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A method by which to forecast house prices at the community level : a case study White, Douglas Arnet 1983

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A METHOD BY WHICH TO FORECAST HOUSE PRICES AT THE COMMUNITY LEVEL: A CASE STUDY By DOUGLAS ARNET WHITE B.A., The University of B r i t i s h Columbia B.Comm., The University of Alberta A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES in The School of Community and Regional Planning i. We accept t h i s t h e s i s as conforming to kthe raqui^red standard THE UNIVERSITY OF BRITISH COLUMBIA November 1983 © Douglas Arnet White, 1983 > In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f CorriKiunity and Regional Planning The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date December 2, 1983 - i i -ABSTRACT The premise on which t h i s thesis i s developed i s that i t would be desirable for planners in c i t i e s such as Vancouver to be able to forecast house prices at the community l e v e l . Given advance warning of house price changes, i t may be possible to devise p o l i c i e s which would influence trends and be in the best in t e r e s t s of the community and the c i t y at large. The f e a s i b i l i t y of making such estimates i s the s p e c i f i c focus of t h i s research. The methodology employed involved the sel e c t i o n of nineteen standard economic indicators as provided on a regular basis by S t a t i s t i c s Canada. These indicators were employed as independent variables i n numerous multiple regressions wherein the dependent variables used represented the averages of annual assessed values f o r a sample of single family dwellings within each of the communities of Shaughnessy, Oakridge and East Hastings Sunrise. Observations for these variables were recorded over the period 1962-1980. The hypotheses tested f o r each of the three communities asserted that a l l or a subset of the nineteen independent variables would prove to be s i g n i f i c a n t l y related to house prices and would y i e l d usefully accurate forecasts of such. U t i l i z i n g same year data for the independent and the - i i i -dependent variables highly s i g n i f i c a n t r elationships were apparent and the hypotheses were supported. The hypotheses were also supported when the independent variables were lagged one year to simulate a forecasting s i t u a t i o n . The strengths of t h i s methodology include the ease with which the values of the independent variables may be obtained on a r e l a t i v e l y current basis and the speed and r e l a t i v e s i m p l i c i t y of computer processing the data. On the other hand, the accuracy of the forecasts during periods of unusual economic change i s open to question and c r i t i c i s m . It i s apparent that for a model of t h i s kind to perform e f f e c t i v e l y i t i s important that the underlying relationships between the forecasting variables and house prices be monitored perhaps on a monthly or quarterly basis. - i v _ TABLE OF CONTENTS CHAPTER 1. INTRODUCTION 1 Forcasting as an endeavour: Its Policy Inplications 1 The Problem 4 The Approach and the Objective 6 Summary' of Inputs 7 Format of Thesis 9 CHAPTER 2. THE_STUDY_AREAS 10 The Comparative Community P r o f i l e s 12 Commentary on Communities 14 CHAPTER 3. METHODOLOGY 1 18 Relevant Attributes of Multiple Linear Regression Analyses 19 The Selection of Economic Indicators as the Independent Variables 21 Expected Correlation Results Inclusive of Variable Name and Code 23 Rationale Behind Expected Correlation Results 24 Underlying Assumptions 34 The Selection of the Sample and the Recording of Valuation Rates 37 Use of Assessment Data to Indicate House Market Values 38 (1) Lagged Related Adjustments 39 (2) Non-Lagged Related Adjustments and Considerations 40 CHAPTER 4. THE_RESULTS 41 Graphs of Unadjusted Relationships 42 Commentary on Graphed Relationships 62 Raw Data Regrssion Runs 65 S t a t i s t i c a l Summaries of Raw Data Regression Runs .. 66 Comment on Signs of S t a t i s t i c s 70 Comment on M u l t i c o l l i n e a r i t y 71 In f l a t i o n Adjusted Regression Runs 73 Summary Commentary 75 House Prices as Forecast from the Generated Equations 1962-1980 78 Commentary on Predictive Results Obtained 1962-1980 82 Forcasting C a p a b i l i t i e s of Generated Regressions Equations 1981-1982 83 The Exceptional Nature of Years 1981 and 1982 83 Comparative Results Generated 1981-1982 85 Commentary of Comparative Results 1981-1982 86 - v -CHAPTER 5. CONCLUSION 89 General 89 Strengths and Weaknesses of the Methodology 93 Directions f o r Further Research 95 BIBLIOGRAPHY 93 APPENDICES 102 Appendix A Description and Defi n i t i o n s of the Economic Indicators 102 Appendix B Average Weekly Wages and Salaries in Selected Industries of B r i t i s h Columbia , 108 Appendix CI Raw Data Correlation Matrix 109 Appendix C2 Lagged Regression Correlation Matrix Appendix D Terminology and S t a t i s t i c a l Concepts 111 113 - v i -LIST_QF_FIGURES F i g u r e 1 - The Geographic L o c a t i o n s of Study Areas .... 11 - v i i -LIST OF TABLES Table 1 - Comparative Community P r o f i l e s 12 Table 2 '- Expected Correlation Results 24 Table 3 - The Vancouver Metropolitan Regional Experienced Labor Force as a Percent of the Aggregate Experienced Labour Force 37 Table 4 - Raw Data Regression Runs 66 Table 5 - I n f l a t i o n Adjusted Regression Runs 73 Table 6 - Shaughnessy Prices 79 Table 7 - Oakridge Prices 80 Table 8 - East Hastings Sunrise - Prices 81 Table 9 - Comparative Results Table 86 -1-CHAPTER_I_z_INTRODyCTION A> E2^ecasting_as_an_Endeavouri_Its_Pglicy_InjBlications Before delving into the s p e c i f i c s of t h i s thesis i t i s relevant to formulate a statement as to how forecasting in general r e l a t e s to planning and government policy making. Without such a statement the f u l l ramifications of the forecasting act and the focus of t h i s study might not be understood. To commence t h i s consideration i t i s important to r e a l i z e that a l l the technological s o p h i s t i c a t i o n which we as a society possess has not produced an enviable record of forecasting. However the pursuit of forecasting i n most f i e l d s continues to be a major endeavour of the technician and policy maker a l i k e . The obvious reason f o r t h i s apparent commitment to producing accurate forecasts i s resultant from the potential benefits to be obtained by being able to address future problems and future opportunities in advance of t h e i r occurence. From a l o g i s t i c a l perspective i t i s noteworthy that of a l l the information used by policy makers forecasts are the least rooted i n discoverable f a c t s . The questions which thus behoves the policy maker i s whether or not to use forecasts and i f so how to use them in l i g h t of t h e i r problematical - 2 -nature. These questions are normally addressed in the context as to how useful a p a r t i c u l a r forecast might be i n helping the policy maker a r r i v e at decisions that maximize his goals and support h i s decisions once made. Once a decision i s made or a policy i s formulated he must consider how authoritative, attention getting and credible the forecast remains i n the service of his policy positions. Hence while forecasting can serve as both i n t e l l i g e n c e and promotion f o r the government policy maker the decision to u t i l i z e forecasts has many parts and requires a comprehensive appraisal. In some respects the appraisal of forecasts puts a greater burden on the policy maker than the o r i g i n a l task of forecasting puts on the forecaster. For example the evaluation of the methodology of various forecasts may in i t s e l f require a technical s o p h i s t i c a t i o n at least as great and possibly greater than that of the s p e c i a l i s t in forecasting. Yet the policy maker ra r e l y has the technical or the o r e t i c a l expertise necessary to e f f e c t i v e l y s c r u t i n i z e the phenomena being projected. Indeed even the choice and analysis of appraisal standards i s a d i f f i c u l t one because there are often multiple and sometimes contradicting goals of forecast formulation and use. The f u l l range of goals includes enhancing the - 3 -r e p u t a t i o n of the f o r e c a s t e r or f o r e c a s t u s e r , s e n s i t i z i n g p o l i c y makers t o f u t u r e o p p o r t u n i t i e s or dangers and improving the q u a l i t y of d e c i s i o n however q u a l i t y i s d e f i n e d . I t i s up t o the p o l i c y maker t o understand the g o a l s and o b j e c t i v e s behind the f o r e c a s t f o r m u l a t i o n and to a s s e s s i t s c o m p a t i b i l i t y with those of h i s own. More o f t e n than not a gi v e n f o r e c a s t i s c o n s i s t e n t o n l y with a l i m i t e d p o r t i o n of the governments a v a i l a b l e p o l i c y o p t i o n s . On these grounds p o l i c y makers f r e q u e n t l y p r e f e r t o i g n o r e the f o r e c a s t s t h a t they r e g a r d as a c c u r a t e but t h a t promote p r i o r i t i e s o t h e r than t h e i r own. .Further they may d i s r e g a r d f o r e c a s t s t h a t emphasize more d i s t a n t problems when the p o l i t i c a l s i g n i f i c a n c e of c u r r e n t concerns i s more c o m p e l l i n g . Thus the u l t i m a t e a c c e p t a b i l i t y of a f o r e c a s t depends not o n l y on i t s p e r c e i v e d a c c u r a c y and p l a u s i b i l i t y , but a l s o on the a c c e p t a b i l i t y o f the p r i o r i t i e s i t appears t o promote. I t i s with an awareness and a p p r e c i a t i o n of th e s e c o n s i d e r a t i o n s t h a t t h i s t h e a i s pursues the i s s u e of house p r i c e f o r e c a s t i n g . B) The_Problera To date, there has been considerable t h e o r e t i c a l documentation as to which factors most often d i r e c t l y cause house prices to fluctu a t e . Research by Weimer 1966, Brown 1968, Horwood 1975 and many others commonly i s o l a t e the following f i v e major causative f a c t o r s : (1) changes i n the amount of migration into or out of a community; (2) changes in the l e v e l of aggregate income; (3) changes i n the c r e d i t terms and inter e s t rates available; (4) changes in various demographic c h a r a c t e r i s t i c s of communities, such as the age composition; and (5) changes in the supply of single family dwelling units. While t h i s thesis acknowledges these factors as being i n f l u e n t i a l at the aggregate c i t y l e v e l , from a planning perspective i t would be b e n e f i c i a l to be able to forecast the cumulative e f f e c t s of these factors on house prices at the l o c a l neighbourhood or community l e v e l . By so doing the planner would be able to make more informed decisions as to probable future scenarios of "neighbourhood development" and would as a r e s u l t be able to formulate more ef f e c t i v e p olicy change to accommodate the growth of the c i t y at large. For example i f i t was forcast that housing prices in a p a r t i c u l a r community would undergo an inordinate increase in the near future, the c i t y may wish to mitigate these - 5 -e f f e c t s by upzoning areas within that community in order to allow f o r the construction of more dwelling units. On the other hand the c i t y might attempt to r e v i t a l i z e or upzone a s i m i l a r community in another part of the c i t y i n hopes of dispersing the anticipated increase i n demand. The advantage to be gained could ultimately be a geographically balanced increase of house prices throughout the c i t y thus allowing for a pattern of r e s i d e n t i a l development and s o c i a l mix which would conceivably be more in keeping with the c i t y ' s broader goals and objectives. Without attempting to conceptualize innumerable d i f f e r e n t s i t u a t i o n s under which accurate forcasting of house prices at the community l e v e l could improve c i t y management, there i s no doubt that at the very least, advantages would be commonly apparent through the enhancement of the knowledge base from which the municipal planner makes decisions. It i s further apparent that while the planner t y p i c a l l y has limited a b i l i t y to a f f e c t any d i r e c t changes i n house prices he does have s u f f i c i e n t p o l i cy tools at his disposal to mitigate or re-inforce the e f f e c t s of these fluctuations i f given advance warning. While the amount of advance warning necessary to f u l l y implement various actions i s indeterminant i t must be r e a l i z e d that merely i n i t i a t i n g such action i n advance of the -6-period of need i s i n i t s e l f a s i g n i f i c a n t achievement. Indeed the accurate forcasting of house prices at the community l e v e l would be b e n e f i c i a l , yet in p r a c t i c a l terms t h i s practise i s s t i l l very much i n i t s infancy. Documented work by the l i k e s of Renshaw 1958, Pendleton 1965, and others are primarly concerned with the forcasting of house prices at the aggregate c i t y l e v e l rather than at the neighberhood or community l e v e l . As a r e s u l t of t h i s lack of established technique there i s considerable scope avail a b l e in se l e c t i n g the most appropiate forcasting methodology. C> The_Ap_B£2§Sh_§Q^_the_0bjectiye In accord with the previously stated problem and upon considerations of numerous technical d e t a i l s as outlined i n Chapter I I I , Multiple Linear Regression Analysis i s selected as the vehicle by which to test the relationships between house prices i n three Vancouver communities and nineteen pre-selected standard economic indicators as defined by S t a t i s t i c Canada. The basic objective of t h i s thesis simply stated i s "To s t a t i s t i c a l l y determine which, i f any, of the selected economic indicators can be used to accurately forcast house prices i n each of the communities of Shaughnessy, Oakridge and East Hastings Sunrise. The basic hypotheses tested assert that a l l or a subset of the subject nineteen standard economic indicators are s i g n i f i c a n t l y related to house prices in the subject communities and can be used as accurate forecasters of such. D) Summary_of_Inp_uts_ In keeping with the stated "Approach" and "Objective of t h i s study the s p e c i f i c s of the inputs are as outlined below. The study period encompasses the years 1962 to 1980 in c l u s i v e , and the economic_indicator§ CI] investigated are a follows. <1> Average Weekly Earnings - Construction Industry in B. (2) Average Weekly Earnings - Forestry Industry in B.C. (3) Average Weekly Earnings - Manufacturing Industry i n B (4) Average Weekly Earnings - Mining Industry in B.C. (5) Average Weekly Earnings - Services Industry in