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Modelling inter-provincial migration between British Columbia and other Canadian provinces during 1966-1970 Dabestani-Sharifabad, Alayar 1975

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MODELLING INTER-PROVINCIAL MIGRATION BETWEEN BRITISH COLUMBIA AND OTHER CANADIAN PROVINCES DURING 1966-1970 by ALAYAR DABESTANI-SHARIFABAD B.A., University of Tehran, Iran, 1969 M.A., University of Tehran, Iran, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION in the Faculty of Commerce and Business Administration We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JANUARY, 1975 I n p r e s e n t i n g this thesis in partial fulfillment, of the requirements fbr an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t permission f o r extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the Head of my Department or h i s r e p r e s e n t a t i v e . I t i s understood t h a t copying o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permission. Faculty of Commerce and Business Administrati The University of British Columbia Vancouver, B.C. January, 1975 i i ' ABSTRACT . In studying population, the migration component i s the most d i f f i c u l t component to analyze effectively. The main purpose of this thesis i s to analyze and quantify the migration flow between Bri t i s h Columbia and other Canadian provinces during the period 1966-70 and develop a model which is capable of forecasting this inter-provincial flow with some known probability of accuracy. In this regard the different data sources which are available are evaluated. Income Tax Return data are found to be more reliable and are available in more detai l ; therefore, this source is used. To find the best possible method of measuring migration flow different methods of migration were considered and theoretical models were found to be more sophisticated and accurate than others. Amongst these various theoretical models, the push-pull theories are the basis of the most theoretical hypotheses of this model. Linear step-wise and ordinary multiple regressions analysis, using computer "UBC TRIP" package' are the methods of investigation used to test the hypotheses. The two complete and simpler models of i n - and out-migration and the complete model of net-migration for B.C. during 1966-70 have been tested. The combination of cross-section and time series analysis with 30 observations for 5 years and 6 regions in Canada (B.C. excluded) at 1 percent significant level with the total of 8 independent variables are the major components underlying the operational results. Distance, unemployment rate, climate, friends and relatives in other provinces were found to be the best explanatory variables. Also, climate was found to be an important variable to attract the migrants to B.C., while high unemployment rate has been the major factor of out-migration from B.C. Finally, some area for further research toward improving the quality of data which can have significant outcome on modelling internal migrations have been sketched. i i i TABLE OF CONTENTS T i t l e Page ABSTRACT ' i Table of Contents i i List of Tables / 7 i i i CHAPTER I Introduction 1 CHAPTER II Basic Concepts and Definitions 4 CHAPTER III Quality Evaluation and Explanation of the Data Sources: 8 on Internal Migration 1. Census Data 8 2. Registration System 11 3. B.C. Tel Data 11 4. Family-Allowance Transfers Data ' 12 .5. Income Tax Return Data 15 6. The Relationship between Income Tax Data and 20 Family-Allowance Data Conclusion 21 CHAPTER IV Methods of Measuring Internal Migration 22 1. Comparative Forecasting 22 2. Historical Trends as an Instrument to Forecast 23 Future Migration (a) Graphic and Mathematical Extrapolation 23 (b) Ratio Method 24 3. Using Direct Census Data 25 iv T i t l e Page • • / ' CHAPTER IV Methods of. Measuring Internal Migration (Cont'd.) 4. Residual Methods or Using Indirect Census Data 27 (a) V i t a l Statistics Method 28 (b) Survival Ratio Method 29 5. Theoretical Models / / 29 Conclusion / 31 CHAPTER V A Review of Current Inter-regional Migration Models 32 1. Size-Distance Theories Model 33 2. Market Mechanism or Economic Opportunity Model 37 3. Push-Pull Theories Model 3 9 4. Input-Output Model of Internal Migration 42 5. Probabilistic Theories Model 4 3 6. Cost-Benefit Model • 44 Conclusion 47 CHAPTER VI The Model 48 Introduction 48 A Theoretical Approach to Migration 48 Theoretical Hypotheses 50 An Operational Test of the Model: The Regression 56 Results (a) The Complete Model 56 1. In-Migration Flow 58 2. Out-Migration Flow 63 3. Net-Migration Flow 66 (b) The Simpler Model 70 V T i t l e Page CHAPTER VI The Model (Cont'd.) Theoretical Problems and Deficiencies of the Model 73 Conclusion 74 t} Area for Further Research and Recommendations on Data Improvements 75 BIBLIOGRAPHY 77 APPENDIX A 83 I APPENDIX B 90 v i LIST OF TABLES Table Page 1. Inter-provincial Migrants Aged 5 Years and Over by Province of Residence in 1966 and 1971 . 10 2. Inter-provincial Movement of Family as indicated by Family-Allowance Transfers Data 1946-73 14 3. Out-Migration from B.C. to Other Provinces and Foreign Countries in 1966-71 Using Income Tax Data 17 4. In-Migration to B.C. from Other Canadian Provinces and Foreign Countries in 1966-71 Using Income Tax Data 18 5. Net-Migration in B.C. during 1966-71 Using Income Tax Data 19 6. Hypothetical Relationships Between Dependent and Independent Variables . 55 7. Mean and Standard Deviation of the Variables / .57 8. Coefficient Correlation Matrix of In-Migration to B.C. . 59 9. Multiple Regression Results of the Complete Model of In-Migration to B.C 60 10.. Partial Correlations between each Independent and Dependent Variables 62 11. Correlation Coefficient Matrix of Out-Migration from B.C 64 12. The Coefficients and Multiple Regression Equations of Out-Migration from B.C , 65 13. Partial Correlations Matrix of Out-Migration from B.C 67 14. Coefficient Correlation and Partial Correlations of Net-Migration in B.C 68 15. Multiple Regression Coefficients for Net-Migration in B.C. during 1966-70 69 CHAPTER I. Introduction Inter-provincial and inter-state migration are a subject of increasing study in Canada and the United States. Numerous attempts have been made to model spatial mobility and thereby s c i e n t i f i c a l l y account for observed regularities in pattern, flows and composition. 1 On the importance of studying migration and i t s effects on the planning and decision-making process, 2 L.O. Stone says: Migration i s an important component of population change, particularly when viewed from the stand-point of a local community. It i s at once an indicator and a generator of social and economic changes, altering the size and the demographic . and socio-economic compositions of population. Through such alteration i t influences the growth potential of a community and the extent to which the community experiences certain social and economic problems. Migration in a society may or may not result in efficient allocation of resources. It may contribute to the rapid development or underdevelopment of 3 a region. Simon Kuznets summarizes the relations between migration and economic development: Internal migration and the redistribution of population by residence among various parts of the country are a major way in which people respond to changing economic opportunities emerging in the course of economic growth. 1. Andrei Rogers. An Analysis of Inter-regional Migration in California, (Berkeley: University of California, 1965), page 1. 2. L.O. Stone. Migration in Canada: Regional Aspects, (Ottawa, DBS, 1969), page 4. 3.. Simon Kuznets "Introduction", in Hope T. Eldridge and Dorothy Swaine Thomas, Population Redistribution and Economic Growth: United States, 1870-1950, Vol. III. Philadelphia, 1964, page 23. 2 People do not migrate solely for economic reasons. Social and other non-economic factors influence an individual's decision to migrate (or not to migrate). In the present study economic and social; demographic and environmental factors 4 rather than only economic factors have been considered. For the purposes of migration projections, attempts have been made to build a model which tries to , .. relate migration in a systematic way to a set of measurable explanatory variables for which reasonable projections already exist or can be prepared readily. The main purpose of this study i s to describe and analyse some of the major factors of migration, namely, inward and outward migration in Br i t i s h Columbia. An attempt has been made to build a mathematical model which can predict future trends of migration with exogenous variables that are easy to predict. • Most migration models, for the lack of data, supposedly, consider only net migration flow (the difference between in-migration and out-migration flow.) This report views i n - and out- migration separately. Consequently, in this report, two models of in-migration and out-migration between Bri t i s h Columbia and six other Canadian Regions 5 have been'produced. Furthermore, internal migration^ may be approached from two different points of view: migraton streams and migration differentials. These are not mutually 4. As w i l l be shown in following sections, most of the migration studies have considered only labour force population as active and representative of the whole migrant population. 5. These six Canadian Regions are: 1-Alberta, 2-Saskatchewan, 3-Manitoba, 4-0ntarip, 5-Quebec, 6-Atlantic (Substitute for the 4 Provinces of Newfoundland, Nova Scotia, New Brunswick and Prince Edward Island.) 6. Internal Migration Uses versus Of External Migration: Considering Immigration and Emigration of people which is the movement out of the boundaries of a country. 3 exclusive conceptualizations; each concentrates on a p a r t i c u l a r aspect of migra-t i o n . A migration stream i s that volume of migrants departing from any one area of o r i g i n f o r any area of d e s t i n a t i o n during a migration i n t e r v a l . A migration d i f f e r e n t i a l i s the d i f f e r e n c e i n c h a r a c t e r i s t i c s between migrants and non-migrants and the d i f f e r e n c e between various types of migrants. Studying migration d i f f e r e n t i a l i s the subject matter of demographic analysis of migrant and therefore not considered i n t h i s study. This study concentrates on the migration streams between B.C. and the other Canadian regions and focuses on the volume and d i r e c -tions i n place-to-place movements rather than the demographic aspects and char-a c t e r i s t i c s of migrants. To t e s t the degree of accuracy and estimation of the model stepwise and ordinary mu l t i p l e regression a n a l y s i s with the combination of c r o s s - s e c t i o n and time-series analyses with 30 observations have b een used. To f i n d the best data sources the r e l a t i o n s h i p between the Income Tax F i l e r s Data and the Family Allowances . Transfers Data, which has been discussed and shown i n the text,' have been tested and found to be very high, but because the a v a i l a b i l i t y and being i n d e t a i l , the former sources of data have been used. 4 CHAPTER II. Basic Concepts and Definitions 1 , . Before beginning the analysis of migration and attempting to build a mathematical model, i t is desirable to establish some basic definitions and to explain a few principles of migration research. Additional concepts and definitions of migration w i l l be introduced when a particular problem i s discussed. Migration: The essential character of migration is change in the place of usual residence in a specified period of time or as a change of residence from one c i v i l division to another. It is possible to get different types of migration, such as inter-regional, inter-provincial, intra-provincial, inter-urban, rural-urban and the l i k e . ; — Migrant: A migrant i s a person who has changed his usual place of residence from one migration defining area or boundary to another at least once during the migration interval. 1. To obtain the concepts and definitions, the following sources have been used: -- United Nations, Department of Economics and Social Affairs, Methods  of Measuring Internal Migration, Manual IV, 1961 (New York, U.N. Publications), pages 1-4. - Hamilton, C.H., "Practical and Mathematical Considerations in the Formulation and Selection of Migration Rates", Demography, No. 2 (1965), pages 429-443. - D.J. Bogue, HJS. Shryock and S.A. Hoermann, Subregional Migration in  the U.S., 1935-40, (Ohio: Miami University, 1957), pages 1-14. - M.V. George, Internal Migration in Canada:. Demographic Analysis (Ottawa, DBS Publications, .1970), pages 5-8. - L.O. Stone, Migration in Canada: Regional Aspects, (Ottawa, DBS Publications, 1969), pages 6-8. 2. This boundary can be either municipal boundary or provincial, county, rural, urban and the l i k e . Migration I n t e r v a l : This i s the duration of the study. I t can be d e f i n i t e ; e.g., one year, f i v e years, etc. or i t can be i n d e f i n i t e ; e.g., the l i f e - t i m e of the population a l i v e at a given date. Area of O r i g i n (departure): For migration, the area (or place) from which a move i s made i s the area of o r i g i n . Area of Destin a t i o n ( a r r i v a l ) : The area i n which a move terminates or the place which a migrant selected f o r the beginning of a new l i f e i s the area of d e s t i n a t i o n . Immigrant: An immigrant i s an i n t e r n a t i o n a l migrant entering the area of de s t i n a t i o n from a place outside the country. Emigrant: Emigrant i s an i n t e r n a t i o n a l migrant, departing to another country by cr o s s i n g an i n t e r n a t i o n a l boundary. External or I n t e r n a t i o n a l Migration: Refers to the movements of immigrants and. emigrants wi t h i n two d i f f e r e n t countries by crossing i n t e r n a t i o n a l boundaries. The d i f f e r e n c e between immigrants and emigrants i s r e f e r r e d to as net external migration. I n t e r n a l Migration: This term r e f e r s to the movements of migrants wi t h i n a l i m i t e d boundary of a country or geographic u n i t to another area within the same country. Migration Stream: A migration stream i s the t o t a l number of moves made during a given migration i n t e r v a l that have a common area of o r i g i n and a common area of d e s t i n a t i o n . Migration D i f f e r e n t i a l or S e l e c t i v i t y : This term r e f e r s to the character-i s t i c s of migrants such as age, sex, economic status, ethnic o r i g i n , l e v e l of educational achievement and the l i k e . Migration d i f f e r e n t i a l s are usu a l l y the common subject of demographic analysis of migration and hig h l y dependant upon the a v a i l a b i l i t y of past data f o r comparison. 