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Economic determinants of interprovincial migration in British Columbia Trépanier, Marie 1984

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ECONOMIC DETERMINANTS OF INTERPROVINCIAL MIGRATION IN BRITISH COLUMBIA by MARIE TREPANIER BACC. ADMINISTRATION DES AFFAIRES, UNIVERSITE LAVAL, 1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE FACULTY OF GRADUATE STUDIES FACULTY OF 1COMMERCE.AND'BUSINESS ADMINISTRATION We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n Business Administration i n DEC 1984 © Marie Trepanier, 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Commerce The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: 4 December 1984 Abstract Given the fundamental importance of population base to the level of economic activity, an accurate population estimate is essential to most planners. Interprovincial migration is the major factor in differing regional population growth. Hence an understanding of the Canadian "footloose" behaviour of individuals i s invaluable. The purpose of this thesis was twofold: f i r s t to find the economic determinants of interprovincial migration for two-age cohorts (the working and the retired), for the 1966-1981 (ex-post) and second to forecast the number of working migrants for 1982 (ex-ante). The case of British Columbia was used. The main sources of migration data were the number of account transfers for family allowance and old age security benefits. Structural and time-series models were investigated. The former were used for explaining and forecasting purposes and the latter for forecasting purposes only. The techniques applied were ordinary least squares for the structural models and unconditional non-linear least squares with back forecasting (Box and Jenkins) for the time-series models. The outcome was that income variables, labour variables, housing prices, personal taxes, cost of li v i n g variables and housing market variables were a l l significant determinants of interprovincial migration. One exception was the out-migration of the elderly group where only housing prices and cost of liv i n g variables had any significance. The results also indicated that f i r s t the elderly were more sensitive to housing i i i p r i c e s , personal taxes and cost of l i v i n g d i f f e r e n t i a l s between B r i t i s h Columbia and the rest of Canada and second the two-age cohorts had similar e l a s t i c i t i e s to migrate for labour and housing market v a r i a b l e s . F i n a l l y , i n combining ex-ante and ex-post r e s u l t s , i t was shown that the optimum solu t i o n for determining net migration of the working was in-migration estimates minus out-migration estimates using the s t r u c t u r a l models. i v Table of Contents Abstract i i L i s t of Tables v i L i s t of Figures v i i i Acknowledgement i x Chapter I INTRODUCTION 1 Chapter II NORTH AMERICAN LITERATURE REVIEW 4 2.1 Introduction For The L i t e r a t u r e Review 4 2.1.1 Empirical Work In The U.S.A 5 2.1.2 Empirical Work In Canada 15 Chapter III THEORY AND SPECIFICATION OF THE VARIABLES 28 3.1 Underlying Theory 28 3.2 S p e c i f i c a t i o n Of The Variables 29 3.2.1 The Dependent Variables 29 3.2.2 The Independent Variables 30 Chapter IV THE DATA 34 4.1 D e f i n i t i o n s And Sources 34 4.1.1 The Dependent Variables 34 4.1.2 The Independent Variables 36 4.2 R e l i a b i l i t y And Limits Of Data 42 4.2.1 The Dependent Variables 42 4.2.2 The Independent Variables 44 Chapter V THE STRUCTURAL MODELS 46 5.1 The Methodology 46 5.2 Diagnostic Checks Of Model Adequacy 58 5.3 Forecasts Based On The F i t t e d Models 60 5.4 Analysis And Testing 62 5.4.1 The Str u c t u r a l Models 62 5.4.2 Comparing The E l a s t i c i t i e s 65 5.4.3 Estimates And Forecasts Of Net Migrants 67 Chapter VI TIME-SERIES MODEL 72 6.1 A Time-series Model For The Working In-migration (FAMALI) 72 6.1.1 I d e n t i f i c a t i o n Of A Model 72 6.1.2 Estimation Of The Model 75 6.1.3 Diagnostic Checks Of Model Adequacy 76 6.2 A Time-series Model For The Working Out-migration (FAMALO) 77 6.2.1 I d e n t i f i c a t i o n Of A Model 77 6.2.2 Estimation Of The Model 78 V 6.2.3 Diagnostic Checks Of Model Adequacy 79 6.3 Forecasts Based On The Model F i t t e d 80 6.4 Analysis And Testing 82 Chapter VII SUMMARY OF FINDINGS AND CONCLUSION 86 7.1 Summary Of Findings 86 7.1.1 Determinants Of I n t e r p r o v i n c i a l Migration 86 7.1.2 Economic E l a s t i c i t i e s To Migrate 88 7.1.3 Selecting The Best Net Migration Model For The Working 89 7.2 Conclusion 96 BIBLIOGRAPHY 99 APPENDIX A - VARIABLES' SYMBOL, DEFINITION AND EXPECTED SIGN 101 APPENDIX B - DESCRIPTIVE MEASURES OF ALL VARIABLES 102 APPENDIX C - VALUES OF ALL VARIABLES:1966(1)-1982(4) 103 APPENDIX D - REGRESSIONS RESULTS AND DIAGNOSTIC CHECKS FOR STUCTURAL MODELS 112 APPENDIX E - REGRESSION RESULTS AND DIAGNOSTIC CHECKS FOR FAMANT STRUCTURAL MODEL 132 APPENDIX F - CHECKING STATIONARITY OF FAMALI SERIES 137 APPENDIX G - DIAGNOSTIC CHECKS FOR FAMALI TIME-SERIES MODEL 149 APPENDIX H - CHECKING STATIONARITY OF FAMALO SERIES ,153 APPENDIX I - DIAGNOSTIC CHECKS FOR FAMALO TIME-SERIES MODEL 165 APPENDIX J - DIAGNOSTIC CHECKS FOR FAMANT TIME-SERIES MODEL 169 v i List of Tables 1. T-Statistics for FAMALI models 49 2. T-Statistics for FAMALO models 50 3. T-Statistics for OLDAGI models 51 4. T-Statistics for OLDAGO models 52 5. Final structural model for the working in-migration (FAMALI) 54 6. Final structural model for the working out-migration (FAMALO) 55 7. Final structural model for the elderly in-migration (OLDAGI) 56 8. Final structural model for the elderly out-migration (OLDAGO) 57 9. Prediction errors for the structural models 61 10. Final structural model for the working net migration (FAMANT) 69 11. Standard errors of residuals for the working structural models for 1966(1)-1981(4) 70 12. Prediction errors for the working net migration structural models 71 13. Guide for choosing the orders of AR and MA components 74 14. Prediction errors for the time-series models 81 15. Prediction errors for the working net migration time-series models 85 16. Summary of levels of significance for the structural models 86 17. Summary of economic variables used in the f i n a l models 87 18. Summary of economic el a s t i c i t i e s tc migrate for the two-age cohorts 88 19. Summary of prediction errors, ex-ante for 1982(1)-v i i 1982(4) 89 20. Summary of standard e r r o r s of r e s i d u a l s , ex-post f o r 1966(1)-1981(4) 90 v i i i L i s t of Figures 1. Actual net migration for the working, 1961(1)-1982(4) 92 2. Best net migration forecasting models for the working, 1982(1)-1982(4) 93 3. Best net migration f i t t e d models for the working, 1966(1)-1981(4) 94 4. Optimum net migration model, for the working, using ex-ante and ex-post r e s u l t s 95 ix Acknowledgement I would like to express my sincere gratitude to the members of my thesis committee, Dr. Dennis Capozza, Dr. Lawrence Jones and Dr. Michael Tretheway. Throughout my research process, they provided me with helpful comments and regular feedback. I would also like to thank Judy Fountain for giving me assistance on more than one occasion. Finally, the completion of my degree and this thesis would not have been possible without the financial support of the following: Canada Mortgage and Housing Corporation, Fonds F.C.A.C. pour L'Aide Et Le Soutien A La Recherche, The Real Estate Council of British Columbia, and The Real Estate Education and Research Association of British Columbia. To a l l of these organizations I am much obliged. 1 I. INTRODUCTION In Canada, population growth rates vary substantially from region to region. If but a single piece of information regarding the economic future were available, the f i r s t choice of most planners would doubtless be an accurate population estimate. Nothing is as fundamental to economic activity in general than the size of the population base. Demand for goods, services and distribution f a c i l i t i e s (...) requirements for schools, hospitals, roads and other public services are closely related to population, as are provincial and local tax bases and entitlements to transfer payment s 1 . The above quote emphasizes the importance of an adequate population forecasting model. In constructing a complete population forecasting model, three factors must be considered: the net natural change (birth minus death), the net foreign migration (immigration minus emigration) and f i n a l l y the net interprovincial migration. The large amount of movement from one province to another is the most important factor in differing regional population growth.2 During the last decade, a substantial number of studies have examined migration 3 factors in the United States, and to a lesser extent, in Canada. Most of these studies have tried to give a variety of explanations for this "footloose" behaviour. 1 Robert Jeacock, A provincial Population Forecasting Model  Emphasizing Interprovincial Migration, p.V. 2 From 1961-79, seven million such moves have been recorded in Canada.Source: idem . 3 Herein 'migration' is defined as the individuals/households movements from one province (state) to another. 2 The general focus of t h i s thesis i s on Canadian i n t e r p r o v i n c i a l migration. The North American l i t e r a t u r e i d e n t i f i e s a v a r i e t y of e x p l i c a t i v e v a r i a b l e s for t h i s r e l o c a t i o n d e c i s i o n of i n d i v i d u a l s . Canadians seem to move to improve t h e i r economic well-being. S p e c i f i c a l l y the unemployment rate and the income i n the sending and r e c e i v i n g provinces as well as the r e l a t i v e cost of l i v i n g are l i k e l y to be important determinants* . V a r i a t i o n i n housing prices may be an important factor ^ of regional d i f f e r e n c e i n the cost of l i v i n g from province to province. Housing prices may have a causal and/or e f f e c t i v e r e l a t i o n s h i p with migration movements. On one hand, r e l a t i v e l y lower housing prices i n a c e r t a i n region could be a determinant v a r i a b l e i n one's choice to locate i n that area (causal). On the other hand, the d e c i s i o n to move to a p a r t i c u l a r place by many people, i n the same period of time, could create an increase i n housing p r i c e s because of a pressure on demand for housing while the supply side stays f i x e d ( i . e . i n e l a s t i c ) i n the short run ( e f f e c t i v e ) . The s p e c i f i c focus of t h i s research i s to i n v e s t i g a t e the former l i n k , that i s , the long term causal r e l a t i o n s h i p of housing prices with the i n t e r p r o v i n c i a l migration of the population i n general (which i s l i k e l y to have a high labour force p a r t i c i p a t i o n rate) and of the e l d e r l y group i n p a r t i c u l a r . 4 R.Jeacock, Op.Cit. p.V., J.Dean, "Tax-Induced Migration i n Canada 1972-79", Western Economic Review, July 82, p.19. 3 In chapter two a representative set of the last decade of American and Canadian literature on interstate and interregional household migration is respectively reviewed. The emphasis is mainly on empirical studies and most of the models are examined in detail because they provide invaluable insight into the variables to include and to avoid in constructing a model of interregional migration. The theory and the specification of the independent and dependent variables in interregional migration is provided in chapter three. In the f i r s t part of chapter four , the definitions and sources of data are examined. In the second part, the degree of r e l i a b i l i t y and/or the limitations of some variables is probed. In order to answer the specific question "Are housing prices a significant determinant of interprovincial migration in the long term?", some basic empirical models, using British Columbia migration flows (dependent variables), for the 1966-1981 quarterly data, and some pertinent independent variables including housing prices, are specified in chapter five. The fin a l models' a b i l i t y to forecast accurately the number of migrants, for the four quarters of 1982, is stressed. In chapter six , the trends and seasonal patterns for the working migrant flows, for the 1966-1981 period, are investigated through some time-series models. Again, precision in forecasting the number of migrants, for 1982, is emphasized. Finally chapter seven summarizes the findings and concludes the study. 4 II. NORTH AMERICAN LITERATURE REVIEW. 2.1 Introduction For The Literature Review The North American literature review that follows looks mainly at empirical studies related directly to economic determinants of individuals' migration. The f i r s t subsection covers a series-debate of articles published in an American journal Annals of Regional Science between 1978 and 1983. This series of articles has been selected because i t provides a dimension not covered in the Canadian literature: the migration determinants, for the working people and for elderly (retired) may be different. In the second subsection, heavy emphasis is put on the Canadian literature. Where relevant, the weaknesses and strengths of the models are stressed. Where necessary the relationship between models is established. The review is not exhaustive but believed to be representative. Throughout the chapter the hypothesized signs of the parameters are found in parentheses beside each of the independent variables. The study by study method of disclosing the information is chosen because i t could allow the literature review to be extended as results of recent empirical work are released on interprovincial/interregional migration. Indeed, interregional migration i s a burgeoning topic. 5 2.1.1 Empirical Work In The U.S.A. In 1978, an a r t i c l e written in the Annals of Regional  Science by Rishi Kumar and Stephen M. Renas5 (K&R thereafter) started a series of 8 articles that could be entitled the '6 years-debate'. In their a r t i c l e K&R show that the failure to include the cost of living variables in a migration equation results in misspecification of the model, and results in bias involving some of the economic variables in the regression, notably the money income variable. The authors assume that individuals are not subject to money il l u s i o n and consequently that they are interested in cost of living information to transform income variables in real terms. To conclude that statement, K&R examine two models built on 36 observations based on Standard Metropolitan S t a t i s t i c a l Areas (SMSAi for i=l-36) in the United States. For the two models the dependent variable is the net number of migrants Mi into SMSAi between 1960 and 1970 expressed as a percentage of the 1960 population. In their f i r s t cross-sectional model (their basic model) the net number of migrants into SMSAi i s function of two measures of income (+), two measures of the cost of living (-) and four more independent variables measuring the unemployment rate (-) , the education level (+ or - ) , the population density (-) and f i n a l l y an annual degree days variable (-). Their second model includes a l l of the variables included in the basic model less the two 5 Rishi Kumar and Stephen Renas,"Cost of living, Labor Market Opportunities, and the Migration Decision:A case of Misspecification?", Annals of Regional Science, July 1978. 6 cost of l i v i n g variables. A comparison of the 2 sets of estimates obtained lead the authors to conclude that the bias resulting from the omission i s severe. When the cost of living variables are not included, the median family income and the unemployment rate variables are not significant. They are significant when the cost of living measures are included. Kumas and Renar's models are significant at the 1% level (F-stat 1 tailed test) and have an adjusted R-squared of respectively .57 and .52. The authors f a i l to give the standard error of the estimate which would give more information on the adequacy of the models. In 1979, subsequent to the foregoing a r t i c l e , Gershon Alperovich 6 comments on K&R basic model. He makes two arguments. First, a migration model, linear in the independent variables, which includes both nominal income and cost of living as separate variables, i s incompatible with the assumption that individuals are not subject to money i l l u s i o n . Second, the uti l i z a t i o n of K&R's basic model does not necessarily give better estimates than a procedure which would ignore the cost of living variable altogether. 6 Gershon Alperovich,"The Cost of Living, Labor Market Opportunities and the Migration Decision: A Case of Misspecification? Comment", Annals of Regional Science, Nov.1979. 7 The author j u s t i f i e s h i s f i r s t argument by the following: The reason for t h i s i s that the requirement f o r absence of money i l l u s i o n imposes a r e s t r i c t i o n on the parameters of these v a r i a b l e s which cannot be f u l f i l l e d i n a l i n e a r representation. If such a model i s estimated, i t constitutes a m i s s p e c i f i c a t i o n i n the form of the equation which r e s u l t s i n bias and inconsistency i n some of the estimated parameters 7 . Alperovich says that i f there are good reasons to expect a l i n e a r s t r u c t u r a l r e l a t i o n s h i p between net migration and the independent variab l e s , the correct r e l a t i o n to be estimated (assuming again that i n d i v i d u a l s are • not subject to money i l l u s i o n ) i s : (1) M= a + b (Y/P) + U i X i + E' where 'M' i s the net migration, 'Y' i s a measure of nominal income, 'P' i s the cost of l i v i n g index (therefore 'Y/P' i s r e a l income), 'Xi' are a l l the other independent variables such as unemployment, education, etc. and 'E' i s the random disturbance. This equation, he says, leads to unbiased and consistent ordinary l e a s t squares (OLS) estimates, whereas the K&R basic model: (2) M= a + b l (Y) + b2 (P) + Z J i X i + E leads to biased and inconsistent OLS estimates because i t 7 Ibid, p.103. 8 assumes that people are subject to money i l l u s i o n , the weights for nominal income and cost of l i v i n g being d i f f e r e n t . Alperovich says these weights should be the same, because with no money i l l u s i o n : (...) holding a l l other v a r i a b l e s constant, areas which o f f e r given l e v e l s of income and given l e v e l s of cost of l i v i n g , w i l l be equally a t t r a c t i v e to migrants as areas which o f f e r income l e v e l s [x] times higher and the cost of l i v i n g i s a l s o [x] times higher 8 . In h i s paper, Alperovich adopts the t r a d i t i o n a l economic assumption of no money i l l u s i o n . In a reply to Alperovich K&R agree that his comments are relevant i f households consider r e a l income i n t h e i r migration decisions. However, according to Kumar and Renas, migrants do not consider r e a l income i n t h e i r r e l o c a t i o n process. They instead examine separately v a r i a b l e s such as money income and cost of l i v i n g . "(...) i t i s very u n l i k e l y that. they ( i n d i v i d u a l s ) would mentally d i v i d e money income by the cost of l i v i n g to a r r i v e at a measure of r e a l income"' . K&R argue i n two ways why they s p e c i f i e d t h e i r basic model as seen above. F i r s t , although money income and cost of l i v i n g v a r i a b l e s are both considered, the former may receive more consideration. Second, on the other hand, cost of l i v i n g v a r i a b l e s may receive more a t t e n t i o n because d i f f e r e n t i a l s 8 Ibid, p.103. 9 R.Kumar and S.Renas,"The Cost of Living,Labor Market Opportunities and the Migration Decision: A Case of Mi s s p e c i f i c a t i o n ? Reply", Annals of Regional Science, Nov.1979. p. 106. 9 between regions are more publicized than geographic money income differentials. From the preceding arguments i t does seem that 'money i l l u s i o n ' i s present in K&R's model, however the author-agrees on the idea of the potentially different levels of awareness. Renas and Kumar then test their theory in comparing their basic model to the Alperovich proposition involving a real income measure. They conclude the superiority of their model and that individuals do not consider real income in that the results of their own model "(...) are generally better than the r e s u l t s " 1 0 of Alperovich proposed model. This conclusion seems weak in two ways. First, how can they conclude that individuals do not consider real income variable only on the basis that an equation including real income does not perform as well as a model including two separate variables for income and cost of living? Second, in examining the results i t does not appear (as they suggest) that their model is "generally better". Despite a higher adjusted R-squared for K&R model (.57 versus .51 for Alperovich proposed model), the F-ratio for the real income equation i s higher (7.10 versus 6.65, significant at the 1% level, one-tail test) which indicates that as a whole, the equation with real income variables i s more significant than the equation with cost of livi n g and nominal income variables, ceteris paribus. Also in Alperovich's proposed model, the unemployment rate is more significant (1% level versus 10%) and 1 0 Ibid, p.108. 