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UBC Theses and Dissertations

Projection of population and industrial employment in the Vancouver C.M.A. Skene, Patricia Aileen Thelma 1974

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PROJECTION OF POPULATION AND INDUSTRIAL EMPLOYMENT IN THE VANCOUVER CM.A. by PATRICIA AILEEN THELMA SKENE B.A. (Honours Economics), University of Western Ontario, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Community and Regional Planning We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA MAY, 1974 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission fo r extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of ^„,. -T^Wk ^ > \ \ ^ ^ J S N ^ e ^ ^ ^ The University of B r i t i s h Columbia Vancouver 8, Canada Date ^>o^~S VV\ i i ABSTRACT The goal of this thesis is to draw together the principal factors affecting regional growth and to apply this knowledge to the Vancouver CM.A. This involves three objectives. The f i r s t objective is to review the literature pertaining to the theory of regional growth. This review appears in Chapters 1, 2, and 4. These chapters constitute an attempt to draw together important factors from an extremely wide f i e l d . This work is designed to provide a framework for evaluation of the state of the art in regional projection models. The second objective is to review the literature to find examples of practical applications of the above theory. Specific examples of population and economic models for projection are examined and their major features are presented in Chapters 3 and 5. A model based on the state of the art is created and reported in Chapter 6. This work involves the use of available regional sectoral employment data and a shift-share model to produce employment projections. These employment projections are then combined with an estimate of the historical relationship between migration and employ-ment in the region to produce an estimate of projected migration. The projected migration is an input to the cohort survival model which projects future population. A check on the consistency of the estimates of population and employment is provided by the calculation of the expected employment rate. i i i In conclusion, the literature review reveals the complexity of the phenomenon of regional growth. It also reveals that large scale computer models have not been highly successful in dealing with the problem. This leads to the conclusion that simple models are more desirable for projection purposes. However, in the present case, the simplicity of the shift-share model is perhaps too great. The model, in general, explains less of past growth than does a simple time trend extrapolation model. The population model, while also simple in structure, per-forms much better. In that case the major factors affecting population growth ( f e r t i l i t y , mortality and migration) are treated separately in the model. It would be desirable to explain the separate components of regional economic growth (labour, capi ta l , technical knowledge). The major l imiting factor to this task is the quantity and quality of regional data available. Until this is improved, regional analysts w i l l be confined to unsatisfactory projection models. UC0 iv ACKNOWLEDGEMENT I should l ike to acknowledge the patient assistance of my advisors H. Craig Davis and Harry Campbell. Professor Davis especially provided guidance throughout the entire process. V TABLE OF CONTENTS Chapter Page ABSTRACT i i ACKNOWLEDGEMENT iv TABLE OF CONTENTS v LIST OF TABLES v i i i LIST OF FIGURES xi 1. MODELS IN PLANNING 1 The Planning Process 1 Computer Models and their role 5 Systems Thinking and Future Planning Practice . . 9 Theoretical Caveats 11 The Present State • . 12 Summation 15 2. FACTORS AFFECTING THE GROWTH OF POPULATION 19 Mortality 20 Ferti 1 i ty 25 Migration 28 Economic Approach 30 Behaviourist Approach 40 3. PROJECTION OF POPULATION — TECHNIQUES AND VANCOUVER PROJECTIONS 43 Data 43 Projection Methods 46 Comparative Forecasting 46 vi Chapter Page Graphic Extrapolation 47 Mathematical Extrapolation 47 Ratio and Correlation Methods 48 Extrapolation Using Regression Methods . . . . 48 Cohort Survival . . . 49 Projections of Vancouver Population 51 GRVD Planning Department Model 51 I IPS Model 58 IDTC Model . . . 59 Urban Canada Projections 64 Summary 68 4. FACTORS AFFECTING REGIONAL ECONOMIC GROWTH 71 The General Framework 71 Capital , Labour and Technical Knowledge 74 Capital 74 Labour 75 Technical Knowledge . . 77 Government Policy 78 Analysis of Regional Growth . 79 5. TOOLS OF REGIONAL ECONOMIC ANALYSIS AND PROJECTION. . 82 The Regional Problem 82 Shift-Share 86 Keynesian Analysis and Multipliers 93 The Economic Base Mult ipl ier 98 v i i Chapter Page Input-Output 103 Neo-Classical Growth Models 107 Econometric Models 109 Computer Simulation 110 Existing Projections for the Greater Vancouver Regional Dis t r ic t I l l 6. A REGIONAL PROJECTION MODEL 115 The Overall Model Structure 115 The Employment Submodel . . . 116 Employment Data 118 The Differential Component 129 Projected National Growth Rates 130 The Submodel Projections 134 The Migration Submodel 136 The Population Submodel 138 Migration Data . . . . . 141 Death Rates and Survival Rates . . . . . . . . 141 F e r t i l i t y Assumptions 144 Population Projections 145 The Unemployment Rate Check 145 Recommendations 150 BIBLIOGRAPHY . 152 APPENDIX A 165 APPENDIX B 175 vi i i LIST OF TABLES Table Page 1. Birth Rates Per 1,000 Used in the GVRD Forecast . . . . 53 2. Migration to the GVRD 55 3. Range of Total Population Forecast GVRD 57 4. HPS Population Projections Vancouver CMA 60 5. Projection of Migrants 61 6. Population of the Lower Mainland 63 7. Vancouver Population Projections 66 8. Projected Total Population, Vancouver CMA 68 9. Comparison of Vancouver Population Projections . . . . 69 10. Lower Mainland Percentage Distribution of Labour Force by Sector 1951-1961 and Forecasts for 1971, 1981 and 2000. 112 11. Distribution of Labour Force in the Lower Mainland by Industry Group 1951-1981 . . . . . . . 113 12. National Employment Indexes . . 119 13. Vancouver Employment Indexes 120 14. Employment Base (1961) Vancouver 121 15. Larger Firm Employment as a Percentage of Total Estimated Employment 123 16. Estimated National Employment 125 17. Estimated Vancouver Employment 126 18. Average Differential Component 1985/57-1970/69 . . . . 131 19. Sectoral Employment Regressed Against Time 132 20. National Growth Rates 133 Table Page 21. Vancouver Employment Projections 135 22. Migration Equations 137 23. Percent Age-Sex Distribution of New Migrants to Vancouver, 1956-61, 1961-66, and 1966-71 142 24. Age-Sex Specific Death .& Survival Rates "143 25. F e r t i l i t y Rates 146 26. Population Projections to 1981 F e r t i l i t y Assumption: 1971 B.C. Rates Over Entire Period . 147 27. Population Projections to 1981 F e r t i l i t y Assumption: 1971 B.C. Rate Less 10%, Over the Entire Period . . . 148 28. Population Projections to 1981 F e r t i l i t y Assumption: B.C. Rates Decline to 1981 . 149 B . l , National Employment Growth Rates by Industry Average Annual Percent Change . . 176 B.2 Shift-Share Model Projection of Sectoral Employment in Vancouver 178 B.3 Regional Employment Projections Forecasts Using Economic Councils National Growth Rates 179 B.4 Percent Error of 5 Year Projections for Total Employment . ;: 181 B.5 5 Year Vancouver Employment Projections . . . . . . . 182 B.6 Regional Employment Projections Based on Simple Time Trend Equation 183 B.7 Percent Error of Total Population Estimates for 1966 186 B.8 Percent Error of Total Population Estimates for 1971 Projections Based on 1966 Projections 186 X Table Page B.9 Estimate of 1966 Unemployment Rate Using Average Actual Participation Rates Over the Projection Period to Calculate the Labour Force 188 B.10 Estimate of 1966 Unemployment Rate Using Average Projected Participation Rates Over the Period 188 B . l l Estimate of 1971 Unemployment Rate Using Average Actual Participation Rates Over the Projection Period to Calculate the Labour Force 189 B.12 Estimate of 1971 Unemployment Rate Using Average Projected Participation Rates Over the Period 189 xi LIST OF FIGURES Figure Page 1. The Harris 7-D Planning Model 3 2. Steps in the Pure Rationality Model . . . . 4 3. Standardized (Age-Adjusted) Death Rates, 1921-70 . . 23 4. General F e r t i l i t y Rate, 1931-71 (Selected Years) . . 24 5. Regions of Br i t i sh Columbia 62 6. Lithwick Population Projection Model . . 65 xi i This thesis deals with forecasting. The underlying cynicism of the writer regarding this type of endeavor is well expressed by G.K. Chesterton in the following quote: The human race, to which so many of my readers belong, has been playing at children 's games from the beginning . . . and one of the games to which it is most attached is called "Keep Tomorrow Dark" and which is also named (by the rustics of Shropshire, I have no doubt) "Cheat the Prophet." The players listen very carefully and respectfully to a l l that the clever men have to say about what is to happen in the next generation. The players then wait u n t i l a l l the clever men are dead, and bury them nicely. They then go and do something else. That is a l l . For a race of simple tastes, however, it is great fun. G.K. Chesterton Napoleon of Notting H i l l CHAPTER 1 MODELS IN PLANNING 1 CHAPTER 1 MODELS IN PLANNING THE PLANNING PROCESS A precise definition of planning continues to elude planning theorists. It has been said that planning is future-oriented decision making. More pragmatically, i t has been defined "as a co-ordination of future actions so that they may reinforce rather than hinder one another."^ The aim of early planning was merely to improve physical surroundings. The realization soon grew, however, that such "improve-ments" lasted a very long time and that consideration of their effects on future generations was important. With this concern for the future, came the desire to make the best possible decision. Since the condition of the c i ty is constantly changing,decision-making ("planning") is a continuous function. Catanese and Steiss in their study of systematic 2 planning characterize planning as a process. Planning involves a continuous study of the urban environment as i t is affected by growth and shifts in population, technological developments, changes in economic act iv i t ies and their dis tr ibution, shifts in the preferences and value systems of various classes and social groups and so forth. It is from this contin-uous, ongoing act iv i ty that problems are identified ^Stan Czamanski, "Regional Policy Planning: Some Possible Implications for Research," Annals of Regional Science, Vol . 4 (Dec. 1970), p. 57. 2 A . J . Catanese and A.W. Steiss, Systemic Planning: Theory  and Application,(Lexington, Mass., 1972), p. 29. 2 and defined. Thus, planners must anticipate trends and needs, in advance, in order adequately to prepare to meet these changes in the urban environment. They refer to the Harris 7-D model of the planning process.(see Figure 1) As pictured, i t is a process of orderly progression from step to step with many allowances for feedback within the process. Such a process for decision-making seems to f i t Yehezkel Dror's conceptualization of the pure rat ionality model of policy making. The steps involved in that model are outlined in Figure 2. The emphasis of the model is on completeness. A l l values and goals are to be considered. A l l relevant information is assumed available and techniques for assess-ment are also assumed available. F ina l ly , a l l poss ibi l i t ies must be considered and weighed. Unfortunately, the achievement of the model seems clearly beyond present capabil i t ies . The model is regarded as an unobtainable ideal because i t requires the analyst to be more comprehensive than is currently possible. Those processes of planning which are suggested in i ts place usually try to marry the pure rat ionality emphasis on com-prehensivenss with practical constraints. Thus the "economically rat ional" model advocates following the pure rat ional i ty process only as far as i t involves reasonable cost. The incremental model advocates making decis-ions at the margin. In i t , a changed policy w i l l be undertaken only 3 when present factors clearly indicate change. However conceptualized, planning emerges as a dynamic process involving normative decision-making. There is a problem-solving aspect o Y. Dror, Public Pol icy-Making Re-examined, (San Francisco, 1968), pp. 129-153. Data (information) Description (theory) Planning Desires (goals) ± Design Deduction (prediction) Decision (choice) Deeds (implemen-tation) Science Real World F i g u r e 1 T h e H a r r i s 7 — D P l a n n i n g M o d e l . INPUT A l l resources needed for pure rationality process A l l data needed for pure rationality process Establishment of a complete set of operational goals and weights.for them -> 3 Preparation of a complete set of alternative policies 4 Establishment of a complete inventory of other values and resources with weights Preparation of a complete set of predictions of benefits and costs of each alternative Calculation of net expectations of each alternative Comparison of net expectations and identification of alternative of highest expectation Figure 2 Steps In The Pure Rationality Model OUTPUT of process 4* 5 to planning since the present state must be analyzed and alternatives for changing i t must be evaluated. However, the analysis does not generate the solution. The generation of alternative solutions is s t i l l part of the art of planning. Analysis can only evaluate those solutions. Thus the planning process incorporates elements of art and intuit ion and of sc ient i f ic analysis. The role of sc ient i f ic analysis is to reduce reliance on intuit ion where such reliance would be a suboptimal strategy. Thus in the Harris model in Figure 1 science (analysis) provides the basis for choosing among designs. A.G. Wilson conceives of a hierarchy of planning functions which involve understanding the problem,design 4 solutions and policy or decision making. It is at the levels of under-standing the problem and of evaluating the policies proposed to solve i t that analytical tools in general and computer models in particular can be useful in the planning process. COMPUTER MODELS AND THEIR ROLE The above section has pointed out the emphasis in the planning process on the examination of as many relevant factors as possible. Britton Harris points out that in an increasingly complex world this 5 is not simple. Ira Lowry comments that planners have turned to A.G. Wilson, "Models in Urban Planning: A Synoptic Review of Recent Literature," Urban Studies, 5 (1968), p. 251. 5 Britton Harris, "New Tools for Research and Analysis in Urban Planning," in Ernst Erber (ed.), Urban Planning in Transition, (New York, 1970), p. 200. 6 computer models because of the inadequacy of other tools and because of the increasing realization of the complexity of the urban system. As he puts i t , "planners are now prisoners of the discovery that in the c i ty everything affects everything else." When models f i r s t began to be popular with planners there were great expectations for what they might be able to help achieve. These early goals included: 1. Understanding factors that influence development and providing a better factual basis for plans. It was fe l t that by understanding the market forces underlying urban structure planners could create more rea l i s t i ca l ly achievable plans. 2. Evaluating interdependences and potential conflicts between separate planning programs. This involves trying to assess secondary effects. 3. Predicting, a 20 to 30 year projection period did not seem out of the question. 4. Controlling and directing urban growth. The implication here is that sufficiently strong causal relationships could be identified and quantified between various control or policy variables and the objective or state variables so that effec-tive policies would become clear through the modelling exercise.^ ^I.S. Lowry, "A Short Course in Model Design," American  Institute of Planners Journal, 31 (May, 1965), p. 158. ^D.B. Lee J r . , "Requiem for Large Scale Models," American  Institute of Planners Journal, 39 (May, 1973), p. 171. 7 The poss ibi l i ty that the use of models would develop the theory of urban structure seemed real during the rise in popularity of computer models.. A theory is an abstraction from rea l i ty . The popular view held that theories could be formulated for the computer in the form of a mathematical model. Experiments could be conducted with the model to determine how well the theories f i t empirical data. It was thought that the rigorous definition demanded by the computer would force the model (theory) builder to make his assumptions exp l i c i t . In the end, the body of urban theory would be advanced. It may be useful to briefly review the steps involved in building a computer model so that a feeling can be gained for what this tool i s . The f i r s t step for the model builder is conceptual. He must determine: (a) What questions the model is trying to answer. (b) The concepts which are measurable and have to be represented in the model. (c) Which of these variables can be controlled by the planner. (d) How the variables are to be categorized, for example, population can be categorized by age, sex, occupation, etc. (e) How to treat time -- whether the model w i l l be dynamic or s tat ic . g (f) What theory i s to be represented. 'A.G. Wilson, op_. c i t . , pp. 258-9. 8 At this stage the system to be modelled has been described. In order to u t i l i z e the computer in the modelling process certain steps must be taken. The theory to be modelled is usually described in mathematical equations. These equations normally involve constants (parameters) which may have been s ta t i s t i ca l ly estimated. This is the process of model cal ibration. The theory is here given meaning in terms of real world observations. When the analyst is reasonably satisfied with the results of this stage, the model can be programmed for the computer. This is an important stage. The program by which the model is solved makes expl ic i t the causal links of the theory. When the computer program is operational, the next step is the verif ication of the model. This involves checking i t for programming errors and errors of logic. The aim is to insure that the model does what i t was intended to do. The final stage is model validation. Here the attempt is made to determine how well the model represents the empirical system. This is often done by seeing how well the model r e p l i -g cates an historical period. At none of these stages can the analyst be sure that he has captured real i ty and the result may be of unknown efficacy due to the poss ibi l i ty of error in any of the many decisions made along the way. The steps outlined are described in greater detail in I.S. Lowry, op_. c i t . and in David Baxter, "Simulation Modelling: The Process, mimeograph, May, 1973. 9 SYSTEMS THINKING AND FUTURE PLANNING PRACTICE In urban analysis, the increasing emphasis is on viewing the ci ty as a complex system. The following quote from Eric Fromm il lustrates quite clearly what this invo lves .^ I- need not remind you that i f we speak of a l iv ing system we speak of something that is coherent, where the whole determines the part, where every change in one part implies a change in every other part, that system thinking is not a linear form of thinking relating to cause and effect, but thinking about a to ta l i ty , about a dynamic process, that the question 'what is the cause" is meaningless, because there is no single cause, that one has to go around i t and look at i t from a l l sides, that one has to find out in what particular way this system dysfunctions, and only then can one determine whether the dysfunction is curable. The systems approach is a realization of complexity. It attempts to represent that complexity in computer models with the aim of controlling the system. Cyberneticians have warned, however, of 'the law of requisite variety 1 which indicates that the control system must be as complex as the system being contro l led .^ This means that the solutions to urban problems w i l l almost certainly not"be simple. W.W. Cooper, C. Eastman, N. Johnson and K. Kortanek, "Systems Approaches to Urban Planning: Mixed, Conditional, Adaptive and Other Alternatives," Policy Sciences, 2 (1971), p. 398. ^ A . G . Wilson, "Forecasting Planning," Urban Studies, 6 (1969), p. 366. 10 The aim of controlling the system has led to the hope that 12 urban simulation models can be used to test policy proposals. There have been experiments with small and f a i r ly simple models to do this . 13 Oates, Howrey and Baumol produced a small model to examine the effects of in-c i ty public expenditure and changes in c i ty tax policies on the f l ight of the middle-class to the suburbs. While i t did not attempt to portray the system in a l l of i t s complexity, (in the way that Fromm indicates is necessary) the model was useful in the analysis of alternative policies . Where does system analysis and simulation modelling lead us? In his "Forecasting Planning" a r t i c l e , A.G. Wilson pictures a planning office in 1890 where planners have complete access to a system of models and a l l the requisite data so that alternative policies may be quickly 14 tested. In effect, policies could be tried in a laboratory situation before large sums were invested in their application to c i ty problems. The technical capability to do this exists now. Wilson admits that i t M.D. Kilbridge, R.P. O'Block, P.V. Tepl i tz , Urban Analysis, Graduate School of Business Administration, Harvard University (Boston, 1970), p. 22. 13 W.E. Oates, E.P. Howrey and W.J. Baumol, "The Analysis of Public Policy in Dynamic Urban Models," Journal of Po l i t i ca l Economy, 79 (1971), pp. 142-153. 1 4 A . G . Wilson,"Forecasting Planning," loc. c i t . , pp. 357-358. 11 is the model system which is the main present weakness but his paper is an optimistic one and leaves the impression that this d i f f i cu l ty w i l l soon be overcome. THEORETICAL CAVEATS The enthusiasm for the use of the modelling technique in planning has not been universal. There have been many perceptive c r i t i c s of the technique. One of the f i r s t questions that springs to mind is that i f models are abstractions from real i ty and simplistic representations of a complex system, what guarantee is there that the modeller has indeed chosen the central elements of the system? May he 15 not have modelled only his own faulty perceptions? If so, is this not potentially dangerous given the human desire to place undue significance on the output of one's hard work even though one realizes 1 g that the underlying assumptions are pulled from thin air,. John Dakin in a thoughtful essay has raised some more basic theoretical questions about the approach]'' "He poses the danger that G.M. Raymond, "Simulation vs. Reality," in Ernst Erber (ed.), Urban Planning In Transition, (New York, 1970), p. 210. '"' l fi A . J . Catanese and A.W. Steiss, Systemic Planning: Theory and  Application, (Lexington, 1972), p. 8. 1 7John Dakin, "Models and Computers in Planning," Plan  Canada, Vol . 6, No. 1 (1965), pp. 11-35. 12 those who use the.method w i l l ask only those questions that i t is capable of answering, that they w i l l seek to quantify where this is inappropriate and w i l l neglect the human element of urban problems. Dakin recognizes that planners are being pushed in the direction of mathematical models by the necessity to produce reasonable arguments based on factual evidence in support of their pol icies . This pressure is the reflection of a belief in the efficacy of logical argument and the desire for certitude . . . . The sense of security engendered by this situation is a trap . . . this is a functional or accommodation use of reason which in the last analysis merely aims at greasing the wheels of the societal status quo. There may be absence of any solid motivation for applying the methods : of reason throughout our society . . . . Our danger is . . . the danger of thinking that society can exist simply to be functionally ef f ic ient . Thus Dakin forces us to touch base with the ethica l , social and anthropological foundations of the urban system which are greatly ignored in simulation models. THE PRESENT STATE The decade of the sixties and the early part of the seventies have seen a f u l l cycle in the popularity of models. In the T960's much work was done on large scale computer models, many of which were begun having in mind the goals l i s ted in Section I I . Those efforts have now 13 been completed and there has been some opportunity for evaluation of their success. Douglass Lee claims that large scale models have fai led 18 and l i s t s seven sins of large scale models. These include: 1. Excessive comprehensiveness— Models were designed to rep l i -cate too complex a system at a single shot and were expected to serve too many purposes at the same time. The state of knowledge of urban structure and process is far too weak to support such an effort. "Including more components in a model generates the i l lus ion that refinements are being added and uncertainty eliminated but, in practice, every additional component introduces less that is known than is not known." The nature of our understanding of urban structure " i s such that the total (in the sense of a comprehensive model) 19 is less than the sum of the parts." 2. Grossness -- The actual level of detail was too coarse to be of use to most policy makers. 3. Hungriness — The models required tremendous amounts of data most of which had to be generated specif ical ly for the project. 4. Wrongheadedness -~ There was a deviation between claimed model behaviour and the equations of statements that actually governed model behaviour. "For most large scale models, limitations or unintended constraints resulting from the structure are almost 20 impossible to perceive and so remain unknown." 18 Douglass B. Lee J r . , o]3. c i t . , pp. 164-168. 1 9 I b i d . , p. 164. 2 0 I b i d . , p. 166. 14 Complexity -- As the number of variables increases in a model, the number of potential interactions between them increases as the square of the number of components. One of the rationales for large models is to allow for these interactions so as to include secondary and tertiary effects, but permitting the interaction does not necessarily mean that the modeller either has any control over i t or learns anything from i t . . . . Because the models contain large but unknown amounts of error and they are too complex, and there are no evaluation measures, modellers have l i t t l e choice except to fudge the models into shape. 21 Thus i t is not surprising when models reproduce rea l i ty . It does not necessarily mean that they can explain i t . Mechanicalness -- A l l large scale models must be implemented on a digital computer. There is always some rounding error. Solutions are often achieved i terat ively ( i . e . one step at a time).and so rounding error compounds in the process. The use of the iterative technique means that the result depends in some part on the order in which the model is solved although i t is seldom clear how sensitive the model is to th i s . Lee comments further on the value of the mathematical formulation of models. There is a popular i l lu s ion that confronting a computer with ones ideas enforces rigor and disc ip l ine , thereby encouraging the researcher to reject or c lar i fy fuzzy ideas . . . i n the more useful sense, the effect is the opposite, i t is a l l too easy to become immersed in the t r i v i a l details of working with a problem on the computer rather than think i t through rat ional ly . 22 Ib id . , pp. 166-7. Ib id . , p. 168. 15 7. Expensiveness -- Such models cost in the millions of dollars. To this latter point one could add D.E. Boyce's comment that "The model building act ivi ty i t s e l f consumed so much of the time and financial resources of each agency that l i t t l e attention could be given to the question of how to use the 23 model once i t was operational . " It appears that most of the large scale models produced in the sixties are not being used on a day-to-day basis for assessing policy as was hoped. In seeking the reason for the failure of models to achieve what was hoped, one returns again to the present l imits of knowledge and understanding of the urban system. Catanese and Steiss comment that It is doubtful that we know enough about urban conditions to optimize, maximize or minimize or even hold anything in steady state. When planners use these terms i t is with the maximum of poetic licence. 24 SUMMATION If the more ambitious goals for models cannot be met, can the technique be useful at a l l ? The f i r s t section of this chapter pointed 23 D.E. Boyce, "The Role of Urban Development Models in the Plan-Making Process," in D.C. Sweet (ed.), Models of Urban Structure (Lexington, Mass., 1969), p. 33. r A.J . Catanese and A.W. Steiss, op_. c i t . , p. 34. 