B.C. <6> Average Weekly Earnings - Trades Industry in B.C. (7) R e t a i l Sales i n B.C. <8> Vancouver Consumer Price Index - Clothing (9) Vancouver Consumer Price Index - Food (10) U.S. Automobiles Entering B.C. (11) Unemployment Rate i n B.C. (12) Personal Income in B.C. (13) Population of B.C. (14) Value of Exports Through B.C. Ports (15) Gross P r o v i n c i a l Product of B.C. (16) Conventional Mortgage Rates (17) Cheques Cashed Against Individual Accounts in B.C. (18) B.C. Building Materials Price Index - Residential (19) B.C. Building Materials Price Index - Non Residential [1]. For the precise meaning and method of c a l c u l a t i o n of each Economic Indicator r e f e r to Appendix A Pg 102. \ r -8-These p a r t i c u l a r indicators were selected for te s t i n g generally on the basis of t h e i r expected influence on house prices at the community le v e l and t h e i r a v a l a b i l i t y of continous information over the study period. The three communities were selected as being representative of three comparatively d i f f erent_cgmmuniti.es C2] within Vancouver. It i s one of the expectations of t h i s study that the economic indicators s t a t i s t i c a l l y determined to be accurate forecasters of house prices w i l l vary in accordance with the d i f f e r e n t c h a r a c t e r i s t i c s of the in d i v i d u a l neighborhoods. Hence by focusing t h i s study on communities with substantial compositional differences t h i s supposition w i l l be addressed. The time period iso l a t e d was selected on the basis of i t s incorporation of at least two North American economic cycles of average length. (As defined by Samuelson and Scott, 1980, the average North American economic cycle approximated nine years over the 1962-1980 study period.) The advantage of spanning at least two economic cycles of average length i s such that the r e s u l t s obtained w i l l be a composite achieved over two somewhat s i m i l a r economic periods thus adding to the i r probable degree of accuracy. [2]. For the purposes of t h i s thesis communities are considered as d i f f e r e n t based on (1) the average income of i t s residents <2> the average education of i t s residents <3> other demographic c h a r a c t e r i s t i c s of i t s residents and (4) the r e s i d e n t i a l amenities of the area. (Refer to Chapter II Pg 10 for a summary of the d i f f e r e n t areas.) -9-E) Format_of_ThGsis Following t h i s introductory chapter. Chapter II describes the major c h a r a c t e r i s t i c s of the communities studied. Chapter III j u s t i f i e s the use of regression analysis, defines and j u s t i f i e s the economic indicators u t i l i z e d for test i n g , and expounds on the data base employed. Chapter IV presents the r e s u l t s obtained both graphical and s t a t i s t i c a l . Chapter V presents the conclusions reached, the l i m i t a t i o n s of the study and suggests directions f o r futher research. i -10-QHAPTER_II_-_THE_STUDY_AR^AS The descriptions which follow are composed of general information of the subject communities. It i s the purpose of t h i s chapter to make clear the relevant differences which existed between these three communities and as a r e s u l t add insight into the degree of influence which might be expected regarding the subject economic indicators and house price fluctuations in each community. Since a complete comparative data base f o r the relevant information selected i s only available i n Census years a l l the s t a t i s t i c s presented herein r e f l e c t 1971 Census data. -11-IHE___gGR9PHIC_L0CeiI0NS_g__Siy F i g ure i .JL<OHCJ<\X, • J t: « • aniiiiiiiiiwiiiirmfrnnft|_t 1 i3 111E11J (111J1111111! 1M111111111111, r '| 111J111 57 AVENUE £ g < / J V f : f r " r •* ~ v i e r o . - — K t u ^ u v f t v I n , i i . . f ~ . . . . (Map adapted from Vancouver .Local Ar.eas, 1975) -12-Co_ga_a_l_e_Co_muni___P_oflies Table 1 (1971 Census Data obtained frora Vancouver Local Areas, 1975.) Shaughnessy Oakridge East Hastings Sunrise 1 1 Population 1 10,370 10r670 28,530 I 1 Area (sq ailes) 1 1.80 1.54 3.80 1 1 Density (persons per sq ac) 1 2157.5 2811.8 3338.1 1 1 Dwellings (total) 1 2910 3530 8450 1 1 single detached 1 2100 2375 7255 1 i Apt 1 740 815 650 1 1 Other 1 70 340 560 1 1 Tenure 1 1 Owned 1 2,085 2,480 6,525 1 1 Rented 1 825 1.050 1.940 1 1 Age (yrs) 1 1 0-14* 1 21.6 17.5 25.6 1 1 15-34* 1 28.5 25.2 27.8 1 1 35-65* 1 36.0 43.7 34.9 1 1 65+12 1 13.9 13.5 11.7 1 1 Marital Status i 1 Single 1 5,025 4,205 12,380 1 1 Harried 1 4,250 5,560 13,175 1 1 Other ^ 1 1.095 905 2.975 1 1Major Groups/Ethnic Origins 1 1 British Isles* 1 6B.7 52.9 40.8 1 1 Chinese* 1 2.7 9.8 9.0 1 1 East European* 1 4.1 4.7 10.6 1 lEducation (yrs) 1 1 None * 1 .7 .7 3.0' 1 1 3 or More Years University *l 26.6 19.4 3.8 1 (Experienced Labour Force 1 1 By Occupation 1 1 Managerial * 1 15.1 11.3 1 1.7 1 1 Proffesional < 1 11.2 9.1 2.7 1 1 Clerical * 1 17.9 19.7 1 18.3 1 1 Sales * i 14.3 21.6 8.9 ! 1 Service * 1 13.3 10.1 18.1 1 -13-Continuatlon of Table 1 1 Shaughnessy Oakridge East Hastings Sunrise 1 1 i 1 IPriaary % 1 1.1 .7 , 3.0 1 (Manufacturing % t 4.7 5.5 18.9 1 IConstruction* 1 2.5 2.9 10.6 f 1Transportation % 1 4.B 6.2 13.5 i 1Experienced Labour Force 1 1 By Industry 1 1 Resource % 1 2.8 2.6 2.0 1 1 Manufacturing t 1 12.4 11.2 21.9 1 1 Construction i 1 2.8 3.4 9.9 1 1 Transportation 1 1 and U t i l i t i e s 1 1 7.6 9.6 14.6 1 1 Trade * 1 15.1 26.1 1B.5 1 1 Finance Insurance i 1 and Real Estate * 1 11.6 10.1 3.7 1 1 Community Business 1 1 and Personal Service f 1 43.6 33.3 25.1 I 1 Government i 1 3.7 3.7 ,4.3 1 1 Income $/yr 1 1 $0 1 .9 .4 .3 1 1 Under 4,080$ f 12.2 8.1 21.2 1 1 4,090-6,980$ 1 11.0 9.6 17.5 1 1 7,080-9,999$ i 7.6 12.5 25.1 1 1 10,880-12,999$ 1 9.6 13.6 17.2 1 1 12,000-15,999$ 1 8.9 12.9 9.4 1 1 16,080 or sore $ 1 49.8 1 42.9 9.3 1 -14-B) Com^ent^r^_on_C^m^unit^es Shaughnessy (Unless otherwise s p e c i f i e d the following information" was extracted from "Vancouver City Planning Dept., 1981) Shaughnessy was o r i g i n a l l y developed as an exclusive • r e s i d e n t i a l neighborhood by the Canadian P a c i f i c Railway i n 1908. Through the study period of 1962-1980 Shaughnessy maintained i t s exclusive q u a l i t i e s to the extent that the neigborhood remained dominated by large l o t s , large homes, and well manicured f o l i a g e lined s t r e e t s . Of the three communities studied Shaughnessy consistently maintained the lowest density of people per acre. It i s also noteworthy that Shaughnessy residents were s i g n i f i c a n t l y better educated with a higher proportion of i t s residents engaged i n the managerial and professional occupations and with a higher percentage of i t s residents were making i n excess of $16,000 a year. It i s inter e s t i n g to note that Shaughnessy residents have, through t h i s study period, continually expressed serious concern about the e f f e c t of fluctuations in the economy aff e c t i n g t h e i r neighborhood. These concerns were r e a l i z e d in the late 1970's when severe land development pressures caused many f i n e houses i n the neighborhood to be demolished and many of the larger l o t s to be subdivided. -15-Oakridge (Unless otherwise s p e c i f i e d the following information was extracted from Mak, Pulle, 1978.) Oakridge i s a community characterized by i t s r e l a t i v e l y young housing stock build a f t e r 1945. It i s a community which had remained largely undeveloped u n t i l a f t e r the Second World War. Between 1956 and 1976 Oakridge experienced a more rapid increase in i t s o v e r a l l population than did any other community in Vancouver. From 1961 to 1976 the t o t a l number of dwelling units i n the community increased by an increment of almost 44%, yet the number of singl e detached houses remained approximately the same. Of p a r t i c u l a r i n t e r e s t , regarding comparison with the other subject communities,, i s the high percentage of Sales Force Personal resident i n Oakridge i e : approximately 21.6% and the low percentage of residents engaged in the manufacturing sector i . e . , 11.2% (1971 Census). Over the period 1962-1980 Oakridge was generally recognized as being a middle c l a s s neighborhood. -16-East_Haating_Sunri.se (Unless'otherwise s p e c i f i e d the following information was extracted from Mak, 1979.) The community of East Hastings-Sunrise i s located at the s i t e of the o r i g i n a l Hastings townsite s e t t l e d i n 1863. This town was the f i r s t permanent settlement on Burrard i n l e t . The townsite was amalgamated with Vancouver in 1911. Rapid subdivisions followed and the community developed into a major r e s i d e n t i a l community bringing with i t a strong mix of d i f f e r e n t ethnic groups. Post-War housing f o r veterans became the stimulus for the housing boom in the l a t e 1940's much of which remains in the neighborhood today. Reflecting i t s working class nature, occupations in the community tended to be i n the c l e r i c a l and service categories i e : 18.3% and 18.1% respectively (1971 Census Data) with a strong d i s p o s i t i o n towards the manufacturing and construction sectors. Its residents i n general were considerably less educated and earned less income than residents i n either of the other 2 subject communities. Over the period 1962-1980 the composition of the housing stock remained r e l a t i v e l y stable with sing l e detached units accounting f o r approximately 72% of the dwelling types. Apartment units approximated another 16% of the t o t a l housing stock (1971 Census). -17-In s p i t e of s i g n i f i c a n t land cost escalations over the past decade i . e , 1969-1979, land costs in East Hastings Sunrise have remained comparatively among the lowest i n Vancouver. r -18-CH_PTER_III METHODOLOGY In addressing the question of the appropiate forcasting methodology to use a number of c r i t i c a l considerations had to be made. F i r s t and formost was the decision of choosing a q u a l i t a t i v e versus a quantitative technique. While the o b j e c t i v i t y of the quantitative technique often makes i t the more desirable of the two options there are times when a lack of h i s t o r i c a l data necessitates that q u a l i t a t i v e analyses be used. For example there are times when a "Subjective Curve F i t t i n g Technique" C3] or a "Delphi Technique" 141 are more appropriately used than i s a "Linear or Multiple Regression Technique". i However, since in the case of t h i s study h i s t o r i c a l data was rea d i l y available f o r both the house prices at the community l e v e l and the economic indicators some form of quantitative methodology was consider to be the most appropiate. [33. Subjective Curve F i t t i n g Technique: Involves Subjectively determining the curve that the values of the forcasted variable w i l l i nscribe over time. (Bowerman, 0 Connel, 1979). C4]. Delphi Technique: Involves u t i l i z i n g a panel of "experts" to produce predictions. This method assumes that the combined knowledge of panel members w i l l produce predictions at least as good as those that would be produce by any one member. (Bowerman, 0 Connel, 1979). -19-Within t h i s parameter there were b a s i c a l l y two forcaating methods from which to choose. 1) A Time Series Approach or 2) A Casual or Deterministic Approach. (Bowerman, 0 Connel, 1979). The Time Series Approach r e l i e s on establishing a pattern of data to be forcast based on h i s t o r i c a l data. This pattern i s then extrapolated into the future f o r forcaating purposes. On the other hand the Casual or Deterministic Approach involves the i d e n t i f i c a t i o n of variables which are thought to be related to the variable to be forcast and then the establishment of a s t a t i s t i c a l r e l a t i o n s h i p between these variables and the variables to be f o r c a s t . Because i t i s the basic objective of t h i s study to determine which i f any of the subject nineteen Standard Economic Indicators can be used to accurately forcast house prices at the community l e v e l the "Causal or Deterministic Approach" was employed. A.) Releyant_Attribu_es_gf_Mult_Ele_Linear_Regression _nalysis_ In keeping with the general parameters of the methodology as previously outlined Multiple Linear Regression Analysis was selected as being the appropriate s t a t i s t i c a l technique to employ. Its a t t r i b u t e s include: - 2 0 -(1) I t s l o n g s t a n d i n g a c c e p t a n c e a s a v a l i d method by w h i c h t o e x p l a i n and p r e d i c t r e s i d e n t i a l h o u s i n g p r i c e s i n an u r b a n s e t t i n g ( r e : Renshaw, 1 9 5 8 , and P e n d l e t o n , 1965 t o name b u t two o f t h e e a r l i e r u s e r s . ) (2) I t s t e c h n i c a l a b i l i t y f o r t e s t i n g h y p o t h e s e s and f o r p r e d i c t i n g v a l u e s o f t h e d e p e n d a n t v a r i a b l e g i v e n known v a l u e s f o r a s e t o f i n d e p e n d e n t v a r i a b l e s and e s t i m a t e d c o e f f i c i a n t s . ( H e b d e n , 1 9 8 1 , 1 0 2 - 1 0 6 ) (3) I t s t e c h n i c a l a b i l i t y t o p r o v i d e a p r o c e d u r e f o r d e t e r m i n i n g a v i s u a l " r § g r § § § i o n _ l i n e " [5] t h r o u g h c o m p u t e r m a n i p u l a t i o n . " I t i s e a s i e r f o r t h e human e y e and b r a i n t o e x t r a c t a p i e c e o f i n f o r m a t i o n f r o m a g r a p h t h a n a t a b l e . " ( L e v e n B a c h , C l e a r y 1 9 8 1 , 52) (4) I t s t e c h n i c a l a p p l i c a b i l i t y f o r u s e i n s t a t i s t i c a l l y a n a l y z i n g d a t a w h i c h i s r e f l e c t i v e o f l i n e a r r e l a t i o n s h i p s b e t w e e n v a r i a b l e s . ( H e b d e n , 1 9 8 1 , 100) - [ 53 . A r e g r e s s i o n l i n e i s t h e b e s t s t r a i g h t l i n e a p p r o x i m a t i o n o f t h e r e l a t i o n s h i p b e t w e e n t h e d e p e n d a n t and i n d e p e n d e n t v a r i a b l e s . ( S j o q u i s t e t a l 1 9 7 4 , 8) > -21-B) Xhe_Selec_ion_o___conomic_Indic Variables,. The o r i g i n of "economic ind i c a t o r s " dates back to the business recession of 1937-38 (Levenbach, Cleary, 1981). At that time an e f f o r t was i n i t i a t e d by the National Bureau of Economic Research i n the U.S. to devise a system that would signal the end of a recession. Since then considerable research and analysis has gone into determining the meanings and warning signals which an accurate tracking of these variables can relay. Today these "economic in d i c a t o r s " have been c l a s s i f i e d into 3 groups; 1) leading indicators, i . e . : those that provide advance warning of probable changes in economic a c t i v i t y , 2) coincident indicators, i . e . : those that r e f l e c t the current performance of the