10 the real income i s significant at the 1% level whereas the nominal income was significant at the 10% level and the cost of livin g at the 5% level in K&R's basic model. In 1981, Richard J. Cebula 1 1 , in a short comment following the foregoing articles, shows an alternative to demonstrate the superiority of an equation including both nominal income and cost of living variables versus an equation with real income. Cebula bases his explanation on the labor force participation rate (LFPR). Because different age groups have different LFPR, he proposes the following hypothesis : the level of income is not as important for every individual (e.g. for retired people), but everyone i s concerned with the differential costs of living because a l l age groups are affected by them, regardless of their LFPR. (...) i t follows that we should expect a regression with separate money income and living cost variables to perform better than a corresponding regression with real income instead 1 2 . Nevertheless, Cebula also sees misspecification in K&R's basic model. Ideally he believes that a model needs to be disaggregated at least to the degree that i t separates migrant 1 1 Richard Cebula,"The Cost of Living, Labor Market Opportunities and the Migration Decision:A case of Misspecification? Comment", Annals of Regional Science, Nov.1981. 1 2 R.Kumar and S.Renas,"The Cost of Living, Labor Market Opportunities and the Migration Decision:A case of Misspecification? Some Additional Evidence", Annals of Regional  Science, Nov.1981. 11 groups having measurably different LFPR levels. Following Cebula's hypothesis, Kumar and Renas attempt to verify i t s t a t i s t i c a l l y . If Cebula's hypothesis is correct, then for those age groups having high labor force participation rates, the equation which includes a real income variable as an explanatory variable should perform better than the one which includes separate money income and cost of living variables. For those age groups having low LFPR, however, the equation which includes separate money income and cost variables should perform better, although we might find that the money income variable is not s i g n i f i c a n t 1 3 . Consequently K&R estimate two regressions for each twelve age groups (20-24 years, 25-29..., 75-up). For the 20-24 age group, regardless of the specification, the explanatory power is weak. They propose that i t could depend upon the fact that this group moves for reasons (eg. schooling) not captured in the conventional explanatory variables. For the 25-29 to 35-39 years age groups the results support Cebula's hypothesis: the regressions with the real income perform better than the ones with cost of liv i n g and nominal income variables. For the 40-44 to 60-64 age groups, the results are inconsistent. The regression with the real income measure has less explanatory power despite their s t i l l high LFPR. To justify these results, K&R's argument is that employed migrants in that range may look ahead to the time of retirement and therefore place more weight on cost of living than on income. This leads to a higher explanatory power of the 1 3 Ibid, p.75. 12 regression with separate nominal income and cost of living variables. The authors underline that this argument is only conjectural 1 4 . The 75-up age group provides strong support for Cebula's hypothesis: the equation with the cost of living has more explanatory power, the coefficient for the cost of liv i n g i s significant at the 1% level, but the nominal income has the wrong sign and is insignificant. Kumar and Renas conclude in saying: "Our findings provide limited support to Cebula's hypothesis. His reasoning is applicable to certain age groups, but not to others" 1 5 . Back on the scene in 1983, Alperovich 1 6 argues among other things that, to accept K&R's reasoning that individuals are not likely to mentally divide money income by the cost of living to arrive at a measure of real income, is to reject the classical consumer theory "(...) which suggests that a major property of rational behavior is that demand functions are homogeneous of degree zero in prices and income"17 , i e . i f price and income both double demand w i l l not change. He also indicates the pl a u s i b i l i t y of Cebula's hypothesis because of two observations. First, the coefficient of the living cost variable i s always 1 4 Dr.Mike Tretheway, at UBC, says the ratio of wealth to income rises with age and accounts for the problems in the 40-65 age group. Dr.Tretheway sees a real wealth effects variable missing in a l l the specifications. 1 5 Ibid, p.79. 1 6 G.Alperovich,"The Cost of Living,Labor Market Opportunities and the Migration Decision: A Case of Misspecification? Comment", Annals of Regional Science, March 1983. 1 7 Ibid, p.94. 13 greater than the coefficient of the income variable. Second, the coefficient of both the income and living cost variables decrease as people get older, but with the former declining faster than the latter. Both observations are "(...) consistent with the idea beyond (sic) Cebula's hypothesis" 1 8 . However, Alperovich argues that the hypothesis may be irrelevant as an explanation of the superiority of the regression proposed originally by Kumar and Renas. Consequently Cebula 1 5 replies in re-explaining the main point of his former analysis. Greater dependability and accuracy should be the central concern, in the absence of appropriately disaggregated migration, using real income per se rather than separate money income and livi n g cost variables gives us less r e l i a b i l i t y and less accuracy and, as a result, less meaningful i n s i g h t s 2 0 . Finally, Kumar and Renas 2 1 respond, but this time with no st a t i s t i c a l ground. They note that "informational d i f f i c u l t i e s " on geographic income differentials (compare to geographic cost of living differentials) may help to explain their s t a t i s t i c a l results in their studies. They also say that "Alperovich i s totally wrong when he suggests that the specification of our 1 8 Ibid, p.97. 1 5 R.Cebula,"The Cost of Living,Labor Market Opportunities and the Migration Decision: A Case of Misspecification? Reply", Annals  of Regional Science, March 1983. 2 0 Ibid, p.97. 2 1 R.Kumar and S.Renas,"The Cost of Living,Labor Market Opportunities and the Migration Decision: A Case of Misspecification? :more on the problems of misspecification and aggregation bias", Annals of Regional Science, March 1983. 14 regression implies money i l l u s i o n and violates the postulates of classical consumer theory" 2 2 . Money i l l u s i o n , which Alperovich repeatedly says is implicit in our analysis , is simply not an issue and i s not required to justify our conceptualization of the problem2 3 . K&R conclude by saying that Alperovich has repeatedly c r i t i c i z e d their empirical findings and offer l i t t l e in the way of empirical evidence or convincing analysis to support his case. They therefore suggest that Alperovich should specify a model as an alternative to theirs and test i t empirically. The author's view is that K&R's basic model does involve money i l l u s i o n . However she agrees that an equation with separate income and cost of living components may provide more meaningful insights into migrants' behaviour, particularly for different age groups. 2 2 Ibid, p.99. 2 3 Ibid, p.100. 15 2.1.2 Empirical Work In Canada In 1974, in a discussion paper, Jarmila Horna 2 4 examines patterns of family migration between the provinces, in particular the proportion of families moving to and from a different province. Her principal data source - as for most Canadian studies - i s the monthly record of interprovincial transfers of family allowance accounts provided regionally by the National Health and Welfare Department. Horna hypothesizes some of the determinant factors that families would consider to move in a particular province: In the case of British Columbia the most decisive factors would be of an economic nature and perhaps the Pacific's pleasant climate, too; while in Quebec cultural and linguistic closeness and barriers would be most important. In Ontario and partly in Alberta, economic and urban pull factors are most influential ; while strong economic and cultural push factors characterize the remaining provinces 2 5 . Horna's hypothesis of different explicative variables for different provinces i s interesting although these push-pull factors, in some cases, may have changed through the last decade. The author does not test her hypothesis s t a t i s t i c a l l y . After analysing the data Horna exposes two findings. First the volume of interprovincial family migration i s associated with the size of a province population level. The most populous 2 4 Jarmila Horna, Patterns of family migration between the  provinces in Canada,1956-1974. Discussion paper, University of Alberta, 1974. 2 5 J.Horna, Ibid, p.8. 15 provinces have the highest gross numbers of migrants (gross migration being the summation of in-migration and out-migration) . Second people tend to move more between contiguous provinces than more distant ones. She concludes that patterns of family migration flows are relatively consistent over the 1956-1974 period. There are provinces which consistently lose (gain) population through family migration: However, due to the changing and unstable patterns of loss and gain over the years, the whole picture of internal migration of Canadian families in receipt of family allowance can be characterized as a state of f l u i d i t y - constant flow and turnover of families -thus depicting the fact that no rig i d structured trends may be safely drawn2 6 . In 1981, Don McRae27 , from the Central Statistics Bureau, builds an econometric model describing the population migration movements between British Columbia and the rest of Canada." In his research, the author uses a structural model with multiple linear regression. The developed model adopts the Push-Pull hypothesis for describing migration flows. This approach views migration as a combination of "push" factors that pressure a migrant to seek better opportunities, and "pull" factors that attract a migrant to a particular location. Consequently, movement between regions i s viewed to result from differences in economic and non-economic conditions in the respective regions 2 8 . 2 6 Ibid, p.13. 2 7 Don McRae, An Econometric Model Describing the movement of the  population between B.C. and the rest of Canada. 1981. 2 8 Ibid, p . l 17 McRae chooses his independent variables with two constraints in mind: f i r s t , the data must be available for a sufficient historical period (to allow as many degrees of freedom as possible) and second, for migration forecasting purposes, the independent variables must have the potential to be forecasted themselves. The above constraints limit the range of usable explicative variables. An unemployment variable, defined as the ratio of unemployment rates between British Columbia and the rest of Canada in time period t, i s included. The author lags this variable because he assumes that i t takes some time for the information to flow between regions. A second independent economic variable i s used in his model, the B.C./Canada ratio of capital expenditures, estimated quarterly from annual figures. Finally, three seasonal dummies are included in order to account for seasonal fluctuations. The dependent variable in his model is the quarterly in and out migration flows between B.C. and the other provinces, divided by 10,000, for the 1968-1980 period. The migration flows are migration estimates, by Statistics Canada, based on the interprovincial transfers in Family Allowance accounts. McRae estimates two regressions. One is the in-migration, where the unemployment variable i s lagged three quarters with a negative expected sign and where the percentage of capital expenditures has a positive expected sign. The second equation, out-migration, has an unemployment variable lagged two quarters 18 with a positive expected sign. The percentage of capital expenditure variable has a negative expected sign, the higher this ratio the lower the out-migration from B.C.. The author does not say why this variable is utilized nor what i t represents. Both equations have seasonal dummies as mentioned above. The author corrects the estimated in and out migration equations for first-order autocorrelation. McRae discloses some results on the "tracking a b i l i t y " of his model. He found out that on average the fitt e d values for quarterly in-migration (out-migration) are off by 7.91% (6.59%) per period and 7.67% (6.17%) over the entire period f i t t e d . Also over the entire period the estimated net-migration (fitted in minus fi t t e d out) i s translated into an error of 25.5% which is considerably bigger than the in migration and out migration taken separately. The estimated net-migration values were calculated as the difference between the estimated [fitted] in and out figures. Consequently, they tend to suffer/benefit from addition/cancellation in the errors associated with the in and out-migration estimates 2 9 . McRae's finding raises the issue as to whether the use of a separate net migration model could yield superior "tracking a b i l i t y " results than the use of estimated net migration as determined by fitt e d in minus fitt e d out. In 1981, T.L.Powrie 3 0 reports the following argument and 2 9 Ibid, p.13. 3 0 T.L.Powrie,"Natural Resource Revenues and Federal-Provincial Fiscal Arrangements", Canadian Tax Journal, July/August 1981. 19 counter-argument: Argument Alberta's large o i l revenues permit the province to have low taxes. Low taxes are an attraction to migrants. Therefore, Canadians wi l l migrate from other provinces to Alberta and w i l l even accept a lower wage in Alberta because of tax advantages of Alberta residence 3 1 . Counter-Argument First, part of the resource revenues are saved by the province and are not used to reduce taxes; second, housing prices and rents are driven up by an inflow of migrants, (this second statement reflects the simultaneous relationships induced by migration). The attractiveness of low taxes is offset (or pa r t i a l l y offset) by the higher cost of housing. The points made in this argument and counter-argument suggest the importance of including such factors as taxes and housing costs in migration modelling. Tax induced migration i s the movement of factors of production (labour, capital, managerial talent, etc.) to p o l i t i c a l jurisdictions which impose lower effective taxes for comparable service levels than other jurisdictions. (...) It is not s t r i c t l y necessary that taxes be lower in the favoured jurisdictions; i t might be that govermental service levels are better for comparable tax burdens 3 2 . This quote, by James M. Dean, alludes to how important tax 3 1 Ibid, p.502. 3 2 James M.Dean,"Tax Induced Migration In Canada 1972-79", Western  Economic Review, July 1982. p.17. 20 factors might be in determining relocation's decisions. He assumes that people wi l l choose to live where they are better off, which makes sense intuitively. There are major differences in tax rates (personal income, provincial sales and small business taxes) among provinces. For example, in 1981, British Columbia, Saskatchewan and Manitoba had personal income tax rates of 16%, 37% and 42% respectively higher than Alberta 3 3 . "There is no reason to believe tax differentials are likely to narrow in the near future" 3 4 . Dean stresses the lack of agreement in the empirical literature regarding whether people consider taxes when making migration decisions. Also one of his conclusions agrees with Powrie who recognized the importance of real cost of living differences between Canadian regions. Using families receiving family allowance benefits as a proxy for migration data, Dean builds an empirical model examining tax-induced migration. The dependent variable is the ratio of migrants from each province of origin to each province of destination, divided by the population of the province of origin. The main independent variables included are the unemployment rate (+) and the real 3 5 income per capita (-) in the province of origin, the unemployment rate (-) and the real income (+) in the province of destination and two tax variables. 3 3 Idem. The paper does not expose how these figures have been determined. 3 4 Ibid, p.19. 3 5 To correct for the interprovincial variations in the cost of li v i n g . 21 The f i r s t tax variable i s the personal income tax rate in each province of origin (+) and destination (-) as a percentage of Basic Federal Tax. Dean emphasizes three shortfalls in using this variable: (1) a l l provinces have a variety of programs which modify this percentage; (2) this measure ignores other taxes such as r e t a i l sales taxes and residential property taxes (the correlation between the former and the provincial income tax rates i s .76, therefore, the omission of r e t a i l taxes avoids a problem of multicollinearity); (3) this measure i s not available for the province of Quebec. The second tax variable is the direct taxes payable in a province as a percent of i t s provincial personal income. The expected signs are the same as the previous tax variable. This second tax variable allows Quebec to be included. The correlation between these two tax variables is only .36. Dean gives an aggregate regression result for the ten provinces. For 617 degrees of freedom, he obtains an R-squared of 60%. A l l independent variables in the model are significant with t-ratios ranging from 1.66 to 17.52. A l l come with the expected sign except for the unemployment rate in the province of origin and of destination and for the tax rate and direct tax burden in the sending provinces. In many studies the unemployment rate also had a sign contrary to expectations. Dean says he was surprised to find that both the tax burden and the tax rate in the province of origin had a negative influence on migration decisions. It would suggest that the higher the taxes in the sending province, the less li k e l y people are to move away. 22 The d i f f i c u l t y here arises partly due to the aggregative nature of the model. When the model was disaggregated by province (...) the tax variables had the correct sign for eight of the ten provinces 3' . The two exceptions being Ontario and Quebec which had a coefficient large enough to overwhelm the other provinces. Dean examined how a change in tax rates would influence migration. He conducted an experiment in Alberta and in British Columbia. For the latter he found out that a one point reduction in provincial income tax rates would increase i n -migration to B.C. from between 3.0 and 15.0 percent, depending on the sending province. " (...) tax rate differences appear to be an important factor in explaining migration flows from other provinces to British Columbia" 3 7 . Dean concludes from his empirical study, that tax factors are "important explanatory variables in studying migration flows", and that a more comprehensive study is "long overdue". The last a r t i c l e considered in this Canadian literature review is a complex study describing the construction of a provincial population forecasting model, with emphasis placed on interprovincial migration. The paper, by Robert L.Jeacock 3 8 for The Conference Board of Canada, i s examined in length in the following because i t represents one of the most exhaustive studies dealing with Canadian interprovincial migration. 3 6 Ibid, p.26. 3 7 Ibid. p.29. The calculations for these results are not shown in his paper. 3 8 R.L.Jeacock, Op.Cit. 23 The dependent variable used in the interprovincial migration model is the out-migration 3 9 flows from one province to the nine other provinces, therefore , 90 equation flows had to be specified. This decision was taken: (...) as a consequence of the belief that the exogenous variables would differ in kind as well as in terms of the degree of influence depending on the provincial origin and destination 4 0 . "[Also] for some independent variables, i t can be d i f f i c u l t to predict in advance the direction of the influence when net-migration equations are used" 4 1 . In an exploratory phase, the author undertook the specification of a general model that related out-migration to a large number of "theoretically defensible" independent variables. It allowed him to discover which variables appeared to have promise for inclusion in a forecasting model. This general equation was applied to each of the 90 equations. The independent variables were, where possible, expressed in levels as opposed to growth rates, lagged one period, and specified in real per capita terms. Four groups of variables were specified, the two main ones being the economic variables (unemployment , employment and income levels) and the impact of government policy on migration variables (eg. federal transfers to persons, federal and provincial income tax payable, etc.) 3 9 This is an upward adjustment of the family allowance transfers estimated by Statistics Canada. 4 0 Ibid, p.27. 4 1 Ibid, p.3. 24 The theoretical explanation for the inclusion of these variables stems from the p o l i t i c a l diversity of Canada, (...), as well as the economic inequality created by the different endowments of natural resources that exist from one region to the next 4 2 . The local property taxes and, provincial sales taxes, were included in the provincial consumers price indexes used to deflate the independent variables and to transform them in real terms. In short, each of the 90 equations included thirteen independent variables, one constant term, and one dummy variable to account for a change in reporting migration data in 1968. The structural model covered the period 1963-1979; with only 17 observations and 15 right-hand-side variables, there were only two degrees of freedom l e f t . (...) the results l e f t much to be desired in a s t a t i s t i c a l sense. They did, however, provide a hint as to which exogenous variables might prove to be useful in forecasting interprovincial migration between one province and another 4 3 . In summary, in this exploratory phase, a l l of the equations had a high degree of multicollinearity and a small adjusted R-squared, the errors were highly autocorrelated, few variables had the expected signs, and the t-statistics were not significant. On the basis cf these results, Jeacock re-specified his model. 