16 out that the basis for plan design was understanding the system. Understanding of the urban system is incomplete, yet i t is possible to describe the current situation and to attempt projections. The next Four chapters describe techniques used in the past to provide the projections of population and economic growth necessary for making policy for the future. It seems that simple models make maximum use of present knowl-edge of the urban system. It has been suggested above that there is not, presently, the theoretical knowledge necessary to build complex models. Further, mathematical models based on empirical data are subject to two types of error. The f i r s t is specification error which arises from a: misunderstanding or purposeful simplification of the 25 phenomenon represented. Thus, a non-linear relationship may be represented l inearly or variables which show small impact may be omitted. The second type of error is measurement error connected with the variables of the system. Alonso points out that gains made in the correctness of specification in a more complex model may be offset by the compounding 27 of measurement errors. This is particularly true when models are used for prediction. The types of error possible in models f i t ted by 28 regression are: 25 William Alonso, "Predicting Best with Imperfect Data,1  American Institute of Planners Journal, 7 (1968), p. 248. 2 6 I b i d . 27 This seems to have been Lee's point. See footnote 20 above. 28 Alonso, op_. c i t . , p. 252. 1. Specification error in the period for which we have calibrated. 2. Further specification error i f conditions in the future differ structurally to some degree from conditions in the calibration period, so that a perfect specification of past relations does not specify perfectly for the future. 3. Measurement (or predictive) errors in the exogenous variables. 4. Measurement errors in the parameters (now variables) in the calibration period. 5. Measurement (or predictive) errors resulting from using past values in place of future values for these parameters/ variables. This compounding of error in the system leads Alonso to suggest: In the research model we are asking what are the relations among the measured variables, and whether they conform to what we would expect from various theories and prior empirical work. We may regard the parameters we obtain not as variables in their own r ight , but as relations among the variables we have measured. But, . . . i f we are using the model for prediction, a l l of our numbers become variables. Further, as variables, they have a larger error when they are predicted for a future state of the system, and the model i t s e l f , as mentioned, may have a large specification error with respect to a future state. From these considerations, i t would seem that a model that seeks to increase our understanding by asking how certain variables relate to each other i s , in a sense, less subject to some of the sources of error than an identical model designed to predict the future. 18 This study w i l l attempt to produce a model that predicts the future in an urban area. In view of the slight theoretical basis for such prediction; the general fai lure of complex models to yie ld results commensurate with the effort involved in their production; and the limited amount of time and manpower available; the emphasis in this study w i l l be on simple models for projection. CHAPTER 2 FACTORS AFFECTING THE GROWTH OF POPULATION 19 CHAPTER 2 FACTORS AFFECTING THE GROWTH OF POPULATION The population of any geographic area changes over time due to the interaction of many forces which affect the rate at which people die (mortality); the rate at which women give birth ( f e r t i l i t y ) and the net numbers of persons who move into or out of the area (migration). The rates of mortality and birth can be expressed in many different ways. They may be "crude" rates. This means that the total number of events in a year (births or deaths) is divided by the base population at the beginning of the year. The "crude" signifies that i t takes no account of age or sex J The rates may also be expressed for certain segments of the population. Thus the number of males between the ages of 15 and 19 who died during the year divided by the total number of males aged 15-19 at the start of the year is an age-sex specific death rate. The rates may also be "standardized" for the effects of differences in age distributions so that countries may be 2 compared on the basis of their overall rates with more accuracy. Nathan Keyfitz and Wilhelm Flieger, Population: Facts and  Methods of Demography,(San Francisco, 1971), p. 3. 2 I b i d . , p. 248. MORTALITY 20 The rate of mortality has been fa l l ing over time throughout 3 4 the world. Mortimer Speigelman, notes several factors which have had an effect on the reduction of mortality. These include improved public health f a c i l i t i e s ; the scope, quality and quantity of health services provided; the generally improved training of personnel in the 5 health services which is an embodiment of improved medical knowledge; the financing of the cost of medical care which produces an increased ab i l i ty to pay and encourages consumers of health services to give early attention to i l lnes s , and l a s t ly , economic progress which has brought a generally higher standard of l iv ing and improved diet. Demographic theorists have suggested three main ways in which mortality as a demographic force may be represented. The f i r s t stream of thought involves deterministic models. These are exemplified by the Gompertz equation which postulates that man's ab i l i ty to withstand his destruction continually decreases with advance in age, the rate of United Nations, Department of Economic and Social Affa irs , Methods of Population Projection by Sex and Age, Manual I I I , Population Studies, No. 25 (New York, 1956), p. 47. ^Mortimer Speigelman, Introduction to Demography, revised edition (Cambridge, Mass., 1968), pp. 88-89. 5 Henry Hightower, "Population Studies," Chapter 3, in W.I. Goodman and E.C. Freund (eds.), Principles and Practice of Urban  Planning, (The International City Manager's Association, Washington, 1968), p. 56. 21 decrease within equally small intervals of time being proportionate to the level of the rate. This model is expressed in terms of the force of mortality which is defined by: , dZ -1 x y x Z dx x where £ are the survivors at age x of a cohort of 100,000 at the X beginning of the l i f e table. The Gompertz model implies a geometric progression of mortality with advance in age, i . e . u = Bc x where B measures the inab i l i ty to withstand destruction and c is the rate of deterioration.^ This type of model does not take into account the s ta t i s t ica l var iab i l i ty usually present in the phenomenon that the model is trying to represent. Stochastic models, on the other hand, contain a probability distribution element in their formulation. The stochastic model attempts to bring into account not only the characteris-tics of the physiological processes that lead to death, but also the random variation in physiological performance. The third approach to explaining mortality l ies with the genetic theories which are based on the assumption that, barring environmental influences, the longevity of an individual is completely dependent upon his genetic constitution. Sziland proposed a mathematical model based on several assumptions. One assumption was Mortimer Spiegelman, op_. c i t . , p. 164. 22 that among the genes needed for a healthy l i f e a number w i l l be faulty at birth through inheritance. Further, the remaining genes for a healthy l i f e are subject to damaging 'aging hi t s ' that occur at random, but at a rate that remains constant from bi r th . The faulty genes accumulate with advance in age. Death occurs when the ratio of the remaining v i ta l genes needed for a healthy l i f e reach a certain c r i t i c a l value. 7 When i t comes to the projection of mortality, however, time trend methods are often used. These take into account the advances in Q technology that can be expected and, since the rate has followed a f a i r l y well-behaved path, such projections do not preform badly. Q Keyfitz postulates that for societies with a low birth rate and a low death rate (generally the more advanced nations) the death rate w i l l continue to f a l l but at a decreasing rate. The Canadian and B.C. rates are shown in Figure 3. It can be seen that they follow the path described above.^ Ib id . , p. 166. Ib id . , p. 157. Nathan Keyfitz, 0£. c i t . , p. 6. 1 0The B.C. death rates are consistently below the Canadian rates. This cannot be due to the age distribution of the populations since the rate shown is a standardised (age-adjusted) one. The reason for the difference between the two regions must then l i e in the fact that the income level in B.C. is higher than in most other Canadian provinces. High income is related to better health care. It is also related to lower f e r t i l i t y rates and so may be the reason that the B.C. f e r t i l i t y rate shown in Figure 4 is lower than the Canadian rate. FIGURE 3 STANDARDIZED (AGE-ADJUSTED) DEATH RATES, 1921-70' rate per 1000 i ! !. I I 1 q2f'2 T4~5~6~7 '""8' 9 TTTl .5 6 7 8 9~7 1 2 3 4 5 6 7 8 9; 1 2 3; 4 5 6 7 8. 9 ; 1 T~TtX~$ t ? '9~r 1930 1940 1 9 5 0 " " ; 1 9 6 0 " ' " 197C SOURCE: S t a t i s t i c s Canada, V J t a l _ S t a t i s t i c s , (Queen's P r i n t e r , Ottawa), Table D-6. 1931 :'"hi.Ln.b:'Xi.: <• FIGURE 4 - GENERAL, FERTILITY RATE, .1931-71 j . i. (SELECTED YEARS)- -: - !--!- ! ' ...L. . 1 . 1 1941 : 1951 1956 57 ; 58 ! 59 j 60 61 62 • 63 64 1 65 66 | ~67 68 69 : 70 • 7l" SOURCE: S t a t i s t i c s Canada, V i t a l S t a t i s t i c s , (QueenVs P r in te r , Ottawa),;. Table B r6... The general rate i s the rate for a l l women 15-49 FERTILITY 25 Whereas mortality seems to be a well defined function, f e r t i l i t y is much less so. In Canada and the United States, the rate has been declining since about 1957.^ However, in some less developed countries, 12 i t has been increasing. Figure 4 shows the path of the general f e r t i l i t y rate in Canada and Bri t i sh Columbia since 1931. There are many factors which influence f e r t i l i t y . They involve not only the 13 biological aspect but also the social and cultural . Ralph Tomlinson expresses i t as follows: Personal though convictions concerning f e r t i l i t y may be, they do not arise spontaneously within each individual ; rather they are the product of the culture in which the person was reared and l ives . A l l cultures contain customs, habits and taboos governing f e r t i l i t y directly or through control over sexual behaviour, indirect ly . Among such normative factors are age at marriage, systems of descent and inheritance, rules concerning legitmacy and promiscuity, divorce regulations, taboos on inter-course, r ites of passage into adulthood, financial or other prerequisites to marriage, status changes conse-quent upon having children, citizenship or tax priviledges to parents, patriotic attitudes, obligations to one's ancestors, and acceptability of abortion or infanticide. Attempts to "explain" the f e r t i l i t y rate must thus take into account the operation of many forces. A generalized l i s t of factors to be considered as affecting exposure to intercourse shows how complex this can be. The factors include: Mortimer Spiegelman, op_. c i t . , p. 261. See Figure 4 in text. 12 Nathan Keyfitz, op_. c i t . , p. 8. 13 Ralph Tomlinson, Demographic Problems, (Belmont, C a l i f . , 1967), p. 42. 26 (a) those governing the formation and dissolution of unions in the reproductive period -- age at which this happens, percent celebates, disruption due to death and divorce of spouses. (b) those governing the exposure to intercourse within unions. (c) factors affecting exposure to conception -- f e r t i l i t y or i n f e r t i l i t y from involuntary or voluntary causes; use of contraception. (d) factors affecting gestation and successful parturition 14 feotal mortality from voluntary and involuntary causes. When the social forces which affect these factors are in turn considered the role of personal tastes is shown to be extremely 15 important. This is perhaps a major reason why demographers do not feel confident in projecting a single f e r t i l i t y rate but instead generate a range. The above is not meant to give the impression that l i t t l e is known about the factors affecting f e r t i l i t y but to emphasize that the rate cannot be projected with great confidence. F e r t i l i t y rates have been shown to be related to several economic and sociological variables. However, the effects of the variables may be different for different segments of the population. For instance, a growth in per capita income may increase f e r t i l i t y by making more resources available or i t may ^Geoffrey Hawthorn, The Sociology of Fertility,(Belmont, C a l i f . , 1967), p. 42. 1 5 I b i d . , p. 60. 27 decrease f e r t i l i t y as the desire for material goods increases relative to the desire for c h i l d r e n . ^ Female employment offers another example. While i t can safely be said that there does not seem to be a recorded instance in which there is a positive relationship between working women and f e r t i l i t y , research shows that where female work and maternal roles are compatible there w i l l be no reduction in f e r t i l i t y . ^ Thus, again, no clear relationship can be postulated with confidence. While these efforts at investigation of the social and economic factors that determine f e r t i l i t y have yielded mixed results, investigation into s ta t i s t ica l models of demographic change has been more successful. The f e r t i l i t y rate is normally projected by one of three methods: 1. the period f e r t i l i t y method, 2. the cohort f e r t i l i t y method, and 3. the parity progression method. The period f e r t i l i t y method analyses f e r t i l i t y in terms of 1 g year to year changes in f e r t i l i t y rates classif ied by age of mother. The cohort f e r t i l i t y method expresses the f e r t i l i t y of a specific birth cohort in terms of the expected lifetime experience of the generation of women. This analysis is in terms of completed f e r t i l i t y and the 19 distribution of births by age of mother. Since cohorts of women are 1 6 I b i d . , p. 79. 1 7 I b i d . , pp. 103-105. 18 Donald S. Akers, "Cohort F e r t i l i t y Versus Parity Progression as Methods of Projecting Births , " Demography, 2 (1967), p. 415. 1 9 I b i d . , p. 416. 28 followed through time, trends that have a sociological cause can be distinguished from mere fluctuations in the rate. Period f e r t i l i t y analysis cannot do this . The parity progression method is a form of the period f e r t i l i t y method and "attempts to represent more nearly the experience of actual groups of women by increasing the specif ic i ty of the rates that i s , the rates are specific not only for age and marital status of mothers but also for the number of children previously born (parity) and the length of time since marriage or the birth of the 20 previous child."" Cohort f e r t i l i t y is the method currently used by 21 the Bureau of the Census in the United States. Any of these methods may be used to project f e r t i l i t y rates into the future. However, because the many factors which may affect these rates have not been controlled for, a range of rate projections is usually developed. MIGRATION The third factor affecting the size of a population is migration. This factor may be of varying importance to different geographical areas. Migration has been the most important factor in the growth of the CMA in the last decade. From 1961-66 net migration accounted for 61.6% of the population increase and from 1966-71 i t Ib id . , p. 416. Ib id . , p. 415. 29 22 accounted for 76.5% of the population increase. Of th i s , internal migration (from the rest of Canada) accounted for 42% in the 1966-71 23 period, leaving 58% of net migration due to foreign immigration. Unfortunately, migration seems to be the least "explained" of a l l forces and is certainly the most unpredictable. In the 1880's N.A. Humphreys commented that "migration was rather distinguished for i ts lawlessness 24 than for having any definite law." This seems to have remained the case. When examining a l l moves, one may indicate four sets of factors which influence the decision. There are: 1. factors associated with the area of or ig in , 2. factors associated with the area of destination, 3. intervening obstacles, and 25 4. personal factors. The sets of positive and negative factors at both the origin and destination may be differently defined for every migrant or prospective migrant. S imi la r i ly , the intervening obstacles may be •pr perceived differently. Thus, when efforts are made to explain 22 Greater Vancouver Regional Di s t r i c t , Planning Branch, Popu- lation Forecast?(Vancouver, Jan. 1973), p. 5. 23 HPS Population Model Data sheets. 24 Everett S. Lee, "A Theory of Migration," Demography, 3 (1966), p. 47. 2 5 I b i d . , p. 50. 2 6 I b i d . , pp. 50-51. 30 migration they are thwarted by the individual nature of the decision to migrate. However, attempts have been made to examine the determinants 27 of migration flows and to test theories of the causes of migration. The theory of migration may be divided into the economic and the behaviourist!'c theories. Economic Approach The economic approach assumes that individuals are rational in their decisions to stay or move. Thus i f the benefits to be gained by a move are known to the individual and i f they outweigh the cost of the move i t is assumed that the move w i l l take place. Economists have usually concentrated their attention on migration streams from one region to another* This involves the use of "macro-data," i . e . the gross or net numbers of migrants from/to an area. Data on individuals. ^The characteristics of migration streams have been carefully analyzed in the United States and Canada. H. Eldridge, ("A Cohort Approach to the Analysis of Migration Differentials , " Demography, 1 (1964) 212-219, and "The Influence of Return Migration Upon Rates of Net Migration," Bulletin of the International Stat is t ical Institute, 40 (1964), pp. 321-349), using USA 1960 census data pointed out that the peak migration ages were 20-24, that return migration occurs between the ages of 30-45, that mobility is higher in periods of prosperity, that people who have moved are more l i k e l y to move again and that there are certain areas of the country which are net receivers of migrants. These United States results have been found generally true for Canadian data. Migration peaks at a somewhat older age group, i . e . 25-29 with 30-24 s t i l l above 20-24 (Marvin, R. Mclnnis, "Age,Education and Occupation Differentials in Interregional Migration: Some Evidence for Canada," Demography, 8 (197T), pp. 195-204. The Maritimes are net losers of migrants while Br i t i sh Columbia gains migrants from a l l provinces. Migration movement in Canada is generally westward. (Richard Lycan, "Interprovincial Migration In Canada: The Role of Spatial and Economic Factors," Canadian Geographer, 13 (1969), pp. 237-254. 31 or "micro-data" is not needed in this approach. The simplest type of analysis deals with the inhibitory effect of distance on migration flows. A simple gravity model to explain migration may be postulated. The gravity model merely specifies that migrants are attracted to an area because of i t s size or the number of employment opportunities available there. They are inhibited by their distance from i t . Thus, an equation for a simple gravity model might be: 28 u attractiveness of j M. . = 1 J (distance from i to j ) a Here distance may be a proxy for transportation costs, earnings foregone while unemployed during a move, non-pecuniary or psychic costs of moving, differentials in psychic income associated with the sending and receiv-ing areas and uncertainty about prospects in the new area due to lack 29 of information. Distance may also be used as an explanatory variable in regression analyses of migration streams. In this case, i t is usually The exponential a^  represents the degree to which distance is considered inhibitory. I t ' s value can be decided by the analyst. In simple studies using the gravity model i t has been assumed to be 2 but the value can be f i t ted to the particular case being studied. P.R. Shaw, "Migration Theory and Fact: A Review and Bibliography of Current Literature",mimeograph, (1971). 32 one of several explanatory variables. The performance of distance in these equations is usually f a i r l y good. Distance proved to be s t a t i s t i ca l ly significant in the works of Mclnnis and of Laber and 30 Chase. In L.A. Sjaastad's study i t proved to be the most influential variable but there was a suspicion of multicol l inear i ty between this 31 variable and income so that Sjaastad somewhat discounted this result . R. Lycan found that the marginal effect of distance declined as distance increased and that other factors tended to become more 32 important. Regional income differentials have also been used to explain migration flows. It is assumed that a rational member of the labour force w i l l move once the wage differential outweighs the cost of moving. Income and the regional differences in income usually perform well as 33 explanatory variables in regression analyses of migration. 30 R. Marvin Mclnnis, "Age, Education and Occupation Differen-t i a l s in Interregional Migration: Some Evidence for Canada," Demography, 8 (1971), pp. 195-204. Gene Laber and Richard X. Chase, "Interprovincial Migration in Canada as a Human Capital Decision," Journal of Po l i t i ca l Economy, 79 (1971), pp. 795-804. 31 L.A. Sjaastad, "The Relationship Between Migration and Income in the United States," Papers and Proceedings of the Regional Science  Association, Vol . 6 (I960), pp. 37-64. 32 Richard Lycan, "Interprovincial Migration in Canada: The Role of Spatial and Economic Factors," Canadian Geographer, 13 (1969), p. 240. 33 See for example - - ' L . A . Sjaastad, "The Relationship Between Migration and Income in the Unitee States," Papers and Proceedings of  the Regional Science Association, Vol . 6 (1960), pp. 37-64; T . J . Courchene, "Interprovincial Migration and Economic Adjustment," Canadian Journal of Economics, 3 (1970), pp. 550-576. John Vanderkamp, "Migration Flows: Their Determinants and the Effects of Return Migration," Journal of Po l i t i ca l Economy, 79 (1971), pp. 1012-1032. M. Mclnnis, op_. c i t . 33 There are, however, several points to be aware of when using income as an explanatory variable in a regression model: 1. Such models often assume constant earnings and this is an inadequate assumption for longer periods of time. 2. Local movement does not appear as responsive to wage differentials as do more distant moves. This is because, at the local leve l , amenity factors may be major factors. Families may move local ly merely because they have purchased a new home. It is major moves that are expected to show correlation to income variables. When the data analyzed includes a l l moves, these local moves may obscure the importance of income. 3. None of the models take into account occupation and train-ing relative to the income migrants are l ike ly to earn at alternative destinations. 4. It is important to isolate the population subgroups that w i l l be directly affected by income differentials when designing the migration measure to be used, e.g. family migrating with the head. 5. There is some reverse migration which,- depending on the wage structure in the areas, w i l l be advantageous to some. There-fore, aggregate income and migration data may not show a clear response to income variables. 34 6. Migrants do not always remain in the same occupation after they move. Thus wage differentials may not parallel the 34 migrants own u t i l i t y calculus. Unemployment differentials are another macro-economic determin-ant whose effect on migration has been examined. It has been found that this is a significant push factor but not as great a pull factor. 35 Vanderkamp, examined Canadian gross migration flows and the effect of unemployment and found that during periods of high overall unemployment migration was less. Courchene, obtained the same result in his analysis of the Canadian data. This finding is consistent with the hypothesis that while the unemployed may be prompted to move they also have fewer finances with which to do so. The research does not suggest that low unemployment rates are a pull factor for migration. This could be because the low rates typify a stable labour market where very few new job opportunities exist . Analysis of census migration data shows that migration is 37 sensitive to age. Most migration occurs at younger ages. This has been attributed to the stage in the l i f e cycle, the greater adaptability of the younger persons to new situations and the act of entry into the 38 labour force. Education is also represented as increasing the •3 A Paul Shaw, o£. c i t . , p.. 96. 3 5John Vanderkamp, "Interregional Mobility in Canada: A Study of the Time Pattern of Migration," Canadian Journal of Economics, 1 (1968), pp. 595-609. 3 6 T . J . Courchene, OJJ. c i t . •37 Hope Eldridge, op_. c i t . 3 8 M.R. Mclnnis, op_. c i t . 35 probi l i ty of migration. Stone found that migration increased monotonic-39 a l ly with education. It is also sometimes suggested that higher levels of education at place j mean that i t is a more cultural ly stimulating and dynamic place to be and thus education is used in some 40 models as an amenity and motivational variable. However, i t is also true that the most highly educated, for example doctors and lawyers, find themselves immobile once they become established in their ~ • 41 profession. Mclnnis has further shown that occupation also has a s i g n i f i -cant bearing on mobility. Service employees were found to be the most mobile group, professionals were also high but "blue col lar" labour was 42 the least mobile. 43 Courchene found that, for the more highly educated migrants, the income-distance trade-off increased and that i t increased more for the younger age groups. When looking merely at age he found that the 44 effect of distance increased with the age of the migrant. Mclnnis, found similar tendencies. 3 9 I b i d . 4 0 R . P . Shaw, OJD. c i t . , p. 101. 4 1 J.D. Tarver, "Occupational Migration Differentia ls , " Social Forces] 43 (1964), p. 237. 4 2 M.R. Mclnnis, op_. c i t . 4 3 T . J . Courchene, op_. c i t . 4 4 M.R. Mclnnis, op_. c i t . 36 Another factor sometimes proposed as influencing migration to place j is the migrant stock at j . This refers to the number of residents born or residing previously in place i who had taken up residence in place j previous to the period in which the researcher is examining migration between place i and j . It is included as a reflection of; (i) possible information flows from place j to i con-cerning differential opportunities, ( i i ) a possible index of friends 45 and relatives in the possible destination. Climatic variables are sometimes included in equations to explain migration as an index of a region's attractiveness but are not always very e f f e c t i v e . ^ A variable which is not usually attempted in regression analysis is the urbanization of the area. Stone has shown by analysis of variance that the degree of urbanization is an important factor in explaining migration. It may represent the extent to which the economy of an urban complex is focussed on the performance of economic functions 47 and thus the probably has relatively high per capita income. 45 P h i l l i p Nelson, "Migration, Real Income and Information," Journal of Regional Science, Vol . 1, No. 2,(Spring 1959). pp. 43-74. M.J. Greenwood, "Lagged Response in the Decision to Migrate,1  Journal of Regional Science, Vol . 10, No. 3,(1970),pp. 375-384. 46 Cicely Blanco, "The Determinants of Interstate Population Movements," Journal of Regional Science, Vol . 5, No. 1,(1963),pp. 79-84. ^ \ . 0 . Stone, Migration in Canada, (Ottawa, 1969). 37 Regression analysis to explain migration has generally been used for the country as a whole and not for one specific area. One reason for this concentration on the nation is the lack of data. Data on migration have been collected in the census since 1961. Thus when census material is published cross-section data are available but there are not sufficient observations to form a time series. Therefore most of the studies reviewed examined the flows between each of the ten provinces and the nine others (90 observations). Looking at one province would cut this down to nine observations and l i t t l e could be achieved s t a t i s t i c a l ly . The other major economic approach to explaining migration is to consider migration as a human capital decision. The "rational man" weighs the present value of his future stream of earnings in his new location against the costs of moving there. Laber and Chase f i t ted 48 this model for Canadian 1961 census data. They assumed that the rate 49 of discount was the same for a l l regions and multiplied the actual earnings by the probability of working in each area. The equation f i t ted was: Gene Laber and R.X. Chase, "Interprovincial Migration In Canada as a Human Capital Decision," Journal of Po l i t i ca l Economy, 79 (1971), pp. 795-804. 4 9 This avoids considering the effect of the discount rate e x p l i c i t l y . 38 where M . . is the net migration from i to j W., W. is expected earnings in regions i and j D.. is the distance from i to j (a proxy for moving costs). Low income e las t ic i t ies were obtained which indicates that migration was not very responsive to income. S. Bowles worked with the same hypothesis to examine outmigration 50 from the Southern states in the United States. Bowles makes the hypothesis somewhat more rea l i s t i c in stating that i t i s large differences in expected life-time earnings that encourage migration and that rough information of this sort is available and understood so that sophisticated 51 present value analyses need not be performed by the potential migrant. He also indicates that the effect of life-time earnings differentials w i l l vary between groups of population. For instance, those with more education are expected to have a higher response since they w i l l probably be more aware of opportunities elsewhere and have more desire for material goods. Similarly younger persons w i l l respond more readily than older persons who face a less acceptable disruption in their Tife-52 style. Bowles also postulates that blacks w i l l respond less to income differentials since, as a group, they have shown higher risk Samuel Bowles, "Migration as Investment: Empirical Tests of the Human Investment Approach to Geographical Mobi l i ty , " The Review of  Economics and Stat i s t ics , Vol. LI I , No. 4, Nov. 1970, pp. 356-362. 