economy and 3) lagging indicators, i . e . : those that confirm the changes previously signaled. (Sobek, 1973). While these c l a s s i f i c a t i o n s pertain to relationships between vaious economic indicators and fluctuations in the economy i t i s l o g i c a l to expect that a r e l a t i o n s h i p also exists between house price f l u c t u a t i o n in a given community and f l u c t u a t i o n s in the economy. However because of obvious time lags apparent between changes i n economic indic a t o r s . -22-changes in the economy, and changes i n house prices i t i s expected that those economic indicators considered as being leading, coincident or lagging with regards to fluctuations in the economy, would not necessarily maintain these same proximate rel a t i o n s h i p s with house price fluctuations at the community l e v e l . For example as noted e a r l i e r these i s extensive evidence to suggest that house prices tend to peak well a f t e r the economy has reached i t s peak. (Samuelsen and Scott, 1980) In e f f e c t many of those leading economic indicators which had signaled a peak i n the o v e r a l l economy of an area would have declined s u b s t a n t i a l l y before the house price peak was achieved. Hence there i s considerable question as to the relevance of these categories with regards to house price forecasting. It i s with t h i s consideration in mind that the variables chosen for t e s t i n g in t h i s study include indicators from a l l of the economic categories outlined above. More s p e c i f i c a l l y the subject Economic Indicators were selected primarily for the following s p e c i f i c reasons. (1) as an aggregate group they represent a broad p r o f i l e of the B.C. and Vancouver economies and as a r e s u l t could be expected to influence house prices in Vancouver (2) as an aggregate group they r e f l e c t those economic factors commonly held to d i r e c t l y influence fluctuations i n house demand and house prices at the -23-i community le v e l (Refer to Chaper I, Pg 4) and (3) that continuous information was r e a d i l y available f o r these indicators over the study period 1962-1980. (Other apparently suitable indicators were rejected due to lack of available information over the same time period, e.g.. Gross Domestic Product of B.C., a measure of the t o t a l product output generated within the geographic boundaries of the province, and E l e c t r i c Energy Generation in B.C., a proxy measure f o r i n d u s t r i a l a c t i v i t y i n the province.) C) Exgected_Cgrrelatign_Results_I Cgde_ Table I below summarizes the author's estimates as to the expected degree_gf_cgrrelatign C6] between these variables and house prices in each of the subject communities. This table i s followed by a written explanation revealing the rationale on which these expected c o r r e l a t i o n r e s u l t s were derived. [6]. High and low Correlation values are indicated based on a a r b i t r a r y judgement by the author as to whether the Correlation C o e f f i c i e n t i e : the degree of association between two variables, i s greater than .66 or 66%. I -24-Expected C o r r e l a t i o n R e s u l t s Table 2 Variable Name and Code Shaughnessy(DI) Oakridge(D2) East Hastings Sunrise(D3) Average Weekly Earnings-Construction Industry in B.C. (Fl) +Low +Low +High Average Weekly Earnings-Forestry Industry in B.C. (F2) +High +High +High Average Weekly Earnings-Manufacturing Industry in B.C. (F3) +Low +Low +High Average Weekly Earnings-Mining Industry in B.C. (F4) +High +High +High Average Weekly Earnings-Services Industry in B.C. (F5) •High +High +High Average Weekly Earnings-Trades Industry in B.C. (F6) +Low +Low +High Retail Sales in B.C. (F7) +Low +High +High Vancouver CPI-Clothing (FB) +Low +Low +High Vancouver CPI-Food (F9) •H.OH •Low +High U.S. Autos Entering B.C. (Fie) ? ? ? Unenployioent Rate in B.C. (FID -Low -Low -High Personal Incoaie in B.C. (F12) +High +High +High Population of B.C. (F13) •High +High +High Value of Exports through B.C. Ports (F14) +Low +High +Low GPP of B.C. (F15) •High +High •High Conventional Mortgage Rates (F16) -Low -High -High Cheques Cashed Against Individual Accounts (F17) +High •High •High Building Materials Price Index-Residential (F18) +Low •High +High Building Materials Price Index-Non Residential (F19) +Low +High •High D) R a t i o n a 1 e _ B e h i n d _ E x _ e c t e d _ C g r r e l a t i o n _ _ e s u _ _ s _ P e r t i n e n t t o a l l o f the expected c o r r e l a t i o n s noted i s the assumpt ion t h a t y e a r l y house demand and house p r i c e s i n any g i v e n community a r e most l i k e l y t o be d i r e c t l y a f f e c t e d by those i n d i v i d u a l s w i t h i n t h a t community moving t o houses from o t h e r accomodat ion i n the same community or those i n d i v i d u a l s wi th s i m i l a r s o c i a l , o c c u p a t i o n a l , income and e t h n i c background from o u t s i d e o f the community, a t t e m p t i n g t o move i n . I t f u r t h e r i s expected t h a t absentee ownership i s minimal -25-(absentee ownership r e f l e c t s a s i t u a t i o n where the owner of a single family dwelling does not l i v e i n the community i n which he owns a house. This expectations i s consistent with the findings that i n each of the three communities i d e n t i f i e d from 70-78% of the dwellings were owner-occupied. (Refer to Comparative Community P r o f i l e s pg. 12). It i s noteworthy that a l l the s t a t i s t i c s quoted in th i s section are, unless otherwise s p e c i f i e d , based on the 1971 comparative s t a t i s t i c s as presented i n the Comparative Community P r o f i l e s . 1) Ayerage__eekly__arnings___Constr Due to the seasonal nature of the construction. Industry and due to the fac t that i t involves such a small percentage of the "ExBer_enced_Industrial_Labgur in Shaughnessy, Oakridge and East Hastings Sunrise, 2.8%, 3.4%, and 9.9% respectively a r e l a t i v e l y low co r r e l a t i o n might be expected between t h i s i n d i c t o r s and house prices within each of the subject communities. Offset t i n g t h i s speculation however i s the f a c t that ^ the Construction Sector t r a d i t i o n a l l y pays higher wage rates than do most of the other sectors of the economy. (Refer to Appendix B>. As a consequence i t could be expected that those [7]. "Experience labor force" excludes the c i v i l i a n n o n - i n s t i t u t i o n a l population 15 yrs of, age and over who at the time of the reference week were looking for work or who had never worked. This i s i n contrast to the "labor force s t a t i s t i c " which includes those employed and unemployed. ( S t a t i s t i c s Canada. 1981). -26-permanently employed t h i s sector might have more income to invest in house purchases than those employed i n other sectors. In East Hastings Sunrise i t i s anticipated that t h i s f a c t would override the low percentage of the Experienced Construction Labor Force S t a t i s t i c i n the community, to the extent whereby a high c o r r e l a t i o n would e x i s t between house prices and the subject indicator. 2) Ayerage__eekly_Earnings___Forestr__I Because of the extreme importance of the Forestry Industry as an economic base i n B.C. i t i s expected that t h i s variable would show a high c o r r e l a t i o n with house prices i n a l l the three communities tested. It i s further expected that because earnings i n the construction industry could be expected to highly correlate with earnings i n the Forestry industry, a higher degree of c o r r e l a t i o n might be apparent with house prices i n East Hastings Sunrise than in either of the other two communities. 3) Average_Weekly_Earnings_-_Manu Because of the r e l a t i v e l y high percentage of i t s residents engaged i n the manufactoring sectors i e : 21.9% i t i s expected that a high c o r r e l a t i o n would e x i s t between t h i s variable and house prices in East Hasings Sunrise. (Manufactoring ranks 2nd out of 9 Labour Force Categories in -27-the community with respect to the percentage of residents involved). 4) Ayerage_Wee_l__Earnings_2_Minin Due to the f a c t that mining maintained i t s e l f as B.C.'s second largest industry over the study period of 1962-1982 (ministry of Economic Development, 1982-83) a high c o r r e l a t i o n between t h i s indicator and house prices i n each of the subject communities i s expected. 5) Ayerage_Weekl__Earnings___Seryice_Industry_in_B_C_ A high c o r r e l a t i o n of t h i s indicator with house prices in a l l of the subject communities i s expected as t h i s sector encompassed the largest number of residents of any industry in a l l the communities being studied. The highest degree of c o r r e l a t i o n was expected in the Shaughnessy area with approximately 44% of i t s residents having been engaged i n t h i s industry. It i s further noteworthy that as the service or t e r t i a r y industry i s primarily an urban function, t h i s sector might be expected to have more of a d i r e c t impact on house prices i n Vancouver than would some of the other noted industries wherein t h e i r functions are more geographically dispersed. -28-1 6) AYerage_Weekl__Earnings___Trad Thia indicator i s expected to correlate highly with indicators #1 i e : Average Weekly Earnings - Construction Industry i n B.C. Hence a low c o r r e l a t i o n with house prices in Shaughnessy and Oakridge, and a high c o r r e l a t i o n with house prices in East Hastings Sunrise i s expected. 7) R§ta________________ The difference i n the correlations expected of t h i s indicator with house prices i n Oakridge, East Hastings Sunrise and Shaughnessy was resultant from an expectation that the more affl u e n t residents of Shaughnessy and Oakridge would spend at somewhat of a constant rate at the r e t a i l l e v e l . Their demand fo r houses however would be expected to fluctuate in a more c y c l i c a l pattern much as the economy fluctuates. In East Hastings Sunrise on the other hand i t i s the authors opinion that both house purchasing, i . e . , house demand and r e t a i l spending, would correspond c l o s e l y with the fluctuations of the economy. 8 & 9) Vancouyer_CPI_Clothing_and__ancguver Both of these indicators are expected to show a high cor r e l a t i o n with house prices i n the lower income community i e : East Hastings Sunrise, due to the f a c t that the i n f l a t i o n (which these indicators measure) has the greatest e f f e c t on -29-those indiv i d u a l s making the least amount of money. More s p e c i f i c a l l y the i n f l a t i o n factor i s more l i k e l y to place residents of the lower income community in the "no buy" s i t u a t i o n than i t i s l i k e l y to place the residents of the more afflu e n t communities in that s i t u a t i o n . 10) y_S___u_os_Entering___C_ This indicator i s a proxy measure for tourism. As tourism i s part of the service industry i t could be expected that the c o r r e l a t i o n of t h i s indicator with house prices at the community l e v e l could approximate the c o r r e l a t i o n of "Average Weekly Earnings - Service Sector" in B.C. with house prices. This being the case i t would be expected that a high c o r r e l a t i o n between U.S. Autos entering B.C. and house prices would be noted in East Hastings Sunrise wherein 18.1% of the residents were involved in the Service Industry. On the other hand there i s some question as to how e f f e c t i v e t h i s variable r e a l l y i s in terms of being a good indicator of economic change and potential house prices f l u c t a t i o n . More precisely t h i s indicator would fluctuate not only on the basis of economic inducements to v i s i t B.C. based on what i s happening to the economy in Canada, B.C. and Vancouver but also based on what i s happening to the U.S. economy. -30-There i a some further question as to whether or not t h i s variable might be inversely correlated with house prices in the subject Vancouver communities. More e x p l i c i t l y i t i s conceivable that more U.S. t o u r i s t s might be expected to venture into B.C. when the B.C. and Vancouver economies are \ depressed (and when house demand i s depressed) r e l a t i v e to the economic conditions which e x i s t in the U.S. While the uncertainties r e l a t i v e to the use of t h i s indicator are numerous i t i s believed that i t ' s consideration i s warranted based on the f a c t that i t maintained i t s e l f as the t h i r d or fourth largest industry in B.C. over the study period. (Ministry of Economic Development, 1982-83.) 11) y_e_plgyment_Rate This indicator i s expected to negatively correlate with house prices i n a l l the communities studied. For example as unemployment increases there would tend to be less \ aggregate irfcome i n a l l of the subject communities and hence less pressure on the demand for house purchases. It i s expected however that i n the lower income community of East Hastings Sunrise wherein a large number of residents have marginal jobs, i . e . , jobs which are exceptionally unstable, the highest negative correlations would be apparent. There i s some question however as to whether or not those engaged in -31-marginal employment are even in the house buying market. 12) Personal_Income_in_B J UC i As the amount of personal income i n each of the communities i n c r i t i c a l to the pressure placed on house prices t h i s indicator i s expected to correlate highly with house prices in each of the three communities. The highest c o r r e l a t i o n might be expected i n East Hastings Sunrise wherein less savings would be apparent and the fluctuations in personal income would largely determine the amount of demand placed on house prices . 13) Po_u_ation_gf_B_C_ As the population of the province fluctuates i t i s expected that so would the demand for house prices in each of the three communities. Since i t would be l o g i c a l to assume that the incomes of the vast majority of the populous migrating into and out of B.C. and Vancouver would be in the middle income brackets i t i s expected that the highest correlations would be noted between t h i s indicator and house prices in Oakridge. 14) Va_ue_g__Exggrts_through_B_C__Po_ As t h i s indicator measures the shipments of commodities through B.C. ports i r r e s p e c t i v e of the province of o r i g i n , i t i s an indicator of the economic a c t i v i t y of Western -32-Canada as a whole. It i s because of the close linkage of the Vancouver Regional economy with the economy of Western Canada (GVRD, 1976) that t h i s indicator should correlate highly with house prices i n some of Vancouver's communities. The speculation would be that t h i s variable might correlate highly with house prices in Oakridge wherein a large percentage of i t s residents are engaged i n the Trade Sector. 