4 2 Ibid, p.5. 4 3 Ibid, p.9. 25 Whereas the i n i t i a l research involved the use of a general purpose equation for a l l province-to-province migration flows, the revised specifications were made on a case-by-case ba s i s 4 4 . In the revised model, the Yukon and the North West Territories are added, increasing the number of equations from 90 to 110. The 110 equations are respecified based on Jeacock's' following c r i t e r i a , in order of importance: (1) The number of independent variables is kept to a minimum to allow as many degrees of freedom as possible 4 5 . Consequently a l l government policy variables are dropped. (2) The t-statistics are to be significant to at least the 5% level. (3) The Durbin-Watson statistics have to be between 1.5 an 2.5. (4) There is to be an absence of serious multicollinearity. (5) The e l a s t i c i t i e s between the dependent and independent variables are to be within "theoretically reasonable bounds". (6) The equations have to f i t the historical data. (...) i t was believed that one could have confidence in the specifications although i t might mean sacrificing something in terms of forecasting accuracy. (...) this approach was deemed superior to one that emphasized forecasting results at the expense of credible specifications 4 6 . In the re-specification some of the independent variables 4 4 Ibid, p.12. 4 5 This is done by using some economic variables that are currently forecasted and for which data are readily available. 4' Ibid, p.12. 26 from the general model are eliminated. The remaining variables are introduced according to the author's "biases". F i r s t , the provincial employment and unemployment rates are used, i f the specification i s not successful, various measures of income are tried, then, a provincial real domestic product variable for particular industries i s employed i f the specification i s s t i l l inadequate. In the new specification, when appropriate, the independent variables enter also in lagged form, as ratios, in per capita and real value terms. The new specification leads to very good results. A l l of the estimated coefficients (201) for the 110 equations have the expected sign, and 99% have a t- s t a t i s t i c greater than 1.85. The measure of forecasting a b i l i t y , the coefficient of var i a t i o n 4 7 indicates that 55% of the equations have an average forecasting error less than 15%. Also, 73% of the out-migration equations have an adjusted R-squared greater than 50%. Only one equation has a "serious" problem of multicollinearity. The variable to appear the most often i s the unemployment rate, followed by employment and subsequently income variables. The f i r s t two indicate that the probability of getting a job "strongly influences" the re-location decision. Other variables "(...) provide only marginal improvement to the s t a t i s t i a l f i t and simulation results of the equations already s p e c i f i e d " 4 8 . The fact that the unemployment is generally successfully 4 7 It is defined as the absolute value of the standard error of estimate expressed as a percentage of the mean value of the dependent variable. 4 8 Ibid, p.16. 27 specified i s in contradiction with most other migration studies which found the variable to be not significant and/or with the wrong expected sign as noted earlier. In British Columbia, the B.C. unemployment rate appears in each of the migration flows to this province. After a l l equations have been estimated on a case-by-case basis, the sum of the out-migration equations for each province i s calculated. Calculations are also made to determine total i n - migration and net migration in a particular province. An assessment of the usefulness of the model must take into consideration the fact that forecasts at the province-to-province level of aggregation (ie.the 110 equations) are lik e l y to be of minor importance from an informational standpoint when compared to a province's total i n - and total out-migration. As previously mentioned, the purpose of specifying and estimating individual province-to-province equations was to reduce forecasting error that occurred when total i n - and total out equations were forecasted directly. The results indicate that this objective was achieved 4' . Jeacock's paper provides many insights in the interprovincial migration f i e l d . His paper terminates the literature review of Canadian interprovincial population moves. 4 9 Ibid, p.19. 28 III. THEORY AND SPECIFICATION OF THE VARIABLES 3.1 Underlying Theory With an interprovincial equilibrium level in the standard of living i t i s assumed that individuals would have no economic incentive to move from one province to another. The standard of livin g i s herein defined as a function of price of housing and five other categories of economic variables (income, labour, personal taxes, cost of living and housing market). As soon as interprovincial differentials take place in one or some of the variables, a disequilibrium level occurs and people are attracted to a particular location because of "pull" factors and are encouraged to move to another location because of "push" factors (McRae;Horna). Therefore i t i s assumed that when the interprovincial standard of living is in disequilibrium there i s an incentive for interprovincial migration. Specifically, people attempt to maximize their economic well-being. It i s also hypothesized that retired people react differently to some economic variables than age groups with high labour force participation rates. First , the retired should have a higher el a s t i c i t y to migrate (than the working) for two categories of variables: housing prices and cost of liv i n g . Second, their income and labour e l a s t i c i t i e s to migrate should be lower. Two models (one for each age group) describing the migration movements (in and out flows) between British Columbia and the rest of Canada are developed, in chapter 5, in order to verify the above hypotheses. Namely, to check the significance 29 of some economic variable differentials in explaining migration flows and to check the different economic-elasticities to migrate of the two age cohorts. In the following i t is also assumed that similar independent variables can be used to determine both in and out migration flows. 3.2 Specification Of The Variables 3.2.1 The Dependent Variables In the American and Canadian literature most studies used a measure of the net number of migrants for the dependent variable. This measure has some shortfalls: i t might be d i f f i c u l t to predict the expected direction of the influence in advance because some ambiguous effects might occur. "For instance, higher moving costs would have a negative effect on out-migration and in-migration and thus an ambiguous effect on net migration" 5 0 . Subsequently, there i s a loss of information in using this measure. If one independent variable seems to be superior among the ones seen in the literature, i t i s the individual out-migration flows from one province to a l l the others. It represents about one hundred equations for the national perspective (Jeacock) and would represent about twenty equations to estimate for a single province as in this thesis. Indeed, nine out-flow equations from British Columbia to each other provinces would have to be estimated as well as the out-flows of the other provinces to 5 0 R.Jeacock, Op.Cit. p.3. 30 British Columbia. In order to do that, the economic variables identifying the standard of living would have to be gathered for each province. As may be recalled, this measure is superior because the factors affecting province-to-province migration (the independent variables) are l i k e l y to dif f e r in "kind" and in their "degree of influence" depending on the sending and receiving province (Jeacock). This method would be ideal for British Columbia's migration flows modelling. It would, however, be a monumental task for a single person because of the extent of the data necessary. This leads to the third method, the one used in this thesis. As is suggested in Section 3.1, the total in-migration and total out-migration flows for British Columbia are used as dependent variables 5 1 . The advantage of this method, over the net migration one, is that the expected direction of the independent variables is usually not ambiguous. The shortfall is that only the economic data in British Columbia and the average Canadian counterpart are taken into account to explain the flows. 3.2.2 The Independent Variables In the models a l l of the variables are formed as a ratio of British Columbia to Canada to capture the differential advantages or disadvantages of a variable in the province compared to the Canadian counterpart. Moreover, some of these 5 1 The data sources and the definitions, for the dependent and independent variables, are provided in chapter four. 31 variables are specified additionally as their provincial absolute value. Finally, seasonal dummies are included in each model to account for seasonal fluctuations. For the variables specified as ratios there is no need to transform the data in real terms. The reason is that the deflators, appearing in both the numerator and the denominator, would cancel anyhow52 . Under disequilibrium, individuals gather and analyze the information about the standard of living in their province of residence and in the potential provinces of destination. Their motivation to maximize their economic well-being and their decision-making process in achieving this goal suggest a number of explicative variables. Some of the variables have been proposed throughout the literature review, the others are experimental but believed to be significant. As seen in chapter two, the data on the variables have to be readily available, they must cover a sufficient historical period to allow as many degrees of freedom as possible and f i n a l l y they must have potential to be forecasted themselves for forecasting purposes. In section 3.1 six categories of variables have been inferred, namely: (1) Income Variables; (2) Labour Variables; (3) Personal Taxes; (4) Price of Housing; 5 2 The Canadian Consumer Price Index (CPI) would have been used to deflate both the provincial and the Canadian data since there is no available CPI for British Columbia. 32 (5) Cost of living Variables; (6) Housing Market Variables. These six categories are specified in a general way below. The motivation of the individuals provides some insight into the expected signs for the co e f f i c i e n t s 5 3 . (1) Income Variables The sign for the in-migration equation i s expected to be positive on the basis that people are lik e l y to be attracted to provinces with higher average income. The expected sign for the out-migration equation may be more ambiguous. On one hand, the higher a province's income, the less incentive individuals have to leave i t . On the other hand, the higher the income, the more risk (eg.uncertainty of finding a job) they may be able to take by leaving i t . (2) Labour Variables With relatively better job opportunities in a location the expected influence on in-migration and out-migration i s positive and negative respectively. (3) Personal Taxes Assuming a nationally uniform level of public services, the higher the taxes the higher the part of their gross income people have to give up so the lower the incentive to move in, and vice versa, the higher the incentive to move out to 5 3 The separate variables included in each category are precisely defined in chapter four 'The Data'. The expected sign for each individual variable is given in APPENDIX A. 33 provinces with relatively lower direct tax burdens. (4) Price of Housing The higher the relative price of housing in the province, the higher the incentive to move out of the province and the lower the incentive to move i n . This makes sense intuitively: assuming interprovincial equality of housing services people prefer to pay less than more. (5) Cost of living Variables The more i t costs to liv e in an area the less likely are people to move in and the more lik e l y they are to move out, to seek for relatively lower prices. Therefore, the in-migration expected sign i s negative and the out-migration expected sign i s positive. (6) Housing Market Variables The expected sign for the in-migration i s positive: relatively better housing market conditions 5 4 would be a pull factor in the province and would not incite individuals to leave the province. Bad housing market relative to the Canadian average would be a push factor. 5 4 A good housing market i s herein defined as a market where the vacancy rate i s large enough to allow people to be selective in their relocation. 34 IV. THE DATA 4.1 Definitions And Sources In the next two sub-sections, the names of a l l the variables are introduced. In the remaining of this thesis, these variables' names are used for c l a r i t y and simplicity 5 5 . The variables are precisely defined and the source of each i s given. Where necessary, some additional information i s also provided. The reader should take note that a variable followed by the '%' sign means that the British Columbia/Canadia ratio i s used. Descriptive measures of a l l variables are found in APPENDIX B. The values of a l l the variables, from the f i r s t quarter of 1966 to the fourth quarter of 198256 are reproduced in APPENDIX C. 4.1.1 The Dependent Variables  FAMALI The variable i s the quarterly interprovincial in-migration of families receiving family allowance benefits. It i s a proxy for migrants in the labour force. The number of migrants i s given by the number of accounts transferred from the other provinces to British Columbia. The original data are quarterly and they can be found in the Canadian Socio-Economic Information 5 5 An alphabetical l i s t of variable names and definitions i s provided in APPENDIX A. 5 6 Again in order to alleviate the text, the notation '1966(1)-1982(4)' i s used; the number in parenthesis indicates the quarter of the year. 35 Management System (CANSIM) Mini-Base, series D269438. The series i s computed by Health and Welfare Canada. FAMALO The variable is the quarterly interprovincial out-migration of families receiving family allowance benefits. It is the number of accounts transferred from B.C. to the other provinces. The data source is the same as FAMALI and are provided in CANSIM series D269452. FAMANT The variable i s the quarterly interprovincial net migration of families receiving family allowance benefits. It i s equal to FAMALI minus FAMALO. This variable w i l l be used for comparison purposes only. OLDAGI This variable i s a proxy for the B.C. quarterly interprovincial in-migration of retired people. It i s the summation of the number of old age security number of accounts transferred from other provinces to B.C. The original data are monthly, therefore each three months period are added to transform them on a quarterly basis. This series i s also computed by Health and Welfare Canada 5 7 . OLDAGO This variable i s a proxy for the quarterly interprovincial out-migration of retired people. The number of old age security 5 7 A special thanks to Messieurs R.Prevost and F.Thibodeau, Programs Statistics Section, Planning , Development and Management Support Division , Income Security Programs Branch, Health and Welfare Canada, that provided the data necessary. 36 accounts transferred from British Columbia to other provinces i s used. 4.1.2 The Independent Variables (1) Income Variables WAGE% This variable is the ratio of British Columbia to the Canadian average for average weekly wages and salaries. The B.C. figure i s found in CANSIM series D1505 and the Canadian one in series D1495. These original data are given monthly, they are based on reports from corporations employing twenty people or more and they relate to the last pay periods in the month58 . In order to transform the monthly series into quarterly data, the mean of each three months period is taken. INCO% This variable represents the quarterly ratio of personal income per capita in British Columbia over the Canadian per capita income. The original data are annual and they are supplied by Statistics-Canada in Catalogue 13-201, "National Income and Expenditure Accounts 1968-1982", Table 36: Personal Income Per Person, geographical distribution in dollars. Because of the yearly nature of the data, the i n i t i a l ratios were calculated on an annual basis. To transform to 5 8 Statistics-Canada, CANSIM University Base Series Directory 1983. Matrix 74. 37 quarterly ratios, the method used in McRae59 is applied: the annual value is assumed to represent the second quarter ratio and the following three quarters are assumed to increase, at a constant rate of change, to the following annual ratio. (2) Labour Variables UNEM% This i s the ratio of the quarterly unemployment rate for those 15 years and over in British Columbia, divided by the quarterly unemployment rate for the same age group in Canada. Both are computed by the Labour Force Survey (LFS) group and are found in CANSIM Mini-Base, series D769173 and D767289 respectively. The CANSIM data are monthly, therefore, the mean for each three month period has been calculated to transform the unemployment rates on a quarterly basis. EM/PO% This i s the quarterly employment/population ratio in British Columbia divided by the employment/population ratio in Canada. These two series are also computed by the LFS group. The CANSIM series are D773355 for B.C. and D773309 for Canada. The ratios are computed monthly for the 15 years and over. Again the monthly data are transformed to quarterly measure by taking the average of each three months period. EMG.% This quarterly variable is the ratio of employment growth 5 9 Don McRae, Loc.Cit. 38 rate in British Columbia over the employment growth rate in Canada. The rates have been calculated using the number of persons employed, 15 years and over, in British Columbia and in Canada. These data are computed by the LFS and they are found in CANSIM series D769169 and D767286 respectively. Before deriving the employment growth rates, the CANSIM monthly series have been transformed to quarterly data by taking the mean of each three months period. JOBID% This i s a quarterly job index variable, where the help wanted index in B.C. is divided by the help wanted index in the country. The help wanted index is based on a measure of the help wanted advertising in the classified sections of 18 newspapers in 17 major metropolitan areas. The basic unit of measurement is the column. The editions of newspapers measured are the Saturday of the labour force survey reference week during each month. Note that no effort i s made to measure the number or type of jobs advertised 6 0 . The CANSIM series are D730178 and D730173 for B.C. and Canada respectively. The source of data i s the labour division of Statistics-Canada. UNEMBC This variable represents the unemployment rate for the 15 years old and over in British Columbia. The source i s identical to UNEM% defined above. Here again, the mean for each three months period has been calculated to transform the rate on a 6 0 Statistics-Canada, Op.Cit. Matrix 105. 39 quarterly basis. EMG.BC This i s the quarterly employment growth rate in British Columbia. Its source is given in the description of EMG.% above. (3) Personal Taxes TAX% This tax variable is a quarterly measure of the direct taxes payable in British Columbia as a percent of the province's total personal income, divided by the Canadian personal direct taxes as a percent of the country's total personal income. The four basic series are found in Statistics-Canada, Catalogue 13-213 "Annual System of National Accounts, Provincial Economic Accounts, Experimental Data 1966-1981", Table 10: Sources and Disposition of Personal Income. A l l of these original data are given on an annual basis, therefore, in order to transform the yearly ratio to quarterly ratios, the same method of transformation described for INCO% is used. (4) Price of Housing H0USE% This independent variable i s a ratio of the quarterly average residential prices in British Columbia . over the quarterly average residential prices in Canada. The former is determined by the British Columbia average sale price of a l l Multiple Listing Service (MLS) property transactions and the 40 latter by the Canadian counterpart 6 1 . 