines, no pretence is made to propose a well developed and con- sistent theory. The framework will provide, however, concepts to work with and will indicate directions in which further research would be valuable. A second objective was to evaluate a new data base, the 1966-1971 Census of Agriculture Match, with respect to its ability to identify individual entrants and exiters and, consequently, to allow an estimate of gross flows into and out of farming. A third objective was to test some of the propositions and hypo- theses implied by the conceptual framework. This was attempted using the 1966-1971 Census of Agriculture Match. Because of the relative inadequacy of this data base, this objective was only partially met, and this prompted a proposal for further empirical research. Relevance of the Study This study is relevant from a policy and program development point of view and from a methodological point of view. First, it is thought that a good knowledge of factors affecting the decision of farm operators to leave farming is necessary to the proper design of policies and programs aimed at affecting the rate of exits from agriculture. It was shown that political willingness pre- sently exists, even though consensus on which direction the programs should act is absent. Second, major methodological issues are tackled. The adequacy of various models of human behavior is evaluated; results and concepts drawn from economics, psychology and sociology are assembled into an expanded theoretical framework of the decision to leave farming. 13 Problems in statistical methodology are also tackled: the empirical analysis rely on both exploratory and confirmatory analysis; statis- tical methods suitable to the analysis of qualitative dependent vari- ables are reviewed and used either in an exploratory mode or a con- firmatory mode. Area Chosen for the Empirical Study The province of Saskatchewan was chosen to test some of the hypotheses which evolved from the conceptual framework. The reasons fOr this choice were: 1. Saskatchewan is essentially a rural agricultural province where no city is of such importance as to upset and distort what can be called a normal pattern of off-farm movement and migration. 2. The Saskatchewan Department of Agriculture has shown a marked interest in the evolution of farm demography and, more specifically, in factors preventing or prompting the decision to leave farming. Definition of Terms For the sake of clarity, definitions of the terms which are central to this study are presented in this section. No pretence is made that these definitions are the best or the only ones. The value of a term lies in the existence of a precise definition (whatever it is) and its consistent use thereafter. Off—farm mobility. Potential ability of a farm operator or a farm worker to cease working in the farm sector. Off-farm movement. The act by a farm operator or a farm worker to cease working on a farm. l4 Q£§;fgrm migration. The act by a farm operator or a farm worker to leave a farm area. Off-farm migration is related to change of geographical location, to change of residence. Off-farm migration can be considered to imply off-farm movement, but off-farm movement may occur without off-farm migration. Exit from farming. A farm operator's cessation of farming acti- vities. In this study, a farm operator is considered to have ceased farming activities when he is not reported to be an operator of a census farm. Entry into farmi_g. The act of starting to operate a farm. In this study this is construed as meaning to start being reported as a farm operator of a census farm. Pre-retirement exit from farmigg, A farm Operator's off-farm movement followed by his involvement in a nonfarm occupation. Pre- retirement exit from farming may or may not be accomplished by Off- farm migration. grjtgr, A farm operator who exits from farming. §taygr, A farm operator who remains in farming over the con- sidered period. In this study this will be construed as meaning a farm operator who is reported as a farm operator of a census farm both at the beginning and at the end of an intercensal period. Pre-retirement exiter. A farm operator who performs a pre- retirement exit from farming. In this study pre-retirement exiters are identified according to their age, a method which, admittedly, is not without shortcomings. 15 Organization of the Thesis This thesis is divided into eight chapters; this first chapter serves as an introduction. Chapter II is a review of literature on off-farm movement and migration. It summarizes theories which have been proposed to explain off-farm movement and migration, empirical studies conducted at either the macro-level or the micro-level, and policy recommendations which have been formulated. Chapter III develops a theoretical framework for the pre-retire- ment decision to leave farming. First, the standard economic model of off-farm movement is critically reviewed. Second, elements for an expanded framework, which are drawn from the economic, psychological, and sociological literatures, are presented. Chapter IV includes a description of the data base used in the empirical analysis, some methodological considerations on inference and data analysis, and a statement of the hypotheses to be confronted to empirical evidence. Chapter V is a review of statistical methods for the analysis of qualitative dependent variables; it covers the standard linear model, logit/probit-type models, discriminant analysis, measures of association in contingency tables and a multivariate log-linear model with exogenous variables. Chapter VI reports on empirical findings ensuing the use of ex- ploratory and confirmatory data analysis methods. Chapter VII outlines a longitudinal survey which could fruit- fully continue the present empirical study. 16 Chapter VIII provides a summary of this research and an over- view of the methodological problems and issues raised in the course of this work. CHAPTER II A REVIEW OF LITERATURE ON OFF-FARM MOVEMENT AND MIGRATION This chapter is divided into five sections. The first section delimits the scope of the review of literature and provides a frame- work through which various studies can be related to each other and to the topic of this research. The second section is a brief review of theories of off-farm movement and migration which have appeared in the literature. In the third and fourth sections, the main empirical studies of off-farm movement and migration, conducted at the macro- level or at the micro-level, are summarized. The fifth section pre- sents some of the policy recommendations made by economists in relation to off-farm movement and migration. General Scope of the Literature From the following review the reader will realize that numerous studies of off-farm movement and migration have been conducted. Their topics are closely related to pre-retirement exit from farming, but the overlap is far from being complete. Approaches vary greatly and, con- sequently, the degree of relationship to pre-retirement exit should be kept in mind. Most of these studies have been prompted by one of the following general trends observed in recent decades: (1) decreasing number of farm operators,(2) decreasing farm labor force,(3) decreasing farm 17 be d4 Thes. farw fart Of 2370;; into ”UT-b1 REFS the éfigfifi é§8tantially from the model of individual behavior underlying standard economic theory. The principles of adaptive behavior ' are as ‘Follows: Human response is a function both of changes in the 1. environment (stimuli) and the "person".... \ 1 6 3 Ibid., p. 314. 73 2. Individuals (and families) function as parts of broader groups. ... 3. Wants are not static. Levels of aspiration are not given once for all time.... 4. ... habitual behavior prevails. Careful weighing of alternatives and choosing what appears most appropriate among the perceived alternatives is not an everyday occurence. This model of adaptive behavior is not based on any a priori principle of rationality or consistent behavior; it is not, therefore, a normative model of behavior. The principles of adaptive behavior, on the contrary, emerged from empirical studies of actual behavior. A 'I though this model has been developed for consumer behavior, it is argued here that the basic principles have a wider application. Most of Katona's work was in relation to short term fluctuation of demand For goods; as a consequence, the questions arise whether the above model of adaptive behavior has been applied to all its potential re 1 evant range, and whether some modifications are needed to tackle other problems than short run cyclical changes in consumers' demand. Simon proposed a "behavioral model of rational choice" which attempted also to bring more realism to the individual model of behavior used in economics.18 The approach is, however, substantially different from Katona's. It consists essentially of substituting for the 91 Obal rationality" of the classical model an "approximate" rationality "h i Ch takes into account the limited access to information and computing c a'3E1city of individuals. The "approximate" rationality is not considered M ' ahGEOrge Katona, "Consumer Behavior: Theory and Findings on Expectations 1 8d Aspirations," American EconomicReview 58 (May 1968): 20-21. ooHer‘bert A. Simon, "A Behavioral Model of Rational Choice," Quarterly Wm of Economics 69 (February 1955): 99-118. 74 as describing actual behavior, as in Katona's model; it does, however, incorporate some simplifying behavioral features, which are, actually used by individuals in order to overcome their cognitive and computational limitations. Thus, increased realism is achieved without the pretence of actually representing individual behavior. Although Katona and Simon proceeded from different starting points, their models bear much resemblance and share some features. In the following sub-sections the specific points of these models will be introduced and discussed, especially as they relate to the decision to leave farming. Habitual Behavior and Genuine Decisions Katona introduced and stressed the distinction between what he 19 ca 1 led "routine behavior" and "genuine decisions". Classical economic theory, through the assumption of "global rationality", i mplies that all economic agents' actions are preceded by a genuine decision. In contrast to this a priori proposition, empirical Observation shows that habitual behavior is the rule, at least for Consumers. Habitual behavior is a form of behavior where all a'l ternatives for action are not weighed nor even considered before behavior takes place. When circumstances are similar to some previously e"(Iountered circumstances, the same behavior is elicited. Unless one a(3"“Ieres to the very strict definition of rationality, habitual behavior \ ‘I 9 Desge for example George Katona, "Psychological Analysis of Business 46(11 sions and Expectations," American Economic Review 36 (March 1946): ‘51; and Katona, "Rational Behavior and Economic Behavior," pp. 309-3l3. 75 cannot be considered as "irrational" since it takes implicitly into account the consequences of previous actions. In many ways, the existence of habitual behavior is consistent with the radical behaviorist theory of "operant conditioning". Habitual behavior, if examined in a context of incomplete and costly information, could (Dossibly be conSidered to be related to a broader concept of rationality; this aspect will be discussed further in connection with the cognitive aspects of behavior. Thus, it is asserted that habitual behavior is the rule and that very specific conditions are required to enable genuine decisions to occur. These conditions consist of an unusual situation for which habitual behavior has been developed; in this case the individual Genuine decisions are no faced with a problem which he has to solve. ‘i.s; a ‘I so made when the expected consequences of the behavior are potentially e 1" ther very favorable or detrimental, or in game theoretical language, when the "regret“ can be large; such situations are rather seldom encountered. The above distinction between habitual behavior and genuine deC ‘3 Sion is considered here to be of substantial theoretical as well as empirical interest in the area of occupational mobility. This is di Scussed below in relation to off-farm movement and migration. Any active individual must at some early time of his life chOOSe to engage himself in some occupation. Reasons for this choice and circumstances of this choice need not be specified at this time. Hence, some active individuals become farm operators. The activity of 1“ . a"filing, of being a farm operator, is considered here as a specific 3 xample of an habitual behavior. It is habitual in the sense that 76 consequences of farming and of other alternative occupations are not considered, examined, scrutinized, weighed every day nor even every year. Farm operators do not decide to continue farming, they just continue to farm. Some, in fact many, farm operators, however, do decide to leave farming. It is asserted here that such a behavior results from a genuine decision. Circumstances elliciting such a citecision are unusual and consequences of such a behavior are far- reaching and involve not only the professional life of the operator but, in general, his private and familial life. The decision to 1 eave farming is not taken on the spur of the moment but certainly i nvolves a long and laborious decision making process. Leaving farming, thus, comes as the outcome of a genuine dec ision and as a rupture of an habitual behavior. The queStion immediately arises as to what circumstances may render a genuine dec ision possible where before only habitual behavior prevailed. Some drastic changes in the environment or some cumulative effect reaChing a threshold can be hypothesized. Theoretical reasoning SI"IO'..I‘ld yield little further insight into what is essentially an amp ‘7 Y‘ical question. Thus, the distinction between habitual behavior and genuine decision leads up to a whole new area of empirical |r~eS-earch: the investigation of the circumstances which prompt a genuine deg: 1‘ sion. It is fundamental to grasp that, irrespective of the actual 3‘ ternatives, a farmer will remain in farming if the prerequirements For a genuine decision do not exist. In this sense behavior depends as mUCh on the subjective readiness to take a decision as on the actual a 1 ternatives open for choice. 77 Level of Aspiration and SatisficinggBehavior Concepts It is not intended, here, to provide the details of different {asychological theories of motivation, but rather to present the common i:hread which is running through them. According to psychological t:heories of motivation, action by an individual stems from drives, defined as felt needs; action ceases when the drives, i.e., the needs, are fulfilled. Drives and needs are of an all-or-nothing nature. Drives are fixed at a point in time but may vary through time; this Inl'i'll be examined below. From the brief foregoing presentation, it is already apparent that psychological theories of motivation differ on a very important po i nt from the model of the economic man: the concept of satiation, wh i ch is entirely foreign to standard economic theory based on max imizing behavior,is central to psychological theory of motivation. psychology considers that an individual acts to fulfill some fixed ( and limited) needs where standard economic theory assumes that i "d ‘ividuals try to reach as high a point in their satisfaction scale as ‘it is possible. Psychological theories view individual behavior 5‘55; ssiitisficing, where standard economic theory views it as maximizing. As mentioned earlier, needs are fixed at any point in time but their level adjusts through time as the individual's level of 639.; ration adjusts itself. Katona sumarized this process as follows: 1. Aspirations are not static, they are not established once and for all time. 2. Aspirations tend to grow with achievement and decline with failure. 78 3. Aspirations are influenced by the performance of other members of the group to which one belongs and by that of reference groups.20 In a formalized way, goals that are chosen by individuals are "a joint-function of one's estimated ability to reach a goal and the ;)leasure or satisfaction estimated to result from having achieved it."21 Some people have argued that a goal-striving behavior (satisficing behavior), where goals are themselves adjusting upwards with successes or downwards with failures, is equivalent to a maximizing behavior. Such argument would be valid if adjustment in ‘l evel of aspiration were instantaneous; but, to assume such i nstantaneous adjustment is to negate the fundamentally dynamic nature of the satisficing model with adjusting level of aspiration. The model, as it stands, includes two different processes, namely, reaching the goals and adjusting goals to past performances. Time is an i mportant variable, and some lag exists between the achievement of 90a ls and the resulting upward adjustment of aspirations. Furthermore, the environment in which individual behavior takes place is constantly evoj ving: new alternatives for action become possible and other a‘l ternatives become impossible; as a result of this changing environment and the time-consuming adjustment of expectations, goals Iehavior, a satisfied farm-family will not be considering off-farm movement 0" migration whereas, according to a maximizing model of behavior, a farm family, independently of its level of satisfaction, Will weigh costs and benefits of leaving farming. Thus, when maximizing behavior is assumed, the decision to leave farming depends on both the “Family's preferences (assuming them unambiguously defined) and the gjjferences between benefits derived from available occupational 3‘ ternatives. When a satisficing behavior is assumed, the level of \benefits derived from farming is a crucial conditioning variable: if this level is sufficient, differences in benefits between other a‘Iizernatives and farming play no role and the operator will stay in farming. From the foregoing discussion, it appears that a satisficing t“'Odel of behavior is consistent with the occurence of habitual 82 behavior, whereas maximizing behavior is not.23 The same habitual behavior (e.g. farming) continues as long as the individual (or the farm-family) is satisfied; it is only when some of his goals cannot be fulfilled that dissatisfaction appears, and that other alternatives come to be considered; this may or may not lead to a change of behavior. Farm-families' level of aspiration. It was explained above riow the level of aspiration of an individual bears on his behavior. It was also stated that the level of aspiration rises with successes and declines with failures, thereby providing an adapting mechanism, and that it is influenced by performances of other individuals belonging to the same group or to reference groups. The proposition concerning the influence of past experiences on the level of aspiration is particularly relevant to off-farm movement. Among farmers' aspirations are some aspirations concerning income. LOwl-income farmers, because of their many failures to improve their 1" ncome position, should have, according to the level of aspiration As a consequence, low income would theory, low income-aspirations. not constitute an incentive for off-farm movement or migration. % It is true that a maximizing behavior can be made consistent with any behavior by resorting to unknown adjustment costs, uncertainty egarding success in alternative jobs, psychic costs and benefits for gifferent alternatives, etc. ...; it must be understood that, if this ‘ S done, the causes or factors of the action taken are explained by, or 7. hferred from, observed behavior itself which is contrary to the aim of the model to explain behavior by its hypothesized causes. Furthermore, he inferred factors are not easily identified and measured. Thus, a atisficing model offers a more operational basis for experimental S tudies. 83 Downwards adjustment of the level of aspiration to match the actual ‘level of income allows such low-income farm families to be satisfied and therefore they would not seriously consider other occupational and 'locational alternatives; despite the availability of an occupation with a higher income, they would continue to stay and farm. Since this (flownward adjustment of the level of aspiration lags behind performances, only families having received low incomes for a long period of time could be satisfied. A sudden and drastic drop in income, would not be followed inmediately by a corresponding downward adjustment of the level of aspiration; the income record of a farm-family thus provides infor— mation on the present level of aspiration concerning income. It is seen that a satisficing model of behavior is not inconsistent with i ncome differentials between farm and nonfarm sectors, nor with ‘3 ncome differentials between regions. Level of aspiration depends also on performance of individuals belonging to the same group or reference groups. If it is assumed that 1 Ow-income farmers consider themselves as belonging to the group made of the farmers of the area, their level of aspiration (concerning "3 hcome) will be positively affected by higher average income in the aV‘ea. Thus, low-income farmers' levels of aspiration will differ a(Icording to whether they are located in a high-income or a low-income 1:ar‘ming area. The same influence can be hypothesized between the a\Ierage income of the reference group and the level of aspiration. The extent to which farmers take urban comunities as their reference Qr‘oups can be hypothesized to be inversely related to the distance to an urban center or directly related to the number and frequency of Q><<:hanges and contacts with an urban center. Given that urban centers are 84 usually characterized by higher monetary income, the level of income aspirations of farmers would be higher the closer they are to an Ieran center. Identification of farmers' reference groups and their (description in terms of past-performances will shed some light on 1Farmers' levels of aspiration and potential for off-farm movement. Fiegional analyses may show that farmers in different regions or sub- r~egions have different reference groups, with different levels of i ncome; this could explain the existence of different levels of aalspiration and lack of incentive for off-farm movement and migration. IZJistance to urban centers can be hypothesized to be negatively related to off-farm movement and migration via its effect on level of aspiration. Consideration of imperfect information can also lead to the same hypothesis on the relationship between off-farm movement and distance to urban centers; this will be examined in the next sub-section. Conclusion. A satisficing model of behavior displays a number of advantages over a maximizing model of behavior: l. It is potentially more useful in analyzing how individual goals are articulated in a group situation (e.g. in a family) and how Qr‘oup decisions are taken. 2. When goals are considered to depend on a level of aS-piration, itself a function of past-performance of the farmers or of ‘3 ndividuals in reference groups, a satisficing model explains the lack of off-farm movement and migration inspite of substantial farm-nonfarm ahd urban-rural income differentials. This phenomenon has usually been QOnsidered as an abnormality in a standard economics context based on a maximizing model of individual behavior. 