15) GPP_of_B_C As t h i s variable i s a good indicator of the o v e r a l l health of the p r o v i n c i a l and l o c a l Vancouver economies i t i s expected that a high c o r r e l a t i o n with house demand in each of the three subject communities would be apparent. There i s some question as to a lag e f f e c t which might be apparent between fluctuations i n GPP and house prices . More s p e c i f i c a l l y a question a r i s e s us to whether or not fluctuations i n GPP would lead actual house prices fluctuations or whether house prices would lead fluctuations i n GPP. 16) C_n_en_i__a___or_gage__at.es As t h i s i s generally agreed to be one of the major determinants of house demand i t i s expected that there would be a high negative c o r r e l a t i o n with house prices in Oakridge and East Hastings Sunrise. It i s speculated, however, that in Shaughnessy, wherein the residents are highly a f f l u e n t , mortgage rates would be of much less importance with regards to a f f e c t i n g house demand. -33-17) Chegues_Ca_hed__gains__Ind_vidua1_A A high c o r r e l a t i o n with house prices i n a l l of the three communities would be expected due to the broad a l l encompassing nature of t h i s variable. A l l of the major determinants of house, demand are included within the scope of aggregate consumer spending. 18) B_C__Building__aterials_Price_I This variable i s expected to correlate most highly with house prices i n the communities of Oakridge and East Hastings Sunrise. The rationale i s such that (1) residents of high income communities such as Shaughnessy would have more f l e x i b i l i t y with regards to making decisions as to whether or not to buy or,build regardless of the prices of building materials, i e : i n general they are not as suseptible to having t h e i r demand f o r houses altered by s l i g h t f l u ctuations in the price of materials and (2) t h i s indicator i s directed at new home constructions f o r the most part. More s p e c i f i c a l l y t h i s indicator would be expected to have p o t e n t i a l l y a greater e f f e c t in communities such as Oakridge and East Hastings Sunrise which are somewhat less developed and i n which there i s more room f o r new home construction. -34-19) B AC_Building_Materials_Price This indicator i s expected to correlate with house prices much the same as does the Building Materials Price Index Residential. This i s due to the f a c t that the construction of commercial buildings can often be translated into a greater demand for housing and hence greater pressure on house prices . More exactly, while the construction of o f f i c e premises i s undertaken to accomodate more workers into an area, new r e s i d e n t i a l house construction i s also often required in turn. In general i t could be expected that fluctuations i n both the Residential and Non Residential Building Materials Price Indexes would vary in accordance with the o v e r a l l a c t i v i t y l e v e l of the economy. <E> ynde_l_ing__ssum_tions Underlying the s e l e c t i o n of 14 of the 19 subject economic indicators i s a s i n g l e c r i t i c a l assumption which requires elaboration. It was assumed that-those economic indicators describing economic a c t i v i t y at the p r o v i n c i a l l e v e l were c l o s e l y linked with the economic conditions at a more l o c a l i z e d Vancouver l e v e l over the study period 1962-1980. Establishing the v a l i d i t y of t h i s assumption i s c r u c i a l to the c r e d i b i l i t y of t h i s study in that i f s i g n i f i c a n t linkages were not apparent, then i t would be -35-l i k e l y -that those relationships appearing to be s i g n i f i c a n t , between p a r t i c u l a r indicators and house prices in the subject communities, would be s t r i c t l y of a spurious nature. This being the case i t would be d i f f i c u l t to have confidence in the forcasting a b i l i t y of any regression equations which may be used to forcast house prices beyond the o r i g i n a l time s e r i e s . In attempting to substantiate the c r e d i b i l i t y of the "underlying assumption" two foundation considerations are noteworthy: (1) due to a paucity of available comparative economic information f o r "Vancouver Proper" versus aggregate p r o v i n c i a l data the economic linkages s i t e d herein focus on the relationships between the province and the Metro Vancouver Region. and (2) due to the lack of continuous economic data over the 1962-1980 study period these linkages were explored as at 1971, i . e . , the middle year of t h i s study. In keeping with these t a c t i c a l concerns three areas of economic linkage were examined. More e x p l i c i t l y the areas of population, income and employment were considered to be of prime importance. Investigation into the s t a t i s t i c a l information available i n these areas revealed the following: -36-(1) The Vancouver Metropolitan Region contained approximately 47% of the population of the province of B.C. ( S t a t i s t i c s Canada, 1971). (2) Approximately 58% of the personal income generated in the province was at t r i b u t a b l e to indivi d u a l s l i v i n g in the Vancouver Metropolitan Region. (Information obtained from 1971 Taxation S t a t i s t i c s as c o l l e c t e d by S t a t i s t i c s Canada, 1971). (3) The Vancouver Metropolitan Region contained approximately 57% of the provinces t o t a l "Experienced Labour Force" ( S t a t i s t i c s Canada, 1971). A breakdown of the Experienced Labour Force by Major Industry Sector reveals more detailed employment linkage information. Refer to Table 3 below. -37-Table_3 Xhe___n_ouv_r__e_ro_o_i__n_Regional E2£S§_§5_§_E§rcent_gf__he_Aggregate_Provi_ Labgur_Fgrce_ ( a l l percentages were calculated based on 1971 Information obtained from the Bureau of Economics and S t a t i s t i c s , Regional Index of B r i t i s h Columbia, 1978, 251-255.) Manufacturing 48% Construction 45% Transportation, Communications and U t i l i t i e s 55% Finance, Insurance and Real Estate 66% Community and Business Services 54% The foregoing population, income and employment s t a t i s t i c s reveal that a substantial economic linkage existed between the Vancouver Metropolitan Region and the province as a whole as at 1971. It i s thus l o g i c a l to assume that those fourteen economic indicators which t e c h n i c a l l y r e f l e c t economic a c t i v i t y at the aggregate B.C. l e v e l , also r e f l e c t economic a c t i v i t y at the more l o c a l i z e d Vancouver Metropolitan l e v e l . (F) Ihe_Selection_of_the_Sam_ Data Thirty eight houses from within each of Shaughnessy, Oakridge, and East Hastings Sunrise were randomly selected and thei r assessment values recorded for the years 1964 to 1981. The reasons f o r recording assessment data for the years -38-1964-1981 rather than for the 1962-1980 period of the study i s r e f l e c t i v e of the valuation,lag which existed between the assessment values and market value of the period. (This problem i a f u l l y discussed in section <G)>. The sample s i z e of 38 properties from each community was chosen on the basis of being as large a sample siz e as would be manageable given the time and resource constraints of the study. (G) Use_of_Assessment__ata__o_Indicate_H As previously noted lagged assessment data was the major source used to est a b l i s h house market value rather than M.L.S. (Multiple L i s t i n g Service) or sales data. The reason for t h i s choice was such that assessment data allowed the value of the same houses to be tracked over the f u l l period of the study thus providing comparative information of house values on a yearly bases regardless of whether or not the house was actually sold. While i n the author's estimation t h i s method provides a more consistently accurate comparative base from which to operate than does sales data, the data adjustments required to complete the f u l l time seri e s of information were complex. More s p e c i f i c a l l y the problem and adjustments required are outlined as follows: -39-1) L_g__d___lat_d_Ad_ust.ments (A) From 1962-1976 residential property assessment values lagged market value by approximately two years. (Vancouver Real Estate Board, 1972/73, A-24) To compensate, property assessment values for the years 1964-1978 were utilized as being representative of market value for this period. (B) 1977 was considered to be the year in which the assessment lag most closely approximated one fu l l year as opposed to two f u l l years, (information as obtained from the Deputy Assessor, B.C. Assessment Authority, 1983) As 1976 assessment values were already used to reflect 1976 market value, 1977 market value was determined based on market information obtained from Real Estate Trends magazine 1977. More specifically the average house price of the Real Estate Trend's sampling of houses sold within each of the subject communities were calculated. (C) Market values for the years 1978, 1979, 1989 were obtained through utilizing assessment values for the years 1979-1980-1981. Within the time serie s 1962-1980 there were periods wherein adjustments were required to compensate for periods of "assessment freeze", or " r e v i s i o n " of the methods used to calculate r e s i d e n t i a l property assessment. More s p e c i f i c a l l y the following major adjustments are noteworthy. -40-N2Dzt§__B§i§_§__Ad_ustments and Considerations Property Tax Assessment Considerations Adjustments 1961-1966 Assessment values were based on 502 of market value. Assessment values Here doubled to represent f u l l market value. 1967 Assessment values were based on 50* of market value but with a limitation of a 52 increase. Assessed values were doubled plus an additional percentage was added based on the average yearly percentage increase of the period preceding and the period following 1967. (Additional percentage added =4.92. More s p e c i f i c a l l y t h i s figure was arrived at by determining the average yearly 2 increase in assessment value i e : market value over the periods 1965-1966 and 1968-1969. i e : 19.82 * .5 = 9.92. Second the 52 limitation of assessment increase was then subtracted from the 9.92=4.92. 4.92 of the 1966 assessed value was then added to achieve the 1957 market value) 1975-1977 Three year freeze on property 2 changes i n yearly market value were determined based on Real Estate Trends sampling of houses sold in each of the -subject communities over the period 1975-1977. -41-CH_PTER_I__-_THE__ESULTS The r e s u l t s herein can be divided into 4 general categories. Listed i n order of presentation they are: 1) A graphical display of the relat i o n s h i p between house prices in the subject communities and the subject economic indicators. 2) The general s t a t i s t i c a l r e s u l t s obtained from the regressions. 3) The forcaating r e s u l t s obtained f o r house prices over the 1962-1980 study period. 4) The forcasting r e s u l t s obtained for house prices for the period 1981-1982 Appendix D explains the various s t a t i s t i c a l concepts and terms employed i n the analysis of the r e s u l t s . - 4 2 -A) Graghs_gf_ Unadj_§_ed__ela__onsh_gs i The following graphs depict, the raw data relationships between house prices in each of the communities of Shaughnessy, Oakridge, East Hastings Sunrise and a hypothetical Mean of D i s t r i c t s with each of the nineteen economic indic a t o r s . It i s noteworthy that the v i s u a l representations can be misleading i f the viewer i s not informed as to what i s important in assessing the r e l a t i v e relationships between any one of the economic indicators and house prices on the various communities. More s p e c i f i c a l l y the f a c t that an indicator might intersect a community house price regression l i n e several times or might l i t e r a l l y be on top of i t at several points, i s no way suggestive of a close s t a t i s t i c a l r e l a t i o n s h i p between the two. The reason for t h i s stems from the f a c t that a mere change i n the units of measurement of the scales f o r either house prices or the economic indicators would immediately change the of the l i n e each year hence producing a very d i f f e r e n t v i s u a l picture with the same data. While something can be learned by noting the points at which the slopes of the l i n e s change and the d i r e c t i o n and degree of change in these slopes r e l a t i v e to t h e i r previous positions, the ambiguity of the graphical scales requires that the resultant conclusions drawn be of a general nature. LEGEND " Shaughnessy - Oakridae - H a s t i n g s - Mean or D i s t r i c t s - Earnings: Construction - o T i m e ! y e a r s Mean property value vs overage v/eeklu earnings: construction Meon P r o p e r t y M a r k e t V a l u e 12000 82100' 152300 223200 1_ " d o L L a r s 233600 361000 — r -S0 100 I S O 200 250 i i i 1— 300 3S0 -300 ISO W e e k l y E a r n i n g s : F o r e s t r u — d o l l i — 500 o r s 550 LEGEND D - S h o u g h n e s s _ • A - Oakr udge o - H a s t i n g s o - Mean o f D i s t r i c t s ? - E a r n i n g s : M a n u f a c t u r i n g T i m e ! y e a r s F i g u r e 3. Mean p r o p e r t y v a l u e v s a v e r a g e w e e k l y e a r n i n g s ! m a n u f a c t u r i n g i ui i ~ i ' ' i f i i i i i 1 1 • i 1 1 1 1 r G2 S3 G4 GS SS G7 G8 S9 70 71 72 73 74 75 7S 77 78 79 80 T i m e : y e a r s Figure 4. Mean property value vs average weekly earnings: mining LEGEND • , 1 i T r 1 1 1 1 1 1 1 1 1 1 1 1 r 82 S3 G4 6S GG G7 68 G9 70 71 72 73 74 75 76 77 78 79 BO Time: years f i g u r e 5. Mean property value vs average weekly earnings: s e r v i c e s LF.GFIND f i g u r e S; Mean property value vs average weekly earnings: trades ~t r y f "f r i i i i 1 1 1 1 1 1 1 , G2 G3 G4 G5 GG G7 G8 G9 70 71 72 73 74 75 7G 77 78 79 80 T ime: y e a r s Figure-7. Mean property value vs r e t a i l sales In B.C. - 5 0 -osz oaz asi oci cs a L I 1 1 1 • i r——• 1 1 ; 1 . 