'The MLS data are compiled in the f i l e RULE:MLS.MIDAS62 . Most of these data were originally taken from Multiple Listing  Service, Annual Report 1979. "It is estimated that MLS accounts for about 60 percent of a l l organized real estate a c t i v i t y " 6 3 . (5) Cost of Living Variables CPI% This variable is the quarterly consumer price index (CPI) in Vancouver 6 4 over the Canadian CPI ( a l l items 1971=100) . The data are reproduced in the f i l e RULE:DATA.MIDAS. Originally these data have been taken from CANSIM D454397 and D451000 se r i e s 6 5 . Before calculating the quarterly CPI ratio, monthly CPIs have been transformed to a quarterly basis by taking the average of each three months period. CPIVAN This is the quarterly Vancouver CPI ( a l l items 1971=100). The source of data and additional information are given under the variable CPI%. The average sale price per MLS transaction is used as a proxy for the average sale price per residential transaction. The similarities of their respective annual values show that the assumption i s not inappropriate. The account RULE is the common computer account for the Urban Land Economics Division of the University of British Columbia. RULE contains a database of many housing and housing related st a t i s t i c s . MLS Annual Report 1979 p . i . As said before there is no available CPI for British Columbia, therefore Vancouver CPI is used as a proxy. In 1984, the series D454397 has been . removed from CANSIM's tape. 41 (6) Housing Market Variables UNOCC% This variable is the quarterly ratio of newly completed and unoccupied dwellings units (houses and duplexes) in Vancouver metropolitan area divided by the Canadian counterpart, which i s given by the total metropolitan areas. Vancouver i s used as a proxy for British Columbia. The data are provided in the annual 'Canada Mortgage and Housing Corporation (CMHC) Canadian Housing Statistics' . VACAN% This variable represents a quarterly ratio of the vacancy rates, in apartment structures of six units and over, for the Vancouver metropolitan area divided by a weighted average of Canadian metropolitan areas surveyed. Because of the nonexistence of vacancy rates data for the province of British Columbia, Vancouver metropolitan data are used as a proxy 6 6 . The sources for the Vancouver area and the Canadian weighted average data are the annual 'CMHC Canadian Housing Statistics'. In CMHC's publications, the given vacancy rates are annually unt i l 1970, and semiannually thereafter. In order to transform to quarterly data, the method used for INC0% i s taken for the annual vacancy rates. For the semiannual data, the method used i s a simple linear interpolation. 6 6 On June 1st 1983, 46.34% of B.C. population was livi n g in the Vancouver metropolitan area. Source: Statistics-Canada, Demography division, Census metropolitan areas. 42 VACVAN This variable represents the quarterly Vancouver vacancy rates (in percentage), in apartment structures of six units and over, for the Vancouver metropolitan area. The source of data is given in the description of the preceding variable VACAN%. VACDUM This variable i s a Vancouver vacancy dummy variable. It has been derived from VACVAN. The dummy takes the value one when the vacancy rate is greater than 'one' and the value zero when the rate is less than or equal to 'one'. The threshold 'one' has been chosen subjectively with the belief that a vacancy rate less then or equal to that value is an indicator of a very tight market. 4.2 Rel i a b i l i t y And Limits Of Data 4.2.1 The Dependent Variables FAMALI FAMALO Family allowance data, although a "reliable indicator of migration v a r i a t i o n " 6 7 and the "only direct method of recording migration in Canada on a monthly basis" 6 8 , have some limits: (1) It i s not possible to find any descriptive information about the type of migrating families nor any characteristics on 6 7 J.Dean. Op.Cit. p.23. 6 8 R.Jeacock. Op.Cit. p.7. 43 the exact region where families come from and where they relocate. Therefore people's decision making process is unknown; (2) The figures of transfers may include temporary and return migration; (3) It represents an under estimation of migrants. In his paper Dean gave the results of a study, undertaken by Statistics Canada in 1982, where 28.2% of recent migrants in British Columbia were single people. However, the largest migrant group to B.C. (married people between 25-44 years old with children) is most l i k e l y to be represented by family allowance transferred account data. • OLDAGI OLDAGO In the same way the old age security number of accounts transferred i s li k e l y to be an under estimation of the number of elderly retired migrants. Also the data have two deficiencies: (1) From January to April 1971 only a few accounts have been transferred because of administrative changes; (2) In some months, especially December and January few transfers are made because of income tax forms'preparation. 44 4.2.2 The Independent Variables Labour Variables Most of the labour variables UNEM%, EM/PO%, EMG.%, UNEMBC and EMG.BC are calculated using the number of persons employed or unemployed in the 15 years and over group. It would have been preferable to use an age group where people receiving family allowance benefits had better chance of being represented (eg.the 35-55 years old group), but unfortunately such age group breakdown is not available for British Columbia. Cost of livi n g variables For Canadian CPI there is a CPI ' a l l items excluding housing'. Unfortunately no equivalent measure is available for Vancouver. Therefore the CPI ' a l l items' had to be used for non-housing prices. As said in one of chapter three's footnote, the series D454397 has been removed from CANSIM's tape during the last year. Therefore, the user of this data could be inclined to question the accuracy of the related variables. Housing market variables One may question the r e l i a b i l i t y of using Vancouver metropolitan vacancy rates as a proxy for British Columbia vacancy rates. Ideally, Vancouver rates should be compared to other locations in the province. Unfortunately, the only other comparable figures found are for Victoria metropolitan area. 45 The data below indicate that the two c i t i e s have similar vacancy-rates over a range of years 6 9 . Vancouver Victoria 1976 0.7 0.6 1977 1.6 2.5 1978 1.4 1.1 1979 0.2 0.1 1980 0.1 0.1 1981 0.1 0.1 6 9 Source: CMHC Canadian Housing Statistics. 1980,1982. 46 V. THE STRUCTURAL MODELS 5.1 The Methodology In this section i s the description of the methodology that yields the specification of a fi n a l model (one for each dependent variable). * First step: Selecting the lags (...) in a country as geographically large and culturally diverse as Canada, decisions to migrate are not l i k e l y to be based on impulse. This suggests that certain economic stimuli bearing on the decision to migrate may have to be present for a period of time before having their predicted e f f e c t 7 0 . The above citation offers a rationale for lagging the independent variables. Furthermore, one has to assume that i t takes some time for the information to flow between regions (McRae). There is no fixed rule for choosing the proper lags. The method described in the following was used, only as a guide, for picking out a promising lag for an independent variable. Each dependent variable was regressed against the seasonal dummies plus one different lag (0 to 4) of each independent variable. For example: FAMALI= a DUMMY1 + b DUMMY2 + c DUMMY3 + d WAGE% FAMALI= a DUMMY1 + b DUMMY2 + c DUMMY3 + d WAGE%-1 FAMALI= a DUMMY1 + b DUMMY2 + c DUMMY3 + d WAGE%-2 7 0 R.Jeacock. Op.Cit. p.4. 47 FAMALI= a DUMMY1 + b DUMMY2 + c DUMMY3 + d WAGE%-3 FAMALI= a DUMMY1 + b DUMMY2 + c DUMMY3 + d WAGE%-4 where WAGE%-1 is WAGE% lagged one period (ie. one quarter); WAGE%-2 is WAGE% lagged two periods. Etc. Then, for each independent variable, the lag with the highest t-statis t i c was recorded for the next step. The estimated period covers 1966(1)-1981(4). Second step: Specifying the basic models In order to determine i f an independent variable was to be included in a basic ( i n i t i a l ) model, the following c r i t e r i a were applied: (1) If the signs on a l l lags were correct then the lag with the highest t - s t a t i s t i c was put in the basic model; (2) If the signs on the four lags were incorrect, then the variable was omitted in the basic model; (3) If the signs on one to three lags were incorrect the variable was also omitted in the basic model. After applying these c r i t e r i a , one i n i t i a l model for each independent variable was specified. 48 • Third step: Developing the basic models further In an effort to further improve the specification of an i n i t i a l model, additional regressions were performed. The results are displayed in Tables 1, 2, 3 and 4. One key c r i t e r i a was emphasized: in the subsequent step (of the selecting process) only the regressions with at least one variable in each category 7 1 would be considered as potential best models. Hence i f in step two a l l the variables of a category had their lagged coefficients with the wrong sign, and therefore were not selected in the i n i t i a l model, then at least one of the variables in that category had to be included in successive regressions. Priority was given f i r s t to a variable rejected i n i t i a l l y by c r i t e r i a (3) and second to a variable rejected by c r i t e r i a (2). For an equivocal situation the variable chosen was the one that had lags with the lowest t - s t a t i s t i c s . This situation occurred just once. These selected variables were put in the regression with lag 0. In subsequent regressions, new lags were tried intuitively. 7 1 As seen in previous chapters, six categories of variables have been defined: (1) Income variables; (2) Labour variables; (3) Personal taxes; (4) Price of housing; (5) Cost of l i v i n g variables and (6) Housing market variables. INCOME VARIABLES LABOUR VARIABLES TAX VAR . HOUSE PRICE COST OF LIVING VAR. HOUSING MARKET VARIABLES MODEL* RS/SD WAGE% INCO% + + UNEM% EM/PO% EMG.% JOBID% UNEMBC EMG.BC + + + - + TAX% HOUSE0/. CPI% CPI VAN UN0CC% VACAN% VACVAN VACDUM + + + + L-0 L-2 1.2 2.6 L-1 L-0 L-0 L-1 L-1 0.8 0.1 0.9 -0.6 0.8 L-4 -1.3 L-2 -2.0 1 B a s i c .89/294 L-0 L-2 1.6 3.2 L-1 L-0 L-0 L-1 L-1 -0.6 0.6 2.6 1.0 0.2 L-4 0.2 L-0 -2.7 L-2 -2 . 5 L-0 2.2 2 .90/275 L-0 L-2 1.7 3.3 L-1 L-0 L-1 -1.0 2.7 0.9 L-4 0. 1 L-0 -2.9 L-2 -2.5 L-0 2 . 2 3 .90/271 L-0 L-2 2.1 3.9 L-0 2.7 L-4 -1.7 L-0 -2.6 L-2 -2.6 L-0 2.0 4 .90/271 L-0 L-2 2.1 3.8 L-0 2 ..7 L-4 -1.8 L-1 -2.7 L-2 -2.4 L-0 2 . 1 5 .90/270 L-0 L-2 1.6 3.7 L-0 2.1 L-4 -1.8 L-2 -2.0 L-2 -2 . 3 L-0 1 .9 6 .89/277 L-0 L-2 1.6 3.8 L-0 1 . 9 L-4 -2.0 L-3 -1.9 L-2 -2 . 1 L-0 1 .9 7 .89/278 L-O L-2 1.7 4.5 L-0 3.2 L-4 -1.6 L-1 -2.7 L-2 -2.3 L- 1 3. 1 8 .91/257 L-0 L-2 1.5 4.6 L-0 3.3 L-4 -1.2 L-1 -2.7 L-2 -2.2 L-2 2.7 9 .91/261 L-0 L-2 1.7 3.5 L-0 3 . 1 L-4 -1.6 L-1 -2.6 L-2 -2.7 L-3 2. 1 10 .91/257 L-2 6.6 L-0 3.1 L-4 -2 . 1 L-1 -2.3 L-2 -1.9 L-1 3.3 1 1 * .90/262 L-2 ' 6 . 4 L-0 2.7 L-4 -1.8 L-2 -1.6 L-2 -2.2 L-2 3. 1 12 .90/268 NOTE L-O, L-1, ...L-4 i n d i c a t e the l a g ; RS: R-squared; SD: Standard d e v i a t i o n of r e s i d u a l s ; T - S t a t f o r the dummies not pr e s e n t e d because of space l i m i t a t i o n s . INCOME VARIABLES LABOUR VARIABLES TAX VAR . HOUSE PRICE COST OF LIVING VAR. HOUSING MARKET VARIABLES MODEL* RS/SD WAGE% INCO% ? ? UNEM% EM/P0% EMG.% JOBID% UNEMBC EMG.BC + - - + TAX% + HOUSE% + CPI% CPI VAN + + UNOCC0/. VACAN% VACVAN VACDUM L-0 0.7 L-0 L-0 1.7 -1.0 L-3 1 .7 L-0 L-0 3.6 -1.1 L-3 L-3 L-2 -2.2 -0.5 -0.6 1 B a s i c .85/217 L-0 0.4 L-0 L-0 2.0 -1.0 L-3 1.9 L-0 4.5 L-3 -4.3 2 .84/215 L-0 0.8 L-0 L-0 2.7 r 1 • 1 L-0 1 . 8 L-3 2 .6 L-0 3 . 3 L-3 -4.0 3 .85/2 10 L-0 0.7 L-O L-0 2.2 -1.0 L-1 1 . 1 L-3 2 . 2 L-O 3 . 2 L-3 -4.0 4 .85/215 L-0 0.4 L-0 L-0 1.7 -0.9 L-2 0. 1 L-3 1 .6 L-0 3 . 5 L-3 -4 . 2 5 .84/217 L-0 0.5 L-0 3.0 L-0 1 . 7 L-3 2.5 L-O 3 . 2 L-3 -4 . 1 6 .85/211 L-0 L-0 3 . 4 L-0 1 . 7 L-3 1.1 L-0 2 .9 L-3 -4 . 3 7 * .85/207 L-0 1 .8 L-0 3.7 L-0 1 .9 L-3 1 .0 L-1 3.0 L-3 -4.6 8 .85/206 L- 1 O. 2 L-0 2.9 L-0 1 .6 L-3 2. 1 L-0 3 . 1 L-3 -4 . 2 9 .85/212 L-2 -0. 1 L-0 2.9 L-0 1 .6 L-3 2 . 2 L-0 3 . 1 L-3 -4.2 10 .85/212 L-0 1 .9 L-0 3 . 9 L-0 1 . 9 L-2 1 . 1 L-1 3 . 1 L-3 -4 . 3 1 1 .86/205 L-0 1-8 L-O 3.7 L-0 1 .9 L-3 1 .0 L-1 3.0 L-3 -4.6 12 .85/206 Note L-0, L-1, ...L-4 i n d i c a t e the l a g ; RS: R-squared; SD: Standard d e v i a t i o n of r e s i d u a l s . INCOME VARIABLES LABOUR VARIABLES TAX VAR. HOUSE PRICE COST OF LIVING VAR. HOUSING MARKET VARIABLES MODEL* RS/SD WAGE% INCO% + + UNEM% EM/P0% EMG.% J0BID% UNEMBC EMG.BC - + + + - + TAX% HOUSE% CPI% CPIVAN UNOCC% VACAN% VACVAN VACDUM + + + + • L-0 L-0 0.7 1.0 L-0 L-0 0.9 0.5 L-4 -2 . 2 L-0 -1.5 1 B a s i c .50/216 L-0 L-0 0.6 0.7 L-0 L-0 0.6 0.5 L-4 -1.8 L-0 -0.3 L-0 -1.4 L-0 0.5 2 .5 1/2 19 L-0 L-0 0.5 0.8 L-0 0.5 L-4 -1.8 L-0 0. 1 L-0 -1.9 L-0 0.6 3 .50/217 L-0 L-0 0.4 0.7 L-0 0.3 L-4 -1.8 L-0 0.3 L-0 -1.5 L-0 0.8 4 .50/218 L-0 1 . 7 L-0 1 . 2 L-4 -2.4 L-2 -2.4 L-0 -1.3 L- 1 1 .5 5 .52/207 L-0 1 .4 L-0 1 .4 L-4 -2. 1 L-2 -1.5 L-0 -1.0 L-1 1 .7 6 .51/209 L-0 1 .9 L-0 1 .4 L-3 -2.6 L-2 -2.5 L-0 -1.4 L- 1 1 .7 7 .53/205 L-0 2 . 1 L-0 1 .5 L-2 -2.7 L-2 -2.6 L-0 -1.5 L- 1 1 .9 8 * .54/204 L-0 2.0 L-0 1 . 2 L-2 -3.0 L-2 -2.5 L-0 -1.4 L-0 1 . 6 9 .55/206 Note L-0, L-1, ...L-4 i n d i c a t e the l a g ; RS: R-squared; SD:Standard d e v i a t i o n of r e s i d u a l s . (D CO I 1-3 INCOME VARIABLES LABOUR VARIABLES TAX VAR . HOUSE PRICE COST OF LIVING VAR. HOUSING MARKET VARIABLES MODEL* RS/SD WAGE% INCO°/o ? ? UNEM°/o EM/P0% EMG.% J0BID% UNEMBC EMG. BC + - - + TAX% + HOUSE0/, + CPI°/o CPIVAN + + UNOCC% VACAN% VACVAN VACDUM L-4 -0.3 L-3 -1.1 L-3 2.3 L-2 1 .3 L-3 0.0 1 B a s i c .42/159 L-4 -0.5 L-3 -1.0 L-3 2.4 L-4 1 .6 L-3 -0. 1 2 . 43/158 L-4 -0.4 L-3 -0.9 L-0 -0.4 L-3 1 . 1 L-4 1 .6 L-3 -0.3 3 .43/159 L-4 -0.5 L-3 -0.6 L-2 -1.3 L-3 0.7 L-4 1 . 7 L-3 -0.7 4 .44/157 L-4 -0.6 L-3 -0.7 L-3 -0.8 L-3 1 . 1 L-4 1 . 7 L-3 -0.5 5 .43/159 L-4 -O. 5 L-3 -0.8 L-4 -0.6 L-3 1 .3 L-4 1 .7 L-3 -0.4 6 .43/159 L-4 -0.4 L-3 -1.0 L-4 -0.7 L-3 1 . 1 L-3 1 .6 L-3 -0.3 7 * .43/160 L-4 -O. 3 L-3 -1.2 L-3 2.3 L-3 1 .5 L-3 -0. 1 8 .42/159 L-0 -0.6 L-3 -0.5 L-2 -1.4 L-3 0.4 L-4 1 .8 L-3 -0.8 9 .45/157 L-0 -0.7 L-2 -0.2 L-2 -1.7 L-3 0.5 L-4 1 .9 L-3 -0.9 10 .44/156 L-0 -0.7 L-2 -0.3 L-2 -1.8 L-1 0.8 L-4 2.2 L-3 -0.7 1 1 .45/155 Note L-0, L-1, ...L-4 i n d i c a t e the l a g ; RS: R-squared; SO: Standard d e v i a t i o n of r e s i d u a l s . 53 • Fourth Step: Selecting the best models After the specification of different regressions, the f i n a l model for each dependent variable was chosen on the basis of credible specifications, of minimum sum of squared errors for the forecast period 1982(1)-1982(4)72 and of minimum standard deviation of residuals for the fi t t e d period 1966(1)-1981(4). For ambiguous situations the ultimate c r i t e r i a was forecasting accuracy. Tables 5, 6, 7 and 8 below display the f i n a l model (coefficients, t-statistics and el a s t i c i t i e s to migrate) for each dependent variable. The R-squared, the standard deviation of residuals and the sum of squared errors are also given for each model. The three seasonal dummies correspond to the f i r s t , second and third quarter respectively. The ela s t i c i t y formula used i s : Elasticity= % Change Dep.Var. Change Dep.Var. Mean Ind.Var. * % Change Ind.Var. Change Ind.Var. Mean Dep.Var. = Coefficient * Mean Ind.Var. Ind. Var. Mean Dep.Var. 7 2 The models have been chosen under the temporary assumption that the regressions were adequate, i e . that the residuals were normal and random. 54 Table 5 - Final structural model for the working i n -migration (FAMALI) Variable Coefficient T-statistic E l a s t i c i t y INC0%-2 JOBID% TAX%-4 H0USE%-1 CPI%-2 UN0CC%-1 DUMMY1 DUMMY2 DUMMY3 CONSTANT 23333 1032 -4543 -1144 -7577 1732 -1309 -1438 -145 1359 6.56 3.10 -2.09 -2.29 -1.87 3.34 -13.78 -15.36 -1.55 2.45 9.00 0.36 -1.65 -0.40 -2.68 0.08 R-squared: .90 Adjusted R-squared: .89 Degrees of freedom: 53 Standard deviation of residuals: 262 Sum of squared errors: 766,978 This f i n a l model i s model 11 in Table 1. 55 Table 6 - Final structural model for the working out-migration (FAMALO) Variable Coefficient T-statistic E l a s t i c i t y WAGE% 347 4 1.63 1.95 UNEMBC 104 3.41 0.36 TAX% 4414 1.73 2.28 H0USE%-3 585 1.12 0.29 CPI% 8671 2.93 4.39 VACAN%-3 -582 -4.33 -0.13 DUMMY1 -516 -6.34 DUMMY2 -636 -8.62 DUMMY3 206 2.76 CONSTANT 561 1.08 R-squared: .85 Adjusted R-squared: .83 Degrees of freedom: 54 Standard deviation of residuals: 207 Sum of squared errors: 885,356 This f i n a l model i s model 7 in Table 2. 56 Table 7 - Final structural model for the elderly i n -migration (OLDAGI) Variable Coefficient T-statistic E l a s t i c i t y WAGE% 4171 2.10 7.45 J0BID% 315 1.47 0.50 TAX%-2 -5042 -2.72 -8.28 H0USE%-2 -1183 -2.63 -1.87 CPI% -5439 -1.54 -8.74 UN0CC%-1 812 1.90 0.17 DUMMY1 -253 -3.53 DUMMY2 -149 -2.02 DUMMY3 96 1.30 CONSTANT 1147 3.62 R-squared: .54 Adjusted R-squared: .46 Degrees of freedom: 53 Standard deviation of residuals: 204 Sum of squared errors: 494,005 This f i n a l model is model 8 in Table 3. 57 Table 8 - Final structural model for the elderly out-migration (OLDAGO) Variable Coefficient T-statistic E l a s t i c i t y INC0%-4 -857 -0.37 -2.64 EMG.BC-3 -16 -0.97 -0.05 TAX%-4 -1085 -0.68 -3.13 H0USE%-3 374 1.13 1.03 CPI%-3 3114 1.57 8.78 VACVAN-3 -10 -0.33 -0.04 DUMMY1 -80 -0.75 DUMMY2 14 0.16 DUMMY3 63 1.04 CONSTANT 109 0.22 R-squared: .43 Adjusted R-squared: .33 Degrees of freedom: 51 Standard deviation of residuals: 160 Sum of squared errors: 359,463 This f i n a l model is model 7 in table 4. 58 5.2 Diagnostic Checks Of Model Adequacy It i s important to check the adequacy of the f i n a l models. Normality and randomness of the residuals must be tested. The results of the regressions and the diagnostic checks are found in APPENDIX D. For FAMALI model, the Durbin-Watson s t a t i s t i c is 2.16, suggesting a lack of f i r s t order autocorrelation in the residuals (evidence that does not reject randomness). (...) the expected value of the Durbin-Watson st a t i s t i c given random disturbances is about 2; larger values point to excessive alternation, while smaller values point to excessive clustering 7 3 . To test for higher order serial correlation, the autocorrelation function i s investigated. A l l residuals, from the f i r s t to the twenty-fourth order are not significantly different from zero. "Given randomness, we would expect about 95 percent of the sample autocorrelations to f a l l within the limits [two-standard error l i m i t s ] " 7 4 . The runs-count (counts of strings of successive observations above and below the mean) i s a third indicator of randomness. If the absolute difference between the observed number of runs [and the expected number of runs from a random process] is greater than two standard errors, the evidence against randomness is strong; i f less than one, the evidence against randomness is weak75 . 7 3 F.Robert Ling and Harry V.Roberts, Conversational Statistics  with IDA, An Introduction to Data Analysis and Regression. p.12-15. 7 4 H.Roberts, Time-Series and Forecasting with IDA, p.8-32. 7 5 R.Ling and H.Roberts, Op.Cit., p.4-32. 59 The absolute difference being only 0.40, the evidence against randomness is weak. To check for normality, the normal cumulative probability plot (NCPP) of the residuals is examined. The most important check is visual examination of the plot. One i s looking for systematic and substantial variation of the sample points from the straight line of the diagonal 7 6 . On the NCPP, the points follow the diagonal closely, suggesting that normality is a good approximation to the shape of the errors distribution. There are other measures that are "supplements to the visual examination" of the normal probability plot: two of them are the skewness and the kurtosis c o e f f i c i e n t s 7 7 . Here is a rough guideline for the interpretation of the skewness and kurtosis coefficients: (...) I have found i t useful to regard skewness coefficients within +0.5 of 0 as representing reasonable conformity with normality. Similarly for the kurtosis coefficient, I have found limits of ±1 from 0 to be useful for judging conformity 7 8 . The residuals again seem to conform with normality, both the skewness and kurtosis coefficients being smaller than the guideline values given above. A bell-shape curve i s drawn when the peaks and valleys of the histogram of standardized values of residuals are smoothed out. This is another hint of normality. Therefore the specification that FAMAL1 residuals are normal and 7 6 Ibid, p.7-18 7 7 For more details on the shape of the distribution associated with these measures refer to R.Ling and H.Roberts books. 7 8 Ibid, p.7-18. 60 random i s accepted. In the same manner, diagnostic checks can be performed on the residuals of FAMALO, OLDAGI and OLDAGO models. The r e s u l t s i n d i c a t e that for these three models, the re s i d u a l s again seem to reasonably conform to normality and randomness, with the exception of one o u t l i e r r e s i d u a l i n OLDAGO model. Given the s p e c i f i c a t i o n that the residuals are normal and random, predictions about future migration, using the f i n a l models, are adequate. 5.3 Forecasts Based On The F i t t e d Models In using the f i n a l models i t i s poss i b l e to forecast migration ( i n and out of B.C.) for the working and for the e l d e r l y . Point predictions are made from the models f i t t e d . "For meaningful external v a l i d a t i o n of new data, the v a l i d a t i n g block of rows should be e n t i r e l y d i s j o i n t from the rows used i n f i t t i n g ( . . . ) " 7 ' . A row i s defined as a l l the observations i n a quarter. The forecast period chosen i s 1982(1)-1982(4). This period, for which the dependent and independent v a r i a b l e s are av a i l a b l e , has not been used i n f i t t i n g the models. The differences between the actual migration data and the point forecasts are c a l l e d p r e d i c t i o n errors. Table 9 below displays the o r i g i n a l s e r i e s , FAMALI, FAMALO, OLDAGI and OLDAGO, as well as the point predictions and the p r e d i c t i o n errors for the forecast period. 