5 1 I b id . , p. 357. 5 2 I b i d . 39 aversion and a high time preference rate ( i . e . they discount more 53 heavily the value of increased future income.) However, blacks are shown to move more than whites due to the presence of discrimination in the South and the expectation of less in the rest of the United States. Bowles attempted to explain the var iab i l i ty of migration rates 54 from the South to the non-South among race-schoollng-and-age groups. The l i f e income hypothesis worked as the preceding discussion suggests in his equations. The discount rate used to evaluate the present value of expected income in each region was assumed to be 1, 6 or 11%. While this was not assumed to vary between regions, i t can be inferred from the foregoing that the rates vary among classes within the population. For instance, i f older persons respond less readily to income differentials this could indicate that they have a higher discount rate for that variable than the one chosen by the study. In summary the economic theory approach has worked moderately well in explaining the flows of migration. However, migration remains a phenomenon which has so far defied complete explanation^ A great deril of the d i f f i cu l ty of prediction derives from the fact that migration decisions are made by individuals who are not necessarily behaving in what the modeller perceives to be a rational manner. The behavioural approach to migration takes this into account. Ib id . , p. 358. Ib id . , p. 359. 40 Behaviourist Approach The behaviourists assume that man does not necessarily seek to maximize his income. He may seek merely to satisfy his needs. Man probably has limited knowledge and operates within the c i rc le of that 55 knowledge. Therefore he may be prompted to move by possible gains but because of uncertainty may stay or move depending on his individual reaction to the factors influencing him. Julian Wolpert has adapted this explanation of human behaviour 56 to the empirical study of migration. He employs three basic concepts: 1. place u t i l i t y , 2. the f i e ld theory approach to search behaviour, and 3. the l i f e cycle approach to threshold formation. Place u t i l i t y involves the notion of the "intendedly rat ional" man who, with limited knowledge and capabil i t ies , does assess the u t i l i t y to be derived from certain courses of action. Each individual has his own set of objectives which he attempts to achieve. There w i l l be some threshold level of u t i l i t y which, i f not achieved, w i l l induce search behaviour. The place u t i l i t y is then "the net composite of u t i l i t i e s which are derived from the individual's integration at some 57 position in space." 55 Herbert Simon, "Rational Choice and the Structure of the Environment," Psychological Review, Vol . 63 (1956), pp. 129-138. Julian Wolpert, "Behavioural Aspects of the Decision to Migrate," Papers of the Regional Science Association, Vol . xiv (1965), pp. 159-169. 5 7 I b i d . 41 The f i e ld theory approach to search behaviour postulates that the individual searches only those poss ibi l i t ies which he perceives and to which he responds. Further, this perception is ruled by the individuals needs, drives and a b i l i t i e s . In this case cluster sampling .is a poss ib i l i ty , i . e . more of the alternatives which are physically close are perceived. The l i f e cycle approach to threshold formation involves the recognition of an expanding action space as the individual matures. Further i t recognizes that differences in sex, race, formal education, family income and status are l ike ly to find expression in shaping the area of movement. This theory emphasizes the role played by uncertainty and the poss ibi l i ty of postponing decisions while awaiting further information. This approach is intui t ive ly appealing. However, i t requires detailed data on migrants which are not currently available. Thus the CO theory remains largely untested. Brown and Longbrake attempted to measure place u t i l i t y within the c i ty by matching household aspiration profiles with dwelling unit profiles and then using regression analysis to examine the major factors affecting migration. L.A. Brown and D.B. Longbrake, "Migration Flows in Intra Urban Space: Place U t i l i t y Considerations," Association Of American  Geographers: Annals, Vol . 60 (1970), pp. 368-384. 42 59 Tauber examined l i f e cycle migration by using the 1958 U.S. residence history survey which allowed the following of individuals through time. However, he admits that such analysis is impossible with census data. The foregoing discussion has emphasized that none of the determinants of population growth is easy to explain. Thus, when predictions of growth are attempted, many assumptions about the inter-actions of the determinants must be made. These may not always be rea l i s t ic but the d i f f icu l t ies to be surmounted in more complete analysis are formidable. K.E. Tauber, "Cohort Migration," Demography, 3 (1966), pp. 416-422. CHAPTER 3 PROJECTION OF POPULATION — TECHNIQUES AND VANCOUVER PROJECTIONS 43 CHAPTER 3 PROJECTION OF POPULATION — TECHNIQUES AND VANCOUVER PROJECTIONS DATA In Canada, data on the population are collected by means of the census every ten years. A census is defined by the United Nations as "the total process of collecting compiling and publishing demographic, economic and social data pertaining at a specified time or times to a l l persons in a country or delimited area."^ A national census is (i) o f f i c i a l l y sponsored, ( i i ) relates to a precisely defined area, ( i i i ) is universal in the sense of covering a l l persons, (iv) is a total enumeration referring to a well defined point in time, (v) is a collec-tion of separate data for each individual and not merely some process of aggregating group totals , (vi) is carried through to the compilation and publication of data by geographic areas and by demographic 2 variables. In Canada, in 1956 and 1966 this system was supplemented by a quinquennial census. At that time the population questions asked were much less complete than those in the decennial census. Only name, sex, marital status, relationship to the head to the household and the United States, Department of Health, Education and Welfare, Methods for Measuring Population Change: A Systems Analysis Summary, (Washington, 1969). 2 I b i d . 44 3 structural type of dwelling were asked. The census data is updated yearly by a v i t a l registration system. As part of this v i ta l registration system, data are gathered on l ive births, s t i l l b i r t h s , marriages and deaths by each province. The 4 federal government s ta t i s t ica l agency then compiles this data. These data are not cross referenced to the census data so that micro-data on individuals are not available. Lack of knowledge of the internal geographic mobility of the population is a major problem with this system of data collection. Moves Within the country are not registered and unless a specific question is asked in the decennial census the only information available may be inferent ia l . For instance, i t is possible to check whether the person resides in the same province as his province b i r th . This allows the researcher to infer whether or not there has been at least one lifetime migration but one can not t e l l more from this data. Even i f a question such as "Where did you l ive five years ago?" is posed i t implies only one move when, in fact, there may have been multiple moves or the person may have moved and returned to the same location. This dearth of information on internal migration is a very important l imiting factor in the study of regional populations. The ideal solution to this data l imitation is a continuous population register. Such a system starts from the census base and 3 < Statist ics Canada, (84-604), Analysis and Methods: Adminis- tration Report of the 1966 Census, (Ottawa, 1970). Statistics Canada, (84-202), Vital S ta t i s t ics , (Ottawa), Annual Publication. 45 records a l l moves and "v i ta l events." The data are kept loca l ly . The system requires very precise data, a disciplined and l i terate population to report regularly changes in demographic status and accurate 5 procedures for matching records and compiling data. Such a system has been in operation in Sweden for centuries and enables detailed demographic analysis for that country. The complete census is an excellent data collection tool be-cause of i ts universality and r e l i a b i l i t y . However, the ten year interval is very long. It makes explanation of the causes of changes in the population d i f f i c u l t due to the lack of knowledge about the intermediate values of pertinent variables. Data for small regions are very hard to f ind. The census publishes the distribution of the population by age (yearly intervals) and sex for the Vancouver Census Metropolitan Area (CMA), Migration figures for 1956-1961 are available from the Census Division of Statistics Canada, However, detailed analyses of the 1966-71 migration flows cannot be expected for some time yet. Provincial v i ta l s tat i s t ics exist on an annual basis from Statist ics Canada. From these, i t i s possible to obtain age specific death rates and birth rates by age of mother. However, these rates are not publicly available from any provincial or federal agency for the Vancouver CMA. If natural increase (births less deaths) in an area over a year or span of years is known and the population at the end dates is also known, i t is possible to United States, Department of Health, Education and Welfare, op. c i t . 46 estimate net migration to the area as a residual: migration = change in population - net natural increase However, for explanation of migration flows i t is more desirable to have estimates of gross i n - and out-migration to a region. PROJECTION METHODS Projection techniques vary widely in sophistication. They can be very simplistic projections of the aggregate population or a highly complex description and projection into the future of the factors bearing on a l l the determinants of the population. In the past, due to lack of data and research time most projections of regional population were quite direct. Several of g there simple methods of projection are outlined below. Comparative Forecasting Here the future growth of the population in an area is assumed to follow the pattern of another older area whose earlier growth has exhibited characteristics similar to the study area. It is only val id to choose areas where the causes of growth are comparable. Walter I sard, Methods of Regional Analysis: An Introduction  to Regional Science, Chapters 2 and 3 on Population Projection and Migration, pp. 5-79, (MIT, 1969). 47 Even then there is no reason to assume that the study region w i l l duplicate the past growth of the pattern area over the same span of time. Graphic Extrapolation This method involves the plotting of growth against time, the drawing by hand of a straight l ine through the points and the extension of that line into the future. If plain coordinates are used the straight line represents arithmetic growth or a constant absolute change per unit of time. If semilog paper is chosen then the straight line represents a constant rate of change per unit time or exponential growth. Any extrapolation assumes that relationships that have existed in the past w i l l continue to exist in the future and with the same intensity. Thus only where i t can be demonstrated that these relation-ships w i l l continue is this method va l id . Mathematical Extrapolation This method assumes that past population growth has followed some law to which future growth w i l l continue to conform. This means of extrapolation is superior to the graphic methods in that the mathematical relationships may be subjected to s ta t i s t ica l analysis and tests and that refinements can be made to the equations in respect of expected future variations in the determinants of growth. Examples of such mathematical relationships include the \ straight l i n e , the parabola, the exponential function, and Gompertz and logist ic curves. 48 The problem with these mathematical means of estimation is that unbounded growth as implied by the parabola and exponential functions seems impossible but there is l i t t l e information on which to base the level of the upper bound for the log i s t i c . Ratio and Correlation Methods It is assumed here that population growth in one area exhibits a relationship to population growth in another area. In this case, a present and future relationship among the factors causing growth is postulated. This is unlike the comparative forecasting technique where the regions needed only to be similar to each other. If there are inter-connections among the social economic, po l i t i ca l and biological factors in the two areas this is not an unreasonable assumption. There must be a projection of the base area growth already in existence. The method allows for future changes in growth while assuming the link between the two regions. This method is often used for open regions such as c i t ies which are linked to national growth. Extrapolation Using Regression Methods This s ta t i s t ica l technique f i t s a l ine (simple regression) or plane (multiple regression) to data which are assumed to have bearing on (explain) population growth. These explanatory variables must be projected into the future in order that population may also be projected. There are drawbacks to this s tat i s t ica l method. As with a l l extra-polation i t is assumed that past causal factors w i l l continue into the 49 future with the same intensity. Further, a good s tat i s t ica l f i t does not necessarily mean that the relevant explanatory variables have been found. Another hidden variable may be controlling the relationship. One should also be aware that the use of this technique involves many assumptions, including the independence of variables, the multivariate normality of the series, etc. Cohort Survival In a l l of the methods so far described, population has been projected as a to ta l . However, as pointed out in Chapter II population growth is influenced by many factors and different segments of the population can be expected to react differently to these factors. Efforts to cope with this complexity have involved examination of the components of population growth. The population can be divided into segments of similar age and/or sex ( i . e . cohorts). The rate of natural increase in the age and sex cohorts of the population can be projected. When individual cohort rates are projected i t is possible to take account of specific factors. For instance, the advent of heart pacemakers can have a great effect on the mortality of males aged 50 and over but much less effect on the population as a whole. One simple method of projecting the growth of the population in cohorts instead of as a whole is the cohort survival technique. Projections of the future rates of mortality for the age-sex cohorts and of the age-specific f e r t i l i t y rates are necessary. These are often obtained by use of the extrapolation methods discussed above and thus are subject to a l l of the p i t f a l l s inherent in that technique. The 50 projection obtained can only be as good as these rate projections. Once these rates are obtained, the simple multiplication of the survival rates by the age and sex groups to which they apply and the multiplication of the female age groups by the appropriate f e r t i l i t y rates produces a projection. Migration is usually accounted for by adding i t in separately. Thus i t must be projected independently. Previous sections have discussed how scanty is the knowledge of the present levels of migration and how scattered the thought on the factors influencing i t . Simple projections of migration based on extrapolation or ratio-methods cannot be expected to be very accurate. This remains the weakest part of any projection. Attempts have been made to make the simple cohort survival technique more responsive to the underlying causes of change in i t s rates. Computer simulation is currently used in this way. Simulation allows the analyst to examine what he considers to be the bases of population dynamics. Thus, a causal model of the change in future fer-t i l i t y rates may be developed which w i l l allow for the effect of working women, etc. on the birth ra te . 7 The use of such models for projection w i l l probably continue to involve the assumption that past relationships which can be quantified (e.g. by regression analysis) w i l l continue to hold. The technique, however, provides the advantage of allowing feedback between the elements of the system. 7Paul Shaw, "Modelling Metropolitan Population Growth and Change: The HPS Simulator," mimeograph, HPS Resource Science Centre, U.B.C., Vancouver, B.C. , Fall 1973. 51 PROJECTIONS OF. VANCOUVER POPULATION Map 1 shows the area included in the Vancouver CMA. This is very similar to the Greater Vancouver Regional Di s t r i c t . The red l ine on the map shows the boundary Of the GVRD. The Vancouver CMA is larger than the GVRD by the populations of Lang.ley, P i t t Meadows and Maple Ridge. The total population of these areas in 1971 was 53,867. Thus projections based on Vancouver data w i l l be larger than those based on the GVRD. Two cohort survival models involving varying assumptions about •therates of f e r t i l i t y , survival and migration have been estimated for the area. The f i r s t such model was prepared by the GVRD Planning g Department G.R.V.D. Planning Department Model Since the cohort survival technique has already been described, attention here w i l l be concentrated on the assumptions which define the models. Age-sex specific birth rates are not available for the Vancouver CMA. However, rates for Bri t i sh Columbia are. The 1970 age specific birth rates for Bri t i sh Columbia were taken as the high estimates of f e r t i l i t y . The GVRD Planning Department also compared the expected Greater Vancouver Regional D i s t r i c t , Planning Department, Population Forecast, (Vancouver, 1973). CWS'JS YJTMJPeuTAN AREA VANCOUVER IffGlCN METROPOUTAINE DE RECENSEHEMT FRINGE ! SCALE — E C H C L L C 1 C I ?. S « in mi.csjrL=i i - . _ j — a CNMILLE 2 0 2 * 6 U E G E N O - L E G E N D E CENSUS SUSOIVISION SUSDIVISIOM 0£ RECENSEMCNT 2 UREANIZEDCORE: N i o v . a u URSANIE ;^ H • • Large*! City V'lte principote Rejoinder Le restc DANLIEUE: U'bon S Urboine JIM* CANADA MAPLE RIDGE [—' (MUN ) l\3 CENSUS OF CA.1ACA,I97I RECENSENEflT DU CANADA, 1971 Map 1 53 births for the area obtained using the Br i t i sh Columbia rates to the actual number of births and found that, for 1966-71, the actual number of births was 10% below the expected. They then lowered each of the 1970 B.C. age specific rates by about 10% to arrive at their medium level estimate of the Vancouver birth rate. The time series of the crude birth rate in the GVRD over the past 10 years indicated that the rate was f a l l i n g . This was extrapolated and then the additional decrease was transferred to the age-specific birth rates. This became the low estimate of the regional birth rate. These rates were held constant over the entire estimation period. The rates are shown in Table 1. TABLE 1 Birth Rates Per 1,000 Used in the G.V.R.D. Forecast Age Group High Medium Low 15-19 58.3 52.1 50.2 20-24 154.4 137.9 135.4 25-29 144.9 129.4 128.0 30-34 72.4 64.7 62.1 35-39 31.0 27.7 25.3 40-44 8.3 7.4 6.2 45-49 0.5 0.4 0.4 Source: GVRD Population Forecast, p. 7. 54 These are quite crude methods of projecting birth rates. The high estimate assumes that current rates for Bri t i sh Columbia w i l l be experienced by the population of Vancouver over the period of projection. Since i t has been shown that rates of f e r t i l i t y are less in urbanized 9 areas than in rural areas and since the Br i t i sh Columbia rate is a mixture of urban and rural rates this provides an obvious overestimate. The rate chosen for the medium projection takes account of the unbanized nature of the area being considered but holds the birth rate constant at the 1970 rate until 2001. This negates the past trend of a declining birth rate. While i t is valid to make such an assumption about the future, the behavioural reactions i t implies should be made exp l i c i t . The low estimate of the birth rate attempts to take into account the past decline in the birth rate by making i t lower for the f i r s t period than that for the 1966-71 period but then this rate is held constant to 2001. These methods f a l l far short of the more sophisticated cohort f e r t i l i t y and parity progression methods discussed in Chapter 2. However, the limited regional data makes them necessary. The only suggested refinement would be a trend extrapolation of the age-specific Bri t i sh Columbia birth rates in line with the period f e r t i l i t y method. It should be remembered in this discussion of birth rates that the accuracy of the birth rate is not an important factor i f the projection is not going beyond 15 years and is for the purpose of projecting the labour force. In that case the labour force 15 years hence is already a l ive . Mortimer Speigelman, Introduction to Demography, revised edition, (Cambridge, 1968), p. 269. 55 Death rates in the region were assumed to be the same as those in Br i t i sh Columbia as a whole. This was done because rates for the region could not be found. The rates then stay the same for the pro-jection period. However, this assumption is reasonable since the rate of mortality has shown some hesitation in i t s downward trend in recent years in developed countr ies .^ Migration to the region in the past was estimated by the residual technique which was described above. The GVRD figures show that migration to the GVRD accounted for 76.5% of regional population growth in the 1966-71 period. TABLE 2 Migration To The GVRD Year Net Migration % of Population Increase 1951-56 57608 55.8% 1956-61 72052 57.6% 1961-66 63054 61.6% 1966-71 103592 76.5% Source: GVRD Population Forecast, p. 5. Four alternative assumptions were made about migration: Nathan Keyfitz and Wilhelm Flieger, Population: Facts and  Methods of Demography, (San Francisco, 1971), p. 159. 56 (a) That i t would be absolutely less. Thus, for each of the future 5 year intervals i t was set at 70,000. (b) That i t would remain about the same, in absolute terms, as the 1966-71 interval but that as population grew this would mean a decline in the rate of in-migration. This estimate involved migration of 100,000 for each interval . (c) That i t would be absolutely greater (125,000) but since this was held constant over the estimation period, the rate of migration should decline after the 1971-76 interval . (d) That migration would increase from 100,000 in 1971-76 to 150,000 in 1996-2001. The use of this method of projecting migration is rather anomalous in the case of the Vancouver CMA where 76.5% of the population growth in the 1966-71 period was derived from migration. The method thus amounts to a f a i r l y detailed projection for about a quarter of the expected population growth with the rest being assumed. The best that can be said is that although such assumptions provide alternative futures, they are in no way related to the capacity of the region either for the provision of employment or housing. The results of the alternative futures indicated by these varying assumptions about migration and f e r t i l i t y are presented in Table 3. TABLE 3 Range of Total Population Forecast G.V.R.D. Migration Per 5 Years Low Medium High Increasing 100,000 (1971) Birth Rate 70,000 100,000 125,000 to 150,000 (2001) 1976 Low 1,136,271 1 ,167,551 1 ,193,653 1 ,167,551 Medi um 1,138,616 1 ,169,923 1 ,196,078 1,169,936 High 1,149,476 1 ,181,021 1,207,348 1,181,001 1981 Low 1 ,251 ,802 1,316,639 1,370,784 1,327,089 Medium 1,256,815 1,321,814 1,376,130 1,332,300 High 1,279,922 1,345,801 1,400,811 1 ,356,301 1986 Low 1,368,442 1,468,614 1,552,213 1,500,707 Medium 1,376,431 1,476,965 1,560,936 1,509,167 High 1,412,534 1,514,951. 1 ,600,434 1,547,444 1991 Low 1,480,590 1,617,315 1 ,731 ,421 1 ,682,863 Medium 1,491,888 1,629,266 1,743,997 1 ,695,037 High 1,541,977 1 ,682,560 1,799,881 1 ,749,230 1996 Low 1,587,670 1 ,762,018 1,907,532 1,873,207 Medium 1,602,957 1 ,778,335 1,924,823 1,889,990 High 1 ,670,133 1 ,850,433 2,000,899 1,964,001 2001 Low 1 ,693,263 1,906,361 2,084,211 2,075,761 Medium 1 ,713,495 1,928,087 2,107,360 2,098,320 High 1,802,764 2,024,522 2,209,592 2,198,217 Source: GVRD Planning Department, Printouts of Population Forecasts. 58 I . I .P .S . Model The second cohort survival model for the area has been done by the Inter-Institutional Policy Simulation group at UBC. The model is an interim step for this group which plans to have a much more sophisticated model which w i l l account for the factors influencing each of the rates and which w i l l interact with other models in the HPS system such as the housing and regional economy models.^ As a step toward achieving this larger aim, the trend f i t t i n g model was developed so that i t could supply population variables to the other HPS submodels. Mortality and f e r t i l i t y were assumed to be the same as the B.C. rates. However, this interactive simulation exercise requires yearly projections of population for input to the other submodels. The accepted method of producing annual projections, given 5 year age intervals is to make projections for every f i f th calendar year 12 and to calculate the intervening years by linear interpolation. The HPS model assumed that each year one f i f t h of each age group moves into the next age group. Migration to the area was based on the 1966-71 total net migration which they estimated as 101,000. This can be approximated as 20,200 per year. The model assumed that the rates of migration would continue as in the past that is that there would be a continuing 13 high rate of in-migration. The current age and sex distribution f l 12 Paul Shaw, op_. c i t . Mortimer Spiegelman, o p . c i t . , p.403. 13 HPS Population Model, data sheets and program. of the migrants was assumed to be constant. This migration assump-tion is subject to the same cr i t ic i sm as is the GVRD's assumption. However, in the more sophisticated version of the model internal migration is made to depend on dwelling starts and foreign immigration 14 is related to employment. The estimates of population for Vancouver CMA produced by this model are shown in Table 4. The HPS projections are quite a bit higher than the GVRD projections. The difference may be attributa-ble to the use of the 1966-71 rates of migration in the projections of the la t ter . The GVRD assumptions about migration involve absolute numbers over a five year period. For most of the GVRD projections this means a declining rate of migration. The HPS model, however, assumes that the current high rate of migration w i l l continue. Further, since their model projects population yearly this rate is compounded much more rapidly than the GVRD rates. I.D.T.C. Model A similar exercise has been undertaken by the Bri t i sh Columbia Department of Industrial Development, Trade and Commerce; 15 Economics and Statist ics Division. The region, in their 14 Paul Shaw, o_p_. c i t . , pp. 5-9. 15 Bri t i sh Columbia, Department of Industrial Developments Trade and Commerce, Economics and Statist ics Branch, Forecast of Population Growth in B.C. to the Year 2000, (Victoria , 1971). 60 TABLE 4 HPS Population Projections Vancouver CMA Year Males Females Total 1971 509384.0 519082.0 1028335 1972 531678.7 544857.2 1076535 1973 559792.9 577227.0 1137019 1974 591440.2 613062.7 1204503 1975 625635.1 651202.2 1276837 1976 656923.5 686172.4 1343095 1977 689951.6 722640.6 1412592 1978 724608.1 760557.0 1485165 1979 760887.0 799973.9 1560860 1980 798862.7 841017.6 1639880 1981 832577.6 877773.9 1710351 1982 868088.7 916312.5 1784401 1983 905563.4 956838.1 1862401 1984 945188.2 999571.4 1944759 1985 987156.8 1044736.2 2031893 1986 1031660.1 1092549.0 2124209 1987 1078877.0 1143217.0 2222094 1988 1128975.0 1196930.0 2325905 1989 1182107.0 1253858.0 2435965 1990 1238406.0 1314151.0 2552557 1991 1297991.0 1377946.0 2675937 Source: HPS Computer Printouts. June 1973. 61 c lass i f icat ion, that corresponds most closely to the GVRD is the Lower Mainland. The boundaries for this are not exactly the same as those of the GVRD but the GVRD would account for most of the population of their region. Their boundaries for the Lower Mainland are shown on Figure 5. Their cohort survival model assumed Brit i sh Columbia mortality rates which are assumed to decrease for most age-sex cohorts over the 30 year projection period. (Rates in this model change every 10 years.) The f e r t i l i t y rates used were the Br i t i sh Columbia rates but they too were assumed to decline. Migration was assumed to increase over the period. This assumption is based on the historical increase of migration to the area. The specific assumptions involved two sets of projections of migrants. The f i r s t projected an increasing number of migrants to 1984 with the number being constant thereafter. The second involved increasing numbers of migrants over the entire period. These are shown in Table 5. TABLE 5 Projection of Migrants Average Annual Number 1970-74 45,000 45,000 1975-79 50,000 55,000 1980-84 60,000 60,000 1985-89 60,000 70,000 1990-2000 60,000 80,000 Source: Brit ish Columbia, Department of Industrial Development, Trade and Commerce, Forecasts of Population Growth in  B.C. to the Year 2000, (Victoria , 1970), p. 8. 