6 Migration Rates: Some analysts use migration rate and some migration ratio. In this study migration rates w i l l be used and applied when the amount of migration i s divided by the population exposed to the likelihood (risk) of migrating, or, in other words, those potential population which have the same probability of movements. Choosing the needed rates depend upon the kinds of migration data used, on the objective of analysis, and on such practical matters as convenience or ease of calculation, customary practice, and popular understanding of what a migration rate means. (Hamilton, 1965, page 429). In-Migration: Every movement is an out-migration with respect to the area of origin and an in-migration with respect to the area .of destination. An in-migrant i s thus a person who enters an area of destination by crossing i t s boundary from some point outside the areas but within the same country. In-Migration Rate =. the total number of in-migrants in the specified migration interval by the total population of the sending area. Symbolically: TIN-MI G ; In-Migration Rate = A-=»BC ? A Out-Migration: An out-migrant i s a person who departs from an area of origin by crossing i t s boundary to a point outside i t , but within the same country. Out-Migration Rate = the ratio between the total number of out-migrants to an outside area to the total population of the origin. Symbolically: OUT-MIG Out-Migration Rate =• BC—»A P B C Net-Migration: Net-migration refers to the balance of movements in the opposing directions or the algebraic difference between in- and out-migration in the specified areas and time intervals. Net migration is a purely mathematical concept and there is no net migrant in the real world. A plus sign denotes a net migration gain and a minus sign denotes a net migration loss, referred to as net in-migration and net out-migration. Net-Migration Rate = the ratio between the. total algebraic net-migration to the multiplication of the population of the area of origin and the area of destination. Symbolically: NET-MI G - , Net-Migration Rate = BC P x P A BC : Which each rate can be multiplied by 100 or as common practice by 1000 • or else depends upon the need of the researcher. Gross-Migration: Gross migration refers to all'movements within the specific definitions of migration that is being applied or in other words, gross migration is the algebraic total of in- and out-migration in specified areas and time intervals. Gross migration is usually used to Illustrate the significance of total moves and mobility of populations within two regions. 8 CHAPTER I I I . Quality Evaluation and Explanation of the Data Sources  on Internal Migration There are a number of sources of data that can be used to measure internal migration. Each has i t s own advantages and disadvantages. In this section attempt w i l l be made to explain and evaluate each possible source of data i n Canada which can be especially useful for a study of B.C. migration. 1 1. Census Data: Census data have been and s t i l l are the major sources of 2 information on internal migration in most countries of the world. The •census data i n Canada conducted completely each ten years and part i a l l y being modified each five years since 1921 by the Federal Agency of Dominion Bureau of Statistics (established in 1918) which in 1971 has changed i t s name to Statistics Canada. In census enumeration, the usual questions about internal migration are: place of birth, place of last residence; duration of residence in the place of enumeration and place of residence on a specific date before the census. The main deficiencies of the census data are: - Errors on the respondents' side such as: faulty memory; faulty know-ledge; misunderstanding of the question; deliberate f a l s i f i c a t i o n for social, p o l i t i c a l or prestige reasons and boundary changes of the geographical units without awareness of the respondents. 1. At the end of this research, a few recommendations w i l l be made with respect to possible improvement in the quality of data sources. 2. United Nations, Department of Economics and Social Affairs, Population Studies, Methods of Measuring Internal Migration, 1970 (New York, 1970), page 3. - Errors on the enumerators' side such as: not giving the respondent enough time to think (does not exist in the case of mailing census); careless .entry on the schedule and misunderstanding of the question and answer. - One of the main problems i s that the timing of migration i s unknown and five years census i s very long. - The census data do not reflect: A - the mobility of persons who died or l e f t Canada between two censuses. B - Multiple moves during the five or ten years period are not included and hence i t underestimates internal migration. Change of definitions and the geographical units in census, makes i t d i f f i c u l t especially for intra-provincial migration for comparison. In the context of Current Census data, this deficiency may be illustrated by the following example In B.C. ten census divisions were established iii 1929 for the 1931 census. They were p a r t i a l l y modified for the 1956 census and have now been discontinued and 3 replaced by the 29 newly created regional d i s t r i c t s in 1971 census. (Table 1 shows the inter-provincial migrants using census data.) With the above defi-ciencies i n census data, the registration system is the better solution for measuring the internal migration. 3. Statistics Canada, Catalog No. 92-712, Vol. 1 - Part 1, Feb.1973. o TABLE 1 Interprovincial Migrants Aged 5 Years and Over  by Province of Residence in 1966 and 1971 Province of Residence in 1966 Nfld. P.E.I. N.S. N.B. Province Que. of Residence in 1971 Ont. Man. Sask. Alta. '• B.C.. Yukon Newfoundland _ 340 3,440 1,740 2,230 17,885 675 285 800 1,445 50 Prince Edward Is. 225 - 2,180 1,335 635 3,565 265 125 505 600 5 Nova Scotia 2,380 1,975 - 7,635 4,345 25,730 1,660 620 3,300 6,075 65 New Brunswick 1,140 1,310 8,315 - 7,905 18,555 1,360 490 2,i55 3,115 20 Quebec 2,145 755 6,090 9,315 99,435 4,330 1,575 7,755 16,740 170 Ontario 6,290 3,060 18,805 12,450 48,370 - 18,245 6,845 ' 23,550 47,395 495 Manitoba 210 400 1,825 1,405 4,630 23,875 - 9,425 17,410 26,915 250 Saskatchewan 180 95 840 475 1,515 11,810 16,365 - 41,910 29,920 465 Alberta 425 190 2,000 1,130 3,305 17,655 7,190 10,575 — 58,915 1,215 British Columbia 420 330 2,490 1,195. 4,740 21,210 6,310 6,085 27,765 _ . 2,560 Yukon 15 15 80 75 ? 90 745 125 80 645 1,960 Northwest Terr. 140 - 105 130 220 830 380 250 1,770 1,105 210 From Outside Canada 4,035 1,500 13,150 9,015 137,620 438,010 31,510 11,730 59,880 114,695 895 Province of Res. in 1966 not stated 6,165 1,285 10,165 7,225 73,080 90,240 12,130 9,805 22,995 43,770 1,045 Total In-Migrants 23,770 11,255 69,485 53,125, 288,685 770,035 100,545v 57,890 210,440- 352,660 7,445 Source: Statistics Canada, Migration Data, 1971 Census, May 31, 1974. Total 0 N.W.T. Migrant 30 105 160 140 400 1,115 550 805 2,225 1,055 130 925 1. Excludes Canadian Stationed abroad in the Armed Forces or Diplomatic Service. 11 2. Registration System: Registration systems population as used in different European countries and Japan are potentially an excellent source of data for the study of past trends on migration. The usefulness of the registers for analyses of internal migration depends upon the way in which they are designed, i t s completeness and i t s periodic assembling of s t a t i s t i c a l data. Various techniques for population registration include: legal identification of individuals, electoral r o l l s , selection for military service, social 4 security records and tax l i s t s . As Walter Isard (1960, page 59) has ; mentioned registers have never been used in the United States and Canada. In the absence of continuous population registration, some limited data of a similar character may be available from such sources as special local censuses, school enrollment data, social security and unemploy-ment insurance data, city directories, wartime rationing-registrations, draft registration and the lik e . Such a system can provide accurate, reliable and sufficient data sources on internal migration. In Canada attempts are being made to use this system such as using tax f i l e r s data which i s the main data sources of this research. 3. B.C. Tel Data: Doing intra-regional or intra-provincial studying of internal migration, one of the reliable sources of data can be the Brit i s h Columbia Telephone Company which has activity almost a l l across the province of B.C. The information that could be collected i s : - Month and year of telephone no. assignment (or the date of in-migrating to the area) 4. Walter Isard, Methods of Regional Analysis: An Introduction to Regional  Science (Massachusetts: The M.I.T, Press, 1960), page 59. 12 - Telephone p r e f i x and area code of previous telephone (or where d i d they come from?) - Occupation - M a r i t a l status - Dwelling tenure Unfortunately, as f a r as i n t e r n a l migration i s concerned, a l l of the above information r e l a t e d to the head of the family without knowing the number of dependents. Also t h i s information i s a v a i l a b l e only f o r persons who have t h e i r own phones. This data covers m u l t i p l e moves and can be more accurate than other data sources. B.C. T e l data would be more u s e f u l i f questions were included, such as: the number of dependents; how long d i d they stay i n the previous address; and b i r t h p l a c e . I t would then be one of the best sources of data on i n t e r n a l migration. 4. Family-Allowance Transfers Data: Another data source f o r i n t e r n a l migration i n Canada i s Family-Allowance Transfers data. These s t a t i s t i c s show the i n t e r n a l migration of f a m i l i e s with c h i l d r e n e l i g i b l e f o r allowances by o r i g i n and des t i n a t i o n . They are published monthly by the Family Allowance D i v i s i o n of the Department of National Health and Welfare. The data are administrative s t a t i s t i c s c o l l e c t e d by the family allowance branch when a change i n address occurs. In t h i s report the annual sums of these monthly t r a n s f e r s a s . i n d i c a t o r s of m o b i l i t y flows w i l l be used which means that m u l t i p l e moves of the f a m i l i e s are included. The main d e f i c i e n c i e s of the data are: - i t covers only f a m i l i e s with c h i l d r e n ; - no d e t a i l i s a v a i l a b l e f o r each c i t y , separately; - i t doesn't include the presumably more mobile group of s i n g l e people and young f a m i l i e s without c h i l d r e n ; 13 - i t gives Information only on migration streams and not migration differentials Family-Allowance Transfers data has a very high correlation coefficient with the Income Tax Filers data. This correlation is discussed further in Section 6. Table 2 shows the interprovincial movement of families i n : to and from British Columbia between April 1946 and March 1974 based on Family-Allowance Transfers data. 14 Table 2 Interprovincial movement of family as indicated by Family-Allowance Transfers Data 1946-73 Period In-Migration Out-Migration Net-Migration to B.C. From B.C. In B.C. 1946 6,950 3,344 + 3,606 1947 8,262 3,144 + 5,118 1948 6,119 3,772 + 2,347 1949 5,101 4,333 + 768 1950 4,551 4,459 + 92 1951 5,996 4,377 + 1,619 1952 6,248 4,742 + 1,506 1953 6,044 5,250 + 794 1954 6,103 4,871 + 1,232 1955 7,082 4,156 + 2,926 1956 9,505 4,543 + 4,962 1957 5,887 6,137 - 250 1958 5,731 5,910 - 179 1959 5,852 5,280 + 572 1960 5,722 5,481 + 241 1961 5,831 5,546 + 285 1962 6,653 5,227 + 1,426 1963 5,378 7,544 - 2,166 1964 5,559 8,577 - 3,018 1965 10,906 5,779 + 5,127 1966 11,810 6,575 + 5,235 1967 10,304 6,958 + 3,346 1968 9,563 6,541 + 3,022 1969 11,183 6,983 + 4,200 1970 10,720 7,199 + 3,521 . 1971 11,106 7,312 + 3,794 1972 11,014 7,080 + 3,934 1973 10,877 9,626 + 1,251 1. Source: Department of National Health and Welfare. Family Allowances Statistics. 2. Each period begins from April of that year to the March of the immediate next year. 15 5. Income Tax Return Data: The Regional and Urban Research and Development Division of Statistics Canada has developed useful information about the move-ment of tax f i lers by age and sex. The basic data on population movement are year-to-year address changes of those persons f i l ing personal income tax returns. Each computer print-out table gives the gross flows between two areas, the net flow, and the error range of the estimates. Each table also contains, for comparison, the total out-flow from each area. Each f i l e has the following information: - Locality code for the current year. t - Locality code for the previous year. - Age of f i l e r . - Sex of f i l e r . - Marital status of f i l e r . - A mobility code indicating international movement. In another sample f i l e , they tried to estimate the number of dependents and their sex and ages. The advantages of the Data are: - It gives information about In-, Out- and Net-Migration separately. - It is in very flexible format and is in enough detail classification to be useful for a l l kinds of migration studies. - It gives the degree of the conservative error range of each printed figure. The deficiencies of the Data are as follows: - The number of dependents and the age groups of each moving f i l e r is an estimation of the available information in the f i les . 16 - It is only in annual bases and doesn't cover the multiple movement of tax f i l e r within a year. - It underestimates the mobility of population. - The delay factor in the availability of the Data poses problems: at present, only 5 observations are available for regression analysis. In this study Income Tax Return Data have been used, though the relationship between the Income Filers data and the Family Transfers data is very high and they can be substituted. This relationship will be shown in the next section. Tables 3-5 show In-Migration, Out-Migration and Net-Migration in B.C. during 1966-71 using Income Tax Return Data. More detailed information about the migration flows which are based on the Income Tax Return Data has been shown in Appendix A. TABLE 3 Out-Migration from B.C. to other Provinces and Foreign  Countries in 1966 - 71 Using Income Tax Data From B.C. • • To: Year • Alberta Saskatchewan Manitoba Ontario Quebec Atlantic Northern Foreign Total 1966-67 11,020 2,986 2,425 7,996 2,211 1,057 1,155 4,819 33,669 1967-68 11,550 3,107 3,018 8,960 2,012 1,123 1,322 7,298 38,390 1968-69 11,890 2,889 " 3,133 9,394 2,010 1,146 1,639 8,546 40,647 1969-70 11,806 2,214 2,460 9,489 2,150 1,420 1,907 9,377 40,823 1970-71 12,508 2,937 2,998 10,363 2,445 1,799 1,869 9,304 44,223 1966-71 58,774 14,129 14,033 46,202 10,828 6,545 7,892 39,345 197,748 Source: Statistics Canada, Regional and Urban Research and Development, Dec. 1973. TABLE A In-Migration to B.C. from other Canadian Provinces and  Foreign Countries in 1966 - 71 Using Income Tax Data To B.C.: From: Year Alberta Saskatchewan Manitoba Ontario Quebec Atlantic Total 1966-67 19,695 7,641 9,577 14,466 3,787 2,070 82,840 1967-68 16,721 7,019 7,509 13,723 4,039 1,917 80,350 1968-69 18,614 8,167 7,239 15,861 4,943 2,381 81,744 1969-70 23,071 12,706 8,651 18,189 6,486 3,209 97,753 1970-71 19,804 10,006 7,244 16,731 5,738 2,411 85,917 1966-71 97,907 45,538 | 40,220 78,968 24,944 11,987 428,603 Source: Statistics Canada, Regional and Urban Research and Development, Dec. 1973. TABLE 5 Net-Migration in B.C. during 1966 - 71  Using Income Tax Data Year Alberta Saskatchewan Manitoba Ontario Quebec Atlantic Northern Foreign Total 1966-•67 + 8,675 + 4,655 + 7.152 + 6,470 + 1,576 +1,013 +280 +19,350 + 49,171 1967-•68 + 5,171 + 3,912 + 4,491 + 4,763 + 2,027 + 794 -155 +20,957 + 41,960 1968-•69 + 6,724 + 5,278 + 4,106 + 6,467 + 2,933 +1,235 -157 +14,511 + 41,097 1969-•70 +11,265 +10,492 + 6,191 + 8,700 + 4,336 +1,789 -395 +14,552 + 56,930 1970-•71 + 7,296 + 7,069 + 4,246 + 6,368 + 3,293 + 612 -289 +13,099 + 41,694 1966-•71 +39,133 +31,409 +26,187 +32,766 +14,166 +5,442- -716 +82,468 +230,855 Source: Statistics Canada, Regional and Urban Research and Development, December 1973. 