7 9 R.Ling and H.Roberts, IDA A User's Guide to the IDA Interactive  Data Analysis and Forecasting System, p.9-11. 61 Table 9 - Prediction errors for the structural models PERIOD FAMALI DATA POINT PREDICTIONS PREDICTION ERRORS % OF ERROR 1982(1) 1982(2) 1982(3) 1982(4) 1874 1817 2536 2364 2158 1584 2772 3123 -284 233 -236 -759 15 -13 9 32 Sum of < Root mec squared in squai errors= 7C •e error= 41 ;6,722 57 PERIOD FAMALO DATA POINT PREDICTIONS PREDICTION ERRORS % OF ERROR 1982(1) 1982(2) 1982(3) 1982(4) 2401 1896 2639 2393 2393 2306 3212 3017 8 -410 -573 -624 0 22 22 26 Sum of ! Root mec squared in squai errors= 8? "e error= 4" 35,869 11 PERIOD OLDAGI DATA POINT PREDICTIONS PREDICTION ERRORS % OF ERROR 1982(1) 1982(2) 1982(3) 1982(4) 536 1034 687 421 282 519 783 814 254 515 -96 -393 -47 -50 14 93 Sum of . Root me£ squared in squai errors= 4< :e error= 3f 33,406 SI PERIOD OLDAGO DATA POINT PREDICTIONS PREDICTION ERRORS % OF ERROR 1982(1) 1982(2) 1982(3) 1982(4) 469 1036 623 292 419 556 669 645 50 480 -46 -353 -11 -46 7 121 Sum of squared error= 359,625 Root mean square error= 300 The yearly average percentage of errors i s 27%, 17.5%, 2.5% and 71% for FAMALI, FAMALO, OLDAGI and OLDAGO respectively. The 62 results seem satisfactory considering the short duration of the forecasting period. The outcomes for the working group wi l l be discussed further in chapter six. 5.4 Analysis And Testing 5.4.1 The Structural Models In this section, the f i n a l models' results produced in Tables 5, 6, 7 and 8 are analyzed. FAMALI For FAMALI fin a l model the signs of a l l the independent variables conform with expectations. Based on 53 degrees of freedom, the coefficients of a l l the economic variables are significantly different from zero at the 5% l e v e l 8 0 . A l l the variables in FAMALI model are lagged, except the labour variable JOBID%. As seen in the f i r s t part of this chapter, one of the rationales for lagging variables is the lapse of time i t takes for the information to flow between regions. Because job index is a measure of the help wanted advertised in the classified sections of major newspapers, i t can be assumed that such information is easily accessed by individuals. Therefore i t is conceivable that the variable does not need to be lagged 8 1 . R-squared for FAMALI f i n a l model is 8 0 In this section a l l tests performed on the coefficents are t-statistics one-tailed tests. 8 1 It should be noted that a variable with lag 0 is probably s t i l l lagged for a period less than one quarter. 63 90%. When the dependent variable is regressed against the seasonal dummies only, R-squared i s equal to 74%. This high percentage indicates that a large proportion of FAMALI's total variation i s explained by seasonality. FAMALO For FAMALO fi n a l model the sign of each variable conforms with expectations. As seen in chapter three, the out-migration expected signs for income variables may be more ambiguous. On one hand, the higher the ratio of average weekly wages, the less incentive individuals have to leave the province. On the other hand, i f they have accumulated a safety cushion over time, individuals may be able to take on more risk by leaving the province. This assumes that weekly income i s correlated to wealth. The positive sign for WAGE% would support this assumption. Its coefficient i s significantly different from zero at the 10% level. A l l the other variables are significantly different from zero at the 5% level, except the ratio of average house prices which is significantly different from zero at about the 15% level. Most variables in FAMALO model are not lagged. Intuitively i t makes sense because a l l variables are partly formed with B.C. information. These data are more quickly accessible to the potential out-migrants than they are to the potential i n -migrant s. The ratios of average housing prices and vacancy rates, on the other hand, are lagged three periods. This may suggest that d i f f i c u l t housing market conditions, depicted by 64 relatively high prices and low vacancies in British Columbia, have to be present for a longer period before reaction. The size and i l l i q u i d i t y of housing assets could be an explanation. When FAMALO is regressed against the seasonal dummies, R-squared is equal to 47%. Adding the economic variables in the regression increases R-squared to 85%. The proportion of FAMALO's total variation explained by seasonality i s not as important as i t was for FAMALI. The economic variables, however, add more to the percentage of FAMALO's explained total variation (38%) than they did for FAMALI (16%). OLDAGI Again, for OLDAGI, the sign of a l l coefficients conforms with expectations. Based on 53 degrees of freedom WAGE%, TAX%-2, H0USE%-2 and UN0CC%-1 are significantly different from zero at the 5% level and JOBID% and CPI% at the 10% level. Three variables JOBID%, WAGE% and CPI% have a lag 0 (ie. less than a quarter). When the economic variables are added to the seasonal dummies, R-squared increases from 33% to 54%. This represents an increase of 21% in OLDAGI's total variation explained by the regression. OLDAGO The results, for OLDAGO final model, are not clear cut. A l l variables have the right sign except TAX%-4. However, based on 51 degrees of freedom, a l l variables are not significantly different from zero at the 5% level. At the 10% level, only the 65 coefficient of CPI%-3 is significant, and H0USE%-3 is significantly different from zero at about the 15% level. A l l the variables in the model have longer lags than in OLDAGI model. This fact is contradictory with the previous case where most lags were shorter for the out-migration than for the in-migration. The author proposes the following behavioural hypothesis: for the retired, relative economic disadvantages may have to be present for a longer period of time (than i t does for the working) before the elderly decide to give up the reputed West Coast moderate climate. This hypothesis could also explain the poor results obtained for the elderly out-migration model. 5.4.2 Comparing The Ela s t i c i t i e s In section 3.1, hypotheses of different economic-elast i c i t i e s to migrate of the two-age cohorts were made. The hypotheses were that: (1) the retired should have a higher elasticity to migrate, than the working, in regard to housing prices and cost of living; (2) the retired should have lower income and labour ela s t i c i t i e s to migrate. In this section the hypotheses are verified. The reader will find the e l a s t i c i t y values in Tables 5, 6, 7 and 8. In-migration ela s t i c i t i e s The retired appear to be more sensitive to housing prices than the working. Indeed, for a 1% decrease in HOUSE% the i n -66 migration of the elderly would increase approximately by 2.6%, whereas the in-migration o f the working would increase only by 0.4%. The elderly seem also more conscious about personal taxes, cost of living and housing market variables. For a 1% decrease in TAX% and CPI%, the number of retired in-migrants increases by approximately 8.3% and 8.7% respectively, compared to 1.7% and 2.7% for the working. A 1% decrease i n UN0CC% leads to an increase of approximately 0.2% of retired migrants versus 0.1% of working migrants. These results corroborate the f i r s t set of hypotheses. The second set of hypotheses is partly v e r i f i e d . The income-elasticity to migrate for FAMALI (9%) is greater than for OLDAGI (7.5%), however, two different variables were in the respective regressions. INC0%-2 was used for the family allocation model and WAGE% was used for the old age security model. Therefore the comparison i s not totally relevant. The labour-elasticities to in-migrate do not confirm the hypothesis: the results show that the working have a lower e l a s t i c i t y for J0BID% (0.4%) than the retired have (0.5%). It should be noted, however, that the difference i s very small. Out-migration el a s t i c i t i e s As was mentionned earlier, the regression results for OLDAGO were not clear cut. Only CPI%-3 and H0USE%-3 had some level of significance. For the remaining independent variables, any comparisons between FAMALO and OLDAGO e l a s t i c i t i e s would be inappropriate. The coefficients of H0USE%-3 were significant, 67 at about the 15% level, in both FAMALO and OLDAGO fi n a l models. CPI%, in FAMALO model, was significant at the 5% level, and CPI%-3, i n OLDAGO model, was significant at the 10% level. Hence, the elasticities to migrate for housing prices and cost of living variables can be compared with some degree of confidence. For out-migration, the retired seem again more sensitive to housing prices than the working. For a 1% increase in H0USE%, the out-migration of the elderly would increase by approximately 1%, whereas the out-migration of the working would increase by 0.3%. People receiving old age security benefits are also more sensitive to the cost of living . For a 1% increase in CPI%, the number of out-migrants increases by nearly 8.8%, compared to 4.4% for people receiving family allowance benefits. These results, again, corroborate the theory. 5.4.3 Estimates And Forecasts Of Net Migrants In the literature review i t was shown that in using net migration as a dependent variable i t may be d i f f i c u l t to predict the direction of influence of some independent variables (Jeacock). It was also shown that estimated net-migration, calculated as the difference between fi t t e d in and out figures, had poorer "tracking a b i l i t y " than in and out migration estimates taken separately (McRae). McRae's finding raised the question as to whether the use of a separate net migration model altogether would yield superior results than the use of estimated net migration determined by fi t t e d in minus fitt e d out. This section examines this issue. 68 A structural model, using the number of net migrants receiving family allowance benefits (FAMANT) as the dependent variable, i s tested. The independent variables used are the seasonal dummies plus a l l the variables used in FAMALI and FAMALO f i n a l models. The coefficients, the t-statistics and the el a s t i c i t i e s to migrate are displayed in Table 10. 69 Table 10 - Final structural model for the working net migration (FAMANT) Variable Coefficient T-statistic E l a s t i c i t y WAGE% 2606 0.73 3.47 INC0%-2 26423 4.57 34.43 JOBID% 1933 3.71 2.28 UNEMBC 71 1.01 0.59 TAXE% -7566 -1.76 -9.24 TAXE%-4 4674 1.21 5.73 H0USE%-1 -1640 -1.84 -1.95 H0USE%-3 -2080 -1.89 -2.42 CPI% -12718 -2.07 -15.22 CPI%-2 -3010 -0.51 -3.60 UN0CC%-1 1016 1.46 0.16 VACAN%-3 406 1.61 0.20 DUMMY1 -1009 -13.78 DUMMY2 -845 -15.36 DUMMY3 -344 -1.55 CONSTANT -388 -0.30 R-squared: .87 Adjusted R-squared: .83 Degrees of freedom: 47 Standard deviation of residuals: 257 Sum of squared errors: 1,258,817 The diagnostic checks performed on the residuals demonstrate the adequacy of the model. The regression results and the diagnostic checks are found in APPENDIX E. The Durbin-Watson statistics, the autocorrelation function and the runs-count, a l l suggest randomness in the residuals. The visual examination of the normal cumulative probability plot of the residuals and the skewness and kurtosis coefficients suggest normality. Based on 47 degrees of freedom a l l the coefficients have 70 their sign conforming with expection 8 2 , except UNEMRC and TAXE%-4. Most variables are significantly different from zero at the 5% level. UN0CC%-1 and VACAN%-3 are significant at the 10% level. WAGE%, UNEMBC, TAXE%-4 and CPI%-2 are not significantly different from zero. Table 11 - Standard errors of residuals for the working structural models for 1966(1)-1981(4) FAMALI: 262 FAMALO: 207 (FAMALI) -(FAMALO): 268 FAMANT: 223 Based on the standard error of residuals, support i s given to McRae*s finding. The estimated net migration (FAMALI minus FAMALO) has poorer "tracking a b i l i t y " than in (FAMALI) and out (FAMALO) migration estimates taken separately. Moreover the use of a separate net migration model (FAMANT) leads to superior results than using FAMALI minus FAMALO models. This new finding raises a further question: would FAMANT model yield better net migration predictions than FAMALI minus FAMALO models? The table below shows the outcomes. For net migration a coefficient' expected sign i s equal to the expected sign for in-migration minus the expected sign for out-migration. Therefore, the expected signs for income variables are ambiguous.(See APPENDIX A.) 71 Table 12 - Prediction errors for the working net migration structural models PERIOD ACTUAL NET (FAMALI) -(FAMALO) o *o FAMANT O. "6 1982(1) -527 -292 55 -376 71 1982(2) -79 643 -814 309 -391 1982(3) -103 337 -327 -298 289 1982(4) -29 -135 466 -966 3331 SSE:Sum squared errors RMSE:Root mean square error AVG%:Yearly avg.% error 630,507 397 -155% 1,258,817 561 825% The percentages of prediction errors, for the net migration of working migrants, cannot be compared to the in and out migration results given in section 5.3. The percentages of errors in the above table are not very relevant because the number of net migrants in each quarter of 1982 is relatively small 8 3 . In using FAMANT the sum of squared errors for the forecast period 1982(1)-1982(4) i s 1,258,817. FAMANT predictions are less accurate than the forecasts using FAMALI minus FAMALO. The latter method leads to a sum of squared errors of 630,507. This value i s approximately half FAMANT sum of squared errors. The two other measures , RMSE and AVG%, also support the superiority of FAMALI minus FAMALO. 3 Indeed, dividing any number by a near-zero one yields a high percentage value. VI. TIME-SERIES MODEL In chapter five, several structural models have been specified for the migration of people receiving family allowance and old age security benefits. Although the bottom line criterion for choosing the fin a l models was forecasting accuracy, emphasis was also placed on selecting models with credible specifications. Hence, some economic variables explaining the in and out migration flows in British Columbia have been identified. These structural models provided the reader with an understanding of the provincial migration process. However, i f the objective of modelling i s s t r i c t l y for forecasting purposes, then time-series models might have just as good predictive power84 . In this chapter, time-series models are built only for the migration of people receiving family allowance benefits. The predictive power of these models are compared to the structural counterparts in chapter seven. 6.1 A Time-series Model For The Working In-migration (FAMALI) 6.1.1 Identification Of A Model The p l o t t i n g 8 5 of the number of family allowance accounts transferred in British Columbia, from the f i r s t quarter 1961 to the fourth quarter 1981 shows a very subtle upward trend and the standardized histogram shows that the data do not vary about the 4 Only i f predictions are made over a short period and i f no major changes occur in factors affecting migration. 5 To follow the development given in section 6.1.1 refer to APPENDIX F. 73 mean. FAMALI's autocorrelation function suggests a seasonality pattern, the seasonal lags (4, 8, 12, 16, 24) dying out very slowly. The sizeable coefficients at lags 4, 8, 12, ... are strong signals of seasonality for quarterly data. They t e l l us that there are substantial correlations between current observations and earlier observations for the same season of the year 8 6 . In trying to get the data stationary, the f i r s t difference of FAMALI is taken. The plot of the data and the histogram indicate that the upward trend i s eliminated but the autocorrelation function shows a definite seasonal pattern. Stationarity must be reached to be able to use a time-series model for predictive purpose. The seasonal pattern observed hints that the seasonal difference of the f i r s t difference should be tried. The new series represents the quarterly growth of the yearly change of in-migrants. The plot, the histogram and the autocorrelation function of this series lead to the apparent conclusion that stationarity i s reached. The trend and the strong seasonality patterns appear eliminated. At this stage, the identification of an appropriate model of the form ARIMA (P,D,Q;BP,BD,BQ) i s necessary to f i t the stationary time-series. 'P' is the number of consecutive autoregressive (AR) parameters, 'D' the number of consecutive differencing operations, 'Q' the number of consecutive moving-average (MA) parameters, 'BP' the number of consecutive AR term 8 6 Harry V.Roberts, Time-Series and Forecasting with IDA, p.9-9. 74 at the seasonal gap, 'BD' the number of consecutive differencing operations at the seasonal gap 8 1 and 'BQ* the number of consecutive MA terms at the seasonal gap 8 8 . The following quote describes how the orders for the AR and MA components are chosen8 5 . Briefly, whereas the autocorrelation function [ACF] of an autoregressive process of order p f a i l s off [dies out], i t s partial autocorrelation function [PACF] has a cutoff after lag p. Conversely, the autocorrelation function of a moving average process of order q has a cutoff after lag q, while i t s partial autocorrelation t a i l s off. If both the autocorrelation and partial autocorrelations t a i l off, a mixed process is suggested 5 0 . Table 13 below summarizes this instruction. Table 13 - Guide for choosing the orders of AR and MA component s PURE AR PURE MA ARMA ACF dies out cuts out at lag q dies out PACF cuts out at lag p dies out dies out The autocorrelation function and the partial autocorrelation function of the stationary series suggest an ARIMA (0,1,1;0,1,1) 8 7 The seasonal gap i s four for quarterly data. 8 8 R.Ling and H.Roberts, IDA A User 1s Guide to the IDA Interactive  Data Analysis and Forecasting System, p.10-2. 8 9 AN AR term i s an observed value of a previous observation, i.e. a lagged variable and a MA term is a lagged disturbance, never observed but estimated from some f i t of the data. 5 0 E.P.George Box and Gwilym M.Jenkins, Time-Series Analysis  forecasting and control, p.175. 75 model. The ACF seems to cut out at lag 2 whereas the PACF seems to t a i l off. These two factors indicate a pure moving average of order 1 in the non-seasonal component. The ACF also appears to cut out at the second seasonal lag (ie. order 8) and the PACF'S seasonal lags seem to die out. A pure MA of order 1, in the seasonal component, i s also suggested. 6.1.2 Estimation Of The Model The estimation of the coefficients of the ARIMA model is the second step. The method used in this thesis i s the Box and Jenkins technique which permits the estimation of ARIMA models by unconditional nonlinear least squares with back forecasting 9 1 . The estimation method works by successive approximations. Providing i n i t i a l estimates for the numerical values of the parameters, the st a t i s t i c a l package permits iterative searches to find the parameter values that minimize the sum of squared residuals. "(...) very rough guesses about starting values often are good enough to lead to quick convergence of the estimation procedure" 9 2 . For this reason the value 0.5 i s chosen as an i n i t i a l estimates for a l l parameters. The estimated model for FAMALI, ARIMA(0,1,1;0,1,1) i s : (1) Xt= .48 E t-1 + .94 E t-4 (4.14) (26.08) (t-stat) 9 1 For more details, see R.Ling and H.Roberts, Op.Cit. p.10-2. 9 2 Ibid, p.10-3. 76 where E t-l= estimated disturbance lagged one quarter (non-seasonal); E t-4= estimated disturbance lagged four quarters (seasonal); Xt= (Yt - Y t-1) - (Y t-4 - Y t-5) i e . the stationary series; where Yt= number of in-migrants at time t. Based on 57 degrees of freedom, the standard deviation of residuals i s equal to 386 in migrants. 6.1.3 Diagnostic Checks Of Model Adequacy It i s important to verify the adequacy of the entertained model. "Diagnostic checks should be done, using only the rows used in f i t t i n g the model" 9 3 , which means using the 1966(1)-1981(4) period. If a model is good, the residuals (difference between actual and f i t t e d values) must be approximately white noise, that i s , on the whole the residuals must appear random and normal. The computer output for the diagnotic checks is reproduced in APPENDIX G. A l l tests are carried out on the residuals. The autocorrelation function performed on the residuals indicates that the model i s random. A l l residuals, from the f i r s t to the twenty-fourth order are not significantly different from zero. The runs count also indicates randomness. 9 3 H.Roberts, Op.Cit. p.8-32. 77 The observed number of runs is not too far out from the expected number of runs. To check for normality, the normal cumulative probability plot (NCPP) of the residuals is examined. On the NCPP, the points seem to follow the diagonal reasonably closely (except for one outlier), suggesting that normality may be a good approximation to the shape of the errors distribution. At the bottom of the NCPP graph, both the skewness and the kurtosis coefficients are greater than the guideline values given in section 5.2. In a further step, when the outlier, indicated on the NCPP graph was deleted, the coefficients f e l l within the guidelines. Consequently, the residuals seem to reasonably conform with normality. Given the specification that the residuals are normal and random, predictions about the future in-migration can be made using ARIMA (0,1,.1;0,1,1). 