0C0'»9£ 009C6Z 0OZ££Z OOBSSt 0G»c9 OOOr.! -51-LEGEND i i 1 i f r 1 1 1 1 1 1 1 1 1 i 1 1 - r G2 83 S4 BS GG G7 G8 G9 70 71 72 73 74 7S 7G 77 78 79 80 Time? years f i g u r e 10.' Mean p r o p e r t y v a l u e vs U,S, autos I n B.C, LEGEND r i 7 ! "f (= i i 1 1 1 1 1 1 1—:—i 1 ( r G2 G3 64 GS GS G7 G8 G9 70 71 72 73 74 7S 76 77 78 79 80 Time: y e a r s figure 11. Mean property value vs Unemployment Rate i f 7 1— i i 1 1 1 1 1 1 1 1 1 1 • - i 1 r G2 G3 Gt GS GG G7 G8 G9 70 71 72 73 74 75 7G 77 73 79 80 T i m e : years figure 12. Mean property value vs Personal Income B.C, LEGEND D - Shaughnesst) ^ " Oakr^dge o - Hastings ° - Mean of D i s t r i c t s ' - Population of B.C. Times years 'Igure 13. Mean property value vs Population of B.C. f i g u r e H . Mean p r o p e r t y v a l u e v s B . C . p o r t E x p o r t s NJ Time: years , f i g u r e 15. Mean property value vs GPP of 8.C, LEGEND t i i i i T 1 i 1 1 1 1 1 i 1 1 1 1 r 52 S3 64 85 GS G7 S8 69 70 71 72 73 74 75 7G 77 78 79 80 T i m e ! y e c r s f i g u r e 16, Mean property value vs Mortgage r a l e LEGEND Timet years f i g u r e 27. Mean p r o p e r t y v a l u e vs cheques cashed -09-a a n . •f in n CO L D _) . _> a —i a O ia C N I t 03 3 ci ^ Pi > a -t-> 0) k ° D O , 5 J C 0) Q_ 0 a , Q _ t N 0) XT- a CM LEGEND a . - S h a u g h n e s s y A - O a k r i d g e o - H a s t i n g s o - Mean o f D i s t r i c t s ' - N o n - r e s i d e n t l a l I n d e x • a Time: years f i g u r e 19. Mean property value vs -Non-resident l a I v. nclyx. -62-< B) Commentary._gn_Gra_hed_R^lat ign^higs J There are two noteable common trends which appear i n the graphed data. (1) An increasing slope of house prices i n a l l three of the subject communities in 1971. <2) An increasing slope of most of the economic indicators i n 1971, 1972, 1973, or 1974. ( i . e . , 15 of the 19 indicators showed the beginings of a sustained upward trend of 3 or more years.) Those indicators which did not reveal t h i s marked upward trend during the early 70's were (1) U.S. Autos entering B.C. (2) Unemployment rate (3) the population of B.C. and (4) GPP of B.C. An explanation of t h i s general upward trend rests with the f a c t that i t was during 1971 that the nation, the province and the c i t y began to emerge from a period of economic slowdown. It wasn't long before wages, sales and prices rose s i g n i f i c a n t l y to the point i n fac t where the post 1971 i n f l a t i o n rate increased to 2 and 3 times the pre 1971 rate. (Vancouver Real Estate Board 1974-75) Hence, the increasing slope exhibited by house prices in the 3 communities of Shaughnessy, Oakridge and East Hastings and the increases noted by the majority of the economic indicators could reasonably be concluded to be a r e s u l t of (1) An increased i n f l a t i o n a r y factor largely resultant from the e f f e c t s of the 1973 OPEC accords and the fa c t that an i n f l a t i o n factor i s b u i l t into the values of home prices and economic indicators a l i k e i . e . , the majority of these values are represented i n -63-"current d o l l a r s " rather than i n constant indexed d o l l a r s and (2) an incresed l e v e l of economic a c t i v i t y in Vancouver aided by (a) the s t a b i l i z a t i o n of int e r e s t rates, (Vancouver Real Estate Board 1972-73), (b) changes i n the c a p i t a l gains tax whereby a personal residence became exempt from c a p i t a l gains upon'sale (Ibid) and (c) the pr o v i n c i a l goverment's home acquisition assitance l e g i s l a t i o n whereby subsidies were provided to f i r s t time home buyers. With regards to an explanation as to why the four indicators previously refered to did not show any consistent upwards trend i n the early 70's i t appears that (1) the number of U.S. Autos entering B.C. i s only p a r t i a l l y connected to the economic conditions e x i s t i n g i n B.C. and Vancouver and as a re s u l t i t s slope appears to bear l i t t l e r e l a t i o n s h i p with house prices and (2) the Unemployment rate, the Population of B.C. and the GPP of B.C. are a l l indicators which appear,to take a considerable length of time to respond to a "recovering economy". As a r e s u l t a lagged r e l a t i o n s h i p of many years might be expected with house prices . Other relevant information made obvious by the graphs includes the observation that house prices i n a l l three of the communities correlate very highly with one another. East Hastings Sunrise however does not appear to correlate as -64-clos e l y with Shaughnessy and Oakridge as these two communities correlate with one another. This trend i s r e f l e c t e d in the years 1974, 1975 and 1976 when house prices i n East Hasings Sunrise experienced a s i g n i f i c a n t decrease i n slope to 1975 and then a sudden and s i g n i f i c a n t increase in slope to 1976. These changes in slope are very d i f f e r e n t from the experience in Shaughnessy and Oakridge where an upward slope was maintained over t h i s period. -65r-<c> R a w _ D a t a _ R e g r e a s i o n _ R u n s Table 4 Adjusted R* Values of those Variables Found  to be Significant at a 95X Confidence Level I 1st Run 2nd Run 1 (significant variables 1 from f i r s t run removed.) 1 lyr Lag 1 I 1 i 1Shaughnessy .9758 Cheques Cashed .9575 Vancouver CPI-Clothing I .9727 Building Material Price 1 Index Residential I .9792 Population of B.C. 1 1 .9745 Cheques Cashed f .9821 Bldng Materials1 Price Idx Rsdtll .9925 Population of 1 B.C. 1 1Oakridge .9607 Cheques Cashed .9833 Building Materials Price Index Residential .9921 6PP of B.C. s .9314 Exports through B.C. Ports 1 .9457 Mortgage Rates 1 1 i .9590 Cheques Cashed 1 .9836 Bldng Materials1 Price Idx Rsdtll .9917 GPP of B.C. 1 1 lEast 1 Hastings ISunrise .9529 Retail Sales .9693 Average Weekly Earning Construction .9525 Average Meekly 1 Earnings Forstry 1 1 .9513 Retail Sales 1 .9705 Bldng Materialsl Price Idx Rsdtll 1 1District 1Means .9727 Cheques Cashed .9784 Building Materials Price Index Residential .9912 GPP of B.C. .9527 Vancouver CPI-Clothing i .9684 Average Meekly Earnings 1 Construction 1 1 .9713 Cheques Cashed 1 .9806 Bldng Materialsl Price Idx Rsdtll .9917 Population of 1 B.C. 1 (D) S t a t i s t i c a l Summaries of Raw Data Regression Run i) Sumaary Statement of Statistics - Shaughnessy. 1st Run Adjusted R* .98 F 728.01 T(F17) 26.98 B 852.10 Constant 21940.86 y=21940+852(Cheques Cashed) 2nd Run Adjusted R .98 F 283.16 T(F8) 7.26 T(F1B) -4.05 T(F13) -2.45 Bl 5591.49 B2 -1767.96 B3 -6.39 Constant -246700.00 y=-246700+559KCPI Clothing)* -1767(Bui Id Wtrls Res) +-6.39(Pop of B.C.) lyr lag Adjusted R .99 F 754.85 T(F17) 11.89 T(F18) -6.07 T(F13) 4.68 Bl -1531.42 B2 1598.09 B3 7.13 Constant 42740.90 y=42740+1531(Cheques Cashed)* -1598(BuiId Mtrls Res) +7 (Pop of B.C.) - 6 7 -2) Sunaiarv Statement of Statistics - Oakridge. 1st Run 2nd Run iyrJLag z Adjusted R .99 z Adjusted R .95 Adjusted R .99 F 750.53 F 157.85 F 677.52 T(F17) 15.94 T(F14) 7.33 T(F17) 15.38 T(F18> -819 T(F16) 2.33 T(F18) -7.96 T(F15) -4.32 T(F15) 3.95 Bl 721.10 Bl .70 Bl 724.28 B2 -748.05 B2 4255.00 B2 -749.58 B3 2.53 Constant -26970.61 B3 2.47 Constant 65353.61 y=-26971+.70(Export Value) Constant 66032.33 y=65354+721(Cheques Cashed) +4255(Mortgage Rates) y=66032+724(Cheques Cashed)+ -750<Bldg Mtrls Res)+2.5(BPP of B.C.) -68-3) Summary Statement of Statistics - East Hastings Sunrise 1st Run 2nd Run lyr lag z Adjusted R .97 Adjusted R .95 Adjusted R .97 F 285.33 F 361.88 F 280.27 T(F 7) 5.79 T(F 2) 19.92 T (F7) 5.87 T(F 1) -3.17 T (F18) -3.37 Bl 18.99 Bl 195.97 Bl 19.81 B2 -197.34 B2 -538.22 Constant -1134.32 Constant -19069.66 Constant 27915.40 y= -1134+18.39(Retail Sales) y=-19979 + 195(Forestry Earnings) y = 27915 + 19(Retail Sales) +-197(Construction Earnings) +-53B(Build Mtrls Res) -69-4) Summary Statement of Statistics - District Means. 1st Run st Adjusted R .99 F 676.90 T(F17) 12.30 T(F18) -6.9B T(F15) 3.38 61 798.14 B2 -763.08 B3 4.02 Constant 63130.92 y=-63131+798(Cheques Cashed) +-763(Bui Id Mtrls Res) +4 (Pop of B.C.) 1 2nd Run Adjusted R .97 F 276.54 T(F 8) 5.91 T(F 1) -3.06 Bl 2577.00 B2 -362.28 Constant -208170.00 y=208170+2577(CPI Clothing) +-362 (Forestry Earnings) lyr_lag Adjusted R .99 F 679.09 T(F17) 11.70 T(F18) -6.19 T(F13) 4.60 Bl 889.59 B2 -961.76 B3 4.13 Constant 27655.47 y=27655+890 (Cheques Cashed) +-962 (Building Htrls Res) +4 (Pop of B.C.) \ -70-(E) Co_men__on___gns_of.Statistics It i s noteworthy that while i n some instances such as with Average Weekly Earning-Constructions F<1) and Building Materials Price Index-Residential (F18) the b values, i . e . : the c o e f f i c i e n t s of x, are negative, t h i s does not mean that these indicators r e l a t e negatively to house prices . In f a c t in a l l the instances i n t h i s study where t h i s occurs economic theory dictates the contrary to be true. This b e l i e f i s further confirmed by the r values exhibited by these indicators i n the Correlation Matricies(Refer to Appendix C) as well as by the graphs previously noted. More exactly the above s t a t i s t i c s have recorded negative values i n these instances as a r e s u l t of the e f f e c t s of m u l t i c o l l i n e a r i t y . (For a more comprehensive discussion of m u l t i c o l l i n e a r i t y refer to pg 71). A quick explanation resides i n the f a c t that c o e f f i c i e n t s i n Multiple Regression are i n f a c t p a r t i a l c o e f f i c i e n t s , representing the e f f e c t s of a s p e c i f i c regressor in the presence of other influences, i . e . : other regressors. As a r e s u l t i t i s possible i n s i t u a t i o n s where extensive overlapping between regressors e x i s t s , that the sign of the c o e f f i c i e n t of one of the included variables w i l l revert to negative when in f a c t the b i v a r i a t e r e l a t i o n s h i p i s not negative. -71-<F) Co__ent_on__ulticgll_neari__ Perusal of both the s t a t i s t i c a l and graphed r e s u l t s suggests the e f f e c t s of m u l t i c o l l i n e a r i t y . More generally m u l t i c o l i n e a r i t y i s a common condition occuring in economic data whereby at least two of the independent variables are highly correlated. One technical e f f e c t of t h i s i s an increase i n the standard error of the estimated c o e f f i c i e n t s and hence an increase the l i k e l i h o o d that the c o e f f i c i e n t s of the independent variables w i l l not be s i g n i f i c a n t l y d i f f e r e n t from zero. The r e s u l t s are such that those variables may be relegated to exclusion from the regression equation. A more complete l i s t of symptoms of m u l t i c o l l i n e a r i t y , a l l of which t h i s study posseses i s as follows: (Hebden, 1981) 1) the simple c o r r e l a t i o n c o e f f i c i e n t s between c o l l i n e a r regressors are high. 2) the explanatory power of the regression does not r i s e s i g n i f i c a n t l y when' a second regressor i s added. 3) the standard deviations of the regression c o e f f i c i e n t s are much larger i n the multiple regression than i n the simple regression on each c o l l i n e a r variable separately. As the purpose of t h i s study i s to forecast house prices using a c o l l e c t i o n of explanatory variables and not to investigate the precise e f f e c t of each variable i n the c o l l e c t i o n , i t i s acceptable to l i v e with the presence of -72-m u l t i c o l l i n e a r i t y . However i n an e f f o r t to to maintain good a t a t i a t i c a l practice two attempts were made to reduce i t s influence. F i r s t l y the Raw Data Regression was re-run using adjusted f o r a l l d o l l a r based variables, indexed to 1971 do l l a r s . This was done i n order to control the common trend of i n f l a t i o n which ex i s t s i m p l i c i t l y i n both the d o l l a r values of the sample house prices and i n the majority of economic indicators ( i . e . , d o l l a r values are for the most part expressed in current terms rather than i n constant indexed terms.) -73-<G> lQ^i___2Q_A_2y__§__B§9E®§§_2D_BaO§ y__i___09_AY§E§9§_Y®9_i.Z_Q§Q§__§S Consumer_P_ice_Inde_ Table 5 i Adjusted R 1st Run 2nd Run ** 1 yr Lag 1Shaughnessy .9270 Cheques Cashed 1 .8964 Personal .9212 Cheques 1 1 .9724 Building Price 1 Income in B.C. Cashed 1 1 Index Residential i .9159 Average weekly 1 1 Earnings 1 ] Construction ] 1Oakridge .9066 Cheques Cashed 1 .8630 Exports thru .8992 Cheques 1 1 .9489 Building Materials! B.C. Ports Cashed 1 1 Price Index 1 .8927 Mortgage 1 1 Residential 1 Rates 1 1 .9611 Average Ukly 1 1 \ Earnings Traders 1 \ lEast Hastings .8589 Retail Sales 1 .8578 Average Ukly .8477 Retail 1 1Sunrise .6982 Av. Ukly 1 Earnings Forestry Sales i 1 Earnings 1 1 1 Constructions 1 1 1 .9298 Average Ukly i 1 | earning Services 1 | IDistrict Hearts .9166 Cheques Cashed i .8851 Personal Income .9100 Cheques 1 1 .9669 Building Materialsl In B.C. Cashed i 1 Residential Price 1 .9095 Averagege Ukly 1 1 Index 1 Earnings 1 I Construction 1 *» excluding significant variables from 1st run -74-It i s noteworthy that the variables chosen as being s i g n i f i c a n t and the adjusted R* values generated by t h i s method were very s i m i l a r to those obtained by the Raw Data Regression Runs. (Refer to pg 63) As a r e s u l t of t h i s s i m i l a r i t y and the d i f f i c u l t i e s associated with converting the I n f l a t i o n Adjusted Regression output of Predicted House Market Values to Actual House Market Values f o r a given year t h i s method was not pursued any further. The second method employed i n attempting to remove the e f f e c t s of m u l t i c o l l i n e a r i t y was the "Logarithmic F i r s t Differences Method" (Kane, 1968, 44 and 331). In time series regressions " F i r s t Differences" tends/to reduce m u l t i c o l l i n e a r i t y through eliminating the e f f e c t s of common trends and c y c l i c a l influences. More s p e c i f i c a l l y t h i s method f i r s t l y takes the log of the dependent variables to remove the variant amplitude of the time seri e s (a constant variance «, throughout the time seri e s i s assumed) and secondly "differences the log y" in order to obtain a constant mean, (i e : i n e f f e c t t h i s involves taking the log of y i n one period and subtracting the log of y in the next period.) The r e s u l t s obtained however were nonsensical and were s p e c i f i c a l l y rejected for the following reasons: (1) The adjusted R values of the independent variables selected were low and as a r e s u l t would not be good predictors of dependent variables. -75-(2) The independent variables selected as being s i g n i f i c a n t did not corroborate with the r e s u l t s obtained by those of the Raw Data Regression Runs or with those of the I n f l a t i o n Adjusted Regression Runs. (H) Summary_Co_mentary The F values generated at the 95% confidence l e v e l by the Raw Data Regression Runs fo r each of the subject communities indicate that i t i s possible to r e j e c t the n u l l hypotheses i n each case. More s p e c i f i c a l l y the i d e n t i c a l n u l l hypotheses assert that there are no s i g n i f i c a n t relationships between any of the subject 19 economic indicators and house prices in any of the communities. Thus i t can p o s i t i v e l y be stated that house prices in each of Shaughnessy, Oakridge and East Hastings Sunrise are s i g n i f i c a n t l y related to various subsets of the subject 19 economic indicators: and that subsets of these indicators can be used f o r forcasting purposes. Due to the high degree of m u l t i c o l l i n e a r i t y present i n t h i s study and the lack of an e f f e c t i v e method fo r removing i t however, the precise contribution of