20 6. The Relationship Between Income Tax Data and Family-Allowance Data Since most of the internal migration researchers in Canada have used the Family-Allowance Data (in the absence of the Income Tax Data) and using the Income Tax Data in this research, I was eager to see how these two sources of data are related and whether or not or in what degree of accuracy one can substitute one of them in the absence of another. To test the relationship, I have run a simple linear least-square regression analysis. Y represents the income tax filers in region A moving to region B (dependent variable) and X is the families of region A which moves to region B (independent variable). The regression of Y on X with the 18 observations for the years 1968-69 to 1970-71 are as follows: Migration Flow Dependent Variable Independent Variable Correlation Matrix Intercept Co-efficient Standard Error of Estimate Significant Level 2 R In-Migration Income Tax F. Allowance .97 765.1 5.78 .37 , .05 .94 Out-Migration Income Tax F. Allowance .98 -.38 4.60 .22 .05 .97 Gross-Migration Income Tax F. Allowance .96 -66 A2 5.63 .30 .05 .91 With these high correlations (.96-.98) and R (.91-.97) the relationship between the two data sources is significant. They are therefore substitutes for one another in relation to high correlation and low standard error of estimates in five percent significant level. 5 . Vanderkamp has found the similar relationship between the two sources of data in 1964 with the correlation coefficient of 0.98 and R2=.961 which are quite close to the conclusion of this report. See John Vanderkamp, "Inter-regional Mobility in Canada: A study of the Time Pattern of Migration", Canadian Journal of Economics, Vol. 1, No. 3 (Aug. 1968), page 599. 21 Conclusion; The studies of different data sources on migration in Canada reveal the fact that, there are not any completely and absolutely reliable and accurate sources of information yet, but among these available sources, the annual Income Tax Data are more fl e x i b l e and In more detail than others. Population Registers i s the best theoretical source of information on migration. Census data on interprovincial migration i s a reliable source with certain limitations, but, because of changes i n definitions, they are not useful for time series analysis of certain periods i n intra-provincial studies of migration. Family Allowances Data are available only for net-migration and deal with the people who have children and are not representative of the highly mobile people with no children at a l l . B.C. Tel Data related only to the family heads and the persons who own phones but show inter-movements of people in certain migration intervals very well. The relationship between the Income Tax Data and the Family-Allowance Transfers Data i s very high and i n the absence of one of them another can be used. This substitution has certain b u i l t - i n limitations which should be considered. 22 CHAPTER IV. Methods of Measuring Internal Migration In population studies, migration seems to be the least explained of a l l and is certainly the most unpredictable factor. In this regard, N.A. Humphreys in the 1880's commented that*: Migration was rather distinguished for its lawlessness than for having any definite law. There are different types of measuring internal migration from very simple to the most difficult and sophisticated one. Selecting any of them depends on the time data sources, accessibility to the computer and knowledge of the researchers. Some of the methods are useful only for measuring the past trends and some for both past and the future. The advantages and disadvantages of the most common methods are discussed in the following paragraphs. 1. Comparative Forecasting: In this method, the future growth of the study area is assumed to follow the pattern of another older area whose earlier growth has exhibited characteristics similar to those anticipated for the study area. By selecting a pattern area whose growth is substantially completed, the 2 entire course of growth of the study area is defined. This method is the least satisfactory method of measuring internal migration because: 1. No exact comparable pattern areas are available; 1. E.S. Lee, "A Theory of Migration", Demography, 3 (1966), page 47. 2. Walter Isard, Methods of Regional Analysis: An Introduction to Regional  Science, chapter 2, "Population Projection", and chapter 3, "Migration Estimate", pages 5-79, (MIT, 1960). 23 2. The future trend of the growth of an area may not be similar to the past trend of a similar area; 3. Migration decisions are influenced by certain factors such as social, political, economic and natural phenomenon which can not be equal in two areas; Considering the above limitations of this method, there are not enough reasons to agree with the current popular opinion that the future trend of migration in B.C. will follow the same trend as existed in California, or similar area. 2. Historical Trends as an Instrument to Forecast Future Migration: There are different ways which migration can be predicted when using the past known trends. These are: (a) Graphic and Mathematical Extrapolations: Graphical extrapolation is perhaps the easiest way of forecasting migration which most of the time has unsatisfactory results. The 3 procedure has been described by Walter Isard as: determine migration totals or rates for some desired sequence of periods in the past; f i f a trend line or curve to the data by use of freehand, graphic or mathematical methods; and extra-polate to obtain total migration for desired periods in the future or to obtain future rates of movement. This process is only valid i f we assume that the relationships that have existed in the past will continue to exist in the future and with the same intensity. Mathematical extrapolation assumes that past population growth has followed some law to which future growth w i l l continue to conform and also mathematical refinements and statistical tests are possible with the expected future variations in the factors of migration growth. In these methods, the 3. Ibid, page 64. 24 longer the past trend periods, the better the results, only i f anything extra-ordinary hasn't happened which, obviously in this case, will cause changes to the future trend. These extrapolative methods are mostly used to check the forecasts made by other methods. (b) Ratio Method The ratio method is similar to the comparative method but with improvements.' In this method, a present and future relationship among the factors causing growth is postulated while in the comparative 3-1 technique the regions needed to be similar to each other. The general different assumptions of the ratio methods which may b.e applicable in internal migrations can be summarized as: a. It assumes that migration for a given area in the future is a simple function (e.g. a percentage) of total population growth of the area. b. It assumes that migration in an area relates to total population growth of some other (larger) area, such as the nation, for which there exists a population forecast. c. It assumes that migration in a given area can be predicted i f there exists forecasts of migration in a different area. d. And finally, migration can be determined by possible determinants of migration, i.e., economic opportunity, social and political phenomena may be natural factors. Accuracy of this method depends upon the correctness of the particular relation-ship selected to establish the ratio. The major weakness of this method as is 3-1 Ibid, page 65. 25 true for the previous mentioned methods is its dependence on the past trend of migration. This method is often used for open regions such as cities whose growth may be linked to national growth. 3. Using Direct Census Data: This method i s useful only when attempts have been made to determine the past trends of migration. In the census enumeration, questions such as: place of birth, place of residence x years ago, duration of last residence will be asked which are the basis of estimating intercensal migration. The simple procedure is to subtract the place of birth information for the earlier census from that of the later census. To show i t symbolically^ assume: 1^ , 0^, and are the in-, out- and net lifetime migrants, respectively at the fi r s t census in province A; 1^* (Xjt ML, are the corresponding migrants in the second census in the same province A; then the net number of intercensal migrants in A would be: M = ( I 2 - 02) - (Ix - 01) = M2 - Mx 4. An "open" area is an area which migration movements is not controlled or directly counted, such as a city, province or regional district while a "close" area is an area which control or enumeration are affected such as a nation. 5 . M.V. George, "Estimation of Inter-provincial Migration for Canada from Place of Birth by Residence Data, 1951-61", Demography, (Feb. 1971), Pages 123-139. 26 This procedure of estimating net intercensal migration is subject to errors in the basic data, and errors caused by mortality, return migration, multiple movements and international migration. Also, this formula gives an estimate of the number of surviving net migrants and not total inter-censal net migrants. The effect of mortality can be considered by studying its effect on the estimates of intercensal net in-migration (^-I^) and net out-migration (C^-O^). To do this let's further assume: S is the overall intercensal survival ratio; * P is the proportion of surviving in-migrants among 1^, who were enumerated at the second census; Surviving in-migrants to A during the intercensal period who were enumerated in the second census; Surviving out-migrants from A during the intercensal period who were enumerated in the second census; then, the number of life-time in-migrants to A at the second census, I^* is equal to: SM ±-SM0 = i 2 -.^-(Ij-S) I± + SM± - (l-DSI^ 27 and the number of out-migrants from A enumerated in the second census will be6: °2 = °1 " ( 1 " S ) 0 l + S M0 " < 1 - p ) S O i This method underestimates the volume of internal migration, because i t does not include multiple movements of migrants during the intercensal period. In this method, the shorter the intercensal period, the better the measurement of internal migration. 4. Residual Methods or Using Indirect Census Data: This method estimates migration using intercensal demographic data., Any change in the population between two dates for any given geographic area is the result of natural increase (births minus deaths) and net migration. So, i f we know the changes in population at two points of time (by the census) and' knowing the number of births and deaths in the same periods (by either vital statistics or survival ratio), the number of migrants are simply the difference of actual and expected^humber of population in the later census. Two residual methods are discussed here: 6. Complete discussion of this method can be found in the following sources: - M.V. George, "Internal Migration in Canada: Demographic Analysis", DBS, 1970, pages 17-30 and pages 233-243. - Walter Isard, "Methods of Regional Analysis; An Introduction to Regional Science", MIT Press, 1960, pages 56-58.n - M.V. George, "Estimation of Interprovincial Migration for Canada from Place of Birth by Residence Data, 1951-61", Demography, (Feb. 1971), pages 123-139. 28 (a) Vital Statistics Methods Vital Statistics method assumes that, in the absence of population migrations, the growth of the population of a given area over a given period of time will be equal to the difference between births and deaths in the area. Any difference between this theoretical change and the actual change, is defined as net-migration during the period. This method also assumes that reliable vital statistics of births and deaths of the residents of the given area are available. The estimate of net migration, then would be: N e t M i - < P t +n,i " Pt,i> " < W where for any given area, Net = net migration for an age grouping i , P , is the population at the earlier census for the age grouping i , t, i P... . is the population at the later census in age group i , B. and D. t+n,i i i are the number of -births and deaths within the age group i , respectively, that occurred to residents of the area during the intercensal period. The accuracy of the estimates for any given level of age group classi-fication depends on the accuracy of statistics on population, births, deaths, as well as the age grouping of the data. The main deficiency of this method is that i t gives only the estimates of net migration. With this method i t is not possible to determine the origin of the in-migrants or the destination of the out-migrants. Not knowing the area of origin and destination, studying the inter-regional migration is almost impossible. 29 With the method, i t is possible to find a relatively small net migration into an area while the amount of in-migrati.on and out-migration is very large or vice versa. This method tends to underestimate the number of migration, because i t doesn't include multiple movements of the migrants during the intercensal period. (b) Survival Ratio Method When the vit a l statistics on the births and deaths are inadequate, this method may be used. This method involves the use of survivorship proba-b i l i t i e s . The basic information required are the number of people at two successive cenuses and a set of survival ratio, obtained either from l i f e tables or census data which can be applied to the population at the first census in order to derive an estimate of the number of persons expected to survive to the second census. The difference between the enumerated popu-lation at the second census and the expected population is the estimate of net migration. This method has disadvantages similar to those mentioned in the Vital Statistics methods and is less accurate. Theoretical Models: In the recent years, most of the researchers in migration areas attempted to identify the factors which affects the migration in a given area. In such models, the relationship between these factors as independent variables with the migration rate as dependent variable and their solution either by a) multiple regression analysis, b) simultaneous equations, c) simulation analysis or d) systems approach are used to explain the past trend and forecast the future trend of migration. 