6.2 A Time-series Model For The Working Out-migration (FAMALO) 6.2.1 Identification Of A Model The plo t ' 4 of FAMALO exhibits a definite upward trend from 1970(2) to 1977(3). The series i s clearly not stationary. Another sign of non-stationarity is the ACF which indicates lags of order 1 and 3 significantly different from zero and the seasonal lags dying out slowly. In taking the f i r s t difference of the original series, the trend i s removed and the autocorrelation of order 1 is now not significantly different 5 4 To follow the development given in this section refer to APPENDIX H. 78 from zero. This derived series s t i l l displays an obvious seasonal pattern. The autocorrelation function i s a good indicator, the lags of order 4, 8, 12, 16 and 20 die out extremely slowly. Again, differencing in taking the seasonal difference of the f i r s t difference seems appropriate. This new series i s the quarterly growth of the yearly change of out-migrants receiving family allocation benefits. The plot of the data and the autocorrelation function exhibit a stationary series: no more trends nor seasonality seem to be in the data. Again, the identification of an appropriate ARIMA model that f i t s the stationary series i s necessary. Referring to the guide in Table 13, ARIMA (0,1,2;0,1,1) i s identified. It seems that the non-seasonal orders of the autocorrelation function cut out after the third lag and die out for the partial autocorrelation function. Therefore, a pure moving average of order 2 i s suggested. For the seasonal orders, the ACF cuts out at the second seasonal lag (lag 8), whereas the PACF dies out. Consequently a pure MA of order 1 i s suggested. 6.2.2 Estimation Of The Model Again Box and Jenkins technique i s used. The i n i t i a l estimate for each three parameters (one non-seasonal MA and two seasonal MA) is 0.5. The estimated model for FAMALO, ARIMA (0,1,2;0,1,1) i s : (2) Xt= .75 E t-1 + -.35 E t-2 + .95 E t-4 (5.66) (2.75) (30.07) (t-stat) 79 where E t-l= estimated disturbance lagged one quarter (non-seasonal); E t-2= estimated disturbance lagged two quarters (non-seasonal); E t-4= estimated disturbance lagged four quarters (seasonal); Xt= (Yt - Y t-1) - (Y t-4 - Y t-5) i e . the stationary series; where Yt= number of out-migrants at time t. Based on 56 degrees of freedom, the standard deviation of residuals is equal to 261 out-migrants. 6.2.3 Diagnostic Checks Of Model Adequacy As for FAMALI's time-series model, the diagnostic checks are performed on the residuals (actual minus f i t t e d values) corresponding to the rows used in f i t t i n g the model, that i s , 1966(1)-1981(4). The residuals must be random and normal before using the model to forecast future values of the number of migrants. The diagnostic checks are exhibited in APPENDIX I. The autocorrelation function of the residuals indicates a random model. For the twenty-four orders the autocorrelation coefficients are not significantly different from zero, they a l l vary within two-standard error limits. The runs-count is another indicator of randomness, the observed number of runs is exactly equal to i t s expected number. Visual examination of the 80 normal cumulative probability plot shows no substantial variation of the residuals from the straight line of the diagonal. Also, the skewness and kurtosis coefficient values are reasonably close to the guidelines given previously. The assumption of no major departure from normality is accepted. Given the specification that the residuals are random and normal forecasts of out-migration can be made using ARIMA (0,1,2;0,1,1). 6.3 Forecasts Based On The Model Fitted Using the two time-series model specified in the preceding sections, i t is possible to forecast the number of in-migrants and out-migrants for a period into the future. For comparison with the structural models, the same forecast period 1982(1)-1982(4) has been chosen. This period, for which the data are actually available, has not been used in the f i t t i n g . The differences between the actual family allocation data and the forecasted data are called prediction errors, not residuals. For the 1982(1)-1982(4) period, FAMALI and FAMALO data as well as the forecasts and prediction errors are displayed in Table 14. 81 Table 14 - Prediction errors for the time-series models PERIOD FAMALI DATA FORECASTS OF FAMALI PREDICTION ERRORS % OF ERROR 1982(1) 1982(2) 1982(3) 1982(4) 1874 1817 2536 2364 2298 2140 3464 3543 -424 -323 -928 -1179 23 18 37 50 Sum of < Root mea squared m squai errors: 2 •e error: 5? 535,330 50 PERIOD FAMALO DATA FORECASTS OF FAMALO PREDICTION ERRORS 1982(1) 1982(2) 1982(3) 1982(4) 2401 1896 2639 2393 1982 2135 2959 2760 419 -239 -320 -367 -17 13 12 15 Sum of squared errors: 469,771 Root mean square error: 343 The yearly average percentages of errors are 32% for FAMALI and 5.8% for FAMALO. When comparing these figures with the structural models in Table 9, i t appears that in-migration of the working i s best forecasted with the structural model whereas the out-migration i s best forecasted with the time-series model. 82 6.4 Analysis And Testing Equation 1 in section 6.1.2 was used to forecast i n -migration data. The model estimated was the following: (1) Xt= .48 E t-1 + .94 E t-4 (4.14) (26.08) (t-stat) Based on 57 degrees of freedom, the seasonal and non-seasonal moving average component are significantly different from zero at the 1% level. Using the prediction errors in Table 14, the sum of squared errors i s computed: i t is equal to 2,535,330. As may be recalled, the model's identification, ARIMA (0,1,1;0,1,1), was determined subjectively but not ar b i t r a r i l y . Overfitting the entertained model with a slightly more general model is another diagnostic check that can be performed. Thus ARIMA (1,1,1;1,1,1) i s tried. The model estimated is as follows: (3) Xt= .44 Y t-1 + .99 E t-1 + .30 Y t-4 + .91 E t-4 (3.72) (42.07) (9.08) (14.77) (t-stat) Based on 55 degrees of freedom, the AR and MA components are a l l significant at the 1% level. The sum of squared errors, associated with the forecast of the 1982(1)-1982(4) period, i s equal to 3,392,835. On the basis of forecasting accuracy, this model i s rejected and the i n i t i a l ARIMA (0,1,1;0,1,1) i s retained. 83 Equation 2 in section 6.2.2 was used to forecast out-migration data. The estimation model was the following: (2) Xt= .75 E t-1 + -.35 E t-2 + .95 E t-4 (5.66) (2.75) (30.07) (t-stat) Based on 56 degrees of freedom, the two non-seasonal moving averages and the seasonal moving average are significantly-different from zero at the 1% level. The sum of squared errors for the forecast period i s 469,771. FAMALO's entertained model ARIMA (0,1,2;0,1,1,) was also determined subjectively. Again as a diagnostic check the entertained model is overfitted using a slightly more general model ARIMA(1,1,1;1,1,1). The model estimated i s : (4) Xt= -.41 Y t-1 + .32 E t-1 + -.13 Y t-4 + .99 E t-4 (-1.87) (1.47) (0.86) (31.6) (t-stat) Based on 55 degrees of freedom, the seasonal MA i s the only component significantly different from zero at the 1% level. "Other things equal statisticians prefer models that have a small number of parameters to be estimated from the data, that i s , models that are parsimonious"'5 . On the principle of 5 5 R.Ling and H.Roberts, Conversational Statistics with IDA, An  Introduction to Data Analysis and Regression, p.7-18. 84 parsimony, this more general model i s rejected, and ARIMA(0,1,2;0,1,1) i s retained. In chapter five a structural model using the number of net migrants receiving family allowance benefits (FAMANT) as the dependent variable was tested. It was shown that using FAMALI minus FAMALO, to predict the number of net migrants, was superior to FAMANT. In the following a time-series model using the number of net migrants receiving family allowance benefits (FAMANT) i s also tested. ARIMA (0,1,1;0,1,1) is the entertained model. The diagnostic checks (APPENDIX J) indicate randomness and normality. The estimated model i s : (5) Xt= .21 E t-1 + .93 E t-4 (1.59) (21.18) (t-stat) Based on 57 degrees of freedom, the non-seasonal MA and the seasonal MA are significantly different from zero at the 10% and 1% level respectively. 85 Table 15 - Prediction errors for the working net migration time-series models PERIOD ACTUAL NET (FAMALI) -(FAMALO) o, ~o FAMANT o "O 1982(1) -527 -843 160 -429 81 1982(2) -79 -84 106 42 -53 1982(3) -103 -608 590 -450 437 1982(4) -29 -812 2800 -667 2300 SSErSum squared errors RMSErRoot mean square error AVG%:Yearly avg.% error 1,746,713 661 914% 833, 456 691% 194 As explained in chapter five, the percentages of prediction errors are not very relevant for these net migration figures. Therefore they cannot be compared to in migration and out migration figures given in section 6.3. In using FAMANT the sum of squared errors for the forecast period 1982(1)-1982(4) i s 833,194. This prediction i s more accurate than the forecast using estimated in-migrants (determined by FAMALI) minus estimated out-migrants (determined by FAMALO), which leads a sum of squared errors of 1,746,713. RMSE and AVG% also supports the superiority of FAMANT. 86 VII. SUMMARY OF FINDINGS AND CONCLUSION 7.1 Summary Of Findings In this section, the findings of chapters five and six are presented in tables and figures format. This way of displaying the information i s chosen for c l a r i t y and simplicity. 7.1.1 Determinants Of Interprovincial Migration Table 16 - Summary of levels of significance for the structural models FAMALI FAMALO OLDAGI OLDAGO INCOME VARIABLES * ** * — LABOUR VARIABLES * * ** — PERSONAL TAXES * * —/WS HOUSING PRICES * *** * *** COST OF LIVING VAR. * * ** ** HOUSING MARKET VAR. * * * — *: Significant at the 5% level **: Significant at the 10% level ***: Significant at the 15% level — : Not significant WS: Wrong sign Except for OLDAGO, Table 16 indicates that income variables, labour variables, personal taxes, housing prices, cost of livi n g variables and housing market variables are a l l significant determinants "of B.C. interprovincial migration. 87 For the elderly moving out of the province, only the ratios housing prices and consumer price index are significant. Table 17 - Summary of economic variables used in the fin a l models FAMALI FAMALO OLDAGI OLDAGO INCOME VARIABLES INC0%-2 WAGE% WAGE% INC0%-4 LABOUR VARIABLES JOBID% UNEMBC JOBID% EMG.BC-3 PERSONAL TAXES TAX%-4 TAX% TAX%-2 TAX%-4 HOUSING PRICES H0USE%-1 H0USE%-3 H0USE%-2 H0USE%-3 COST OF LIVING VAR. CPI%-2 CPI% CPI% CPI%-3 HOUSING MARKET VAR. UN0CC%-1 VACAN%-3 UN0CC%-1 VACVAN-3 88 7.1.2 Economic E l a s t i c i t i e s To Migrate Table 18 - Summary of economic elas t i c i t i e s to migrate for the two-age cohorts FAMALI FAMALO OLDAGI OLDAGO *INCOME VARIABLES 9.00 1.95 7.45 — *LABOUR VARIABLES 0.36 0.36 0.50 — PERSONAL TAXES -1.65 2.28 -8.28 — HOUSING PRICES -0.40 0.29 -1.87 1.03 COST OF LIVING VAR. -2.68 4.39 -8.74 8.78 "HOUSING MARKET VAR. 0.08 -0.13 0.17 — NOTE (1) The elas t i c i t y values for the insignificant variables are not shown. (2) The reader should be careful in comparing the ela s t i c i t i e s within a category preceded by an asterisk '*' because different variables may have been used in the regressions. See table 17. For in-migration in B.C. the elderly are much more sensitive to personal taxes, housing prices and cost of living differentials than the working. The two-age cohorts have similar e l a s t i c i t i e s for labour and housing market variables. For the income variables category, inferences cannot be made because two different independent variables were used. For the out-migration case, comparisons can be drawn only for two categories of variables. The e l a s t i c i t i e s to migrate, for the ratios of housing prices and cost of living, are again 89 larger for the retired than for the working. 7.1.3 Selecting The Best Net Migration Model For The Working Table 19 - Summary of prediction errors, ex-ante for 1982(1)-1982(4) STRUCTURAL MODELS TIME-SERIES MODELS (FAMALI) -(FAMALO) SSE= 630,507 RMSE= 397 AVG%= -155% SSE= 1,746,713 RMSE= 661 AVG%= -914% FAMANT SSE= 1,258,817 RMSE= 561 AVG%= 825% SSE= 833,194 RMSE= 456 AVG%= 691% SSE= Sum of squared errors RMSE= Root mean square error AVG%= Yearly avg. percentage of error The foregoing table indicates that the net-migration (FAMANT) time-series model is more accurate than in-migration estimates minus out-migration estimates (FAMALI minus FAMALO) time-series models in forecasting the net migration of people receiving family allowance benefits. Contrarily, a structural model based on FAMANT is less accurate than using FAMALI minus FAMALO. If forecasting accuracy was the only concern, FAMALI minus FAMALO structural models would be optimum for predicting the number of net migrants. The second best solution would be FAMANT time-series model. This last model could be preferred to the former i f one wants to minimize the costs. Indeed time-series models are cheaper than structural models, both in terms 90 of time and money because less data must be gathered. In this study the forecasting period covered only four quarters, therefore the choice of an optimum model should not be based only on forecasting accuracy. It should be based on a combination of measures. Ex-ante forecasting accuracy is one and ex-post "tracking a b i l i t y " of the model is another'6 . The "tracking a b i l i t y " of a model can be measured by the standard deviation of residuals. It indicates the goodness of f i t on the fitted model. The standard errors of residuals, for the 1966(1)-1981(4) fitt e d period, are displayed in Table 20. Table 20 - Summary of standard errors of residuals, ex-post for 1956(1)-1981(4) STRUCTURAL MODELS TIME-SERIES MODELS (FAMALI) -(FAMALO) 268 384 FAMANT 223 371 Based only on the standard deviation of residuals (ex-post), i t appears that the optimum model would be FAMANT structural model, followed by FAMALI minus FAMALO structural models. The two time-series models would come afterwards. Finally, in combining ex-ante and ex-post results, the author would suggest that FAMALI minus FAMALO structural models 5 6 As may be seen in Figure 1, the actual net migration for the f i r s t quarter of 1981 was quite unpredictable. Therefore, using only forecasting accuracy as a measure could be misleading in the choice of an optimum model. 91 is the optimum solution for determining net migration. The second best model could be either FAMANT structural model or FAMANT time-series model. FAMALI minus FAMALO time-series models would definitely be ruled out because they lead both high prediction errors and high standard deviation of residuals. The following figure illustrates some of these outcomes. 92 Figure 1 - Actual net migration for the working, 1961(1)-1982(4) 93 Figure 2 - Best net migration forecasting models for the working, 1982(1)-1982(4) CO cn 94 Figure 3 - Best net migration fit t e d models for the working, 1966(1)-1981(4) 95 Figure 4 - Optimum net migration model, for the working, using ex-ante and ex-post r e s u l t s 96 7.2 Conclusion In chapter one i t has been shovm that an accurate population estimate i s essential to most planners. Net interprovincial migration is the most important factor to be considered in constructing a complete population forecasting model. The general focus of this thesis has been the specification of some economic variables explaining the migration of the working and retired groups in and out of British Columbia. A l l the economic variables used in the fi n a l models appear to be significant determinants of interprovincial migration. Particularly, personal income per capita or average weekly wages, job index from newspapers or unemployment rate in B.C., personal taxes as a percentage of total personal income, average housing prices, consumer price index, newly completed and unoccupied houses or vacancy rates are a l l inf l u e n t i a l . Except for the unemployment rate in B.C., a l l the above variables have been expressed as British Columbia/Canada ratios. For the out-migration of the elderly group only the ratios of the average housing prices and consumer price index are significant. The specific focus of the research has been to investigate the question 'Are housing prices a significant determinant of interprovincial migration in the long term"? In light of the results the answer is yes. The B.C./Canada ratio of housing prices is significantly different from zero at the 5% level for the in-migrants and at the 15% level for the out-migrants. These results hold for the two-age cohorts. More confidence is 97 given to the in-flows outcome than the out-flows one. The results also indicate support for the hypothesis that the retired age-cohort should have higher housing prices-elasticity to migrate than the working group. On one hand, for a 1% decrease in the ratio of housing prices, 0.4% of working versus 1.87% of retired would in-migrate. On the other hand, for a 1% increase in the ratio of housing prices, 0.29% of working versus 1.03% of retired would out-migrate. The working migrants are not too sensitive to the ratio of housing prices. Finally, although the 'mandates' of this thesis have been answered, i t would be interesting to extend the research. First, the f i n a l models, for the.working and for the retired, could be further tested in using other Canadian provinces data. The author believes that, in general, the results should be similar except for the out-migration of elderly people, where the outcomes should be better. One explanation, for the poor results obtained for the out-migration of retired people in British Columbia, was that the elderly may be more reluctant to leave a province that has the most moderate climate in the country. Second, the f i n a l models could be spread in the future as more observations become available. The weight given to forecasting accuracy could be increased as one would have more f l e x i b i l i t y to expand the forecasting period without shortening the number of degrees of freedom. One restraint of this study was the limited number of observations available. Indeed, several economic variables did not exist before 1966. Future research on interprovincial 98 migration should be increasingly promising as more data w i l l be available. 99 BIBLIOGRAPHY ALPEROVICH, Gershon, "The cost of living,labor market opportunities and the migration decision: a case of misspecification?: Comment", Annals of Regional Science, Nov 1979, pp.102-105. ALPEROVICH, Gershon,"The cost of living,labor market opportunities and the migration decision: a case of misspecification? Comment", Annals of Regional Science, March 83, pp.94-97. BOX,E.P.George and Gwilym M.JENKINS, Time-Series Analysis  forecasting and control. Revised Edition, Holden-day, 1976, 575p. CANADA MORTGAGE AND HOUSING CORPORATION, Canadian Housing  Statistics. Statistical Services Division, Ottawa. CEBULA,Richard J.,"The cost of living,labor market opportunities and the migration decision: a case of misspecification? -A Comment", Annals of Regional Science, Nov 1981, pp.73-74. CEBULA,Richard J.,"The cost of living,labor market opportunities and the migration decision: A case of misspecification? Reply", Annals of Regional Science, March 83, pp.97-98. CHATFIELD,C., The analysis of Time-Series: An Introduction. Second Edition, Chapman and Hall, New York, 1980, 268p. COLLABORATION, MLS Annual Report 1979. Prepared by Economis & Research Department, The Canadian Real Estate Association, 57p. DEAN, James M.,"Tax-induced migration in Canada 1972-79", Western Economic Rewiew ,Vol.1,No.2,Institute for Social And Economic Research, Faculty of Arts, University of Manitoba ,July 82, pp.17-31. HORNA, Jarmila, Patterns of family migration between the provinces in Canada, 1956-1974 .Discussion Paper No.12,Dept.of Sociology, University of Alberta, Population Research Laboratory,1974. JEACOCK, Robert L., A provincial Population Forecasting Model  Emphasizing Interprovincial Migration. A Technical Paper from the Conference Board of Canada, Sept.1982,102p. KUMAR,Rishi and Stephen M. RENAS, "The cost of living,labor market opportunities and the migration decision: A case of misspecification?", Annals of Regional Science, July 1978, pp.95-104. 100 KUMAR,Rishi and Stephen M. RENAS, "The cost of living,labor market opportunities and the migration decision: A case of misspecification?: Reply", Annals of Regional Science, Nov.1979, pp.106-108. KUMAR,Rishi and Stephen M. RENAS, "The cost of living,labor market opportunities and the migration decision: Some additional evidence", Annals of Regional Science, Nov.1981, pp.74-79. KUMAR,Rishi and Stephen M. RENAS, "The cost of living,labor market opportunities and the migration decision: More on the problems of misspecification and aggregation bias", Annals of Regional Science, March 83, pp.98-100. LING,F.Robert and Harry V.ROBERTS, Conversational Statistics with IDA, An Introduction to Data Analysis and Regression. The SPSS Series in Data Analysis, The Scientific Press McGraw- H i l l . 1982. LING,F.Robert and Harry V.ROBERTS, IDA A User's Guide to the IDA  Interactive Data Analysis and Forecasting System. The SPSS Series in Data Analysis, The Scientific Press McGraw-Hill. 1982. MCRAE, Don, An econometric model describing the movement of the  population between British Columbia and the rest of Canada. Central Statistics bureau, January 1981, 14p. POWRIE, T.L.,"Natural resource revenues and Federal-Provincial f i s c a l arrangements", 29, Canadian Tax Journal ,July/August 1981, pp.499-502. ROBERTS,Harry V., Time-Series and Forecasting with IDA. The SPSS Series in Data Analysis, The Scientific Press McGraw-H i l l . 1984. STATISTICS-CANADA, CANSIM University Base Series Directory 1983, Ottawa, February 1983. 101 APPENDIX A - VARIABLES' SYMBOL, DEFINITION AND EXPECTED SIGN VARIABLE DEFINITION SIGN IN OUT CPI% Ratio of consumer price index - + CPIVAN Consumer Price index,Vancouver - + EMG.BC Employment growth rate in B.C. + EMG.