85 3. It does not resort to a residual such as "psychic income" to explain behavior, and is therefore more adapted to empirical studies. Cognitive Aspects of Behavior The major contention made in this sub-section is that individual behavior is dependent on or elicited by perceived changes in reality; this entails that the study of the process of perception or cognition is of paramount importance to understand and explain individual behavior. This contention can be explained further by :stating what it rules out: (l) behavior is not elicited by objective treality or, in other words, a change in objective reality is truly a sstimulus only insofar as this change is perceived by the individual, (2) behavior is not considered capricious or random since it is elicited by changes in real conditions (as they are perceived). Thus, t><>th the changes in the environment ang_the perception of these changes play a role in individual behavior. COQnition as Limited Knowledge As it was explained earlier, the standard model of individual behavior ignores all cognitive aspects of behavior. In recent years ‘tlliough, economists have attempted to relax the assumptions of perfect knowledge and foresight which appeared as more and more unrealistic; these assumptions were eliminating from the'analysis important economic ‘Elgztions such as job-search, information gathering, speculation and management. These efforts have resulted in two main approaches: (1) the Bernoullian decision theory whose development is concomitant with a 86 revival of cardinal utility theory and a renewed interest in Bayesian theories of probability.24 (2) the information-as-a-commodity approach which retains the deterministic framework but simply includes information as an additional commodity; information is then produced and exchanged just as another commodity. This approach may be theoretically interesting but is of very little practical interest.25 In both cases, economists have tackled the problem of cognition in a 'very formal way: some axiomatic model of individual behavior (rational or consistent) is assumed without any reference to empirical evidence; :such models of individual behavior are, again, normative rather than [positive. These approaches to uncertainty are aptly called: economics vuith limited knowledge; the word limited expressing that the difference between the objective reality and perceived reality is a matter of a saugantitative lack of information; this implies that by securing more of izlie same kind of information this gap is reducible. Uncertainty and ‘l ilnited knowledge are concepts related to a strictly quantitative <2<3nception of information and cognition.26 For a good everview of Bernoullian .decision theory see Dillon, .‘ O O 0 I Ikev1ew of Bernoullian Dec151on Theory." sThe shape of the production function with respect to information is §§I1pposed to be known (with certainty). The problem of measuring 1 nformation, which is essential for any application of the theory, is evaded. 6It.should be stressed that Knight's classical distinction between $3 ituations of uncertainty and of risk is negated by the Bernoullian ‘tlheory of decision. Subjective probabilities assigned by the individual "ita events are a measure of the uncertainty attached to these prospects; '1<) reference to (objective) probabilities of these prospects is needed. 87 Uncertainty (or limited knowledge) can occur at different levels. First, an individual may not know of all possible courses of action which are available to him, though he may know that more are available to him than he is aware. Second, some consequences of the action chosen may be completely ignored or some mutually exclusive consequences may be known as possible without knowing which one will actually occur. The mere fact that the individual realizes that he has a limited knowledge is also very important, since, in this case, he can decide to look for, buy or produce more information. The approaches described above, despite their limitations, are :successful in making such phenomena as search for nonfarm . (apportunities, return migration, and information disseminating public FJrograms consistent with the standard economic model of economic behavior. Search for nonfarm occupation alternatives is possible, because iilie farm operator knows that some nonfarm occupations are available, Eirid necessary because he has no immediate and complete knowledge of '1zlmem. The fact that the labor market is not characterized by the exehange of a homogenous product with a well-known price, together with ‘tllie existence of limited knowledge imposes search of both sellers and buyers of labor. Search itself is a costly process since it uses resources; one Of the main elements of the cost of search is the opportunity cost of ‘tl‘hne'spent in search activities. The assumption of a deterministic "‘1elation between information and production (i.e. ultimately returns) ‘3 8 only a way to displace the incidence of uncertainty. Actually, the 88 relationships between search and information and additional information Individuals take into account this and returns are not deterministic. The element of uncertainty in their strategy for job—search. information-as-a-commodity approach fails to account for the important role of strategy in search. The strategy followed by farm operators in searching for nonfarm occupations will heavily depend on their psychological make-up. Blau and othersZI proposed a conceptual scheme of occupational choice which accounts for uncertainty and which can be adapted to «off-farm movement, considered as a change of occupation. Farm (operators seriously considering leaving farming have some preferences (:oncerning nonfarm occupations in which they would engage; these rareferences may be conceived as being a ranking of these occupations. Whether or not they will actually enter the occupation ranking the fi'ighest in their preference does not depend only on their choice but 61 so on someone else's choice. In most cases, actual opportunities o‘f’ farm operators are determined by other agents who can be aggregated Under the label "selector".28 At every moment farm operators do not know with certainty these alternatives. Some subjective probability ?‘ - 7Peter M. Blau et al., "Occupational Choice: A Conceptual Framework," ‘1 '1 Personality and Social Systems, eds. Neil J. Smelser and illiam J. Smelser (New York: John Wiley and Sons, 1970), pp. 559-57l. 28 . . ,. Thus, the term "selector" 15 used here as a generic name meaning all 7‘ individuals, practices, agencies and institutions which have some power <3 choose among job applicants and on which job applicants have no Q(antrol . 89 of actually getting a job is attached to each of these occupations. The actual nonfarm occupational choice is a compromise between the farm operators' preferences and these likelihoods of getting a job. These probabilities are certainly revisable on the basis of experience, and this revision is an essential element of job search which bears heavily on the strategy followed. Failures to secure jobs in occupations ranking high in their preferences will force farm operators to look for lower-ranking occupations; as a consequence, the level of aspiration concerning occupational choice will be lowered. Since search is a process, time is also an essential element of job-search: how long will (or should?) a farm operator wait until he adjusts «downwards his level of aspiration? All these elements of job-search Ipear directly on whether the pre-retirement decision to leave farming ‘is made or not. Engagement of a farm operator in part-time nonfarm work is 14sually deemed to increase off-farm mobility, because information on nonfarm occupational opportunities is a by-product of this engagement, ialt little or no cost to the farm operator. Viewed in this way, off-farm \noork may not facilitate off-farm movement, because, as it was stressed I:Defore, the nature of this information on nonfarm occupation may not IZDe conducive to off-farm movement. What can, however, reasonably be ‘5! ssumed is that farmers with off-farm experience are likely to make IDetter informed choices, and that consequently less return movement or Migration will occur among them. Return movement and migration are phenomena yet very little investigated, but whose existence has been 90 been proven.29 Such return movement is inexplicable in a world of certainty, maximizing behavior and stable preferences, but, it is explicable within the context of Bernoullian decision theory. An individual may make the right choice in term of some criterion (e.g. expected value of utility) and, still, consequences may yield a lower utility, thereby justifying a reversal of the previous decision. Dissemination in farming areas of information concerning the nonfarm labor market and living conditions in urban areas influences decisions made by-farm operators in two ways: (l) it provides them with knowledge of nonfarm job opportunities which they did not have before, and (2) it provides them with more precise expectations conCerning the (consequences of off-farm movement. Thus, dissemination of information is a policy variable. But too many have assumed the direction of the effects of increased information to farm operators. A priori, better known opportunities and clearer expectations as to the consequences of a3 pre-retirement decision to leave farming could favor remaining in irarming. The effect of such increased information depends on how this ‘information is interpreted by the individual farm operators. ::295ee for example: Dale E. Hathaway and Brian B. Perkins, "Occupational I“iobility and Migration from Agriculture," In Rural Poverty in the Eggnited States, A Report by the President's National Advjsory Commission (:In Rural Poverty (Washington: Government Printing foice, l968), Dp. 185-237; and Eldon D. Smith, "Nonfarm Employment Information for Rural People," Journal of Farm Economics 38 (August 1956): 8l3-827. 9] In summary, the approach taken by traditional economists to tuackle the cognitive aspects of behavior, has been through the use of a. strictly quantitative concept of information. In the following $11bsection different concepts and conclusions are presented, inspired by a school of psychology. known as Gestalt psychology. The Gestalt Theory of Perception Katona summarized the main results of the Gestalt psychology (Jr: ‘the importance of perception for human behavior: The response is determined by what the stimulus means to the respondent; it changes when the meaning of the stimulus changes. Meanings are not just a matter of subjective interpretation. It is the setting or context of the stimulus, the greater whole of which it forms a part, which determines the meaning of the stimulus. The same stimulus may elicit different responses if it is pegfieived or understood as the part of the one or other whole. Katona goes on to explain that, since the individual's reaction depends on the meaning attached to the stimulus, the question of how meaning is acquired will yield the answer to the question of what ‘j‘ETIGEanines reaction. Meaning can be acquired through mere repetition ("‘ 1tlirough understanding. Understanding implies organizing or re‘Organizing different parts into a new whole where individual parts Eiopemz ”mueaom .cowuucam auwpmnaaocn was“ ace .cowpucse auwpwnmnoca comcwp umcwmcumcoucz use cu:_mcumcoo .P_me:mwm \\\ cowuee_xocaa< m:_4 cmxogm max o ms . vmcwecpmcoo < cappucze was» '91 JD a covueewxoeaa< mama coxocm \\ teammeumcou :owuuc:$ \\\ gmchP umcwmcumcooca e Amuxva 135 variables: bunched data on one side will provide very different estimates from the one obtained with data covering regularly the whole span.7 This last point may not be very relevant to experi- mental situations since, in such cases, the analyst can control the values taken by the explanatory variables; it may, however, be very relevant to nonexperimental situations where the explanatory variables are not controled. Because there is heteroskedasticity, the proper estimator is Aitken's generalized least squares estimator (O.L.S.). If the dis- turbances are assumed not to be autocorrelated, the O.L.S. estimator is a form of weighted least squares where the weights used are the inverse of the variances of the disturbances. These variances are equal to E(yt)(l-E(yt)), and can be consistently estimated by yt(i-yt), where yt is the calculated value obtained from an O.L.S. estimator; yt may lie outside [0,1] and, consequently, some of the estimated variances may be negative, which is theoretically impossi- ble. In view of this ultimate difficulty the above two-step estima- tion procedure seems often impractical. A third possible approach to estimating the linear model, be— sides 0.L.S. and O.L.S., consists of the use of a constrained least squares estimator. Figure 1 shows that the broken line ABCD is a close approximation of the true sigmoid curve except in the two corners B and C. The process of fitting a broken line to a number of points is, however, rather complex; two major shortcomings of this 7See Nerlove and Press, Log-Linear and Logistic Models, p. 8. 136 method are: (1) it is reliable only in large samples, and (2) it ignores all the distributional properties of the error terms. As a consequence of the aforementioned inadequacies of the linear model in the case of a binary dependent variable, some other models were developed and are presented below. The Logit/Probit-Type Models Logit and probit models were originally developed in relation to experiments studying the toxicity of drugs in terms of their qualitative effect (e.g., death) on a population of animals or vege- tables. In their early development, 1ogit and probit models applied only to the case of a one binary variable dependent on a single con- tinous variable. Also, since biologists could experiment on large populations with controls on the independent variable, the data were grouped by value of the independent variable and the dependent vari- able was considered to be the frequency of occurence of the qualita- tive effect for each group; thus, the models were truly applied to the study of a continuous limited variable dependent on a continuous independent variable. These models were thereafter extended to deal with several independent variables and ungrouped data. The common feature of the logit/probit-type models lies in the use of a sigmoid-like function mapping the probability pt of the event, belonging to [0,1], into a transform taking values on the interval [-w , +‘w]. The transform of pt is then expressed as a linear function of the exogenous variables: _ -1 2t - F (pt) an im W111 It. and Thu 1 On: 137 and 2t = xtB, imply pt = F(xtB). where pt = the conditional probability that y = 1 given xt, F = a nondecreasing function of xtB, x = a 1 x (1+k) vector of independent variables, a (1+k) x 1 vector of coefficients. Choosing different transform functions of p will yield different models. It should be clear that any cumulative distribution function (c.d.f.) can be chosen. The most widely used, the logit and the probit models are presented below. The logit model is obtained when the c.d.f. of the standardized logistic distribution is used as transformation; pt is given by: -x 8 pt = l/(l + e t ). Then, logit (pt) is defined as follows: logit(pt) = 1n [pt/(l-pt)]. It follows that logit (pt) = xtB + at, and E [logit (pt)] = xtB. Thus logit (pt), which takes values on [-w, + 00], can be regressed on xtB and B can be estimated using O.L.S. Pr ”915 Neil Hum 03: be the 138 The probit model is related to the c.d.f. of the standard normal distribution: V Pt = (Um) It exp (-1/2u2) du, —oo vt = xtB, th observation. xt = the vector of exogenous variables for the t Probit and normit are defined respectively as: Probit (pt)= v + 5, t Normit (pt)= vt. The logit and probit models can be estimated in two ways: (1) minimum logit x2 (normit x2), and (2) maximum likelihood. The minimum logit x2 (normit x2) is equivalent to applying weighted least squares on the logits (normits). A solution requiring neither approximation nor iteration can be obtained. The maximum likelihood function is: = T y l-y L(B) t1] Pt t (1-Pt) t y l-.Y = 2‘1 [F(Xt8)] t [1'F(xt8)] t“ This function can be maximized with respect to 8, usually by numerical methods since analytical methods generally lead to solving a system of nonlinear equations. The minimum logit x2 (normit x2) estimators have been shown to be asymptotically equivalent to the maximum likelihood estimators; they are RBAN (regular best asymptotically normal) and therefore as; eii of SQL tag ex; tic 910 Mr con tha com 039 is GY‘Q murn N0" 0 _" 139 asymptotically efficient.8 These results imply that, for large samples, either method can be used indifferently. Little is known theoretically of their properties in small samples. Estimators based on the least squares principle (minimum logit x2 or normit x2) present some advan- tage over maximum likelihood estimators since only knowledge of the expectation and not of the specific functional form of the distribu- tion is required. On the other hand, (1) the values of the logit x2 (normit x2) obtained in the minimum logit x2 (normit x2) are unstable when few observations exist for each group of observations, and (2) the logit x2 (normit x2) estimation method breaks down when some groups of observations contain only ones or zeros. ’This latter point is of special interest to economists who rarely work in an experimental situation and who very often wish to consider many exogenous variables. In such conditions, it is likely that there will be only one observation for each value of the linear combination of the exogenous variables; thus, the minimum logit x2 (normit x2) method is usually not applicable. Berkson9 proposed the use of "working values" for cells containing only zeros or ones; this is not possible, however, when all cells contain only zeros or ones. Grouping of observations may therefore be necessary to use the mini- 10 mum logit x2 (normit x2) method. Monte Carlo studies show that 8Ashton, The Logit Transformation, p. 34. 9J2 Berkson, "Estimate of the Integrated Normal Curve by Minimum Normit x with Particular Reference to Bio-Assay," Journal of the American Statistical Association 50 (June 1955): 534. 10Daniel McFadden, "Quantal Choice Analysis: A Survey," Annals of Economic and Social Measurement 5 (Fall 1976): 373. minh larg maxi logi the a 10 this take Iimi vari feds Pear Und, tlc the. 0f 140 minimum logit X2 estimation with grouping yielded lower variances, larger biases, and comparable mean square errors when compared to maximum likelihood estimation; this would tend to show that minimum logit X2 , after grouping data and correcting for the bias, is possibly the best method. It should be stressed that grouping of data implies a loss of information which is positively related to the extent of this grouping; consequently, the aforementioned results are to be taken with caution and on the understanding that grouping is of a limited extent. It can be stated that when the number of exogenous variables increases there comes a point where grouping is no longer feasible; maximum likelihood methods should then be used. The goodness of fit of the model can be assessed through the 2 or logit x2 (or normit X2)- Pearson X Tests of hypothesis can proceed in two ways: 1. Using the property that minimum logit X2: minimum normit x2 and maximum likelihood estimators are asymptotically normally distributed, and estimating asymptotic variances from sample variances. 2. Using the likelihood ratio test obtained by dividing the maximum likelihood under the null hypothesis by the maximum likelihood under the alternative hypothesis; this likelihood ratio is asympto- tically distributed as chi-square and easy to obtain when maximum likelihood estimation is performed. The logit and probit functions are very similar and, usually, the logit model is favored on the basis of the ease of computation of its likelihood function. Dis sta vec or tic cm be! the sex lir use We dE\ aPl so be' Wh: 141 Discriminant Analysis Discriminant analysis belongs to the family of multivariate statistical techniques related to factor analysis. Suppose that a vector of continuous variables is observed on a set of individuals or objects known to belong to a certain number of different popula- tions; then, discriminant analysis can help the experimenter in dis- covering whether or not a reduced set of variables discriminates well between these populations. Discriminant analysis can also enable the experimenter to classify an individual or object into one of several populations, on the basis of the individual's score on the linear discriminant function. Thus, discriminant analysis can be used for two purposes: (1) descriptive, or (2) decision-making; here we will concentrate on the former. Discriminant analysis will be described in detail in the section devoted to the case of one polytomous variable. All the results apply to the special case where individuals belong to two populations, so that a binary variable specifies the population to which they belong. A few specific points deserve to be mentioned here. Only one discriminant function exists and it is the long-known linear discriminant function of Fisher,11 _ 2 a '1 1 whose corresponding eigenvalue is: e = (N1N2/N2)(y]'y2)' T-1 (y1-y2)’ 1]R. A. Fisher, "The Use of Multiple Measurements in Taxonomic Problems," Annals of Eugenics 7 (September 1936): 179-188. T1 M US ta‘ the The of 0&8 142 where N1, N2 = the number of individuals in populations 1 and 2, N = N1 + N2 y], y2 = the mean vectors of observed variables for populations 1 and 2, T the total covariance matrix. The eigenvalue, e, is the Mahalanobis D2 premultiplied by N1N2/N2 which is a measure of the distance between two groups of observations using the metric distance defined by the total covariance matrix.12 In the two-class case, linear discriminant analysis is comput- tationally equivalent to ordinary least squares estimation of a linear model with a binary dependent variable.13 The regression line and the discriminant function only differ by multiplicative constants. The choice between the two procedures should be based on what kind of distributional assumptions the experimenter is ready to make. One Polytomous Variable In the above section, the case of one binary qualitative depen- dent variable was examined. A qualitative variable can also describe the fact that an individual may belong to more than two categories; such a qualitative variable is called a polytomous variable. Two methods are presented below: a multinominal logit model and dis— criminant analysis. 12Jean-Marie Romeder, “Methodes et Programmes d'Analyse Discriminante (Paris: Dunod, 1973), pp. 49-50. 13This point is examined in detail in George W. Ladd, "Linear Probability Functions and Discriminant Functions," Econometrica 34 (October 1966): 873-885. V1 at $6 01“ whe 0:! 96c 143 Multinomial Logit Theii14 extended the dichotomous (binomial) logit model to the case of a polytomous variable. He started from the version of the dichotomous logit model, where explanatory variables are of two types: (1) explanatory variables related to the categories of the dependent variable, in which case they enter as a ratio, (2) explanatory vari- ables related to the individual, in which case they enter by them- selves. More formally the odd ratio is:15 m Bh n Yk (p/l-p) = exp(a) hzlxh k2] (yk1/yk2) . or in a logarithmic form, m 11 109(p/1-p) = a + hElBh 109(xh) + kilvk 109(yk1/yk2). where xh = a variable related to the individual facing a binary choice (h = 1,. . .,m), yk = a variable taking different values for the different alter- natives facing the individual (k = 1,. . .,n), a’Bh’Yk = parameters to be estimated. In the case of a multinomial logit model with P alternatives, , P each alternative has a probability pi such that 2 pi = l. The i=1 ' odd ratioican be expressed similarly for each pair of alternatives: 14H. Theil, "A Multinomial Extension of the Linear Logit Model," International Economic Review 10 (October 1969): 251-259. ‘5Ibid.. pp. 251-252. whe due of par sid bil act pro Var INTI Sul- Dig met 144 B .. n Ykl' pixpj = exp (aij) hE] xh . where Isj = 1,. . .,P. _Many constraints exist on the coefficients of these equalities due to certain symmetries and "circularity" relations; the number 16 This number of of parameters is, thus, only (m + l)(P - l)1+ n. parameters may become large when the number of alaternatives con- sidered in the model becomes high. The ratios of pairs of proba- bilities can be estimated using these:equalities;estimation of the actual values of these probabilities can be obtained using the pro- perty that they add up to one. A mathematical expression for the infinitesimal changes in probabilities resulting from infinitesimal variations in explanatory variables can be derived as well as a global measure, based on information theOry, of the change in the probability structure re- sulting from changes in explanatory variables. Discriminant Analysis As mentioned previously discriminant analysis is a statistical method which is used to find a set of linear discriminant functions.17 These discriminant functions allow the analyst to determine if a subset of variables discriminate effectively between the several populations considered and to classify yet unclassified cases (indi- viduals or objects) into one of the original populations. 16Ibid., p. 253. 