30 In multiple regression analysis, which has been used in this report, linearity has been assumed with the form of equation of: M i j = b0 + b l X 1 + b2 X 2 + ™ + bn X n + u0 Where x^, x^* > represent the values taken by the several independent variables such as, climate, income differentials, unemployment rates, and etc., and b^, b^t » b^ are constant coefficient which can be either positive or negative and M „ represents migration from i to j and UQ is error term. Any coefficient, say b2» indicates the change in M^ . to be associated with a unit change in the corresponding variable x 2 when allowance has been made for the other independent variables. Most of the theoretical models emphasize the costs and returns of the migration in the terms of cost-benefit analysis for a migrant. Economic factors, especially comparison of job opportunity in the origin and destination are the most important factors which can influence the decision to migrate, but in this study other factors such as social, natural and environmental variables as well as economic factors have been considered. The main disadvantages of this technique are: *"• - It assumes that causal relationships existing in the past or present will continue to operate in the future with the same relative intensity. - High correlation coefficients are sometimes misleading, since a high degree of correlation implies no necessary causal relation-ship between the dependent and independent variables. - Certain conditions are necessary i f the derived statistical in-ferences are to be valid. These are such that multivariable normality must exist for establishing the significance of co-efficients. Linear assumption is not always true and multi-31 collinearity between the independent variables are the most constraints of this method. Conclusion: There are different methods of measuring internal migration from the simplest one such as graphical extrapolation to the most difficult theoretical models. Any method of measuring internal migration is not a complete method and each one has its own advantages and disadvantages. The basis of selecting them depends on the availability of data, time, cost and the knowledge of'researchers. Comparative analysis and graphical and mathematical extrapolation methods, are the simplest and least satisfactory methods i f our objective is to forecast migration flow with a certain degree of accuracy, they wholly depend upon the past trends and can not be the basis for forecasting. Direct or indirect measures of the census data with application of either vital statistics or survival ratio are reliable measurements only for net migration which cannot be indicators of in-migration or out-migration. Theoretical models are the most sophisticated and elaborate methods and have significantly contributed in the past ten years to the explanation of the importance and magnitude of major general factors which can affect the decision of a migrant. In this report multiple linear regression analysis has been used to build a suitable theoretical model of internal migration in B.C., which is discussed in the following chapter. 32 CHAPTER V. A Review of Current Inter-regional Migration Models In the previous section we reviewed the different methods of measuring internal migration. In this section most of the current migration models will be reviewed. The number of theoretic models of internal migration have greatly increased in recent years. Researchers believe that migration is clearly patterned and with accurate data and advanced mathematical models may be forecast with a resonable degree of accuracy. There are six distinct conceptual approaches to modelling migration: - Size-Distance theories models, - Market Mechanism or Economic opportunity models, - Push-Pull theories models, - Input-Output models, - Probabilistic theories models, and - Cost-Benefit models. Each one of the above migration model categories has adopted specific mathematical expression: for example Size-Distance theory models have been formulated as gravity models, push-pull theories models as regression models, and probabilistic theories models as stochastic processes and simulation models. Each model views either economic factors, and or behavioral factors as important phenomena which influence migrants. This section will briefly review some of the most important models of internal migration. Attempts will be made to support each model with an example. 33 1. Size-Distance Theories Models*: Size-Distance theories models (also called gravity models) are based on the Newtonian Gravity concept. Gravity models of migration are quite simplistic and do not have much explanatory power. Size-Distance theories oriented models merely specify that migrants are attracted to an area because of the size or its attractiveness and better availability of job opportunity and that they are inhibited by their distance from i t . The assumptions of a general gravity model can be shown symbolically as: M.. - K f(s) where: = the number of migrants from i to j ; K = constant derived from actual data; f(s) = a function of size or the attractiveness of the two areas; and f(d) = a function of distance between i to j . 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 receiving areas and uncertainty 2 about prospects in the new area due to lack of information. Two well-known gravity types models worth mentioning here are Zipf's and Stouffer's models. 1. I have borrowed the titles from: Andrei Rogers, An Analysis of Inter-regional Migration in California, (Berkeley, 1965), pages 2-19. 2. P.R. Shaw, "Migration Theory and Fact: A Review and Bibliography of Current Literature", mimeograph, (1971). 34 Zipf hypothesizes that the total flow of migrants between two areas of i and j have direct relationship between population of i (P^) and population of j (P^) "and inverse relationship with the shortest transportation distance between them, (Dij). These relationships may be shown symbolically as: P P M = K l i l i 3 Dij 3 Zipf concluded that "The theoretical reasons for expecting that the inter-community movement of goods (by value) and of persons between any two communities, P^  and T^, are separated by an easiest transportation distance, D, will directly proportionate to the product, P^  x V^* a n (* inversely proportionate to the distance, D." Stouffer in his famous work in 1940 assumed4 that "There is no necessary relation-ship between mobility and distance." Instead Stouffer's model introduces the concept of intervening opportunities. It proposes that the number of persons going a given distance is directly-proportional to the number of opportunities at that distance and inversely proportional to the number of intervening oppor-tunities . Here, opportunities are defined in terms of total in-migrants. In a later 3. George K. Zipf, "The r l r 2 Hypothesis: On the Intercity Movements of D Persons", American Sociological Review, (December 1946), page 686. 4. Samuel A. Stouffer, "Intervening Opportunities: A Theory Relating Mobility and Distance", American Sociological Review, (Dec. 1940), page 846. 35 5 statement Stouffer changed some of his original definitions. Intervening opportunities now are defined as the total number of in-migrants to points lying inside a circle, not centered at i , but one having as its diameter, Dij, the straight line connecting i and j . His formula then becomes: M i _ » j = c M l i i where: Mi—*j = number of migrants flowing from i to j ; Mi. = total out-migration from i ; M.j =* total in-migration to j ; Kj - total number of in-migrants from a l l places; and M Q = total number of out-migrants from a l l places. Gravity models have been tested several times* and Stouffer's model provides better results. / The major deficiencies of the "Size-Distance" Model are: - They are not able to express causal structure of the movements. - The usual operational difficulties associated with gravity models are present. *. The bibliography of testing the Gravity Model is enormous. The literature i s surveyed In Gerald A.P. Carrothers, "A Historical Review of the Gravity and Potential Concepts of Human Interaction", 22 Journal of the American  Institute of Planners, 94-102, (May 1956); and in Walter Isard and David E. Brahmall, "Gravity, Potential, and Spatial Interaction Models," Ch. 11 of Isard et al., Methods of Regional Analysis: an Introduction to Regional  Science (The Technology Press and John Wiley and Sons: New York and London, 1960). 5 . , "Intervening Opportunities and Competing Migrants", Journal of Regional Science, 2 (Spring 1960), Pages 1-26. 36 - These models are essentially an extrapolation of observed data. - D remains constant as distance, while i t is indicator of transportation and psychic costs, and cannot be constant. Gravity models with the above deficiencies cannot be used for forecasting purposes. Therefore, in order to make i t more sensitive with the factors which influence a migrant, in the late 1950's a Dutch Demographer^, Somermeijer developed a new model on the basis of Zipf's Interactance Hypothesis with the help of indices of attractiveness (F) of each destination. Somermeijer's indices of attractiveness included such features"as per capita income, percent unemployed, degree of urbanization, recreational resources, and quality of dwellings^. His formula with dividing directional flows are as follows: (In-Migrants to j from i) M. . 1 *J (Out-Migrants from j to i) Mj—»l J*K + C(Fj - Fi)l P i P j >»(Dij)a %K - C(Fj - Fi) I P i P j W j ) * Gross migration is the sum of the above two formula, or the equivalent Zipf formula: (Dij) 3 6. An English-language discussion of Somermeijer's work will be found in H. ter Heide, "Migration Models and their Significance for Population Forecast", 41 Milbank Memorial Fund Quarterly, (Jan. 1963), pages 56-76. 7. Ira S. Lowry, Migration and Metropolitan Growth: Two Analytical Models 1966, pages 9-11. 37 2. Market Mechanism or Economic Opportunity Model: Comparative economic opportunity between the two areas is the driving motivational force which is manifested in inter-regional migration pattern. Migration of the labor force is important here, and according to this thesis, employment, opportunity of better occupation and salary are the major consideration in any decision to move. g In 1966 Ira S. Lowry proposed the following conceptual form of the model: M i - . j • K U. W. L, L 4 Uj W± Dij Where the symbols are defined as follows: M. . = number of migrants from place i to place j ; L. L. - number of persons in the non-agricultural labor force at i and j , respectively; U. U. = unemployment as a percentage of the civilian non-agricultural labor force at i and j , respectively; W. W. = hourly manufacturing wage, in dollars, at i and j , respectively; Dij = airline distance from i to j , in miles. This formula can be transformed in log form which is easy to use in a multiple linear regression: Log M±_^ - Log K + Log U ± - Log - Log W± + Log W^  + Log L ± + Log L^ - Log Dij 8. Ira S. Lowry, op_, cit., page 12. 38 Andrei Rogers in 1967 with a few modifications tested the Lowry's model for California and suggested the following modified formula as Lowry-Rogers model: "My - K IL WS, lF i . L F 1 Dij Where: My = number of migrants from i to j ; U. U. = civilian unemployment rate at i and j , respectively LF. LF. = labour force eligibles at i and j , respectively; WS. WS. = per capita wages and salaries at i and j , respectively, and; Dij = shortest highway mileage between the major county seats at i and j . Later, Rogers eliminated the unemployment variable (because of the unexplainable behaviour of it) and finally suggested the following model: WS. LF LF. 1 • J WS, Dij The log-transformed form of Rogers' model suitable in multiple regression anlaysis is: to8taMU = b0 + b i ^ n W S 1 + b2 L o g n W S j + b3 L o g n L F i + bu L o g n L F j + b5 L o g n D i j The market mechanism model has an accessible causal interpretation and the model assumes that the interchange between each pair of places is independent 9. Andrei Rogers, "A regression Analysis of inter-regional Migration in California", The Review of Economics and Statistics, (May 1967), pages 262-264. 39 of that between each other pair. This makes is possible to apply cross-sectional analysis on migration among places. The major deficiencies of this model are: - The relationships between migration and the independent variables cannot be interpreted strictly in terms of undirectional causation, in other words, i t cannot show the feedback relationships between dependent and independent variables. - It does not identify population subgroups whose migration behaviour may not be related to the values of the variables mentioned above*". - In this model non-economic factors such as behavioral or natural factors have not been considered. Although market mechanism, or economic opportunity model is superior to the Size-Distance model but because of its deficiencies and its inability to explain non-economic variables i t cannot be the basis of our forecasting purposes; thus, next we will try to explain the push-pull theory model which has over-corned some of the deficiencies in previous models. 3. Push-Pull Theories Model: Push-Pull theories of internal migration views causes of migration in both the origin and the area of destination for a migrant. Andrei Rogers summarized the theories as**: 10. P.R. Shaw and Chris Guild, Elements of the Population Submodel HPS, (Nov. 1972), mimeograph, page 5. 11. Andrei Rogers, An Analysis of Inter-regional Migration in California, (Berkeley, 1965), page 7. 