62 -REGIONS OF I. East Kootenay 6. Kamloops-Lillooet ,2. West Kootenay 7. Lower Coast 3. Okanogan 8. Central Interior 4. Lower Mainland 9. Northwest British Columbia 5. Vancouver Island 10. Peace River E C O N O M I C S A N D S T A T I S T I C S 1 9 7 1 63 Population projections for the Lower Mainland produced by this model are shown in Table 6. These projections are based on the f i r s t set of migration assumptions. TABLE 6 Population of the Lower Mainland Year Total Population 1951 649,200 1961 907,600 1966 1,021,700 1969 (estimated by Stat., Canada) 1,124,200 Projections •1980 1,515,000 1990 1,980,000 2000 2,440,000 Source: B.C. Department of Industrial Development, Trade and Commerce; Economics and Statist ics Division, Forecast of Population  Growth in B.C. to the Year 2000. The differences between these projections and those of the GVRD and HPS are again most l ike ly due to the migration assumptions which are higher than the GVRD's. Since the only source for these projections was a government publication i t was not possible to discern i f the actual computation of the model could have provoked differences. 64 Urban Canada Projections The Urban Future monograph^ in the Urban Canada series, ut i l ized another model to estimate the population of urban centres in Canada. Vancouver was only one of many such centres. Their approach was based on the demand for labour generated by increasing industrial production. The Lithwick model used Systems Research Group Canada 2000^ estimates of national outputs and assumed a constant regional share of national production for each region. The method of estimation is shown in Figure 6. Alternative assumptions about the growth of output were employed. Those underlying the results presented in Table 7 are as follows: NI — manufacturing is aggregated to one sector and a l l sectors grow at the national rate. N4 -- There is increasing productivity so that less labour is needed than in NI. A l l sectors grow at the national rate. N5 -- The labour force in a c i ty is divided between two groups. The f i r s t comprises those supplying domestic needs who maintain their minimum share. (This is defined via the minimum requirements for self sufficiency technique). The growth rate of this f i r s t group is calculated by deflating A. Goracz, I . Lithwick and L.O. Stone, The Urban Future, Urban Canada, Research Monograph #5, (Ottawa, 1971). ^Systems Research Group, Canada Economic Projections to the  Year 2000, (Toronto, 1970). 65 Lithwick Population Projection Model  Methodology Generalized Forecasting Model Growth of Output of Industry Growth of Labour Demand for Industry I Growth of Labour Demand by Industry X in City Y I Growth of Total Labour Demand in City Y I I Growth of Total Growth of Total Output in City Y\ Population in City Y I \ * Growth of Labour ^Growth of Per Capita Income in City Y Income in City Y Figure 6 Source: A Goracz, I, Lithwick, L.O. Stone, The Urban Future,  Urban Canada Research, Monograph No. 5. output growth by productivity increase. The second group are those involved in supplying export markets. This group experiences growth at the national rate. TABLE 7 Vancouver Population Projections (I. Lithwick) (millions of persons) Year NI N4 N5 1971 1.0696 0.9400 0.9001 1981 1.5982 1.2466 1.1439 1991 2.5357 1.7804 1.5823 2001 3.8854 2.4818 2.1367 This method ignores the demographic factors in population growth entirely and ut i l izes a form of the ratio projection technique, where the region is assumed to grow at the same rate as the nation. 1 o Stone's projection involved a similar approach. Labour demand determined population growth. The national level forecast of output as divided by the productivity index to produce the demand for 'A. Goracz, I. Lithwick, L.0. Stone, op_. c i t . 67 labour in each sector. The CMA share of national output was approximated from decennial census data going back to 1941 and then projected forward on the basis of alternative futures. Attempts were made to explain migration by f i t t i n g multiple regression equations linking 1961-66 values of net migration and i n -migration to lagged 1956-61 values of these variables as well as 1956-61 growth rates of employment, the 1961 level of the ratio of employment to population and some other less obviously economic variables. Natural increase in the population in the CMA was estimated using CMA natural increase rates which had been linked to the national rate of increase and to the current and lagged net migration rat io . The model was thus somewhat sensitive to the interactions between net migration and natural increase. The parameters of this model were then used in the forecasting period to project the ratio of the natural increase rate in a given 5 year period for a particular CMA to the corresponding rate for Canada as a whole. This ratio was then applied to the national value of the natural increase rate to obtain the rate for the CMA in question. With the projected natural increase rate and migration, population projections were calculated. These projections for the Vancouver CMA are shown in Table 8. 68 TABLE 8 Projected Total Population, Vancouver CMA (L.O. Stone) (rounded to thousands) 1976 1981 1986 1991 1996 2001 Alternative A 1102 1229 1382 1560 1772 2026 Alternative B 1026 1091 1170 1265 1384 1533 Alternative C 1180 1379 1623 1913 2260 2676 Source: L.O. Stone, The Urban Future, Table 19. SUMMARY Table 9 shows clearly the academic nature of the projection exercise. The difference between the HPS and the GVRD projections which u t i l i z e the same technique and data base can probably be attributed to their differing assumptions regarding migration. A l l the projections shown are firmly based on the current state of the art . They do refer to s l ight ly different geographical areas (not, however, s ignificantly different). It is obvious that only gross estimates of the future population of the region are obtainable using the current state of the art . Thus, i t can be stated that, with the continuation of past trends, Vancouver's population can be expected to reach 2 to 2.5 TABLE 9 Comparison of Vancouver Population Projections Agency/Area 1981 1986 1991 1996 2001 GVRD / GVRD (medium, medium) 1,321,814 1,476,965 1 ,629,266 1,778,335 1,928,087 11PA/Van. CMA 1,710,351 2,124,209 2,675,937 - -B.C. Dept. IDTC Lower Mainland 1 ,515,000* - 1 ,980,000* - 2,440,000* I. Lithwick Van. CMA (NY-1) 1,246,600 — 1 ,780,400 2,481,800 L.O. Stone Van. CMA (series I-A 1-D) 1,229,000 1,382,000 1,560,000 1,772,000 2,026,000 (1980, 1990, 2000). Source: Prior Tables Cited. CT) mill ion persons by 2001. 70 '^However, one should bear in mind Jerome Pickard's quip that: "We can say with some certainty that barring any unfore-seen catastrophe, the population of the United States in the year 2000 w i l l approximate 300,000 persons, give or take some millions (or perhaps a dozen mil l ions , more of less." Peter A. Morrison, Demographic Information for Ci t ies : A Manual for  Estimating and Projecting Local Population Characteristics, A Report prepared for the Department of Housing and Urban Development, Rand Corporation, (Santa Monica, 1971), p. 44. CHAPTER 4 FACTORS AFFECTING REGIONAL ECONOMIC GROWTH 71 CHAPTER 4 FACTORS AFFECTING REGIONAL ECONOMIC GROWTH THE GENERAL FRAMEWORK Regional economic growth may be analyzed in the same manner as national economic growth. The region is a sub-unit of the nation and subject to essentially the same growth processes. There are, however, some complications to the analysis of a region. The region is an open area and external factors are of major importance. Since physical distances are shorter between most regions than between most nations and since po l i t i ca l and institutional barriers usually do not exist between regions, the region has higher factor mobility and also more trade than the nation. Further, since regions in a nation belong to a common currency area, monetary theory is irrelevant to regional trade, ( i . e . the equilibrating mechanism of exchange rates does not exist between regions)J Unfortunately, the very openness of regions means that neither factor flows nor commodity flows are easily monitored and, in Canada, few are. Thus the interactions to be discussed are empirically d i f f i c u l t to trace. Horst Siebert, Regional Economic Growth: Theory and Policy, (Scranton, Pa. , 1969), pp. 49-51. 72 In examining growth determinants, the i n i t i a l resource endowments of a region are important in determining i t s i n i t i a l advan-tages. The direction of growth in a region as in an open economy relies on the comparative advantage of the region. Economists usually hypothesize that factors of production are seeking their best use defined in terms of the highest return. In a completely eff icient economy, this would imply that the marginal physical product per dollar of factors would be equated throughout the economy. This ideal result is probably never attained across regions. However, economists feel that the forces which would lead to eff icient equilibrium are operating in the economy. It is usually assumed that i t is only the imperfections of the system which frustrate i t s attain-ment. Thus, i t is hypothesized that capital w i l l flow to regions where the capitalrlabour ratio is low and where the marginal efficiency of investment is high. Similarly, labour moves to areas with high capital:labour ratios where wages are high. It is also assumed that when regions trade, growth occurs through the demand for those products in which the region has a comparative advantage. Thus regions concentrate production in goods that require large inputs of the factors which are relatively abundant in their area. While these relat ively simple theories may not appear sufficient to explain growth completely in a specific region, they are valuable as they concentrate on the essential forces determining growth. Growth in a region is a result of the interaction of supply 73 and demand forces. Demand forces help to determine the growth of production in an area. If a region has a comparative advantage in producing goods for which there is l i t t l e demand i t is not l ike ly to grow quickly. Further, i f i t produces goods for which there is only local demand, i t w i l l not be earning export dollars and thus may find the financing of growth d i f f i c u l t . The supply forces of growth may be represented in a generalized production function for the region. 0 = f(K, L, Q, T r , T, SQ) . where 0 = output K = capital L = labour Q = land T r = transportation T = technical knowledge 2 SQ = social system Transportation is part of the capi ta l , land and labour factors and consideration of i t may be combined with them. The social system is a vague concept when used in this context. The values and attitudes promoted by the social system are important in determining the responses of the owners of factors of production. However, the effect of the social system is d i f f i c u l t to make exp l i c i t . 2 I b i d . , p. 24. 74 The land component of the production function is most impor-tant when the spatial aspects of growth are being considered. It is possible to abstract the analysis away from this spatial dimension. This involves the assumption that land is not a constraining factor on development and so involves some lack of realism. However, i t allows the analyst to gain an understanding of how growth may occur in a region considered as a single point in space. More detailed analysis of the region in i t s spatial dimension may be carried out at a later date. Thus, although there are six factors of production l i s ted in the generalized production function, i t is possible to concentrate attention on only three of them. These factors: capi ta l , labour, and technical knowledge, are commonly considered the most important elements of the production function. It is worthwhile spending some time discussing the factors which induce changes in them. CAPITAL, LABOUR AND TECHNICAL KNOWLEDGE Capital The amount of capital available to a region is determined by the supply and demand for investment funds. The supply of investment funds is dependent on savings. Regional savings are, in turn, dependent 3 on regional income. However, not a l l investment funds are supplied 3 I b i d . , p. 28. 75 from within the region so that the relative pro f i tab i l i ty of regional investment is also important. This is so because a higher rate of return w i l l lure funds from other regions. However, there are several reasons why capital might not flow to regions where the rate of return is higher. There may be imperfect knowledge and investors may be unaware of the opportunity in the region of high return. There may be uncertainty or risk differentials so that even though investors are aware of a potentially higher rate of return they are reluctant to invest. Further, the nature of the investment project may be such that only a large amount of capital can be invested. Such i n d i v i s i b i l i t i e s may prevent marginal adjustments in response to sl ight differences in the rate of return. It may also happen that the capital in the area, receiving the low rate of return ( i . e . where capital is overabundant) is "sunk" in the form of buildings or machinery and 4 is thus incapable of being transferred to the high return area. Labour The supply of labour i s , in the long run, dependent on the f e r t i l i t y of the population. In the short run, wage increases may encourage greater participation in the labour force, although this effect is subject to the incomerleisure trade-off. Wage differentials may also cause an increase in migration. H.W. Richardson, Regional Economics: Location Theory, Urban  Structure and Regional Change, (London: 1969), pp. 292-305. 76 The mobility of labour is important to regional growth. This mobility is encouraged by differentials in income between areas, provided that the potential migrants respond to such inducements. The rate of response is dependent on several factors. One of these is the quality of communication of opportunities between regions. Ignorance of opportunities to be had in other regions can mean that response to income differentials w i l l be less than i t would be were the communication system operating better. The cost of moving must also be considered. This cost can reflect either only the transportation costs of moving oneself and household possessions or i t may also include the psychic cost of leaving a physical location or friends to which one is attached. These extra costs may make a response to the income differential uneconomic. There may also be intervening opportunities between the region from which the potential migrant starts and the area with the relatively high income. That i s , there may be areas closer to the migrant where a s l ight ly smaller income gain can be attained but where the remaining wage differential is equal to the extra travel costs that would be involved in going to the higher wage region. There are also social factors to be considered in the determin-ants of migration. Whether a potential migrant is open to the messages of higher income depend on his personal aspiration level and his reference group. Thus i f the potential migrant is content where he i s , he may display economic non-rationality and disregard the infor-5 mation he is receiving about higher income to be gained elsewhere. 5 Horst Siebert, op_. c i t . , pp. 35-62. 77 Other than the potential migrant's non-response, there may be other factors which inhibit the response of labour to higher wages. There may be s k i l l s differences between workers who wish to migrate and those required in the high wage area. There may also be barriers to entry of the local labour market. If labour is responsive to the income incentive to migrate i t may receive a disincentive i f the high wage area cannot physically accommodate i t s immigrants. Thus problems of congestion, evidenced in housing shortages and not enough schools, within the region may discourage migration. Technical Knowledge Mobility of technical knowledge between regions is important since i t is unlikely that a l l regions w i l l experience the same rate of discovery of new knowledge. New technical knowledge is assimilated in stages. The f i r s t stage is innovation when the new process is f i r s t applied. This is followed by imitation as other firms follow sui t . Innovation is restricted by several factors. If the new process applies only to certain firms and to existing structures the mobility of innovation w i l l be inhibited by the spatial location of those firms. The ava i l ab i l i ty of funds for investment also inhibits innovation. Since these funds come partly from retained earnings the given spatial distribution of funds influences innovation. Further, innovations w i l l be undertaken only where certain profit H.W. Richardson, op_. c i t . , pp. 292-297. 78 requirements are met. The presence of "innovative personalities" also influences the acceptability of innovations. Lastly, the size of firm may have some effect since large firms can better compensate for risk in one area by act ivi ty in others. Imitation of new technical knowledge may be stalled because of the patent system, or because of the time lag between when an innovation occurs and communication of i t s existence reaches a potential imitator. Imitators are also subject to the restrictions of profit margins, a v a i l i a b i l i t y of funds and size of f i r m . 7 It can also happen that the new technical knowledge is "embodied" in new physical capital . In this case, adoption of the new knowledge must wait unti l the old capital is replaced. This can be a i 8 slow process. GOVERNMENT POLICY Government policy may influence a l l of the factors of producti Governments may intervene directly to encourage mobility by providing increased information about jobs in other areas. They may also make direct grants to potential migrants to enable them to search for jobs in new areas and to help with their moving expenses. Horst Siebert, op_. c i t . , pp. 70-73. H.W. Richardson, 0£. c i t . , p. 311. 79 Governments may also invest directly in regions by building infrastructure (roads, sewers, etc.) or by giving capital assistance to firms to invest in a region. Governments also involve themselves in encouraging the develop-ment of new technical knowledge through grants for sc ient i f ic and indus-t r i a l research and by sending free information on new developments to manufacturers. ANALYSIS OF REGIONAL GROWTH Regional growth viewed from the supply side involves the inter-action of a l l of the factors.of production. Analysis of the supply side involves examining the factors which influence each factor of production and examining how the factors of production themselves influence each other. The demand side, which has so far only been alluded to, works in conjunction with supply forces. Either may provide a constraint or impetus to growth. Demand forces operate through regional consumption, exports, government spending and investment (where this uses produced goods). The factors which influence these items are complex. For exports, government spending and some investment these factors may also be outside of the control of the region. Thus, the region may only be able to react to changes in them and do l i t t l e to influence those changes. Regional consumption is tied closely to regional income and so is intimately related to both the factors of production (the supply side) and to external demand forces. The level of regional 80 spending is determined by the interaction of these forces. For a complete analysis of regional growth both the supply and demand forces must be examined. The foregoing has, hopefully, shown that a great deal is involved in such an analysis. It is worth noting that while the system responses that were postulated at the start of this chapter are f a i r l y uncomplicated, in the end the analyst is examining many relevant factors. Thus i t is possible to explain a great deal about regional growth starting from basic premises. H. Siebert indicates that the analysis of regional growth determinants should solve three basic problems. First i t must formulate empirically testable hypotheses which explain the variations in growth determinants. Second, i t must specify the expansion effects caused by variations of determinants. Third i t should explain the changes in the spatial structure stemming from variations in the growth determinants. 9 Unfortunately, the regional analyst runs into d i f f i cu l ty in attacking the very f i r s t problem. It is d i f f i c u l t to test hypotheses about regional growth because the necessary data to do so, by and large, do not exist . This makes testing theories which examine the interaction of factors of production at the regional level very d i f f i c u l t . The analyst is then thrown back to the simpler, more general theories which can be tested. Thus i t is possible to observe whether the average per capita Horst Siebert, op_. c i t . , p. 28. 81 income between regions is converging or not but i t is not possible to make pronouncements on the marginal efficiency of investment between regions. Further, due to the inadequacy of the data on labour mobility one can only say that income differentials appear to be an important determinant of migration flows. The exact degree to which income influences migrants to any given region is unlikely to be known. Thus when the analyst attempts to predict growth for a region he is often limited to such simplistic models as shift-share or economic base. These are not very satisfying to work with. They usually exhibit f a i r l y large errors of prediction and because they operate at a very high level of aggregation i t is not usually clear what causes most of the error. Thus, the end result is a poor prediction with l i t t l e feeling of having understood the growth process. The object of this chapter has been to give the reader an understanding of the complexity of the regional growth process. It is hoped that this background w i l l allow the techniques of regional analysis that are commonly used to be seen in perspective. These techniques are presented in the next chapter. CHAPTER 5 TOOLS OF REGIONAL ECONOMIC ANALYSIS AND PROJECTION 82 CHAPTER 5 TOOLS OF REGIONAL ECONOMIC ANALYSIS AND PROJECTION THE REGIONAL PROBLEM The tools of regional analysis are not, on the whole, highly sophisticated. The analyst who uses them usually experiences no l i t t l e doubt concerning their efficacy. There has been less theoretical work done in the f i e ld of regional economic growth than in national economic growth. In part, this is due to the historical lack of knowledge about the regional economy. Further, problems at the national level were considered more pressing and so data about the national economy were collected and analyzed. Regional data were not. The reason for this was partly the expense connected with data generation and partly the conceptual d i f f i cu l t ie s involved. These conceptual problems are related to the special position of a region vis a vis the nation. A region forms part of a nation. While a nation may, in many cases, be considered self-sufficient a region cannot. For instance, both region and nation must trade with other areas. In the case of the nation, such trade flows are automatic-a l ly recorded for the purpose of ascertaining the national trade balance and tar i f f s payable. However, for the region such is not the case. While a l l trade with foreign countries originates from regions, foreign trade stat is t ics do not reflect the region of origin either because to do so would reveal the company of origin (contrary to the agreements 83 of the Secrecy Act) or because the f inal product exported may have been processed in many regions of the country so that the region of origin is not clear. Further, a great deal of a region's trade is carried on within the nation and since no t a r i f f barriers exist between regions of the same nation in North America such flows are unmonitored. Another impediment to data collection in and thus knowledge of the regional economy is the company which operates throughout the nation but keeps i t s accounts only at the head off ice. It may be impossible for this type of firm to determine the regional origin of i t s products and regional factors inputs. Thus data on corporate profits are corres-pondingly intractible at the regional level . Public s ta t i s t ica l agencies do not estimate regional corporate profit and the analyst who attempts to do so usually has to make some f a i r l y unrealistic assumptions.^ The fact that the regional economy must be considered "open" means that many factors which determine i t s growth are outside i t s control. For instance, national policies may have a significant effect or demand for i t s products may be largely determined in another region. It can be seen that theoretical attempts to explain regional growth face many d i f f i c u l t i e s . Projection of growth in a region is even more d i f f i c u l t . The regional analyst knows that certain factors and conditions induce growth at the national level and assumes that these are also of some import at the regional level . For instance, increases in demand variables such as private consumption, government spending, investment and exports can lead to the expansion of. production. Increases in investment as \alman Goldberg, "The Measurement and Allocation of Corporate Profits in Regional Sector Accounts," Journal of Regional Studies, Vol . 8, No. 2 (1968), pp. 159-163. 84 well increase the capacity of the productive sector. The supply of labour and increases in technical knowledge work with this increase in capital to achieve growth. Even at the national level there is contro-versy regarding the specific factors in which growth originates. However, the above factors are commonly recognized to have some significant impact. When the focus shifts to the regional l eve l , i t is necessary to take some special considerations into account. A region within a nation buys from and sel ls to many other areas both for final consumption and intermediate production. These trade ties become very important when growth"in the region is under analysis. To the extent that a region buys i t s intermediate products from other regions, any increase in the demand variables w i l l not be fe l t to the fu l l extent within the region but w i l l be to some extent passed on to the regions from which i t imports. Furthermore, through trade, the region's economy may be closely linked to that of others. If the region under consideration were to experience an increase in demand for i t s products the effect of this increased income could be transmitted via trade linkages to other regions and might, eventually, feed back to the region under study in the form of further change in demand. In the process, the effect of the demand increase could be amplified or dampened. It is because of the "openness" of the regional economy that trade relationships are so important. The discussion up to this point has focussed on aggregate growth determinants. However, i t may also be of interest to examine specific industries and how the linkages between them and/or their 85 individual growth patterns affect the total economy. Such analysis allows a government wishing to stimulate growth and having knowledge of the rapidly expanding industries in the area to concentrate on increasing the demand for the products of those industries and on fac i l i t a t ing the supply of labour and capital to them. Drawing this together produces a rather formidable l i s t of aspects with which a framework for analysis and projection of growth in a region should attempt to deal. These include: 1. Demand variables — consumption, government spending, investment and exports. 2. Supply variables -- labour force, capital stock (investment being the change in this) and technological change. 3. Level and origin of imports. 4. Interregional feedbacks -- specification of the trade 1inkages. 