17Only linear discriminant analysis will be considered in this section. la ar ap fo Th of Dr nan Dam Qua Let Th R01 145 Discriminant analysis is quite often used and presented inde- pendently of any distributional assumptions; when this is done, dis- criminant analysis is considered as a descriptive multivariate statistical method which provides a specific insight into what is a complex mass of data. Statistical inference, in the sample to popu- lation sense, is then disregarded, and the analyst works in the data analysis framework which was discussed in Chapter IV. Such an approach is taken here in presenting discriminant analysis and, there- fore, distributional assumptions will be introduced at the end.18 This presentation is consistent with the essentially descriptive role to which discriminant analysis was confined in the empirical part of this study. Discriminant analysis requires the existence of several groups or populations of individuals. Typically, a group is described by a name; for example animals belong to different species, each having a name. The belonging to a certain population can be expressed by a qualitative (usually unordered) variable. Let: x be the set of N individuals or objects x, on which p variables are measured (x is, thus, a p-vector); X is partitioned into K classes y; . Y be the set of classes y, with Ny individuals each; wx = l/N be the weight assigned to x. The total weight of the scatter X is 18The presentation proposed in this section is based on: Romeder, Analyse Discriminate. The SC& 0? The CEIl‘ Whel the axis be and The 07‘ 146 Wx = XIWXIX cX}= 1. The total weight of the scatter y is w = Z{wx|x ey}. y y will also represent the mean vector or center of gravity of the scatter y: y = (l/wy) X {wxxlxeY} or y = (1/Ny) )3 {xlch}. The total variance of the scatter X, with respect to its mean, or center of gravity is: - 2 VX = 2{wx (x-x) Ix ex}, where x is the overall mean vector of x. Let u be a vector in the Rp space. The variance of u for X is the variance of the orthogonal projection of the scatter x on the axis defined by u. Thus. total variance of u is - - 2 Vx(u) - Z{wx u(x x) IXEXIs between-class variance is VY(u) = my u(y-x)2Iy av}. and within-class variance is _ 2 Vy(u) - >:{wx u(x 3’) IX ey}. The theorem of Huygen19 implies that Vx(u) = £{Vy(u)|y eY} + VY(u), or in other words: total variance - sum of within-class variances + between-class variance. 19Ibid., p. 41. To the Aga The as l COVl' As 1 axe Wel CT‘i tln 0f 0r 147 To these total, within-class, and between-class variances correspond the total, within-class, and between-class covariance matrices: T = (tij), tn. = (l/N)Z{(x1. - 2].) (xj - ij)|xcx}. N = (WU), w-ij = (l/N){Z{(x.i - yi)(xj - yj)|x €y}ly€Y}’ B =(b1j)’ b1j= Z{(Ny/N)(y1-- i1)(.¥j " ij)I,YEY}. Again, the theorem of Huygen implies the following equality: T = W + B. The total, within-class and between-class variances can be expressed as quadratic forms, using the total, within-class, and between-class covariance matrices: Vx(u) = u T u', VYM Vy(U) As stated above, the objective in discriminant analysis is to identify u B u', u W u'. axes, i.e., linear combination of variables, which "discriminate" well between the different classes of individuals. In linear dis- criminant analysis, an axis will be considered to be more discrimina- ting the higher the between-class variance will be, as a proportion of the total variance. More formally, the problem of finding the factorial axis which discriminates the best between the classes reduces to the following problem: max [u B u'/u W u'], u or, equivalently, max [u B u'/u T u']. u 15‘ A51 iSi the val fac to all dis der the is the has an,- De 148 The first discriminanting axis u1 solution of the above problem, 1 is the eigenvector of T' 8 corresponding to the largest eigenvalue 1,. As with all others eigenvalues of 1-18, A2 lies between 0 and l and is a measure of the discriminating power of this axis.20 Similarly, the second discriminating factorial axis u2 is 1B corresponding to the second largest eigen- the eigenvector of T' value AZ. This second axis is orthogonal to the first and is the factorial axis which discriminates the best among the axes orthogonal to the first axis. Similarly, other axes are the eigenvectors corresponding to all the eigenvalues taken in decreasing order. Each is the best discriminating axis among those which are othogonal to the previously derived factorial axes. The discriminating power of each of these axes, as measured by the corresponding eigenvalue, is zero when the between-class variance is zero, i.e., when the mean vectors of each class project on u at the same point, and is one if the within-class variance is zero, i.e., if all vectors of each class project on u in the same point. The sum of the eigenvalues corresponding to the factorial axes has no particular meaning, contrary to the case in principal component analysis; more precisely, it cannot be interpreted as being the percentage of the total variance explained by these factorial axes. The number of discriminant axes is K-l, where K is the number of a priori classes considered, provided that the number of individuals 20Ibid., pp. 45-47. than ing assu vari accc for func Of; the are The 01‘ ”hi 149 (N) is greater than the number of variables (P) which itself is greater than the number of classes. So far, no distributional assumptions have been made concern- ing the variables observed on the individuals. If the variables are assumed to follow multivariate normal distributions with equal co- variance matrices and if individuals are classified into each class according to a maximum likelihood principle, the partitioning line for classification purposes are hyperplans in RP and the discriminant functions obtained are the ones previously obtained, independently of any distributional assumptions. This is illustrated below for the two-class case. The multivariate normal distributions for the two populations are: 2a‘P’2 Izl'”2 expl-l/2(x-ui>' Z49th”: f](x) 2a'P/2 lzl'I/z exp[-l/2(x-u2)' z"(x-p2)l. 21 f2(x) The classification rule is thus x c yi if f1 (x)/f2 (x) > 1, OY‘ N ll log f](x) - log f2(x) > 0, Where Z "% (X'u])' 2-](X‘11-l) + 1/2 (X'Uz) 2“] (X‘UZ)9 ' -1 [x - 1/2 (u] + u2)] 2 (u, - U2)- Thus, when the variables are distributed as multivariate normals with equal covariance, and when the maximum likelihood principle is adopted 2lPeter A. Lachenbruch, Cheryl Sneeringer, and Lawrence T. Revo, “Robustness of the Linear and Quadratic Discriminant Function to Certain Types of Non-normality," Communications in Statistics 1 1973): 41. the it pla tio max 658 dis of the 1an Sta am no to ha We al 150 the discriminant functions are linear. If the parameters are unknown, it is reasonable to replace them by the sample estimates; thus, re- placing p] and p2 by y] and y2, one finds the same discriminant func- tion as previously derived without normality assumptions, through maximization of the ratio of between-class variance to total variance. When normality is assumed, but different covariance matrices are assumed for each class, the same method would lead to a quadratic discriminant function. Classical tests can be performed using the strong assumptions of multivariate normality and equal covariance matrices. A test for the equality of the mean vectors of several classes is based on Wilk's lambda (A) which can be approximated either by a F statistic or a x2 statistic.22 There is some evidence that the robustness of linear discrimin- ant analysis is low and that, consequently, it is badly affected by non-normality; especially, the number of misclassifications increases for some non-normal distribution and not for others. On the other hand, some results showed that linear discriminant analysis performs well for discrete data.23 22Romeder, Analyse Discriminante.pp. 77-81. 23Lachenburg, Sneeringer, and Revo, "Robustness of Discrimin- ant Functions," pp. 53-54. Mea lal tai 151 Several anlitative Variables Measures of Association in Contingengy Tables A contingency table is a convenient way to cross-classify popu- lations of individuals or objects with respect to two or more quali- tative variables (polytomies). In the simple case of two polytomies, A and B, a contingency table has the following format: B Total 1 2 B 1 x11 x12 x18 x1 2 "21 "22 "28 x2 A a xa1 xa2 "' xaB xo. Tota1 x.1 x.2 ... x B x.. where xij = the actual count of cell i, j, . = ' f .., x.J the sum over 1 0 x13 xi. = the sum over 3 of xij’ x = the sum over i and j of xij and is equal to N the number of observations. Other representations of this table could be obtained using the same format but replacing xij by j’ the expected cell count, rij’ the proportion of observations falling in cell i,j, "'i usual Goodn varil Meas City tend A1Sc tote of a t101 Pro Ger Prl / (II-DO -. . W—J— 152 p ,the probability of an observation falling in cell i,j. ii After having displayed such a cross-classification, the analyst usually seeks to assess the degree of association between the polytomies. Goodman and Kruskal expressed their concern for a proper use of the various measures of association: Our major theme is that the measures of association used by an empirical investigator should not be blindly chosen because of tradition and convention only, although these factors may properly be given some weight, but should be constructed in a manner having operational meaning within the context of the particular problem. Measures of association will be discussed here, for the sake of simpli- city, in the case of two polytomies; many of the results can be ex- tended straightforwardly to the case of three or more polytomies. Also, contingency tables will be considered to cross-classify the total population, and not a sample; the discussion of the measures of association will therefore evade the problem of sample to popula- tion inference, and will be in terms of actual cell counts (xij) or proportions of observations (rij). General Considerations Before the various categories of measures of association are presented, several general comments should be made. The choice of the adequate measure of association depends heavily on the caracteristics of the polytomies and of the way their relation- ship is to be considered. The following points are relevant: 24L.A. Goodman and W.H. Kruskal, "Measures of Association for Cross-Classifications," Journal_of American Statistical Association 49 (December 1954): 732-764. This section relies heavily on the above article. the the bri Thi be If trl' sur nou me.“ OY‘l It: no to 01‘ 153 (1) existence or nonexistence of an underlying continuum, (2) existence or nonexistence of an underlying order, (3) synmetry or asymmetry of the way in which polytomies enter the analysis, and (4) definition of the categories of the polytomies. These points are now discussed briefly. A polytomy may have been dervied from a continuous variable. This process implies a loss of information, and consequently, it may be worthwhile to restore the continuum, even at a substantial cost. If the continuum is not restorable one may want to assume some dis- tribution for the underlying continuous variable and choose a mea- sure of association appropriate for this distribution; a multivariate normal distribution is commonly assumed, in which case the appropriate measure of association should be based on the correlation coefficient. A polytomy may possess an underlying order. Ignoring this order implies a loss of information; on the other hand the order itself may not be relevant to the question examined. When there is no reason to believe that an underlying order exists, one may want to constrain the measure of association to be independent of the order in which the classes of the polytomies are tabulated. Such con- siderations dictate whether or not an ordinal measure of association should be chosen. 7 If a causal relationship is thought to exist on theoretical grounds, the analyst may want to consider each of the polytomies in a different way, thereby introducing an asymmetry in the contingency table; on the other hand if no causal relationship is assumed, poly- tomies may be treated symmetrically. ati pol hav lev aci tic on an. de th 1‘6 154 Finally, it should be stressed that the measured level of associ- ation in a table may depend very much on how the classes of each polytomy are defined; thus, a precise statement of how these classes have been defined should always accompany the reporting of a measured level of association. The foregoing discussion outlined the importance of the char- acteristics of the polytomies on the choice of a measure of associa— tion; some general remarks on the use of measures of association and on some of their desirable properties are also necessary. One should not confuse the concept of independence and its corrollary the test of independence, with the concept of association and its corrollary the measure of association. A test of indepen- dence should be used to ascertain whether a relationship between the polytomies is likely to exist, and a measure of association is required to assess the type and extent of a relationship. The concept of association is very imprecise, due to the multi- dimensional nature of a particular association. More precisely, in a axB two dimensional contingency table there are axB-l total degrees of freedom, a-l for the rows, and B-1 for the columns, which implies (a-l)(B-l) degrees of freedom for the association; this implies that (a-l) (B-l) functions are necessary to specify completely the table. This explains why many measures of association have been developed, none of themdescribing completely the association. The high number of potential candidates as measures of associ- ation has led some statisticians to require that a measure of associ- ation be invariant under the following transformation: whel This the sta; and sid tio whe the con wit ati 0n ta ba or Pl 155 where ti and sj are numbers that preserve the equality IErij = 1. This transformation changes the marginal distributions without changing the cross—product ratios in the table. A measure of association which stays invariant under the above transformation is dubbed "margin-free" and one which is not invariant, "margin-sensitive." It can be con- sidered that a margin-sensitive measure of association mixes informa- tion on the marginal distributions with information on the association, whereas a margin-free measure does not. Measures of association are often normalized so that they take the values 0 in case of independence and +1 or -1 in the case of complete association; what complete association means varies, however, with the measure. Normalizing measures of association loses its attractiveness as their interpretability increases. The foregoing subsection was devoted to general considerations on measures of associations which laid down the way for the presen- tation of some measures classified into traditional measures, measures based on optimal prediction, measures based on optimal prediction of order, measures of reliability or agreement, and measures based on proportion of explained variance. Traditional Measures The traditional measures are mostly based on the Pearson chi- square statistic defined as: Z 2 j (xij - xi x.j/") /(xi x J.ln). Yu 3F 01 156 For the special case of a 2 x 2 contingency table the following Yule coefficients are commonly used: Q = (xllx22 ' x12X21)/(xllx22 T xlzle)’ and Y V8?£'“fi§ZVV§F§+’§§EL Other measures are: the mean square contingency, ¢2 the coefficient of mean square contingency, P = VIyZ/n)/(1+x2/n) ; = XZ/n; Cramer's V, v = J627min[(o-l)a(B-1)]; Tschuprow's T, T=40mnnpu. The x2 statistics is well known to provide a good test of inde- pendence; this does not ensure, however, that it is a good measure of association. The traditional measures of association have the major drawback of not enabling comparison of measured level of association between different contingency tables. This is so because they have no operational meaning. Measures Based on Optimal Prediction Consider a two-dimensional table obtained from polytomies A and B without underlying order and continuum. The experimenter's ability to predict the value of the B polytomy may depend on whether 12111 V3 is kn 1119 Dr V6 1116 157 the value of the A polytomy is knOwn or unknown to him. When the ‘ value of A is unknown the experimenter will predict that the B class is the one with largest marginal proportion. When the value of A is known, the best guess is that the B class is the one with largest proportion in the observed A class. This provides the basis for the measure of association defined by: A = (Prob. of error A unknown) - (Prob. of error A known) b (Prob. of error A unknown) Ab is to be interpreted in terms of the proportion by which errors in predicting B can be expected to be reduced by the knowledge of the value of A for each individual. Goodman and Kruskal listed the following properties for the Ab measure of association: (i) Ab is indeterminate if and only if the population lies in one column, that is, lies in one 8 class. (ii) Otherwise the value of Ab is between 0 and 1 inclu- sive. (iii). Ab is 0 if and only if knowledge of the A classi- fication is of no help in predicting the B classi- fication. . . . (iv) Ab is 1 if and only if knowledge of an individual's A class completely specifies his B class. . . . (v) In the case of statistical independency Ab, when determinate, is zero. The converse need not hold: , Ab may be zero without statistical independence holding. (vi) A Ab is unchanged by permutation of rows and columns.25 25Goodman and Kruskal, "Measures of Association," p. 742. 158 Syllmetrically, Aa can be defined and interpreted in terms of .the increased ability to predict the A polytomy when the B classification is known. Another measure of association, A, is defined which is based on the same principle and is interpreted in terms of the increased ability to predict alternatively the A or B polytomy when alternatively the B or A classification is known. The major shortcoming of Aa, Ab and A is that their value depends on marginal frequencies; in other words two tables displaying the same conditional frequencies but different marginal frequencies will yield different values for Aa, Ab and A, i.e., Aa’ Ab’ and A are margin sensitive. When one is interested in comparing patterns of conditional frequencies for different tables this can be attained by weighting columns and rows so as to obtain equiprobability of the classes for the different tables. Another measure of association related to optimal predication is the uncertainty coefficient which is based on information theory.26 The expected information, or entropy, or uncertainty of a bi- variate distribution is: a 8 WW) = if] 321 pij 109 (l/pij). The expected information or uncertainty of the marginal distributions are: (1 H(A) = .73] p1. log(l/p1. ). . l= ‘ 26See Henri Theil, Egonomics and Information Theory (Chicago: Rand McNally, 1967), pp. 33-35. and COT val th 159 and H(B) = . J p_j 109(1/p.j). ll MID ...n The expected information of the conditional distribution, or conditional uncertainty is: a B H(BIA) = ii] jElpij logipiolpij). The asymmetric uncertainty coefficient were B is the dependent variable is defined as: ucB = [H(B) - H(BlAll/H(B). Likewise, the a symetric uncertainty coefficient where A is the dependent variable is defined as: ucA = [H(A) - H(AIB)]/H(A). The asymmetric uncertainty coefficient is the proportion by which "uncertainty" in the dependent variable is reduced when the value of the independent variable is known. UCA (UCB) lies between 0 and l. Asymnetric uncertainty coefficient can be defined as: uc = [H(A) + H(B) - H(A.B)l/[H(A) + H(B)]. Measures Based Upon Optimal Prediction of Order Suppose that two individuals are picked at random from the popu- lation; each falls into a cell of the table. If there is indepen- dence between the polytomies A and B, one would expect the order On the A polytomy for the individuals randomly taken is not related to the order on the B polytomy; if a positive association exists these 160 orders should be positively related and conversely, if a negative _ association exists these orders should be negatively related. On this basis, Goodman and Kruskal proposed the following measure of association: Y = (“S ‘ 1T(1)/(1 ' Wt): where n = the probability of like ordering for two randomly selected individuals, Trd = the probability of unlike ordering, "t = the probability of ties, i.e., of two randomly selected individuals falling in the same cell. Thus, v is the difference between the conditional probabilities of like and unlike order, given no ties. The properties of v are: (i) y is indeterminate if the population is concentrated in a single row or column of the cross-classification table. (ii) v is 1 if the population is concentrated in an upper-left to lower-right diagonal of the cross-classification table. (iii) 7 is O in the case of independence, but the converse need not hold except in 2 x 2 case.2 Another measure based on the same principle, but taking into account the occurrences of ties, was proposed: Tauc = ("s - Nd)/[(m - ll/m] where . m = M1" (0.8), a.B = the dimensions of the contingency table. 27 Goodman and Kruskal, "Measures of Association," p. 749. Mea cat inc CEC til Pol tt 161 Measures of Agreement Suppose that a population of individuals can be classified into categories using two procedures; if complete agreement exists, individuals will be classified into the same category by the two pro- cedures. The assignment can be displayed as a two-dimensional con- tingency table with the same polytomy. No ordering is assumed. The simplest measure of agreement is the proportion of the population who have been classified identically by the two procedures: p = Z r i il Goodman and Kruskal proposed a measure, Ar, which can be inter- preted as "the relative decrease in error probability as we go from the no information situation to the other-method-known situation."28 Ar = [ § rii - 0.5(rM. + r M)]/[l - 0.5(rM. = r M)], where rM and r M are the marginal frequencies of the modal classes. The properties of Ar are: 1., Ar ranges between -1 and +1 2._ A= -1 when all frequencies in diagonal cells (rii) are zero and the modal probability is one 3., Ar = 1 when the two classification procedures always agree 4.. A is indeterminate only when both methods always classify individuals into one and the same class 5.. Ar takes no particular value when independence exists. 28Ibid., p. 757. si tr of It 11 CE Cl 162 Measures Based on Proportion of Explained Variance Bishop et al.29 propose a measure of association for two-dimen- sional tables based on the proportion of explained variance; it is, therefore, an analogue for qualitative variables of the coefficient of determination which is commonly used for continuous variables. It is defined as: Taub = [ §(1/xj ) f x2 j - (l/n) Z x2 J/[n-(l/n) g x: J. Goodman and Kruskal30 interpretes Taub as the relative decrease in the proportion of incorrect predictions when prediction of the row category is based on the conditional proportions rij/r.j instead of on the marginal proportions only. Conclusion Goodman, Kruskal, Costner and others have stressed the importance of choosing a measure of association which is adapted to the purpose at hand and which takes into account the peculiarities of the contin- gency table. They also urged the use of measures of association which have an operational interpretation and especially of those measures which can be interpreted in terms of the proportional reduction in error of estimation made possible by the relationship.31 29Y. M. M. Bishop, S. E. Fienberg, and P W. Holland, Discrete Multi- variate Analysis: Theoryland Practice (Cambridge, Massachusets: The MIT Press. 1975), pp. 390- 392. 30 31H.L. Costner, "Criteria for Measures of Association," American Sociolpgical Review 30 (June 1965): 341-353. Goodman and Kruskal, "Measures of Associations," pp. 759-760. 