40 Most commonly this point of view emphasizes the thesis that internal migration can best be explained as a response to changing economic opportunities brought about by the dif-ferential impact of economic growth....Higher wages, improved income opportunities, and better working conditions are typical economic variables that are cited along with those of a principally non-economic nature such as educational opportunities, and housing conditions. The "push" factors pressure a migrant to move from the origin to find a better opportunity and the "pull" factors in the destination attract the migrant with factors such as better job opportunities, better salary, better education, entertainment, better climate and other personal satisfactions. There are no "laws" of migration in this model, rather, each model-builder, depending on his study area, chooses certain factors such as socio-economic, psychological, political and natural environment and tries to relate them by the regression analysis. In the analyses, an attempt has been made to determine the influence of each factor acting simultaneously but independently of the others. The general form of the push-pull theories relations can be shown as: Y = b + b, x, + b- x- + + b x + u o 1 1 2 2 n n where: b Q = intercept or constant term; b. b_ —-, b = partial regression coefficient; x l j x 2 , X q = independent variables which reflect the characteristics of migrants and both the place of origin and destinations; 41 Y *» dependent variable which can be any migration rate (in-, out- or net-migration) or an absolute migration number;. u = residual term. 12 Donald Bogue in a very detailed analysis and tabulation of internal migration in the U.S., has pointed out that in studying migration, migration stream analysis should relate rates of in-, out-, and net-migration to differences in the socio-economic environmental conditions existing at both origin and destination area. He distinguished between Metropolitan and Non-Metropolitan areas and considered 12 independent variables. This model has many variables which makes i t difficult to test, but with the level of its operating difficulties 13 we agree with Lowry's conclusion as : Bogue's findings are impressive. On the whole, they point to the driving influence of employment differentials, educational attainment, and the mobility of white-collar • - employment. Tarver's model*^ is more sophisticated than Bogue's model. He included demographic variables as well as social and economic variables. He uses net-migration rate only and included interaction components in the model. The general form of Tarver's model i s : Y = b Q + Z± + Z 2 + Z 3 + Z XZ 2 + Z ^ + Z 2,Z 3 + Z 1,Z 2,Z 3 + U 12. Donald J. Bogue, Henry S. Shryock and Siegfried A. Hoermann, Subregional  Migration in the United States, 1935-40, Vol. 1, 1957, page 65. 13. Andrei Rogers, OP. CIT, page 9. 14. James D. Tarver, "Predicting Migrations", Social Forces, 39 (March 1961), pages 207-213. 42 Where: Y = 1940 - 1950 state net-migration rate; t>o • intercept; Z^  » set of economic variables; "* set of social variables; V Z^  • set of demographic variables; U = error term. In Tarver's model independent variables account for 72 percent of the variation ] in Y while the introducing of an interdependence contribution, he improved 26 percent of the predictive accuracy of a regression migration model. •Other push-pull models are similar though containing less independent variables and as a result most of them have less explanatory power. In this report, the chosen model is a series of push-pull models which will be . fully discussed in the next section. 4. Input-Output Model of Internal Migration: Esse Lovgren*^ in 1957 has followed an especially interesting and methodologically unique attempt to analyze the migration stream in Sweden using Leontief input-output model. He hypothesized that there is close association between a l l the in-migrants from different origins to a certain destination and a l l the out-migrants from this destination to a l l other places. 15. Esse Lovgren, "Mutual Relations Between Migration Fields: A Circulation Analysis", in Migration in Sweden: A Symposium, Eds. David Haunerberg, Bruno Odeving (Lunds, Sweden: Department of Geography, The Royal ' University of Lund, 1957), Pages 159-169. 43 In place of the usual focus on interindustry response to a given change in final demand in a typical input-output model Lovgren sets up an analysis of Sweden's interarea migratory response to a given change in the migration to Stockholm*^. The results are very impressive, however, Lovgren's method would be difficult to apply in Canada. The main reasons are: 1. Sweden has a registration population system which can be accessed to provide accurate sources of data. 2. The nature of the two countries are different (distance between the cities, information and others). 5. Probabilistic Theories Model: The probabilistic theories model generally adopts one of two directions: analytic or synthetic. The analytic approach views movement as a simple phenomenon wherein population units undergo changes of state according to a set of "transition" probabilities. In these models no causal structure is implied. The synthetic approach considers movement as a complex chain of events about which a great deal of empirical information is available. The problem here becomes one of synthesizing this piecemeal information, concerning various classes of units, into a stochastic process which has a reasonably close correlation to happenings in the external world*^. Probabilistic theories models are especially suitable for simulation on an electronic computer. However, they are very expensive in terms of computer time and need detailed data. 16. Andrei Rogers, OP. CIT, page 14. 17. Andrei Rogers, OP. CIT, pages 14-15. 44 Dan Price in 1958 has suggested the following formula which gives the probability 18 of an individual moving from one state to another PO^A^) = f(A,B,C,D) + f(X,Y,Z) + f(A,B,C,D) (X,Y,Z) where: I± = i t h individual; Aj = j*"* 1 area of origin; A^ «= k*"*1 area of destination. f(A,B,C,D) = function defining the individual's proclivity to migrate; f(X,Y,Z) = function selecting the appropriate point of destination in relation to the individual point of origin; f(A,B,C,D) (X,Y,Z) = interactions between the individual's characteristics and other areas. According to Price's conclusion, movement of a person from one area to another relates to the characteristics of the individual and the characteristics of the area of origin and destination. 6. Cost-Benefit Model: An early attempt to migrate may be considered within a general model of investment in human capital. The costs of the investment, such as moving costs, must be compared with the potential returns, such as the income differentials accruing to the transferred workers. 18. Dan 0. Price, "A Mathematical Model of Migration Suitable for Simulation on an Electronic Computer", in Proceedings of the International Population  Conference, (Vienna: International Union for the Scientific Study of Population, 1959). 45 19 Sjaastad's model • based on the cost-benefit model. He assumes that a person moves only If the value of a l l future monetary benefits from moving is greater than the monetary costs involved. 20 The cost-benefit model can be expressed by the following equations *1=1 (I + r ) J X where: Y ^ j = earnings in the j t b year at the destination; Y Q J = earnings in the j t b year at the origin; T = cost of moving;-N =• total number of years in which future returns are expected; r = rate of interest used to discount future earnings. The determination of the interest rate and the total number o f years (N) to be used in the above formula presents a problem which is typical of most cost-benefit analyses. 21 Paul Shaw gives a better illustration of a cost-benefit model including elements of decision-making process and amenity considerations. In the basis of his proposals, prospective migrants are not only concerned with, but are 19. Larry A. Sjaastad, "The Costs and Returns of Human Migration", Journal of Political Economy, Supplement on "Investment in Human Beings", Vol. 70, No. 5, Part 2 (1962), Pages 80-93. 20. Alden Speare, "A Cost-Benefit Model of Rural to Urban Migration in Taiwan", Population Studies, 1971, 25(1), Pages 117-130. 21. Paul Shaw and Chris Guild, OP. CIT, Pages 5-6. 46 able to calculate, expected pecuniary and non-pecuniary benefits of relocation. He uses the following decision-making formula to predict migration: where: M - migration of an individual (or homogeneous group) from i to j ; R\j = returns to the individual at place j ; = returns to the individual at i and costs foregone in relocating; I = earnings at place i and j specified to A = age, E = education, S = s k i l l level, Z = other socio-economic conditioners of earnings potential e.g. race, sex; U = probability of unemployment at place i or j ; A = non-pecuniary returns at place i , j ; ^ = costs incurred in moving to place i to j including physical costs, earnings, foregone while travelling and costs of installation at j . The cost-benefit model, attempts to explain internal migration in terms of its various causal factors. However, determining the time process for costs and returns as they occur and estimating actual accounting discount rates makes a definite conclusion very difficult to obtain. (some threshold value); 47 Conclusion; Examining, explaining and predicting internal migration has been the purpose of 'many studies in different countries during the past thirty years. For forecasting purposes, natural increase and ratio methods are not adequate, therefore theoretical models have been the subject of the most recent studies. Each model from the simplest one such as size-distance model to the most difficult probabilistic model has its own advantages and disadvantages. Use-fulness of each model depends on the knowledge of the model-builder, purposes of the study, availability of data and other factors. These factors will a l l be considered in the following chapter describing the development of the B.C. model. 48 CHAPTER VI. THE MODEL  Introduction: Most internal migration studies base their analytical framework on the classical model of factor mobility and resource allocation. Migration from i to j will occur i f Income (wage, salary and other disposable income) increases. Due to this increase in migration flow, allocation of resources are perfect and in the long-run a country will have economic adjustment or the efficinet allocation of resources. The underlying classical assumptions are: (1) the goal of maximizing income for each individual, (2) perfect knowledge of migrant about different areas, (3) migrants are many in number and homogeneous in skills and tastes, and (4) there are no barriers to mobility. This paper represents a model that considers economic aspects of migration, but also eliminates some of the unnecessary classical assumptions and substitutes more real l i f e variables. The following section consists of a theoretical approach to migration and some ex ante theoretical hypotheses. These hypotheses are tested with the aid-of multiple regression analysis. Finally, problems and deficiencies of this approach are examined and suggestions are made for further research. A theoretical approach to migration: There is no unique theoretical approach to migration. The important variable is the migrant himself. Migrants are selective people who differ from each other in terms of personal factors, their attitudes toward the future and meaning of l i f e and other values. Each migrant responds differently and finds his own unique solution. When we examine a l l the movements as aggregation, 49 there are four distinct factors which can influence any one decision. They are: 1) Factors associated with the area of origin, 2) Factors associated with the area of destination, 3) Intervening obstacles, and 4) Personal factors^. The combination of positive and negative factors at both the origin and destination may be differently defined for every migrant or prospective 2 migrant. Similarly, intervening obstacles may be perceived differently. Intervening obstacles are such things as distance and inconvenience of traveling. Personal sensitivities, Intelligence, and awareness of conditions 3 elsewhere also enter into the evaluation. It is difficult to develop a general theory of migration. The usual procedure is to examine the determinants of migration flow by making a theoretical hypothesis and then, testing the theories to find the causes of migration. However, causes and effects of migration may change over time and in the long-run may be different than in the short-run. The difference is often referred t 4 to as return migration. *"* In bringing a l l factors together, there are two approaches to explain migration theory: 1) Economic Behaviour Approach 2) Non-Economic or Behavioristic Approach 1. Everett S. Lee, "A Theory of Migration", Demography, 3 (1966), page 47. 2. Ibid, pages 50-51. 3. Ibid, page 48. 4. For further information on return migration refer to: John Vanderkamp, "Migration Flows; Their Determinants and the Effects of Return Migration", Journal of Political Economy, pages 1012-1031. 50 The economic approach assumes that individuals are rational in their decisions to move or to stay. Their decisions are based on costs and benefits in the future. The economic approach describes migration as a decision involving investment in human capital."* The behavioristic approach assumes that a migrant doesn't necessarily want to increase his money income, but is attempting to satisfy his needs.^ These needs can be either economic or non-economic factors such as climate, living with relatives or other natural and cultural phenomena. Considering a l l of the possible combinations in explaining migration flows, attempt is made here to hypothesize various factors of migration which seem most relevant for B.C. Theoretical Hypotheses: A decision to migrate is influenced by factors such as the area of origin, destination, personal factors and intervening obstacles. Obviously, an individual will migrate only i f the present value of expected future stream of inccme is greater than the cost of relocating and other foregone income at origin. Income here means a l l the possible benefits, not only monetary and tangible ones. Thus, an individual will tend to move i f the net benefit (benefits minus costs) is positive. In this section attempts will be made to isolate push and pull factors at the origin and destination and give a series of hypotheses which can be tested. Regional income differentials usually attract people (especially labour force) to move. The significance of this variable has been tested several times by 5 . See Sjaastad (1962) for this approach. 6. For more information on this approach see: Julian Wolpert, "Behavioural Aspects of the Decision to Migrate", Papers of the Regional Science  Association, Vol. 14 (1965), pages 159-169. 