% Ratio of employment growth rate + EM/P0% Ratio of employment/population + FAMALI Number of working in-migrants based on family allowance benefits Dep.Var. FAMALO Number of working out-migrants based on family allowance benefits Dep.Var. FAMANT Number of working net migrants equal to FAMALI minus FAMALO Dep.Var. HOUSE% Ratio of average house prices - + INC0% Ratio of personal income per capita + ? JOBID% Ratio of job index in newspapers + OLDAGI Number of elderly in-migrants based on old age security benefits Dep.Var. OLDAGO Number of elderly out-migrants based on old age security benefits Dep.Var. TAX% Ratio of taxes as a % of total personal income - + UNEM% Ratio of unemployment rate - + UNEMBC Unemployment rate in B.C. - + UN0CC% Ratio of newly completed and unoccupied houses,Vancouver + VACAN% Ratio of vacancy rates + VACDUM Vacancy dummy,Vancouver + VACVAN Vacancy rates,Vancouver + WAGE% Ratio of average weekly wages + ? Note Ratio: British Columbia/Canada data. 102 APPENDIX B - DESCRIPTIVE MEASURES OF ALL VARIABLES VARIABLE MINIMUM MAXIMUM MEAN STD DEV DATE 1966.10 1982.90 1974.50 4.94 FAMALI 1694.00 4243.00 2794.50 773.51 FAMALO 1102.00 3173.00 2011.80 496.28 OLDAGI 8.00 1328.00 621.57 280.79 OLDAGO 0.00 1036.00 364.35 208.60 WAGE% 0.08 0.15 0.12 0.02 INCO% 0.07 0.12 0.10 0.01 UNEM% 0.81 1.54 1.16 0.16 EM/PO% -0.04 0.02 -0.01 0.01 EMG.% -0.71 1.45 0.71 0.40 JOBID% 0.63 1.66 1.00 0.21 UNEMBC 4.13 14.03 7.27 1.90 EMG.BC -4.23 7 .18 0.90 3.14 TAX% -0.05 0.07 0.03 0.02 HOUSE% 0.78 1.41 1.02 0.15 CPI% -0.01 0.04 0.01 0.01 CPIVAN 83.90 270.55 143.37 55.02 UNOCC% 0.02 0.41 0.13 0.08 VACAN% 0.04 1.07 0.40 0.26 VACVAN 0.10 4.10 1.17 0.98 VACDUM 0.00 1.00 0.53 0.50 DUMMY1 0.00 1.00 0.25 0.44 DUMMY2 0.00 1.00 0.25 0.44 DUMMY3 0.00 1.00 0.25 0.44 Note (1) A l l the numbers have been rounded to 2 decimals. (2) The variables WAGE%,INCO%,EM/PO%, TAX%,CPI% had the constant one substracted at each observation for computational precision.. 103 APPENDIX C - VALUES OF ALL VARIABLES:1966(1)-I982(4) DATE 1966.124 1966.374 1966.624 1966.874 1967.124 1967.374 1967.624 1967.874 1968.124 1968.374 1968.624 1968.874 1969.124 1969.374 1969.624 1969.874 1970.124 1970.374 1970.624 1970.874 1971.124 1971.374 1971.624 1971.874 1972.124 1972.374 1972.624 1972.874 1973.124 1973.374 1973.624 1973.874 1974.124 1974.374 1974.624 1974.874 1975.124 1975.374 1975.624 1975.874 1976.124 1976.374 1976.624 1976.874 1977.124 1977.374 1977.624 1977 .874 FAMALI 2160.000 2026.000 4086.000 3824.000 1866.000 1752.000 3354.000 3375.000 1752.000 1694.000 2653.000 3469.000 1754.000 1860.000 3234.000 3687.000 2402.000 2115.000 2969.000 3526.000 2110.000 1782.000 3561.000 3603.000 2100.000 1882.000 3164.000 3480.000 2498.000 2405.000 3760.000 4040.000 2539.000 2764.000 4113.000 3878.000 2534.000 1833.000 3049.000 2807.000 1992.000 2255.000 3050.000 2944.000 2193.000 1902.000 3299.000 3196.000 FAMALO 1249.000 1102.000 2028.000 1970.000 1474.000 1551.000 2189.000 1970.000 1540.000 1487.000 1664.000 2044.000 1340.000 1306.000 2178.000 1616.000 1883.000 1184.000 1939.000 2458.000 1618.000 1497.000 2187.000 1830.000 1286.000 1444.000 2087.000 1872.000 1713.000 1561.000 2295.000 2236.000 1677.000 1777.000 3159.000 2706.000 2411.000 2102.000 3173.000 2567.000 2343.000 2077.000 3114.000 2852.000 2053.000 1713.000 2738.000 2238.000 OLDAGI 81.000 385.000 558.000 686.000 250.000 8.000 948.000 389.000 19.000 796.000 1083.000 696.000 358.000 726.000 681.000 546.000 301.000 489.000 942.000 719.000 11.000 286.000 1192.000 785.000 197.000 232.000 303.000 1328.000 802.000 611.000 939.000 843.000 602.000 547.000 776.000 892.000 248.000 447.000 573.000 657.000 503.000 508.000 665.000 678.000 413.000 555.000 687.000 714.000 OLDAGO 56.000 252.000 301.000 277.000 103.000 7.000 696.000 131.000 9.000 325.000 508.000 229.000 195.000 345.000 390.000 253.000 273.000 208.000 574.000 298.000 0.000 378.000 479.000 297.000 85.000 124.000 166.000 1013.000 243.000 303.000 445.000 406.000 188.000 242.000 420.000 129.000 129.000 419.000 442.000 384.000 387.000 452.000 599.000 522.000 310.000 481.000 467.000 970.000 104 1978.124 1978.374 1978.624 1978.874 1979.124 1979.374 1979.624 1979.874 1980.124 1980.374 1980.624 1980.874 1981.124 1981.374 1981.624 1981.874 1982.124 1982.374 1982.624 1982.874 2123.000 2057.000 3659.000 3027.000 2281.000 2164.000 4243.000 4082.000 2827.000 2595.000 3974.000 4239.000 2841.000 2608.000 2626.000 3796.000 1874.000 1817.000 2536.000 2364.000 1811.000 1546.000 2669.000 2082.000 1884.000 1608.000 2391.000 2134.000 1540.000 1600.000 2470.000 2087.000 1924.000 1832.000 2311.000 3083.000 2401.000 1896.000 2639.000 2393.000 464.000 697.000 952.000 641.000 662.000 718.000 1175.000 927.000 833.000 769.000 955.000 667.000 775.000 618.000 596.000 485.000 536.000 1034.000 687.000 421.000 323.000 427.000 517.000 294.000 295.000 385.000 377.000 325.000 277.000 442.000 440.000 321.000 422.000 486.000 684.000 431.000 469.000 1036.000 623.000 292.000 DATE WAGE% INCO% UNEM% EM/POi 1966.124 .118 .121 1.205 -.018 1966.374 .121 .116 1.365 -.025 1966.624 .117 .114 1.378 -.016 1966.874 .099 .112 1.543 -.029 1967.124 .116 .110 1.275 -.005 1967.374 .117 .108 1.307 -.022 1967.624 .116 .102 1.302 -.025 1967.874 .103 .096 1.482 -.010 1968.124 .098 .089 1.245 .002 1968.374 .101 .083 1.345 -.022 1968.624 .098 .086 1.331 -.021 1968.874 .095 .090 1.383 -.019 1969.124 .081 .093 1.170 -.011 1969.374 .093 .096 1.030 .010 1969.624 .105 .094 1.111 -.007 1969.874 .105 .092 1.260 .007 1970.124 .096 .090 1.164 .023 1970.374 .081 .088 1.354 -.002 1970.624 .079 .089 1.430 -.022 1970.874 .094 .089 1.429 -.023 1971.124 .084 .090 1.157 -.007 1971.374 .107 .090 1.179 -.009 1971.624 .126 .091 1.176 -.014 1971.874 .113 .092 1.180 .001 1972.124 .103 .093 1.178 .014 1972.374 .096 .094 1.290 -.005 1972.624 .110 .097 1.263 -.028 1972.874 .116 .101 1.291 -.032 1973.124 .102 .105 1.236 -.004 105 1973.374 .116 .109 1.242 -.014 1973.624 .115 .107 1.167 -.018 1973.874 .111 .106 1.195 -.022 1974.124 .117 .104 1.000 .001 1974.374 .108 .102 1.097 -.008 1974.624 .140 .097 1.233 -.016 1974.874 .137 .092 1.318 -.022 1975.124 .125 .086 1.216 -.001 1975.374 .140 .081 1.155 -.002 1975.624 .131 .083 1.277 -.037 1975.874 .127 .084 1.283 -.031 1976.124 .134 .086 1.225 -.018 1976.374 .141 .087 1.284 -.021 1976.624 .146 .091 1.209 -.012 1976.874 .131 .094 1.111 -.002 1977.124 .138 .097 1.059 -.004 1977.374 .138 .101 1.042 .004 1977.624 .140 .101 1.061 -.002 1977 .874 .131 .101 1.034 -.011 1978.124 .130 .101 .989 .013 1978.374 .134 .102 .903 .015 1978.624 .147 .103 .983 .002 1978.874 .129 .104 1.088 -.006 1979.124 .121 .105 1.022 -.001 1979.374 .128 .106 1.026 -.001 1979.624 .147 .108 1.045 -.012 1979.874 .142 .109 1.000 -.008 1980.124 .134 .111 1.027 .006 1980.374 .144 .113 .856 .013 1980.624 .154 .106 .860 0.000 1980.874 .148 .100 .844 .012 1981.124 .142 .093 .807 .025 1981.374 .150 .087 .849 .015 1981.624 .144 .084 .899 .001 1981.874 .146 .081 .966 .015 1982.124 .137 .078 1.017 .012 1982.374 .142 .076 1.060 -.009 1982.624 .143 .073 1.157 -.025 1982.874 .138 .070 1.150 -.018 DATE EMG.% JOBID% UNEMBC EMG.BC 1966.124 .960 .752 5.100 4.776 1966.374 .960 .697 4.367 4.776 1966.624 1.274 .692 4.133 5.754 1966.874 1.274 .667 4.733 -3.407 1967.124 .241 .697 5.867 -.920 1967.374 .741 ' .732 4.967 3.460 1967.624 .974 .745 4.167 4.424 1967.874 .476 .634 5.533 -1.774 1968.124 .707 .740 6.767 -3.434 1968.374 .602 .839 6.233 3.188 106 1968.624 • 1.103 .887 5.367 4.976 1968.874 .738 .977 5.533 -1.627 1969.124 .664 .979 5.967 -2.294 1969.374 1.449 .990 4.600 7.182 1969.624 .570 1 .000 4.333 1.643 1969.874 .415 1 .021 5.333 -1.332 1970.124 .504 .968 6.633 -2.125 1970.374 .607 .925 7.900 3.089 1970.624 .503 .818 7.867 1.661 1970.874 .946 .934 8.100 -2.747 1971.124 .442 .908 8.367 -1.693 1971.374 1.002 .871 7.467 4.564 1971.624 .961 1 .047 6.467 4.291 1971.874 .084 1 .021 6.767 -.194 1972.124 .543 .981 8.167 -1.975 1972.374 .618 .955 7.867 2.840 1972.624 .489 .992 7.367 1.846 1972.B74 .969 .976 7 .833 -2.629 1973.124 -.714 1 .023 8.367 1.335 1973.374 .897 1 .161 6.667 5.445 1973.624 .964 1 .115 5.833 2.736 1973.874 .900 1 .171 6.133 -1.858 1974.124 -.071 1 .188 6.100 .178 1974.374 .872 1 .124 5.633 4.333 1974.624 .873 1 .136 6.000 3.458 1974.874 1.054 .984 6.900 -3.195 1975.124 .433 .975 9.367 -1.940 1975.374 .969 .934 7.933 4.972 1975.624 .019 .876 8.300 .066 1975.874 .770 .937 8.467 -2.117 1976.124 .526 1 .000 9.633 -1.570 1976.374 .909 .933 9.033 3.618 1976.624 1.251 .897 8.100 4.463 1976.874 .747 .942 7.700 -2.811 1977.124 1.072 .974 9.533 -3.235 1977.374 1.147 .974 8.333 5.456 1977.624 .889 .954 8.067 3.205 1977.874 1.230 .940 8.100 -3.835 1978.124 .048 .878 9.433 -.127 1978.374 1.061 .955 7.733 5.404 1978.624 .737 .876 7.667 2.943 1978.874 1.154 .854 8.267 -3.373 1979.124 .701 .891 9.133 -1.436 1979.374 1.017 .924 7.900 4.494 1979.624 .809 1 .101 6.900 3.301 1979.874 .624 1 .091 6.800 -1.547 1980.124 .193 1 .084 8.767 -.461 1980.374 1.231 1 .206 6.733 4.587 1980.624 .731 1 .200 5.933 2.491 1980.874 .318 1 .410 5.767 -.783 1981.124 -.033 1 .656 6.700 .054 1981.374 .808 1 .600 6.167 3.363 1981.624 .614 1 .500 6.200 1.666 1981.874 .621 1 .485 7.700 -2.739 107 1982.124 1.066 1.428 10.067 -4.227 1982.374 .059 1.170 11.200 .137 1982.624 -.171 1.013 13.033 -.220 1982.874 .829 1.159 14.033 -3.527 DATE TAX% HOUSE% CPI% CPIVAN 1966.124 .070 .792 .019 83.900 1966.374 .067 .782 .009 84.000 1966.624 .064 .811 .011 84.900 1966.874 .062 .792 .008 85.100 1967.124 .059 .807 .013 85.900 1967.374 .057 .842 .015 87.300 1967.624 .056 .877 .010 88.300 1967.874 .055 ;844 .019 89.300 1968.124 .054 .'841 .014 89.900 1968.374 .053 .867 .008 90.200 1968.624 .053 .867 .008 91.300 1968.874 .052 .887 .007 92.000 1969.124 .052 .889 .006 92.600 1969.374 .052 .884 .006 94.400 1969.624 .045 .898 -.009 94.100 1969.874 .038 .926 -.002 95.300 1970.124 .031 .888 -.005 95.900 1970.374 .024 .893 .002 97.500 1970.624 .026 .914 -.006 97.200 1970.874 .027 .916 .001 97.700 1971.124 .029 .899 0.000 98.067 1971.374 .031 .828 -.001 99.333 1971.624 .025 .939 -.004 100.533 1971.874 .018 .946 .004 102.033 1972.124 .012 .966 .009 103.700 1972.374 .006 .947 .011 104.833 1972.624 .010 .974 0.000 105.767 1972.874 .013 .990 0.000 106.833 1973.124 .017 .997 .001 108.967 1973.374 .021 .973 .004 111.700 1973.624 .024 .963 -.001 114.367 1973.874 .026 1.013 .001 116.600 1974.124 .029 1.045 .002 119.567 1974.374 .031 1.014 .007 124.100 1974.624 .033 1.065 .012 128.467 1974.874 .035 1.102 .013 132.200 1975.124 .037 1.137 .010 134.633 1975.374 .040 1.087 .011 137.767 1975.624 .038 1.086 .012 142.600 1975.874 .035 1.100 .011 145.300 1976.124 .033 1.085 .015 147.767 1976.374 .031 1.077 .038 153.433 1976.624 .023 1.077 .037 155.567 1976.874 .014 1.095 .038 157.967 1977.124 .006 1.089 .030 160.200 108 1977.374 -.003 1.055 .026 163.267 1977.624 .004 1.039 .021 166.000 1977.874 .011 1.058 .018 169.167 1978.124 .017 1.068 .017 172.067 1978.374 .024 1.006 .016 176.067 1978.624 .019 1.060 .010 179.400 1978.874 . .013 1.061 .009 182.133 1979.124 .008 1.053 .006 185.733 1979.374 .003 1.018 .002 189.700 1979.624 .007 1.068 .000 193.200 1979.874 .010 1.013 -.009 195.833 1980.124 .014 1.061 -.011 199.767 1980.374 .018 1.094 -.008 205.900 1980.624 .019 1.129 -.007 211.967 1980.874 .020 1.257 -.005 218.367 1981.124 .021 1.378 .003 227.333 1981.374 .022 1.397 .007 235.367 1981.624 .009 1.409 .009 242.833 1981.874 -.003 1.313 .014 250.067 1982.124 -.015 1.327 .012 255.900 1982.374 -.027 1.299 .006 262.200 1982.624 -.039 1.250 .005 267.367 1982.874 -.051 1.222 .000 270.550 DATE UNOCC% VACAN% VACVAN VACDUI 1966.124 .018 .559 3.500 1.000 1966.374 .060 .484 3.000 1.000 1966.624 .105 .560 2.000 1.000 1966.874 .065 .600 1.500 1.000 1967.124 .050 .688 1.400 1.000 1967.374 .078 .769 1.300 1.000 1967.624 .099 .688 1.200 1.000 1967.874 .099 .579 1.000 0.000 1968.124 .122 .545 1.100 1.000 1968.374 .147 .481 1.200 1.000 1968.624 .143 .433 1.250 1.000 1968.874 .119 .364 1.300 1.000 1969.124 .093 .333 1.280 1.000 1969.374 .089 .300 1.260 1.000 1969.624 .106 .333 1.240 1.000 1969.874 .096 .395 1.200 1.000 1970.124 .080 .444 2.000 1.000 1970.374 .076 .540 2.700 1.000 1970.624 .078 .545 2.400 1.000 1970.874 .071 .553 2.100 1.000 1971.124 .061 .704 3.100 1.000 1971.374 .052 .820 4.100 1.000 1971.624 .071 .778 3.500 1.000 1971.874 .086 .718 2.800 1.000 1972.124 .073 .619 2.600 1.000 1972.374 .074 .533 2.400 1.000 109 1972.624 .108 .417 1.500 1.000 1972.874 .119 .222 .600 0.000 1973.124 .124 .258 .800 0.000 1973.374 .145 .294 1.000 0.000 1973.624 .181 .214 .600 0.000 1973.874 .169 .182 .400 0.000 1974.124 .216 .167 .400 0.000 1974.374 .331 .120 .300 0.000 1974.624 .406 .105 .200 0.000 1974.874 .285 .083 .100 0.000 1975.124 .205 .083 .100 0.000 1975.374 .197 .167 .200 0.000 1975.624 .229 .167 .200 0.000 1975.874 .266 .083 .100 0.000 1976.124 .327 .167 .200 0.000 1976.374 .234 .364 .400 0.000 1976.624 .221 .417 .500 0.000 1976.874 .190 .538 .700 0.000 1977.124 .172 .786 1.100 1.000 1977.374 .156 1.067 1.600 1.000 1977.624 .152 .842 1.600 1.000 1977.874 .125 .696 1.600 1.000 1978.124 .119 .652 1.500 1.000 1978.374 .115 .652 1.500 1.000 1978.624 .125 .500 1.400 1.000 1978.874 .122 .438 1.400 1.000 1979.124 .131 .387 1.200 1.000 1979.374 .128 .300 .900 0.000 1979.624 .098 .200 .600 0.000 1979.874 .068 .069 .200 0.000 1980.124 • .043 .037 .100 o.oco 1980.374 .054 .040 .100 0.000 1980.624 .046 .042 .100 0.000 1980.874 .040 .045 .100 0.000 1981.124 .051 .053 .100 0.000 1981.374 .121 .063 .100 0.000 1981.624 .192 .071 .100 0.000 1981.874 .194 .083 .100 0.000 1982.124 .162 .077 .100 0.000 1982.374 .172 .429 .600 0.000 1982.624 .152 .500 .900 0.000 1982.874 .121 .905 1.900 1.000 DATE DUMMY1 DUMMY2 DUMMY3 1966.1 1.0 0. 0. 1966.4 0. 1.0 0. 1966.6 0. 0. 1.0 1966.9 0. 0. 0. 1967.1 1.0 0. 0. 1967.4 0. 1.0 0. 1967.6 0. 0. 1.0 110 1967.9 0. 0. 0. 1968.1 1.0 0. 0. 1968.4 0. 1.0 0. 1968.6 0. 0. 1.0 1968.9 0. 0. 0. 1969.1 1.0 0. 0. 1969.4 0. 1.0 0. 1969.6 0. 0. 1.0 1969.9 0. 0. 0. 1970.1 1.0 0. 0. 1970.4 0. 1.0 0. 1970.6 0. 0. 1.0 1970.9 0. 0. 0. 1971.1 1.0 0. 0. 1971.4 0. 1.0 0. 1971.6 0. 0. 1.0 1971.9 0. 0. 0. 1972.1 1.0 0. 0. 1972.4 0. 1.0 0. 1972.6 0. 0. 1.0 1972.9 0. 0. 0. 1973.1 1.0 0. 0. 1973.4 0. 1.0 o.. 1973.6 0. 0. 1.0 1973.9 0. 0. 0. 1974.1 1.0 0. 0. 1974.4 0. 1.0 0. 1974.6 0. 0. 1.0 1974.9 0. 0. 0. 1975.1 1.0 0. 0. 1975.4 0. 1.0 0. 1975.6 0. 0. 1.0 1975.9 0. 0. 0. 1976.1 1.0 0. 0. 1976.4 0. 1.0 0. 1976.6 0. 0. 1.0 1976.9 0. 0. 0. 1977.1 1.0 0. 0. 1977.4 0. 1.0 0. 1977.6 0. 0. 1.0 1977.9 0. 0. 0. 1978.1 1.0 0. 0. 1978.4 0. 1.0 0. 1978.6 0. 0. 1.0 1978.9 0. 0. 0. 1979.1 1.0 0. 0. 1979.4 0. 1.0 0. 1979.6 0. 0. 1.0 1979.9 0. 0. 0. 1980.1 1.0 0. 0. 1980.4 0. 1.0 0. 1980.6 0. 0. 1.0 1980.9 0. 0. 0. 1981.1 1.0 0. 0. I l l 1981.4 0. 1.0 0. 1981.6 0. 0. 1.0 1981.9 0. 0. 0. 1982.1 1.0 0. 0. 1982.4 0. 1.0 0. 1982.6 0. 0. 1.0 1982.9 . 0. 0. 0. 112 APPENDIX D - REGRESSIONS RESULTS AND DIAGNOSTIC CHECKS FOR STUCTURAL MODELS REGRESSION RESULTS FOR FAMALI *VARIABLE COEFFICIENT STD.ERROR T-STAT DUMMY1 -1 .3089E+03 9 .5012E+01 -13 .776 DUMMY2 -1 .4381E+03 9 •3641E+01 -15 .358 DUMMY3 -1 .4449E+02 9 .2986E+01 -1 .554 INCO%-2 2 .3333E+04 3 .5580E+03 6 .558 JOBID% 1 .0322E+03 3 .3324E+02 3 .097 TAX%-4 -4 .5433E+03 2 .1706E+03 -2 .093 H0USE%-1 T .1437E+03 5 .0004E+02 -2 .287 CPI%-2 -7 .5772E+03 4 .0622E+03 -1 .865 UN0CC%-1 1 .7315E+03 5 .1773E+02 3 .344 CONSTANT 1 .3624E+03 5 .5673E+02 2 .447 *UNADJUSTED ADJUSTED MULTIPLE R 0.9504 0.9417 R-SQUARE 0.9032 0.8868 STD. DEV. OF RESIDUALS N = 63 = 2.6159E+02 *ANALYSIS OF VARIANCES SOURCE SS DF MS F 54.94 REGRESSION 3.38379E+07 RESIDUALS 3.62682E+06 TOTAL 3.74647E+07 9 3.75977E+06 53 6.84306E+04 62 6.04270E+05 113 DIAGNOSTIC CHECKS FOR FAMALI *DURBIN-WATSON STAT. = 2.1569 *AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 .25 .25 1 -0.094 0.123 + * + 2 -0.021 0.122 4- * + 3 -0.092 0.121 + * + 4 0.190 0.120 + * + 5 0.032 0.119 + * + 5 -0.114 0.118 + * + 7 -0.236 0.117 * + 8 -0.025 0.116 + * + 9 0.046 0.115 + * + 10 -0.120 0.114 + * + 11 0.045 0.113 + * + 12 -0.126 0.112 + * + 13 0.052 0.110 + * + 14 0.024 0.109 + * + 15 -0.078 0.108 + * + 16 -0.055 0.107 + * + 17 0.081 0.106 + * + 18 -0.098 0.105 + * + 19 0.057 0.104 + . * + 20 0.042 0.102 + * + 21 0.034 0.101 + * + 22 0.078 0.100 + * + 23 0.005 0.099 + * + 24 -0.131 0.098 + * + .50 .75 +1 -1 -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 34 EXPECTED NUMBER OF RUNS = 32.43 STANDARD-DEVIATION OF RUNS = 3.93 (OBS.-EXP.)/(STD.DEV.) = 0.40 -++—++ 1 +++-++-++ ++ ++-+-+-+++-+++ +-+ = VALUE > MEAN - = VALUE < = MEAN '++++-+—+-+ 114 *NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS -2 + + 1 + + 1 1 1 + 1 1 + 2 + 2 1 4 4 2 2 1 1 4 5 1 4 1 4 2 2 1 3 1 + 2 2 + 2 1 1 -3 + - + -+ -2 MEAN = 0.0 STD.DEV = 2.6158E+02 SKEWNESS = -3.3041E-01 KURTOSIS = -1.0185E-03 115 *PLOT OF RESIDUALS (FIRST YEAR PLOTTED IS 1966) Y-SCALE -983.0 -783.0 -583.0 -383.0 -183.0 17.0 217.0 417.0 617.0 66- 2 : * : - 3 : - 4 : * : 67- 1 : * • : - 2 : * : - 3 : * : - 4 : * : 68- 1 : * : - 2 : * : - 3 : * : - 4 : * : 69- 1 : * : - 2 : * : - 3 : • * . - 4 : * : 70- 1 : * : - 2 : * : - 3 : * : - 4 : * : 71- 1 : * : - 2 : * : - 3 : * : - 4 : * : 72- 1 : * : - 2 : * : - 3 : * : - 4 : * : 73- 1 : : * : - 2 : * : - 3 : * : - 4 : * : 74- 1 : -* : - 2 : * : - 3 : * - 4 : * : 75- 1 : * : - 2 : * : - 3 : * : - 4 : * : 76- 1 : * : - 2 : : - 3 : * : - 4 : * : 77- 1 : * : - 2 : - 3 : * : - 4 : * : 78- 1 : * : 116 - 2 - 3 - 4 79- 1 - 2 - 3 - 4 80- 1 - 2 - 3 - 4 81- 1 - 2 - 3 - 4 -983.0 -783.0 -583.0 -383.0 -183.0 17.0 217.0 417.0 617 "HISTOGRAM OF STANDARDIZED VALUES OF RESIDUALS ABS. FREQ. 10 * - * - * - * - ** * 5 * * *** * * _ * * **•* *** * ****** *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -5 -4 — "5 -1 MEAN = 0.0 STD. DEV. = 2.6158E+02 SAMPLE SIZE = 63 *MEAN AND STANDARD DEVIATION BASED ON 63 ACTIVE ROWS VARIABLE MEAN STD.DEV. FAMALI 2846 777 RESIDUALS 0 242 117 REGRESSION RESULTS FOR FAMALO •VARIABLE COEFFICIENT STD.ERROR T-STAT. DUMMY1 -5 .1632E+02 8 •1465E+01 -6 .338 DUMMY2 -6 .3633E+02 7 .3805E+01 -8 .622 DUMMY3 2 .0607E+02 7 .4711E+01 2 .758 WAGE% 3 .4742E+03 2 .1312E+03 1 .630 UNEMBC 1 .0434E+02 3 •0609E+01 3 .409 TAX% 4 .4137E+03 2 .5492E+03 1 .731 HOUSE%-•3 5 .8456E+02 5 .2005E+02 1 .124 CPI% 8 .6710E+03 2 .9608E+03 2 .929 VACAN%-•3 — D .8153E+02 1 .3425E+02 -4 .332 CONSTANT 5 .6368E+02 5 .2027E+02 1 .083 MULTIPLE R R-SQUARE •UNADJUSTED 0.9240 0.8539 ADJUSTED 0.9108 0.8295 STD. DEV. OF RESIDUALS = 2.0660E+02 N = 64 •ANALYSIS OF VARIANCES SOURCE SS REGRESSION 1.34673E+07 RESIDUALS 2.30494E+06 TOTAL 1.57723E+07 DF MS F 9 1.49637E+06 35.06 54 4.26841E+04 63 2.50354E+05 118 DIAGNOSTIC CHECKS FOR FAMALO •DURBIN-WATSON STAT. = 2.2308 •AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM )ER CORR. MODEL -1 -.75 -.50 -.25 C ) .25 1 -0.149 0.122 + * + 2 0.112 0.121 + * + 3 0.207 0.120 + *+ 4 -0.145 0.119 + * + 5 0.073 0.118 + * + 6 -0.034 0.117 + * + 7 -0.172 0.116 + * + 8 -0.018 0.115 + * + 9 -0.078 0.114 + + 10 -0.043 0.113 + * + 11 -0.074 0.112 + * + 12 -0.007 0.111 + * + 13 0.023 0.110 + * + 14 0.117 0.109 + * + 15 0.147 0.108 + * + 16 -0.095 0.107 + * + 17 0.144 0.105 + : *+ 18 0.064 0.104 + : * + 19 -0.117 0.103 + * + 20 0.017 0.102 + * + 21 -0.034 0.101 + * + 22 -0.099 0.100 + * : + 23 -0.072 0.099 + * : + 24 -0.096 0.097 + * + .50 .75 +1 -1 -.75 -.50 -.25 .25 .50 .75 +1 AUTOCORRELATIONS 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNTS OF RESIDUALS OBSERVED NUMBER OF RUNS = 36 EXPECTED NUMBER OF RUNS = 32.97 STANDARD-DEVIATION OF RUNS = 3.96 (OBS.-EXP.)/(STD.DEV.) = 0.76 - + - + H— + H— + - + + - + + + + + H + + - + + + + + + + H—H + + - + - + — 1 - + -H + + = VALUE > MEAN - = VALUE < = MEAN 119 "NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS -1 -3 + + + 1 1 1 + 1 1 + 3 + 1 3 4 5 4 1 5 1 2 3 1 4 2 2 3 1 2 1 1 1 2 1 1 1 + + 1 -+ -3 -2 -1 MEAN = 0.0 STD.DEV = 2.0659E+02 SKEWNESS = -5.8570E-02 KURTOSIS = -5.7445E-01 120 *PLOT OF RESIDUALS (FIRST YEAR PLOTTED IS 1966) Y-SCALE -580.0 -430.0 -280.0 -130.0 20.0 170.0 320.0 470.0 620.0 66- 1 : * - 2 : * - 3 : * - 4 : • * 67- 1 : * - 2 : * - 3 : * - 4 : * 68- 1 : * - 2 : * - 3 : - 4 : * 69- 1 : * - 2 : * - 3 : * - 4 : 70- 1 : * - 2 : * - 3 : - 4 : * 71- 1 : * - 2 : * - 3 : - 4 : 72- 1 : * - 2 : * - 3 : * - 4 : * 73- 1 : * - 2 : * - 3 : - 4 : * 74- 1 : * - 2 : * - 3 : * - 4 : 75- 1 : * - 2 : - 3 : * - 4 : * 76- 1 : * - 2 : * - 3 : * _ 4 . * 77- 1 : * - 2 : - 3 : * 121 - 4 : * 78- 1 : * - 2 : * - 3 : - 4 : * 79- 1 : * - 2 : * - 3 : - 4 : * 80- 1 : * - 2 ': - 3 : - 4 : * 81- 1 : * - 2 : * - 3 : - 4 : * -580.0 -430.0 -280.0 -130.0 20.0 170.0 320.0 470.0 620 "HISTOGRAM OF STANDARDIZED VALUES OF RESIDUALS ABS. FREQ. — * * _ ** * * ****** _ * * * * * * * * _ * * * * * * * * * * _ * * * * * * * * * * * * * * _ * * * * * * * * * * * * * * * * ** * -5 -4 -3 -2 -1 0 1 2 3 4 5 MEAN = 0.0 STD. DEV. = 2.0659E+02 SAMPLE SIZE = 64 "MEAN AND STANDARD DEVIATION BASED ON 64 ACTIVE ROWS VARIABLE MEAN STD.DEV. FAMALO 1992 500 RESIDUALS 0 191 122 REGRESSION RESULTS FOR OLDAGI "VARIABLE COEFFICIENT STD.ERROR T-STAT. DUMMY1 -2 .6347E+02 7 •4607E+01 -3 .531 DUMMY2 -1 .4943E+02 7 .4038E+01 -2 .018 DUMMY3 9 .6245E+01 7 .4103E+01 1 .299 WAGE% 4 .1707E+03 1 .9889E+03 2 .097 JOBID% 3 .1542E+02 2 .1523E+02 1 .466 TAX%-2 -5 .0421E+03 1 .8538E+03 -2 .720 HOUSE%-2 -1 .1832E+03 4 .4922E+02 -2 .634 CPI% -5 •4390E+03 3 .5381E+03 -1 .537 UN0CC%-1 8 .1232E+02 4 •2693E+02 1 .903 CONSTANT 1 •1493E+03 3 .1758E+02 3 .619 MULTIPLE R R-SQUARE "UNADJUSTED 0.7329 0.5372 ADJUSTED 0.6772 0.4586 STD. DEV. OF RESIDUALS = 2.0402E+02 N = 63 "ANALYSIS OF VARIANCES SOURCE SS REGRESSION 2.56038E+06 RESIDUALS 2.20608E+06 TOTAL 4.76646E+06 DF MS F 9 2.84487E+05 6.83 53 4.16241E+04 62 7.68783E+04 123 DIAGNOSTIC CHECKS FOR OLDAGI *DURBIN-WATSON STAT. = 1.8826 •AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 0.057 0.123 + * + 2 -0.205 0.122 +* + 3 0.004 0.121 + * + 4 0.032 0.120 + + 5 0.066 0.119 + . * + 6 -0.014 0.118 + * + 7 -0.212 0.117 +* + 8 -0.103 0.116 + * + 9 0.107 0.115 + * + 10 0.114 0.114 + * + 11 -0.009 0.113 + * + 12 0.059 0.112 + * + 13 -0.024 0.110 + * + 14 -0.093 0.109 + * + 15 -0.002 0.108 + * + 16 -0.038 0.107 + * + 17 -0.053 0.106 + * + 18 0.061 0.105 + * + 19 -0.059 0.104 + * + 20 -0.125 0.102 +* + 21 0.198 0.101 + * 22 -0.002 0.100 + * + 23 -0.162 0.099 + * + 24 -0.065 0.098 + * + -1 -.75 -.50 -.25 0 .25 .50 .75 +1 • : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) •RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 28 EXPECTED NUMBER OF RUNS = 32.30 STANDARD-DEVIATION OF RUNS = 3.91 (OBS.