each regressor to the determination of house prices i n any of the subject communities cannot be made. More s p e c i f i c a l l y neither the x incremental R values, the values of b, or the Beta Co e f f i c i e n t s can be r e l i e d on to e f f e c t i v e l y represent the precise r e l a t i o n s h i p which e x i s t s between ind i v i d u a l -76-regressors and the dependent variable, or any p a r t i c u l a r regressor and any other. It i s important however to note that in each of the 3 communities over 95% of the var i a t i o n in house prices as expressed by the adjusted R values, i s explained by the various subsets of the 19 economic variables. As i t i s not the major objective of t h i s thesis to investigate the precise e f f e c t of each of the s i g n i f i c a n t regressors on house prices, but rather to be able to forecast house prices i n the d i f f e r e n t communities using a c o l l e c t i o n of s i g n i f i c a n t regressors t h i s problem can be accepted. Since the s i g n i f i c a n c e l e v e l i s high i n a l l cases as are the R values the resultant equations can be used f o r forcaating with a reasonable degree of confidence. A caveat however i s placed on such forecasts wherein i t i s assumed that the same mul t i c o l l i n e a r r elationships w i l l hold i n the future. This may not always be true and the forecaster must always be cognisant of t h i s f a c t . With the above noted r e s t r i c t i o n s placed on the interpretation of the strength of individual regressors v a l i d comment i s limited to noting the consistency by which cert a i n of the regressors re-appear as being the most s i g n i f i c a n t within and between s p e c i f i c communities. For example "Cheques Cashed" appears to dominate Shaughnessy and Oakridge as having -77-the greatest influence over house prices to the extent in f a c t , whereby t h i s was the only regressor selected as being s i g n i f i c a n t under the 1 year lag regression run. A s i m i l a r s i t u a t i o n e x i s t s to a lesser degree i n the East Hastings Sunrise Community where Re t a i l Sales appears to be the " i n d i c a t o r " with the dominating influence over house prices. Of the nineteen independent variables entered into the step-wise regressions f o r each community only two or three were isola t e d i n each case as being s i g n i f i c a n t at the 95% confidence l e v e l ( i . e . , that i s t h e i r b values were s i g n i f i c a n t l y d i f f e r e n t from zero). It i s expected however that due to the high degree of c o l l i n e a r i t y between the variables there are many more highly s i g n i f i c a n t variables which,would have appeared during concurrent runs had the s i g n i f i c a n t variables from the previous run been removed. This propostion i s supported by perusing the r e s u l t s of the i second runs wherein i t i s noted that the adjusted R 's of the selected variables maintained a high value close to those of f i r s t runs. -78-<I) Hou§e_pr__e§_as__orcas___ro___he__ene l9y§tions_1962 - 1980. (Due to the f a c t that achieving the best predicive equations with the highest R i s a t a c i t objective of t h i s thesis the Results of the 2nd Regression Run are not presented.) The use of the 1st Run equations as indicated below are s p e c i f i c to predicting house prices for a p a r t i c u l a r year, given the values of the s i g n i f i c a n t independent variables for the same year. The use of the 1 year lag equations are s p e c i f i c to forcaating house prices for a p a r t i c u l a r year, given the values of the s i g n i f i c a n t independent variables of the preceeding__ear. The r e s u l t s as l i s t e d below represent the values f o r Actual House prices. Predicted House prices and the Differences between the two i n current d o l l a r terms and percentage terms. -79-Sh§ughrjessy_Prices Table 6 First Run Predictive Equation: y=21940+852(F17) l_yr_Lag Predictive Equation: y=42740+1531(F17)+ 1598(F18> +7<F13) • Actual Predicted Error <Error Actual Predicted Error flError 1982 39552 41539 -1987 5.0 1963 41179 41195 -16 .0 1963 41179 43244 -2065 5.0 1964 42212 45778 -3566 7.8 1964 42212 46993 -4781 11.3 1965 47926 47287 638 1.3 1965 47926 50572 -2446 5.1 1966 49578 49417 160 .3 1966 49578 54321 -4743 9.6 1967 57069 52191 4877 8.5 1967 57069 57133 -64 .1 1968 59173 57067 2105 3.6 1968 59173 61735 -2562 4.3 1969 60927 67542 -6615 10.9 1969 60927 70341 -9414 15.5. 1970 66175 60658 5516 8.3 1978 66175 70938 -4763 7.2 1971 71365 79052 -7687 10.8 1971 71365 77329 -5964 8.3 1972 104980 98009 6896 6.6 1972 104900 89003 15902 15.1 1973 130108 123300 -6747 ' 5.1 1973 130000 108900 21225 16.3 . 1974 143180 151000 -8465 5.9 1974 143160 135600 7476 5.2 1975 177400 178200 ,-792 .4 1975 177400 161700 15743 8.9 1976 200100 206100 -5939 2.9 1976 200100 187500 12623 6.3 1977 200600 194200 6479 3.2 1977 200600 199100 1534 .8 1978 207000 198480 8641 4.2 1978 207000 220800 -13782 6.7 1979 229000 245600 -16599 7.2 1979 229000 266400 -37466 16.4 1980 363900 356300 7619 2.1 1988 363900 348100 15736 4.3 - 8 0 -Q§_ridg__Price_ Table 7 First Run 1 yr Lag Predictive Equation: y=65354+721(F17)+ -748<F18)+2.5(F15> Predictive Equation; y=66032+724(F17)+-750(F18> +2.5(F15) Actual Predicted Error ffiror Actual Predicted , Error 5_rro) 1952 16525 17627 -1102 6.6 1963 16260 17685 -1425 .8 1963 16260 17389 -1129 6.9 1964 16493 18107 -1614 9.7 1964 16493 17839 -1346 8.2 1965 17926 17854 71 .4 1965 17926 17626 304 1.6 1966 19775 19363 411 2.1 1966 19775 19171 603 3.0 1967 22069 19454 2614 11.8 1967 22069 19294 2774 12.6 1968 23269 20594 2774 11.9 1968 23369 20468 2900 12.4 1969 24609 24136 472 1.9 1969 24609 24055 553 2.2 1970 25783 277% -2013 7.8 1970 25783 27746 -1963 7.6 1971 28318 33297 -4979 17.6 1971 28318 33387 -4989 17.6 1972 41345 38059 3285 7.9 1972 41345 38093 3251 7.8 1973 51268 45776 5491 10.7 1973 51268 45843 5424 10.5 1974 56395 58643 2248 4.0 1974 56395 58698 2303 4.1 1975 69930 72166 -2236 3.2 1975 69930 72198 -2268 3.2 1976 75756 79441 -3685 4.9 1976 75756 79475 -3719 4.9 1977 75945 73349 2595 3.4 1977 75945 73425 2519 3.3 1978 78813 75915 2897 3.7 1978 78813 76013 2799 3.5 1979 91314 96645 -5331 5.8 1979 91314 96688 -5374 5.8 1980 161100 158200 2920 1.8 1980 161100 158100 3064 1.9 -81-East_Hastings_Sunrise_Prigea First Run Predictive Equation: y=-l134+18.98(F7) +-197(Fi) Actual Predicted Error flErrqr 1962 12368 11207 1160 9.3 1963 12218 12381 -163 1.3 1964 12269 14408 -2131 17.4 1965 12833 15406 -2573 20.0 1966 13623 13400 222 1.6 1967 15228 14958 269 1.7 1968 16402 19678 -3276 19.9 1969 17934 21078 -3684 20.5 1970 18544 18498 45 .2 1971 20124 23104 -2980 14.8 1972 32198 25460 6737 20.1 1973 42180 37925 4254 10.1 1974 45976 45624 351 .8 1975 45195 43096 2178 4.8 1976 56557 50258 6298 11.1 1977 56840 52589 4250 7.4 1978 57063 60133 -3070 5.3 1979 61707 70661 -8954 14.5 1980 91623 90548 1074 1.2 Table 8 / l_yr_Lag Predictive Equation: y=27915+19(F7)+-583(F18) Actual Predicted Error %Error 1963 12218 10361 1856 15.2 1964 12269 12281 -12 .1 1965 12833 13377 -544 4.2 1966 13623 13541 81 .6 1967 15228 14391 836 5.4 1968 16402 15864 537 3.2 1969 17394 17628 -234 1.3 1970 18544 14988 3555 19.1 1971 20124 26112 -5988 29.8 1972 32198 31098 1099 3.4 1973 42180 39197 2982 7.1 1974 45976 46309 -333 .7 1975 45915 48155 -2960 6.4 1976 56557 55702 854 1.5 1977 56840 56084 755 1.3 1978 57063 62161 -5098 6.9 1979 61707 68634 -6927 11.2 1980 91623 82082 9540 10.4 -82-<J) Commentar__gn_Pr___c__ye^ 1) _______ Upon c o n s i d e r a t i o n o f a l l o f t h e s u b j e c t c o m m u n i t i e s , t h e a c c u r a c y o f t h e y e a r l y p r e d i c t e d h o u s e v a l u e s r a n g e d f r o m .10% t o 20.90% o f a c t u a l v a l u e . The a c c u r a c y o f p r e d i c t i o n i n O a k r i d g e was t h e h i g h e s t w i t h an a v e r a g e o f 6.60% y e a r l y e r r o r . S h a u g h n e s s y a v e r a g e d 7.50% y e a r l y e r r o r and E a s t H a s t i n g s S u n r i s e 10.90% y e a r l y e r r o r . T h e r e were no common c r o s s commun i t y t r e n d s o b s e r v e d w i t h r e g a r d s t o t h e y e a r s i n w h i c h p r e d i c t i o n s p r o v e d t o be most o r l e a s t a c c u r a t e . 2) l y r_Lag T a k i n g i n t o a c c o u n t t h e t h r e e s u b j e c t c o m m u n i t i e s t h e a c c u r a c y o f t h e y e a r l y p r e d i c t e d h o u s e v a l u e s r a n g e d f r o m .03% t o 29.70% o f t h e a c t u a l v a l u e . The a c c u r a c y o f p r e d i c t i o n i n S h a g h n e s s y was t h e h i g h e s t w i t h a n a v e r a g e o f 6.40% y e a r l y e r r o r . O a k r i d g e a v e r a g e d 6.60% y e a r l y e r r o r and E a s t H a s t i n g s S u n r i s e 7.70% y e a r l y e r r o r . T h e r e were no common c r o s s commun i t y t r e n d s o b s e r v e d w i t h r e g a r d s t o t h e y e a r s i n w h i c h p r e d i c t i o n s p r o v e d t o be t h e most o r l e a s t a c c u r a t e . -83-(K) Fgrcas__ng_Ca_ab_li_ies_g__Gen 1981 - 1982_ While i t i s important to have an understanding of the predictive equations generated over the time seri e s 1962-1980, for the purposes of t h i s thesis i t i s equally important to understand the forcasting c a p a b i l i t i e s of these equations for periods external to the regression years. In an attempt to draw conclusions in t h i s area, the 1 year lagged regression equations as l i s t e d below were used to generate house prices values for the exceptional years of 1981, and 1982. ("Indicator" values for 1980 were used to produce house prices values f o r 1981 and 1981 "Indicator" values were used to produce house prices for 1982) Shaughnessy Oakridge East Hastings Sunrise y=42748 + 1531(F17) y=66032 + 724(F17) y=27915+19(F7) + -1598(F18) + 7(F13) + 750<F18) + 2.5(F15) + -53B(F18) (a) Ihe_Exce2_ignal__ature_gf_Years_1981_and_1982 (The following information was summarized from the Real Estate Board of Greater Vancouver 1981, 8-12.) The two years immediately p r i o r to 1981 saw the economy and housing market of Greater Vancouver i n boom conditions. Prosperity brought on by a high U.S. demand for -84-B.C.'s lumber exports was the i n i t i a l stimulus which resulted in an increased flow of funds into the B.C. economy. This in term produced higher incomes within the province, created more jobs, attracted immigration into the region and ultimately increased the demand for houses within Vancouver. As the supply of houses over the short term was b a s i c a l l y f i x e d the newly generated increase in demand resulted in s i g n i f i c a n t house price increases. Those persons who already owned homes prior to 1979 or who had bought during 1979 and early 1980 had witnessed substantial gains i n the value of t h e i r property. A speculative fever of sorts developed on the part of investers whereby house prices were driven up to an a l l time high. By the second quarter of 1981 Vancouver found i t s e l f in a si t u a t i o n of having the highest priced housing in the country. It was during t h i s period of Vancouver's record prices that the U.S. embarked on a t i g h t money policy i n an attempt to curb i n f l a t i o n and reduce t h e i r national d e f i c i t . Consequent r i s i n g i n t e r e s t rates in the,U.S. c u r t a i l e d the demand for housing therein as investors found t h e i r borrowing and purchasing powers reduced. The d i r e c t r e s u l t was a sharp decline in U.S. housing s t a r t s and a corresponding reduction in B.C. lumber exports to the U.S. With t h i s p r i n c i p a l source of revenue into the province having been severely reduced the -85-extremely high house prices within Greater Vancouver could no longer be supported. Ultimately by the middle of 1981 house prices began t h e i r rapid decline through to the end of 1982. <M> Comparative_Results_Generated In order that some r e l a t i v e judgement could be made as to the degree of forecasting c r e d i b i l i t y of these forecasting equations f o r the years of 1981-82, values f o r each of 1980, 1981, and 1982 were generated using a st r a i g h t 10_yr_-_linear Extrapolation [8] of the average percent change of house prices in each of the communities over the preceding 10 years. (While the r e s u l t s f o r the years 1980 were included to give an indication as to the comparative r e l a t i o n s h i p between the two forecasting methodologies over the 1962-1980 study period, the commentary herein i s focussed on the years of 1981 and 1982.) The following r e s u l t s represent Actual and Forecasted House Prices in current d o l l a r terms. [83. The 10 yr Linear Extrapolation Method averages the % change of house prices over the previous 10 years and projects that percentage change i n house prices for the next year i . e . : the forcasted year. -86-Comparat ive R e s u l t s T a b l e , Table 9 Actual Average 10yr Average Percent Lagged Regression Percent Saaple House Price Extrapolation Error Hethod Forcast Error Forcast from Actual from Actual i 1 1 Shaughnessy 363,900 i 1 270,907 25.5* i I 356,300 2.0* ! 