51 different researchers^ and in general can be summarized as: the present value of expected future income at the destination is an attracting factor to move and the present value of expected future income in the origin is an economic benefit foregone by moving. Therefore, we expect that the migration rate will be positively associated with the present value of the stream of income differences between the area of origin and destination. Income in this model is real disposable personal per capita income. Definition and detailed calculation are reviewed in Appendix B. Sources of hypotheses are the result of a l l previous migration studies and the current economic, social, political and natural conditions of the Province of British Columbia. Some of these hypotheses at the final testing are not significant (i.e. Dwelling starts) which will be shown later. The main theoretical hypotheses are the following; Hypothesis I: Internal migration is positively related to the real dis-posable personal per capita income between two regions i and j , the greater the income differentials between i and j , the higher the migration that will occur. Hypothesis II: The unemployment rate has a positive relationship with out-migration. Hypothesis III: The greater the unemployment rate in B.C. the smaller the in-migration to B.C., they are negatively related. A high unemployment rate can be a significant "push" factor of migration but 8 Canadian experiences show that when the unemployment rate is low, migration 7. See for example L.A. Sjaastad, "The Relationship between Income and Migration...", (1960), pages 37-64, and T.J. Courchene, "Interprovincial Migration and Economic Adjustment", (1970), pages 550-576. 8. John Vanderkamp, "Internal Mobility in Canada: A Study of the Time Pattern of Migration", Canadian Journal of Economics, 1 (1968), pages 595-609, T.J. Courchene, op. cit., page 554. 52 flow does not function entirely to increase in-migration. The reason is that the people in the labour force are interested in a relatively stable situation in making any decision to migrate, not just the unemployment rate which can have different trends at different times. Distance has been used in most of the migration studies and i t represents not only the costs of movements but as a proxy for the effect of the distance on information about economic opportunities in other regions. Also, i t indicates the earnings foregone during transition and the psychic costs and distribution of moving and uncertainty about income and job opportunities at the destinations. Therefore, Hypothesis IV: Migration rate between i and j is negatively related with the relative distance between i and j in relation to a l l other regions. In this view, relative distance has more effect than the simple distance between i and j . Hypothesis V: The lower (better) the climate index , the greater is the rate of migration. 10 In studying internal migration in Canada, specially for B.C., this variable seems to have the great influence. 9. The term lower climate index shouldn't be confused with the lower temperature. For more explanation refer to the Appendix B. 10. For more information about the Index please refer to Appendix B. In this Index the general climate index for B.C. has assumed 100 and the other regions will increase when the climate situation is not as good as B.C. 53 Hypothesis VI: The greater the number of friends and relatives in B.C., the better is the availability of information about B.C. and the higher will be migration to B.C. Therefore, they are positively related. As a proxy for friends and relatives, the number of persons born in i and living in j at the beginning of the period have been used. For more detail please see Appendix B. Hypothesis VII: The labour force participation rate is positively related to migration. The labour force participation rate is the ratio between the labour force and the population of 14 years of age and over. Hypothesis VIII: The greater the number of immigrants from other countries 0 to B.C., the higher is migration rate in B.C. Immigration rate in B.C. in relation to the natural increase of population is relatively high and this high rate has influence on the mobility of the existing population. Hypothesis IX: A relative change in dwelling starts in B.C. and other regions has positive relationship with migration rate. Dwelling starts rate was included, because other migration studies have considered i t to be important, but as we will see later i t is not significant in this model. As well, since housing starts respond to demand factors, the implicit causality of using starts as an independent variable to predict migration is suspect. Dwelling starts can by hypothesized as: The higher the dwelling starts in a region, the better are job opportunities for different skills and therefore, the higher is migration rate. Given this reasoning, employment would be a more suitable variable. 54 Hypothesis X: The independent variables of migration have a different relationship with in-migration and out-migration. Therefore, net-migration (the difference between in- and out-migration) can not be a good substitute. Most migration studies have considered net-migration rate. The most important reason is the lack of data. 1 1 Considering "push" and "pull" factors in the area of origin and the destination, each characterized by its own merits, i t is necessary to distinguish between in- and out-migration separately. 11. In Canada, most of the interregional migration studies have used the Family Allowance Data which before 1968, were given by net-movements of families of children the region's. 55 The above hypotheses can be summarized as follows: Table 6 Hypothesized Relationships Between Dependent and Independent Variables Variables Operational Definition DWELST Dwelling Starts Hypothesis Hypothesis Hypothesis In-Migration Out-Migration Net-Migration to B.C. from B.C. in B.C. pos. related pos. related pos. related CLIMTE Climate Index neg. related neg. related neg. related UNEMPR Unemployment Rate neg. related pos. related neg. related DISTCE Relative Distance neg. related neg. related neg. related INCOME Real Disposable Personal Per Capita Income pos. related pos. related pos. related LFPART Labour Force Participation Rate. pos. related pos. related pos. related IMMIGR Immigration Rate pos. related pos. related pos. related FRIEND Friend & Relatives pos. related pos. related pos. related pos. = positively neg. = negatively By testing those theoretical hypotheses with suitable statistical method, a model for internal migration in B.C. has been accomplished. 56 An Operational test of the model: the regression results 12 To make an operational test of the model, a regression analysis package has been used. To testing the complete model, step-wise regression was selected. In step-wise regression, independent variables are ranked according to their ability to reduce the variation in dependent variable that remain unexplained at each step. In the simpler model, ordinary multiple regression analysis was used. Normality of data and a simple linear relationship are assumed. The complete model using a l l 8 variables will be discussed first and then the simpler model using only selected variables. (a) The Complete Model: In the complete model of internal migration in B.C., 8 independent variables and 3 dependent variables have been used. Data sources have been shown in detail in Appendix B. Distribution of each variable around its mean, and the standard deviations of each variable are shown by the following table: 12. James H. Bjerring and Paul Seagraves, "UBC TRIP: Triangular Regression Package", Computer Centre, U.B.C., Vancouver, June 1974. 57 Table 7: Mean and Standard Deviation of the Variables Name Mean Standard Deviation In-Migration 5.74 4.74 Out-Migration 2.64 2.53 Net-Migration 0.0016 0.0014 Dwelling Starts 1.25 1.66 Climate 1.87 0.36 Unemployment Rate 0.82 0.39 Distance 1.38 0.70 Income Differentials 0.84 0.11 Labour Force Participation Rate 0.98 0.07 Immigration Rate 4.83 6.63 Friend & Relatives 0.17 0.10 The diversion of dwelling starts and immigration rates between the six regions outweigh a l l the rest. This model based on the combination of time series (5 years from 1966-70) and cross-sectional analysis. The number of observations are 30 which is the result of multiplication of the 5 years in 6 regions. 58 To find out the relationships between each variables their directions and the magnitude of this relationship, the following Correlation Matrix table has 13 been established. 1. In-Migration Flow The correlation coefficient matrix of in-migration to B.C. from the six other Canadian regions between 1966-70 are summarized in Table 8. One of the advantages of multiple regression analysis is its power of prediction. In this sense, step-wise multiple regression analysis have been used. The result can be summarized as Table 9. 13. A coefficient of correlation is an index of the direction and magnitude of a relation. The formula for calculation i s : where: x = fx - x and Table 8; Correlation Coefficient Matrix of In-Migration to B.C.' VARIABLE IN-MIG DWELST CLIMTE UNEMPR DISTCE INCOME LFPART IMMIGR FRIEND IN-MIG 1.00 DWELST 0.23 1.00 CLIMTE -0.33 -0.11 1.00 UNEMPR -0.67 -0.08 0.32 1.00 DISTCE -0.96 - 0 : 2 5 0.27 0.59 1.00 INCOME 0.25 0.03 -0.61 -0.68 -0.10 1.00 LFPART 0.43 0.09 -0.70 -0.60 -0.30 0.86 1.00 IMMIGR 0.25 0.31 0.10 -0.07 -0.16 -0.02 -0.10 • 1.00 FRIEND 0.57 0.15 -0.85 -0.67 -0.47 6.81 0.86 -0.03 1.00 Since the relationship between in-, out-, and net-migration and independent variables are different the results of in-migration to B.C. will be discussed f i r s t . 14. For the definition of variables, please see the Appendix B. The above table not only illustrates the direction and magnitude of each independent variable with the in-migration but the direction and magnitude of any other independent variables with another independent variable as well. The direction of relation in a l l variables are the same were hypothesized in the Table 6. In conclusion, the operational test of the model verifies the theoretical hypothesis which was made before. (15) Table 9: Multiple Regression Results of the Complete Model of In-Migration to B.C. Coefficient for Standard Equation Intercept X^  X^  X^  X^ 2 Error of No. DWELST CLIMTE UNEMPR DISTCE INCOME LFPART IMMIGR FRIEND R Estimate 1 -0.208 -0.128 (0.911) 1.975 (1.896) -0.451 (0.124) -5.475 (73.7) -4.294 (0.45) 11.689 (2.33) Q.098 (8.15) 11.680 (1.97) .961 1.099 2 -1.178 -0.133 (1.03) 2.177 (2.85) -5.624 (144.23) -2.889 (0.35) 10.866 (2.32) 0.097 (8.36) 12.157 (2.28) 0.96 1.076 3 0.021 -0.126 (0.96) 1.803 (2.65) • -5.802 (270.73) 8.694 (2.08) 0.092 (8.25) 9.047 (2.29) 0.96 1.061 4 -0.198 1.874 (2.88) -5.745 (273.3) 8.562 (2.02) 0.083 (7.32) 9.197 (2.37) 0.959 1.06 5 6.478 2.184 (3.92) -5.621 (268.23) 0.078 (6.266) 15.303 (13.04) 0.955 1.082 6 11.958 -5.79 (273.1) 0.084 (6 .'61) 8.176 (12.02) 0.948 1.14 7 12.738 -5.97 (250.78) 7.43 (8.34) 0.932 1.26 15 - A l l of the variables are significant at .01 level. - Degree of Freedom is(30-J^=29. - Bracketed figures beneath the regression coefficients are F-Ratio. 61 The f u l l regression equation of in-migration to B.C. during 1966-70 from other 6 regions with using Equation No. 1 can be written as: Y « -0.208 - O.mXj^ + 1.975X2 0.099X? + 11.68Xg In each step, the number of independent variables as has been shown in the table 9 was reduced. The 4 Independent variables: Climate, Distance, Immigration to B.C. and Relatives and Friends are the most significant variables, explaining 2 R = .955 or 96 percent of the variance of in-migration to B.C. It remains to explain the partial correlations between the variables. Partial correlations show the relationship between an independent and dependent variable holding a l l other independent variables constant. Partial correlations are shown in the following table 10: - 0.451X- - 5.475X. - 4.29X- + 11.689X£ + 3 4 5 6 0.961 R* = 0.95 1 6 —2 2 16. R is adjusted R for degree of freedom. Its formula is: K 2 - 1 - a-R2) where n is the number of observations, and k is the number of independent variables. CM Table 10: Partial Correlations Between Each Independent and Dependent Variables VARIABLE IN-MIG DWELST CLIMTE UNEMPR DISTCE INCOME LFPART IMMIGR Y - IN-MIG 1.00 Xj - DWELST -0.038 1.00 -X 2 - CLIMTE 0.371 -0.03 1.00 Xg - UNEMPR -0.239 * 0.125 -0.612 1.00 X, - DISTCE 4 -0.95 -0.207 -0.273 0.418 1.00 X5 - INCOME 0.274 -0.042 0.522 -0.704 0.54 1.00 Xg - LFPART 0.246 -0.02 0.186 -0.178 0.229 0.51 1.00 X ? - IMMIGR 0.45 0.287 0.098 -0.038 -0.202 0.145 -0.01 1.00 X g - FRIEND 0.49 0.035 -0.852 -0.522 -0.47 0.869 0.85 -0.124 1.00 63 As has been shown in Table 10, the least explained variable is dwelling starts and the best explained variables are distance, friend, immigration rate and climate. 2. Out-Migration Flow: To explain the complete operational model of out-migration from B.C. to other 6 Canadian regions during 1966-70 the same definitions and formula are used. The correlation coefficient matrix of out-migration which illustrates the direction and magnitudes of relations is contained in Table 11. The comparison of this table with Table 6 (theoretical hypothesis relationships) shows that a l l the hypothesized relations are correct except for the unemployment rate. Here, again distance (-0.87), friend (0.69) and climate (-0.64) are the most important variables in explaining out-migration from B.C. The relationship and coefficient quantities of variables and the multiple regression equations are shown in Table 12. The complete regression equation considering a l l of the variables for out-migration from B.C. as shown in Equation 1 of Table 12 i s : Y - -1.969 + 0.35^ - 0.22X2 + 1.912X3 - 3.106X4 + 0.226X5 + 0.637Xg - 0.014X? + 6.857X. R2 = 0.976, << = .01 9 VARIABLE IN-MIG DWELST CLIMTE UNEMPR DISTCE INCOME LFPART OUT-MIG 1.00 • DWELST 0.27 1.00 CLIMTE -0.64 -0.1113 1.00 UNEMPR -0.51 -0.081 0.32 1.00 DISTCE -0.87 -0.25 0.27 0.588 1.00 INCOME 0.35 0.034 -0.605 -0.679 -0.1 1.00 LFPART 0.59 0.093 -0.7 -0.598 -0.298 0.858 1.00 IMMIGR 0.017 0.309 0.104 -0.067 -0.164 -0.019 -0.099 FRIEND 0.693 0.13 -0.919 -0.493 -0.332 0.773 0.818 IMMIGR FRIEND 1.00 -0.149 1.00 ) VD (17) Table 12; The Coefficients and Multiple Regression Equations of Out-Migration from B.C. Coefficient for: Standard Equation Intercept X^ X^  X^  X^  X^  Xg" 2 Error of No. DWELST CLIMTE UNEMPR DISTCE INCOME LFPART IMMIGR FRIEND R Estimate 1 -1.968 0.035 (0.512) -0.219 (0.126 1.912 (15.581) -3.106 (167.01) 0.226 (0.007) 6.537 (5.61) -0.014 (1.01) 6.857 0.982 (8.27) 0.4 2 -1.978 0.035 (0.529) -0.2 (0.126) 1.88 (38.8) -3.09 (508.82) 6.68 (10.16) -0.013 (1.22) 6.98 .982 (13.87) 0.39 3 -2.426 0.03 (0.5) 1.92 (48.54) -3.1 (539.82) 6.64 (10.45) -0.013 (1.17) 7.55 .981 (62.87) 0.38 4. -2.42 1.94 (51.73) -3.12 (581.95) 6.65 (10.73) -0.01 (0.84) 7.62 .981 (66.01) 0.38 5 -2.51 1.96 (52.78) -3.09 (595.12) 6.64 (10.76) 7.74 .980 (70.33) 0.378 I 17. - Significant level of a l l the variables is .01. - Degree of Freedom is 29. - Bracketed figures beneath the regression coefficients are F-Ratio. 