5. Industrial disaggregation. In what follows the various commonly employed techniques of regional analysis and projection w i l l be discussed. After a brief description of the technique, the requirements of each for projection w i l l be discussed and examples presented to i l lus trate the use of the technique. The emphasis in this review is on the region as a point in space. Spatial aspects within the region are not considered. Thus the elements of location analysis (e.g. comparative cost techniques) are neglected in the discussion. Further, since the major interest of the chapter is the growth of the economy as a whole, techniques which 86 comprehensively examine parts of i t are also excluded (e.g. industrial complex analysis). SHIFT-SHARE Shift-share analysis is real ly a descriptive technique. It points to some factors which may explain why some regions grow faster than others. By use of a series of growth rates i t seeks to indicate whether the differential in growth between regions or between a region and the nation is attributable to differences in industry mix or efficiency. Industry mix refers to the hypothesis that the region may be growing more slowly than the nation because the industries located there are slow growth industries, i . e . these industries are growing slowly throughout the nation. Thus the region, to speed i t s growth may consider examining poss ibi l i t ies of altering i t s industry mix, perhaps by attracting new industries. Regional efficiency, on the other hand, refers to problems in the productivity of local labour and capital . It indicates that those industries located in the region are not growing at the same rate as are their national counterparts. If regional efficiency appears to be lower in the region than the nation, investigations would have to be conducted to discover the reason for this lower efficiency before policy could be prescribed. In shift-share analysis,growth in regional industry is compared to national industrial growth to 87 indicate where differences in growth occur. However, to find the reasons for such differences, further analysis must be undertaken. The basic premise of shift-share is that the region would be expected to grow at the same rate as the nation i f there were no differ-ences in industry mix between the economies and no regional advantage or disadvantage for any industry. For each industry in the region a share component (G^) is calculated: G. = R° i £ - R° 1 N° 1 where G^  i s growth in industry i between time periods o arid t R? is employment in industry i in period o is total national employment in period t N° is total national employment in period o The total share component i s ; G = E G. G.j represents the share of growth that industry i should have accounted for had i t grown at the national average over the period o to t . This component usually has a non-zero value. This is to be expected since few industries behave as the average of a l l . Two Other components are introduced in an effort to better describe the pattern of industrial growth in the region. They too are formed by adding and subtracting growth rates. 88 The industrial mix (or proportionality) component indicates how regional employment would have grown i f the region had had the same industrial mix as that of the nation. The proportionality component for industry i is calculated as: N t p. = Ro — ) 1 N° N° l where N.j is national employment in industry i The total proportionality component i s : E P. i 1 If employment in slow growth industries is higher in the region than in the nation, this component w i l l be negative and indicate a poor industrial mix in the region. The differential component shows how actual employment in industry i at time t compares with what i t would have been had industry i grown in the region as i t did in the nation (The nation represents the average of a l l regions). Should this term be negative for an industry i t would indicate that, in the region, industry i i s not pre-forming as well as i t is in the nation. That i s , the industry is less efficient in the region. The differential component is represented as: 89 D. = Rl - R° N i 1 1 1 ~6" NT 1 The total differential component is D = I D . i 1 For the regional economy as a whole: G + P + D = R t - R ° It can be seen that the technique merely involves the sum of several growth rates. Shift-share is a descriptive tool . In order to form regional policy i t is necessary to know why and where regional disadvantages occur. The industrial mix and differential components serve to indicate where more research may produce frui t ful results. There is a temptation to take shift-share beyond this and to use i t in the projection of regional growth. When this is done the technique suffers from several theoretical and practical l imitations. On the theoretical side, D.B. Houston^ asserts that shift-share cannot be considered a growth theory. D.B. Houston, "The Shift and Share Analysis of Regional Growth: A Crit ique," Southern Economic Journal , (Apri l , 1967), pp. 577-581. 90 The assumption that the region should grow as the nation does is simplistic and may obscure the causes of regional growth. Further, he states that the economic behaviour underlying the two kinds of shifts is not readily discernible and that economically we have very l i t t l e basis for distinguishing between the competitive and mix effects. F inal ly , he states that even i f one believed that the distinction between the components were theoretically relevant, the results are valid only i f a l l goods are sold in the national market. At the practical l eve l , i t can be shown that the value of the components is not invariant with the level of disaggregation. Thus the sum of either shift component for disaggregated data is unlikely to equal that same shift component calculated for aggregated data. H. James 3 Brown has also shown that, at the industry leve l , the sign of the differential component in one period is not related to i t s sign in the next. This shows great ins tabi l i ty in this component. However, when the total differential component is calculated for a region i t is 4 consistent in sign between periods. Since this merely indicates that regions which do well or poorly in one period can expect the same over-a l l performance in the next, Brown does not feel that this weakens his cr i t ic i sm of the component for use in the projection of industrial growth.5 J H . James Brown, "Shift Share Projections of Regional Economic Growth: An Empirical Test," Journal of Regional Science, Vol . 9, No. 1 (Apr i l , 1969), pp. 1-18. 4 Christos C. Paraskevopoulos, "The Stabi l i ty of the Regional Share Component: An Empirical Test," Journal of Regional Science, Vol . 11, No. 1 (1971), pp. 107-112. H. James Brown, "The Stabi l i ty of the Regional-Share Component: A Reply," Journal of Regional Science, Vol . 11, No. 1 (1971), pp. 113-114. 91 Judging shift-share against the cr i ter ia set out at the start of this chapter for regional growth projections. The model scores poorly. The method takes no specific account of any of the economic variables cited in the c r i t e r i a . Neither demand variables, supply variables nor the trade sector is considered. The technique does show industrial de ta i l . However, i t does not show linkages between industries but only compares their preformance in the region with their performance in the nation. Thus there are serious drawbacks to using shift-share as a method for the production of growth projections. It has, however, been so used. In order to project growth using shift-share, the values of the share, proportionality and differential components must f i r s t be ascertained. Projections, by industry, of national growth must therefore be available. Then, since, G. + P. + D. = - R? i i i i i Regional employment estimates are given by R* = Gi + P i + Di + R? In this calculation, the analyst may assume that the components remain constant or that they change in reflection of expected changes in the economy. For instance, C.F. Floyd^ assumed that the regional and c Charles F. Floyd, "Shift and Share Projection Models: A Reformulation," Annals of Regional Science, (June, 1973), pp. 40-49. 92 national growth rates converged over time as did G.R. Walters in the Bay Area Simulation Study. 7 The following two examples show how the shift-share approach o can be used. Hellman and Marcus develop a form of shift-share analysis to project industrial growth in New Jersey. They begin by assuming that the region maintains a certain share of national employment. They explain growth in terms of a proportional growth element and a differen-t i a l growth element between the region and the nation for each industry. In this case, proportional growth is equal to national growth. For the differential element the economy is sp l i t between local market oriented industries and export industries. For local market industries the differential growth is the growth in the region's population share. Population here is assumed to be representative of markets for local ly oriented industry. For export industries, economies of scale and 9 localization and agglomeration economies are estimated and projected. Unfortunately, when the authors tested their projections against naive projection models they discovered that their model did not perform wel l . Davis and Goldberg^ suggest another way in which shift-share Centre for Real Estate and Urban Economics, Jobs, People and  Land: Bay Area Simulation Study. Special Report No. 6, Institute of Urban and Regional Development, University of Cal i fornia, Berkeley, 1968. o D. Hellman and Matityahu, Marcus. A Cr i t i ca l Analysis of  Employment Projection Models: A Test Case of New Jersey, Water Resources Research Institute (Rutgers, New Jersey), 9 I b i d . , p. 31. ^°H.Craig Davis and Michael A. Goldberg, "Combining Inter-sectoral Flows and Shift-Share Techniques: A Hybrid Regional Forecasting Model," Annals of Regional Science, (June, 1972), pp. 106-115. 93 can be used in regional economic projections. They suggest that i t be used to project f inal demands which can then be fed into an intersectoral flows model to produce projections of regional employment by industry. The differential component^ is made to rely on externalities such as density, pollution congestion and agglomeration factors. This is an attempt to explain the differential component and is the approach suggested 12 by Brown to remedy the weakness in this component. Since this model was not empirically tested i t is not possible to say how the shift-share approach would have performed here. KEYNESIAN ANALYSIS AND MULTIPLIERS Keynesian analysis is aggregate economic analysis. This type of analysis has been used often at the national level . In the analysis, various demand categories are explained. The sum of these explains total income. It involves estimation of a consumption function, an investment function, import and export functions, equations showing government expenditures, direct and indirect taxation, transfer payments, income and perhaps wages and prices. At the national level the s ta t i s t ica l estimation of such equations is not too d i f f i c u l t because accounts for the national economy exist in time series for long ^ I n this case, the differential component is the same as described in the theoretical section here. 12 H. James Brown, "Shift-Share Projections of Regional Economic Growth: An Empirical Test," Journal of Regional Science, Vol . 9, No. 1 (Apr i l , 1969), p. 16. 94 periods. However, for a regional economy, such economic aggregates have usually not been calculated. For a few provinces social accounts have recently been complied but this has not been done for smaller regions. No regional time series data on these demand variables exist. F i r s t , since Keynesian models project aggregate demand variables, they may not be meaningful to regional policy makers who 13 may not find themselves in a position to influence these variables. A regional government might not have the power to affect government expenditures in the region (especially given heavy involvement of the federal and provincial levels of government.) Nor might they be able to change interest rates and so influence the level of investment. Thus i t may not be worthwhile for the regional analyst to pursue such an approach i f the object of his analysis is to produce a model usable by policy makers. Second, some of the premises upon which national models are founded must be altered for regions. For example, regional economies are extremely open and their factors of production highly mobile. The region often has l i t t l e control over i t s markets and may face a perfectly elastic demand curve for most of i t s products. 1 4 In that case, demand should not be the main exogenous variable since the model would then be explaining l i t t l e . Similarly local capital investments may not depend on local savings and these two variables may never be in balance. Thus Stanislaw Czamanski, An Econometric Model of Nova Scotia, Regional Studies Series No. 2. Institute of Public Affa irs , Dalhousie University, Halifax, 1968, p. 59. 14 I.e. the region has no influence upon the demand for i t s products. 95 an analysis which focussed on this relationship would be inappropriate. A simple regional model for a Keynesian type of analysis may be represented as: INCOME Y = C + I + G + X - M . . . . ( 1 ) CONSUMPTION FUNCTION C = a + cY d . . . . (2) DISPOSABLE INCOME Y d = Y - T . . . . (3) TAXES T = tY . . . . (4) DISPOSABLE INCOME Y d = (1-t) Y . . . . (5) IMPORT FUNCTION M = b + mYd . . . . (6) Y = : regional income C = : regional consumption G = = regional government expenditure X = = regional exports M = : regional imports I = = regional investment . If equations 2-6 are substituted into equation 1 and solved for Y, the result i s : Y = [1 - (c * I) (1 + t)J x (a - b + I + G + X) The second term is mainly comprised of exogenous variables ( i . e . those determined outside the model) while the f i r s t term is made up of the parameters of the model, the propensities to consume and to 15 Stanislaw Czamanski, op_. c i t . , p. 59. 96 import and the rate of taxation. This f i r s t term is a simple regional multipl ier . When one of the demand variables is increased, regional income w i l l rise and may rise my more than the original demand increase due to the responding effect. The multiplier shows the magnitude of this responding effect. The Keynesian model does not usually involve disaggregation of industry although, at the national l eve l , such models have been linked to input-output models and disaggregation achieved in this manner.^ However, i f the data problem can be overcome the Keynesian model f u l f i l s most of the other c r i ter ia for a desirable analytic framework discussed above. For the regional economy, the demand and trade variables are exp l i c i t ly explained by functions in the system. The supply variables are, however, generally ignored. It is possible to allow for inter-regional feedbacks in the system by modelling the other economy and linking i t to the region through the trade sector. Against these advantages of using this framework i t is necessary for the analyst to weigh the d i f f i cu l ty in obtaining data and the possible drawback of producing a model of too great a level of aggregation to be useful in regional policy making. This type of model has often been used for prediction. If the equations of the system have been adequately estimated s t a t i s t i c a l l y , there is a good poss ibi l i ty that, given estimated projections of the Economic Council of Canada, The Economy to 1980: Staff  Papers (Ottawa, 1972), paper 1. 97 exogenous variables, the model w i l l produce reasonable aggregate projections. There have been many regional projection models which have 17 18 taken this approach. The Glickman model of Philadelphia consists of 13 structural blocks and explains the growth of 18 industrial sectors. However, for a l l of these, sectors, output responds to demand conditions only. Population in the model is dependent on industrial output, wages and the natural rate of increase. This model also attempts to explain growth in subregions. It estimates the major economic variables for the City of Philadelphia and calculates the values of these for the suburban areas as a residual (regional value less the City of Philadel-phia value). 19 The Czamanski model for Nova Scotia is also a demand oriented model. It has seven submodels which explain the iron and steel industry, other manufacturing and employment, output and investments, households, government and trade def ic i t s , population and immigration and welfare. " N . J . Glickman, An Area Strati f ied Regional Econometric Model, RSR I Discussion Paper Series: No. 58, Regional Science Research Institute, Philadelphia, Penn., Oct. 1972. Stanislaw Czamanski, An Econometric Model of Nova Scotia, Regional Studies Series No. 2, Institute of Public Affa i r s , Dalhousie University, Halifax, 1968 . B.C. Telephone Company, An Experimental Forecasting Model of  the Br i t i sh Columbia Economy, Socio-Economic Studies Division, Aug. 1973. L.M. Hartman and David Seckler, "Toward the Application of Dynamic Growth Theory to Regions," Journal of Regional Science, Vol . 7, No. 2, (1967), pp. 167-173. 18 N.J. Gl ickman, op_. c i t . Stanislaw Czamanski, op_. c i t . 98 The level of industrial detail i s highly aggregated, the sectors explained being five in a l l : 1. iron and steel , 2. agriculture, forestry and fisheries, 3. commercial services, 4. government, and 5. manufacturing. Iron and steel and manufacturing include capital stock in their pro-duction functions where capital stock is defined as the sum of past investment. However, this is as close as the model comes to explaining supply factors. In the main, i t concentrates on demand and makes the usual assumption for this type of model that capital and labour adjust to aggregate demand. THE ECONOMIC BASE MULTIPLIER The lack of data at the regional level is a major stumbling block to regional Keynesian analysis. The economic base technique seeks to avoid this problem. In this analysis, the whole of the economy is divided into two classif ications: basic (or export) production and service production. "Basic production" refers to production the region exports to other areas thereby acquiring money from outside. "Service production" is production which is used local ly . The hypothesis is that growth in the export sector induces growth in the service sector. 99 The growth in the export sector i s , however, determined exogenous!y and the determinants are not explained in the model. Algebraically the model may be represented as: Y = b + s s = aY Y = b(l - a) or Y = k b where: Y = income b = base sector s = service sector k = base multiplier = 1/(1 - a) For a given change in the basic sector, the model gives a rough prediction of the overall economic effect. The model involves several assumptions. F i r s t , i t assumes that exports are the sole engine 20 of economic growth. As T. Lane states, this may be quite reasonable in the short run in an urban economy where the trade sector is a very large proportion of total ac t iv i ty . "However, in the long run i t is highly plausible that elements other than exports may play a strategic 21 role in the in i t i a t ing of growth and change. Growth requires not 20 T. Lane, "The Urban Base Mult ip l ier : An Evaluation of the State of the A r t , " Land Economics, Vol . 42, No. 3, (Aug., 1966), 345. Ibid. 100 only aggregate demand levels to sustain i t but also a supply of factors of production to support i t . Economic base merely assumes the avai l-22 ab i l i ty to these factors. The economic base model further assumes that the measurements taken of various variables describe an equilibrium condition in the economy and further that there is an equilibrium at the end of the prediction period. This would mean that a l l interactions among variables in the economic system had'worked themselves out at the two periods of measurement. Unfortunately, the system is changing 23 constantly and this is a d i f f i c u l t assumption to satisfy. Usually, in the economic base technique, industry in the region is not disaggregated and each export industry registers i t s effect on the total economy through the base mult ipl ier . This is a single number, applicable to a l l export industry and means that an increase in any export industry is assumed to have a homogeneous effect on the rest of the economy. Thus an x dollar increase in dairy exports is hypothesized to have the same effect as an x dollar increase in steel exports. Obviously, this.need not be the case. The economic base method does not allow for interregional feedbacks or the effect of investment in the region. Thus, while i t overcomes the Keynesian multipl ier ' s problem of impracticability i t loses much of the technique's explanatory power. There are other problems in applying economic base to growth projections. Employment is often used as the measurement of base act ivi ty R.A. Siege!, "The Economic Base and Mult ipl ier Analysis," Urban Affairs Quarterly, Vol . 2, No. 2, (1966), p. 33. 101 because such figures are available and easy to obtain. However, positing parallel changes between output and employment in the long run denies 24 productivity improvements which are l i k e l y to accrue. Further, when the economic base technique is used for forecasting, the base multiplier is usually assumed to remain constant. The multiplier represents the net responding effects that take place within the economy. To assume i t constant means that the average propensities to consume and import 25 remain constant. It is unlikely that, over a long time period, this assumption would represent rea l i ty . If the level of personal income 26 in the region changes these propensities w i l l most l ike ly change. Furthermore, the base ratio may change over time i f structural changes, 27 increasing or decreasing the specialization of the economy, occur. When the economic base technique is used for projection of regional growth, projections of the base sector must f i r s t be generated. Then the base multiplier is used to project total employment. Examples of models using the export base theory of growth 2 4 Ib_id. , p. 28. 25 The marginal propensity to consume determines responding within the economy and the marginal propensity to import determines the spending leaks from the area. T. Lane, op. c i t . , p. 341. C M . Tiebout, "The Community Income Mult ip l ier : A Case Study," in R. Pfouts (ed.), The Techniques of Urban Analysis, (West Trenton, N . J . , 1960), p. 349. 27 Gerald S i rk in , "The Theory of the Regional Economic Base," Review of Economic and Stat i s t ics , 41 (1959), p. 429. 102 28 are abundant. The model is f a i r l y easy to implement. It is not purely descriptive as is shift-share but i t s assumptions about growth should be kept in mind when i t is used. 29 The Susequehanna River Basin model employed an economic base framework. Employment in the household sector was represented as a linear function of total population. Employment in the business serving sector was a linear function of total ac t iv i ty . Some export sector employment was projected exogeneously but the model also attempted to project some of this sector endogenously by creating relative cost indices for each industry. These indices comprised labour costs, transport costs, and raw material costs which were affected by other reactions in the model. Thus, the labour costs index included relative wages which were made to respond to industrial mix and the degree of local labour market tightness. It can be seen that here the economic base technique was used as a starting point and expanded. " C a l i f o r n i a Development Model and Oahu Model as Described in H.R. Hamilton, et.a]_., Systems Simulation for Regional Analysis, (Boston, 1969), pp. 74-80. U.S. Department of the Interior, Pacific Northwest - Population, Employment and Housing Units Projected to 1990, Bonneville Power Adminis-trat ion, Branch of Power Requirements, Portland, Oregon, Feb. 1973. Suggestions for the use of this approach were also found in w.R.D. Sewell and B.T. Bower, Forecasting the Demands for Water, Policy and Planning Branch, Department of Energy Mines and Resources, (Ottawa, 1968) and in E.V. Bowden, "The Methodology of Long Range (50 year), Projections of Regional Growth: An Appraisal and a Possible Approach," Annals of Regional Science, 3 (June, 1969), pp. 76-85. H.R. Hamilton, et a]_., op_. c i t . 103 INPUT - OUTPUT One of the more sophisticated tools of regional analysis is the input-output technique. Input-output examines the demand and supply relationships of the various industries in the local economy. It stresses their inter-relationships and thus allows the analyst to deal more comprehensively with the reverberations that take place throughout the economy in response to changes that may occur in the demand for the products of only one industry. The basic input-output table is called the transactions table. In i t , the names of industries appear both along the top and down the side. Thus the processing matrix is symmetrical. Each row indicates where an industry sells i t s products. Products which are inputs to other industries are considered intermediate products while those which are not used as inputs to further production are part of final demand. Each column indicates where an industry purchases i t s inputs. There is a final demand sector composed of columns added to the table which disaggregate the sectors to which goods are sold for f inal consumption. After this basic table has been drawn up, the next step in the 1-0 technique is to calculate a table of direct coefficients known as the A matrix. This involves dividing each column entry by the total of the column. Each entry then represents the proportion of the column industry's inputs contributed by the row industry. From the A matrix, a table of direct and indirect coefficients is calculated. When this is done each column shows the total effect on the output of the other 104 industries in the economy of a dollar increase in delivery to final demand by the column industry. In matrix notation this technique is represented as: X = (I-A)" 1 Y where A = matrix of direct coefficients Y = final demand vector X = total output (I-A)~^ = matrix of direct and indirect coefficients. This is an analytical solution and as long as none of the i n i t i a l values changes the solution w i l l always be the same. The technique is useful in impact analysis where one or more elements of the f inal demand vector is changed and the system is solved to determine the effects on the whole economy sector by sector of those changes. The technique can also be expanded to show interregional flows. Essentially another matrix for the alternate region is bui l t and their trade flows determined. Since this allows the tracing of effects between regions at a level of fine industrial detail i t i s the most powerful of the tools yet considered in this review. The 1-0 model can be combined with a Keynesian model that would explain the growth of the f inal demand variables. 3 ^ The major drawback of the technique when considered for use in projection is the fact that the table of direct coefficients is H.C. Davis and M.A. Goldberg, "An Economic Model of the Vancouver Region," U.B.C. mimeograph, May, 1973. 105 assumed.to remain constant. The I-0 matrix involves a snapshot of the economy. At one point in time the relationships between industries and each industry's technology is recorded but then relationships are not allowed to change. The effects of technological change, the entry of new industry to the regional market, possible changes in factor prices and product mix are a l l ignored. This makes the technique a poor one for prediction of effects in the local economy beyond the short term. Several techniques for allowing change in the A matrix to occur in response to growth over time 31 have been suggested but unfortunately no really satisfactory method has yet been developed. The technique is very powerful and desirable to employ in many ways but i t is also extremely data intensive. Since the aggregates needed as inputs to other techniques do not exist at the regional level i t is not surprising that the micro-level data required for an 1-0 table do not in general exist . Construction of such a table usually requires a special survey and takes a great deal of time and expense to prepare. °'These include: (1) the use of informed judgement. (2) projection of the a-jj's from past changes in the A matrix. A time series for the A matrix would have to be available in order to do this . (3) accepting the assumption of economic succession, examine the matrices of more advanced countries. (4) find the coefficients for the most advanced firms in the industry and assume that other firms in the industry w i l l eventually adopt the same production practices and so have the same a-jj's in the future as these firms have now. This is the best practices method. Miernyk, wm. H. The Elements of Input-Output Analysis, New York, 1969, pp. 117-125. 106 It is generally agreed that, due to the constancy of the A matrix over time, input-output is not suitable for the generation of long range projections. However, i f this degree of non-realism is 32 acknowledged and accepted the technique can be used in projection. There have also been attempts to update the A matrix and so use the technique. The 1-0 table has also been used to generate expected growth by industry in the total economy given employment growth in 34 a set of export industries. 35 The Davis and Goldberg proposal involves an 1-0 model linked to a simulation model. The simulation model would project the final demand variables for the short run. It would attempt to explain expected regional growth in consumption, investment (residential and business), government expenditure and exports and imports. In order to allow for changes in the A matrix they plan a location survey to account for the future location of new plants in the area, consultation with management regarding the possible purchase patterns of new firms as well as anticipated technological changes. They also hope to accommodate J^Ivan M. Lee, Conditional Projections of California Growth, Giannini Foundation, Monograph No. 19, Feb. 1967, University of Cali fornia, Division of Agricultural Sciences. 33 The Ohio River Basin Study attempted to.update the 1947 national 1-0 table before they began their projections, H.R. Hamilton, et al_., op_. c i t . , p. 71. H.C. Davis and M.A. Goldberg, "An Economic Model of the Vancouver Region" U.B.C., Mimeograph, May, 1973, propose various ways of updating their 1-0 table during the projection period. 34 The New York Metropolitan Regional Study as reported in H.R. Hamilton, e_t al_., op_. c i t . , p. 60. 35 H.C. Davis and M.A. Goldberg, "An Economic Model of the Vancouver Region," U.B.C. , Mimeograph, May, T973. 