1 Oakridge 161,100 1 110,764 31.2* i 158,200 1.8* 1 1 East Hastings Sunrise - 91,623 1 72,382 21.0* i 82,082 10.4* 1 1 1311 i 1 1 1 Shaughnessy 428,535 • 1 430,494 0.45* 1 1 336,341 21.5* I 1 Oakridge 160,734 i 195,414 21.5* 1 158,929 1.1* i 1 East Hastings Sunrise - 104,350 1 107,474 2.9* 1 77,955 25.3* 1 1 1982 1 | 1 1 Shaughnessy 358,255 1 1 509,956 41.5* 1 1 430,174 20.0* 1 1 Oakridge 130,930 1 194,970 48.9* 1 201,956 54.2* 1 1 East Hastings Sunrise - 82,860 1 122,402 47.7* 1 66,165 20.1* 1 <N) Commentary o f Comparat ive R e s u l t s 1981 - 1982 The 10 y r Average E x t r a p o l a t i o n Method proved to y i e l d the more a c c u r a t e r e s u l t s i n 1981. i e : The average e r r o r r e p r e s e n t e d 8.2% o f the a c t u a l Sample p r i c e w h i l e the average e r r o r term y i e l d e d by the R e g r e s s i o n Method r e p r e s e n t e d 15.9% of the A c t u a l house p r i c e . C l o s e r s c r u t i n y o f the r e s u l t s i n 1981 i n d i c a t e t h a t the R e g r e s s i o n Method f o r c a s t e d a d e c l i n e i n house p r i c e s i n -87-Shaughnesay, Oakridge and East Hastings rather than an increase. While at f i r s t glance t h i s might seem to be a falsehood such i s not the case. It must be remembered that the absolute peak for house prices in Vancouver was A p r i l 1981 (Real Estate Board of Greater Vancouver, 1982, 10) and that by the end of 1981 house prices i n most communities, Shaughnessy and East Hastings included, were lower then they had been at the beginning of 1981. (Royal Trust, 1982, 32). In e f f e c t the Regression Method i m p l i c i t l y forcasted house prices to peak sometime between the end of 1980 and the end of 1981. Because yearly values of economic variables were used ( i e : accumulated values as of year end) the l y r lag Regression Method as employed herein forecasted lower prices 12 months into the future as they would e x i s t at December 1981. (In theory there w i l l always be some error between actual sample house prices as represented by assessments data and the forecasted house prices as determined by year end economic indicator values. Such i s the case because both processes are not s p e c i f i c a l l y targeted to represent house prices as of the same month i . e . , assessment date tends to r e f l e c t house prices over the l a s t four months of the year, (information obtained from the B.C. Assesment Authority) while the accumulated yearly Economic Indicators r e f l e c t values through the l a s t month of the year). -88-It i s noteworthy that only once before within the 1962-1980 study period had the Regression Method forecasted a decline i n house prices. In 1977 declines of 5.7% and 7.6% had been forecast f o r Shaughnessy and Oakridge respectively (See pg 79,80). In these cases Actual House Prices within the sample did not decline, but showed no s i g n i f i c a n t change over t h e i r 1976 l e v e l s . Upon consideration of the r e s u l t s obtained i n 1982 i t i s noteworthy that the Regression Method proved to be more accurate than the "10 yr. Average Extrapolation Method." Their average percentage errors from "actual average sample house p r i c e s " were 31.4% and 46.0% respectively. It i s inte r e s t i n g that while actual house prices declined throughout 1982 (Royal Trust, 1982) the 10 yr. Average Extrapolation Method forcasted substantial increases in house prices in a l l of the three subject communities while the Regression Method forcasted a decrease i n East Hastings Sunrise and increases in Shaughnessy and Oakridge. Over the two year period i n c l u s i v e of both 1981 and 1982 the average yearly percent error term produced by the Regression Method was 23.7% whereas the average yearly error term produced by the "10 yr Extrapolation Method was 27.1%. It i s noteable that the average yearly error yielded by the Regression Technique over t h i s 2yr perio'd i s approximately 4 times the 6.2% average yearly error term generated by t h i s method over the 1962 - 1980 period. \ -89-CH_PTER___CONCLySION A. General^ This study employed regression analysis to determine s t a t i s t i c a l l y which, i f any, combination of 19 standard economic indicators could be used to forcast house prices in the Vancouver communities of Shaughnessy, Oakridge and East Hastings Sunrise. It was expected that d i f f e r e n t indicators would be found to be s t a t i s t i c a l l y s i g n i f i c a n t i n each of the communities as a r e s u l t of each community being very d i f f e r e n t in population composition and physical amenities. The findings herein confirmed the b e l i e f that s t a t i s t i c a l l y r e l i a b l e predictive equations f o r each community i could be generated from the subject economic indicators. Three equations were i n fac t formulated. In a l l of these cases both the R values and the si g n i f i c a n c e l e v e l , i . e . : F values, were high and the standard errors r e l a t i v e l y low such that a reasonable degree of confidence could be placed i n t h e i r predictive a b i l i t i e s . As previously noted however the high degree of m u l t i c o l l i n e a r i t y present between the regressors excludes any of these equations from being good functional models wherein i t i s required to know the precise estimates of the e f f e c t s of each variable i n the equation. The major expectation of t h i s study as noted above was -90-not confirmed. In f a c t two " i n d i c a t o r s " consistently stood out from the rest as being the most dominant predictorsC93 in the three subject communities. More s p e c i f i c a l l y "Cheques Cashed" was consistently the most dominant regressor isolated in both Shaughnessy and Oakridge, while in East Hastings Sunrise, Ret a i l Sales tended to be the most dominant regressor. This lack of any c l e a r d i f f e r e n t i a l pattern between each of the communities suggests two probable explanations: (1) that the economic linkages between the d i f f e r e n t sectors of the economy were high enough to obscure the c h a r a c t e r i s t i c differences between the communities. This suppositon i s supported by the high correlations c o e f f i c i e n t s between variables as presented i n the Correlation Matrices (Refer to Appendix C.) For example the c o r r e l a t i o n s c o e f f i c i e n t s of Average Weekly Earnings i n Manufacturing with house prices in both Shaughnessy and East Hastings Sunrise i s .96 even though East Hastings Sunrise had almost twice the percentage of i t s residents d i r e c t l y experienced or involved in that industry. (2) That the c h a r a c t e r i s t i c differences between the three communities were not substantial enough on t h e i r own merits to warrant description by d i f f e r e n t dominant regressors i n each case. [93 Dominant regressors or predictors re f e r s to those variables which explained the greatest percentage of the variance in house prices within the community samples. -91-As to s p e c i f i c a l l y why Cheques Cashed and R e t a i l Sales consistently surfaced as being the dominant influences on house prices, i t would appear that the very broad nature of t h e i r d e f i n i t i o n s had much to do with t h e i r r e l a t i v e positions. E s p e c i a l l y i n the case of Cheques Cashed which i s in c l u s i v e of cheques cashed f o r house buying purposes and i n general i s more of an a l l encompassing variable than i s R e t a i l Sales. Yet contained within the values of either indicator at any p a r t i c u l a r time are a l l the major components which influence d i r e c t l y house price f l u c t u a t i o n s as defined e a r l i e r . (Refer to Chapter I Pg 4) The rationale behind the importance of these variables for forcaating purposes can be more precisely explained by understanding that both "Cheques Cashed" and "Reta i l Sales" f e r r e t out a c r i t i c a l dictum of consumer spending. Consumers spend "not only based on what t h e i r income i s t h i s year but also on what they think t h e i r income and the state of the economy w i l l be next year" (Samuelsen & Scott 1980, 226). In e f f e c t Cheques Cashed and R e t a i l Sales f o r any given year take into account a consideration of an ind i v i d u a l ' s subjective forecast of income and general economic conditions f o r the following year. The resultant current spending in turn would appear to a f f e c t future spending to the extent that a s e l f -92-f u l l f i l l i n g prophesy i s created whereby spending on purchases o£ houses and other commodities are made based on future expectations and the future in turn i s shaped by current spending practises. It can be speculated that "Retail Sales" and not "Cheques Cashed" surfaced as being the most powerful regressor in East Hastings Sunrise due to the proposition that R e t a i l Sales more c l o s e l y r e f l e c t s the spending habits of those who reside and who are l i k e l y to reside i n East Hastings Sunrise. The difference in spending habits between the "East Hastings residents" and those i n Shaughnessy and Oakridge may be such that r e t a i l a c t i v i t y f o r the higher income populace stays r e l a t i v e l y consistent over time, while r e t a i l purchases for lower income communities varies more with the o v e r a l l conditions of the economy. In e f f e c t f o r the residents, or potential residents, of East Hastings Sunrise as the demand for house purchases drops so does the demand f o r r e t a i l goods. This speculation i s supported at some length by basic economic theory i e : the "Pigou E f f e c t " (Samuelson & Scott, 1981, 226) wherein i t i s noted that those with a l o t of cashed saved or with a l o t of assets are not as suseptible to the spending fluctuations of the less wealthy. This of course assumes that those i n d i v i d u a l s creating housing demand i n East Hastings -93-Sunriae did not in general have as high a net worth as those potential purchasers of houses i n Shaughnessy or Oakridge. It i s considered that no other individual regressors in t h i s study demonstrated trends which warrant explanation. While Average Weekly Earning - Construction, and Building Materials Price Index - Residential recur a number of times, in no instance was either selected as being a " most powerful regressor". As a r e s u l t of t h i s and the d i s t o r t i n g e f f e c t s of m u l t i c o l l i n e a r i t y no further consideration of these indicators were undertaken. <B) Strengths_and_Weaknesses_of_the_Methodolggy_ Before deving into the p r a c t i c a l i t i e s of the strengths and weaknesses of the methodology employed from the "users perspective" there i s an important conceptual issue which should be c l a r i f i e d . It should be noted that the methodology employed herein was consciously t a i l o r e d so as to avoid the undercutting issues against "claims of c a u s a l i t y " . More s p e c i f i c a l l y i t was the author's decision that (1) because there appears to be an indeterminant number of indices involved in "causing" house prices to fluctuate and (2) because "causality can not be s t a t i s t i c a l l y established" (Kenny, 1977, 260) any methodology which considered attempting to es t a b l i s h causal factors as such was rejected. Rather i t -94-was the authors choice to employ a methodology which would merely test a se l e c t group of economic indicators which were suspected of having a s t a t i s t i c a l l y close r e l a t i o n s h i p with house prices and to determine i f accurate house price forecasts could be generated therefrom. In terms of the conceptual v a l i d i t y of t h i s thesis the elimination of any s t a t i s t i c a l l y indefensible claims of "causality" i s considered a d e f i n i t e strength of the methodology employed. In p r a c t i c a l user terms the strengths of t h i s basic forcasting approach as outlined i n t h i s study can be summarized as (1) y i e l d i n g a r e l a t i v e l y high degree of accuracy. (Compared to the 10 yr Average Extapolation Technique f o r example) and (2) the ease with which values for the forcasting variables can be obtained, CIO] and (2) the r e l a t i v e speed with which r e s u l t s can be obtained by computer manipulation. CIO]. The values f o r most of the subject indicators are col l e c t e d by S t a t i s t i c Canada on a monthly or quaterly basis. While there values often take from 2 to 3 months to be confirmed and published, accurate estimates can normally be obtained within 30 days of the target period. The only indicator which does not have accurate estimates ava i l a b l e as outlined i s the GPP of B.C. wherein i t normally takes from 6 months to 1 year. -95-The basic weakness of the forcasting approach outlined revolved around the f a c t that the forcaster must r e l y on information concerning events which have ocurred in the past. Hence as noted e a r l i e r the basic standard employed i n t h i s approach to forcasting i s that the pattern which has been i d e n t i f i e d i n the past w i l l continue i n the future. As i s noteworthy in 1981-82 t h i s pattern may not always p e r s i s t . It i s as a consequence the forcaster's job to attempt to anticipate when such a change i n pattern w i l l take place so that appropiate changes in the forcasting system can be employed before forecasts become too inaccurate. Di_ec__o__For_Fur_he__Res_arch In accord with maintaining the basic objectives and the basic methodology employed i n t h i s study the r e s u l t s derived suggest that continued research in three major areas could s i g n i f i c a n t l y improve the accuracy of the forecasting models produced. F i r s t l y an e f f o r t should be made to better understand the economic linkages which e x i s t between the aggregate p r o v i n c i a l economy, the economy of the Vancouver Metropolitan Area, the economy of "Vancouver City Proper" and house prices therein. More s p e c i f i c a l l y t h i s process would involve a comprehensive input/output analysis and a gathering on a - 9 6 -r e g u l a r b a s i s of those key s t a t i s t i c s which e x h i b i t the s t r o n g e s t economic l i n k a g e s between the d i f f e r e n t g e o g r a p h i c a l r e g i o n s and house p r i c e s a t the Vancouver community l e v e l . T h i s would allow the model b u i l d e r t o more p r e c i s e l y d e f i n e the aggregate group of v a r i a b l e s t h a t he wishes to i n c l u d e i n h i s r e g r e s s i o n s and by so doing e l i m i n a t e many of the o v e r l a p p i n g v a r i a b l e s such as are apparent i n t h i s study. A second d i r e c t i o n f o r f u r t h e r r e s e a r c h would r e s i d e with the t e s t i n g of the r e l a t i o n s h i p s between the Economic I n d i c a t o r s on a monthly or q u a r t e r l y b a s i s depending on the a v a i l a b i l i t y o f the s t a t i s t i c a l i n f o r m a t i o n . T h i s would allow the r e s e a r c h e r or the model b u i l d e r t o g a i n a more p r e c i s e understanding of the r e l a t i o n s h i p s between the dependent and independent v a r i a b l e s as they develop over the course of a year. I t i s c o n c e i v a b l e t h a t r e s e a r c h i n t h i s area c o u l d d e t e c t short-term p a t t e r n s of change i n r e l a t i o n s h i p s which c o u l d a c t as warning s i g n a l s f o r major longterm economic change and major house p r i c e f l u c t u a t i o n s a t the community l e v e l . A f i n a l area f o r suggested f u t h e r r e s e a r c h p e r t a i n s to more c l e a r l y i s o l a t i n g those c h a r a c t e r i s t i c s a t the community l e v e l which tend t o have the most d i r e c t i n f l u e n c e on house demand and which are r e c o g n i z a b l y d i f f e r e n t i a t e d between -97-communities. This would enable the model builder to trace the l o g i s t i c s of changes in the economy to changes i n the c h a r a c t e r i s t i c make-up of the i n d i v i d u a l communities and ultimately to changes i n house prices therein. This tracking of sequenced events would provide a tool by which the forecaster could better monitor those events which are l i k e l y to d i r e c t l y a f f e c t his forecasts. As a concluding comment, while the methodology used t h i s thesis i n no way purports to being the best or most e f f i c i e n t means by which to achieve forecasts f o r house prices in the subject communities, i t does break new ground by testing the v a l i d i t y of using t h i s p a r t i c u l a r approach to accomplish i t s stated