163 Lpg:Linear Models of Contingengy Tables Suppose that a set of P. qualitative variables are observed on a certain population of N individuals; each individual can be classified on the basis of the value taken by each qualitative variable for him. We mentioned above that a convenient structure for displaying such a data set is a P- dimensional contingency table. In this section log- linear models for contingency tables are presented, and problems in estimating them as well as in testing hypotheses arediscussed. Some general comments concerning contingency tables and the objectives served in using log-linear models are necessary. A contingency table is called complete when all cells have a strictly positive probability; in other words these tables display no structural zeros. A complete table may display some cells with zero counts due to sampling; these are called sampling zeros. As it will be explained below, the estimation of incomplete tables is substan- tially more difficult than the estimation of complete tables, and requires special methods. Estimation of tables with sampling zeros does raise some difficulties, but methods available for tables without sampling zeros can be used once some precautions are taken. A model describing the underlying data structure of a multi- dimentional contingency table is a mathematical relationship involv- ing the cell probabilities (p6) or the expected count (me). Bishop et a1.32 list the following four objectives an experi- menter may hold when fitting a model to a data-set: 32Bishop, Fienberg, and Holland, Discrete Multivariable Analysis, p. 311. 164 1. To describe the data: the model then helps him to underf stand the relationship between the variables and provides a "smoothing device" by which the most important structural elements of the data are highlighted. I 2. To obtain summary statistics of different subtables (config- urations) allowing him to decide whether or not the dimensionality of the table can be reduced. 3. To detect outliers, by assessing the goodness of fit of the model for each individual cell. 4. To test whether some variables are associated and to assess the magnitude of their association. The above definition of models and statement of the purposes they may serve leads us to the actual presentation of log-linear models for contingency tables. The special case of three qualitative variables (three-dimensional table) will be taken as example for expository purposes. Models for Three—Dimensional Tables Log-linear models can involve either cell probabilities (pijk) or expected cell counts (mijk); the fellowing presentation will use expected cell counts. The log-linear model is defined by: m..k = exP(Uijk)/§ i 13 . i exp(”iik)’ or, in logarithmic form by: Lijk ‘ 1°9 "‘ijk : Uijk‘log [E g E exp(uijk)]s 165 where Uijk is a parameter specific to each cell. Since the second_ term is constant over all cells of the table it can be expressed as a single term: u. By using a parameterization similar to the one used in the analysis of variance (ANOVA) model Uijk can be expressed as follows: Uijk ‘ ul(i) * u2(j) * u3(k) * u23(ii) + ”23(jk) + ul3(ik) I "123(ijk)‘ Thus, another equivalent form of the log-linear model is Hp“”(Np)‘“*ho)*%o)‘%q>*%ao) I “23(jk) I ul3(ik) I "123(ijk)’ i = 1,. . .,J; j = 1,. . .,I; k = 1,. . .,K; where the u-terms are parameters on which the following constraints are imposed: Eu . = Eu . = EU - = 0, 1 1(1) j 2(3) k 3(k) §ul2(ii) = §“l2(ij) = §"23(jk) = Eu23(jk) = §“l3(ik) = Eul3(ik) = 0’ §“123(ijk) = §u123(ijk) = Eu123(ijk) = 0° In words, each u-term must sum to zero over each of the indexing variables. Following the terminology of the ANOVA model the u-terms are interpreted as main and interaction effects: 1. u is the overall mean or overall effect 2. u,, "2’ U3 are the main effects of variables 1, 2, 3 166 3. ”12’ u23, u13 are the two-factor interaction effects 4. u123 is the three-factor interaction effect. A three-factor effect measures the variation between the two fac- tor effects in the two-dimensional tables defined by the values of the third variable. In the same way, a two factor effect measures the variation in the main effect of one variable for the different values of the second variable. Alternatively, a two-factor effect can be interpreted as the average two-factor effect on the same variables for the different values of the third. This implies that if any two- factor effect is constant over the two-way subtables, the three-factor effect is equal to zero. These results, presented for the three- dimensional table case, can easily be extended to higher dimension tables. The model presented above is only one of the many log-linear models possible for a three-way contingency table. It is character- ized by the fact that all u-terms are assumed to be different from zero; such a model is called a saturated model; one in which some u-terms are assumed equal to zero is called an unsaturated model. Whether or not a model is saturated has implications with regard to estimation as well as interpretation of the relationship between variables. The class of hierarchical models is of special interest and requires definition. First, two u-terms are called relatives when one is subscripted by only a subset of those variables subscripting the second; the u-term with a higher number of subscripts is called a higher relative of the other (e.g., u123 is a higher relative of 167 u12 but also of u23, u13 and u], ”2’ U3). A model is said to be hierarchical if the fact that any u-term is zero implies that all higher relatives are zero. The importance of such hierarchical models is such that it is worthwhile to give their interpretation in the case of a three- dimensional table: 1. Three-factor effect absent, i.e., “123 = O: the two-factor effects for all two-dimensional subtables are constant, and there is "partial association" between each pair of variables 2. Three-factor and one two-factor effect absent, e.g., ul23 ‘ ul2 = 0‘ the": Lijk = “ + ul(i) + u2(j) + u3(k) + ”23(jk) + ”13(ik) and variables 1 and 2 are conditionally independent, given the level of variable 3 3. Three-factor and two two-factor effects absent, e.g., ul23 = "l2 ‘ ul3 ‘ 0‘ the": Lijk ‘ " + ul(i) + u2(3) * u3(k) + "23(jk) and variable 1 is independent of variables 1 and 2 4. Three-factor and all two-factor effects absent, i.e., "123 = ul2 = "13 = “23 ' 0‘ the": Lijk ‘ " + ul(i) + u2(j) + “3(k) and this is the complete independence model. 5. Noncomprehensive models where one, at least, of the main effects is zero, e.g., "1(i) = 0: one variable plays no role and the dimensionality of the table can be reduced by summing up the array over the nonintervenlng varlable; then Lijk = u + u2(j) + "3(k)' Whatever the dimension of a table, the number of independent parameters in a saturated log—linear model is equal to the number of cells in the table. 168 Models for Higher-Dimension Tables The model presented above for a three-dimensional table can be extended to higher-dimension tables. A simpler notation can be used, which allows a model of any dimensionality. L6 = u + u] + u2 + ... + u12,+ ... + u12 ... P In such notation, 6 represents the complete index set; subsets of this index set can be expressed by indexing e, e.g., e], 62. This notation. thus, expresses indifferently probabilities (or their logarithm) of different cells; the indexing is used to indicate in which collapsed subtable (configuration) such cells are considered: e.g. 6] = 1,2. Lel ‘ ul + "2 + "12‘ O! 3 0. CD II 1839435, 2 ‘ ul * u3 + “4 I ”5 + u13 + "14 + ul5 + u34 + “35 +U +1.1 45 l ul34 + ul45 345 + “1345' Log-linear models can describe completely the structure of a table; this is shown by the possibility of reconstructing a complete table once the proper number of parameters (1 x J) has been specified, i.e., once a saturated log-linear model has been specified. The main case where hierarchical models cannot adequately de- scribe the data structure of a table is when synergism occurs, i.e., when two factors need to be present together for an effect to appear. When contingency tables are of high dimensionality, it is ob- viously interesting to reduce this dimensionality in order to ease the analysis. Reducing the dimensionality of arrays, by summing over 169 certain variables, however, implies a loss of information and may mask some important structural features. It is therefore of important theoretical interest, as well as of practical interest, to know under what conditions arrays can be collapsed. The following theorem states, in general terms, when variables in a contingency table are collapsible: Theorem: Suppose the variables in an s-dimensional array are divided into three mutually exclusive groups. One group is collapsible with respect to u-terms involving a second group, but not with respect to the u-terms involv- ing only the third group, if and only if the first two groups are independent of each other (i.e., the u-terms linking them are 0).33 The practical implications of the above theorem are important. If a table is described by a log-linear model where all two-factor effects are different from zero, collapsing the table by summing over any variable will change the u-terms. In other words, the common practice of examining all two-way marginal tables is very misleading in all cases where variables are interdependent. A_contrario, an array can be collapsed by summing over any variables that are inde- pendent of others; by virtue of the above theorem, the u-terms will not be affected. Maximum Likelihood Estimation Procedures for Complete Tables The discrete probability density function for the table depends on the sampling scheme by which the data set was obtained. The three most common sampling schemes are the independent Poisson, simple 33Ibid., p. 47. ’ 170 multinomial, and product multinomial sampling schemes, corresponding respectively to the cases where total sample size is not constrained, total sample size is fixed, and the number of observations for certain groups is fixed. Since the kernel of the likelihood function is identical for the three above sampling schemes, the same estimation procedure can be used. In the following, estimation procedures will be examined for these sampling schemes only. Sufficient statistics are easily obtained; they are configura- tions of sums (i.e., collapsed tables obtained by summing over certain variables). Simple rules exist, based on what u-terms are included in the model, which allow the determination of which configurations constitute the minimum set of sufficient statistics. The practical implication is that it is possible to derive maximum likelihood esti- mates of the cell probabilities without estimating the u-terms, and without having to derive the kernel of the likelihood function. For some models it is possible to write maximum likelihood estimates of the cell probabilities as direct functions of the suf- ficient statistics; these models are sometimes called gjrggt_models. For others, this is not possible and one must resort to iterative methods. Iterative methods yield, in any case, the closed-form esti- mates when they exist; in practice, estimates are obtained using pro- grams which are based on iterative methods, and therefore, successful whether or not direct estimates exist. Simple rules exist which allow the prior determination of which models have closed-form estimates; it suffices here to mention that no model has such closed-form estimates unless at least one two-factor effect is equal to zero. 171 If estimates of u-terms are desired (e.g., to assess the extent of relationship between 2 variables), they can be obtained as linear fUnctions of the cell probability estimates subject to the constraints that their sums over each indexed variable are equal to zero. Goodness of Fit Several measures of goodness of fit are available. The first is 2 the classical Pearson x defined as: x2=§o€npbaL where: x6 = the observed cell count, pa = the fitted cell count. x2 is asymptgtically distributed as chi-square with the appropriate degrees of freedom (see below). The second measure of goodness of fit is the likelihood ratio statistic defined as: 62 -2 2 x9 log(me/xe) 2 3 x6 log(xe/me). 62 is also asymptotically distributed as chi-square with the appro- priate degrees of freedom. The 62 statistic is less familiar to users and somewhat awkward to compute; it is, however, minimized by maximum likelihood estimation methods, which designates it as the best measure of goodness of fit when such estimation methods are used. Furthermore G2 can be broken down into parts in two meaningful ways: conditionally and structurally. 172 Let, L(x) = 2 x6 log XB’ and, L(m) = 3 x6 log me. then, 62 = -2[L(n) - L(x)]. Since, for any saturated model, the maximum likelihood estimate of the expected cell count is the actual cell count (me = x6), L(m) = L(x) and G2 = O. For any unsaturated model L(m) < L(x) and, consequently, oz is positive. In the special case of pgstgg_models, G2 can be decomposed con- ditionally. Two log-linear models A and B are said to be nested when one (e.g., 8) contains only a subset of the u-terms contained by the other (A).' Then, the likelihood ratio measure of goodness of fit for model B, 02(8), can be decomposed into two constituents: (l) a measure of the distance between the estimated expected cell counts under model 8 (a3) and those obtained under model A (m3), and (2) a measure of the distance between the estimated expected cell counts under model A (fig) and the observed cell counts (x). This result is easily derived from the above expression of 02: -2[L(a3) - L(Xl] = -2[L(fi3) - L(fiA) + L(mA) - L(X)] = -2[L(n3) - L(fiA)l -2[L(fiA) - L(x)] 62(8) = 62(B1A) + G2(A), G2 (BIA) is the conditional measure of goodness of fit for model B given 173 model A. The following result holds: if G2(A) and 62(8) are asympto- tically distributed as chi-square with respectively nA and nB degrees of freedom, G2(A|B) is asymptotically distributed as chi-square with nB - nA degrees of freedom (nA and nB are the degrees of freedom in models A and B). ‘The above decomposition can be repated and, therefore, the results can be extended to any number of nested models. This con- ditional decomposition is particularly useful since it permits a test for the presence of any subset of u-terms, and especially for a single interaction term. As mentioned previously, closed form estimates of the expected cell counts, when they exist, are functions of the minimum set of suffi- cient configurations. In this case, G2 can be computed directly from these configurations, by adding the 62 for each sufficient configura- tion constituting the minimum set; this decomposition of the G2 stat- istics in term of the G2 of these configurations is called the struc- tural decomposition. Internal Goodness to Fit 2 and G2 statistics are overall measures of goodness of fit; when X contingency tables possess many cells it is useful to examine also the internal goodness of fit, i.e., to check each cell for the deviation of the estimated cell count from the actual cell count. This procedure may reveal outliers, which can occur even when the overall fit of the model is good, or specific patterns of positive and negative deviates leading to the choice of a different model. 174 Testing of Hypotheses Different hypotheses concerning the structure of the data can be expressed in terms of the main and interaction effects of a log-linear model. For example, direct interaction between two specified variables is equivalent to the two-factor effect involving these variables being different from zero; conversely the hypothesis that these two variables are conditionally independent is equivalent to stating that the same two-factor effect is zero, and other two-factor effects are different from zero. If one wants to test for interaction between two variables, two models can be fitted to the data, one including the two-factor effect, one excluding this term, and two measures of fit are obtained: 5%) and 62(3) (or x2(A) and x2(3)). The difference 62(A) - 92(3) (or x2(A) - x2(B)) is asymptotically distributed as chi-square with nA - nB degrees of freedom. The two models fittedare nested since the model corresponding to conditional independence contains one less u-term. If the difference A62 = G2(B) - 62(A) (or sz = x2(B) - x2(A)), which measures the increase in goodness of fit when the two-factor effect is added, is significant at the chosen level, the two-factor effect is to be considered as different from zero and the null hypo- thesis that the two variables are conditionally independent can be rejected. The advantages of the above method of hypothesis testing are that: (l) the same criterion is used for estimating the model as well as the testing of hypotheses, (2) it is applicable even in the case where the table contains structural zeros, and (3) it is applicable to any level of u-terms as well as any subset of u-terms describing a hypothesis. 175 Hypothesis testing can also rely on the property that maximum likelihood estimators are asymptotically distributed as normal. Asymptotic t-ratios can be obtained for each coefficient in the model and be used for testing whether this coefficient is different from zero. Choice of a Model Since many log-linear models are possible for a specified con- tingency table, the problem arises of how to choose the "best" model. In this respect the problem does not differ substantially from the choice of a regression model; it is difficult to lay down strict rules which would lead systematically to the best model (the criterion to judge a model is itself not easy to choose and depends greatly upon the objective of the experimenter). Generally, the choice of a mddel is reduced to a subset of all possible models, subset defined by the objectives of the study, any g_pripri_knowledge concerning the variables, and the sampling scheme. The choice of a model comes out of a search procedure in which models are successively fitted and their goodness of fit assessed. Several systematic search procedures have been proposed;34 only one will be presented here. The first step consists of fitting hierarchical models with u-terms of uniform orders. Thus, for a P-dimensional table, one fits the model with the P-order u-term, then the model with all (P-l) - order u-terms (i.e., without the P-order term), and so on down to the complete independence model with only main effects. These models are nested and embody a set of nested hypotheses. Using a theorem stating 34Ibid., pp. 311-343. 176 that likelihood ratio statistics provides a means to perform indepen- dent tests of nested hypotheses and using the conditional decomposition of G2 presented above, it is possible to narrow down the set of adequate models to the intervening models between two models with terms of uniform order. These intervening models are themselves models which are nested into the model with terms of higher uniform order. The same test can be used to choose between these alternative intervening models. In choosing models one should remember that a simpler model (i.e., including less parameters) is often more informative than a more complex one, because it is more likely to reveal the main struc- tural features of complex data and because it may often yield more stable estimates of the cell probabilities. A further problem in relation to the search for the best model, which by no means is specific to log-linear models of contingency tables,35 consists in using the same data for choosing a model and testing hypotheses. Since the model is built on the basis of the information contained in the data, it reflects more and more, with each step of the search procedure, the idiosyncrasies of the sample and less and less the characteristics of the population. One way of dealing with this problem could be to give up some degrees of freedom, but the question as to how many should be given up is unresolved. Another remedy is to split available data into two or more parts and to choose the model using one part and to test it on the other part(s). 35See for example 1. Dudley Wallace, "Pretest Estimation in Regression: A Survey," American Journal of Agricultural Economics 59 (August 1977): 431-443. 177 Multivariate Log-Linear Models with Exogenous Variables36 Nerlove and Press developed a multivariate log-linear model with exogenous variables to analyze relationships between several quali- tative variables which are thought to be jointly dependent on a set of exogenous continuous variables. Their model can be described either as an extension of the univariate logit model to the case of several qualitative dependent variables, or as the introduction into the log- linear models for contingency tables of main and interaction effects which are functions of exogenous variables. The second presentation is easier and it will be followed here; many results and discussion included in the section in log-linear models of contingency tables apply to the Nerlove-Press model and consequently only differences will be emphasized in this section. The Model The model is similar to the one defined for contingency tables; the definition in terms of cell probabilities and with the simplified notation for any number of dimensions is as follows: p6 = exp(Ue)/§ exp(U6). Taking the logarithm: r I e - 109 pe= Ue - 109I€ exp(Ue)] 36This section is based on the following works: Marc Nerlove and S. James Press, Univariate and Multivariate Log-Linear and ngistic Models, Rand Report R-l307-EDA/NIH, (Santa Monica: Rand Co., Dec. 1973); Idem, "Multivariate Log-Linear Probability Models for the Analysis of Qualitative Data," Center for Statistics and Probability, Discussion Paper No. 1, Northwestern University, Evanston, 1976. 178 or, L6 u + U9, -109[§ exp(Ue)]. Using the same parameterization as before it follows that: where, u L9 = u + u] + u2 + ... + uP + u + u + ... 12 23 + ... + ul2 ... P The effect of exogenous variables on the jointly dependent qualitative variables can be introduced into the model by stating that US is a function of these exogenous variables. When restricted to be linear, this function takes the following form: = ' * where x is a vector of exogenous variables and U*e is itself expended in terms of the convenient parameterization described previously: u1 E x'ut, u12 E x'ufiz, “12..P 5 x'”iz...e Nerlove and Press present their model as a generalization of the log- linear model of contingency tables. If x is constant, the model re- duces to the ANOVA-type model presented before; if x contains true exogenous variables the model can be described as the analogue of the analysis of corariance; it is of the ANACOVA-type. 179 Maximum Likelihood Estimation If a multinomial sampling scheme is assumed, the likelihood function (LF) can be derived as follows: pe(n) E Pr {nth observation falls in cell 6}, pe(n) = exp(Ue)/g exp(Ue). LF = r ir[pe(n)l 9 . n=le where, v (n) = 1 if observation n falls in cell a 0 0 otherwise The u-terms may be assumed to depend on exogenous variables in which case ='* Ue xnUe . U8 is, like U6 decomposed into main effect and interaction effects: *:**+ +~k+”+* ”9 ul I ”2 "' ul2 ‘ ul2 ...P. Estimates of the cell probabilities can be obtained by maximizing the likelihood function either with respect to the u-terms in the case of an ANOVA-type model or with respect to the u*-terms if the model is of the ANACOVA-type. From the above formulation of the likelihood function, it is clear that the estimation procedure breaks down when the table dis- plays structural zeros. When the table is complete (i.e., no struc- tural zeros exist), but some sampling zeros occur, the fully saturated model cannot be estimated since some pe terms vanish from the likeli- hood by being raised to a zero power; unsaturated models, with the 180 proper number of nonexistent parameters can, however, be fitted. Conditional Probabilities and Conditional Estimators Conditional probabilities and estimators will be presented tak- ing the trivariate dichotomy case as an example. In the case of dichotomies the constraints that every u-term sums to zero over each of the indexing variables implies that every u-term takes only one absolute value, the sign of which depends on the value (0,1) taken by the indexing variables. Thus, the trivariate dichotomy model is as follows: 1°9 plll T u T ul T “2 T u3 T ul2 T ul3 T u23 T ul23 T°9 pllo T u T ul T “2 T “3 T “12 T ul3 T ”23 T ”123 T°9 ploo T ” T ul T ”2 T "3 T ul2 T “13 T u23 T u123 T°9 pooo T “ T ul T u2 T u3 T “l2 T “l3 T “23 T ul23 1°9 p001 T u T ul T u2 T ”3 T ”12 T ul3 T u23 ”123 1°9 p0ll T u T ul T ”2 T u3 T ul2 T ul3 T u23 T ”123 T°9 plpl T ” T ul T u2 T u3 T ”12 T ul3 T ”23 T ul23 1°9 pmo T “ T ul T u2 T ”3 T ul2 T ul3 T u23 ul23 Conditional probabilities can easily be computed from the well-known equality: P(A|B) = P(A)/P(B) Thus PTyl T ‘lyz T 1’Y3 T I) T plll/(pOll T p111) exp(“T"lT“2T”3T“l2T"l3T“'23“123) exP("T“lT‘T'2T“3T“l2T‘1'l3T”23T“l231m““T“lT‘T'zTu3Tul2T“l3T“23T"123I 181 exP(ul+u12+u13+u123) - exp[T("lT“lzT“l3T“l23I]T exPTul+u12+u23+u123T 1 1 + exp[-2(u]+u]2+u13+u]23)] More generally the conditional probability of a cell is given by the formula:37 1 l + exp[-2(u]+u12v2 +u13v3+u123v2v3] p(y] = 1|y2.y3) = where. V m 1 if ym = l vm 0 otherwise. It is seen that conditional probabilities are also of a log-linear type but in u-terms which are different from those present in the original model. In the above formulation, nothing prevents the u-terms to be themselves functions of a set of exogenous variables; whatever func- tion form the dependence of the u-terms on exogenous variables takes, it is preserved in the conditional distribution. Thus, one can advocate the estimation of the original model from the above conditional probabilities rather than from the joint distri- bution. Such an estimation procedure would be analogous to the esti- mation of the equations of a system of linear equations through ordinary least square. In both cases, such a method is not entirely satisfactory since it does not take into account that the dependent variables (whether qualitative or quantitative) are jointly dependent. 