107 relative price changes. Unfortunately, these ideas have not yet been carried out so that i t ' i s not possible to say how practicable they are. NEO-CLASSICAL GROWTH MODELS The analytical tools thus far discussed have relied completely on demand to explain growth. The assumption implici t in them is that i f demand for regional products grows, the regional labour force w i l l respond and capital w i l l flow in or that which exists w i l l be more fu l ly u t i l i zed . However, the analysis of real world regional problems has revealed regions to which capital w i l l not flow and in which the labour force through lack of education or training does not respond to increased demands for their services. The neo-classical growth model concentrates on supply relation-ships. It focusses on labour, capital and technology as the c r i t i c a l elements of production. The model assumes that demand exists for a l l that is produced. Thus the model postulates a production function for the economy: Q = f (L ,K,T) . The equations of the model attempt to explain the past changes in the supply of labour and capita l . Also, attempts are usually made to define the role of technological change in the growth process. It is possible, using such a model to disaggrate the industries within the economy. Further, the model can be expanded to include the effects of imports, interregional flows as was judged 108 desirable in the basic c r i t e r i a for a framework of regional analysis. However, i t usually neglects demand variables. This type of model can be used to produce regional projections by industry. It means producing a regional production function for each industry to be considered, projecting future changes in those industries and solving the complete system to estimate the effects on the entire labour force and capital supply. Finding the information on regional industries in order to produce these functions would probably be quite d i f f i c u l t . F.W. Bel l ' s model examined supply relationships in a regional context. In his model capital investment takes place to f i l l the gap between the actual and desired levels of capital stock. The desired stock. The desired stock of capital is a log-linear function of regional output and the level of technology. Capital , the rate of technological change, and produced income combine through a Cobb-Douglas production function to yie ld the demand for labour. The labour supply is determined mainly on the basis of population. Thus the demand and supply of each factor is explained in the aggregate. The system can be solved to yie ld the level of unemployment. Bell f i t ted his equations on data for 1947-1962. Then, beginning at 1947, he used the model to forecast the demand and supply of labour to 1962. The model accurately predicted turning points during this period and Bell had enough confidence 37 in i t to produce projections to 1980. 3 6 F.W. B e l l , "An Econometric Forecasting Model for a Region," Journal of Regional Science, Vol . 7, No. 2 (1967), pp. 109-127. 3 7 I b i d . , pp. 120-125. ECONOMETRIC MODELS 109 When applied to real world data the neo-classical and Keynesian models are usually econometric models. This means that the equations of the system are estimated s t a t i s t i c a l l y , on the basis of time series or cross-section data. In this type of model, there is always the problem of possiblemis-specification through oversimplific-ation. In the estimated equation, important variables may be omitted or the wrong functional form adopted without the s ta t i s t ica l tests indicating an unsatisfactory f i t . There is also the danger of auto-correlation. This results in downward biases in the standard errors of the regression coefficients and may lead to considering that insignificant variables are significant. Unfortunately, the remedies for autocorrelation may be inappropriate in models for forecasting. The use of f i r s t differencing could lead to poor forecasts for time periods more than a few periods in the future. Generalized least squares produces estimators which are highly sensitive to mis-specification errors. Thus one can expect significant s ta t i s t ica l problems when using econometric models for forecasting. Charles Richter, "Some Limitations of Regional Econometric Models," paper presented to the annual meeting of the Western Regional Science Association, Feb. 26, 1971. no COMPUTER SIMULATION In computer simulation, a system is represented mathematically and solved on the computer. Simulation models differ from econometric models in that the equations of the system need not be s t a t i s t i ca l ly f i t ted . Instead the equation parameters and growth paths are postulated and experimental "runs" or solutions of the model are produced on the computer. By changing the parameters one by one, in separate runs i t becomes clear to which parameters and assumptions the model is most sensitive. Further research can then be conducted to make these conform, as closely as possible, to rea l i ty . Any of the analytical tools discussed above may form the basis of a simulation model. The technique allows the analyst who has only base year data to make assumptions about the growth paths of variables in the system and to experiment with projections. In Chapter I , criticisms of large scale mathematical models were discussed. Harry Richardson has made specific criticisms of the 39 concentration on models in urban economics. He feels that models may be an inappropriate tool for urban economics since they relate only to one dimensional space whereas urban studies require at least two dimensions. Further, he feels that the models produced are generally oversimplified and neglect the more advanced work in the f i e l d . He Harry W. Richardson, "A Comment on Some Uses of Mathematical Models inj>Urban Economics," Urban Studies, 10 (1973), pp. 259-270. I l l also fears that the quantity of energy being devoted to the production of models may tap that which would ordinarily flow to the development of new theory. The merit of these comments does not affect the use of models in projection of growth since models allow the analyst to make maximum use of present tools. EXISTING PROJECTIONS FOR THE GREATER VANCOUVER REGIONAL DISTRICT The Greater Vancouver Regional Dis t r ic t Planning Department has produced a set of economic projections for the region broken down 40 by broad industrial classifications to the year 1981. The method used was:. 1. to examine the proportionate share of the labour force presently employed in each sector, 2. to make an educated guess (by reviewing trends in industry) as to whether that industry could be expected to increase i t s share of employment or decline and by how much, 3. thus, to adjust the expected proportionate share of that industry in regional employment in the future. These adjusted shares are shown in Table 1, 4. To move from these proportionate shares through population projections for the region to estimates of employment in the future. These estimates are shown in Table 2. 40 Greater Vancouver Regional Distr ict Planning Department, The Lower Mainland Economy: Trends and Prospects, Vancouver, 1970. TABLE 10 LOWER MAINLAND PERCENTAGE DISTRIBUTION OF LABOUR FORCE BY SECTOR 1951-1961 AND FORECASTS FOR 1971, 1981 and 2000 SECTOR INDUSTRY GROUP ACTUAL FORECAST 1951 1961 1971 1981 2000 Range Mean Primary Agriculture 4.4 2.9 1.6 1.0 Extractive 4.3 2.8 1.4 0.8 Total Primary 8.7 5.7 3.0 1.8 1.2 1.5 Secondary Manufacturing 24.0 18.9 19.0 19.0 Construction 7.1 6.8 6.8 6.8 Total Secondary 31.1 25.7 25.8 25.8 . 22-26 24.0 Tertiary Transport Group 11.4 11.4 11.6 11.6 Trade 19.2 19.5 19.5 19.5 Finance Group 4.2 5.1 5.5 5.5 Services** 24.0 23.3 24.9 25.9 Public Administration and Others* 1.4 9.3 9.7 9.9 Total Tertiary 60.2 68.6 71.2 72.4 72-77 74.5 Source: GVRD Planning Department, The Lower Mainland's Economy: Trends and Prospects. Notes: Data of 1961 Census not s t r i c t l y comparable with earlier censuses due to changes in definit ions. * Public Administration employment grouped with "services" until the 1961 Census. * * Community, business and personal services. ^ 113 TABLE 11 DISTRIBUTION OF LABOUR FORCE IN THE LOWER MAINLAND BY INDUSTRY GROUP 1951-1981 Economic Act iv i ty LABOUR FORCE IN 1,000's ACTUAL FORECAST ESTIMATES 1951 1961 1971 1981 Agriculture 11.1 9.6 7.6 6.8 Extractive 11.1 9.4 6.6 5.4 Total Primary 22.0 19.0 14.3 12.2 Manufacturing 60.3 62.6 90.4 129.2 Construction 18.0 22.5 32.4 46.2 Total Secondary 78.3 85.1 122.8 175.4 Transport Group 28.8 37.9 55.2 78.9 Trade 48.6 64.7 92.8 132.6 Finance Group 10.7 16.7 26.8 37.4 Services 60.9 77.2 118.5 176.1 Public Administration and Others 3.7 30.8 46.2 67.3 Total Tertiary 152.7 227.3 338.9 492.3 Source: GVRD, Planning Department, op_. c i t . , p. 12. Notes: *Based on a 1971 regional labour force estimate of 476,000 persons. This assumes a regional population of 1,150,000 persons, 41% of whom are in the labour force. **Based on a 1981 labour force of 680,000 persons. This assumes a regional population of 1,510,000 persons, 45% of whom are in the labour force. 114 This is a qualitative sort of analysis. The GVRD report does not indicate what techniques were used to determine the estimated change in industry shares of employment. Although the GVRD report looks at various industries and evaluates past trends in the area, when the analysis moves to employment estimates i t makes the assumption that the entire projected labour force w i l l be employed. Though the region has been expanding rapidly in the past due to high in-migration, this may seem unlikely but may not be an unreasonable assumption. The only objection to the method used is perhaps, that i t would be more satisfy-ing to see some of the interaction between demand and supply in the regional market explained. However, as a forecasting exercise the approach may be quite va l id . CHAPTER 6 A REGIONAL PROJECTION MODEL 115 CHAPTER 6 A REGIONAL PROJECTION MODEL THE OVERALL MODEL STRUCTURE The projection model created in this study is comprised of three components: the employment submodel, the migration submodel and the population submodel. The employment submodel projects regional employment using the shift-share technique. This projected employment is fed into a regional migration equation which projects the total number of migrants over the projection period. The total number of migrants is received as input to the population submodel. This submodel projects population using the cohort survival technique. A schematic outline of the model follows: EMPLOYMENT PROJECTION i Jobs at Projection Date Jobs Migration Projection Migrants - Over ^ Period Unemployment Rate POPULATION PROJECTION Labour Force at Projection Date Figure 7 In equation form the model i s : 116 M = f(J) . . . . . . (1) Pop = g(P*. M) . . . . (2) L = h(Pop) . . . . (3) Or substituting equations 1 and 2 into equation 3 J = jobs produced by the employment projection model M = migrants g = the population growth function P* = i n i t i a l population h = the participation function L = labour force L = h{g[P*, f(.J)]} • (4) or L = f (P * . M, J) where THE EMPLOYMENT SUBMODEL The basis for projection of sectoral industry growth in Vancouver from 1971-1981 is the shift-share model. The basic equation for this model i s : 117 +4.1 + M t + 1 + N * + 1 N t + 1 * R - N-R^ 1 = R t ( L - ) + R. (-—- _ ) + R ^ - ^ - - -J-y) . . . . (5) The weaknesses of this model were stressed in Chapter 5. That chapter also discussed the alternative techniques available to the researcher. An aggregate model which did not distinguish sectoral employ-ment, such as the economic base model or Keynesian multiplier analysis, would not have been suitable for this study. The study was begun as a research project for the Westwater Research Centre at U.B.C. That agency conducts environmental research into water quality in the Lower Fraser River. To be useful to them projections into the future by industry were necessary. It was expected that waste loadings might be applied to the projections yielded by the model so that some idea of future demands on water quality could be obtained. It is quite l ike ly that even the sectoral breakdown available may be too broad for this purpose so that use of a more aggregated model would not have been useful. It might have been preferable to use a projection technique that relied on a regional input-output table. However, at the time work for this study was undertaken, no completed input-output table for the Vancouver region existed. Such a table is being developed by Professor H. Craig Davis in the School of Community and Regional Planning at U.B.C. but at this writing the table is s t i l l subject to revision. Thus, i t was not possible to use projection techniques which relied on an input-output table. 118 Thus, while realizing the weaknesses of the shift-share technique, i t was considered that this method attempted to explain more about the regional growth process-than straight trend extrapolation would have. Employment Data In an empirical model i t is important to know the source of the data used. What a model really represents (as opposed to what i t purports to represent) depends on i t s data base. The strength or weakness of that base determines the strength of the model. The employ-ment submodel relies on published regional employment data. Stat ist ics Canada, in Review of Employment and Average Weekly  Wages and Salaries (72-201) publishes employment indexes on an annual basis for Canada, the Provinces and Selected Metropolitan Areas. The sectors published for Vancouver are l i s ted in column 1 of Tables 12 and 13. These indexes were available from 1957 to 1970 and are shown in Tables 12 and 13. The base year for the index is 1961. Large firm employment data for that year for Vancouver were obtained from Statist ics Canada and are presented in Table 14. The indexes are based on the monthly survey of employment in large firms (more than 20employees) and so are not in themselves representative of total employment. Publication 72-201 includes a table showing large firm employment as a percentage of total employment by industry division for Canada and the provinces. This is reproduced TABLE 12 NATIONAL EMPLOYMENT INDEXES SIC 100-399 100-147 100-139 250-259 251 252 270-274 300-309 400-421 404 421 500-579 500-519 504-505 543-548 600-629 630-699 631 642 702-704 731-737 731 850-899 861-869 871-879 875 031-899 INDUSTRY Manufacturing Food & Beverages Foods Wood Products Saw, Shingle & Planing Mills Veneer & Plywood Mills Paper & Allied Industries Metal Fabricating Construction General Contractions Special Trade Contractors Transpor. .CoffifnLin. & Other Util Transportation Watertransport & Services Communication Wholesale Trade Retail Trade Food Stores Department Stores Financial Instituations Insurance & Real Estate Insurance Carriers Service Business Services Personal Services Hotels,Restaur. & Taverns Industrial Composite NATIONAL E f 1957 1 1 C 5 . 5 2 9 9 . 1 3 9 c. 9 4 1C 2 . E F LCY KENT INDEXES IS53 19 59 I960 1 C 0 . 1 1 0 2 . C I O C . 6 9 9 . 2 1 0 0 , 6 I C O . 9 9 9 . 0 I C O . 2 c 9 . 9 9 9 .2 9 9 . C I C Q . 2 196 1 1 C C . 0 ICO .0 1 C 0 .0 1CG.C 1962 103. 3 1 0 1 . 5 101 .9 1 C 4. 2 1963 106 . 10 1. 10 1. 1C7. 1964 1 1 1 1 . 1 2 10 3 .3 6 10 3 . 5 4 1 1 1 . 2 5 9 4 . 9 6 1 C 1 . 2 7 1 0 0 . 0 9 1 . 7 9 0 . 7 9 6 . 9 9 9 . 7 1 0 1 . 0 97, 10 0. G ICO .0 1 C 0 .0 1 C C . C 102. 5 110 .0 102. 1 8 1 1 0 . 6 9 1 2 C . C 10 144 .8 "102.9 107 ."5 303.4 1C0.Q 1 C 6 . 6 1 C C . ^ l l ? . l 105 .9 1CO.O 101 .1 3 17.4 122 .7 1C 9 • 4 l C C . C . . _ i 9 j _ i 1C = . 1 2 1 . 10 3. i d . 100 . c c . 2 10 9 .2 9 12 9 . 6 ? 1 0 6 . 8 196 5 1 1 7 . 2 1C6. 6 1 C 7 . 1 113 .4 1 1 1 . 6 1 3 1 . 5 111 .1 1966 12 3 .5 1 C 9 . 9 110.1 113.1 1967 1 2 3 . 2 1 1 C * 11 C . C 1 0 8 . 3 1968 1 2 2 . 1 1 1 0 . 2 10 9 .8 10.3 .4 1969 1 2 5 . 2 1 C 9 . 1 I C S . 5 1 1 3 . 0 197C 122 .8 1 0 9 . 1 I CI. 1 1C £ . 1 1C9 .9 13 5 . 3 117 .5 9 1 1 4 . 5 0 1 0 4 . 1 6 I O C . 5 125 .7 1 1 8 . 4 1 3 4 . 7 136.2 123 .9 123. 5 1 0 3 . 9 12 6 .6 J 1 3 i f L 13 3. 6 1 2 2 . 5 11 5. 2 10 5 .4 122 .7 117_. 6 i3~0. 1 119 .4 111 .2 1 1 1 . 7 12 3 . 0 12_1_.7__ 135. 7 1 1 9 . 1 1 1 0 . 7 106 . £ 111 . C 121 .1_ "13 3 . 9 113 . C 1 0 3 . 6 11 105 .9 12 106 .4 JJLl°Iil. " 1 4 1 C 1. 2 15 1 C 4 . 9 16 I C Q . 4 9 4 , 9 1 0 1 . 3 102 .6 1 C O . 0 1 C 4 . 5 1 C 4 . 7 I O C . 3 1 C C . C 104 .1 105 ._3_JUH i 3 1C0_,0. 105 .3 99. 7 99 . 3 10 6 IOC 9 e 1 C 4 . 4 TcT .6 102 .2 1 C O . G 9 9 . 7 IOC 10=.5 1 C 4 . 3 ^7 .8 l c c ' c 1 C 1 « 2 1 0 3 99 .0 100 .7 10 2.6 1CO..C. 101.. 1 10 L . 0 1 1 0 . 6 7 10 1.8 ,9 10C._0 '. 2 3 0 2 .7 ,4 1 0 5 . 5 .4 1 0 c . 4 127. C 10 4 .3 _10 2^4 1 C 5 . 2 1 0 8 • 9 11 C . o 34C.2 107 .5 _103. 1 106.6 116 .5 117.5 141 .5 i 1 1 . 0 107 . 8 ' 10 2 .9 1 1 8 . 8 121. 1 17 9 3 .4 18 3 4 . 1 _1_9 _9.2._C 2.6"' 8 5 . 9 2 1 9 1 . 1 22 92 . 1 9 3 . 8 87.7-9 3 . 2 96. 9 9 8 . 5 9 2 .1 96 .5 g6 . 0 9 6.1_ 9 2 . 9 95 . 1 9 6 . 2 -3-1. 55 9 7 . 4 9.3.4 9 5. 6 9 8 . G 9 3 . 9 1 C C . C 1 C C . C ICC .0 "1 C C . C 1 C 0 . C 1 CO .0 101 .7 1C1. 5 ljG_0 ._S I C 3 . 4 1C2. 3 10 2 .0 104 104 _10 4 Tea ICS 10 5 . 4 1 0 9 . 6 . 9 1 1 2 . 3 .8 11 0 . 2_ .4 11 " . 6 . 8 108 . £ . 0 1 0 7 . 4 1 1.6. 2 117 . 5 I 15 .5 12 0 . 0 II 1. 5 109 .6 23 24 9 1.8 84 .4 9 1. C 9 2 .6 9 5.2 9 6 . 6 8 3 . 3 9 4 . 0 9 6 . 5 9 7 . 0 9 B . 9 99 i - I 1 C 0 . C ICO .0 1 CO .0 101. 7 10 2. 1 100 .9 26 9 5 . 7 27 ICC .0 9 5 . 2 9 7 . 7 9 9 . 2 100 .4 1 0 2 , 2 100.7 1 C C . C ICO .0 101. 102. 106 1C9 104 10 5 104 . 1 1 1 4 . 7 . C 12 C . 6 . 9 1 1 2 . 1 12^.9 3.3 7. 3 1 2 0 . 0 124 .6 125 .9 J2j ; .8_ " 124.4 114. 9 13 2 . C 139.1 156 .7 12. 8 . 4 13 3 . 0 12 8. 6 14 4 . 2 1 0 9 . 5 1 0 5 . 6 9 9 . 8 1 1 6 . 3 J 2 2.JL 13 3 . 2 1 4 0 . 3 131 . 6 151 .1 1 1 1 . 9 " l C l . r 2 1 2 1 . 3 1.29. 0 14 7 .6 1 1 2 . 6 1 C 6 . 9 I C C . 7 1 2 5 . 7 13 2 .8 128 .7 122. 3 119 .2 1 3 4 . 3 1 2 7 . 4 122 .4 1 4 0 . 7 1 4 8 . 4 1 3 6 . 2 3 4 3 .5 1 3 2 . 4 1 2 4 . 7 1' 2 . £ 151 .6 T ' - S . ? 1 3 7 . 5 12 6 . 6 . 9 1 1 4 . 8 .4 10 8 .2 1 2 4 . 6 11* .3 _130._4 137.1 ' 120.7 1 5 3 . 4 167 .4 14 1.4 15 1^0 12 2. 6 157 .8 173 .1 14 5 . 7_ 15 7 .4 122 . 7 1 7 1 . 8 1 8 9 . 6 157 . 2 1 7 8 . 5 1 9 4 . 8 1 6 2 . 3 1 7 4 . 0 126. 9 1 8 2 . 7 127 .1 Source: Statistics Canada, Review of Employment and Average Weekly Wages and Salaries (72-201), (Ottawa), Table 4. TABLE 13 VANCOUVER EMPLOYMENT INDEXES SIC 100- 399 100- 147 'i 00- 139 250- 259 251 252 270- 274 300-•309 400-421 404 421 500- 579 500- 519 504- 505 543-•548 600- 629 630- 699 631 642 702-•704 731-•737 731 850-•899 851-•869 871-•879 875 031-•899 Source: INDUSTRY c p n P N f l i FMpi rvwENT INO^XES „ „ , ' V 1 ^ 8 1 Q M 1__61 1262 I 2 i 3 126£ + 1J_6J_ 12th 1567. l_i6S 1 1 6 9 197C. M . .. . , H T c TFKe ^oTTo i o 4 . c tcc .c K 2 . 8 1C6 .4 io<;.« 1 1 7 . 5 123.4 121.6 119.7 126.5 121 »-^ ! ! ? l J f ! C * U n . n . ? . . . 2 lll.t i o T . 3 104.2 100.2 100.0 5 9 . 3 ? 6 . 9 9 6 . 7 I C C . 5 105 .6 102.6 102 .7 1 C 1 . 3 c f , Food & Beverages 'i. i t c . s J . U H . 3 i u t . i n / i . c x v u . v , Foods 2 1 C 7 . 1 I C S . 7 1 C 3 . 9 1 0 3 . 2 1 C C . C 99 .6 9 6 . 5 9.5.5 1 0 1 . 2 104 .9 1 0 1 . 0 1 0 0 . 7 9 3 . 5 Wood Products 4 1 0 6 . 4 1 0 5 . 6 9 7 . 4 104 .3 1CC.C 1 0 1 . 7 1 C 6 . 3 1 0 9 . 4 1 1 0 . 5 1Q9.7 1 0 6 . 1 1 0 3 . 3 1 1 0 . 0 1 0 3 . 6 Saw,Shingle & Planina M i l l s 5 1 0 2 . 9 1 0 3 . 3 9 0 . 7 1 0 3 . 3 1 C 0 . 0 9 9 . 0 1 0 0 . 6 1 0 0 . 1 9 0 . 6 9 8 . 5 9 1 . f i 9 4 . 6 9 5 . 3 6 5 . C Veneer & Plywood M i l l s 6 9 7 . 2 9 7 . 2 9 6 . 5 9 9 . 1 1CC.C 1 0 7 . 4 118 .1 1 2 6 . 8 1 2 7 . 6 128 .3 1 2 4 . 7 1 2 6 . 4 131.0 1 1 9 . 1 Paper 5 A l l i e d Indus t r ie s 7 8 6 . 2 ______ 2 =3.7 3 9 . 4 U C . C 103 .7 112 .6 1 1 4 . e 1 17. 7 122. 8 1 2 6 . 3 12 5 .4 1 3 3 . 3 1 3 6 . 0 Metal F a b r i c a t i n g 6 146.4" 12 8^2 1 2 9 . 3 12 c". 5 IC ' J .O U4 . 'o " 1 2 4 . 3 137".4 16 9 . 2 166.9" 17 5".'"5 163."2 1 8 6 . 2 1 ST.T" Const ruct ion 9 1 5 2 . 6 1 1 4 . 2 1 1 1 . 7 113 .2 1C0 .C 101 .9 105 .1 1 2 1 . 0 1 3 C . 0 133 .3 1 5 2 . 7 1 4 3 . 2 173.0 1 4 0 . C General Contractors 10 1 5 6 . 5 1 2 6 . 6 143 .5 1 1 1 . 3 1 C 0 . 0 9 ° . 2 l o g . 2 1 2 7 . 7 1 3 7 . 7 140 .9 1 6 4 . 8 1 6 5 . 6 1 9 6 . 1 1 5 2 . 6 Specia l Trade Contractors 11 1 5 9 . C 1 1 4 . 7 1 2 5 . 6 1 1 6 . 5 1C0.0 1 0 2 . 0 1 0 3 . 4 11 9 . 7 1 3 3 . 3 1 3 6 . 3 1 5 6 . 3 1 5 C . 6 1 6 4 . 7 15 9 . 9 Transpor . , Commun. & Other U t i l . 1 2 . 1 1 0 . 5 1 C 6 . 9 1 0 5 . 0 I O C . 6 1CC.C I C C . 3 103 .4 1 0 6 . 4 1 1 2 . 0 1 1 3 . 9 1 1 5 . 8 1 1 8 . 6 1 2 3 . 5 1 3 2 . 5 Transportat ion L I Watertransport & Services Communication Wholesale Trade R e t a i l Trade ' 17 - J i . c > ^ ->•• • - -Food Stores I 8 t a * 9 1 6 * 2 3 3 ' 8 9 6 ' 1 1 - G 0 « ' - 1 0 3 . 1 1 C 7 . 2 1 1 4 . C 132 . 5 144. 5 15 1. 5 1 5 4 . 4 1 3 7 . 5 1 5 9 . 5 Department Stores LI 51i .2__9 5._9 9 3 . 4 98._1__1_C0 .0 J 0 _ . 6 _ 1 0 4 . 2 _ 1 0 6 . 4 i ] 3 . 8_11 8_2_1 26_. 3_130_. 8 139._4_ 1 2 9 . 2 F i n a n c i a l I n s t i t u t i o n s " ~2C 9 C . F ' 9 0 " . 2 9 4 . T 97.5 IccTc' 10270 105. 6 ~11 U ' 6 " T l f . l 124 .1 12 8 ."2 1 4 0 . V 1 6 1 . 4 17 472 Insurance & Real Estate 21 8 6 . 4 8 3 . 0 9 3 . 2 9 6 . 4 1C0 .0 100 .2 1 0 4 . 0 1 0 7 . 2 1 C 6 . 7 1 C 8 . 3 1 1 9 . 7 1 2 6 . 5 1 2 3 . 2 1 4 C . 4 Insurance C a r r i e r s 2 2 6 6 . 7 9 C . 4 95 . 4 9 8 . C 1CO.0 1 0 0 . 4 1 0 5 . 2 106 .7 1 0 7 . 6 111 .4 12 1.0 1 1 9 . 3 1 2 2 . 7 1 2 4 . 6 Service 23 1 0 0 . 1 1 0 0 . 3 9,3. 4 9 6 . 9 K C . C 1C1. 5 102. 7 11 6 . 7 1 3 2 . 3 146 .2 1 5 4 . 7 1 5 8 . 9 181 . 6 1 9 3 . 8 Business Services 2 4 £ 5 ' < ; 7 5 - 7 9 2 « 7 5 7 ' 6 1CO.0 1 0 4 . 0 106 .4 13 2 . C 1 6 2 . 0 184 .9 1 9 1 . 7 1 9 1 . 7 2 1 8 . 0 2 3 2 . 7 Personal Services 25 1 1 5 . 5 1 1 2 . 1 I C S . 5 105 . C l_CjC.0_ ^ 9 . 5 I O C . 6 1 0 9 . 7 1 1 8 . 9 130 .8 1 3 9 . 9 148.1 _1_72._9_ 163.1 H o t e l s , Restaur & Taverns " 2 6 ~ U 0 ' . 9 16V.2 1 0 6 . 5 -104. iT'l'ccTc 9 9 . 4 1C1™. 1 "112 .2 12 C "14 0". 5" 1 5l"."° 16T7s"" 196.2 ' '20 9'Va I n d u s t r i a l Composite 2 7 1 C 9 . 1 1 0 2 . 8 1C-+.3 1 0 1 . 8 1 C C . 0 1 0 1 . 0 104 .3 10 9 . 6 1 1 7 . 9 124 .2 1 2 7 . 7 1 2 9 . 6 1 4 0 . 0 141.1 Statistics Canada, Review of Employment and Average Weekly Wages and Salaries ( 7 2 - 2 0 1 ) , (Ottawa), Table 4. ro o TABLE 14 Employment Base (1961) Vancouver SIC EMPLOYMENT 100-399 Dur Non Dur 100-147 100-139 25 251 252 27 30 400-421 404,421 404 421 500-579 500-519 504-505 54 600-699 600-629 630-699 631 642 7 70 73 731 850-899 86 87 875 031-899* 48815 26638 22177 10791 9499 13643 7868 4161 3399 3220 7463 5403 2807 2596 26198 12381 4364 8303 31237 11620 19617 3055 10600 9654 5536 4118 2852 16264 3624 7450 5725 140462 Excluded are SIC 041-047, 801-809, 821-828, 831. 122 in Table 15,. As can be seen, this information was not provided for every year and, further, the industry divisions are broader than those of Tables 12 and 13. Also, these data were available in published form only for the provinces and not the metropolitan areas. In order to use these data, which were v i r tua l ly the only regional sectoral data available, i t was necessary to make some rather heroic assumptions. F i r s t , the B.C. survey coverage was assumed to apply equally well to Vancouver. Second, for the years 1961-63 where only global coverages were available, the 1964 coverages were used. These were also used for 1957-60 where there was no indication of the coverage. For 1965, where no coverage was available 1964 and 1966 coverages were averaged. This was a matter of convenience for which there is no real just i f icat ion other than the lack of time needed to do otherwise. It w i l l be noted that the 1961-63 industrial composite coverage is much lower than the 1964 estimate. Thus, the assumption of the 1964 coverages produces an underestimate of employment in 1961-63 and quite l ike ly also underestimates the 1957-60 period. The 1964 rates were used because they provide coverages on a sectoral basis. Since these coverages vary significantly between sectors and there is otherwise no indication of the sectoral breakdown for 1961-63, i t was thought that the lesser evi l was involved in using the 1964 rates. With more time, efforts could have been devoted to calculating the sectoral breakdown for 1961-63. Using 1964 as a model for sectoral distr ibution, i t might have been possible to calculate different rates so that the composite coverage was 61 percent in B.C. It is not clear, TABLE 15 LARGER FIRM EMPLOYMENT AS A PERCENTAGE OF TOTAL ESTIMATED EMPLOYMENT 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C. Can. B.C Forestry 81.2 74.3 83.8 76.1 83.8 76.1 81.0 73.4 78.0 70.8 77.4 72B Mining i n c l . Mi l l ing 94.5 93.3 94.8 88.1 94.8 88.1 93.4 93.3 94.1 88.3 94.2 89 S Manufacturing 91.7 89.1 93.0 89.8 93.0 89.8 91.2 88.1 90.8 87.5 90.4 87D Construction 62.7 56.7 65.4 64.6 65.4 64.6 63.0 56.6 60.6 53.3 59.8 525 Transportatioi Communicatioi Other U t i l -i t i e s i 89.5 90.3 89.6 88.3 89.6 88.3 89.7 88.5 89.7 88.5 89.0 88.1 Trade 62.6 61.9 63.0 63.2 63.0 63.2 62.1 59.5 61.0 59.8 61.4 589 Finance Insur-ance & Real Estate 85.0 76.7 84.2 73.6 84.2 73.6 81.7 69.9 80.6 72.2 81 .4 724 Service 50.0 50.4 49.6 47.6 49.6 47.6 18.3 20.3 19.2 21.6 19.2 227 Industrial Composite 62.0 61.0 62.0 61.0 62.0 61.0 77.9 74.1 76.4 74.4 78.4 74.4 58.4 55.4 57.7 55.2 56.7 552 Co 124 since no investigation has been carried out, whether the data exist to do this . Alternatively, the assumption that the B.C. coverage applied to Vancouver could have been abandoned had a sample coverage for Vancouver for a control year been calculated. It would then have been possible to calculate the rate of change in the B.C. coverage and to assume that this rate applied to the change in the Vancouver coverage as wel l . This extra work should have improved the quality of the data. However, i t s t i l l involves some assumptions linking the region to the province. Time was the major constraining factor here; only so much was available for data manipulation. Since, the main objective of the study was to develop an integrated model this extra manipulation was not done. Employment estimates were calculated from the indexes by use of the following equation: (industry index) x (base year employment) T (B.C. coverage for) . . . (6) ( in that industry ) ( that industry ) " It can be shown that the use of the B.C. coverages did produce some errors in the estimates of total employment. From Tables 12 and 13 i t can be seen that some of the sectoral classifications include others. (This can be seen from the SIC codes). It is possible, with employment data, to subtract employment in the included category and obtain employ-ment in the rest of that SIC class. For instance, when this is done with Food and Beverages (100-147) subtracting Foods (100-139) leaves Beverages (141-147), soft drinks, d i s t i l l e r i e s and breweries). This can be done throughout Tables 12 and 13 to produce Tables 16 and 17, sectors 1-27. Originally 28 sectors were calculated. 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Lf- sr cr- IP o r-J O l .c 0 - <- p"1 in CNJ CO (NJ 01 CC L0 sj in o ; a- OJ CO LP CO »—* rH r-> n -1 CO C N ' r-l f-H CvJ c .—[ CO C 1 Q'J U ' , Cr r~ CNJ CO O l CO •v" LP> r-r-^ ir^  (N! r- U" r-t Sl' -t St' m in L P . P - <"\! CO cr o cr 0- O r r-.—, LO —1 <r o, O c\ vU C J m o <r U i r- o r- o in v+ vO v0 <r r- l C N ; ro r f i (NJ 0>J cr- LP. - T sr CM ex.- CNJ Vj' c;' r " i __• .—i ' ' CO r-* O i CNJ r-l r—• c n CNI (N.1 0 s CO c <j c O l r~ 01 OJ C I P- LP, a a- o IT, (NJ o tf\ •X' o CO in r- o cr- 'X' PJ LP m CNJ CO c- \j\ p- o o CNJ r-- CX! o CM' P-r- un C . r*j » o r: .—i •V co t- cr- cr ro O *-< C N ' re-. CO cr vi.) sr Si" CN1 CC CNJ r- r 0 r~i r-H .—1 O l Co -^1 —t ,-1 < Lr'> CC s: Oj IT, c . Cv, h -f— IT, LT'I r-* m if, 0'- L P cr r— CC 10 OJ cr cu ( X ! CNj IT. sj- CC" .—[ C" o r • c- o- 0'' sO c -c cr; o < m 01 >—' 6 (NJ <; r— IC\ OJ OJ cr', CC r". o r-l Ov U~ 01 c P- sr in CN. a 0 - a . ~* *~' ' 1 "~ . . . P"; 0 '• CN1 ^J- O.. C'v _; r- O : I— _. co vi.. ^. r-|r~ cr. ST c u- r-i r- O', m cc c p~ r-,. r- C'~ c- f~ CNJ <- PvJ (.•• r- CNJ SJ- vC' <J L P -LO O i COt sC r— s. t\! r— r- r~ c- CO f\J CN^: cc LT. <r CNJ cr P-P l sr uo *~ t - r- P^ *~* f i IT- C?. c L P c m ip, C \ cc a nj CT' IT- . cc CvJ a"' r-l a: r— CN c: sr| o CO p-CO in CM oo C\J ir, r-j « o cc r- <r P I «—i -r, f'•' 1 j cc uo m L P : p.- S j r-l CI' Sl' --( rv LP. <r CO O m CN' CX: CO r-l P-—* " ('•': CO Osi - J « LO •c O'- o p*i ••1' in O- CO a- o r\ P ! PvJ r-l m .» CO CN' CJ ' sr r- co vCl >o CN) INj •o a- , jr I P . u!o-, rs O iol ^ J C co cc sr Ice co o 01 if\ IIP, ip. ^ 0 - jm ir-ro CNI CJ. jCO r-•il <j ! C o-oo r*- co ir- in .n a- o r- ,in o r-o O J o. ico ^ —I co in o !cv co o o cr C N jej oj m. s.- m. r-i icj- m ! f--CC' P , P I OJ r - l P - LP CO cr Cv o ro ','1 0" CC cr rv r- p - cc- CN. r-i r-t <• (NJ P I P J Pvl (0 LP ro UN P - ur. G'- O cr os r- s i |a. ~c cc co iin O O r» CNJ sr ^< co oi co o r- <-0- . IP- CO 0- SI m. r~ sr o r - cc ip, <--0 r-l sr IP. C"' r-i r- sr -f C' oo oi CNJ sr S5 o —i oj m -* sr co r-" i in cc o i os sr sr r-0 ' CNJ » J . rl cc — co m co, m, cc o- o-o o cj^  o- o- o ip, -t o C O C O O CNJ CNJ C O m c\ C o O .-j o-rs cr- CN, co ro CNJ r- os -j- r~-CO CNJ sO CNJ -r -c o -j r— CNJ m r. c" 01 C ir- s; jcu a; , s j r- to 125 TABLE 17 ESTIMATED V^NCOUVF'? N' PLOY'"if NT 1 9 6 7 7 26 9 3 . 1759. 11413. 266 6. 19' 2 01 0 9 . 1 6 8 ? . ' 10949 . ? 5 0r> . 1 939 2 ]. 5 6 1 . 19 43. 11077 . 2 3 98 . 1960 20 62 3 . 1 6 1 8. 1 1.002. 2 2 2 0 . 1961 19935 . 1450 . 1C661 . 1 8 1 1 . 10 9087 . 453 9 . 3.7 r. 3 . ""5 3 6 T 7 5084 . 7 74 8. 91 22. 4 5 3 5 . 3 2 1 ? . 1 1 1 2 I 3 7 23 0 , 6411 . 89 6 2 , 4 6 3 7. 3 5 J 2 . 62 67 . 14 J 5 1 6 5 3 1 I . 113 74. •21533. 63? 5 . 8 7_4 0 . 50?6 ." 1092 4. ? 0 5 3 7 . P0C9. 4 5 0 7 . 31 93. . 42 32 . 73 52. 575 1. 6.125. 9122 . 4 6 2 8 . 3 4 1 0 . 8 831 . 4670 . 3815. 1962 2 0 6 4 6 . 1408 . 