66 2 R in these 5 equations in Table 12 shows that by eliminating 4 independent variables, there is not too much change in the explanatory power of the equation. As a result, we can write the out-migration equation with only 4 independent variables as follows: Y - -2.5145 + 1.956X- - 3.095X. + 6.642X. + 7.745X-3 4 6 8 R2 = .975 oC = .01 As was explained in the previous section, partial correlation illustrates the explanatory power of each independent variable. Distance alone, can explain 98 per cent of change in out-migration. The importance of distance in most of the migration studies relates to the cost of moving, uncertainty at the destination, information effect, psychic costs and so on. Friend (86%), unemployment rate (82%), and labour force participation it rate (55%) are also important in explaining out-migration flow. 3. Net-Migration Flow: *•* Most of the migration studies in Canada, have chosen net-migration as their dependent variable. Gross migration data is seldom available. In this report emphasis is on gross-migration (in-, and out-migration) rather than net-migration. However, because of the necessities for comparison with other migration studies and testing fitness of the model with a l l of the three independent variables, a summary net-migration results will be explained below. The following table shows that correlation coefficient and partial correlations of independent variables with net-migration in B.C. during 1966-70. * The Partial Correlation Matrix of Out-Migration from B.C. is shown below. Table 13: Partial Correlations Matrix of Out-Migration from B.C. VARIABLE OUT-MIG DWELST CLIMTE UNEMPR OUT-MIG 1.00 DWELST 0.08 1.00 CLIMTE -0.032 0.526 1.00 UNEMPR 0.82 0.109 -0.35 1.00 DISTCE -0.98 -0.244 0.133 0.542 INCOME -0.085 0.082 0.256 -0.788 LFPART 0.55 0.014 0.064 -0.43 IMMIGR -0.184 0.31 -0.141 -0.046 FRIEND 0.859 0.049 -0.851 0.096 DISTCE INCOME LFPART IMMIGR FRIEND 1.00 0.78 1.00 0.195 0.585 1.00 -0.169 0.387 0.007 1.00 -0.817 0.55 0.76 -0.15 68 Table 14: Coefficient Correlation and Partial Correlations for Net-Migration in B.C. Algebraic Name Variable Name Coefficient Correlation Partial Correlation Y Net-Migration 1.00 1.00 *1 Dwelling Starts 0.126 -0.186 X2 Climate Index -0.022 0.703 X3 Unemployment Rate -0.661 0.053 X4 Distance -0.84 -0.81 X 5 Income Differentials 0.117 -0.233 X6 Labour Force Participation Rate 0.243 -0.132 X7 Immigration Rate 0.34 &. 304 X8 Friend (Information) 0.63 0.666 As Table 14 shows, the direction of variables are„same as was hypothesized in Table 6. Distance (81%), Climate (70%), Friend (67%) and Immigration rate (30%) are the most significant variables in explaining net-migration in B.C. The results of regression coefficients, R and standard error of estimates of net-migration (S.E.^.) have been summarized in the following Table 15. Table 15; Multiple Regression Coefficients for Net-Migration In B.C. during 1966-70 Coefficient for: Standard Equation Intercept X j ^ ^ ^ ^ X g X ? Xg 2 Error of N o - DWELST CLIMTE UNEMPR DISTCE INCOME LFPART IMMIGR FRIEND R Estimate 1 -0.019* -0.01 (2.29) 0.13 (7.69) -0.085 (1.23) -0.1 (13.12) 2 0.17 -0.0096 (2.14) 0.13 (7.84) -0.05 (0.56) -0.11 (17.32) 3 0.012 -0.01 (2.39) 0.16 (17.62) -0.12 (26.83) 4 -0.09 -0.01 (2.48) 0.16 (20.81) -0.14 (56.7) 5 -0.13 0.17 (21.71) -0.13 (51.21) 6 -0.149 0.18 (25.37) -0.136 (49.73) -0.46 (2.51) 0.4 (.95) 0.004 (4.92) 0.76 (3.94) .898 .00054 -0.27 (1.58) 0.0034 (3.998) 0.92 (6.87) .894 .00054 -0.18 (1.05) 0.0031 (3.61) (1.05) (12.09) .891 .00053 0.0033 (4.16) 0.81 (18.34) .886 .00053 0.0026 (2.55) 0.83 (18.5) 0.89 (20.78) .875 .862 .00055 .00057 18 - A l l of the variables are significant at .01 level. - Degree of Freedom is 29. - Bracketed figures beneath the regression coefficients are F-ratio. * A l l of the regression coefficients have been multiplied by 100. 70 Using equation number 1, the regression equation for net-migration would be: Y = -0.00019 - 0.0001X. + 0.0013Xo - 0.00085X, - 0.001X. - 0.0046X- + 0.004X, + 1 2 3 4 5 6 0.00004X7 + 0.0076Xg R2 = .898, o<= .01 R2 = .87 In each iteration step-wise multiple regression tests a new independent variable and its contribution to explaining the dependent variable. In comparison with others, i f i t is non-significant, i t will be dropped from the equation. Using this technique the best equation was: Y - -0.0015 + 0.0018X2 - 0.0014X4 + 0.0089Xg R2 = 0.862, R2 - .85 <* = .01 Using 8 independent variables leads to the problem of multi-collinearity. The simpler model with less variables reduces this problem. b. The Simpler Model: In this model, the results of the complete model have been used. In addition 19 the definition of friend and relatives have been changed. For brevity, only the equations and their specification for in-migration, and out-migration appear here. 19. In the previous model, the operational definition of the independent variable "Friend" for time t in j was the number of migrants in time t-1 from i who were living in j . In this model, this definition has changed to the multiplication of 5 i f there is only 1 year data, by 4 i f there are 2 years data available plus the previous year data and so on. For more explanation please refer to Appendix B. 71 At the significanat level of 1 percent and with 30 observations (degree of freedom 30 - 1 = 29) and substituting a T-test for the F-test the results of in-migration equation to B.C. during 1966-70 with using 5 independent variables are: L) In-Mig Ratio - 9.0437 + 1.322 (CLIMTE) - 0.5675 (UNEMPR) - 5.5076 (DISTCE) (4.46) (5.67) (4.99) + 0.0832 (IMMGR) + 11.2766 (FRIEND) „ (0.61) (6.44) R = .953, S.E.Y. = 1.124 (see footnote #20.j I The above equation can be substituted by a simpler equation with less variables by including 3 independent variables which seems are good enough to explain the pattern of in-migration flow. The regression equation of these 3 independent variables to explain in-migration to B.C. can be written as: In-Mig Ratio = 11.8729 - 5.7353 (DISTCE) + 0.0867 (IMMIGR) + 8.1414 (FRIEND) (4.99) (0.614) (6.44) R2 = .948, S.E.Y. = 1.1438 The simpler out-migration equation in the same condition as in-migration model (d = .01, DF = 29) with 5 independent variables i s : Out-Mig. Ratio = 0.9325 + 2.2914 (UNEMPR) - 3.3 (DISTCE) + 3.75 (INCOME) -(3.9) (2.64) (3.9) 0.0187 (IMMIGR) + 8.0394 (FRIEND) (-1.69) (5.35) R = 0.976, S.E.Y. = 0.43 20. The bracketed number below coefficients are the T-value. S.E.Y. = Standard Error of Estimate of Y (dependent variable). 72 If we exclude the two variables "income" and "immigration" for possible multi-collinearity the final equation of out-migration from B.C. to 6 other Canadian regions in 1966-70 would be: Out-Mig Ratio = 3.7124 + 1.567 (UNEMPR) - 2.944 (DISTCE) + 10.233 (FRIEND) (3.9) (2.64) (5.35) R 2 - 0.972, S.E.Y. = 0.4489 73 Theoretical problems and deficiencies of the model; Choosing the multiple regression method to test the model raises a few questions which make the analysis difficult. The major deficiencies of this method are: 1. Linear assumption of the model is not realistic. Some factors should be considered jointly since they are inextricably linked in determining migration. 2. Multiple regression, as a technique, is much less useful in accounting for migration streams between areas when tempting to consider a l l streams simultaneously. 3. Between the independent variables there are considerable degree of inter-dependency and multi-collinearity which the method has ignored. 4. The data have not been tested for normality and try to be standardized. Comparing the data and the results requires data sources which have been measured identically with the same degree of importance. The assumption of normality of the data requires more research. 5. Usually, multiple regression equations are used for prediction purposes. These equations assume the future trend of migration and their characteristics are the same as have been in the past. This assumption is simplistic and cannot be guaranteed to be continued in the future. 74 Conclusion: An individual migrant is influenced by different factors in making his decision. These factors may be at the origin or destination. They may be personal factors or intervening obstacles. A complete model is assumed to take into account a l l of these phenomena. With reference to "push" and "pull" factors at origin and destination and general characteristics of a migrant, a theoretical hypothesis can be made to indicate the future trend and pattern of migration flow. To test these hypotheses a model has been built based on past experiences and linear multiple regression analysis. Two operational tests have been conducted: "the complete" and the "simpler" one. The complete model is an elaborate model which gives a general equation with 8 independent variables on in-, out-, and net-migration in B.C., separately. Their correlation coefficients, partial corre-lations and the regression coefficients are stated. The simpler model on the other hand, ignores some of the independent variables which seem non-significant in explanation of the dependent variables. The method of multiple regression analysis, though i t is inadequate to explain a l l aspects of migration flow, is well-known, acceptable and allows easy interpretation of the results. Among a l l the independent variables, distance, unemployment rate, climate and the potential number of friends or relatives found to be the most important explanatory variables while dwelling start rates was not a significant variable. 75 Area for Further Research and Recommendations on Data Improvements: Two areas for further research and four suggestions about improvements in the quality of the data sources will be recommended here. 1. Analysis in internal migration requires an extensive data base. In the present study, data was only available for a five-year period. Since more Income Tax Filers Data will be available in the future, this will allow an update of this study. Furthermore, intra-provincial analysis of migration is possible with using those income tax data. Such a comprehensive analysis hasn't been done for British Columbia as the published available sources indicates. 2. "Path Analysis" and "Canonical Analysis" should be included in the multiple regression analysis. Path analysis is a method of determining the relative . magnitudes of effects of a given change in a certain network or a controllable variable. .Canonical analysis allows variables to interact simultaneously. Geometrically, the canonical correlation can be considered as a measure of the extent to which individuals occupy the same" relative positions in the P-dimensional space as they do in the q-dimensional space. Finally, i t is important to better standardize the data in using multiple regression analysis. 3. Since no complete data sources on internal migrations in B.C. are available, there are a few possible solutions to this important deficiency, namely: a) Population Registers are the best sources of internal migration flow. A few modifications and additions to the Driver's Certificate Application or the like would make them as equally valuable source for intra provincial migration. 76 b) The Hospital Insurance Benefits and the B.C. Medical Plan are the second best sources of data; however, they are not presently accessible and are not regularly published. c) B.C. Tel Data could be very useful i f i t included a few other questions on their request form from the clients and provided an attempt to tabu-late them in such a way to be useful in the migration research. d) Census definitions are not comparable between census periods. Any use of them historically is misleading. Comparative study of the different definitions (e.g. Census Divisions, Regional Districts, etc.) are desirable. And the final word, survey of migration with separate sampling when needed is very costly and inefficient which makes any of the above four suggestions more economically feasible. BIBLIOGRAPHY 1. Anderson, I.B. Internal Migration In Canada: 1921 - 61 - Study No. 13, Economy Council of Canada, Ottawa, Queen's Printer, 1966. 2. Antonova, I.F. 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"The Costs and Returns of Human Migration", Journal of Political Economy, 70 (Oct. 1962), pages 80-93. 54. Skene, P.A.T. Projection of Population and Industrial Employment In the Vancouver CM.A., Unpublished Master Thesis, U.B.C, The Department of Community and Regional Planning, 1974. 55. Stone, L.O. Migration in Canada: Regional Aspects Ottawa: Statistics Canada, 1969. 56. Stott, A.G.E. Influencing Interregional Migration, Unpublished Masters Thesis, U.B.C, The Department of Community and Regional Planning, 1974. 57. Stouffer, S.A. "Intervening Opportunities: a theory relating mobility and distance", American Sociological Review, 5 (845-867). 58. Systems Research Group. Canada; Economic Projections to the year 2000. Toronto, 1970. 59. Tarver, J.D. "Predicting Migration", Social Forces, 39 (1961), pages 207-213. 60. United Nations, Department of Economic and Social Affairs. Methods of Measuring Internal Migration, Manual IV, Population Studies, No. 47 (1961). 61. Vanderkamp, J. 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"The P ^ Hypothesis: On the Inter-city movement of Person", ~D American Sociological Review (Dec. 1946), pages 677-688. / 83 APPENDIX A In-Migration, Out-Migration, Immigration and Emigration Flows Between the 10 Census Divisions \ in B.C., other Canadian Provinces and the Foreign Countries from 1966 to 1970. 84 Sources of the data on this appendix are based on the Income Tax filers data. The ten census divisions in B.C. were established in 1929 for the 1931 census and they were partially modified for the 1956 and 1961 census. For the 1971 census they were totally replaced by the 29 newly created Regional Districts. Data for the foreign countries refers to the total immigration and emigration flows in that period between each Division and other countries. In order to obtain net-migration flows between the specified areas, i t is necessary to subtract each in-migration data from its corresponding out-migration data. The usefulness of these data in terms of their accuracy and reliability has been discussed in the main text. Table A-l: Total In-Mlgratlon and Immigration Flows between each Census Division In B.C and other Canadian Provinces and Foreign Countries in 1966-70 From: Year Division 1 D.2 D. 3 D.4 1966-•67 693 887 2, 121 8,372 1967-•68 486 769 2, 300 7,012 Alberta 1968-•69 738 773 2, 666 7,947 1969-•70 1 ,192 1,027 2, 839 9,520 1970-•71 1 ,500 808 2, 351 8,102 Total 1966-•71 4 ,610 4,264 12, 277 40,953 1966-•67 43 63 22 899 1967-•68 8 50 80 932 Atlantic 1968-•69 51 55 104 1,103 1969-•70 102 66 79 1,481 1970-•71 68 37 68 966 Total 1966-•71 272 270 353 5,380 1966- 67 174 541 522 16,851 1967- 68 204 637 728 19,965 Foreign 1968- 69 262 498 549 16,208 Countries 1969-•70 251 433 653 16,405 (Immigra- 1970- 71 370 497 687 14,722 tion) Total 1966- 71 1 ,261 2,606 3, 139 84,151 To: D.5 D.6 D.7 D.8 D.9 D.10 Total B 2,903 987 126 1,406 768 1,432 19,695 2,705 996 45 1,030 365 1,013 16,721 2,581 1,048 42 1,161 422 1,236 18,614 3,275 1,522 54 1,589 673 1,380 23,071 2,742 1,422 30 . 