-EXP.)/(STD.DEV.) = -1.10 H h + H + + + + + + + H + H — + + + + - + + + + + - + + + - + + + + = VALUE > MEAN - = VALUE < = MEAN 124 •NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS 2 2 1 1 + 1 + + 2 1 1 + 2 1 2 2 2 2 4 1 2 3 2 3 5 2 3 + 4 + 3 1 1 -3 -2 -1 MEAN = 0.0 STD.DEV = 2.0402E+02 SKEWNESS = -1.9076E-01 KURTOSIS = -4.4569E-01 125 *PLOT OF RESIDUALS (FIRST YEAR PLOTTED IS 1966) -629 Y-SCALE .0 -479.0 -329.0 -179.0 -29.0 121.0 271.0 421.0 571.0 66- 2 - 3 - 4 67- 1 - 2 - 3 - 4 68- 1 - 2 - 3 69- 1 - 2 - 3 - 4 70- 1 - 2 - 3 - 4 71- 1 - 2 - 3 - 4 72- 1 - 2 - 3 - 4 73- 1 - 2 - 3 - 4 74- 1 - 2 - 3 - 4 75- 1 - 2 - 3 - 4 76- 1 - 2 - 3 - 4 77- 1 - 2 - 3 - 4 78- 1 126 - 2 - 3 - 4 79- 1 - 2 - 3 - 4 80- 1 - 2 - 3 - 4 81- 1 - 2 - 3 - 4 * * * * * * * * * * * * -629 .0 -479.0 -329.0 -179.0 -29.0 121.0 271.0 421.0 571 "HISTOGRAM OF STANDARDIZED VALUES OF RESIDUALS ABS. FREQ. 10 * ** * * * * * * * ** * ** * * * * * * * ** ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -5 -4 -3 -2 -1 0 1 2 3 4 5 MEAN = 0.0 STD. DEV. = 2.0402E+02 SAMPLE SIZE = 63 "MEAN AND STANDARD DEVIATION BASED ON 63 ACTIVE ROWS VARIABLE MEAN STD.DEV. OLDAGI 627 277 RESIDUALS 0 189 5 * * * 127 REGRESSION RESULTS FOR OLDAGO "VARIABLE COEFFICIENT STD.ERROR T-STAT. DUMMY1 -8 •0022E+01 1 .0712E+02 -0 .747 DUMMY2 1 .4456E+01 8 .9819E+01 0 .161 DUMMY3 6 .2993E+01 6 .0639E+01 1 .039 INCO%-4 -8 .5741E+02 2 .3311E+03 -0 .368 EMG.BC-3 -1 .5662E+01 1 •6157E+01 -0 .969 TAX%-4 -1 .0849E+03 1 .5890E+03 -0 .683 HOUSE%-3 3 .7355E+02 3 .3160E+02 1 .127 CPI%-3 3 .1141E+03 1 .9794E+03 1 .573 VACVAN-3 -1 •0036E+01 3 •0566E+01 -0 .328 CONSTANT 1 .1164E+02 5 •0487E+02 0 .221 MULTIPLE R R-SQUARE "UNADJUSTED 0.6534 0.4269 ADJUSTED 0.5707 0.3257 STD. DEV. OF RESIDUALS = 1.5957E+02 N = 61 "ANALYSIS OF VARIANCES SOURCE SS REGRESSION 9.67227E+05 RESIDUALS 1.29855E+06 TOTAL 2.26578E+06 DF MS F 9 1.07470E+05 4.22 51 2.54618E+04 60 3.77629E+04 128 DIAGNOSTIC CHECKS FOR OLDAGO *DURBIN-WATSON STAT. = 2.4079 •AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 -0.212 0.125 +* : + 2 -0.145 0.124 + * : + 3 0.064 0.123 + * + 4 0.011 0.122 + * + 5 0.004 0.121 + * + 6 0.030 0.120 + * + 7 -0.155 0.119 + * + 8 -0.208 0.117 +* + 9 0.082 0.116 + * + 10 0.074 0.115 + * + 11 -0.084 0.114 + * + 12 -0.072 0.113 + * + 13 0.121 0.112 + * + 14 -0.057 0.111 + * + 15 0.197 0.109 + * 16 -0.058 0.108 + * + 17 -0.074 0.107 + * + 18 0.114 0.106 + . * + 19 -0.106 0.105 + * + 20 0.106 0.103 + * + 21 0.147 0.102 + *+ 22 -0.155 0.101 +* + 23 -0.110 0.099 + * + 24 0.013 0.098 + * + -1 -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 34 EXPECTED NUMBER OF RUNS = 31.10 STANDARD-DEVIATION OF RUNS = 3.82 (OBS.-EXP.)/(STD.DEV.) = 0.76 ++-+—++-++—+-+—++ + + +—+-++-+-++ ++—++—+++-+ = VALUE > MEAN - = VALUE < = MEAN 129 "NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS OBS. IN ROW 32 AN OUTLIER; PLOTTED AS 3.4 + + + + + + + + + 1 1 + 1 1 + 12 + 3 + 2 1 + 3 2 + 4 + 4 1 1 4 5 4 3 2 1 2 1 2 + 3 + 1 + 1 1 + 1 + + 1 -3 + - + -+ -2 -1 MEAN = 0.0 STD.DEV = 1.5957E+02 SKEWNESS = 1.1358E+00 KURTOSIS = 1.9495E+00 130 *PLOT OF RESIDUALS (FIRST YEAR PLOTTED IS 1966) Y-SCALE -372.0 -247.0 -122.0 3.0 128.0 253.0 378.0 503.0 628.0 66- 4 : * 67- 1 : * - 2 : - 3 : - 4 : * 68- 1 : * - 2 : * - 3 : - 4 : * 69- 1 : * - 2 : * - 3 : * - 4 : * 70- 1 : * - 2 : * - 3 : * - 4 : * 71- 1 : * - 2 : * - 3 : - 4 : * 72- 1 : * - 2 : * - 3 : - 4 : * 73- 1 : * - 2 : * - 3 : - 4 : * 74- 1 : * - 2 : * - 3 : - 4 : * 75- 1 : * - 2 : - 3 : * - 4 : * 76- 1 : * - 2 : - 3 : * - 4 : 77- 1 : * - 2 : - 3 : - 4 : 78- 1 : * - 2 : - 3 : 131 - 4 : * 79- 1 : * - 2 : * - 3 : * - 4 : * 80- 1 : * - 2 : * - 3 : - 4 : * 81- 1 : * - 2 : * - 3 : * - 4 : * -372.0 -247.0 -122.0 3.0 128.0 253.0 378.0 503.0 628 •HISTOGRAM OF STANDARDIZED VALUES OF RESIDUALS ABS. FREQ. _ * * _ ** _ * **** ^ * * * * * * _ * * * * * * * * _ * * * * * * * * * _ * * * * * * * * * * ** _ * ************* * * * -5 -4 -3 -2 -1 0 1 2 3 4 5 MEAN = 0.0 STD. DEV. = 1.5957E+02 SAMPLE SIZE = 61 *MEAN AND STANDARD DEVIATION BASED ON 61 ACTIVE ROWS VARIABLE MEAN STD.DEV. OLDAGO 357 194 RESIDUALS 0 147 132 APPENDIX E - REGRESSION RESULTS AND DIAGNOSTIC CHECKS FOR FAMANT STRUCTURAL MODEL REGRESSION RESULTS FOR FAMANT •VARIABLE COEFFICIENT STD.ERROR T-STAT DUMMY1 -1 .0088E+03 1 .3236E+02 -7 .622 DUMMY2 -8 •4521E+02 9 .6107E+01 -8 .794 DUMMY3 -3 .4425E+02 0 •9404E+01 -3 .463 WAGE% 2 .6054E+03 3 .5519E+03 0 .734 INCO%-2 2 .6422E+04 5 .7818E+03 4 .570 JOBID% 1 .9327E+03 5 •2113E+02 3 .709 UNEMBC 7 .1324E+01 7 .1002E+01 1 .005 TAXE% -7 .5649E+03 4 .2938E+03 -L .762 TAXE%-4 4 .6734E+03 3 .8753E+03 1 .206 H0USE%-1 -1 .6401E+03 8 .9107E+02 -1 .841 H0USE%-3 -2 .0795E+03 1 .1009E+03 -1 .889 CPI% -1 .2718E+04 6 .1330E+03 -2 .074 CPI%-2 -3 •0096E+03 5 .8692E+03 -0 .513 UN0CC%-1 1 .0164E+03 6 .9425E+02 1 .464 VACAN%-3 4 .0570E+02 2 .5163E+02 1 .612 CONSTANT -3 .8839E+02 1 .3174E+03 -0 .295 •UNADJUSTED ADJUSTED MULTIPLE R R-SQUARE 0.9318 0.8682 0.9090 0.8262 STD. DEV. OF RESIDUALS = N = 63 2.5670E+02 •ANALYSIS OF VARIANCES SOURCE SS DF MS F 20.65 REGRESSION 2.04100E+07 RESIDUALS 3.09706E+06 TOTAL 2.35071E+07 15 1.36067E+06 47 6.58949E+04 62 3.79147E+05 133 DIAGNOSTIC CHECKS FOR FAMANT *DURBIN-WATSON STAT. = 2.0488 *AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 -0.032 0.123 + + 2 -0.239 0.122 * + 3 -0.072 0.121 + * + 4 0.074 0.120 + * + 5 0.187 0.119 + * + 6 -0.197 0.118 + * + 7 -0.195 0.117 + * + 8 0.050 0.116 + * + 9 0.024 0.115 + * + 10 -0.038 0.114 + * + 11 -0.024 0.113 + * + 12 -0.029 0.112 + * + 13 0.178 0.110 + * 14 -0.064 0.109 + * + 15 0.122 0.108 + * + 16 -0.050 0.107 + * + 17 -0.008 0.106 + + 18 0.021 0.105 + * + 19 -0.184 0.104 * + 20 0.004 0.102 + * + 21 0.093 0.101 + + 22 -0.089 0.100 + * + 23 -0.138 0.099 +* + 24 -0.034 0.098 + * + -1 -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 34 EXPECTED NUMBER OF RUNS = 32.30 STANDARD-DEVIATION OF RUNS = 3.91 (OBS.-EXP.)/(STD.DEV.) = 0.43 — h + + + + + H — + — K + - + h + + —I + + + - + + + - H + + H + — h - + + = VALUE > MEAN - = VALUE < = MEAN 134 •NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS + + + 1 + + 1 1 1 2 + 1 1 + 3 + 3 1 1 3 5 1 4 4 1 1 4 5 3 1 1 3 + 3 + 2 + 1 1 + 1 1 + 1 + + 1 - + -3 -1 MEAN = 0.0 STD.DEV = 2.5669E+02 SKEWNESS = 2.7228E-01 KURTOSIS = -9.7591E-01 135 *PLOT OF RESIDUALS (FIRST YEAR PLOTTED IS 1966) Y-SCALE -666.0 -466.0 -266.0 -66.0 134.0 334.0 534.0 734.0 934.0 66- 2 * • * 3 . 4 : * * 67- 1 -2 3 4 * * * 68- 1 . * _ - 2 * - 3 * - 4 * 69- 1 2 3 _ _ * * * - 4 * 70- 1 2 .3 4 * * * 71- 1 -2 3 4 * * * 72- 1 _ * _ - 2 * — 3 4 73- 1 * -2 3 4 * * * 74- 1 2 * - 3 * - 4 * 75- 1 2 3 _ * _ * * - 4 * 76- 1 2 3 4 * * * * 77- 1 _ * . -2 3 4 * * 78- 1 _ _ * _ . 136 - 2 : * - 3 : - 4 : * 79- 1 : * - 2 : - 3 : * - 4 : * 80- 1 : * - 2 : * - 3 : - 4 : * 81- 1 : * - 2 : * - 3 : - 4 : * -666.0 -466.0 -266.0 -66.0 134.0 334.0 534.0 734.0 934 •HISTOGRAM OF STANDARDIZED VALUES OF RESIDUALS AES. FREQ. ** * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - 5 - 4 - 3 - 2 - 1 0 1 2 3 t MEAN = 0.0 STD. DEV. = 2.5669E+02 SAMPLE SIZE = 63 *MEAN AND STANDARD DEVIATION BASED ON 63 ACTIVE ROWS VARIABLE MEAN STD.DEV. FAMANT 842 616 RESIDUALS 0 223 137 APPENDIX F - CHECKING STATIONARITY OF FAMALI SERIES 'SEQUENCE PLOT OF STANDARDIZED VALUES OF FAMALI ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 50 138 HISTOGRAM ABS. FREQ. _ * ** * _ * * * * * * * * * * _ * * * * * * * * * * * * * _ * * * * * * * * * * * * * * * * * * _ ****************** - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 MEAN = 2.7946E+03 STD. DEV. = 7.5673E+02 SAMPLE SIZE = 63 139 ''AUTOCORRELATION FUNCTION OF FAMALI S.E. AUTO- RANDOM ORDER CORR. MODEL .75 -.50 -.25 .25 .50 .75 +1 1 0.150 0.123 + * + 2 -0.540 0.122 * + + 3 0.083 0.121 + * + 4 0.714 0.120 + + 5 0.042 0.119 + * + 6 -0.663 0.118 * + + 7 -0.063 0.117 + + 8 0.537 0.116 + + 9 -0.056 0.115 + * + 10 -0.666 0.114 * + + 11 -0.071 0.113 + * + 12 0.474 0.112 + + 13 -0.042 0.110 + * + 14 -0.563 0.109 * + + 15 -0.030 0.108 + * + 16 0.460 0.107 + + 17 -0.074 0.106 + * : + 18 -0.501 0.105 * + : + 19 0.032 0.104 + :* + 20 0.440 0.102 + : + 21 -0.038 0.101 + * + 22 -0.411 0.100 * + : + 23 0.051 0.099 + :* + 24 0.453 0.098 + : + -1 -.75 -.50 -.25 .25 ,50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) 140 •PARTIAL AUTOCORRELATION FUNCTION OF FAMALI ORDER PARTIAL AUTO COR -1 -.75 -.50 -.25 0 .25 .50 .75 1 0.1537 -2 -0.6266 - * 3 0.4812 -4 0.4118 - • 5 -0.2397 - * 6 -0.2708 - * 7 -0.0254 - * 8 -0.0648 - * 9 -0.1367 - * 10 -0.0942 - * 11 0.1403 -12 -0.1272 - * 13 0.0079 -14 0.0122 - * 15 -0.0785 - * 16 -0.1052 - * 17 -0.1843 - * 18 -0.0753 * 19 0.1126 -20 -0.0009 - * 21 0.0609 - • * 22 0.0105 - * 23 -0.1118 - * 24 -0.0490 - * 141 •SEQUENCE PLOT OF STAND.VALUES OF 1st DIFFERENCE FAMALI ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 50 142 HISTOGRAM ABS. FREQ. 10 ** * * ** * * * *** * * * * * * * * * * * *** * ***** * *** ******************** -4 -3 -2 MEAN = 7.9122E+00 STD. DEV. = 9.7631E+02 SAMPLE SIZE = 63 143 •AUTOCORRELATION FUNCTION OF 1st DIFFERENCE FAMALI S.E. AUTO- RANDOM ORDER CORR. MODEL -1 .75 -.50 -.25 0 .25 1 -0.070 0.123 + + 2 -0.793 0.122 * + + 3 -0.030 0.121 + + 4 0.796 0.120 + + 5 0.026 0.119 + * + 6 -0.771 0.118 * + 7 -0.026 0.117 + * + 8 0.729 0.116 + + 9 0.029 0.115 + * + 10 -0.726 0.114 * + + 11 0.011 0.113 + * + 12 0.642 0.112 + + 13 0.018 0.110 + * + 14 -0.639 0.109 * + + 15 0.004 0.108 + * + 16 0.615 0.107 + + 17 -0.032 0.106 + * + 18 -0.588 0.105 * + + 19 0.052 0.104 + . * + 20 0.537 0.102 + + 21 -0.043 0.101 + * + 22 -0.512 0.100 * + + 23 0.035 0.099 + + 24 0.495 0.098 + + .50 .75 + -1 -.75 -.50 -.25 .25 .50 .75 + * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) 144 •PARTIAL AUTOCORRELATION FUNCTION OF 1st DIFF. FAMALI PARTIAL ORDER AUTO COR -1 -.75 -.50 -.25 0 .25 .50 .75 1 • • • • • ~ 1 -0.0625 - *: 2 -0.8098 - * : 3 -0.5081 - * : 4 0.1985 - : * 5 0.1273 - : * 6 -0.1237 - * : 7 -0.0861 - * : 8 -0.0002 - * 9 -0.0387 - ' *: 10 -0.2706 - * : 11 0.0454 - :* 12 -0.1234 - * : 13 -0.0787 - * : 14 0.0179 - * 15 0.0232 - * 16 0.0728 - :* 17 -0.0663 - *: 18 -0.2290 - * : 19 -0.0407 - *: 20 -0.1273 - * : 21 -0.0339 - *: 22 0.0840 - : * 23 0.0023 - * 24 -0.1331 - * : 145 'SEQUENCE PLOT OF STAND.VALUES OF SEASONAL DIFF. OF 1st DIFF. FAMALI. ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 50 55 146 HISTOGRAM ABS. FREQ. * * * * * * **** * **** * ** * * * * * ** * * * * * * * ** ******** * ***** ************ -5 -4 -3 -2 MEAN = -1.8052E+01 STD. DEV. = 4.9265E+02 SAMPLE SIZE = 63 147 •AUTOCORRELATION FUNCTION OF SEASONAL DIFF. OF 1st DIFF. FAMALI S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 -0.342 0.123 * + : + 2 0.0 0.122 + * + 3 0.099 0.121 + * + 4 -0.334 0.120 * + + 5 0.157 0.119 + * + 6 0.132 0.118 + * + 7 -0.137 0.117 + * + 8 0.017 0.116 + * + 9 0.027 0.115 + * + 10 -0.222 0.114 +* + 11 0.276 0.113 + +* 12 -0.159 0.112 +* + 13 0.067 0.110 + •* + 14 0.192 0.109 + * 15 -0.230 0.108 * + + 16 0.035 0.107 + •* + 17 0.0 0.106 + * + 18 -0.158 0.105 +* : + 19 0.207 0.104 + 20 0.050 0.102 + :* + 21 -0.183 0.101 * : + 22 0.119 0.100 + : * + 23 -0.160 0.099 + * : + 24 -0.041 0.098 + * : + -1 -.75 -.50 -.25 ( ) .25 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) 148 •PARTIAL AUTO. FUNCTION OF SEASONAL DIFF. OF 1st DIFF. FAMALI PARTIAL ORDER AUTO COR -1 -.75 -.50 -.25 0 1 -0.3416 - * 2 -0.1328 - * 3 0.0610 - * 4 -0.3193 - * 5 -0.0742 - * 6 0.1613 - * 7 -0.0081 - * 8 -0.1600 - * 9 0.0201 - * 10 -0.1457 - * 11 0.1104 - * 12 -0.1358 - * 13 0.0619 - * 14 0.1857 - * 15 -0.0094 - * 16 -0.1326 - * 17 -0.0373 - * 18 -0.0830 - * 19 0.0647 - * 20 0.0427 -21 -0.0512 - * 22 -0.0403 - * 23 -0.0548 - * 24 -0.1121 - * 149 APPENDIX G - DIAGNOSTIC CHECKS FOR FAMALI TIME-SERIES MODEL •AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 0.013 0.122 + * + 2 -0.056 0.121 + + 3 -0.141 0.120 + * + 4 0.119 0.119 + * + 5 0.027 0.118 + * + 6 -0.049 0.117 + + 7 -0.197 0.116 + * + 8 -0.106 0.115 + * + 9 0.007 0.114 + * + 10 -0.140 0.113 + * : + 11 0.018 0.112 + * + 12 -0.078 0.111 + * + 13 0.115 0.110 + * + 14 0.081 0.109 + * + 15 -0.100 0.108 + * + 16 -0.096 0.107 + * + 17 -0.021 0.105 + * + 18 -0.076 0.104 + * + 19 0.076 0.103 + * + 20 0.039 0.102 + * + 21 -0.046 0.101 + * + 22 -0.031 0.100 + * + 23 -0.032 0.099 + * + 24 -0.035 0.097 + * + -1 -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 28 EXPECTED NUMBER OF RUNS = 32.72 STANDARD-DEVIATION OF RUNS = 3.93 (OBS.-EXP.)/(STD.DEV.) = -1.20 —++—++ +-++++—++-++ +++++-++ ++—+++-+++-+++++—+ + + = VALUE > MEAN - = VALUE < = MEAN 150 N^ORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS OBS. IN ROW 63 AN OUTLIER; PLOTTED AS -3.4 -2 -1 -3 + + -+ + + + + + + 1 + + 1 + 1 1 2 + 2 2 1 4 4 1 5 3 3 3 2 1 4 + 4 2 1 1 2 1 2 + 1 1 1 1 1 -3 -2 -1 MEAN = 3.3952E+01 STD.DEV = 3.6552E+02 SKEWNESS = -9.7812E-01 KURTOSIS = 2.5387E+00 151 •SCATTER PLOT OF 64 STANDARDIZED VALUES OF RESIDUALS VS. FITTED VERT OBS. IN ROW 63 AN OUTLIER; PLOTTED AS -3.4 1 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 2 1 1 1 1 1 1 1 1 -1 1 1 -3 1 2 1 1 -2 -1 MEAN STD.DEV. VERT. VAR. 3.3952E+01 3.6552E+02 HORIZ. VAR. 2.8009E+03 7.6129E+02 152 *MEAN AND STANDARD DEVIATION BASED ON 64 ACTIVE ROWS VARIABLE MEAN STD. DEV. FAMALI 2834.89 775.901 RESIDUALS 33.9517 365.521 153 APPENDIX H - CHECKING STATIONARITY OF FAMALO SERIES 'SEQUENCE PLOT OF STANDARDIZED VALUES OF FAMALO ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 * 50 55 60 65 HISTOGRAM ABS. FREQ. 154 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -3 -1 MEAN = 2.0472E+03 STD. DEV. = 4.8729E+02 SAMPLE SIZE = 63 155 •AUTOCORRELATION FUNCTION OF FAMALO S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 0.307 0.123 + +* 2 -0.013 0.122 + * + 3 0.306 0.121 + +* 4 0.694 0.120 + + 5 0.211 0.119 + * + 6 -0.161 0.118 + * + 7 0.079 0.117 + * + 8 0.540 0.116 + + 9 0.032 0.115 + * + .10 -0.305 0.114 * + + 11 -0.074 0.113 + * + 12 0.387 0.112 + + 13 -0.084 0.110 + * + 14 -0.359 0.109 * + + 15 -0.070 0.108 + * + 16 0.294 0.107 + + * 17 -0.106 0.106 + * + 18 -0.354 0.105 * + + 19 -0.110 0.104 + * + 20 0.271 0.102 + +* 21 -0.089 0.101 + * + 22 -0.306 0.100 * + + 23 -0.072 0.099 + * + 24 0.247 0.098 + + * -1 -.75 -.50 -.25 ( J .25 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) 156 *PARTIAL AUTOCORRELATION FUNCTION OF FAMALO PARTIAL ORDER AUTO COR -1 -.75 -.50 -.25 0 1 0.3362 -2 -0.1408 - * 3 0.4152 -4 0.5685 -5 -0.1434 - * 6 -0.2397 - * 7 -0.2106 - * 8 0.3342 -9 -0.1191 - * 10 -0.0929 - * 11 -0.1198 - * 12 0.1425 -13 -0.1618 - * 14 0.1157 -15 0.0384 -16 -0.0094 - * 17 -0.0491 - * 18 -0.1018 - * 19 0.0664 - * 20 0.0430 - * 21 0.0523 -22 0.1082 -23 0.0781 -24 -0.1492 - * 157 *SEQUENCE PLOT OF STANDARDIZED VALUES OF 1st DIFF. FAMALO ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 50 158 55 60 65 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 HISTOGRAM ABS. FREQ. _ * 10 * _ * _ * ** 5 * * * * _ * * * * * * _ * * * * * * * ** * __ ******** * **** * * * * * * * * * * * * * * * * * * * * - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 MEAN = 1.4587E+01 STD. DEV. = 5.6850E+02 SAMPLE SIZE = 63 159 *AUTOCORRELATION FUNCTION OF 1st DIFFERENCE FAMALO S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.21 .25 .50 .75 1 -0.261 0.123 * . + 2 -0.463 0.122 * + : + 3 -0.071 0.121 + *: + 4 0.625 0.120 + + 5 -0.063 0.119 + *. + 6 -0.431 0.118 * + + 7 -0.184 0.117 +* + 8 0.708 0.116 + + 9 -0.109 0.115 + * + 10 -0.417 0.114 * + + 11 -0.161 0.113 + * + 12 0.655 0.112 + + 13 -0.128 0.110 +* + 14 -0.386 0.109 * + + 15 -0.084 0.108 + * + 16 0.554 0.107 + + 17 -0.103 0.106 + * + 18 -0.353 0.105 * + : + 19 -0.120 0.104 + * : + 20 0.540 0.102 + + 21 -0.096 0.101 + * : + 22 -0.320 0.100 * + : + 23 -0.073 0.099 + * : + 24 0.463 0.098 + : + -1 -.75 -.50 -.25 .25 .50 .75 + AUTOCORRELATIONS 2 STANDARD ERROR LIMITS (APPROX.) 160 •PARTIAL AUTOCORRELATION FUNCTION OF 1st DIFF. FAMALO PARTIAL ORDER AUTO COR -1 -.75 -.50 -.25 0 .25 .50 .75 1 1 -0.2572 - * : 2 -0.5793 - * : 3 -0.6437 - * : 4 0.0543 - :* 5 0.2192 - : * 6 0.2023 - : * 7 -0.3440 - * : 8 0.1116 - : * 9 0.0421 - :* 10 -0.0091 11 -0.2137 - * : 12 0.0954 - : * 13 -0.1839 - * : 14 -0.0830 - * : 15 -0.0731 - *: 16 0.0632 - :* 17 -0.0130 18 -0.0556 - *: 19 -0.0267 - *: 20 -0.0710 - *: 21 -0.1592 - * : 22 -0.1423 - * : 23 0.0404 - :* 24 -0.0704 - *: 161 •SEQUENCE PLOT OF STAND.VALUES OF SEASONAL DIFF. OF 1st DIFF. FAMALO. ROW 6 = 1967(2) ROW 10 15 20 25 30 35 40 45 50 162 55 60 65 -5 -4 - 3 - 2 - 1 0 1 2 3 4 HISTOGRAM ABS. FREQ. - * * * _ * * * * 5 * *** * * - * * *** ** * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -5 -4 -3 -1 MEAN = -1.4524E+01 STD. DEV. = 4.6134E+02 SAMPLE SIZE = 63 163 •AUTOCORRELATION FUNCTION OF SEASONAL DIFF. OF 1st DIFF. FAMALO S.E. AUTO- RANDOM ORDER CORR. MODEL -1 .75 -.50 -.25 0 .25 .75 +1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 -0.526 0.005 0.435 -0.594 0.254 0.037 -0.146 0.130 0.0 -0.086 -0.021 0.050 -0.111 0.062 0.124 -0.151 0.102 -0.021 -0.153 0.102 -0.027 0.035 0.012 0.048 123 122 121 120 119 118 0.117 0.116 0.115 114 113 112 110 0.109 0.108 0.107 0.106 0.105 0.104 0.102 0.101 0.100 0.099 0.098 + + + + + + + + + + + + + + +* + + +* + + + + + + + + + + + + + + + + + + + + + + + + + + + + -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) 164 *PARTIAL AUTO. FUNCTION OF SEASONAL DIFF. OF 1st DIFF. FAMALO PARTIAL ORDER AUTO COR -1 -.75 -.50 -.25 0 .25 .50 .75 1 1 -0.5264 -2 -0.3769 - * . 3 0.3860 -4 -0.2630 -5 -0.2370 - * • 6 -0.1687 -7 0.2920 -8 -0.0660 -9 -0.0484 -10 -0.1691 -11 -0.0486 - *. 12 -0.0817 - * 13 -0.0676 -14 -0.0984 - * . 15 0.1651 -16 0.0015 - * 17 -0.0787 -18 -0.1664 - * 19 -0.0381 -20 -0.1187 - * • 21 -0.0526 - * • 22 0.0872 -23 -0.0285 -24 -0.0184 - * 165 APPENDIX I - DIAGNOSTIC CHECKS FOR FAMALO TIME-SERIES MODEL •AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 +1 1 -0.019 0.122 + * + 2 -0.023 0.121 + * + 3 0.064 0.120 + : * + 4 • -0.117 0.119 + * : + 5 -0.006 0.118 + * + 6 0.010 0.117 + * + 7 -0.016 0.116 + * + 8 0.167 0.115 + * + 9 0.011 0.114 + * + 10 -0.168 0.113 + * + 11 -0.188 0.112 * + 12 -0.112 0.111 + * + 13 -0.069 0.110 + * + 14 0.053 0.109 + * + 15 0.086 0.108 + * + 16 -0.038 0.107 + * + 17 0.018 0.105 + * + 18 -0.114 0.104 + * + 19 -0.207 0.103 * + 20 -0.108 0.102 + * + 21 -0.008 0.101 + * + 22 0.085 0.100 + . * + 23 0.082 0.099 + . * + 24 -0.080 0.097 + * : + -1 -.75 -.50 -.25 0 .25 .50 .75 +1 * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) •RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 33 EXPECTED NUMBER OF RUNS = 33.00 STANDARD-DEVIATION OF RUNS = 3.97 (OBS.-EXP.)/(STD.DEV.) = 0.0 + - + + -M 1— + + + + - + + + + + --M— + - + + + H 1 hH A — + + H— + + - + + = VALUE > MEAN - = VALUE < = MEAN MEAN = 12.24 166 *NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS -1 -2 + 1 1 1 1 + 2 + 3 + 4 + 2 2 5 5 1 2 3 5 4 1 4 2 2 1 2 2 2 + 2 1 + + 1 + + 1 1 -3 + - + -+ -3 -1 MEAN = 1.2241E+01 STD.DEV = 2.4528E+02 SKEWNESS = 4.7829E-01 KURTOSIS = 1.3179E+00 167 *SCATTER PLOT OF 64 STANDARDIZED VALUES OF RESIDUALS VS. FITTED 1 1 -2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -3 -3 -2 -1 VERT. VAR. HORIZ. VAR. MEAN STD.DEV. 1.2241E+C1 2.4528E+02 1.9795E+03 4.8231E+02 168 *MEAN AND STANDARD DEVIATION BASED ON 64 ACTIVE ROWS VARIABLE MEAN STD. DEV. FAMALO 1991.72 500.354 RESIDUALS 12.2407 245.283 169 APPENDIX J - DIAGNOSTIC CHECKS FOR FAMANT TIME-SERIES MODEL *AUTOCORRELATION FUNCTION OF RESIDUALS S.E. AUTO- RANDOM ORDER CORR. MODEL -1 -.75 -.50 -.25 0 .25 .50 .75 + 1 0.023 0.122 + * + 2 -0.093 0.121 + * + 3 -0.136 0.120 + * + 4 0.136 0.119 + * + 5 0.164 0.118 + * + 6 -0.171 0.117 + * + 7 -0.122 0.116 + * + 8 -0.057 0.115 + * + 9 0.062 0.114 + * + 10 -0.123 0.113 a. * + 11 -0.052 0.112 + * + 12 -0.076 0.111 + * + 13 0.078 0.110 + * + 14 -0.048 0.109 + * + 15 0.0 0.108 + * + 16 -0.098 0.107 + * + 17 -0.087 0.105 + * + 18 -0.022 0.104 + * + 19 -0.086 0.103 + * . + 20 0.014 0.102 + * + 21 -0.007 0.101 + * + 22 -0.041 0.100 + * + 23 -0.065 0.099 + * + 24 0.095 0.097 + * + • • • • • • • • -1 -.75 -.50 -.25 0 .25 .50 .75 + * : AUTOCORRELATIONS + : 2 STANDARD ERROR LIMITS (APPROX.) *RUNS-COUNT OF RESIDUALS OBSERVED NUMBER OF RUNS = 33 EXPECTED NUMBER OF RUNS = 32.97 STANDARD-DEVIATION OF RUNS = 3.96 (OBS.-EXP.)/(STD.DEV.) = 0.01 -++ ++-+++-+-+-+—+-+++—+++++-+ ++—++-++++-+++-+—+ + = VALUE > MEAN - = VALUE < = MEAN MEAN = 10.22 170 •NORMAL CUMULATIVE PROBABILITY PLOT OF RESIDUALS -1 -2 + + 1 + + 1 + 1 1 1 + 1 2 + 2 1 4 + 4 4 1 4 1 5 1 5 3 2 2 2 1 3 3 1 1 1 1 2 + 1 1 + + + + + -+ -3 -2 -1 MEAN = 1.0219E+01 STD.DEV = 3.7073E+02 SKEWNESS = -3.9841E-02 KURTOSIS = 3.6978E-01 171 •SCATTER PLOT OF 64 STANDARDIZED VALUES OF RESIDUALS VS. FITTED -1 1 12 2 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 -3 -2 VERT. VAR. HORIZ. VAR. MEAN STD.DEV. 1.0219E+01 3.7073E+02 8.3295E+02 6.0352E+02 172 *MEAN AND STANDARD DEVIATIONS BASED ON 64 ACTIVE ROWS VARIABLE MEAN STD. DEV. FAMANT 843.172 610.904 RESIDUALS 10.2190 370.733 

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