10618. 18 14 . 8742 . 5016 . 3 956 . 1 563 21493 . 14 4 8 . 1 C2 8 8. 1878. 1964 2 2 2 5 0 . 1 409 . 1.0131. 1990. 4755 . 4 0 5 6 . 551 C . 3 614". 36 3 3 . 4 951. 49 15 . 1 0 1 8 8 . 9 f) ^ C 'J 5334 . 5 9 3 6 . 900 0. 5 14 2 . 91 58 . 1 9 ? ? 3 . 4 578 . 6 1 0 6 . •8 878. 4 1 2 0 . 38 81 . 4362 . 4 6 7 0 . 5801 . 8 740. 4 833 . 91.95 . 1 8772-' 5 C 1 9 . 9039 . 18 416. 88 84 . 55 15. 42 9 5 . 44 52. 389 1. 52 08 . 4734. 62 34 . 861 5. 60 55"." 9094 . 185 4 7. 8839 . 5 9 2 2 . 4379 . 4 966 ."' 4 124. 632.2 54 80 . 64 54 . ?,bl5j_ 6461 . 9278 . 192 9 8 . 17 IS 19 1. 06 06 . 3400 . 1698 7. 100 82, 3 7 6 1. 1 64 2? 1 0 0 9 ? . 4432-1 68 50 2 0 2 1 2 2 6 5 18. 13 4 1. 3 2 9 3 . 6 5 1 0 . 1 36 8. 3 3 6 1. . 67752". 14 57 . 3 5 47 . 96 42 . 4 743 . 16 7 9 9 . 70 37 . 157.?. 3 6 4 4 . 96 3 2 . 4 935 . 17 124. 9 6 48 . 5 088 . 17398. 1 0.2 6 8 . 5291 . 173 4 4. 721.8 . 1651. 3 718, 7 3 62 . 1652 . 3733. 23 905 3. 6 17 7 . 4 4 7 6 . 1 0514. 54 4 3 4 15 5 9050 . 6 6 6 6 . _ 3 ° 4 1 _ . 87 31 . 70 18. 3651 . 26 I 2 5 ° 7 . 77' 2 0 6 8 0 7 . ? P. 9 . 124 16. 19 4 8 6 5, 3.2097 l n 7 7 0 8 . 0 . 13 8 7 0 . 1 9 2 9 6 9 . 0 . 10298 . 7 1.90. 34?3_. 11 359." 185557 . 1 6 7 1 7 . 10 5 6 8 . 74 78. 34 17. 76 22. 16 72 . 2912. 1 06 20 . . 10919 . 5626 . 1822 0 . ~8012^ 1793 . 3968, 1965 24592 . 1378. 10753 . 2246. 1966 26374 . 1593. 1 1 096. 2091. 1 967 26579 . 1.6 45 . 106 84 . 72 5 8. 86 7 8 . 5939 . 4 4 7 5 . 60 98 . 3921. 63 7 8 . 5710 . 67 5 7 . 92Bd. . 6 9 2 0'7 93 9 3 . 2 0 1 5 9 . 1 1769. 6 5 3 5. _1 92_70__. 86 71. 1377. . 4 081. 8630 . 5945. ___464 8_._ 6707. . 3 800. 6122 . 5477 . 7355 . 9728 .. 744 8"."" 9262 . 2 1 6 5" . 1 2580. 6 985 . 9334. 1771 . 4317 . 80 42 . 5778 . _47S1 62 9 3 ." 41.99. 7161 1963 2 6171, 1722 10858 2353 . 1 ° 6 9 2 8 3 9 3 . 1 8 00. 1069 3 . 2 352 . 1970 2 7 3 1 7 . 1 793 . 10536. 2 36 6281 . 7707 . J 0 2 5_2_. " "77To." 8689. 2 2 0 ? 7 . 1 3149 . 73 23 . _2 11_33_._ 5 64 3." 7 0 0 9 . 468 9 . 7651 -33 86. 117 9 1.. 191453 . 17047 . 1 1.4 84 . 197708. 17185. 11952 . 9491 . /vjlL-1274 5 ." 207755 . 1 7 7 ! 5 . 138 5 4 . 11981 . 3473 . 1460 5. 27 318 7. 1806 1, 1 5405 . 1 4077 . 3 573._ 16 898". 23 4481 . 18654. 16367. 14 595 . 3 6 3 9 . 18? 5 77 74 1089 . 19807 . 8448 . 5970 . ___4 33 8._ 5965 . 4421 . 3213 . 6907 . 7761 . _l_06 7O._ " 7727". 3950. 2.4171 . 144 0 7 . 7 8 7 5 . 2 3147. 1 1 L70 . 2535 . 4 863 . 38,733. 34223 . _ 877 1_. " 4 5'.31 . ' 323590 . 21609 . 8569 . 6 2 3 0 . 5178 . 6 8 5 7 . 4 9 00 . 1 0 3 2 7 . 3996 . 7 6 6 9 . J . 2 0 1 0 ._ ( 5 9 3 . 91 63 . 2 6 1 5 5 . 76 87 . 5696 . 53j 3 . • 6 35'5~ ? 7 e ? . 8 212. TWoT. 7851 . 124 67, 73 96" 1.3137. 2 7087, 1 6 4 2 3 . 7074 . 2 47J 0_^ "12375 . 7 7 5 0 . 4 847 . 17101. 82 73. 2 5 0 5 ! 4 0133 . 3 6 5 7 6 . 7 9 7 7 . 1 3""?, 2 8 . 30 77. 4 9 0S . 4 1611. 37150 . 7 13 0 520 0"2. 5?~512. 3 5 6 2 4 4 . 359043 , 0 . 21.631, 127 KEY TO TABLES 16 & 17 The industrial sectors represented in Tables 16 and 17 are: 1. Other Manufacturing — Tobacco, Rubber, Leather, Textiles, Knitting M i l l s , Clothing, Furniture and Fixtures, Printing and Publishing, Primary Metal Industries, Machinery except e l ec t r i ca l , Transportation Equipment, Electrical Products, Non-Metallic Mineral Products, Petroleum and Coal Products, Chemicals and Chemical Products, Misc. 2. Foods. 3. Beverages. 4. Other Wood Products. 5. Saw Shingle and Planing M i l l s . 6. Veneer and Plywood M i l l s . 7. Paper and Al l i ed Industries. 8. Metal Fabricating. 9. Construction - Engineering. 10. Building - General Contractors. 11. Building - Special Trade Contractors. 12. Storage, Electrical Power, Gas and Water. 13. Transportation except Water Transport and Services. 14. Water Transport and Services. 15. Communications. 16. Wholesale Trade. 17. Variety Stores, Automotive Product Stores, Apparel and Shoe Stores, Household Furniture and Appliance Stores: Liquor, Wine and Beer Stores. Key to Tables 16 & 17 Continued 18. Food Stores. 19. Department Stores. 20. Financial Institutions. 21. Insurance and Real Estate. 22. Insurance Carriers. 23. Other Services -- Recreation Services and Misc. 24. Business Services. 25. Personal Services excl . Hotels, Restaurants and Taverns. 26. Hotels, Restaurants and Taverns. 27. Industrial Composite. 28. Government -- Federal and Local. 1 2 9 represented a l l inclusive industry sectors subtracted from the industrial composite (Sector 28). Sector 27 then estimated employment in forestry and mining. For Vancouver, this sector was negative throughout the entire time period. For Canada, i t was positive and of a reasonable size. Since the large firm employment figures for Vancouver yielded a positive employment figure for this sector i t appears that the use of the B.C. coverage rates has caused some error in the data. Since without much more work on the data series this error can not be corrected this sector has been abandoned in the projections. A 28th employment sector has been added to the data. This is government employment. Statist ics Canada publishes employment in metropolitan areas in local and federal government. Unfortunately, figures are not available for provincial government employment in specific metropolitan areas. However, the sector was large enough with just local and federal government employment to warrant inclusion. The zeros in Tables 16 and 17 indicate the years in which data were not available. The Differential Component At this stage, employment at the national and regional level for 28 sectors had been calculated for the years 1957-1970. It was next necessary to calculate the historical differential component for the shift equation. The yearly rates of change in employment from 1957-1970 were calculated for each industrial sector for both the nation and the region. The national growth rate was then subtracted from the regional, i . e . 130 R: N* ( — ir-y ) was calculated. R^  The results of this operation are graphed in Figures 8 to 35 (Appendix A). The behaviour of this component can best be described as errat ic . This is the kind of behaviour H. James Brown has led us to expect.1 Because of this erratic behaviour no assumption can be made about the future behaviour of the component. It had been hoped that i t could be postulated that the national and regional sectoral growth rates would converge over time. The data seem to prove otherwise. Thus, for use in the shift-share model, the average of this component is used. This average value appears below each graph and again in Table 18. Projected National Growth Rates To operationalize the shift-share model, estimates of the national growth rates over the projection period were needed. In order to produce estimates of expected national sectoral growth a time trend was f i t ted to the national employment data. The time trend is an equation of the form: Employment = a + b x time . The results of this regression are shown in Table 19. H. James Brown, "Shift-Share Projections of Regional Economic Growth: An Empirical Test," Journal of Regional Science, Vol . 9, No. 1 (Apr i l , 1969), pp. 1-18. TABLE 18 AVERAGE DIFFERENTIAL COMPONENT 1958/57 - 1970/69 1. Other Manufacturing .0023 2. Foods -.0062 3. Beverages -.0143 4. Other Wood Products ..0198 5. Saw, Shingle & Planing Mil l s -.0231 6. Veneer & Plywood Mi l l s .0090 7. Paper & Al l i ed Industries .0221 8. Metal Fabricating .0086 9. Construction - Engineering .0080 10. General Contractors .0368 11. Special Trade Contractors -.0141 12.:. Storage & U t i l i t i e s .0068 13. Other Transportation .0261 14. Water Transport & Services .0368 15. Communication -.0134 16. Wholesale Trade -.0048 17. Other Retail Trade .0073 18. Food Stores .0252 19. Department Stores -.0013 20. Financial Institutions .0145 21. Insurance & Real Estate -.0032 22. Insurance Carriers .0030 23. Other Services -.0350 24. Business Services -.0161 25. Other Personal Services -.0119 26. Hotels, Restaurants & Taverns -.0271 27. Industrial Composite .0003 28. Government -.0035 TABLE 19 SECTORAL EMPLOYMENT REGRESSED AGAINST TIME D E P I NO C O N S T C O E F F F R A T I G F P R O S S T B ERR S T D ERR S T D ERR R S Q . VA R V AR A e (3 ) ( 3 ) ( A ) ( 3 ) ( Y ) CM AN T R E N D 0. 10 4 25 07 0 . 2 4 3 3 D 0 5 5 2 . 5 1 0 . 0 0 0 0 0 . 2 9 1 0 0 05 3 4 3 3 . 0 . 5 5 6 S 0 05 0 . 8 1 4 0 F+ 3 T R E N D 0. 2 9 3 7 E 05 2 8 3 . 7 1 5 . 6 2 0 . 0 0 2 0 6 0 8 . 5 7 1 . 7 8 1 1 6 4 . 0 . S 6 5 5 FO CO T R E N D 0 . 1 8 2 3 E OS 1 7 7 9 . 9 4 . 1 9 0 . 0 0 0 0 15 5 4 . 1 8 3 . 3 2 9 7 2 . 0 . 8 8 7 0 WD CO TR E N D 0 . 25 2 9 t OS - 1 S 3 . 7 5 . SS 5 0 . 0 3 4 7 6 0 6 . 1 71 . 5 0 1 1 5 9 . 0. 3 1 6 3 SA V + S T R E N D 0 . 4 S 1 7 E 05 6 9 5 . 0 4 5 . 5 8 0 . 0 0 0 0 8 7 2 . 6 1 0 2 . 9 • 1 6 6 9 . 0 . 7 9 1 6 VE NE ER T R E N D 0 . 15 3 5 E 05 3 2 8 . 3 1 3 . 8 5 0 . 0 0 2 9 7 4 3 . 7 8 3 . 3 3 1 4 3 2 . 0 . 5 3 5 8 FA ?E R T R E N D 0 . 1 1 S 7 E 05 2 4 0 5 . 9 1 . 1 4 0 . 0 0 0 0 21 3 5 . 2 5 1 . 9 4 0 8 4 . 0 . 8 8 3 6 KE TF A3 T R E N D 0. 12 7 9 E OS 3 4 7 7 . . 3 G . 2 3 0 . 0 0 0 1 48 9 6 . 5 7 7 . 6 9 3 6 4 . . 0 . 7 5 1 2 C O N sir? T R E N D 0-15 35 E 05 - 1 4 2 3 . 4 . 2 9 7 0 . 0 5 8 1 5 8 2 0 . 6 8 6 . 6 0 . 1 1 1 3 D 05 0 . 2 6 3 6 Gt NC ON T R E N D 0 . It 3 9 E 03 - 1 2 7 8 . 2 . 0 5 9 0 . 1 7 42 7 5 5 1 . 8 9 0 . 8 0 . 1 4 4 4 D 05 0 . 1 4 6 5 SP CO N T R E N D 0 . 1 1 3 0 E OS 5 4 9 1 . 5 4 . 9 2 0 . 0 0 0 0 6 2 8 1 . 7 4 0 . 9 0 . 1 2 0 1 0 05 0 . 8 2 0 7 C. U T TL T R E N D 0 . 8 3 S 8 E 05 1 0 2 2 . 2 5 . 2 2 0 . 0 0 0 3 1 7 2 4 . 2 0 3 . 4 3 2 3 3 . 0 . 6 7 7 6 TR A \ ' S T R E N D 0. 36 5 1 E OS 3 0 0 . 5 1 . 0 4 1 0 . 3 2 9 3 66 5 3 . 7 3 4 . 8 0 . 1 2 7 2 D 05 0 . 0 7 9 9 WA T E R T T R E N D 0 . 4 1 3 7 E 05 - 8 5 . 9 4 2 . 1 S 9 0 . 1 6 1 1 5 1 4 . 1 6 0 . 6 5 9 8 3 . 3 0 . 1 5 4 3 co y, y UN T R E N D 0.14 S O E OS 2 3-9 6 . 2 3 . 8 2 0 . 0 0 0 4 4 1 4 4 . 4 8 8 . 8 7 9 2 5 . 0 . 6 6 5 0 V . T R A D T R E N D 0.29 5 0 E OS 8 03 5 . 4 8 . 7 6 0 . 0 0 0 0 98 1 5 . 11 5 8 . 0 . 1 8 7 7 0 05 0 . 8 0 2 5 R . T R A D T R E N D 0 . 2 5 2 1 " OS 0 . 1 0 0 1 D 0 5 St . 4 3 o . o o o o 0 . 1 0 5 7 D 0 5 1 2 4 8 . 0 . 2 0 2 3 D 05 0 . 8 4 30 FO OD S i T R E N D 0 . 3 S 9 6 E 05 6 2 3 5 . 1 4 7 . S 0 . 0 0 0 0 4 3 51 . 51 3 . 2 8 3 2 1 . 0 . 9 2 4 8 DE P T S T T R E N D C 1 5 9 1 E OS 6 8 9 3 . 1 2 5 . 1 0 . 0 0 0 0 5 2 2 4 . 61 6 . 2 9 9 9 1 . 0 . 9 1 2 5 FT NA NC T R E N D 0 . 1 1 9 S E OS 6 7 3 9 . 1 3 4 . 6 0 . 0 0 0 0 4 9 6 1 . 5 3 5 . 3 9 4 8 9 . . 0 . 9 1 3 1 RE AL T R E N D 9 73 0 . 1 1 0 4 . 6 1 . 6 3 o . o o o o : 1 1 9 3 . 1 4 0 . 7 2 2 8 1 . 0 . 8 3 7 0 I N S U R T R E N D 0.72 7 3 E 05 2 2 9 3 . 9 8 . 9 7 0 . 0 0 0 0 19 5 3 . 2 3 1 . 0 3 7 4 6 - 0 . 8 9 1 9 C S r P T R E N D - 0 . I S SO F 05 0 . 3 S S 3 D 0 5 1 8 . 1 4 0 . 0 0 1 2 0 . 7 3 0 1 0 05 86 1 2 . 0 . 1 3 9 S D 06 0 . 6 0 1 8 B I 7 S E R T R E N D ' - 0 . 13 8 5 E 05 0 - 3 5 S 4 D 0 5 1 9 . 0 9 0 . 0 0 1 0 0 . 6 91 4 0 0 5 81 5 6 . 0 . 1 3 2 2 D 06 0 . 6 1 4 1 0 . P £ R S T R E N D . 0 . 3 7 5 9 E 05 3 1 3 3 . S . 7 1 5 0 . 0 2 2 7 . 0 . 1 0 2 5 0 O S 1 2 0 9 . 0 . 1 9 6 0 S 05 0 . 3 5 8 9 KG T E L T R E N D 9 0 S 8 . 0 . S S 6 6 D 05 1 6 . 3 9 0 . 0 0 1 7 0 . 1 I 8 6 0 0 6 0 . 1 3 5 9 0 05 0 . 2 2 6 9 D 06 0 . 5 7 7 4 TO T A l_ 1 T R E N D 0 . 3 7 S 1 E 07 0 . 2 3 4 3 D 0 6 2 7 . 3 2 0 . 0 0 0 2 0 . 3 3 0 9 D 0 6 0 . 4 4 9 3 D 0 5 0 . 7 2 8 4 D 06 0 . 6 9 4 8 GO VT T R E N D 0 . 3 7 S 1 E " 05 0 . 2 2 1 0 D 0 5 8 . 2 5 7 0 . 0 1 3 6 0 . 6 5 2 0 D 0 5 7 6 9 1 . 0 . 1 2 4 7 D 06 0 . 4 0 7 6 ro 133 TABLE 20 N A T I O N A L G R O V i T H R A T E S ' " ~~ A C T U A L A C T U A L R E G I E S R E G R E S R E G R E S R E G R E S R E G R E S P EGRE $ Oo 2 7 0 2 Oo 0 5 6 3 0 . 10 3 7 - 0 . 0 1 7 9 Oo 1 3 9 0 • 0 o 1 3 3 9 C 2 2 9 4 Oo 3 1 3 6 :Q o 1 ° . l . -Oo GO 7 1 0 . 5 0 8 4 0 . 1 4 6 3 0 . 2 44-7 C . C 7 1 2 0 . 0 8 5 6 0 . 0 5 1 4 0 . C 7 3 8 J_._3J?J9 0_ 0 „ 1 0-6 7 0 . 0 4 6 1 0 . 0 4 6 4 - 0 . 0 3 4 5 Oo 0 7 1 4 0 . 0 9 6 7 0 . 0 5 6 4 0 . 0 4 4 0 - 0 . 0 3 5 7 0 . C 6 6 1 G . C 6 6 2 0 . 0 8 7 9 0 . 0 4 2 2 0 . 0 4 2 4 • 0 . 0 3 7 1 0 . 0 6 2 5 C O 8 1 1 0 . C 6 9 2 - 0 . 0 0 9 1 ...P.. 2 9 2 5 0 . 3 1 9 6 0 . 4 5 1 1 0 . 6 0 1 7 C . 1 5 8 6 G . 3 4 3 0 0 . 1 3 ] 3 0 . 1 8 4 0 C . 3 4 4 1 0 , 0 3 3 3 0 . 0 9 3 4 0 . 1 1.9 7 - 0 , 0 4 8 6 : 0 o 0 4 4 5 0 . 1 9 5 5 0 . 0 5 4 3 0 . 4 3 8 6 0 o 6 1 8 8 . 1 . 2 4 7 7 O o 3 3 6 7 4 . 6 4 1 5 4 . 2 5 6 9 0 . 0 3 4 8 0 . 0 6 4 8 0 . 1 6 3 7 Co 1 6 7 5 ~ 0 . 2 2 4 7 0 . 2 5 1 0 0 . C a 5 4 0 . 1 C 6 9 - 0 . 0 5 1 1 - 0 o C 4 6 6 Oo 1 6 3 5 0 . 0 5J_5_ 0 . 0 1 0 3 • 0 . 0 1 0 9 0 . 0 7 5 5 C . T I o F 0 , 1 6 5 6 0 . 7 0 0 3 3 0 7 9 6 2 - C . . . 7 3 4 0 „ 0 0 0 0 Co 2 5 0 0 0 . 2 5 5 3 . . 0 . 3 2 7 4 C . 1 3 C 6 0 . 4 1 . 7 4 - 0 . 0 0 2 2 0 . 3 32 1 0 „ 2 3 0 7 0 , , 1 - 5 8 0 . 1 7 8 1 0 . 2 2 1 1 . . p . 3 6 2 0 O o 1 3 6 4 1 . C 9 8 9 1 . 0 8 4 3 0 . 2 9 4 2 0 , 9 6 8 9 0 . 2 3 7 9 ' 0 . 2 2 T l " 0 . 0 7 8 7 0 . 0 9 6 6 • 0 . 0 5 3 8 0 . 0 1 0 7 • 0 . 0 1 1 0 0 . 0 7 0 2 . '61 1 C 1 3 " 0 . 1 4 2 1 0 . 1 9 5 7 • 0 . 0 4 8 9 0 . 1 4 G 5 0 . 0 4 9 0 0 . 01 0 6 • 0 . 0 1 1 1 0 . 0 6 5 6 C . 1 5 1 1 0 . 1 9 1 0 0 . 2 6 5 8 0 . 0 9 6 9 0 . 1 2 4 4 O o 1 6 3 7 C . C 8 0 8 0 . C 4 0 5 Go C 4 C 7 - C . 0 3 8 5 0 . C 5 3 8 C . C 7 5 0 0 . 2 1 8 0 0 . 0 ^ 3 0 0 , 0 9 3 6 0 o 0 6 8 5 0 . 1 4 4 9 0o 1 9 7 3 0 . 1 7 9 0 0 . 0 9 6 1 0 . 0 8 5 6 - 0 . 0 7 3 6 0 . ! 2 6 6 0 . 1 6 4 8 0 . 0 7 3 0 0 . 0 8 8 1 - G o C 5 6 9 0 . 1 9 0 4 0 . 2 4 5 2 0 . 0 5 6 3 0 . 1 5 9 9 0 . 1 9 6 9 - 0 . 1 0 6 5 - 0 . 0 5 1 4 C . 1 2 3 2 0 , C 4 6 7 • 0 . 0 8 8 3 0 . 4 0 6 8 0 . 1 0 9 8 - 0 o 0 9 6 8 0 . 2 3 9 2 0 . C 9 3 9 0 . 0 1 0 5 - 0 . 0 1 1 2 C * 0 6 1 6 O o 0 8 3 3 G . 1 1 0 7 0 . 1 4 0 6 0 . 0 2 1 7 0 . 0 2 1 7 .9 • 1 r' 0 . 2 4 6 2 " 0 . 3 4 2 6 0 „ 5 1 1 5 0 . 0 2 1 3 - 0 . 0 2 2 1 _ _ 0 . 1 3 3 0 • 0 . 7 9 7 6 0 . 2 5 6 2 0 . 3 3 8 4 0 . 1 3 1 3 Oo 1 5 3 3 0 . 2 1 0 0 0 . 1 2 0 C 0 „ 5 2 3 6 0 . 5 2 0 2 0 . 2 / 7 2 0 , 4 9 2 1 _ C . 1 C.Z 2 T . 1 'i 5 1 0 . 1 C 7 2 0 . 3 4 3 6 0 . 3 4 2 2 0 . 1 1 6 1 0 . 1 3 2 9 0 . 17_35 c.'c^&s' Go 2 5 5 3 C . 2.5 5 0 0 . .369 3 0 . 4 6 2 6 0 . 7 3 0 4 ~ 0 " . ~ 2 B b 5 " 2 . 8 1 6 8 2 . 7 6 9 0 0 . 2 6 9 7 0 . 3 1 6 3 0 . 6 3 8 3 0 . 1 8 52 0 . 3 2 9 8 0 . 1 6 1 2 0 . 1 5 6 2 C 1 5 6 3 Oo 2 4 8 0 0 . V 3 8 8 0 . 1 3 51." 0 . 2 1 9 ! • 0 . 7 3 8 0 0 . 7 3 4 7 0 . 6 2 5 1 2 . 4 0 3 6 0 . 4 9 9 6 0 - 4 7 5 8" 0 . 3 8 4 6 0 . 7 0 6 2 0 . 3 3 3 1 " 0 . 3 2 2 4"' 13.4 The trend equations allow projection of national employment into the future. The stat is t ics associated with the estimated coeffic-ients indicate that the equations do not explain a l l of the variation in employment. However, i t was not practicable to expand the scope of the study to include an examination of national growth. The time trend equations were used to estimate sectoral employ-ment in 1960, 1961, 1966, 1971, 1976, 1980 and 1981. From these, the growth rates by sector from 1960 to 1970; from 1970 to 1980; from 1961 to 1966; from 1966 to 1971; from 1971 to 1976 and from 1976 to 1981 were calculated. Further, the actual growth rates between 1960 and 1970 and between 1961 and 1966 were calculated. These are shown in Table 20. The Submodel Projections The shift-share equation was used in conjunction with several of the calculated growth rates to project employment in the future. In this section the projections of the submodel for 1976 and 1981 are shown 2 in Table 21. The model was also used to project from 1960 to 1970 and from 1961 to 1966 and 1971. These projections were then compared to 3 actual employment in those years and estimates of the errors of pro-jection were calculated. This work is reported in Appendix B. The employment projections for 1976 use 1971 regional employment 2 Sector 29 is the sum of sectors 1-26 plus 28. The data manipu-lation using the B.C. coverage rates applied to Vancouver data means that this is not the same as the sum of sectors 27 and 28. 3 1971 actual regional employment was calculated using the average monthly large firm employment which is published in Statist ics Canada publication 72-002. To this the 1970 B.C. survey coverage was applied to estimate total employment. 135 TABLE 21 VANCOUVER EMPLOYMENT PROJECTIONS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 P R O J E C T E D ! 9 7 6 3 0 8 0 0 c 3 2 1 9 4 7 . 6 3 9 0 8 4 . 2 5 _ a 4 G 5 . 6 2 6 I J j ^ i L T 8 1 7 . 7 2 7 8 6 3 . 3 9 3 6 7 6 . 5 3_ 1 7 1 5 7 6 . 2 1 1 0 9 2 4 . 5 5 8 4 3 7 c 9 5 T 2 8 9 G c 32 8 4 6 5 a 1 0 1, 2 6 7 3 . 7 ^ _ " 3 T 4 ~ B 5 o 2 4 1 7 4 6 7 , 7 9 " " 2 6 7 6 1 . 4 3 1 6 0 5 8 o 4 1 3 B 6 6 o 59__ 6 C S 5 . G O 5 2 1 1 8 . 9 1 4 9 9 1 3 J L 3 8 _ 5 7 6 T o 9 3 7 1 4 R 3 c 1 9 4 , 2 6 5 0 3 * SO P R O J E C T E D l c 8 1 3 3 3 5 9 = 8 2 2 0 1 4 . 4 9 2 4 o i l 9 :•> 14 T 3 5 9 T 7 0 8 7 0 5 . 7 C 6 7 0 0 o 0 5 " 6 3 7 0 . 9 8 8 6 4 5 . 7 0 . 3 4 9 6 . 7 5 1 2 1 I t . fit 8 8 8 9 . 3 8 " 1 3 3 6 2 . 1 0 8 6 8 1 . 8 0 1 3 2 8 4 . 6 1 " 1 A T T 4 O 2. 5 1 9 5 2 8 . 9 8 1 1 3 1 . 1 . 2 9 _ - 2 9 " 8 4 0"o3 3 1 8 4 2 5 . 4 2 4 5 2 5 o 0 6 6 6 9 2 . 2 6 6 3 6 2 6 . 7 7 6 1 8 4 3 . 8 7 6 6 C G . 8 2 8 7 2 7 9 . 8 1 4 R 5 8 ° > 0 « 5 0 " 2 5 3 8 7 7 0 6 6-5 7 2 8 2 . 2.0 " 2 8 7 2 7 . 9 9 5 2 1 2 . 3 5 . 4 0 136 the 1971-1976 estimated national growth rates. The 1981 projections use 1976 projected employment and 1976-81 estimated growth rates. THE MIGRATION SUBMODEL Migration forms the l ink between the submodel which projects employment growth and that which projects population growth. In this submodel the net number of migrants to Vancouver is dependent on the number of jobs projected. The specific equation used is a regression of net migration over a 5 year period against the average number of jobs over that same period. This is equation 1 in Table 22. Other relationships were t r ied . Net migrants were also regressed against the absolute change in jobs over the period and the average rate of change of employment. Net migrants divided by average employment was regressed against time. The results of these regressions appear as equations 2-4 in Table 22. In most cases the R s ta t i s t ic is poor (except in the chosen relationship). In a l l cases the F-statist ic shows a high probability of obtaining the coefficients shown even i f no relationship existed between the variables. The poor quality of the regressions is a direct result of the limited number of observations used. There are only three observations on migration which can be matched to regional employment data. These are the totals between 1956-61; 1961-66; 1966-71. TABLE 22 MIGRATION EQUATIONS Dependent Variable Independent Variable * a * b F-Ratio b F-Prob b R2 Migrants Average Jobs -1188.0 (20630.0) 0.3442 (0.08605) 16.00 0.1775 .9412 Migrants Change in Jobs 65870.0 (13630.0) 0.2447 (0.1683) 2>113 0.3870 .6788 Migrants Average Rate of Change in Jobs 68510.0 (14280.0) 231500.0 (189900.0) 1.486 0.4390 .5978 Migrants/Average Jobs Time .3618 (0.04989) -0.0114 (0.02309) 0.2437 0.7003 .1959 Equations are of the form dependent = a + b ( i n d e p e n dent variable) Figures in brackets are standard errors. CO 138 Thus, the equation uses a l l observations that are available. The limited data on migration in Canada and the reasons for this l imit were discussed in Chapter 3. Unfortunately, there is no way around this constraint. However, the linking of the two projection models was considered essential. To merely assume a projection for migration when migration counts so heavily in population increase in the region was judged to be inadvisable. Thus the relationship obtained from the regression (number 1 in Table 22) is used even though i t s s tat i s t ica l significance is extremely low. Postulating a simple l ink between the number of migrants to the area and the number of jobs in the region ignores most of the migration l iterature reviewed in Chapter 2. This was a matter of expedience. Data to quantify and project relationships between variables such as education, wage differentials or migrant stock and migration to Vancouver are not available. THE POPULATION SUBMODEL The cohort survival technique is used to project population. The model projects population every five years. The sequence of events which occurs in the model is that migrants over the projection period are input at the beginning of the model but in the calculation of popu-lation change are assumed to have arrived evenly distributed over the period. 139 Births are calculated by the equation: (1 F P O P ( I - l ) + \ FPOP(I) + ^ X | F MIGRANTS(I-l) + \ x • 1 F MIGRANTS(I)) x 5.0 x the BIRTH RATE(I) * 1000.0 . . . . (7) where FPOP is the female population of that age class F MIGRANTS is the female migrants of that age class ( I ) , (1-1) are five year classes, e.g. 20-24 and 15-19, respectively. The form of this equation is due to the five year projection period and the fact that the data available give a yearly birth rate. Thus, the birth rate for each age class expresses the probability that, in any year, x number of births w i l l occur. Over a five year period each woman is exposed to this rate five times. This rate is also expressed as births per thousand, so, to apply as a probability to each woman at ' r i sk ' ( i . e . of the f e r t i l e ages) i t is divided by 1000. However, since we are dealing with a model that projects over a five year period some of the women who were in a lower age group at the start of the period w i l l move to the (I) age group during the period of projection and w i l l be subject to that birth rate. The assumption is that women are evenly distributed throughout their age classes and that half move forward. Female migrants are treated in the same manner except that only half are assumed to have been in the area for the period. 140 4 The final event in the model is the aging process. In the aging process a l l age classes are moved ahead one five year age class by being multiplied by a survival rate (a figure less than one). The final age class is a cumulative one (85+) and so i t is treated s l ight ly differently. The equations for the aging process appear below. A l l five year age groups 0-84 were treated as follows: POP(I) = POP(I-l) x survival rate (1-1) + | x MIGRANTS (1-1) x survival rate (1-1) + | x MIGRANTS (I) x survival rate (I) . . . . (8) the 85+ equation was POP(I) = POP(I-l) x survival rate (1-1) + POP(I) x survival rate (I) | x MIGRANTS (1-1) x survival rate (1-1) + MIGRANTS (I) x survival rate (I) . . . . (9) Where POP is population in the t time period MIGRANTS is the net migration over the period t to t + 5 (I),(I-1) are age classes as before. This is done for each five year age group and for each sex. 4 Women in the births equation are not aged since the f e r t i l i t y rate takes account of women who die before giving b i r th . 141 Migration Data The net migration figure received as input to the model is a single number. This is distributed between the sexes in the same manner as migrants have been his tor ica l ly distributed. The sex d i s t r i -bution is then further apportioned between the 5 year age classes in the same manner as the average age distribution of migrants to Vancouver over the period 1956-71 as measured at the three census counts. This data was obtained from the HPS population study worksheets and is shown here in Table 23. Death Rates and Survival Rates The assumption made is that the average B.C. death rate for 1965-70 applies over the projection period. As has been stated in Chapter 3 this is not an unreasonable assumption. The death rate seems to have eased i t s downward path. Further, since this model projects only 10 years into the future any error introduced by this assumption w i l l not be greatly compounded. The age-sex specific death rates appear in Table 24. The survival rates for each age-sex class are calculated from these death rates in the following manner: 5 (1 - death rate) = survival rate The rate is raised to the power of 5 since the individual is exposed to the probability of dying five times over the projection period. The survival rates so calculated are also shown in Table 24-TABLE 23 PERCENT AGE-SEX DISTRIBUTION OF NET MIGRANTS TO VANCOUVER, 1956-61, 1961-66, and 1966-71 Males Approximate Females Approximate Age 1956-61 1961-66 1966-71 Average 1956-61 1961-66 1966-71 Average 5-9 13.50 12.92 9.85 11.39 13.99 13.66 10 >.'19 11.93 10-14 7.81 6.99 7.30 7.14 8.21 6.32 6.29 6.30 15-19 3.57 4.58 7.90 6.24 6.52 9.95 10.56 10.26 20-24 8.20 18.87 17.85 18.36 15.40 24.44 23.02 23.73 25-29 16.64 21.75 30.50 20.96 15.58 14.24 21.38" 13.24 30-34 9.61 10.94 10.64 8.31 5.07 6.07 35-39 12.24 7.02 11.98 7.51 4.57 8.37 7.99 4.00 40-44 6.67 3.35 3.68 10.59 8.79 6.30 45-49 3.63 .49 7.16 2.00 4.60 -5.40 6.52 3.52 50-54 4.02 3.00 3.50 3.61 1.43 2.10 55-59 2.44 .04 3.85 2.44 2.60 1.12 6.59 2.60 60-64 .86 .45 1.41 -.86 2.20 2.10 65-69 3.03 3.01 2.26 2.63 4.46 3.80 3.36 3.58 70-74 2.87 2.64 2.10 2.14 3.82 75-79 -.11 -1.42 1.36 -2.74 -1.48 4.10 4.27 80+ 5.01 5.37 3.00 3.65 Totals 41534 • 28955 52832 36205 29940 48874 Source: Inter-Institutional Policy Simulator, Population Submodel Worksheets. 143 TABLE 24 AGE-SEX SPECIFIC DEATH & SURVIVAL RATES Death Rates Survival Rates Males Females Males Females 0-4 0.0051 0.0040 0.9748 0.9802 5-9 0.0006 0.0004 0.9968 0.9981 10-14 0.0004 0.0003 0.9980 0.9985 15-19 0.0015 0.0005 0.9924 0.9973 20-24 0.0019 0.0006 0.9903 0.9969 25-29 0.0018 0.0007 0.9909 0.9963 30-34 0.0020 0.0011 0.9900 0.9943 35-39 0.0024 0.0014 0.9880 0.9929 40-44 0.0037 0.0021 0.9816 0.9895 45-49 0.0057 0.0034 0.9717 0.9833 50-54 0.0099 0.0049 0.9556 0.9755 55-59 0.0140 0.0074 0.9321 0.9634 60-64 0.0226 0.0111 0.8920 0.9456 65-69 0.0342 0.0174 0.8403 0.9161 70-74 0.0501 0.0275 0.7735 0.8698 75-79 0.0753 0.0453 0.6760 0.7932 80-84 0.1169 0.0822 0.5369 0.6512 85+ 0.1989 0.1721 0.3300 0.3890 144 The age-sex specific death rates for the period 1960-70 were regressed against time. The intention was to use the projected rates from this equation as an alternative mortality assumption. However, the equations resulting were largely s t a t i s t i c a l ly insignificant and when used for projection yielded increasing mortality rates in half the cases. Thus i t seemed that a time trend alone was insufficient to project mortality rates and this approach was abandoned. F e r t i l i t y Assumptions The same basic model is run with three different f e r t i l i t y assumptions to produce varying projections of total population. Since the model projects only 10 years into the future, these varying assumptions have no effect on the estimated labour force (1981's labour force is already al ive. ) The three alternative assumptions are that f e r t i l i t y rates in the region: 1. Remain at the 1971 B.C. level throughout the period. 2. Are 10% lower than the 1971 B.C. rates throughout the period. This 10% is the figure by which the GVRD found the Vancouver 5 rates to differ from the B.C. rates. 3. Are equal to the average f e r t i l i t y rate over the period assuming that f e r t i l i t y rates decline in each five year period. The amount of decline comes from a time trend regression which uses the yearly rate of change in f e r t i l i t y rates from 1960-71 as i t s dependent variable. 5 G . V . R . P . , Population Forecast, (Vancouver, 1973). 145 The rates corresponding to these assumptions are shown in Table 25. Population Projections The population projections for 1976 and 1981 using the three different f e r t i l i t y assumptions are shown in Tables 26, 27, and 28. Tests were also performed on the population submodel in order to show how error in the submodel is affected by various assumptions. These tests are reported in Appendix B. The preferred version of the model is that with declining f e r t i l i t y rates since the error of prediction is smallest with this version. (See Appendix B). It should be noted that these projections are higher than those produced by the GVRD population porjection model. The difference l ies in the estimate of migration which is 156,208 for 1971-76 and 178,221 for 1976-81. This is higher than the GVRD's assumptions. THE UNEMPLOYMENT RATE CHECK The calculation of the unemployment rate is a check on the reasonableness of the operation of the model. The only interaction between the submodels is the migration function which influences only the population estimate. Population does not influence the employment situation at a l l . The unemployment rate gives some impression of the consistency of the two submodels. 146 TABLE 25 FERTILITY RATES per 1000 Age Groups 1971 B.C. 1971 B.C. - 10% Estimated Average B.C. 1971-76 1976-81 15-19 49.0 44.1 44.9 35.8 20-24 141.2 127,1 126.0 93.0 25-29 136.5 122.8 129.5 117.0 30-34 67.5 60.7 57.9 37.2 35-39 26.2 23.6 19.9 8.3 40-44 6.2 5.6 3.8 0.6 45-49 0.4 0.4 0.3 0.1 147 TABLE 26 POPULATION PROJECTIONS TO 1981 FERTILITY ASSUMPTION: 1971 B.C. RATES OVER ENTIRE PERIOD P O P U L U I O N T I M E T C v « \ - v \ ^ P O P U L A T I O N T I M E T + 5 C UAICO") M A L E S F E M A L E S T O T A L M A L E S F E M A L E S T O T A L 4 0 5 5 0 . 3 8 7 0 5 . 7 9 2 5 5 . 5 0 0 5 5 . 4 5 4 7 4 . 5 5 5 3 3 . 4 8 3 9 5 . 4 6 1 8 0 . <4 5 7 5 . - 4 3 2 2 6 . 4 1 5 0 1 , 6 4 7 2 7 . 5 1 6 1 0 . 4 9 4 6 5 . 1 0 1 C 7 5 . 5 6 1 0 6 . 5 3 3 2 0 . 1 0 9 4 2 6 . 4 7 4 0 G . 4 6 5 1 5 . 5 3 9 1 5 . 5 7 0 0 2 . 5 5 2 7 3 . 1 1 2 2 3 0 . 4 6 8 5 5 . 4 9 3 7 0 . 5 6 2 2 5 . 5 5 9 8 G . 5 8 0 6 5 , 1 1 4 0 4 6 . 4 2 5 3 0 . 4 1 2 5 5 . 8 3 7 8 5 . 6 2 0 3 5 , 6 3 7 3 6 , 1 2 5 8 2 5 , 3 4 2 9 5 . 3 3 36 5 , 6 7 6 6 0 . - - _ . 5 1 7 1 2 . . . . . 4 8 8 2 9 . 1 0 ^ 5 4 0 . 3 3 6 5 C . 3 C 9 5 5 . 6 4 6 4 5 , 4 1 5 0 5 . 3 7 0 7 2 . 1 8 5 8 1 . 3 3 ^ 0 0 . 3 2 1 1 0 „ 6 6 0 1 0 . 3 8 0 4 4 . 3 4 4 2 2 , 1 2 4 6 7 . 3 2 5 9 G . 3 4 4 4 5 . 6 7 4 3 5 . 3 5 6 7 4 . 3 5 6 G 9 . 7 1 2 8 3 , 2 8 4 5 0 . 3 1 1 7 5 . 5 9 6 2 5 . 3 4 0 5 3 . . 2 6 0 3 6 . 1 0 1 2 5 . 2 6 8 1 0 . 2 8 6 4 0 . 5 5 4 5 0 . 2 9 5 5 9 . 3 2 0 8 0 . 6 1 6 4 0 c 2 1 3 3 5 . 2 2 6 3 5 . 4 3 9 7 0 . . . 2 6 1 0 5 . . . _ 2 . 9 3 1 P . . _ 3 5 3 1 9 , 1 6 7 5 5 . 1 3 0 0 0 . 3 4 7 6 5 . 2 0 3 6 4 . 2 3 2 7 3 . 4 3 £ 4 2 . 1 1 8 2 0 . 