1,193 532 1,124 19,804 14,206 5,975 297 6,379 2,760 6,186 97,907 613 52 31 141 184 22 2,070 452 43 23 162 151 16 1,917 660 82 12 179 115 20 2,381 777 119 68 262 241 14 3,209 655 98 101 194 212 12 2,411 3,157 395 235 938 904 83 11,987 2,425 577 299 1,248 914 618 24,169 3,063 577 215 1,503 963 400 28,255 2,690 596 132 1,239 631 252 23,057 3,103 631 111 1,404 700 238 23,929 2,838 607 110 1,356 988 228 22,403 14,119 * 2,988 867 6,750 4,196 1,736 121,813 Table A-l: (Continued) Year Division 1 D.2 D.3 D.4 1966--67 126 225 596 5, ,670 1967--68 57 123 605 4, ,525 Manitoba 1968--69 67 106 724 4, ,226 1969--70 183 165 785 5, ,197 1970--71 166 111 572 4, ,320 Total 1966--71 599 730 3, ,282 23, ,939 1966--67 73 40 55 491 1967--68 10 33 97 525 Northern: 1968--69 73 80 89 619 1969--70 57 63 70 709 1970--71 60 112 122 643 Total 1966--71 272 329 434 2, 987 1966-•67 140 322 422 8, 819 1967--68 96 264 627 8, 648 Ontario: 1968--69 157 264 777 10, 509 1969--70 308 290 912 U, 569 1970--71 292 312 858 10, 321 Total 1966-•71 993 1,451 3, ,596 49, 866 1966-•67 23 86 75 2, 714 1967-•68 24 44 82 2, 971 Quebec: 1968-•69 69 48 163 3, 627 1969-•70 171 107 209 4, 690 1970-•71 108 86 176 4, 082 Total 1966-•71 395 370 705 18, 085 1966-•67 158 323 819 3, 207 1967-•68 135 209 1, 043. 3, 041 Saskatche- 1968- 69 229 365 1, 211 3, 394' wan 1969- 70 764 435 1, 847 4, 706 1970- 71 871 457 1, 297 3, 654 Total 1966- 71 2,157 1,788 6, 217 18, 002 D.5 D.6 D.7 D.8 D.9 D.10 Total 1,612 380 53 385 266 291 9,577 1,306 260 76 297 170 90 7,509 1,210 293 17 279 223 94 7,239 1,196 395 55 383 207 85 8,651 1,307 284 42 240 127 75 7,244 6,631 1,612 243 1,584 994 635 40,220 262 63 6 128 134 183 1,435 167 27 8 99 81 120 1,167 220 67 1 115 93 124 1,482 175 64 7 137 94 136 1,512 133 79 - 142 128 158 1,580 958 300 22 622 529 720 7,176 2,587 464 135 661 658 258 14,466 2,325 454 ' 85 568 521 135 13,723 2,499 437 92 628 390 108 15,861 2,957 579 108 765 587 114 18,189 3,057 466 128 679 506 112 16,731 13,424 2,400 548 3,302 2,661 727 78,968 403 81 93 102 131 79 3,787 470 52 50 123 175 48 4,039 609 90 50 99 174 14 4,943 647 183 43 209 221 6 6,486 633 165 32 177 248 31 5,738 2,763 571 269 709 949 178 24,994 1,373 431 40 699 237 354 7,641 1,260 430 13 479 174 235 7,019 1,441 489 22 561 173 282 8,167 1,994 967 57 1,128 505 303 12,706 1,532 705 47 773 402 268 10,006 7,600 3,022 179 3,640 1,491 1,442 45,538 Table A-2: Total Out-Migration and Emigration Flows between the Canadian Provinces, Foreign Countries and each B.C.'s Census Division in 1966-70 To; Year Division 1 D.2 D.3 1966-•67 606 797 719 1967-•68 545 868 934 Alberta 1968-•69 582 743 1,029 1969-•70 576 614 1,089 1970-•71 731 500 1,097 Total 1966-•71 3,039 3,522 4,868 1966-•67 20 56 17 1967-•68 23 48 28 Atlantic 1968- 69 19 40 39 1969-•70 28 70 60 1970-•71 39 62 57 Total 1966- 71 129 275 201 From: D.4 D.5 D.6 D.7 D.8 D.9 '4,131 1,162 575 67 1,190 472 4,590 1,254 534 68 935 454 4,844 1,046 564 50 • 1,029 459 4,911 1,500 627 50 909 412 5,403 1,442 668 34 1,057 487 23,879 6,404 2,969 269 5,120 2,285 416 313 32 25 74 85 492 345 32 5 69 55 596 240 16 17 57 72 637 428 44 3 77 49 926 365 94 14 82 130 3,066 1,692 218 64 360 390 D.10 Total (from B 1,301 11,020 1,368 11,550 1,541 11,890 1,118 11,806 1,089 12,508 6,416 58,774 19 1,057 26 1,123 50 1,146 24 1,420 30 1,799 150 6,545 I Table A-2: (Continued) To: From: Year Division 1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 D.10 Total (from 1966-•67 30 97 48 1, 485 309 103 42 161 77 73 2,425 1967-•68 51 109 133 1, 743 429 112 27 179 118 117 3,018 Manitoba 1968-•69 41 134 198 1, 897 320 107 11 166 80 179 3,133 1969-•70 28 59 108 1. 479 391 86 13 133 110 53 2,460 1970-•71 59 73 107 1, 727 467 94 42 217 178 34 2,998 Total 1966-•71 209 472 594 8, 330 1. 916 503 135 • 856 5,562 456 14,033 1966-•67 56 79 31 422 128 32 9 133 109 156 1,155 1967-•68 51 107 40 443 150 52 5 133 141 200 1,322 Northern 1968-•69 28 68 47 662 156 83 7 187 149 252 1,639 1969-•70 66 140 48 802 189 79 21 187 150 225 1,907 1970-•71 59 105 108 720 187 114 18 199 130 229 1,869 Total 1966-•71 261 499 274 3, 048 810 361 60 838 679 1,062 7,892 1966-•67 176 198 258 4, 912 1, 262 211 61 403 354 161 7,996 1967-•68 107 322 278 5, 727 1, 178 313 100 381 374 180 8,960 Ontario 1968- 69 83 323 275 6, 365 1, 036 304 77 359 393 179 9,394 1969-•70 89 190 308 6, 249 1, 463 207 74 413 412 84 9,489 1970-•71 136 230 339 7, 037 1, 327 247 51 488 430 78 10,363 Total 1966-•71 592 1,264 1,458 30, 289 6, 266 1,283 363 2,044 1,963 682 46,202 Table A-2: (Continued) To: From: Year . Division 1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 D.10 Total (from 1966-•67 45 73 25 1,557 246 37 26 98 87 17 2,211 1967-•68 29 78 33 1,423 195 38 20 71 87 38 2,012 Quebec 1968-•69 18 50 48 1,467 188 17 25 61 95 41 2,010 1969-•70 24 52 24 1,556 244 38 14 76 110 12 2,150 1970-•71 27 55 43 1,674 271 81 12 96 180 4 2,445 Total 1966-•71 144 309 174 7,676 1,144 210 97 . 403 559 112 10,828 1966-•67 146 162 199 1,122 420 111 15 517 149 145 2,986 1967-•68 113 166 212 1,243 436 207 44 344 201 141 3,107 Saskatche- 1968-•69 71 142 196 1,368 301 199 18 310 183 101 2,889 wan 1969-•70 64 103 166 952 399 139 7 162 114 108 2,214 1970-•71 111 136 • 231 1,315 438 182 16 289 129 90 2,937 Total 1966-•71 505 709 1,003 6,000 1,994 837 100 1,622 775 584 14,129 1966-•67 52 145 120 3,203 673 115 77 213 163 58 4,819 1967-•68 67 204 157 5,164 885 167 56 242 208 148 7,298 Foreign 1968-•69 63 194 232 5,939 1,089 193 55 • 315 273 193 8,546 Countries 1969-•70 94 198 300 6,513 1,172 210 55 370 329 136 9,377 (Emigration) 1970-71 116 232 256 6,384 1,169 273 45 437 311 81 9,304 Total 1966-•71 392 973 1,065 27,204 4,988 958 289 1,577 1,284 615 39,345 90 APPENDIX B Specifications and Definitions of the Variables and their Sources 91 In this appendix, attempt has been made to point out the data sources which have been used In the model. Definitions of each dependent and in-dependent variable and the way which each variable in the model has been calculated wi l l also be explained. 1. Dependent Variables; Dependent variables in this model are in-migration, out-migration and net-migration rates. In-migration rate has been defined as the ratio between In-migrants from each 6 regions to B.C. between 1966-70, to the total population of each sending area. Symbolically: IN-MIG. = IN-MIG.^ AB P. A Out-migration rate is the ratio between the total number of out-migrants from B.C. to each 6 regions to the total population of B.C. in 1966-70. Symbolically: OUT-MIG. = 0 U T- M I G-BA  P B . Net-migration rate is the ratio between the difference between In- and Out-migrants and the multiplication of both the sending and receiving regions. Symbolically: NET-MIG. = <IN-MIG-AB) - ^'^'B^ P A « PB Data sources for dependent variables are Statistics Canada: Regional  and Urban Research & Development and The Census publications. 92 2. Independent Variables To run the model, two sets of ordinary and stepwise multiple regression analyses have been used. Altogether, 8 independent variables have been considered: 1. Dwelling Starts Rate (DWELST): Dwelling start rate is the ratio between the annual percentage change in dwelling starts from each region vis-a-vis B.C. Further one-year time lags in the process of decision-making have been assumed. If we assume that: D S ^(A) = Dwelling Starts in time t-1 in Region A, and; D S t(B), D Sfc_1(B) = Dwelling Starts in time t-1 in B respectively. The formula for calculating the rate of change in dwelling starts would be as follows: This formula is similar to the calculation of elasticity in economics which measures the rate of change rather than the magnitude of absolute number. The data hve been obtained from the Central Mortgage and Housing  Corporation: Canadian Housing Statistics, 1973, Tablel2. D s t(A) = Dwelling Starts in time t in Region A, and; DWELST Rate = D St(A) - D S(._1(A) . D St(B) - D S ^ B ) 9 3 2. Climate (CLIMTE): In a country as large as Canada, measuring climate as a degree of per-formance for a potential migrant is very difficult. Mean daily temperature and its maximum and minimum, the number of frost free days, darkness, wind-chill, and precipitation can a l l be important in decision-making. In this regard, a Climatological Index Map for the use of Treasury Board Officials which evaluates the relative advantages and disadvantages of various isolated posts in Canada has been used. On the basis of this index map, the following climate index has been obtained: Region Index British Columbia . 100 Alberta 123 Saskatchewan 200 Manitoba 321 Ontario 162 Quebec 192 Atlantic 215 Northern 262 As these indices show, the greater the percentage of difference, the higher the probability to move.1 1. The climate information and the index map were kindly given to me by Mr. Phil Suckling, Ph.D., Department of Geography, U.B.C. 94 Unemployment Rate (UNEMPR): The unemployment rate is the number of unemployed persons expressed as a percentage of labour force (total employed and unemployed persons) 14 years of age and over. In the model, the ratio of unemployment rate between B.C. and other regions has been used. Statistics Canada "The Labour Force" is the data source for this variable. Distance Ratio (DISTCE): As an indicator of the distance variable, the highway mileage between chief metropolitan centres of the Canadian provinces has been used. In the model, the distance ratio is the highway mileage between Vancouver and the major city of another region to the average distance of that city centre to a l l other regions. Symbolically, the formula i s : DISTCE DISTCE = V >A DISTCE i = i 1 — * A / 5 The data source of this variable is the "Canada Yearbook 1972" by Statistics Canada. Income Differentials (INCOME): With the assumption of a one-year time lag, this variable is actually Real Disposable Personal Per Capita Income which has been calculated as follows: Total personal disposable income in any region has been divided by the population of that region in the same year to get per capita income. 95 This figure is divided again by the Consumer Price Index to obtain the real income figure. In the model this obtained value has been used as the income variable. Statistics Canada "The Economic Review, A General  Review of Recent Economic Developments" by John Turner, in April 1974, is the major source of this variable. Labour Force Participation Rate (LFPART): The labour force participation rate is the total male and female labour force (as a percentage of the population 14 years of age and over) expressed as a percentage of the population of 14 years of age and over. In the model, the ratio of labour force participation rate in each region to the equivalent rate for B.C. has been used. The data source is. "The  Labour Force" (71-201) by Statistics Canada. Immigration Rate (IMMIGR): Immigration rate is the ratio between the number of immigrants to each region and B.C. in each year during 1966-70. The formula for calculating immigration is the same as the elasticity formula which has been explained under Dwelling Starts. Statistics Canada is the data source of this variable. Information Rate (FRIEND): This independent variable is the number of persons born in " i " and living in " j " at the beginning of the period. To calculate this variable, the income tax return data is availabe for only 5 years (1966-70). In the fir s t year (1966) FRIEND equals the number of in- or out-migrants. In the second year (1967) FRIEND is the average number of the fi r s t two years. In the third year FRIEND is the average of the fi r s t three years, and so on. 96 The following two tables are the input data after final calculation and adjustment, as have been used in the model. 97 Table B-l: List of Input Data on the In-Migration to B.C. During 1966-70. Region Period Depen-dent vari- Independent Variables able UN- IN- LF- IM-IN-MIG DWELST CLIMTE EMPR DISTCE COME PART MIGR FRIEND (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 1966-67 11.41 1.12 1.23 .59 .41 .87 1.09 .78 .34 67-68 11.22 .98 1.23 .53 .41 .92 1.07 4.13 .34 Alberta 68-69 12.21 5.16 1.23 .59 .41 .91 1.06 .67 .34 69-70 14.8 .74 1.23 .46 • .41 .94 1.06 6.45 .33 70-71 12.42 2.16 1.23 .86 .41 .92 1.06 6.48 .33 66-67 8.01 1.35 2.0 .59 .69 .80 .96 .90 .13 67-68 7.33 .75 2.0 .33 .69 .85 .94 .92 .13 Saskat- 68-69 8.51 -.97 2.0 .35 .69 .74 .93 .28 .14 chewan 69-70 13.26 -1.08 2.0 .39 .69 .81 .94 14.41 .15 70-71 10.63 6.77 2.0 .62 .69 .77 .94 30.12 .15 66-67 9.95 .69 2.31 .59 1.08 .83 1.02 .90 .17 67-68 7.8 .35 2.31 .56 1.08 .82 1.00 6.09 .16 Mani- 68-69 7.46 1.21 2.31 .69 1.08 .86 .99 .34 .16 toba 69-70 8.84 3.04 2.31 .46 1.08 .89 1.05 12.70 .14 70-71 7.37 1.83 2.31 .90 1.08 .84 1.05 7.33 .13 66-67 2.08 1.3 1.61 .59 2.08 .98 1.03 1.03 .25 67-68 1.93 .86 1.61 .56 2.08 .99 1.03 .87 .26 Ontario 68-69 2.18 1.98 1.61 .61 2.08 1.00 1.02 1.02 .26 69-70 2.46 .07 1.61 .59 2.08 1.03 .99 4.28 .26 70-71 2.22 .40 1.61 .62 2.08 1.02 .99 5.66 .26 66-67 .66 1.14 1.92 1.29 2.15 .79 .98 .88 .06 67-68 .69 .16 1.92 1.04 2.15 .79 .99 1.62 .07 Quebec 68-69 .83 2.5 1.92 1.04 2.15 .81 .98 1.33 .07 69-70 1.08 -.35 1.92 1.10 2.15 .82 .97 9.32 .08 70-71 .95 -.54 1.92 1.38 2.15 .81 .96 15.60 .08 66-67 1.05 .59 2.15 1.76 1.87 .62 .89 .79 .04 67-68 .96 .15 2.15 1.42 1.87 .63 .89 1.25 .04 Atlan- 68-69 1.19 3.29 2.15 1.29 1.87 .65 .87 .83 .04 tic 69-70 1.58 1.14 2.15 1.24 1.87 .68 .86 -2.44 .04 70-71 1.18 .65 2.15 1.46 1.87 .67 .85 10.27 .04 98 Table B-2: List of Input Data on the Out-Migration to B.C. During 1966-70. Region Period Depen-dent vari- Independent Variables able UN- IN- LF- IM-4' (1) OUT-MIG DWELST CLIMTE EMPR DISTCE COME PART MIGR FRIEND (2) (3) (4) (5) (6) (7) (8) (9) (10) (U) 1966-67 7.53 1.12 1.23 .59 .41 .87 1.09 .78 .40 67-68 7.75 .98 1.23 .53 .41 .92 1.07 4.13 .40 Alberta 68-69 7.80 5.16 1.23 .59 .41 .91 1.06 .67 .39 69-70 7.57 .74 1.23 .46 .41 .94 1.06 6.45 .39 70-71 7.84 2.16 1.23 .86 .41 .92 1.06 6.48 .39 1 66-67 3.13 1.35 2.0 .59 .69 .80 .96 .90 ' .11 67-68 3.25 .75 2.0 .33 .69 .85 .94 .92 .11 Saskat- 68-69 3.01 -.97 2.0 .35 .69 .74 .93 .28 .10 chewan 69-70 2.31 -1.08 2.0 .39 .69 .81 .94 14.41 .10 70-71 3.12 6.77 2.0 .62 .69 .77 .94 30.12 .09 66-67 2.52 .69 2.31 .59 1.08 .83 1.02 .90 .09 67-68 3.13 .35 2.31 .56 1.08 .82 1.00 6.09 .09 Manitoba68-69 3.23 1.21 2.31 .69 1.08 .86 .99 .34 .09 69-70 2.51 3.04 2.31 .46 1.08 .89 1.05 12.70 .09 70-71 3.05 1.83 2.31 .90 1.08 .84 1.05 7.33 .09 66-67 1.15 1.3 1.61 .59 2.08 .98 1.03 1.03 .29 67-68 1.26 .86 1.61 .56 2.08 .99 1.03 .87 .29 Ontario 68-69 1.29 1.98 1.61 .61 2.08 1.00 1.02 1.02 .30 69-70 1.28 .07 1.61 .59 2.08 1.03 .99 4.28 .30 70-71 1.37 .40 1.61 .62 2.08 1.02 .99 5.66 .31 66-67 .38 1.14 1.92 1.29 2.15 .79 .92 .88 .08 67-68 .34 .16 1.92 1.04 2.15 .79 .99 1.62 .08 Quebec 68-69 .34 2.5 1.92 1.04 2.15 .81 .98 1.33 .07 69-70 .36 -.35 1.92 1.10 2.15 .82 .97 9.32 .07 70-71 .41 -.54 1.92 1.38 2.15 .81 .96 15.60 .07 66-67 .54 .59 2.15 1.76 1.87 .61 .89 .79 .04 67-68 .56 .15 2.15 1.42 1.87 .63 .89 1.25 .04 Atlan- 68-69 .57 3.29 2.15 1.29 1.87 .65 .87 .83 .04 tic 69-70 .70 1.14 2.15 1.24 1.87 .68 .86 -2.44 .04 70-71 .88 .65 2.15 1.46 1.87 .67 .85 10.27 .04 I 

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