37See Nerlove and Press, LogeLinear and ngistic Models, p. 50. 182 Such an estimation procedure does present some advantages and conse- quently deserves some attention. A conditional likelihood function can be generated from the expression of the conditional probability: N yln 1-yln LF*(u],u]2,u]3,u]23) = n21 [J/[l+exp(-2tn)l] [J/[l+exp(2tnT] where, tn T ul T U12V2n T ui3"3n T “l23V2nV3n’ m indexes the dependent variables (m = l...3) n indexes the observations (n = l...N), 1 if ymn = l. and, v = mn . 0 otherwise. This conditional likelihood function can be maximized with respect to the u-terms or, if the u-terms are considered to be functions of exogenous variables, with respect to the corresponding u*-terms. The estimators based on the maximization of the conditional likelihood function are called conditional estimators. Justification for the use of conditional estimators for jointly dependent qualitative variables can be derived from the fact that it is always possible to infer the joint distribution of qualitative vari- ables from the knowledge of their conditiOnal distribution, whereas this is not generally possible for jointly dependent continuous variables. Conditional estimators, as defined above, are consistent, asymp- totically unbiased and asymptotically normally distributed, but, 183 because the joint dependence of the qualitative variables is ignored, they are generally not efficient. Conditional estimators possess some advantages: (1) they are less costly to derive because they are easier to compute than full maximum likelihood estimators, (2) they allow the use of the many available univariate logit programs, and (3) estimates may be close approximations of the full maximum likeli- hood estimates. These conditional estimators can, however, only be used for exploratory purposes,since testing hypotheses by means of the likelihood ratio test requires the use of the maximum likelihood method based on the joint distribution of the dependent variables. Computer Programs Many univariate logit programs are available and they can be used to obtain conditional estimates. Nerlove and Press developed a program which can handle up to four dichotomous variables which are jointly dependent on up to six- teen exogenous variables. Main effects only are allowed to be linear functions of exogenous variables, and interaction terms are assumed to be constant. Programs for polytomous variables and with interaction effects dependent on exogenous variables are being developed. Joint Estimation Using Generalized Least Squares 38 proposed an estimation method of models with Zellner and Lee jointly dependent dichotomous variables using the generalized least squares estimator (G.L.S.). The case of a system of linear probability 38Zellner and Lee, "Joint Estimation," pp. 387-392. 184 functions is chosen for expository purposes, although the method can be generalized with little modification, to logit or probit probability functions. as follows: where: pi pz pM j '— _‘ T— "l 7] O 0‘] Bl u1 0 X2. 0 82 u2 = + ...t 1..? 0 . . . XM_1L _ BM _1. L UM ..d The system of M linear probability functions can be represented Tj x 1 vector of observed proportions for the jth binary variable, a Tj x Kj matrix of observations on Kj exogenous variables, a K. x 1 vector of coefficients, J a Tj x l disturbance vector. The above system can be represented can be represented more simply as follows: where: Ub'c'c l'lll U The covariance matrix XB + u. - (pi, pés . . ospfi)'s " (8.9 I: . . osBfi)'s (ui, ué, . . .,uM)'. is: 185 ll D120m 12 22 °°° D2M D D 0 M1 M2 °°° MM ._ -1 where Djk are diagonal matrices whose coefficients are expressable in terms of the probability that dichotomous variables take the value 1 for each group of observations.39 The covariance matrix (2) can be estimated consistently using single equation procedures. Once such a consistent estimate 2e of 2 has been obtained, Aitken's generalized least squares estimator, _ I ‘1 '1 I '1 b - (X 2e X) X Xe P. can be used to obtain joint estimates. The major shOrtcoming of this method is that it requires grouped data, i.e., several observations for the same values of the exogenous variables. When the number of qualitative dependent variables and particularly when the number of continuous exogenous variable is high. the grouping of observations can only be achieved by loosing much information. In such circumstances, maximum likelihood estimation methods can still be used. Also, this method is only valid for dichotomous dependent variables. 39For the derivation of the exact expression see Zellner and Lee, "Joint Estimation," pp. 388-390. 186 Conclusion This chapter has provided an overview of the statistical methods for the analysis of qualitative variables. It only touched the sur- face of a vast field, trying to demonstrate that standard econometric methods which are familiar to applied econometricians are very inade- quate and that adequate techniques do exist or are presently under development. Some of the statistical methods reviewed in this chapter are more adapted to exploratory data analysis; these are: (1) measures of association in contingency tables (mainly two-dimensional contingency tables), and (2) discriminant analysis (for a dichotomous or poly- tomous dependent variable). Other methods, which impose a more constraining statistical structure on the data, are more adapted to confirmatory data analysis, although some exploration is needed to arrive at a model to be tested. This review showed that several statistical methods are avail- able for the analysis of a single dichotomous variable; computer programs are readily available and, consequently, no major obstacle should hinder the use of these methods by applied econometricians. In connection with the use of contingency tables, the distinc- tion between tests of independence and measures of association was emphasized. This distinction is often ignored by applied econome- tricians even though it has some very significant implications for the interpretation of empirical results.40 40This is exemplified in Chapter VI. 187 Log-linear models of multidimensional contingency tables allow the analysis of several polytomous variables considered to be jointly dependent; computer programs are available and documented.41 Exogenous variables can be introduced into such log-linear models in the main effects or in the interaction effects. To date, a program for up to four dichotomous variables with exogenous variables entering only ’into the main effects is available; development of programs for polytomous variables and variable interaction effects are under way. A major shortcoming of the log-linear models of contingency tables, with or without exogenous variables, is that polytomous variables are treated as if there was no underlying order. Consequently, if such ordering does exist, some information is lost. Several of the above statistical methods were used to analyze the available data on off-farm movement. Discriminant analysis and two-dimensional contingency tables were used in an exploratory mode. A log-linear model of a three-way contingency table with exogenous variables was explored on part of the data and tested on other parts. 4TSee, for example, S. J. Haberman, “Log-Linear Fit for Contin- gency Tables," Applied Statistics 21 (1972): 218-225. CHAPTER VI EMPIRICAL FINDINGS This chapter is divided into three main sections. In the first section, an overview of the extent of total exit and pre-retirement exit from farming in Saskatchewan between 1966 and 1971 is provided. In the second section, exploratory results obtained from cross- classifications and discriminant analyses are presented. In the third section, a log-linear model of pre-retirement exit from farming, con- sidered as jointly dependent with involvement in off-farm work and residence on the farm, is(1) chosen and estimated using only part of the data, and (2) tested on other parts. Extent of Exit and Pre-retirement Exit from Farming_ The Census of Agriculture Match1 permits a data link between two censuses as exemplified in Table 5. This particular one displays farm operators in Saskatchewan cross-tabulated by age class in 1966 and age class in 1971 for stayers, tabulated by age class in 1966 for exiters, and tabulated by age class in 1971 for entrants. Table 5 was the main instrument in assessing the validity of the Census of Agriculture Match: matches in cells, off the diagonal are potential mismatches. 1For a description and an assessment of the Census of Agricul- ture Match see the section "The Data-Base" in Chapter IV. 188 189 .va cu Acv messcoo use Aopv op “av mace. co cocuommcwpcc one up ecmccc mcmxcum "maoz .supcz occupcucem< mo camcou Pumpimmmc "muezom mccce Nccm cmcc cccc cccc cc_NN ccmc_ cccc Nccm camp cc mecca -cmco co cmcEzz mccm, c_e Rec ccc. cc_c cccm mch ccec _ch oceeccec _mccc mcccm ccm_c Nccc cccc cccc c_cc _ccc. cmcm_ cccc Fem Ac_c-ficc _eccc “_cc mccm ccc_ ccmc __ m m, cc mm mm _P Accc cc casc cmmc ccmm ecc_ ccc_ _c cc cc cc .cp me cw Am_c cc-cc ccce .ccc mccc cc emmc cm_ cc mc_ cc. N~_ cm Acpc cc-cc cccc_ .mcm cccc cm cc_ cecc mcc _c_ Nc cc, cc Ac_c cc-cc Nccmm cc_c Nccc_ cc cc ch ccmc cccc New cc. cm A~_c cc-cc cmmcm cmcc Ncccc mm cc cm cc c_cc cmcc mmF cc Apcc cc-mc emc__ ccmm mccc cm cm cm cc ch cmcm cccc c_ Ac_c cm-m~ _mcm cme mcc_ c _ c m cm cm _ccc ccp Ace cc cacec Acc ARV Ace Acc Acc Amc Ame Rec cccc cc cc co>c cc-mc cc-cc cm-mc cm-cc cc-mc cm-c~ mm cecec mcouccmao Amvlflcv cc conscz mcaccxc _eccc _ccc cc oc< ccc_ cc occ cczwzuucxmcm ._Nm_ use oom_ cc mm< xn emcecmmccu mcmuwxm use .mucccpcm .mcmxmpm mo eonszz .m mpnmh 190 Table 5 provides estimates of the gross flows into and out of farming for the 1966-71 period. During this period an estimated 24,083 farm operators left farming while 15,355 entered farming, thereby reducing the total number of farm operators from 85,431 to» 76,703. Exiters represented 39.2 percent of 1966 farm operators and entrants represented 20.0 percent of 1971 farm operators. The estimate of the gross rate of exit is considerably larger than the estimate of the net rate of exit. This result strengthens the plea made earlier for the use of data on gross rates of exit and entry, rather than net rates. The Census of Agriculture Match, however, provides an estimate of gross flows which is biased downwards since it masks all entries and exits followed by counter movement occurring within the intercensal period. These results confirm those of Hathaway and Perkins.2 The percentage of exiters varies according to the 1966 age class of farm operators as shown below: Age-Class in l966 Percentgge of Exiters Under 25 28.8 25 — 34 20.1 35 - 44 17.2 45 - 54 21.6 55 - 59 32.2 60 - 64 46.6 65 - 69 56.3 Over 70 67.3 The percentage of exiters is higher for young farmers under 25 and between 25 and 34 than for mature farm operators between 35 and 44; for age-classes above 45, the percentage of exiters increases with age. 2Hathaway and Perkins, "Occupational Mobility," p. 186. 191 Age of farm operators was used to define and select pre-retire- ment exiters; 65 was considered to be the normal retirement age and, consequently, all age-classes under 65 in 1966 were considered to represent pre-retirement exiters. Exploratory Results from Cross-Tabulations and Discriminant Analyses As explained in Chapter IV, an exploratory data-analysis frame- . work was adopted for this section. Briefly stated, such a framework consists of "looking at the data" in order to observe possible relation- ships. This look, however, is not free of prior knowledge but cor- responds merely to low level of such prior knowledge; also, the structure imposed on the data by the statistical methods is weak. The exploratory approach was used on a limited subset of the data. More precisely, it was used on data concerning census division 7 of Saskatchewan. Two statistical methods were used: (1) analysis of contingency tables for relationships between decision regarding continuation of farming and categorical or categorized variables, and (2) linear discriminant analysis to identify continuous variables which discriminate well between stayers and exiters. Contingency Tables Cross-tabulations of farm operators by decision regarding farm- ing and by residence on the farm, age, off-farm income, sales of agricultural products, days of off-farm work, tenure, total capital value, and acreage of improved land, are in Appendix B. Each table is provided for all operators as well as for farm operators less than 65 years old. 192 2 For all tables, the x statistic takes high values; thus, the test of independence based on the x2 statistic leads to the rejec- tion of the independence hypothesis at a level of significance of less than 0.01. Two types of measures of association are displayed: the asymmetric A's and the asymmetric uncertainty coefficients (UC).3 TA and UCA fOr which the decision regarding farming is considered ~ as dependent are especially relevant. For all tables, TA and UCA (as well as T8 and UCB), take very small values as summarized in Table 6. These results imply that knowledge of the value taken by the independent variable entails very little gain in the ability to predict the dependent variable. The conjunction of low level of significance for the rejection of the independence hypothesis and of low values for the measures of association is not contradictory. As was explained in Chapter V, the X2 statistic is not a proper measure of association because it lacks any operational interpretation. The above results clearly exemplify the difference between a test of independence, i.e., the test for the existence of an association between variables, and the measure of an association. In this particular case, it can be concluded that rela- tionships most like1y_exist between pre-retirement exit from farming and the variables considered, but that these relationships are very 3As explained in Chapter V, A (or A ) can be interpreted as the proportion of improvement in the ability t8 predict the value of A (or B), considered as a dependent variable, once the value of the other variable, considered as independent, is known; UCA (or UC ) can be interpreted as the proportion by which "uncertainty" in the fiependent variable is reduced by knowledge of the value of the independent variable. 193 Table 6. Measures of Association Between Pre- Retirement Exit and Some Selected Variables A Aa UCAb Residence 0.000 0.021 Age 0.000 0.027 Off-Farm Income 0.000 0.007 Sales of Agricultural Products 0.072 0.070 Days of Off-Farm Work 0.000 0.017 Tenure 0.000 0.029 Total Capital Value 0.053 0.066 Acreage of Improved Land 0.043 0.059 3A A is known as the asymmetric lambda measure of association, pre- -retirement exit is here con- sidered as the dependent variable. b UCA is the asymmetric uncertainty coefficient; pre- retirement exit is here considered as the depen- dent variable. weak. The very 1ow levels of significance for the xz-tests are obtained through the availability of a large number of observations. Discriminant Analyses Discriminant analysis allows multivariate exploratory data analysis, whereas cross-tabulations are convenient only in the bi- variate case. Tables 7 to 12 display results of the discriminant analyses which were performed with the groups of stayers and exiters below 65 years of age. Table 7 displays standardized coefficients of the discriminant function including a first set of variables describing the general structure of the farm: AVAGE, TOTAREA, LDOWNED, LDRENTED, $LDBLD, 194 $MACH. $STOCK. TOTCAP. and 0FFWORK.4 The discriminating power of this function is very low, as indicated by an eigenvalue of 0.053 and a Wilk's lambda of 0.949. Variables with highest weight in discriminant function are TOTCAP, $MACH, $LDBLD, and AVAGE; variables with lowest discriminating power are LDRENTED. $GRAIN, and LDOWNED. Table 8 displays standardized coefficients of a second discrim- inant function where TOTAREA, TOTCAP, and TOTSALES have been deleted, ' and ARCROP, ARIMP, ARSF, WAGES, TAXES, TOTRENT, $CATTLE, and $PIG have been added. The discriminating power is also low: the eigenvalue is equal to 0.069 and Wilk's lambda is 0.936. Variables with highest standardized coefficients are $MACH, $STOCK, ARCROP, $WHEAT and those with smallest coefficients are $GRAIN, $PIG, and $CATTLE. Table 9 displays standardized coefficients of a third discrim- inant function in which percentage variables have been included: %LDOWNED, %ARCROP, %ARIMP, %ARSF, %ARWOOD, %ARUNIMP, %$WHEAT, %$GRAIN, %$CATTLE, %$PIG,%$LDBLD, and %$MACH. Discriminating power is again very low, with an _eigenvalue of 0.047 and a Wilk's lambda of 0.955. Variables with largest discriminating power are %ARUNIMP, %ARCROP, %ARSF. %$LDBLD, TOTCAP, %$WHEAT, %ARIMP and AVAGE. Variables with lowest discriminating power are %LDOWNED, %ARWOOD, TOTSALES, and TOTAREA. Table 10 displays coefficients of a discriminant function where distances to towns (DISTl, DIST2, DIST3, DIST4), productivity of capital and land (PRODCAP, PRODLDl) are introduced; also, transformations 4 A.1. Description of variables can be found in Appendix A, Table 195 Table 7. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE -O.442 TOTAREA -0.301 LDOWNED -0.159 LDRENTED -0.008 $LDBLD -O.74O $MACH 0.767 $STOCK 0.336 TOTCAP 1.149 OFFWORK -O.315 $WHEAT -0.368 $GRAIN -0.083 TOTSALES -0.207 Note: Eigenvalue = 0.053 Canonical correlation = 0.225 Wilk's Lamda = 0.949 Chi-square = 46.4 DF = 12 Level of significance = 0.0 Percentage of correctly classi- fied cases = 58.6 Proportional chance criterion = 64.6 Score of mean of stayers = 0.123 Score of mean of exiters = -0.411 196 Table 8. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE -0.30l LDOWNED -O.126 LDRENTED -0.24l $LDBLD -0.l75 $MACH 0.700 $STOCK 0.682 ARCROP 0.634 ARIMP 0.135 ARSF 0.144 OFFWORK -0.239 WAGES -0.232 TAXES -0.371 TOTRENT 0.213 $WHEAT -0.428 $GRAIN -0.036 $CATTLE -0.118 $PIG 0.081 Note: Eigenvalue = 0.069 Canonical correlation Wilk's Lambda = 0.936 Chi-square = 59.2 DF = 17 Level of Significance Score of mean of stayers Score of mean of exiters = 0.254 = 0.00 0.139 -O.463 197 Table 9. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE -0.405 TOTAREA -0.09l TOTCAP 0.509 OFFWORK -0.340 TOTRENT 0.272 TOTSALES -0.085 %LDOWNED -0.077 %ARCROP 0.686 %ARIMP 0.482 %ARSF 0.603 %ARWOOD 0.082 %ARUNIMP 0.910 %$WHEAT 0.489 %$GRAIN 0.343 %$CATTLE 0.311 %$PIG 0.180 %$LDBLD -0.577 %$MACH -0.234 Note: Eigenvalue = 0.047 Canonical correlation = 0.213 Wilk's Lambda = 0.955 Chi-square = 40.68 DF = 18 Level of significance = 0.0 Percentage of correctly classi- fied cases = 62.5 Proportional chance criterion = 64.6 Score of mean of stayers = 0.115 Score of mean of exiters = -0.393 198 Table 10. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE 0.233 OFFWORK -0.049 TAXES 0.478 TOTRENT -0.124 %LDOWNED -0.110 %ARCROP -0.l78 %ARSF -0.038 %$WHEAT -0.046 %$LDBLD 0.528 %$MACH 0.239 DISTl -0.04l DIST2 0.361 DIST3 -0.131 DIST4 -0.282 PRODCAP 0.080 PRODLDl -0.107 LNTOTAR -0.407 LNTOTCAP -0.755 LNTOTSAL -0.051 Note: Eigenvalue = 0.124 Canonical correlation = Wilk's Lambda = 0.890 Chi-square = 102.7 DF = 19 0.332 Level of significance = 0.0 Percentage of correctly classi- fied cases = 68.3 Proportional chance criterion = 64.6 Score of mean of stayers Score of mean of exiters -O.176 0.599 199 of variables are considered: LNTOTAR, LNTOTCAP, and LNTOTSAL. The discriminating power is higher than for previous discriminant func- tions, but is still low in absolute terms, as indicated by an eigen- value of 0.124 and a Wilk's lambda of 0.890. Variables with largest standardized coefficients are LNTOTCAP, %$LDBLD, and TAXES; variables with lowest standardized coefficients are %ARSF, DISTl, %$WHEAT, OFFWORK, LNTOTSAL and PRODCAP. Table 11 displays results from a fifth discriminant analysis where percentage variables have been deleted, distances, producti- vities, other variables describing the structure of the farm, or transformations of these variables are included. The eigenvalue and Wilk's lambda are respectively equal to 0.127 and 0.887. Variables with highest discriminating power are LNTOTCAP, TOTCAP, LNTOTAR, DIST2 and DIST4. Variables with lowest discriminating power are PRODCAP, OFFWORK, LNTOTREN, and DISTl. Table 12 provides the standardized coefficients of a last dis- criminant function with all variables with some discriminating power in previous functions and some others of particular theoretical interest. Discriminating power is somewhat higher than for previous discriminant functions but still low in absolute terms: eigenvalue is 0.144 and Wilk's lambda is 0.874. Variables with largest stand- ardized coefficients are LNTOTCAP, %$LDBLD, LNTOTAR, TOTCAP. Variables with lowest standardized coefficients are PRODCAP, TOTSALES, OFFWORK, LNTOTREN, DISTl and %LDOWNED. In Chapter IV a set of hypotheses was stated with respect to the relationships between pre-retirement exit from farming and certain 200 TABLE 11. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE 0.168 TOTAREA 0.168 TOTCAP 0.623 OFFWORK 0.025 TOTRENT -0.154 TOTSALES -0.094 DISTl -0.066 DIST2 0.317 ‘ DIST3 -0.155 01514 -0.309 MECHl -0.292 PRODCAP 0.005 PRODLDl 0.175 LNTOTAR -0.364 LNTOTCAP -0.954 LNTOTREN -0.044 LNTOTSAL -0.132 LNOFFWOR -0.159 Note: Eigenvalue = 0.127 Canonical correlation Wilk's Lambda = 0.887 Chi-square = 106.7 DF = 18 Level of significance Percentage of correctly classi- fied cases = 71.5 Proportional chance criterion = 64.6 Score of mean of stayers Score of mean of exiters 0.0 0.336 -0.175 0.579 201 Table 12. Standardized Coefficients of Discriminant Function for Exiters and Stayers, 64 or Less, Census Division 7, Saskatchewan Variable Standardized Coefficient AVAGE 0.170 TOTAREA 0.217 TOTCAP 0.369 OFFWORK 0.034 TAXES 0.233 TOTRENT -0.160 TOTSALES -0.024 %LDOWNED -0.068 %$LDBLD 0.420 %$MACH 0.194 DISTl -0.057 01512 0.279 DIST3 -0.105 DIST4 -0.264 MECHl -0.273 PRODCAP 0.009 PRODLDl 0.189 LNTOTAR -0.408 LNTOTCAP -0.943 LNTOTREN —0.034 LNTOTSAL -0.105 LNOFFWOR -0.180 Note: Eigenvalue = 0.144 Canonical correlation = 0.355 Wilk's Lambda = 0.874 Chi-square = 119.3 DF = 22 Level of significance = 0.0 Percentage of correctly classi- fied cases = 71.1 Proportional chance criterion = 64.6 Score of mean of stayers Score of mean of exiters -O.188 0.623 202 variables. In the following paragraphs, results from discriminant analyses are used to provide evidence for or counter-evidence to these hypotheses. Hypothesis 1 states that pre-retirement exit from farming is negatively related to age. AVAGE was not found to be a powerful discriminating variable; furthermore, in all discriminant analyses pre-retirement exit appeared to be positively related to age. Thus, - results seem to provide counter-evidence to Hypothesis 1. The fact that age enters linearly in discriminant analysis may explain these unexpected results. Hypothesis 2 states that pre-retirement exit from farming is positively related to farm operator‘s involvement in off-farm work. OFFWORK was found to have low discriminating power; it was sometimes positively related and other times negatively related to pre-retirement exit. These results do not support Hypothesis 2. Hypothesis 3 states that pre-retirement exit from farming is negatively related to the degree the family owns the farm land. LDOWNED and %LDOWNED were found to have little discriminating power. LDOWNED was found to be positively related to pre-retirement exit (but, so was LDRENTED) and %LDOWNED was found to be sometimes positively and other times negatively related to pre-retirement exit from farming. These results do not support Hypothesis 3. Hypothesis 4 states that pre-retirement exit is negatively related to total acreage, total capital value, and total sales of agricultural products. TOTAREA was found to have little discrimina- ting power, but LNTOTAR showed greater discriminating power; it is 203 disturbing, however, to observe that coefficients of TOTAREA and LNTOTAR take opposite signs when these variables are both included in the discriminant function. TOTCAP and LNTOTCAP were found to have high (in relative terms) discriminating power in all discrim- inant functions. Again, it is disturbing to observe that coefficients of TOTCAP and LNTOTCAP take opposite signs when these variables are both included in a discriminant function. When only one of TOTCAP - and LNTOTCAP is included in the analysis, pre-retirement is found to be negatively related to that variable; this result provides evidence for Hypothesis 4. TOTSALES and LNTOTSALES were found to have very little discriminating power; this does not support Hypothesis 4. In summary, the composite Hypothesis 4 is supported only with respect to the hypothesized negative relationship between pre-retirement exit and total capital value of the farm. Hypothesis 5 states that pre-retirement exit from farming is negatively related to productivity of land and capital. PRODLDl was found to have little discriminating power and to be negatively related to pre-retirement exit. PRODCAP was found to have very little dis- criminating power. These results provide only weak and partial evi- dence to Hypothesis 5. Hypothesis 6 states that pro-retirement exit is negatively related to mechanization. MECHl was found to have little discrimina- ting power and to be negatively related to pre-retirement exit. These results provide some evidence in support of Hypothesis 6. Hypothesis 7 states that pre-retirement exit from farming is negatively related to distance to towns. DISTl and DIST3 were found 204 to have very little discriminating power and to be negatively related to pre-retirement exit from farming. DIST2 and DIST4 were found to have some discriminating power and to be respectively positively and negatively related to pre—retirement exit. Empirical evidence seems, therefore, to be ambiguous: on one hand distance to large urban centers (Saskatoon and Regina) is negatively related to pre-retirement exit, but on the other hand distance to small or medium urban centers is , either not related or related positively to pre-retirement exit from farming. Hypothesis 8, concerning relationship between pre-retirement exit from farming and residence, was not investigated because of the theoretical problems involved in including qualitative variables in discriminant analysis.5 A Multivariate Log-Linear_Mpdel of Pre-retirement Exit from Farmipg In the preceding sections statistical analysis of available data was performed, with the decision regarding exit from farming being considered as dependent. Two other decisions made by the farm opera- tor should be considered as jointly dependent with the decision regarding farming: (l) the decision concerning place of residence, and (2) the decision concerning involvement in off-farm work. In this section a log-linear model of jointly dependent binary 6 variables is used to investigate: (1) the interaction between the 5See section on discriminant analysis in Chapter V. 6See section entitled "Multivariate Log-Linear Model with Exogenous Variables" in Chapter V. 205 three above mentioned decisions, and (2) their dependence on a set of exogenous variables. The statistical analysis proceeded in two main stages: (1) the choice of a model using only part of the data set, and (2) the testing of this model on other parts of the data set. Choice of a Model The first step in the search for an adequate model consisted of fitting several saturated7 log-linear models in which main effects are function of different sets of exogenous variables. This method was necessary because the Nerlove-Press program, which was used, is limited to a maximum of 16 exogeneous variables.. 0n the basis of the findings using discriminant analysis some variables, e.g., DISTl and DIST3, were not even considered for inclu- sion. The objective of this first step is to select the set of exo- genous variables to be included in the model to be tested. This exploration can be conducted using conditional estimates; both condi- tional and full maximum likelihood estimates are, however, displayed in the tables mainly to illustrate the fact that conditional and full likelihood estimates are close. Table 13 displays conditional and full maximum likelihood estimates of a saturated model including the following exogenous variables: AVAGE, TOTAREA, LDOWNED, TOTCAP, TOTRENT, TOTSALES. %LDOWNED, %$LDBLD, %$STOCK, MECHl, PRODCAP, PRODLDl, LNTOTAR, 7See Chapter V for detailed explanation: a saturated model is a model where all interaction effects are present. cc.chF- . cc_coeac cooe._ax._ cc eecccaccc. .cocucc-u ucuouaexme oca momocccocaa c. noc:o_e c~.- .mm.~-c “cc.-c 89..- M2,- 28.- 591cc Rec.-c Acm.~-c Ace.-c can .i 0m; . u «wee... NQ—mua Acc._-c Ac—.c ANN.-V m__.- ccpc. cccc.- can” Ace.-c Aec.m-c Ace.-c ~ccc.- cc~.- eccc.. Nccczadc “cc.-c Acc.m-c Acc.P-v Nccc.- cc~.. eccc.- Nccmcc Acc.-c Ace.-c Acc._-c Nccc.- ~ccc.- eccc.- ccxc Nxmozumo maumue h~xu Bug: 57553:: 355325 953: 8:95.wa PP$ 23(JES cwmmcw. AMMPW. "cwcuw nc~.cnw Acc.c Acc._-c “cc.-c .cc.c Acc.-c Anc._c A-.c-c Amm.cc “cc m_c cc_cc. _chcc. cNNccc.- chcccc.- ccccccc. ccpccc.- c.ccccc. cFNc.- cm.” ~g¢czccc “Wmcmw- Awwcmc AcWNMW Ac. NWW Acm.c ANM.~c Amc.c “cc.c Acc.,-. Ac~._-c Acc.~c Aec._c Am~.m-c Ncc cecc. cpmcc. mcccccc. cc.cccc. cecccc.- acmccc.. .cmccc.- mcccc. cc.c- ~c_mcc A__._c Acc.-c ANA.F-c Acm.~-. A~,._c Am_._-c Acc.-c .cc._-c Amc.c “cm..c Aec.~c Ac~.~c Acc.nc “c—cc. cpcc. c-.- c-.- cmec. _chc.- __Ncccc.- cecccc.- chcccc. c-ccc. mcccccc. _cccc. .c.~ can“ eacccesd sccpcaacaca _cec_o_ceoc ace ea cacac macaeccau ccae._oscs ess.xaz c .Nm.c Acc.c Ac..-. Acc.m-c A . . - .- . . . . . . . .- .- Fm c Ace _ c Acc c “cc c Acc -c A_c _c ANc c-c ANN cc cccccc ncccc ccmc Ncc cc_cc. cccccc. cccccc. ccccccc.- nchccc. ecpccc.- c_ccccc. cpcc.- c_.n ccccxeec Rec.-c Ac_._c Acc.cc Acc.~-. Acc.c Ac~.~c Acc.c Accc.c A_c._-c A_~._-c Acc.~c Ac,._c .mc.m-c m_cccc.- chc. cme. ccc.- acme. Ncmcc. cmccccc. mcmccccc. cccccc.- cwcccc.- c_mccc. meccc. c_.m- cccmce Am_..c Acc.-c A_c._-c “cm.~-c Acc._c Amc.F-c Amc.-c Acc._-c ch.c Amm._c Acc.~c Ac~.~c .cc.cc .mccc. ..cc.- ~c~.- mc~.- ~m~c. cc.cc.- chcccc.- cccccc.- c_ccccc. cNNccc. ccccccc. ccccc. c~.~ ecu“ - cco_c025clwu_c_caooca ucconlwda co comma mwucecumu coochuxcc asacxoz 4 mcccc scmccezc accccczc ccccczs accccca cczzccsc musemccc czccccc accccc cczzccs ccecccc ccccc czccmzcc ape..ca> - acoucoaoo macadac =_c: coxwzuuoxmom .N cowmcsco maccuu .muucecumm _cco.ucvcou sac: . chTLoQEou .mcuoccm cocuocceuc~ oucccc>ccp vac oucccc>cm ucccmcou vcc mecca—cc> maocooOxu co ucovcuaco «cumccm can: co mouaecumu uoOchoxcc Eaecxcz m_ ocncp 207 LNTOTCAP, LNTOTSAL, and TAXES. Asymptotic t-ratios can be used to decide which variables should be included in the model. Asymptotic t-ratios associated to coefficients of MECHl, PRODCAP, PRODLDl, LNTOTSAL, and TAXES are low in all three equations and, therefore, these variables need not be included in the final model. Table 14 displays estimates of a similar model which involves AVAGE, LDOWNED, $MACH, %LDOWNED, %$LDBLD, %$STOCK, DIST2, DIST4, LNTOTAR, LNTOTCAP and LNTOTSAL as exogenous variables. Asymptotic t-ratios associated to coefficients of DIST2, %$LDBLD, %LDOWNED, and $MACH are small and, therefore, these variables need not be retained in the final model. Table 15 displays estimates of a model which differs from the one displayed in Table 14 only by the deletion of $MACH and 01812. The asymptotic t-ratio corresponding to DIST4 is small in all three equations and consequently DIST4 need not be retained in the final model. In Table 16, which displays estimates of another similar model, the asymptotic t-ratios associated to TOTRENT are small, and similarly, TOTRENT will not be retained. In summary, exogenous variables whose coefficients have large enough t-ratios and which deserve to be retained in the model are AVAGE, TOTAREA, LDOWNED, %LDOWNED, %LDBLD, %$STOCK, LNTOTAR, and LNTOTCAP. The second step in the search for a suitable model consists of determining what level of interaction among dependent variables should be chosen and, for that level, what interaction terms should be retained. 208 om.oo~p- n eocuucam coaccpox_— co ezuccomoca mo_ucc-u accoucsxmc «co mumosucuccc c. mmcamcu Ace.-c Acm.~-c ..c.-c 88.. cm, . - 88.. 8.823 Acc.-c Acm.~-c “cc.-c «$9. 2._— . . man .0. Nommmm “cc.-c .-.c Ace.-. mccc.- cc_c. mecc.- ccxc Acc.-c Acc.c-c Ame.-c m-0.- nm_.- ~0mo.- Nxxozmuo .cc.-c Ac_.m-c Acc._-c c-c.- cc~.- m_cc.- Nccmcc “cc.-. A~c.-c Acc._-c c-c.- Nccc.- m_cc.- ccxc peace“ ee_coecacec Nccczdec Nccmmm. c_xc acacccsacc moooccc ecccoacace_ acaccascc Ac~.,-c Amc.-c Acc.~-c A_c._-c A-.c Ac_._-c Apm.c Acc.c “_c.-c “cc.-c Ac~.c-c AcF.cc 28.- :8; SN; 829. :88. 58.. ctcc. ccccc. £88.. :38: 28.- Sc Ncccztc Acm.cc Aec.mc Amm.m-c .em._c “cc.-c Ace.mc AmN.c A_m._c ANN.-c Acc.-c Acc._c Ae~.m-c ~_cc. ccc. cc~.- ccccc. ccccc.- ccmc. ccpcc. ceccc. .ccccc.- ccmcccc.- ccccc. ac.~- Nccmcc Amc.-c Acc.~-c Amc.~-c Aec._-c ANc._c A__._-c Acc._c Acc.-c Acc.-c .cc.~c Acc.~c Acc.~c cNFc.- ccm.- ,cN.- ccmcc.- cmmcc. emccc.- ceccc. ccccc.- cccccc.- cccccc. mcpc. cc.. ccxc ecccoecd »c_c_aacoca .eeocc_ceac and co coaac macaecc c e x c ANM._-V Acm.-c Acc.~-c Acc.c-c Ac_.c Ac_._-c .c~.c Acm.c “cc.-c Acc.-c Acc.c-c Amc.cc cmcc.- Neec.- cm~.- mcccc.- cmmccc. ccccc.- cc.cc. cc_cc. cc_cc.- _NNccc.- cpcc.- cc.” Nccczddc Acm.Pc Amc.mc apn.~-c Acc._c “cc..-c Acc.cc Acc.c Acc._c Ace.-c Acc.-c Ac_._c Acc.c-c mmcc. .cm. ec.N- mcccc. chcc.- mmcc. mcmcc. ccccc. cpmccc.- ccccccc.- mcccc. cc.~- cccmcx c.- ..- . - . - . AF_._-c Acm._c Acc.-c Acc.-~ Acc.~c. Acc.- Acc cc Mflmc.w Ammma-c Acmcm.~ umwcm.~ wwmcmw Fcecc.- ccccc. Pm_cc.- cemccc - cccccc cc_c cc _ c_xc .ecccoesa sc__.caceca cecoc ago ea caaac maceeccmm cease—accc emecxe: c scmccczc accccczc ccccczc ccm_c Nemcc ccccmcc coccccc cczzcccc Iccz» cczzccs ccccc execmzcc onwuuwmu” eccecmrzcc: N cccmc>co camcou .meuoecumm _ccocucucou sac: Smtcaeou .30th 530.235 32.33:. 95 cactus; 2.323 new 333;; 32303 .8 23:33 3335 5a: mo «32.3mm 30229.: .5538: .3 ~33 Pm.mo~_- ”cowuucau woosw—oxcp v0 EcupLoQOJ a mccucc-» ucuounexmc use conveyances c. mecca.“ 209 Amm.~-c Acc.-c Ac~._-c Acc.c-c Acc.~-c Acc._-c Ame.-c Ac~.Pc Acc.c acc._-c Aac.c-c Acc.cc Ann.-c cm,.- camc.- c_cc.- cm..- c-.- cc~cc.- _cccc.- ncmcc. cc_cc. _ccccc.- c_~c.- P~.c Ngcczedc cecc.- Acc.-c Acm.~-c Ace.-c Acc._c Ac_.c-c ~ccc.- cmp.- cccc.- cccc. cc.~- cccmcc Acc.-. 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Tests based on the likelihood ratio can be performed to decide whether to include the trivariate and bivariate terms. These tests must be based on the full maximum likelihood estimates. The test for the trivariate interaction effect is based on: -2 log A = -2 [-1208.17 + 1207.92] = .50. 2 This statistic is asymptotically distributed as X with one degree of freedom. Thus the trivariate interaction term is not to be con— 8 sidered different from zero at a level of significance of .15. The statistic for the test for bivariate interaction terms is -2 log A = 12.40 asymptotically distributed as X2 with three degrees of freedom; thus, the bivariate interaction terms can be considered to be globally different from zero at a .15 level of significance. Tests for individual bivariate interaction effects, based on the models displayed in Tables 20, 21, and 22, lead to the following conclusions at a .15 level of significance: 1. The interaction effect between EXIT and OFFWORKZ is not significantly different from zero (-2 log A = .89). 2. The interaction effect between EXIT and RESIDZ is signifi- cantly different from zero (-2 log A = 2.44). 8Choice of a high level of significance is justified at this stage by the desire to avoid type II errors, i.e.. to avoid deleting interaction terms which are actually different from zero. 212 ~o.~o~—c "cocuucau voocc—oxwp mo Ecuwgoooa a .co.ucc-u ocuoucech use mocugucucaa c. «menace .cc.-. .cc. .. .c..-c .c..~-c .c~.c-c ..c..-c .cc..c .mc.. ..c..-c .-.~. .c..c-c .cc.c. cc..- .c..- cc.c.- ..~.- c.~.- ccccc.- chcc. cc.cc. Nccccc.- ccccccc. .ch.- N~.c ~xcczcec .cc.-c ..c.N-c .Nc.-c .cc.c. .cc.~-. .c.c. ..c.c .cc.mc .cc..-c .c...c ..c.. ....c-c c.cc.- ”...- cccc.- ccc. ~.~.- cccc. c.ccc. ccccc. .ccccc.- c.~ccc. ccccc. cc.c- cc.ccc .Nc..-. .c~.c .Nc.-. .cm.c-. .c..c-. ..c..-c .c..~. .cc.-. .Nc.cc .c..cc .cc.~. .c..c. N.... 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Nccccc.- mcccccc. .ccc.- c~.c Nccczccc .c... .ec.~c .cc..-c ..c... .cc.c .cc.c-c c.ccc. c.ccc. c.cccc.- cc.ccc. ccccc. cc.c- cc.ccc .c..~c .c..-. .c..c. .cc.cc .c~.~c ..c.c. cc.cc. ...cc.- .ccccc. cc.cccc. ccccc. cc.~ ..xc cea.coe=c a....ccccca .cec.c.ceec ac. :0 cacec cacae.ccc ccac..ac.. ece.xaz c .NN... ..c.. .cm..-. .m..~. .Nc.c-. ....c. ccccc. cc.cc. ccmccc.- ccccccc. c.cc.- cc.c Ncccacec .N... .cc.~. .cm..-c ...... .cc.. .cc.c-c ccccc. ccccc. cccccc.- chccc. .Nccc. cc.c- cc.ccc .c..~c .c..-c .c..cc .cc.c. .c~.~c .cc.cc ccccc. ...cc.- .ccccc. cc.cccc. .cccc. cc.~ ..xc . cc.coecc cc...cecccc cc.cc ace cc cacec cccee.ccc cocc..ax.. sce.xe: < Nxmozmuo monmm Fme cccccccc cczzcccu cczxcc. cccccc. occ ceaccecc c.ca.ca> cuumccm cocuucemuc. occ.cc>.m caomccm c.cz ucovcunoo c co.c_>_o ccccmu .coucecccm .ccocucucou cu.3 coccecQEou .cuocccm cocpuccwuc. occ.cc>.m accuccou ccc cc.ccccc> ccoccmoxm co acmccmcma cuumccm c.cz co couce.ucm coo:..m¥.4 Ececxc: .- c.cc» 218 3. The interaction effect between RESIDZ and 0FFWORK2 is significantly different from zero (-2 log A = 11.82). Consequently, the bivariate interaction term between EXIT and 0FFWORK2 is not retained in the model. The third step in the search for an adequate model consists of deleting some of the exogenous variables for sgme_of the equations. This is done on the basis of the asymptotic t-ratios corresponding to the coefficients of the exogenous variables. One further problem arises in relation to the presence of both TOTAREA and LNTOTAR in the model; coefficients of both variables are significnatly different from zero but possess opposite signs. 0n the basis of their asymptotic t-ratios, it was decided to use LNTOTAR only. Full maximum likelihood estimates of the final model for census division 7 are displayed in Table 23. Testing the Model The model was estimated on a number of other census divisions, namely, census divisions 1, ll, 15 and 17; estimates are displayed in Tables 24, 25, 26, and 27. Tests for the coefficients are based on asymptotic t-ratios, with a large number of degrees of freedom and a .05 level of significance. First, the equation for EXIT is examined. The constant term and the coefficient of LDOWNED are significantly different from zero in none of the census divisions. The coefficient of AVAGE is signi- ficantly different from zero in all census divisions. The coeffi- cients of %$LDBLD and RESIDZ are significantly different from zero in three census divisions and coefficients of LNTOTAR and LNTOTCAP 21S) m~.oNNF- “coccuccc ccogccmxc. co Ezuccccoc .cocuuccw cu...cccoea accon on» :o emcee mcc coucecucm uoochwxc. Ezecxcz .1 cocucc-u ocuouceccc men cmcmeucmcca c. cacamcc .cc.c-c .cc.~-c .cc.c-c .cc.c-c .cc... NNN.- ..~.- .cN.- cccc. cc.c Nccczecc .cc.c-c .ce..-c .cc.cc .cc.N-c .cc.cv .cc.~. ..c.c-. NNN.- ccc.- .cc. cNN.- cccc. ccccc. cc.c- cc.ccc .c...-c .c~.c-. .cc.-c ..N.m. .cc.cc .Nc.~. .cN.cc. cccc.- cec.- cc..- cc.c. cccccc. ccccc. cc.. ..xc Ncchccc cc.ccc ..xc acc.c.zc cc.c.zc ccc.ccc cccccccc cczccccc cczzccc ccc>< .zc.czcc - a.cc.ce> .cumccm cc.cuccmcc. mcccec>cm cucmccu :ccz «cavemamo . c.cocc.>co ccccwu .ccumccm cc.cuccouc. mucccc>cm accuccou ccc cocccccc> ccocmmoxm co ucmucmqmo cuumwwm :ccz we ammuwecucm coogc—mx_4 Enecxmz .mm m.ach 220 m~.NNNF- ”cocpuccc uoo:..mxc. co Ecucccmoc .cocuucac cpc.ccccocc accow mcp co cocoa mcc cmucscucm coozc.mxc— Ezecxcz t. cocace-u ocuouceccc mcc coconucmccc cc cognac; .cc.c-c ..c.-. ....c-. .cc.c-c .cc.cc ..N.- cccc.- ch.- cc.c.- .c.~ Nccczccc .cc.c-. .cm.~-c ..c.cc ..c.N-c ..c.cc .c~.~c .cc.c-c ..N.. c...- ccc. cNN.- cccc. ccccc. cc.c- cc.ccc .cN.N-V .c..-c .cc.N-c .cc.. .c...c .ec.c. .c..- c...- c.cc.- c-.- .chc. cNNcccc.- cccc. Nccc - ..xc Ncchccc cc.cce ..xc acc.c.zc cc.c.zc ccc.ccc cccccccc cczccccc cczzccc ccc>< .zc.czcc a.ca.ca> cucmccu cocpucemuc. mucccc>cm cuumwcm c.cz ucwucmcmo . coccc>co caccmu .cuummmm cocuuccmuc. .cN c.cc. mucccc>cm uccpcccu ccc cmcccccc> ccccmmcxm co pcmccwcmo cuomccm :ccz co ecoucscpcm noocc.mxc4 Eaecxmz 221 cc.ccccrec.coccc cccc..ox.. cc cc.cceccc .cocuuccm >u...cccoca accow one :o comma mew cmpcecucm noocc.mx_. Eaecxmz .1 cocucc-u ucuoccsccc mcc cmcmzucmccc :. cmgamcc .cc.c-c .c~.-c .Nc..-c .cc.c-. .cc c. ch.- ch.- .c..- Nch.- cc N Nccczecc .cc..- ....N-c .N..c. .cc.c .cc.cc ..c.~c. .cch-c ch.- c.cc.- c.c. chc. cccc. ccccc cc N- cc.ccc .c..N-c .cc..-c .cc.~-c .cc.Nc .c..-c. ....c~ .cc... c.cc.- cc..- ch.- c.ccc. cc.ccc - cc.c ch ..xc Ncchccc cc.ccc ..xc acc.c.zc cc.c.zc ccc.ccc cccccccc cczccccc cczzccc ccc>< .zc.czcc a.ce.ca> .coaccc cc.coecoce. ace.ce>.c ccoaccc e.ez peaceocac .. cc.cc>.o ccccmu .cpomccm cocuucemuc. mpcccc>cm uccuccou ccc cc.cccec> ccocomoxm co ucmucmcmo muumwcu cccz mo «cmucecucm noocc.wx_4 Eascxcz .mm acne» 222 cc.cc~.- ”cc.ccecc ccce..ox.. cc ccccceccc .ecccoccc cc...cecccc cc.cc ace cc coccc ace cocaeccco cccc..ax.. Ececxcz t. cocucc-u ucpoucexcc occ cmcmcucmecc cc cognac; .cN.c-c .c...-c .c..c-V .c~.c-c ....c. ccc.- .c..- .c..- cccc.- cc.~ Ncchccc .cN.c-c .ce.c-c .cN.cc ..c.N-c .cN.cc ..c... .cch-. ccc.- cc..- c.c. .NN.- cccc. ccmcc. cc .- cc.ccc .c..c-c .cc.c-c .ec..-c .cc.~. .cc.. .cc.c. .cc... cc..- ccc.- c...- ccccc. cc.ccc. cc.c. c~c., ..xc Nccczccc cc.ccc ..xc acc.c.zc cc.c.zc ccc.ccc cocccccc cczccccc cczzccc ccc>c .zc.czcc a.ce.ca> ucmucmcmo ccumccm cocuuccmuc. muc.cc>.m muumccm c.cz m. coccc>co czccmu .cuummmm co.pucemuc. mecccc>cm accuccou ccc cocccccc> ccocwmoxm co acmccmcmo cuummcm cccz co acmucscpcm uoo:..mxc4 Ececxmz .om c.cch :— 223 co.mN.F- “coccoccc coocc.mx_. co Ecucccmoc .cocuoccc mac—camcoec accow as» :o umccc mew cmucscucm cco:..oxc. Ececxcz i cocucc-u ucpoucsxcc men cmcmgccmccc cc cmccmcc .cN.c-c .cN.-c .Nc..-c .cc.c-c .Nc.cc ch.- cc..- c...- ech.- cc.~ Nccczecc .cN.c-c .cc..-c .c..cc .cc..-. ..c.cc ..c.c .cc..qc ch.- cmcc.- Ncc. cc..- cccc. cc.cc. e.c - cc.ccc .cc..-c .c..c-c .Nc.-c .cc.cc .c... .cc.c. .c.... chc.- c.c.- cccc.- ccccc. cc.ccc. cc.c. .ccc ..xc Nccczccc cc.ccc ..xc ecc.c.zc cc.c.zc ccc.ccc cccccccc cczzcccc cczzccc cc<>< .zc.czcc m.cc.ec> cuumccm cc.cucee.c. mucccc>cm cuumccm c.cz ucmccwcmo c. cocc.>.o ccccmu .cuumccm cocuucemcc. mucccc>cm cccpccou ccc cc.ccccc> ccccmmcxm co acmccwcmo cuumccm c.cz co acmucecucm voogc.mxcc asecxcz .NN c.cch 224 in two census divisions. EXIT is positively related to AVAGE, a result which contradicts Hypothesis 1 of Chapter IV. EXIT appears unrelated to LDOWNED, a result which contradicts Hypothesis 3. It appears that EXIT is positively related to %LDBLD; such a relation- ship was not considered in the hypothesis. The hypothesized negative relationship between EXIT and LNTOTAR and LNTOTCAP is still uncertain. EXIT is consistently negatively related to RESIDZ; this result sup- ports Hypothesis 8 according to which nonresident farm operators are more likely to leave farming before retirement age. As far as the RESIDZ equation is concerned, the main results consist of the strong positive relationship with %$STOCK and the strong negative relationship with OFFWORKZ. This can be interpreted as it follows: residence on the farm is positively related to the importance of the livestock enterprise on the farm and is negatively related to the farm operator's involvement in off-farm work. As far as the OFFWORKZ equation is concerned, the major result (apart from the already mentioned interaction with RESIDZ) consists of the existenceTOfa negative relationship with AVAGE. In summary, the statistical analysis of the data using the log-linear model leads to the rejection of all hypotheses stated in Chapter IV except: (1) parts of Hypothesis 4 concerning the rela- tionship between pre-retirement exit and total capital value and total acreage, and (2) Hypothesis 8, concerning the positive rela- tionship between pre-retirement exit from farming and nonresidence on the farm. 225 Conclusion The foregoing empirical analysis is disappointing in many respects. Most of the hypotheses presented in Chapter IV are not supported by the statistical analysis of the data. Although it was recognized at the outset that some of the major variables bearing on the decision to leave farming were not available in the data-base, some relationships between pre-retirement exit and available variables were expected to be identified. Two main conclusions should be drawn from the foregoing empirical analysis: 1. The decision to leave farming before retirement is not clearly related to a limited set of farm factors; pre-retirement exit is'a complex phenomenon which requires detailed analysis based on specially collected information. 2. The failure to identify clear relationships between pre- retirement exit from farming and the considered exogenous variables raises some doubts about the adequacy of the Census of Agriculture Match as a data-base for a study of exiters (or entrants). From a statistical point of view two important methodological issues were encountered. First, tables of contingencies analyzed in the exploratory phase of the data analysis yielded some highly signi- ficant value for the x? statistic, thereby leading to the conclusion that relationshps between variables certainly exist; but in attempt- ing to measure those associations between variables, it was discovered that they were very weak. In summary, the following were exemplified: 1. The x? statistic is a poor measure of association and an 226 experimenter should rely on other measures such as those which were used in this study; 2. Very significant results concerning the existence of a relationship are consistent with very weak relationships (in the sense that knowledge of one variable is of little help in predicting the value of the other). Second, in the confirmatory phase of the analysis, the follow- ing approach was taken: a model was chosen and estimated using part of the data-set and, then, tested on other parts of this data-set. It followed that several coefficients which apparently were signifi- cantly different from zero, on the basis of asymptotic t-ratios ob- tained using the first part of the data, were shown to be not significantly different from zero, when the model was tested on other parts of the data-set. Thus, it was clearly exemplified that one is likely to arrive at misleading results ifamodel is chosen, estimated, and tested on the same data. The method used in this study is the proper one, provided enough observations are available. The general dissatisfaction with the rather sophisticated statistical analysis of available secondary data, prompted a proposal for further research based on "ad hoc" information, which is presented in the following chapter. CHAPTER VII PROPOSAL FOR FURTHER EMPIRICAL RESEARCH: A LONGITUDINAL SURVEY The objective sought in this chapter is twofold: first, to present a critical assessment of the empirical analysis and, second, to propose an additional empirical study to evaluate further the theoretical framework proposed in Chapter III. Thus, this chapter is divided into two sections. The first section reviews the main propositions of the theoretical framework and discusses the limitations of available secondary data with respect to testing these propostions. In the second section, a proposed longitudinal survey is outlined. Assessment of the Analysis of Secondary Data The empirical analysis whose results were presented in Chapter VI will be assessed on the basis of its ability to substantiate the theoretical framework proposed in Chapter III. As a preliminary to this assessment, the main elements of the theoretical framework are inventoried in the following subsection. Highlights of the Conceptual Framework The general thrust of the approach in Chapter III is to sub- stitute an empirically relevant model of individual choice for an axiomatic one. In order to develop such a model, theoretical concepts and empirical results have been drawn from several disciplines. 