1 5 0 8 5 , 2 6 9 0 5 , 1 5 6 8 7 , 1 9 0 7 3 , 3 4 7 6 0 , 8 5 5 5 . 1 2 1 3 5 . 2 0 7 3 0 . 1 0 3 5 8 . 1 5 8 0 2 . 2 6 2 0 0 , 6 3 3 0 . 6 7 7 5 . 1 5 1 5 5 . 6 8 7 1 . 1 2 0 1 9 . 18 8 8 8 . • 4 6 3 0 . 6 5 0 5 . 1 1 1 3 5 o 5 4 1 2 . 9 2 8 5 . 14 6 9 7 . T O T A L S T O T A L S 5 3 6 5 5 C . 5 4 5 4 0 5 . 1 0 8 2 3 5 5 . 6 4 4 2 4 6 . 6 5 0 2 3 6 , 1 2 5 4 4 7 5 . ' L A B O U R F O R C E J O B S U N E M P L O Y M E N T R A T E 5 1 3 6 6 1 . 5 0 4 5 7 2 8 2 . 0 0 1 0 . 5 7 6 0 P O P U L A T I O N T I M E T + 5 -M A L E S F E M A L E S T O T A L 6 3 9 3 6 . 5 8 C 7 9 , 1.22 0 1 5 . 5 3 0 1 7 . 4 8 6 3 7 . 1 0 1 6 5 4 , 5 2 0 6 1 . 4 5 6 6 3 , 1 C I 7 3 0 . 6 2 2 6 4 . 5 5 5 5 6 . 1 2 2 2 2 0 . ^ 6 6 7 6 9 . . 6 8 4 5 0 . 1 2 c 2 1 9 . 1 3 2 8 C , 7 4 5 C 3 . 1 4 7 7 3 8 „ 7 6 9 5 5 , 7 2 3 6 5 . 1 £ 9~ ~ 0 . 6 3 " ? 7 6 , ~ " 5 2 ° 9 6 , 1 1 6 7 7 2 . 4 6 4 6 6 , 4 C 5 7 3 . 67 4 5 5 . 4 0 0 8 C . 3 8 ^ 3 7 , 7 8 5 1 9 . 3 6 9 8 3 , 3 7 4 9 6 . 7 4 4 7 4 o 3 5 2 8 6 . 3 7 C 5 9 . 7 2 3 ' - 3 . 2 9 2 8 6 . 3 2 8 6 7 . 6 2 1 5 3 . 2 5 1 6 3 , 2 9 3 5 4 . c c - 0 2 1 . 1 8 9 4 7 . 2 4 2 7 1 . 4 2 1 -9 , 1 3 3 6 6 . 1 5 6 4 8 . : - ° 2 i 5 . . „ _ 8 2 3 9 . 1 5 2 . 1 8 , 2 3 4 5 7 . 5 9 5 9 . 1 2 6 2 5 , 1 8 6 2 3 o T O T A L S 7 7 2 1 0 2 . " " l 5 4 5 ' 1 * 9 . . " "' . 1 0 9 5 ijNFvCH. ' i V E . N T R A T 148 TABLE 27 POPULATION PROJECTIONS TO 1981 FERTILITY ASSUMPTION: 1971 B.C. RATE LESS 10%, OVER THE. ENTIRE PERIOD P O P U L A T I G N T T M E T C l ( l ^ O > P O P U L A T I O N T I M E T + 5 M A L E S F E M A L E S T O T A L M A L E S F E M A L E S T O T A L 4 0 5 5 C « 3 8 7 C 5 . 1 9 2 5 5 . 4 5 0 5 2 . 4 0 9 2 5 . . 6 5 5 7 6 . 4 8 3 9 5 o 4 6 1 8 0 . « 4 5 7 5-. 4 3 2 2 6 . 4 1 5 0 1 , 6 4 7 9 7 . 5 1 6 1 Co 4 9 4 6 5 . 1 0 1 C 7 5 . 5 6 1 C 6 . 5 3 3 2 0 . 1 C 9 4 3 6 . 4 7 4 0 0 . 4 6 5 1 5 . 5 3 5 1 5 . 5 7 0 0 2 . 5 5 2 7 8 . 1 1 2 .2 3 G . 4 6 3 5 5 . 4 9 3 7 0 . 5 6 2 2 5 . 5 5 9 8 0 . 5 9 0 6 5 . 1 1 4 0 4 6 . 4 2 5 3 0 . 4 1 2 5 5 . 8 3 7 8 5 . 6 2 0 3 5 . 6 3 7 8 6 . 1 2 5 6.2 5 , 3 4 2 5 5 . 3 3 3 6 5 . _ 6 7 6 6 0 . . 5 5 7 1 2 . 4 8 6 2 9 . 1 0 4 5 4 0 . 3 3 6 5 0 . 3 0 9 9 5 . 6 4 6 4 5 . 4 1 5 0 9 . 3 7 0 7 2 . 7 3 5 8 1 . 3 3 9 0 0 . 3 2 1 1 0 . 6 6 0 1 0 . 3 3 0 4 4 . 3 4 4 2 2 . 7 2 4 6 7 , 3 2 9 9 0 . 3 4 4 4 5 . 6 1 4 3 5 . 3 5 6 7 4 . 3 5 6 0 9 , 1 1 2 8 3 . 2 8 4 5 0 . 2 1 1 7 5 . 5 9 6 2 5 , 3 4 0 9 3 . 3 6 0 3 6 . 7 0 1 2 9 . 2 6 8 1 0 . 2 8 6 4 0 . 5 5 4 - 5 0 . 2 9 5 5 9 . 3 2 0 3 0 . 6 1 6 4 0 . 2 1 3 3 5 . . „ 2 2 6 3 5 . _ 4 3 9 7 C . . . . 2 6 5 0 5 . 2 9 3 1 0 . 5 5 8 1 9 . 1 6 7 5 5 . 1 . 8 0 0 0 . 2 4 1 5 5 . 2 0 3 6 4 . 2 3 2 7 3 . 4 3 6 4 2 . 11 8 2 0 . 1 5 0 3 5 . 2 6 9 C 5 . 1 5 6 8 7 . 1 5 0 7 3 . 3 4 7 6 0 . 3 5 5 5 . 1 2 ! ? 5 . 2 0 7 8 0 , 1 0 3 5 8 , 1 5 6 0 2 . 2 6 2 C G . 6 3 8 0 . 8 7 7 5 0 1 5 1 5 5 . 6 8 7 1 . 1 2 0 1 3 , 18 8 8 8 . 4 6 3 0 . 6 5 0 5 . 1 1 1 3 5 . 5 4 1 2 . 5 2 6 5 . 1 4 6 5 7 . . . T O T A L S ..... .. T O T A L S 5 3 6 9 5 0 . 5 4 5 4 0 5 . 1 0 8 2 3 5 5 . 6 3 9 2 3 9 . 6 4 5 6 3 7 . 1 2 8 4 9 2 2 . L A B O U R F O R C E - J 0 3 S U N E M P L O Y M E N T R P O P U L A T I O N T I M E T + 5 5 1 3 6 6 1 . 5 0 4 5 7 2 8 2 . 0 0 1 0 . 9 7 6 0 M A L E S F E M A L E S T O T A L 5 7 5 3 3 . 5 2 2 6 7 . 1 C 5 8 C 5 . . 4 3 1 3 5 . 4 4 1 7 9 . 5 2 3 1 4 . 5 2 0 6 1 . 4 5 6 6 3 . 1 C1 1 3 C . 6 2 2 6 4 . 5 9 9 5 6 . 1 2 7 7 2 0 o 6 6 7 6 5 . 6 8 4 5 0 . 1 3 5 2 1 9 . 7 3 2 3 C . 7 4 5 C 3 . 1 4 7 7 3 3 . 7 6 9 5 5 . 7 2 3 6 5 . 1 4 9 9 2 0 . 6 3 7 7 6 . 5 2 9 9 6 . 1 1 6 7 7 ? . 4 6 4 8 6 . 4 C 9 7 0 . £ 7 4 5 5 . 4 0 0 8 0 . 3 9 3 7 o 1 8 5 1 8 , 3 6 9 8 8 . 3 7 4 3 6 . 7 ^ 4 7 4 . 3 5 2 8 6 . 3 7 C 5 8 . 1 2 34 3 , 2 ^ 2 8 6 . . 3 2 3 6 7 . 6 2 1 5 3 . 2 5 1 6 3 . 2 9 8 5 4 . 5r - 0 2 1 . 1 3 5 4 7 . .24 ? 7 1 . <• 2 2 1 8 . 1 3 5 6 6 , 1 9 6 4 9 , 2 ^ 2 1 5 . 8 2 3 9 . 1 c 2 1 3 . 2 ^ 4 5 7 . 5 a 5 5 . 1 2 6 2 5 . 18 6 2 3 , T O T A L S 7 6 0 8 2 2 . 7 6 2 8 2 1 . ~ 1 5 2 3 6 3 9 . L A B O U R F O R C E J O B 3 l j N c w P | . O Y ^ E M T R A T E £ 5 2 c , 2 7 . 6 0 5 2 1 2 3 5 . O C 2 0 . 1 6 5 6 TABLE 28 149 POPULATION PROJECTIONS TO 1981 FERTILITY ASSUMPTION: B.C. RATES DECLINE TO 1981 P O P U L A T I O N T I M E T U ^ - V \ ^ P O P U L A T I O N T I M E T + 5 M A L E S F E M A L E S T O T A L M A L E S F E M A L E S T O T A L 4 0 5 5 0 . 3 8 7 0 5 . 7 9 2 5 5 . 4 5 0 7 2 . 4 0 9 4 3 . 8 6 0 1 5 . 4 3 3 9 5 . 4 6 1 3 0 . C 4 57 5 . 4 3 2 2 6 . 4 1 5 0 1 . 6 4 7 2 7 . 5 1 6 1 0 o 4 9 4 6 5 . 1 0 1 0 7 5 . 5 6 1 0 6 . 5 3 3 2 0 . 1 C 9 4 2 6 . 4 7 4 0 0 . 4 6 5 1 5 . 9 3 9 1 5 . 5 7 0 0 2 . 5 5 2 7 3 . 1 1 7 2 3 0 . 4 6 8 5 5 . 4 9 3 7 0 . 9 6 2 2 5 . 5 5 9 8 C . 5 3 0 6 5 . 1 1 4 C 4 6 . 4 2 5 3 0 . 4 1 2 5 5 . 6 3 7 8 5 . 6 2 0 3 9 . 6 3 7 3 . 6 . 1 2 5 8 2 5 . 3 ^ 2 9 5 . 3 3 3 6 5 0 _ . 6 7 6 6 0 . 5 5 7 1 2 . 4 3 8 2 9 o 1 G 4 5 4 0 . 3 3 6 5 Co 3 C 9 9 5 . 6 4 6 4 5 . 4 1 5 0 9 . 3 7 C 7 2 . 7 8 5 8 1 . 3 3 9 0 0 o 3 2 1 1 0 . 6 6 0 1 G . 3 8 0 4 4 . . 3 4 4 2 2 . 1 2 4 6 7 . 3 2 9 9 0 . . 3 4 4 4 5 . 6 7 - 3 5 . 3 5 6 7 4 . 3 5 6 0 9 „ 7 1 2 3 3 . 2 8 4 5 0 . 2 1 1 7 5 , 5 9 t: 2 5 . 3 4 0 9 3 . 2 6 C 3 6 . 7 0 1 2 9 . • 2 6 8 1 0 e 2 8 6 4 0 . 5 5 4 5 G . 2 9 5 5 9 . 3 2 0 8 0 . 6 1 i 4 C o 21 3 3 5 . 2 2 6 3 5 . _ 4 3 9 7 0 . 2 6 5 0 9 . .. 2 9 3 1 0 . . 5 5 3 1 9 . 1 6 7 5 5 . 1 8 0 C O . 3 4 7 5 5c 2 0 3 6 4 . . 2 2 2 7 8 . 4 3 f. 4 2 . 1 1 3 2 0 . 1 5 0 8 5 . 2 6 9 C 5 . 1 5 6 8 7 . 1 9 0 7 3 . 3 4 7 6 0 . 3 5 9 5 . 1 2 1 3 5 . 2 0 7 3 0 , , 1 0 3 9 3 . 1 5 3 0 2 . 2 6 2 0 0 . 6 3 8 0 . 8 7 7 5 . 1 5 1 5 5 . 6 3 7 1 . 1 2 0 1 3 . 1 8 8 8 8 . 4 6 3 0 . 6 5 0 5 . 1 1 1 3 5 . 5 4 1 2 . 9 2 8 5 . 1 4 6 9 7 . ' T O T A L S T O T A L . - : 5 3 6 < ? 5 0 . 5 4 5 4 0 5 . 1 0 8 2 3 5 5 , 6 3 9 2 5 9 . 6 4 5 7 0 5 . 1 2 8 ^ 9 6 1 . L A B O U R F O R C E J O 8 5 U N E M P L O Y M E N T R A T E 5 1 3 6 6 1 . 5 C 4 5 7 2 8 2 . C C 1 C * 9 7 £ C - .-P O P U L A T I O N T I M E T + 5 1'*°' *•< ^ 7 M A L E S F E M A L E S T O T U . 4 4 6 4 3 . 4 G 5 5 3 . 8 C 1 9 6 . 4 3 1 5 5 . 4 4 1 9 7 a 9 2 I 5 2 . 5 2 0 6 1 . 4 9 5 6 3 , 1 0 1 7 3 0 . 6 7 2 6 4 . 5 9 9 5 6 . 1 2 7 2 2 0 . 6 6 7 6 9 . 6 8 4 5 0 o 12 c 2 1 9 . 7 3 2 3 0 . 7 4 5 0 3 . 1 4 7 7 8 3 . 7 6 9 5 c . 7 8 3 6 5 . 1 4 9 3 2 0 . 6 3 7 7 6 . 5 2 ^ 6 . 1 1 6 7 7 ? . 4 6 4 8 6 . 4 0 0 7 0 . 8 7 4 c ; 5 . 4 0 0 S C . 3 8 - 3 7 „ 7 * 5 I 3 c 3 6 9 8 8 . 2 7 4 - 3 6 . 1!- 7 4 . 3 5 2 8 6 . 3 7 0 5 3 . 7 . ' 3 4 3 . 2 9 " ' 8 6 . 3 2 8 6 7 0 6 2 1 5 3 „ 2 1 6 8 . 2 9 3 5 4 . " " 5 - 0 2 1 . " 1 8 9 4 7 . 2 4 271 . . * 8 2 1 3 . . 1 3 5 6 6 ^ . 1 9 6 4 3 . 3 2 8 1 5 . 8 2 3 9 . 1 c 2 1 3 „ 2 3 4 5 7 . 1 2 6 2 5 . 1 3 6 2 3 . T O T A f 3 7 4 7 9 4 7 . 7 5 1 1 8 5 . 7 4 C 9 C - S 9 J O 3 9 U N F M P I . O Y M E M T P f t T F The unemployment rate is calculated as follows: 150 Labour force - jobs x 100.0 = unemployment rate . . . . (10) Labour force The estimate of jobs is that produced by the employment submodel. Labour force is calculated from the male and female projected populations between the ages of 15 and 65. Each of these groups has a participation rate applied to i t . The participation rates used for the 1976 and 1981 projections were calculated from a time trend extrapolation based on the B.C. participation rates for each sex. Thus, participation in the labour force is assumed to grow over the projection period. The estimates of the unemployment rate for 1976 and 1981 are 10.97 and 20.17 percent respectively. These are high rates. The 1981 rate probably also reflects the compounding of error throughout the model. RECOMMENDATIONS What has so far been achieved is a regional projection model in which the population submodel is dependent upon the employment sub-model. The employment model could be made dependent on population in the region. For instance, employment in the service sector might be made a function of the population leve l . The projections themselves are subject to considerable error. However, i t seems that much of this error could be removed by refinement 151 of the regional employment data series. The preferred solution would be to have better information made available from Statist ics Canada. However, since that presently seems unlikely at the regional l eve l , suggestions have been made in the section on employment data as to how this series could be improved. B I B L I O G R A P H Y 152 BIBLIOGRAPHY ALONSO, WILLIAM. "Predicting Best With Imperfect Data," American  Institute of Planners Journal. 7 (1968),248-255. ANDERSON, I.B. Internal Migration in Canada: 1921-61. 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"The Decision Process in Spatial Context," Annals  of the Association of American Geographers. 54 (1964), 537-558. . "Behavioral Aspects of the Decision to Migrate," Papers of the Regional Science Association. 14 (1965), 159-169. "The Basis for Stabi l i ty of Interregional Transactions," Geographic Analysis. 1 (1969), 152-188. APPENDIX A n o , j ; " • ! , . . ' - I i : . I > i APPENDIX B. TESTS OF THE EMPLOYMENT AND POPULATION SUBMODELS 175 TESTS OF THE EMPLOYMENT SUBMODEL The employment submodel was subjected to three experiments. The f i r s t experiment dealt with the effects of different national growth rate assumptions over a ten year projection period. The second experiment dealt with five year projections and estimated the errors resulting from the use of the time trend to project national growth rates. Changes in the error of estimation resulting from projecting in the second period on the basis of the f i r s t period projection were also examined. In the third experiment, the projections of the shift-share model were compared to a simple trend extrapolation. For these experiments the period of projection was from 1960 or 1961 to 1970 or 1971. The data base was the same as for the projection submodel of Chapter 6. The projections were derived in the same manner. It was of some interest to ascertain how sensitive the model was to different national growth rates. Thus in the f i r s t experiment, the submodel was used to project from 1960 to 1970 using three different estimates of national growth for that period. The estimates were: 1. The actual 1960-70 national growth rate calculated from the estimated national employment shown in Table 16 of Chapter 6. 2. The 1960-70 national growth rate estimated from the time trend regressions shown in Table 19 of Chapter 6. 3. Estimates of the 1960-70 national growth rates produced by the Economic Council of Canada.1 These rates are shown in Table B . l . 1 Economic Council of Canada, The Economy to 1980, Staff Paper No. 7, p. 226. 176 TABLE B.l NATIONAL EMPLOYMENT GROWTH RATES BY INDUSTRY AVERAGE ANNUAL PERCENT CHANGE 1960-70 1970-80 Agriculture -3.1 -2.1 Forestry -1.6 1.2 Mines, Quarries, Oil Wells 4.9 2.1 Manufacturing 2.5 .2 Construction 2.7 3,7 U t i l i t i e s 3.0 - .8 Transportation Storage & Communication 2.2 2.0 Wholesale & Retail Trade 2.9 3.0 Finance, Insurance & Real Estate (includes housing) 5.0 4.3 Community, Business, Personal Services (distinct from the entire service sector which is more comprehensive) 6.4 6.1 Public Administration & Defence 3.8 3.4 Total 3.1 3.1 Source: Economic Council of Canada, The Economy to 1980: Staff Papers,, (Ottawa, 1972), Table 7.3. p. 226. 177 Table B.2 shows the projections of employment to 1970 and the percent error of projection for estimates 1 and 2 above of the national growth rate. (Columns 1-3 are the result of estimate 1 and columns 4-6 are the result of estimate 2. Columns 1-3 may be regarded as the best prediction possible from the submodel. In this case the submodel receives as input the actual national growth rates over the period of projection and the average differential shi f t . For projections into the future, assumptions are made about both these inputs, thereby introducing further error into the submodel. < The error introduced by the use of national growth rates calculated from the time trend equation is estimated in columns 4-6 of Table B.2. The use of estimated national growth rates is the only difference between the projections of columns 2 and 5. The error of estimation increases s ignif icantly. It should be noted that the estimation of rates from the time trend within the time period over which the regression was f i t ted probably involves less error than extrapolation beyond that period. The rates for 1971-76 and 1976-81 used in the projections shown in Chapter 6 may be expected to involve more error s t i l l . Table B.3 shows the projections obtained from the shift-share model when the growth rates provided by the Economic Council were used. In this case, the model performed even worse. This probably is a result of the aggregate nature of the rates provided. For instance, in this test, the growth rates for the f i r s t eight sectors are assumed to be the same as a l l are classif ied as manufacturing industries. TABLE B.2 SHIFT-SHARE MODEL PROJECTIONS OF SECTORAL EMPLOYMENT IN VANCOUVER PROJECTED I9 6 0 - 7 G . . ACTUAL IS 70 PERCENTAGE P P R C P - 3 . 9 3 2 5 -5 .2392 1 3 . 7 5 3 3 32 .47 1 4 - 7 . 1 3 9 5 - 1 9 . 7 4 0 3 - 1 6 . 0 0 0 4 __-4. 562.9 2 0 . 9 1 0 3 0 . 8 0 4 1 _11.30.4C - 2 0 '."8 59 4 - 3 3 . 0 7 4 6 4 .71 C7 - 6 . 6 9 1 8 - 1 7 . 7 7 1 5 - 6 . 7 2 3 L . 3 . 6158 13 .7641 11 .7259 0 . 5 3 2 6 17. 6379 - 0 . 9 9 6 2 14 .120 2 6 .9874 6 . 7 3 4 0 . 1 0 0 . 0 0 0 0 7 . 3 5 2 6 PROJECT EO .19 60-70 2516 6 1 7 58 11874 ,24CC ,4420 .4500 2 111 . 10233 . _ 5 5 8 2. 4 1 3 4 . 5460 . 369 7. 8350 0500 J 5 0 0_ 6 210 29 20 6 5 20 5 2 26 . 7426 . 66 28 . 9 4 3 8 . 52 19. 104/40. 22 60 6560 1320 57 80 6360 1100 13015. _JZ 2.8.8... 22 9 81 . 10394. 2.7 22 . 4200 72CC 5660 02 66 3400 6690 4 6 7 7 . C 6 6 0 330 18 .8800 26^37 .8^00 . • 5R89 .7890 40079 .C300 2 8 Q 4 3 4 . 1 0 0 0 C.COOO 304668 .7000 ACTUAL 19 70 27317 . 1 7 9 3 , 10536. COOO 0000 oooo 286 3. 7 6 8 7 . 5696. 5 3 13 . 6 8 5 5 . 3782. COOO 00 00 COOO cooT cooo COOO 32 1 2 . 7907 . 7 8 51 . 1246 7 . 7896. 1118 7. COOO COOO cooo_ 0000 COOO COOO 2708 7, 1 7 101. _ 8 2 7 3, 75 ) ;"1. 13328. 3077, 00 00 COCO 00 0.0. 00 90 COCO COOO 49C8 4 16 11 37150 7180 5 291 2 3590^3 . COOO . CO 00 .0000_ . 00 00 . COOO .00 00 21631 386671 . COOO .COOO p c c R C E N T A G E RR _R - 7 . 8 7 3 2 - 1 . 9 2 7 4 12 .7036 -26.2352 33 .1215 - 1 . 9 8 82 :"22. f792 ' -20 .345 3 - 2 . 2 2 4 9 •36.3587 -6 .0496 •15. 5759 _ -24 .2915 -33 .8952 - 6 . 6 7 6 3 ^ -11 .9008 -23 .3891 89 9 4_ -3 .2630 -22 .0112 - 1 1 . 5 1 5 4 -4 -20, •Jq -17 -24 ,7052 ,6487 ,JLO 4_0_ ,96~9 5 , 2534 - 1 9 . 3 8 7 3 -100.0000 - 2 1 . 2 0 7 2 179 TABLE B.3 REGIONAL E M P L O Y M E N T P R O J F C T T C N S F O R E C A S T S U S I N G E C O N C O U N C I L S N A T I O N A L G R O W T H R A T E S P R O J E C T E D 1 9 6 0 - 7 0 2 5 8 2 6 . 1 7 0 0 2 0 1 2 . 4 6 8 0 1 3 5 9 5 . 1 6 C 0 2 8 1 8 . 9 5 5 0 1 1 1 9 1 . 7 7 0 0 " 5 8 2 6 . 6 4 4 0 4 3 3 7 . 8 5 5 0 5 4 8 1 . 1 9 5 0 5 1 8 3 . 5 6 2 0 7 2 0 0 . 4 6 0 0 _6_6 9_8_«._51_4.0 7 7 5 7 . 1 5 6 0 1 1 2 2 4 . 8 5 0 0 6 4 6 2 . 4_6G0_ L 1 0 5 0 . 0 30"0 2 4 7 0 5 . 3 9 0 0 J ^ 2 5 G 8 . 5 6 0 0 6 2 3 7 . 9 8 3 0 2 1 6 4 8 . 8 6 C G _10 6 5 7 . 5 3 0 0 2 2 9 3 . 0 9 7 0 5 4 7 6 . 9 2 5 0 1 4 0 1 2 . 2 5_G_p_ 11 3 9 6 . 52 0 0 5 9 4 4 . 1 8 7 0 J_4 5_sJ L O 0_ 2 5 2 8 4 7 0 2 0 0 0 .•C. CO 0 0 2606^4 ,_60p0_ A C T U A L 1 9 7 0 27 3 1 7 . C O 0 0 1 7 9 3 . 0 0 0 0 1 0 5 3 6 . C O 0 0 2 8 6 3 . 0 0 0 0 7 6 8 7 . C O 0 0 5 6 9 6 . C O 0 0 5 3 1 3 , 0 0 0 0 6 8 5 5 . C O O O 3 7 8 2 . C O O O 3 2 1 2 . 0 0 0 0 _ 7 9 0 7 . C O 0 0 7 8 5 1 . C O O O 1 2 4 6 7 . 0 0 0 0 7 3 9 6 . C O O O 1 1 1 8 7 . C O C O 2 7 C 8 7 . C 0 0 0 _ ! 7 1 OXs CO GO ' l 2 73 .~CO"o"o ' 2 5 0 5 1 . 0 0 0 0 1 3 ? 2 3 . C C 0 0 50 7 7 . 0 0 0 0 4 ^ 0 3 . 0 0 0 0 4 1 6 1 1 . C 0 0 0 _ 3 7 1 5 0 . 0 0 0.0 7 1 8 0 . 0 0 0 0 5 2 9 1 2 . G O 0 0 3 8 JO'- 3 . 0 0 0 0 2 1 6 3 1 . C O O O 3 8 6 V 7 1 . _ C C 0 0 P E R C E N T A G E E P R C R - 5 . 4 5 7 5 1 2 . 2 4 0 2 2 9 . 0 3 5 3 - 1 . 5 3 8 4 4 9 . 5 9 3 5 2 . 2 9 3 6 - 1 3 . 3 5 3 9 - 2 0 . 0 4 0 9 3 7 . 0 5 8 7 - 1 2 . 3 1 7 8 - J 3 o 2 7 8 G _ - 1 . 1 9 5 3 - 9 . 9 6 3 4 - 1 8 . 1 5 5 3 - 1 . 2 2 4 3 - 8 . 7 9 2 4 - 2 6 c 3 9 ^ 3 - 2 4 ' . 5 9 8 2 - 1 3 . 5 8 0 8 - 2 0 . 0 3 6 5 - 2 5 . 4 7 6 2 11 . 5 9 1 7 - f c f e . 3.23 2_ ' - 6 9 . 3 8 3 0 - 1 7 . 2 1 1 9 . - 6 3 . 3 1 1 1 - 2 9 . 5 7 7 4 - 1 . 0 0 . 0 0 0 0 . - 3 2 . 5 7 9 7 180 In the second experiment, two five year projections were generated: from 1961-1966 and from 1966-1971. As noted above, the aim here Was to see what changes in the error of estimate would be produced in the projections by the use of: (a) the trend equation to produce national growth rates, (b) the projections of the f i r s t period to project the second. Table B.4 summarizes the results of this experiment. The errors shown there represent errors of estimation of total employment. The fu l l results for each sector are shown in Table B.5. The last experiment with the employment submodel was a compari-son of the results obtained using the shift-share equation to estimate secotral employment in 1966 and 1971 and those obtained by use of a simple time trend equation f i t ted to Vancouver employment data. The results of the projection based on the time trend are shown in Table B.6. The percent errors of projection can be compared to those appearing in columns 6 and 12 of Table B.5. It can be seen that the absolute value of the error of projection for the shift-share submodel was less than that of the simple trend extrapolation in 13 sectors in 1966 and only 5 sectors in 1971. Thus, i t appears that the economic submodel is not a very satisfactory one. 181 TABLE B.4 PERCENT ERROR OF 5 YEAR PROJECTIONS FOR TOTAL EMPLOYMENT Base Year G r o w t h R a t e s Actual Projected 1961 Actual Employment -2.975 (1-3)* -0.346 (4-6) • = 1966 Actual,Employment Projected Employment -21.642 (7-9) -20.619 (10-12) The figures in brackets denote the columns of Table B.5 to which this summary number refers. TABLE B.5 5 YEAR VANCOUVER EMPLOYMENT PROJECTIONS PROJECTED ACTUAL " ERO tHT AC' PROJECTED .ACTUAL PERCENTAGE PRC J FCTED ACTUAL PEPCENTAGE PP.CJECTEO ACTUAL PEP.CE NT AGE iSof , 1-766 ERROR 1966 -1966 .EPF. 3 P. 1 = 71 1<571 ERROR 19.71 1971 ERF. OP 1 2 4 6 5 8 . 9 4 2 6 3 7 4 . 0 0 - 5 . 7445 2 2 1 0 7 . 9 1 2 6 3 7 4 . 0 0 - 1 6 , 1 1 5 4 269 7 7 . 11 28252. 00 2 . 5 6 6 5 2<289 .96 2 8 2 5 2 . 0 0 7 - 1 4 . 0 2 3 9 2 1 5 4 4 . 2 5 1 5 « 3 . 0 0 - 3 , 0 6 0 ? 1 5 0 7 . 8 5 1593 .00 - 5 . 3 4 5 0 1653 .22 1880 .00 - 1 2 . 0 6 3 0 15 6 4-55 1 6 3 0 . 0 0 - 1 6 . 7 ( 3 2 3' U API . 1 3 1 1 C 9 6 . 00 2. 970 I 1 1 0 0 3 . 2 1 1 1 0 9 6 . P C - (7 8362 1 1 4 2 8 . 8 7 3836 . 00 2 9 . 3 4 4 4 1 1 3 3 3 . 3 0 8636 . 00 2 8 . 2 6 2 8 4" ' i~?39 .94 209l7o0 - 7 . 2 ? . ' l 1 7 3 4 . 3 8 2091 .00 - 1 4 . 6 6 3 9 2 0 5 7 . 7 5 2447 . 00 - 1 5 . 9071 1 7 5 6 . 01 2447 . 00 - 2 8 . 2384 5 0 7 7 8 . 7 3 86 3 0 . 0 0 7 , 5 1 7 1 9 2 5 7 . 54 8630 .00 7 . 2715 9 0 0 6 . 2 6 8 C 8 7 . 0 0 11 . " 6 7 1 966 1 . 16 3C87. 00 1 9 , ^ 5 3 J 6 2 « r . 15 5 9 4 5 . 00 5 . 8 3 9 8 5 1 6 3 . 6 1 5945.OC ^ 1 3 . 14 36 6 5 2 2 . 8 5 5670 . 00 _ 1 5 . 0 4 1 4 _ 5 6 6 5 . 5 1 5 6 7 0 . 0 0 - 0 . 0 7 9 2 7 4 5 0 4 . 36""" ' 46 4 3 , 0 0 " - 3 . C 9 0 2 4 2 5 5 . 6 3 4 6 4 3 . 0 0 - 8 ".44 18 •" T l 4 7 ' . 6 6 ~5 2S% GO-2"; 5 9 8 8 " " <"TT'3Tl0 "5 2 8 5. 00 " - 10'. £ 2 1 2 " 3 i . 3 S 4 . f p , 6 7 0 2 . 00 - 2 7 . 1 1 6 1 4 C 7 7 . 6 8 6702 . 00 - 3 9 . 1573 7 4 7 6 . 0 7 7 1 3 3 . 0 0 4 . 8 0 9 7 4 5 4 8 . 6 4 7 132 .00 - 3 6 . 2 3 1 0 .) 4 1 ' 0 . 1 7 3 8 0 £ . CO 13 . 703 2 -3485 . 50 • 3800 .00 - 6 . 2 7 6 3 36 36 . 22 3853. 00 - 5 . 6 2 6 3 3 3 3 5 . 2 7 3 8 5 3 . 00 -13 . 4 3 7 0 TO 6 0 4 4 . 1 8 6122 . 00 - 1 , 3 7 1 2 4912 . 87 6 1 2 2 . 0 0 - 1 9 . 7505 6062.66 11 718. 00 - 4 3 . 2676 46 64 . 72 11718 . 00 -58."4851 11 6CP-8. 74 54 7 7 . 00 1 1 . 1 6 9 1 5 4 0 8 . 45 5 4 7 7 . 0 0 - 1. 2517 6 2 9 5 . 2 6 9699 .00 - 3 5 . 0 9 3 7 6 2 1 6 . 4 6 9699 . 00 - 3 5 . 9062 12 _ 6656 „ ! 4 _ 7 3 5 5 . ^ 0 _ - 9 . 5 C 1 8 _6_479..07 7355 .00_ -1 1. 9093 7783.779 799 2. 00_ _ - 2 . 6 0 5 2 « 56^30 7 9 9 2 . 00 - 1 4 . 2 0 4 2 13 " 941 8 . 6 6 9 7 2 3 . 0 0 - . 3 . 1799 9 2 0 5 . 59 9723 .00 - 5 . 3 7 0 ! 1CG85.98 124 3 4 . 0 0 - 1 8 . 8 8 3 8 9 5 4 4 . 36 124 34 . 00 " " -2372399 14 • 5 * 7 4 . 0 3 74 4-3.00 - 2 8 . 5173 4 9 5 8 . 17 7 4 4 3 . 0 3 - 3 3 , 4295 7 6 4 0 . 1 6 3253.. 00 - 7 . 4 2 5 7 5086 .03 8 2 5 3 . 0 0 - 3 8 . 3 7 2 9 1 C i n 5 7 7 . 0 0 9 7 6 2 . 00 1 4 . 1 9 7 8 9766 . 00 9262 . 00 5 . 4 4 1 6 9 7 8 3 . 0 8 12045. 00 - 1 8 . 7374 1 C 3 2 0 . 7 1 12045 . 00 - 1 4 . 3 1 54 TC 2182 6 . 2 0 21659700 0 . 7 7 1 9 2 0 9 3 8 . 2 8 21659 . 00 - 3 . 3 2 7 6 2 3 8 7 9 . 0 4 28830 .00 - 1 7 . 1 7 2 9 2 3 0 8 4 . 4 5 28830 . 00 - 1 9 . 9 2 9 1 17 1186 ' - . „ f2 12580 . 00 - 5 . 67C7 1 1 2 9 7 . 3 7 12530 .00 - 1 0 , 1 9 5 8 1 4 4 5 9 . 4 5 15435. 00 - 6 . 3204 1 2 9 0 5 . 1 9 15435 .00 -15 . 8 7 1 3 13 6 7 Q T . 0 4 _ 6 9 8 5 . 0 0 _ „ - 9 . 8 3 4 7 6 2 6 0 . 0_4_ 6985 ,00 - 1 0 , 3 7 3 8 6 J 2 7 . 9 8 8161 ,00 4 . « 9 6 7 7<4 2_i_88_ 8 2 6 1 ._CO _-6._34 87_ 19 " 7 1 3 8 2 . 7 3 1 9 8 2 5 . 0 0 7 . 3 5 7 4 2 0 1 5 1 . 52 19 8 2 5 . 0 0 1. 647.0 2 2 7 9 4 . 7 8 23638 .00 - 3 . 7 7 0 8 2 3 1 7 0 . 2 i 23688 . 00 - 2 " . 1659 20 ' 9 1 6 9 . C ? 93 3 4 , 0 0 - 1 , 7 6 7 5 8 9 1 8 . 5 5 9334 ,00 - 4 , 4 5 0 9 1 1 1 5 3 . 7 9 13751 .00 - 1 8 . 8 5 1 1 1 C 6 6 2 . 1 3 13751 .00 - 2 2 . 4 6 2 9 21 7i 3 6 . 7 5 1771 »oo 23 . 447 4 2 243 , 3 8 17 71 .00 2 6 . 6729 2 2 3 6 . 0 6 3204 . 00 - 3 0 . 2102 26 3 2 . 4 9 3 204 .00 -11 . 5952 12" < , n i , 7? 4317 . 00 - 2 . 3692 4 2 3 6 . 29 431 7. 00 - 1 . 8697 4 8 4 7 . 9 9 5 4 8 1 . 00 - I f75492 4 7 5 7 . 3 4 5481 . 00 - 1 2 . 2 0 3 1 23 1 4 7 3 5 , 9 5 1 5 4 0 5 . 0 0 - 7 , 5 8 8 6 2 1 2 5 4 . 0 3 15405 .00 3 7 , 9 6 8 3 2 2 9 3 1 . 8 8 39828 ,00 - 4 2 . 4 2 2 7 2 1 6 3 8 . 7 4 39828 . 00 - 2 0 . 5 6 1 6 24 1 1 7 4 1 , 5 6 _ 140 77 ,0 0 - 2 0 . 14 24. 1 4 8 7 0 , 3_5 14077.QQ 5 . 6 3 57 2 1 1 7 3 . 21 3JjS4_3.00 ^ 3 . 1 7 5 2 6 223 6 6 . 4 9 37 64 3. 00 - 4 0 . 5826 25~~"1374. 7 3 3 5 7 3 . 00 - 5 . 5490 4 3 8 9 . 31 35 73, 00 2 2. '6465 4 3 4 2 . 6 2 4 916. 00 - 1 1 . 6 6 3 5 5 3 3 4 . 7 6 4 9 1 6 . 00 8 . 5 1 8 3 " 26 1 * 3 9 1 . 4 4 16893.00 - 8 , 9156 2 2 0 5 6 . 9 0 16898 . 00 3 0 . 5 2 9 6 2 4 7 5 5 . 5 6 548.77. 00 - 5 4 . 8890 3 23 13 . 36 54677 . 00 - 4 1 . 1 1 6 8 27 7 33 37 4 ._50__734481 ,00 - 0 . 4 3 4 7 2 3 4 7 0 9 . 30 234481 . 00 C . C 9 7 4 279618 ,50 367201 .00 - 2 3 . 8 5 ! 4 2 7 9 8 9 0 . ° 0 267.-C1. 00 - 2 3 . 7772 28 "19> ? 9 . 56 16654 . 00 3. 0854 . 2 0 4 5 4 . 9 1 186 54 .00 9 . 6 54 2 2 2C41 . 56 22024. 00 0 . C 9 7 2 4 1 6 9 . 5 2 2 2 0 2 4 . 00 9 . 7 4 1 7 23 2 5 3 5 7 ? . 8 0 26 1349 .00 - 2 , 9 7 5 4 2 6 0 4 4 3 . 3 0 261349 . 00 - 0 . 3 4 6 4 3067C9.6O 2 9 1 * 2 2 . 0 0 -21 . 6 4 2 2 - 1 0 1 3 . 90 391422 . 00 - 2 0 . 6 1 9 2 183 TABLE B.6 REGIONAL EMPLOYMENT PROJECTIONS BASED ON SIMPLE TIME TREND EQUATION R"E G I C N A L " ~ E M T n r O W E l V T ~ P R U J 1 9 6 6 1 9 7 1 "" 2 5 C 7 5 . 2 0 2 0 8 . , 1 6 1 1 . 1 6 5 6 . 1 C 6 8 8 . 1 0 5 1 2 . 2 2 7 C . 2 3 1 2 = i 1—7—1 6 1 M l • 5 7 0 4 • . 6 4 1 2 . 4 6 2 8 . 5 4 8 7 . - 5 T T 5 5 T ....—^5-1--; 4 1 1 5 . 4 1 3 9 . 7 2 C 6 . 6 1 G 4 . T^45T6 . 7 2 T T T ^ 7 1 3 4 . 7 9 0 3 . 1 G 2 6 1 . 1 1 4 6 C . 7-C'O'D . T T 3 W " . 5 4 5 2 . 9 1 2 3 . 2 2 4 2 7 . 2 4 6 8 5 . — 1 M 5 4 . - F5T8~Z3 . 6,7 C 2 . 8 4 5 6 . 2 1 C C 6 . 2 4 3 3 4 . r——r—pj—7 ' 9 "5T4- , 1 .t. 5 o l . 2 18 4 . 2 7 6 2 . 4 3 5 6 . 5 0 6 2 . 2 T / 7 7 . 2r5)Tf£T7 . 2 C / 15 . 2 2 7 6 4 . 5 2 7 1 . 6 6 G 2 o - 2 - e 5 - A - b . • • " 4 3 3 2 5 . 2 6 3 10 0 , 3 2.9 6. 5 C . 1 5 4 3 8 . 2 . 2 3 2 6 . PTFT^TiTTnrrjT^ S~ 1 9 6 6 1 9 7 1 - 4 . 9 1 C - C . 1 5 4 ~v«\ 3 0 " - 1 1 . 5 1 5 - 3 . 6 7 7 1 8 . 5 6 8 8 . 5 6 0 - 5 . 5 3 7 - 1 . 5 3 8 6 .118 - 4 . 0 5 4 1 3 . 0 8 6 , - C . 4 3 0 3 , 8 2 2 - 3 . 5 T 4 " 8 . 2 8 5 7 . M 3 6 1 7 . 7 3 9 - 2 C . 8 4 1 . 1 / . b l O " ^r2~5~TTf7 r8 - 3 . C 0 5 - 1 . 1 1 4 5 . 4 7 5 - 7 . 8 3 2 " - 6 T " 0 T ' 5 " — T 7 T 6 9 ~ ~ 2 . 4 8 3 - 2 4 . 2 18 2 . 5 4 6 - 1 4 . 2 7 6 i (—~i 4378731 2 . 5 1 / - 4 . C 3 7 4 . 1.1 1. 5 . 5 5 7 2 . 7 2 7 6 . 2 X 4 -2 2 . 3 2 0 - 1 2 . 7 6 4 1 . 8 3 C . - 7 . 6 6 4 ~ 5 3 T 9 8~9 4 7 . 1 8 3 - 1 2 . 5 6 1 4 7 . 5 2 3 2 4 . 2 5 6 - - Z 1 T 0 - 5 T ~ 1 4 . 2 3 8 - 1 C . 2 2 6 - 1 7 . 2 4 0 1 . 3 8 0 TESTS OF THE POPULATION SUBMODEL 184; The major assumptions in the cohort survival submodel deal with the expected value of the f e r t i l i t y rate and the number of migrants to the area. The three f e r t i l i t y rate assumptions are outlined in Chapter 6 and the differences that they make to the projections can be seen in tables 26-28 there. There is only one assumption made concern-ing migration in Chapter 6. The number of migrants is determined by the migration submodel which relies upon the projected number of jobs in 1976 and 1981 to generate migrants over the period. The test of the population submodel involved the following data inputs: 1. The use of 1961 population as a base, 2. Average B.C. mortality 1961-66 by age and sex group, 3. The same age distribution of migrants as the population sub-model since that distribution was calculated for the period now to be projected. The sex distribution used was that which applied to the 1961-66 period, 4. Three assumptions regarding f e r t i l i t y rates. These were, that f e r t i l i t y rates: (i) remain at the 1961 B.C. level throughout the period, ( i i ) are 10% lower than the B.C. rates throughout the period, ( i i i ) are equal to the average f e r t i l i t y rate over the period, assuming that the f e r t i l i t y rates decline in each five year period. The amount of decline is determined by the same regressions as were used in Chapter 6. 185 5. Three assumptions regarding migration over the projection periods: (i) migration is equal to actual migration, ( i i ) migration is projected by the migration submodel which receives the actual number of jobs in 1966 and 1971 as input, ( i i i ) migration is projected by the migration submodel which receives the number of jobs projected by the employment submodel for 1966 and 1971 as input. The migration assumptions may be seen as progressively adding more sources of error to the estimation. The percent error of estimates produced by these varying assumptions in 1966 and 1971 are shown in Tables B.7 and B.8. The effect of trending the participation rate was also tested. The average of actual participation rates over the period was used as well as the average participation rates produced by the same trend equation as was used to produce participation rates for the 1971-81 period. The labour force, calculated by applying these participation rates to the projected population, was compared to the actual number of jobs in 1966 and 1971 and to the projected number of jobs for those periods. Unemployment rates were calculated. The unemployment rates are presented in Tables B.9 to' B.12. The population submodel generally overprojects population as is seen in Tables B.7 and B.8. The employment underprojects the 186 TABLE B.7 PERCENT ERROR OF TOTAL POPULATION ESTIMATES FOR 1966 Migration Assumptions F e r t i l i t y Assumptions High Medium Low Actual Migration 3.083 1.964 2.039 Migration Projected Using Actual Jobs 4.992 3.871 3,947 Migration Projected Using Projected Jobs 5.002 3.880 3.956 TABLE B.8 PERCENT ERROR OF TOTAL POPULATION ESTIMATES FOR 1971 1971 PROJECTIONS BASED ON 1966 PROJECTIONS Migration Assumptions F e r t i l i t y Assumptions High Medium Low Actual Migration 2.239 .217 -2.041 Migration Projected Using Actual Jobs 6.182 4.118 1.779 Migration Projected Using Projected Jobs 3.327 1.267 -1.065 187 number of jobs as seen from Tables B.4 and B.5. This leads to high unemployment rates when the two submodels are run together (column 2 of Tables B.9 - B.12). When the unemployment rate is calculated using actual jobs in 1966 and 1971 the rates remain high in 1966 but become very low (often negative) in 1971. These negative rates are troubling. They could be a result of the age distribution of migrants that was assumed. This age distribution was calculated as an average of the 1956-71 period. On the whole, this average is less than the 1966-71 distribution of migrants in the labour force age groups. (See Table 23 of Chapter 6). It would then be logical that the unemployment rate calculated for migration assumption 2 be positive in 1971 even though others are negative since that estimate of migration is the highest estimate for the 1966-71 period. The main purpose of the unemployment rate is as a consistency check between the models. As such, i t seems to show that the gap between the projections of the two models is quite large and increases in the second projection period. This is probably due to an accumulation of error. 188 TABLE B.9 ESTIMATE OF 1966 UNEMPLOYMENT RATE USING AVERAGE ACTUAL PARTICIPATION RATES OVER THE PROJECTION PERIOD TO CALCULATE THE LABOUR FORCE Migration Assumptions Employment Actual Employment Projected Employment Actual Migration 11.04 11.35 Migration Projected Using Actual Jobs 13,08 13.38 Migration Projected Using Projected Jobs 13.09 13.39 TABLE B.10 ESTIMATE OF 1966 UNEMPLOYMENT RATE USING AVERAGE PROJECTED PARTICIPATION RATES OVER THE PERIOD Migration Assumptions Employment Actual Employment Projected Employment Actual Migration 11.21 11.52 Migration Projected Using Actual Jobs 13.24 13.54 Migration Projected Using Projected Jobs 13.25 13.55 189 TABLE B . l l ESTIMATE OF 1971 UNEMPLOYMENT RATE USING AVERAGE ACTUAL PARTICIPATION RATES OVER THE PROJECTION PERIOD TO CALCULATE THE LABOUR FORCE Migration Assumptions Employment Actual Employment Projected Employment Actual Migration -2.93 18.29 Migration Projected Using Actual Jobs 1.58 21.87 Migration Projected Using Projected Jobs -1.80 19.19 TABLE B.12 ESTIMATE OF 1971 UNEMPLOYMENT RATE USING AVERAGE PROJECTED PARTICIPATION RATES OVER THE PERIOD Migration Assumptions Employment Actual Employment Projected Employment Actual Migration -3.30 18.00 Migration Projected Using Actual Jobs 1,23 21.59 Migration Projected Using Projected Jobs -2.17 18.90 

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