227 228 Income maximizing and utility maximizing variants of the axio- matic economic model of choice were described in relation to the decision to leave farming. The behavioral assumptions were briefly and critically reviewed. On the basis of findings in psycholoQY. a general model of behavior and choice was proposed, to be used as a frame on which other elements could be added to fit the specificity of the decision to leave farming. The main features of this general model of adaptive behavior are: (1) human behavior depends on changes in the environment as well as on the person itself, (2) individuals act as parts of larger groups, (3) individual behavior is essentially of a satisficing nature, i.e., individuals try to attain some prede- termined goals called wants and aspirations, (4) wants and aspirations are not static, and (5) habitual behavior prevails in most circumstances. Farming can be considered as a form of habitual behavior whereas exit from farming is the result of a genuine decision. Any habitual behavior takes place with the individual having a certain organized perception of reality which is consistent with the habitual behavior. As long as this perception is unchanged the same habitual behavior will prevail; for a genuine decision to take place. the organized perception needs to change and become inconsistent with the habitual behavior. Very little is known empirically about the transition from habitual behavior to genuine decision and the accompanying restructur- ation of the perceived environment. Empirical study of this transi- tion and restructuration in the special case of a farmer considering leaving farming would shed some light on the circumstances and factors affecting the decision to leave farming. 229 Farmers' behavior is to be considered as satisficing: farmers strive to attain goals and aspirations whose level is itself the result of past performances as well as performances of people with whom they associate. Thus, as long as a farmer satisfies his wants and aspirations, there is no reason for him to leave farming. The decision to leave farming often implies drastic changes in all family members' lives. Very likely, these consequences may be beneficial for some and detrimental to others, according to each individual's goals. Conflicts in goals may arise and the resolution of these conflicts will bear on the action taken. Consequently, the decision to leave farming is to be looked at as a collective decision. The level of aspiration depends on past performances among which is income remunerating the operator's labor. This implies that not only present income, but also the history (trend and variations) of income bears on the decision to leave farming. Past incomes are factors influencing the decision through the mediation of the level of aspiration. Any genuine decision, and consequently the decision to leave farming, is based on a perceived economic and social environment. Perception of this economic and social environment plays, therefore, a decisive role in whether the decision to leave farming is made. Perception is both a filtering and a structuring process; in other words, some elements of the environment remain unknown to the farmer (this is limited knowledge) and the elements which are known are. organized into a whole which acquires a certain meaning. The extent to which farmers ignore relevant elements is ill-documented. The 230 process by which known elements, especially nonfarm job opportunities and urban conditions of life, are organized appears to be completely unknown. Imperfect information, with respect to nonfarm occupation alter- natives, once it is recognized by the farmer, leads to a process of collection of information usually called job-search. According to the proposed theoretical framework, job-search does not, however, proceed unless the farmer is dissatisfied with his present situation and is considering other alternatives. Job-search and the accompanying information gathering are part of the reorganization of perceived environment. Factors prompting such a job-search, as well as its duration, intensity and other characteristics, are ill-known.1 Imperfect information, even after a job-search, may explain the occurrence of decision-making errors and their possible corollary, return migration. The relationship between the amount of knowledge of working conditions in nonfarm occupations and of urban living conditions, and return migration, remains to be investigated. People, in deciding on an action, take into account benefits and costs occurring only over a limited time span, which is called the time perspective. The action taken is independent of the conse- quences occurring outside the individual's time perspective. Conse- quently, the length of this time perspective, because it determines what consequences are or are not accounted for, bears directly on the 1The so-called job-search literature deduces characteristics of the job-search on the basis of an assumed maximizing behavior and is, therefore, essentially normative. What is proposed here is a posi- tive study of the search process. 231 individual decision. If the concept of time perspective has any real basis, an inquiry into farmers' time perspective and the factors affecting it is of interest. The decision to leave farming is affected by the farmer's and the family's attachments to their community as well as to farming as an occupation. Shortcomings of Available Secondary Data The data-set which was used in this study and the procedure by which it was obtained were described in Chapter IV. The list of vari- ables which were available for each observation can be found in Appendix A. A major advantage of the Census of Agriculture Match is that it is exhaustive. Potentially, all stayers, exiters, and entrants be- tween 1966 and 1971 can be identified for all provinces of Canada. Thus, the Census of Agriculture Match allows for good estimates of all gross flows of farmers in and out of agriculture, for each pro- vince or for any desired region within a province. In this study only data concerning Saskatchewan were used. At the time this study is being completed, a l97l-1976 Census of Agriculture Match is being perfbrmed, based on an improved metho- dology in the light of the experience acquired with the 1966-1971 Match. Thus, the same type of analysis could be conducted in the near future for the 1971-1976 period. Furthermore, the 1966, 1971 and 1976 censuses can possibly be linked together to constitute a three-census Match. The large size of the Census of Agriculture Match renders it 232 quite unwieldy. When multivariate statistical analysis need be performed, samples must be taken. The main shortcomings of the Census of Agriculture Match in relation to a study of off—farm movement and migration is the limited scope of the information collected in the census. The great majority of the information collected in the census is related to the farm business and, especially, to the physical aspects of agricultural production. Most of this information is a priori irrelevant to the decision to leave farming and, therefore, was left out of the simpli- fied data-base used in this study. As mentioned before, only infer- mation describing the overall structure of the farm was retained. Information concerning the farmer and the family is limited to the age class of the operator, involvement in off-farm work and whether or not the operator resides on the farm. No information con- cerning get_income either from farm or nonfarm sources is available. Only one piece of information, which was thought to be theore- tically relevant, could be added to the data-set: distances from the farm to the nearest communities of four different sizes. A comparison of the infermation available from the Census of Agriculture Match to the information which wOuld be necessary to sub- stantiate the previous summarized conceptual framework, clearly shows the inadequacy of the Census of Agriculture Match. For example, the theoretical framework calls for information on present income from farm and nonfarm sources, potential income from nonfarm employment sources for the operator and the family, operator's and spouse's skills and education, family members' goals and ways these goals are 233 acknowledged as valid,attachment to the community and farming as an occupation, knowledge of nonfarm employment opportunities, perception of urban living conditions, etc. The Census of Agriculture provides no such elements of information. In the future more socio-economic information on the operator and the family as well as information on net income are likely to be collected; the census will, however, fall short of the requirements for a detailed study of factors affecting pre-retirement exit from farming. If such a study is to be performed, ad hoc infbrmation has to be collected through a specially designed survey. A brief proposal for such a survey is described in the following section. A Longitudinal Survey In this section, the overall objectives of the survey are .stated, then the desirable features of a survey designed to reach these objectives are listed, and, finally, an outline of the infor- mational content of such a survey is presented. Objectives of the Survey The overall objective of the survey is to substantiate the following elements of the theoretical framework presented in Chapter III: 1. Existence of a satisficing mode of behavior 2. Relevance of community satisfaction and satisfaction with farming as an occupation 3. Discrepancy between perceived and actual socio-economic environment 4. Importance, intensity and duration of the search process 234 5. Dynamics of the decision process 6. Relevance of Operator's and spouse's formal education and professional skills 7. Relevance of the group nature of the decision 8. Influence of the length of the operator's and spouse's time perspecitve and relationship between socio-economic variables and the length of the time perspective 9. Interaction between off-farm movement and involvement in off-farm work. Desirable Features of the Survey The pre-retirement exit from farming is a dynamic phenomenon; in classical economic parlance, it is an adjustment to a temporary dis- equilibrium. In the light of the theoretical framework proposed in this study, the decision to leave farming is a lengthy process, involving the transition from a habitual mode of behavior to an action based on genuine decision; this transition is accompanied by a reor- ganization of the perceived environment. Given the highly dynamic nature of the decision making process, a longitudinal survey, where information is collected for at least two different points in time, seems to be recommended. I The survey should be as much as possible composed of direct questions calling for simple answers. Given the type of information sought, some nondirect questions should, however, be used. The care with which questionnaires are to be completed together with the dif- ficulty in recruiting and training qualified interviewers call for a survey of limited size. The size of the survey, however, must be' sufficient to allow reliable statistical analysis. The major depen- dent variable is the decision to leave farming, which is a qualitative 235 variable. Other considered variables are qualitative, e.g., community satisfaction, satisfaction with farming, off-farm work, residence on the farm, nonfarm job-search, and migration. Hence, the statistical methods to be used will be those reviewed in Chapter V. The multi- variate log—linear model with exogenous variables used in this study would, most likely contribute a major part to the data analysis. Ex- perience with this model shows that, when several jointly dependent variables are used in conjunction with many exogenous variables, the number of observations should not be smaller than 300 to obtain stable estimates. Thus, the survey should include around 400 farm operators. Such a limited survey cannot pretend to cover a representive sample of a province; it is bound to be exploratory. To avoid, however, being too specific to a certain location, the farmers interviewed should be sampled out of municipalities belonging to several different census divisions. The survey is to be longitudinal and to consist of two inter- views at two or three year intervals. A short interval is necessary so that the same person can be traced to the new residence in case of moving between the first and second interview. A long enough interval is required to ensure the existence, among the sampled farmers, of a sufficient number of pre-retirement exiters, with and without migration. The sample of farmers should include only farmers of age below retirement age since the study of farmers' retirement decisions is not an objective of this survey. All farmers who moved between the two interviews should be traced to their new location whether or not they have left farming. 236 Informational Content It is not intended here to draft questionnaires for the proposed longitudinal survey, but merely to outline the type of information to be collected and, sometimes, to indicate the format in which this information would be collected. In the proposed survey, two interviews are planned implying that two different questionnaires will be prepared. The second inter- view, however, may cover different ground depending on whether the farmer has stayed in farming or has left farming. The first interview will aim at collecting the following information: 1. A description of the farm-business (acreage, type of farm, total capital value, total sales, total debts, net farm income, time worked in farm activities, etc.). 2. The socio-economic characteristics of the operator and family (age, level of formal education, vocational training, technical or professional skills, number and ages of children, existence of a potential successor, off-farm work involve- ment,nonfarm incomes, etc.). 3. Measures of community satisfaction and satisfaction with farming as an occUpation.2 2These measures would be based on so-called attitude-scaling methods. Several community satisfaction scales have been developed and could easily be adapted to a survey of Saskatchewan farmers. See, for example, Vernon Davies, "Development of a Scale to Rate Attitude of Community Satisfaction," Rural Sociology 10 (September 1945): 246- 255; Clinton Jesser, “Community SdtiSfaCtion Patterns of Professionals in Rural Areas," Rural Sociology 32 (March 1963): 56-69; Ronald Johnson and Edward Knop, “Rural-Urban Differentials in Community Satisfaction," Rural Sociology 35 (December 1970): 544-548. 237 4. The operator's and spouse's expectations concerning nonfarm occupational alternatives (expected income, location, etc.). 5. The operator's forecast as to whether he will still be farming two or three years hence. In the case of a stayer, the second interview will cover the following points: 1. A description of the farm-business. 2. The socio-economic characteristics of the operator's family that may have changed since the first interview. 3. Measures of community satisfaction and satisfaction with farming as an occupation. 4. A measure of job—search3 performed in the last year and reason(s) why this search did not result in the farmer leaving farming. 5. The operator's forecast as to whether he will be farming in the near future. In the case of pre-retirement exiters, the second interview will cover the following points: 1. A description of family members' new occupations (type of work, income, location, etc.). 2. The extent of migration in relation to off-farm movement. 3. Measures of community satisfaction and job satisfaction.4 3Such a measure should be a scale based on a series of questions related to the occurrence of behaviors corresponding to increasing degrees of active involvement in collection of infbrmation and job- search. 4To be measured by attitude scales as mentioned before. 238 4. A self-assessment of the change in family members' welfare since off-farm movement. 5. The operator's estimated likelihood of returning to farming. Data Analysis Some of the information collected should allow the refining of the conceptual framework presented in this study. No formalized data analysis would be performed on this information which may be expressed in a literary form. Other information will lenditself to formalized data analysis of both an exploratory and confirmatory type, in accordance to the methodological position described in Chapter IV, and using statistical methods described in Chapter V. Conclusion In this chpater we have outlined the main features of a survey designed to make progress along the lines proposed in the theoretical framework. Much work remains in defining both the implementation pro- cedure and the informational content of the survey. Given the multi- disciplinary nature of the study, such a survey would benefit greatly from the cooperation of sociologist(s), geographer(s) and psycholo- gist(s), especially in the design of the questionnaire. CHAPTER VIII SUMMARY. CONCLUSIONS. AND METHODOLOGICAL CONSIDERATIONS This chapter is divided into two main sections. The first section summarizes the study and conclusions. In the second section some methodological problems, which arose in conducting this research, are presented and discussed. Summary and Conclusions At any point in time, the number of farm operators is equal to the number of farm operators one period earlier, minus the number of farm operators who left farming during that period, plus the‘ number of new farm operators who decided to enter farming during that period; the number of farm operators is, thus, the aggregate and cumulative result of individual entry and exit decisions. Causes which affect these individual entry and exit decisions will, there- fore, affect farm demography. Low incomes in farming, both in relative and in absolute terms, have been noted consistently during recent decades, even when income from off-farm sources has been accounted for. Movement of both hired and self-employed labor out of the farm sector has been and still is considered as the only long term solution. The concern for Canadian farm operators' welfare has led to the development and implementation of many government programs, both 239 i "1 240 provincial and federal, aimed at affecting off-farm movement and migration, income from farming, or both. These programs, which purport to bear on individual decisions, have not been designed, however, on the basis of a precise knowledge of the factors affect- ing these individual decisions. This research was primarily founded on a belief that the understanding of the variations in the gross movements of farm operators into and out of agriculture is to be based on the under- standing of the individual decisions to enter farming, to leave farming before retirement, or to retire from farming. Similarly, the design of appropriate programs aimed at modifying these flows, require a clear understanding of these individual decisions. Three main objectives were set for this study: 1. To provide a conceptual framework for the analysis of the decision to leave farming before retirement. 2. To appraise the ability of the Canadian Census of Agri- culture Match to identify entrants and exiters, and its usefulness as a major data source for analytical studies of entry and exit from farming. 3. To test as many hypotheses, concerning factors affecting off-farm movement, as the available data would permit. In the process of attaining these objectives the following tasks were performed: 1. A review of the literature on off-farm movement and migration. 2. Development of a theoretical framework for the analysis of 241 the pre-retirement decision to leave farming, drawing on economics as well as psychology and sociology. 3. Evaluation, both before and after data analysis, of a new longitudinal data base: the Canadian Census of Agriculture Match. 4. Formulation of hypgtheses concerning factors influencing the pre-retirement exit of farm operators. 5. A review of statistical methods for the analysis of quali- tative dependent variables. 6. An exploratory and confirmatory data analysis of the decisions to leave farming before retirement. 7. A sketch of a proposed longitudinal survey which would fur- ther the understanding of pre-retirement exit from farming. A summary of the aforementioned tasks follows as well as a presentation of conclusions. A broad review of literature showed that: 1. Some confusion in concepts and words which have been used in the literature (e.g., mobility, movement, migration, off-farm migration, etc.) has been hampering the development of incisive empirical work. 2. The use of aggregate data which provide estimates of net flows in and out of agriculture is inadequate to identify factors of the individual's decision to leave farming. 3. Access to a longitudinal data base is, consequently of the most necessity to yield reliable results on the causes of the decision to leave farming. 4. Empirical studies yielded conflicting results about the 242 factors influencing the decision to leave farming, especially with respect to the effect of the farm operator's involvement in off-farm work and distance to urban employment centers. The standard economic model of off-farm movement was briefly presented and its behavioral assumptions were critically reviewed. Standard economic theory postulates a certain type of behavior, namely a utility or profit maximizing behavior. The theoretical frame- yprk_which was proposed is at variance with this theory in that an attempt was made to draw on positive studies of human behavior in general, and that detailed observation and description of the exit decision-making process was advocated. Briefly stated a behavioral approach was proposed. The highlights of the proposed theoretical framework for the analysis of the decision to leave farming before retirement are: l. Farming is considered as a form of habitual behavior and pre-retirement exit from farming is the outcome of a genuine decision. 2. Farm operators' behavior is looked upon as being of a satisficing nature. 3. The decision to leave farming is viewed as a group decision, where the group is the family. 4. Goals of the members of a family are likely to diverge; hence, resolution of these conflicts is of paramount importance to the decision to leave farming. 5. Goals of the farm operator and other family members are. constantly adjusted upwards or downwards according to successes or failures in meeting past goals. 243 6. Any individual or group decision is based on reality as it is perceived and not as it is; perception is characterized by imper- fect information and by the organizing of known elements into a meaningful whole. 7. In the process of deciding, individuals only take into account consequences of their choice which occur in a limited period called their "time perspective." 8. The farm operator's and his family's attachment to the local community and to farming as an occupation are important factors re- lated to the decision to leave farming. 9. The decision to leave farming before retirement is contin- gent on other agents' decisions to provide alternative employment; these agents are given the generic name of "selector." This study drew upon a newly available lppgipudinal data base: the Canadian Census of Agriculture Match. This data base was obtained by linking (matching) 1966 and 1971 agricultural census records per- taining to the same farm operator. The matching procedure was based on the surname, first name, and initials of the farm operator. At the onset of this study, the Census of Agriculture Match was assessed on the basis of the age consistency of matched farm operators. The quality was deemed insufficient for the study of off-farm movers and a complete manual match was performed for Saskatchewan, using a more precise and systematic set of matching rules. A major advantage of the Census of Agriculture Match is that, theoretically, it covers all farm operators in an area. Thus, it is potentially a good basis for providing estimates of gross flows of 244 farmers into and out of agriculture. A major shortcoming of the Census of Agriculture Match in relation to a study of the pre-retirement exit of farm operators is the limited scope of the information which is available. The main available variables considered to be relevant to this study were: residence on the farm, age-class of operator, total area of farm, area owned, area rented, value of land and buildings, value of machinery, value of livestock, total capital value, days worked off the holding, total rent, total value of agricultural products sold, type of farm, and tenure. Some variables thought to be essential for a study of pre-retirement exit of farm operators were not available in the Census of Agriculture Match. These are: level of education, num- ber of dependents, net income from farming and from nonfarm sources, nonfarm occupation alternatives, etc. The only variables which could be added to the Census of Agriculture Match were distances from the farm to four classes of towns. Only a limited number of hypotheses were formulated: those for which the available data base could provide supporting evidence or counter evidence. Pre-retirement exit from farming was hypothesized to be positively related to the farmoperator's involvement in off- farm work and to nonresidence on the farm; it was hypothesized to be negatively related to farm operator's age. degree of ownership of farm land, total acreage, total capital value, total sales of agri- cultural products, productivity of land and capital, degree of mech- anization, and distances to towns. The pre-retirement decision to leave farming can be expressed for each farm operator by a binary variable whose values are: 245 0-1 (or stayer - exiter). Such a binary variable is a special case of what are called qualitative variables. Other decisions related to pre-retirement exit, such as residence and involvement in off-farm work can also be expressed by qualitative variables. Thus, the major dependent variables of the empirical study appeared to be qualitative. Consequently, the statistical techniques which are most commonly used by applied econometricians for the analysis of continuous variables were not applicable. A review of statistical methods for the analysis of qualitative dependent variables was necessary before any empirical analysis could proceed. This review showed that the analysis of contingency tables and discriminant analysis were well suited for exploratory data analysis and that a multivariate log-linear model recently developed by Nerlove and Press was the most adapted for confirmatory data analysis. The exploratory and confirmatory data analysis performed on the Census of Agriculture Match led to the following conclusions: 1. Pre-retirement exit of farm operators is positively (and not negatively, as it was hypothesized) related to the operator's age. 2. Pre-retirement exit of farm operators is positively related to the value of land and buildings expressed as a percentage of total capital value. Thus, farm operators whose assets consist mainly of land and buildings are more likely to leave farming before retirement. 3. Pre-retirement exit of farm operators is negatively related to residence on the farm. Farmers not living on their farm are more likely to leave farming before retirement. It should be noted how- ever, that underenumeration in the 1971 Census of Agriculture may have involved a high number of nonresident farm operators. This 246 would explain, in part, the strong relationship found between pre- retirement exit and nonresidence which was evidenced. 4. Results were unconclusive concerning the hypothesized nega- tive relationship between pre-retirement exit, and total acreage and total capital value of the farm. 5. Hypotheses concerning relationships between pre-retirement exit of farm operators on one hand and off-farm work, age, degree of ownership of farm land, total sales of agricultural products, pro- ductivity of land and of capital,degree of mechanization and dis- tances to towns, on the other hand, were not supported. In summary, empirical findings were mostly negative: data pro- vided supporting evidence only for the hypotheses concerning the negative relationships between pre-retirement exit, on the one hand, and total acreage, total capital value, and residence on the farm, on the other hand. This led to two major further conclusions: 1. The decision to leave farming before retirement is very complex, depending on more than farm-business variables. 2. The negative findings raise some doubt about the ability of the present state of the Census of Agriculture Match to identify exiters, entrants, and stayers properly. The largely negative results of the empirical analysis based on the best available secondary data prompted a proposal for a longi- tudinal survey_of farm operators aimed at collecting infbrmation to substantiate the proposed theoretical framework. This survey would cover approximately 400 farm operators at an interval of two or three years. Farm operators who left farming between the two interviews 247 would be traced to their new setting and interviewed. Information collected in these interviews would (1) serve as an input to further developments in the theoretical framework, and (2) be subject to exploratory and confirmatory data analysis. Methodological Considerations A Behavioral_Approach The behavioral approach in economics is not new, but it remains of minor importance. It has taken some extension in two areas: (1) the study of large organizations, either firms or public adminis- trations, and (2) the study of consumer behavior to which Katona made major contributions. Thus, the adoption of a behavioral approach in studying the decision to leave farming before retirement, is an extension of this approach to a new domain. Simple as it may seem, the decision to leave farming is the result of a complex decision making process and, as such, deserves a behavioral study. A conceptual framework was proposed to assist in empirical analysis; thus, the main concern was to provide a model of behavior, a set of concepts, which were empirically tractable. For example, a utility maximizing income model can be advocated if the concept of "psychic income" derived from farming is introduced; unfortunately, such psychic income is difficult to measure independently and, con- sequently, leads to an imprecise empirical analysis; on the other hand, measurement of satisfaction from farming as an occupation and attachment to the local community can be measured on an ordinal scale. In summary, a behavioral approach, by bringing detail into the 248 analysis of the decision-making process was thought to provide concepts with greater empirical relevance. Statistical Methods and Inference The approach to inference and data analysis taken in this study is at variance with that taken in the vast majority of empirical economic works. Three types of inference are usually recognized: deductive inference, inductive inference and reductive inference. Deductive inference consists of logical proof by which statements, or con- clusions, are derived from prior statements, or premises, using the rules of logic. Inductive inference involves making inferences from the particular to the general or, more specifically, making infer- ences from experiences in the past or in specific settings to pre- dict experiences inthe future or in other settings. Reductive in- ference consists of the description and the study of facts and the generation of hypotheses explaining these facts. The hypothetico-deductive method, which is predominant in the economic profession, blends deductive and inductive inference. It has been very fruitful but, when strictly applied, it leaves little scope for reductive inference. At the same time as economists have adopted the hypothetico-deductive method they have emphasized the use of ever more sophisticated methods for confirmatory data analysis. The stand taken in this research is that neither deductive, inductive, nor reductive inference should be neglected; reductive inference, or the process of idea formation, should be given more importance than it is given in the hypothetico-deductive method. As 249 the relative importance of inductive inference is reduced and the relative importance of reductive inference increases, a wider range of statistical methods are used. Inductive inference still-requires the confirmatory data analysis of classical statistics, but reductive inference requires exploratory data analysis of a new type. Tukey recently expressed the need for such a broad approach to data analysis: The principles and procedures for what we call confirma- tory data analysis are both widely used and one of the great intellectual products of our century . . .We can no longer get along without confirmatory data analysis. Bgt we need not start with it ................. Today, exploratory and confirmatory [data analysis]_can-- and should--proceed side by side.1 While the data analysis was being performed, two important technical points, which had been stressed in the chapter on statis- tical models, were vividly exemplified. First, the problems of ascertaining the existence of an associa- tion between two (or more) variables and of measuring this association are distinct; they consequently require different procedures, namely, tests of independence and measures of association, which rely on different statistics. Thus, very significant results in a test of independence (indicating that variables are most likely dependent) ppg very weak associations are perfectly consistent; a large number of observations will ensure statistical significance even in the 2 case of weak association. For example, the cross-tabulation of farm 1John W. Tukey, Exploratory Data Analysis (Reading, Massachu- setts: Addison-Wesley Publishing, 1977), pp. vi-vii. 2See Table B.l in Appendix B. 250 operators, 64 years of age or less of age, by decision regarding farming and tenure in census division 7 of Saskatchewan has a x2 statistic of 27.62 which ensures that decisions regarding farming and tenure are dependent at a level of significance of less than 0.01. Nevertheless, the AA and UCA3 are respectively smaller than 0.001 and equal to 0.029; this means that the ability to predict the deci- sion regarding farming when tenure is known is either unchanged or increased by 2.9 percent, depending on the prediction method. Thus, the association between the two variables is very weak. Second, it is important to choose the structure of a model on limited part of the data set and to test it on the other part(s). Such procedure is possible only with a large enough data set. In this empirical study the data base was divided in several parts: one for each census division with approximately one thousand obser- vations for each. A log-linear model of the pre-retirement exit from farming was chosen based partially on statistical tests using data pertaining to one census division. This model was then esti- mated and tested for other census divisions. The stringent procedure showed that some coefficients which appeared to be significantly different from zero following the choice and estimation of the model on part of the data, were not significantly different from zero when the model was tested on data pertaining to other census divisions. This exemplifies the danger of the very common practice consisting of chosing and testing a model on the same data. Such a practice_ 31A is the asymmetric A and UCA the uncertainty coefficient when the decision regarding farming is considered to be dependent. 251 misleads the experimenter in failing to reject hypotheses which, on the basis of a more correct statistical procedure, should be rejected. APPENDICES APPENDIX A NAMES AND DESCRIPTIONS OF VARIABLES APPENDIX A NAMES AND DESCRIPTIONS OF VARIABLES Table A.1 Names and Descriptions of Variables Variable Variable Year Description Number Name 1 EXIT 66 Stayer-Exiter Variable 0.0 Stayer 1.0 Exiter 2 66 Census Division Number 3 66 . Census Subdivision Number 4 66 Census-Farm Number 5 66 Crop District Number 6 RESID 66 Residence on the Farm in Previous Year 1.00 9-12 months 2.00 5-8 months 3.00 1-4 months 4.00 non-resident 7 AGECL 66 Age Class of Operator 1.00 under 25 2.00 25-34 3.00 35-44 4.00 45-54 5.00 55-59 6.00 60-65 7.00 65-69 8.00 over 70 8 AGEDl 66 Age Class-Dumy la 9 AGEDZ 66 Age Class-Dumny 2a 10 AGE03 66 Age Class-Dumy 33 ll AVAGE 66 Average of Age Class of Operator 12 TOTAREA 66 Total Area of Farm (Acres) 13 LDOWNED 66 Area-Owned (Acres) 14 LDRENTED 66 Area-Rented (Acres) 15 LDMAN 66 Area-Managed (Acres) 16 $LDBLD 66 Value of Land and Buildings ($100) 17 $MACH 66 Value of All Machinery ($100) 252 253 Table A.1 Continued Variable Variable Year Description Number Name . 18 $STOCK 66 Total Livestock Value ($100) 19 TOTCAP 66 Total Capital Value ($100) 20 ARCROP 66 Area-Cropland (Acres) 21 ARIMP 66 Area-Improved Land-Pasture (Acres) 22 ARSF 66 Area-Summer Fallow (Acres) 23 ARWOOD 66 Area-Woodland (Acres) 24 ARUNIMP 66 Area-Other Unimproved Land (Acres) 25 OFFINC 66 Off-Farm Income 1.00 Under $750 2.00 $750-P1us 26 OFFWORK 66 Days Worked Off Holding 27 WORKERS 66 Number Year Round Workers 28 WAGES 66 Cash Wages Paid ($10) 29 TAXES 66 Taxes ($10) 30 RENT$ 66 Rent on Cash Basis ($10) 31 RENTSH 66 Rent on Share or Kind Basis ($10) 32 TOTRENT 66 Total Rent = V30 + V31 33 $WHEAT 66 Value-Wheat Sold ($10) 34 $GRAIN 66 Value-Other Grains Sold ($10) 35 $CATTLE 66 Value-Cattle Sold($10) 36 $PIG 66 Value-Pigs Sold ($10) 37 $POULTRY 66 Value-Hens and Chickens Sold ($10) 38 $DAIRY 66 Value-Dairy Products Sold ($10) 39 TOTSALES 66 Value-Total Sales ($10) 40 INST 66 Institutional Farm 1.00 Yes 2.00 No 41 66 Type of Farm 1.00 Dairy 2.00 Cattle-Hogs-Sheep 3.00 Poultry 4.00 Wheat 5.00 Small Grains 6.00 Field Crops 254 Table A.1 Continued Variable Variable Year Description Number Name 41 00 Fruits and Vegetables 7. 8.00 Forestry 9.00 Misc. Specialty 10.00 Mixed-Livestock 11.00 Mixed-Field Crops 12.00 Mixed-Other 42 66 Economic Class .00 $35,000 and over .00 $25.000 - 34,999 .00 $15,000 24.999 .00 $10.000 14.999 9,999 7.499 4.999 3.749 2,499 1.199 13.00 $ 50 - 249 21.00 Institutional 43 66 Part Time Work .00 None .00 Less than 7 days .00 7 - 12 days .00 13 24 days 48 days 72 days 96 days 126 days 156 days 228 days 365 days U \l U" C IIIIII _a N O O 69 N 0"! O I O O \l w llllllll 11:00 229 44 66 Tenure 1.00 Owned 2.00 Rented 45 66 Size of Farm 69 239 399 559 759 O O \l O lllllll 255 Table A.1 Continued Variable Variable Year Description Number Name 45 8.00 760 - 1.119 9.00 1,120 - 1,599 10.00 1,600 - 2,239 11.00 2,240 - 2,879 12.00 2.880 - Plus 46 66 Total Capital Value 1.00 Under $1.950 2.00 $ 1,950 - 2.949 3.00 $ 2.950 - 3.949 4.00 $ 3,950 - 4.949 5.00 $ 4.950 - 7,449 6.00 $ 7,450 - 9,949 7.00 $ 9.950 - 14.949 8.00 $ 14,950 - 19,949 9.00 $ 19.950 - 24.949 10.00 $ 24,950 - 49,949 11.00 $ 49,950 - 99,949 12.00 $ 99,950 - 149,949 13.00 $149,950 - 199,949 14.00 $199,950 - And Over 47 66 Acreage Improved Land 1.00 O 2.00 l - 2 3.00 3 - 9 4.00 10 - 69 5.00 70 - 129 6.00 130 - 179 7.00 180 - 239 8.00 240 - 399 9.00 400 - 559 10.00 560 - 759 11.00 760 - 1,119 12.00 1120 - 1.599 13.00 1600 - And over 48 66 Cattle-Sheep 1.00 Yes 2.00 No 49 %LDOWNED 66 Percent-Area-Owned 50 %LDRENT 66 Percent-Area-Rented 51 %LDMAN 66 Percent-Area-Managed 52 %ARCROP 66 Percent-Area-Cropland 53 %ARIMP 66 Percent-Area-Impr. Pasture 256 Table A.1 Continued Variable Variable Year Description Number Name 54 %ARSF 66 Percent-Area-Summer Fallow 55 %ARWOOD 66 Percent-Area-Woodland 56 %ARUNIMP 66 Percent-Area-Other Unimproved 57 %$WHEAT 66 Percent-Value-Wheat Sold 58 %$GRAIN 66 Percent-Value-Other Grains Sold 59 %$CATTLE 66 Percent-Value-Cattle Sold 60 %$PIG 66 Percent-Value-Pigs Sold 61 %$POULTRY 66 Percent-Value-Poultry Sold 62 %$DAIRY 66 Percent-Value-Dairy Products Sold 63 %$LDBLD 66 Percent-Value-Land and Buildings 64 %$MACH 66 Percent-Value-All Machinery 65 %$STOCK 66 Percent-Value-Livestock 66 DISTl 66 Distance to Town (2,500-5,000) in miles 67 DIST2 66 Distance to Town (4,000-10,000) " " 68 DIST3 66 Distance to Town (10,000-40,00) " " 69 DIST4 66 Distance to Town (40,000 Plus) " " 7O 71 Area-Owned (Acres) 71 71 Area-Rented (Acres) 72 71 Total Area of Farm (Acres) 73 71 Value Land-Building ($100) 74 71 Value Machinery-Equipment ($100) 75 71 Value Livestock ($100) 76 71 Total Capital Value ($100) 77 71 Days Part Time Work 78 71 Value Total Sales ($10) 79 71 Type of Farm 80 71 Economic Class 11.00 50,000 - Plus 12.00 35,000 - 49,999 13.00 25,000 - 34,999 14.00 15.000 - 24,999 15.00 10,000 - 14,999 21.00 7,500 - 9,999 Table A.1 Continued 257 Variable Variable Year Description Number Name 22.00 5,000 - 7,499 31.00 3,750 - 4,999 32.00 2,500 - 3,749 41.00 1.200 - 2.499 42.00 250 - 1.199 43.00 50 - 249 51.00 Institutional 81 71 Farm Size (Acres) 1.0 l - 2.00 3 - 9 3.00 10 - 69 4.00 70 - 239 5.00 240 - 399 6.00 400 - 559 7.00 560 - 759 8.00 760 - 1.119 9.00 1,120 - 1,599 10.00 1,600 - 2,239 11.00 2,240 - 2,879 12.00 2,880 - Plus 82 71 Total Capital Value 1.00 Under $2,950 2.00 $ 2,950 - 4,949 3.00 $ 4,950 - 7,449 4.00 $ 7,450 - 9,949 5.00 $ 9.950 - 14.949 6.00 $ 14.950 - 19.949 7.00 $ 19,950 - 24,949 8.00 $ 24,950 - 49.949 9.00 $ 49.950 - 74.949 10.00 $ 74,950 - 99.949 11.00 $ 99,950 -l49,949 12.00 $149,950 -l99,949 13.00 $199,950 - Plus 83 71 Part Time Work (Days) 1.00 None 2.00 Less than 7 3.00 7 - 12 4.00 13 - 24 5.00 25 - 48 6.00 49 - 72 7.00 73 - 96 8.00 97 - 126 9.00 127 - 156 10.0 157 - 228 11.00 229 - 365 258 Table A.1 Continued Variable Variable Year Description Number Name 84 71 Length of Residence in Previous Year 1.00 9 - 12 months 2.00 5 - 8 months 3.00 l - 4 months 4.00 Non-resident 85 MECHl 66 Mechanization = V17 over V12 86 MECH2 66 Mechanization = V17 over V20 + V21 + V22 87 PRODCAP 66 Product. Capital = V39 over V19 88 PRODLDl 66 Product. Land = V39 over V12 89 PRODL02 66 Product. Land = V39 over V20 + V21 + V22 90 LNTOTAR 66 LN of Total Areab 91 LNTOTCAP 66 LN of Total Capital Valueb 92 LNTOTREN 66 LN of Total Rentb 93 LNTOTSAL 66 LN of Total Salesb 94 LNOFFWORK 66 LN of Days of Off-Farm Norkb 95 RESIDl 66 Residence on the Farm in Previous Year 0. Non-resident l. l - 12 months 96 RESIDZ 66 Residence on the Farm in Previous Year 0. 0 - 4 months 1. 5 - 12 months 97 OFFWORKl 66 Days Off Farm Work 0. None 1. Some 98 OFFWORKZ 66 Days Off Farm Work 0. O - 24 days 1. 24 - 365 days aAGEDl, AGEDZ, and AGED3 are three binary variables used to express the eight-class qualitative variable AGECL. bLN Stands for "natural logarithm of." APPENDIX B CROSS-TABULATIONS APPENDIX B CROSS-TABULATIONS Table B.1 Farm Operators by Decision Regarding Farming and by Length of Resident on Farm, Census Division 7, Saskatchewan Decision Residence on the Farm Total Regarding (Months in Previous Year) Farming 9-12 5-8 1-4 0 Stayer 555 37 15 133 740 (75.5) (60.7) (75.0) (62.1) (71.8) Exiter 180 24 5 81 290 (24.5) (39.3) (25.0) (37.9) (28.2) Total 735 61 20 214 1030 Notes: Figures in parentheses are percentage of column totals. x2 = 18.70. DF = 3. Level of Significance = 0.0. A = 0.0, A = 0.0. A B ucA = 0.015. ucB = 0.011; 259 260 Table 8.2 Farm Operators, 64 or Less, by Decision Regarding Farming and by Length of Residence on Farm, Census Division 7, Saskatchewan Decision Residence on the Farm Total Regarding (Months in Previous Year) Farming 9-12 5-8 1-4 0 Stayer 529 29 15 120 693 (80.6) (65.9) (83.3) (65.6) (76.9) Exiter 127 15 3 63 208 (19.4) (34.1) (16.7) (34.4) (23.1) Total 656 44 18 183 901 Notes: Figures in parentheses are percentage of column totals. x2 = 21.80, DF = 3, Level of Significance = 0.00. A = 0.0. A = 0.0, A B ucA = 0.021. ucB = 0.015, ccc.c - cc: ccc.c - ccc c.c - c. c.c - cc cc.c - cccco.c.ec.c cc .cscc c - cc cc.cc - cx .mc ace» ccm. ccouccmco Eccc coe c.ccuccc com cucuccpcum ccc.c - ccc ccc.c n cc: c.c - c. .c..c .... cc.c - aoecc...cc.c cc .cscc c - cc cc.c.. - cx c.cuou cE:.ou co mmcucmucmc mec cmcmzucmccc cc cognac; 261 ccc. c. cc c. .c. .cc ccc cc. .c .c.c. .c.ccc ...ccc .c.ccc .c.ccc .c.ccc .c.ccc .c.c.. .c.c.. .c.ccc ccc cc cc cc cc cc cc cc c. ccc.xc .c..cc .c..c. ...ccc .c..cc .c.c.. .c.ccc .c.ccc .c..cc .c..c. ccc cc cc cc cc ccc cc. ... cc cccccc c. cc.c cc-cc cc-cc cc-cc cc-cc cc-cc cc-cc cc cccec cc.ccec couch mccuccmma cocccuwa mm< ccxmcuucxccm .c xuccou .mm< ca ucc occELcc occuccmwm cocmcuwa an .ccouccmco Eecc m.m c.cch 262 Table 8.4 Farm Operators by Decision Regarding Farming and by Off-Farm Income, Census Division 7, Saskatchewan Decision Off-Farm Income Total Regarding «—-- Farming Under $750 Over $750 Stayer 610 130 740 (72.6) (68.4) (71.8) Exiter 230 60 290 (27.4) (31.6) (28.2) Total 840 190 1030 Notes: Figures in parentheses are percentages of column totals. x2 = 1.15. DF = 1, Level of Significance = .28. A = 000$ A :7: 0.0, A 8 00A = 0.001, ucB = 0.001. 263 Table 8.5 Farm Operators, 64 or Less, by Decision Regarding Farming and by Off-Farm Income, Census Division 7, Saskatchewan Decision T Off-Farm Income Total Regarding Farming Under $750 Over $750 Stayer . 564 129 693 (78.8) (69.7) (79.5) Exiter 152 56 208 (21.2) . (30.3) (20.5) Total 716 185 901 Notes: Figures in parentheses are percentages of column totals. 2 6.27, DF X = = 1, Level of significance = 0.01. AA = 0.00, A3 T 0'0: UCA = 0.007, UCB = 0.007. 264» ..acmccccwe we: ccc caucuocc .cc:u.=uccmc co cwpcc cc.c: ccc .cELcc .ccocuaucucc. a omo.o owe-o cc.c - ccecoccceccc cc .ascc .. - cc u: Nmo.o mwo.o mw.pm ccc <4 x c c.cuou ce=.ou co comcucmucmc ccc cmcmgucmccc c. cmczmcc ccc. c cc cc cc .. cc cc. cc. c.c cc. cc c. .ccc. .c.cc. .c.ccc .c.cc. ...ccc .c.ccc .c.ccc ...ccc .c.ccc .c.ccc .c.c.. .c.c.. .c.c.. .c.cc. ccc c c. cc c. cc cc cc cc cc c. c c ccccxc .c..cc .c.ccc .c.ccc .c.c.. .c.c.c .c.cc. .c.ccc .c.ccc .c.ccc ....cc .c.ccc .c.ccc .c.c.. cc. c c c cc cc c. c.. cc. cc. cc. cc c. cccecc .cce. ccc cc... ccc.c- ccc.c- ccc.c- ccc..- ccc.c- ccc.c.- ccc.cc- ccc.cc- cc.c ccc cc.ccec .c.c. cc ccc ccc.. ccc.c ccc.c ccc.c ccc.c ccc.c. ccc.c. ccc.cc ccc.cc cnwwumwwm .cv caucuocc .cc:u.=uccm< co cc.cm cczmzuucxccm .c coccc>co caccmu .cuoccocc —cccu.coccm< co cc.cm cc ccc cccsccc mcccccmmm cocccomo cc ccouccmco Econ o.m c.cch 265 ..cccccccms no: ccc cauccocc .cc:p.=uccmc co cc.cc gucnz ccc .cEccc .ccocucucucc. a c.c.c - ccc ccc.c - ccc c.c.c - c. cc.ccc - c. cc.c - aoeeoccccccc cc .c.cc .. - cc c..c. - cx c.cpoc cE=.ou co ccmcucmucmc ccc cmcmcpcoccc cc cmcamcc .cc c c. .c .c cc cc cc. cc. cc. cc. cc c. .ecc. ...ccc .c.cc. ....cc .c.ccc .c.ccc .c.ccc .c.ccc .c.ccc ...ccc .c.c.. .c.c.c .c.c.c .c.ccc ccc c .. c. c. cc c. cc .c cc c. c c ccccxc .c.ccc .c.ccc .c.cc. .c.cc. ..c.c.c .c.cc. ...... .c.ccc .c.cc. ...ccc .c.ccc ...ccc .c.ccc ccc c c c .c cc cc cc. cc. cc. c.. cc c. cccccc .cce. ccc cc... ccc.c ccc.c- ccc.c- ccc.c- ccc..- ccc.c.- ccc.cc- ccc.cc- cc.c ccc cececcc .cccc cc ccc ccc.. ccc.c ccc.c ccc.c ccc.c ccc.c. ccc.c. ccc.cc ccc.cc cc.cccccc corn—bun A“. cpuacoca .cc:u.=uccm< co cmccm cczmzuucxccm .u coccc>ca caccwu .cuuccocc .cc:u.:u.cm< co cc.cm ccc mc.Eccc mcccccmwm cocccuwo cc .ccmc ccc cc .ccouccwco seem ~.m c.ccc ccc.c - ccc c.c.c c.c - c. c.c c..c - cceccccceccc cc .c.cc c. - cc cc.c. c.cuou cE=.cu co cmmcucmucmc ccc cmcmgucmecc cc cognac; ccc. cc cc .. .c c. cc cc cc cc cc ccc .eccc "w . A2 .c.ccc .c.ccc .c.ccc .c.c.. .c.ccc ...... cc.cc. .c.ccc .c.c.. .c.ccc .c.c.. .c.ccc ccc .c c. c c c c. . c c c c.c caccxc .c..cc ...ccc .c.ccc .c..c. .c..cc .c.ccc .c.ccc .c.ccc .c.cc. ...ccc .c.cc. .c..cc ccc cc cc c c. c. c. c. cc c. .c ccc cccccc ccc-ccc ccc-cc. cc.-.c. cc.-cc cc-cc cc-cc cc-cc cc-c. c.-c c.. cecz cececcc .ccc» ccccccmme cocccumo xcoz seem-ccc co ccco :czmzuucxccm .c coccc>co ccccmu .xcoz scum-ccc co ccca An ccc accsccc occcccmmm cocccuwo cc mcouccmgo scam m.m o—nc» N < u :3 moo-o u: ccc.c ll r< c.c c c.c no.0 n muccuPcccmcm co Pm>m4 op u no -.np N c.cuou :E:.oo co cmmcucmocmc ccc cmcmgpcmcca cc cmcamcc 267 .cc cc cc .. cc c. cc cc cc cc cc ccc .ccc. ...ccc .c..cc c.cc. .c.c.v .c.ccc .....c .c.ccc .c..cc .c.c.. .c.ccc .c.c.. .c.ccc ccc cc c. c c c c c c c c .c. ccccxc cc.ccc .c.ccc .c.ccc .c..cc .c.ccc .c.ccv .c.ccc .c.cc. .c.ccv .c.ccc .c.ccc .c.ccc ccc cc cc c c. c. c. c. cc c. cc .cc cccccc ccc-ccc ccc-cc. cc.-cc. cc.-cc cc-cc cc-cc cc-cc cc-c. c.-c c-. c cc.cccc .cccc occcccmwm xcoz Eccc-cco co mace cocccuao cczmguccxccm .c coccc>co ccccmu .xcoz seem-ccc co ccco cc ccc m:.Eccc acccccmmm cocccumo cc .ccoc co co .ccouccmco seem m.m c.cc» 268 Table 8.10 Farm Operators by Decision Regarding Farming and by Tenure, Census Division 7, Saskatchewan Decision Tenure Total Regarding Farming Owned Rented Owned-Rented Managed Stayer 292 64 380 4 740 (62.8) (68.8) (81.5) (66.7) (71.8) Exiter 173 29 86 2 290 (37.2) (31.2) (18.5) (33.3) (28.2) Total 465 53 466 6 1030 Notes: Figures in parentheses are percentages of column totals. 2 x = 41.00, DF = 3, Level of significance = 0.00. AA = 0.0, AB = 0.15, UCA = 0.034. UCB = 0.021, 269 Table B.ll Farm Operators, 64 or Less, by Decision Regarding Farming and by Tenure, Census Division, Saskatchewan Decision Tenure Total Regarding ‘ Farming Owned Rented Owned-Rented Managed Stayer 259 63 367 4 693 (69.8) (70.0) (84.6) (66.7) (76.9) Exiter 112 27 67 2 208 (30.2) (30.0 (15.4) (33.3) (23.1) Total 371 90 434 6 901 Notes: Figures in parentheses are percentages of column totals. 2 X = 27,52, DF = 3, Level of Significance = 0.00. AA = 0.0. AB = 0.096, UCA = 0.029. 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