objective. It i s hoped that others in the planning profession can both u t i l i z e and b u i l d upon the knowledge gained as a consequence of t h i s endeavour arid can as a r e s u l t develop more accurate house price forecasting models in the future. -98-BIBLIOGRAPHY Ascher, W. Forecasting: An Appraisal f o r Policy makers and Planners. John Hopkins University Press. Baltimore, 1978. Bowerman B, 0 Connell R. Forcasting and Time Series. Duxberry Press, Belmont C a l i f o r n i a , 1979. Brown. G. An Analysis of the University Housing Market. Faculty of Business Administration, University of B r i t i s h Columbia, 1968. Bureau of Economics and S t a t i s t i c s . Regional Index of B r i t i s h Columbia, Department of Industrial Development Trade and Commerce. V i c t o r i a , 1978. Bureau of Economics and S t a t i s t i c s . Summary of Economic A c t i v i t y in B r i t i s h Columbia. Department of Industrial Development Trade and Commerce. V i c t o r i a , 1964. Dienthey T., Madel J., Werthman, C. Planning and the Purchase Decision: Why People Buy in Planned Communities. Centre for Planning and Development Research. University of - C a l i f o r n i a . Berkely, 1975. Draper, N. and Smith H. Applied Regression Analysis. John Wiley and Sons Inc. New York, 1966, pg 59. Emerson J., Lampheas F., Urban and Regional Economics-Structure and Change. Allyn and Bacon Inc. ' Boston, 1975. Ezekiel, M. Fox, K. Methods of Correlation and Regression Analysis. John Wilby and Sons, New York 1959. pg 192. Government Information Services. B.C. Quick Facts Government of B r i t i s h Columbia. V i c t o r i a , 1982. Government of the Province of B r i t i s h Columbia. Summary of Economic A c t i v i t y in B r i t i s h Columbia. Department of Industrial Development Trade and Commerce. V i c t o r i a , 1970. -99-Greater Vancouver Regional D i s t r i c t . Lower Mainland O f f i c i a l Regional Plan Update Technical Memorandum No. 5 - Lower Mainland Economic Forecast 1976-86. Vancouver, 1977, pgs 3,4. Greater Vancouver Regional D i s t r i c t . The Regional Economy. A Summary Background Report f o r the Liveable Region 1976/1986. Vancouver, 1976. Pg 18. Greater Vancouver Real Estate Board. Real Estate Trends in Metropolitan Vancouver Vancouver. Issues 1960, 1962, 1966, 1968, 1972, 1973, 1974, 1976, 1977, 1978, 1980. Hebden, J . S t a t i s t i c s For Economists. P h i l i p Allan Publishers Limited, Deddington Oxford, Great B r i t a i n , 1981. Horwood, P. An Analysis of Factors a f f e c t i n g the Demand for Housing in B r i t i s h Columbia, U.B.C., 1976. Jancsek, J . Property Tax Assessment Applications of Multiple Regression Analysis in C a l i f o r n i a . Centre f o r Real Estate and Urban Economics. Inst i t u t e of Urban and Regional Development. University of C a l i f o r n i a Berkely, 1972. Kaiser, E. A Producers Model f o r Residential Growth: Analyzing and Predicting the Location of Residential Subdivision Centre f o r Urban and Regional Studies, I n s t i t u t e f or Research in Social Sciences, University of North Carolina. Chapel H i l l , 1968. Kane, E. Economic S t a t i s t i c s : Econometrics an Introduction to Quantitative Economics. Harper and Row Ltd. New York, Evanston and London, 1968, Pgs 44,331. Kenny, D. Correlation and Causality. Wiley-Interscience. New York, 1979. Kruerkeberg, D. S i l v e r s A., Urban Planning Analysis: Methods and Models. John Wilky and Sons. New York, Brisbane, Toronto, 1974. Pgs. 259-274. Lee, D. J r . Requiem For Large-Scale Models AIP Journal Vol. 39 No. 3, 1973, Pgs 163-178. -100-Lowry, Ira. A Short Course in Model Design, AIP Journal, Vol. 31, 1965. Pgs 158-166. Levenbach, H. Cleary J. The begining Forcaster, Lifetime Learning Publications, Belmont C a l i f o r n i a , 1981. Mak, E. Hastings Sunrise: community p r o f i l e . Vancouver City Planning Department, Vancouver, 1979. Mak, E. P u i l l e t . Oakridge Community P r o f i l e , City Planning Department, Vancouver, 1978. Muller, T. Economic Impacts of Land Development: Employment, Housing and Property Values. Urban In s t i t u t e . Washington D.C. 1976. Nowlan, D. The Fundamentals of Residential Land Price Determination. Centre f o r Urban and Community Studies. University of Toronto, 1978. Ministry of Economic Developement, B r i t i s h Columbia Regional Index 1978. Province of B r i t i s h Columbia, 1978. Pendleton, W. S t a t i s t i c a l Inference in Appraisal and Assessment Procedures, The Appraisal journal XXXII January, 1965 pgs 73-82. Renshaw, E. S c i e n t i f i c Appraisal. National Tax Journal XI (December, 1958), p. 314-316. Samuelsoh P. and Scott, A. Economics an Introductory Analysis. McGraw-Hill Company of Canada Limited. Toronto, 1980. pgs 226, 283. Sjoquist D., Schroeder L., Stephen P. Interpreting Regression Analysis: A Heurestic Approach. University Programs Modular Studies Morristown, New Jersey, 1974, pgs 1-42. Vancouver City Planning Commission, Goals f o r Vancouver, Vancouver, 1980 Vancouver City Planning Department. The F i r s t Shaughnessy Plan. Vancouver, 1981. -101-Vancouver City Planning Department. Understanding Vancouver 2. Vancouver, 1979. Vancouver City Planning Department, Vancouver, Local Areas, Vancouver, 1975. Weimer, A. Hoyt, H. Real Estate. The Ronald Press Company. New York, 1966. -102-APPENDIX A Q§§S£iption_and_Defenitiona_of The following descriptions and d e f i n i t i o n s were obtained through interviews with S t a t i s t i c s Canada personnel. lQdicatgrs_l2§ 1) Average Weekly Earnings - Construction Industry in B.C. 2) Average Weekly Earnings - Forestry Industry i n B.C. 3) Average Weekly Earnings - Manufacturing Industry in B.C. 4) Average Weekly Earnings - Mining Industry in B.C. 5) Average Weekly Earnings - Services Industry i n B.C. 6 ) Average Weekly Earnings - Trades Industry in B.C. A l l of the above information in each Industry i s obtained by surveying large firms with 20 or more employees every month whereupon t h e i r gross pay r o l l in the l a s t payperiod of the month i s ascertained. Earnings of a l l employees excluding casuals who work less than seven hours a week are considered. The basic calcuation i s : Grgss_Pay.rol 1_ = mean gross earnings per employee Number of Employees per week These "in d i c a t o r s " r e f l e c t measurement i n d o l l a r terms. Indicatgr_7_-_Retail_Sales_in Reta i l sales are calculated on the basis of receiving monthly sales information from a l l the chain stores registered in B.C. and on estimates of sales of independent stores based on a random 10% sample. -103-Thia " i n d i c a t o r " r e f l e c t s measurement in mi l l i o n s of d o l l a r s . I n d i c a t o r _ 8 n_Vancouver___CPI_Food 9 -Vancouyer_CPI_Clothing The Consumer Price Index for Food and Clothing measures the percentage change through time i n the cost of purchasing a constant "basket of food" or basket of clothing respectively. Both standards ( i e : baskets) are of an unchanging or equivalent quantity and quality consisting of items for which there are continually measurable market price over time. Changes in the costs of these baskets are therefore only due to pure price movement i . e . : i n f l a t i o n . It i s noteworthy that both the basket of food and the basket of clothing are weighted to r e f l e c t the buying practices of the average l o c a l c i t i z e n s . Measurements of these indicators r e f l e c t percentage change in the index. Indicator_lQ___U_____utos_En_ering_B_C_ This s t a t i s t i c i s calculated based on headcounts by customs o f f i c i a l s . In e f f e c t t h i s " i n d i c a t o r " acts as a proxy measure f o r Tourism in B.C. This indicator i s measured by thousands of Autos per year. -104-lD^i£§l:2^_ii_Z_yD§!BFJl9Zni§Dt_B§te_i ______ The unemployed includes those persons who during the reference week: (a) were without work, had a c t i v e l y looked for work i n the past four weeks, and were available for work. <b> had not a c t i v e l y looked for work i n the past four weeks but had been on layo f f f o r twenty-six weeks or less and were available f o r work. (c) had not a c t i v e l y looked f o r work i n the past four weeks but had a new job to s t a r t in four weeks or less from reference week, and were available f o r work. The unemployment rate i s the number of unemployed persons as a percent of the labour force, (the labour force i s composed of that portion of the c i v i l i a n n o n -institutional population 15 years of age and over who, during the reference week, were employed or unemployed.) This indicator i s measured in percentage terms and r e f l e c t s yearly change. Indicator _12_-_Pe_sonal_Incom_,__n_B_C_ The majority of t h i s data i s gathered from Tax Return information. The major components of t h i s indicator include wages and s a l a r i e s , m i l i t a r y pay and allowances, net income from non-farm unincorporated businesses, and net professional -105-income and accrued net income ( i . e . : investment income) This indicator i s measured in m i l l i o n s of d o l l a r s per year. Isdicator_13_2_Pogulation_of _B J LC i This information i s calculated based on the census information every f i v e years plus V i t a l S t a t i s t i c updates on births and deaths, immigration, and various proxy measures which estimate i n t e r p r o v i n c i a l population flows in noncensus years. Measurement i s r e f l e c t e d in terms of m i l l i o n s of people. Indicator_14_;_Value_of_Exporta_through_B iC i_Ports The export s t a t i s t i c s supplied are only f o r products shipped through B.C. ports i r r e s p e c t i v e of the province of o r i g i n . S t a t i s t i c s herein do not include exports of B.C. o r i g i n which leave Canada vi a customs ports i n other provinces. The c r i t e r i a f o r designations as a product exported through B.C. ports i s clearence at a Canadian custom port within the borders of B.C.. Customs ports are located at a i r p o r t s , sea ports and at U.S. border points, and at other sp e c i f i e d B.C. locations. Information from customs documents i s used to designate "the product" as having cleared. Measurement r e f l e c t s m i l l i o n s of d o l l a r s . -106-lQdicator_15_ z_GPP_of_B iC i This indicator measures the t o t a l product att r i b u t a b l e to B r i t i s h Columbia residents. It excludes output of non-resident working in B.C. but includes residents output outside the p r o v i n c i a l boundaries. Also excluded are debt service charges and income accruing to non-residents from t h e i r investments in B.C. while income accruing to residents of B.C. from investment in other countries and the rest of Canada i s included. Measurement r e f l e c t s m i l l i o n s of d o l l a r s . iDd i c a tor _l§_z_Con vent iona l_Mgrtgage_Rat.es Average l y r mortgage Rates charged by conventional lenders i . e . : banks and t r u s t companies. These rates represent mortgage loans which are not NHA (National Housing Act) insured. Measurement i s in percentage terms. •> Indicator_17_-_Chegues_Cashed_A 5_C_ S t a t i s t i c s contained under t h i s heading are r e s t r i c t e d to those d o l l a r amounts debited by the banks to deposit accounts of a l l personal and corporate customers either current or savings. The basic data i s c o l l e c t e d from the banks and supplied to S t a t i s t i c s Canada by the Canadian 1 -107-Bankers Association. Measurement r e f l e c t s b i l l i o n s of d o l l a r s per year. Indicator___________BuiIding Z_B§§iden_i_l A panel of representative manufacturers are surveyed once a month as to the cost of Building Materials. (The same data base of manufacturers are used to determine the non-residential index wherein adjustments re: the weighting of materials are made to r e f l e c t the differences in construction*practices.> Measurement r e f l e c t s percentage change from indexed value. Indie_tor_l___________ilding__a_er_ala_Pr_ce_I_de__ Z_N2Q_________i_l A panel of representative manufacturers are surveyed once a month as to the cost of Building Materials. Measurement r e f l e c t s % change from indexed value. -108-R P P E N D I X B AVERAGE WEEKLY WAGES AND SALARIES IN SELECTED INDUSTRIES OF BRITISH COLUMBIA M a n u - C o n - I n d u s t r i e Y e a r F o r e s t r y M i n i n g f a c t u r i n g s t r u c t i o n T r a d e S e r v i c e C o m p o s i te 1961 $ 96.33 $ 97.35 $ 88.84 $1.03.97 $ 70.06 $ 61.80 $ 84.99 1962 102.53 101.42 91.32 103.62 71.82 62,94 87.10 1963 105.38 103.43 94.70 108.54 74.24 64.59 90.10 1964 112.23 108.00 99-11 116.38 76.63 66.22 94.11 1965 123.48 120.05 105.09 130.66 79.87 71.24 100.71 1966 128.23 131.21 110.87 158.00 84.01 76.75 107.42 1967 139.06 143.00 119.69 166.43 88.57 78.61 114.50 1968 150.82 152.43 128.44 I62.il 96,63 83.02 1.20.76 1969 158.05 160.28 137.78 178.62 106.13 88.00 129.35 1970 ( e s t . ) 162.00 177.00 146.00 200.00 114.00 94.00 1.38.00 1971 178.03 190.93 162.67 224.68 123.06 102,eo 152.50 1972 196.76 206.00 178.81 246.71 132.36 109.56 165.08 1973 225.06 227.00 193.27 246.59 148.09 1 1 9 . 1 7 178.29 1974 247.48 262.28 217.70 282.75 167.14 132.75 200.55 1975 278.13 297.51 252.77 344.41 190.00 149.38 229.97 1976 327.38 330.66 288.34 378.23 212.20 169.32 259.52 1977 350.11 359.60 314.65 424.69 231.00 182.09 284.13 1978 382.21 3 8 3 . 4 1 339.66 476.66 236.08 189.21 301.26 1979 416.70 426.60 369.52 515.94 256.46 202.50 327.14 1980 479.70 4 8 4 . 3 6 411.90 546.96 285.31 225.15 363.51 Source: Employment and Average Weekly Wages and Salaries, Dominion Bureau of St a t i s t i c s , Ottawa. 1970 Estimates by the Economics and Stat i s t i c s Branch, V i c t o r i a . -109-APPENDIX CI RfiW DfiTft COR • • • • H 0 L T I n i F l F2 F3 F4 F5 F6 rt i.oqo 0.995 0.000 0.997 0.000 0.996 0.000 0.996 o;ooo 0.994 0.000 F2 0.993 0.000 1.000 0.999 0.999 0.000 0.999 0.000 0.997 0.000 0.996 O.OOO i T3 0.997 0.000 0.999 0.000 1.000 0.999 0.999 jO.000 0.999 0.000 0.998 0.000 r* 0.996 0.000 0.999 0.000 0.999 0.000 1.000 0.999 0.999 0.000 0.998 O.OOO ra 0.996 0.000 0.997 0.000 0.999 0.000 0.999 • 0.000 1.000 0.999 0.999 0.000 F6 0.994 0.000 0.996 0.000 0.998 0.000 0.998 0.000 0.999 0.000 1.000 0.999 FT 0.994 0.000 0.999 0.000 0.998 0.000 0.998 0.000 0.996 0.000 0.994 0.000 F8 0.992 0.000 0.998 0.000 0.996 0.000 0.998 .0.000 0.994 0.000 0.993 0.000 Ffl 0.990 0.000 0.995 0.000 0.994 0.000 0.994 0.000 0.990 0.000 0.989 0.000 no 0.690 0.001 0.670 0.002 0.674 0.002 0.696 0.001 0.689 0.001 0.692 0.001 F11 0.660 0.002 0.630 0.004 0.657 0.002 0.648 0.003 0.668 0.002 0.679 0.001 F12 0.995 0.000 0.999 0.000 0.999 0.000 0.998 0.000 0.997 0.000 0.996 0.000 F13 0.936 0.000 0.926 0.000 0.931 0.000 0.939 0.000 0.942 0.000 0.94S 0.000 F14 0.975 0.000 0.987 0.000 0.982 0.000 0.983 0.000 0.976 0.000 0.974 0.000 F1S 0.951 0.000 0.941 0.000 0.947 0.000 0.052 0.000 0.956 0.000 0.959 0.000 F16 0.874 O.OOO 0.883 0.000 0.884 • 0.000 0.897 0.000 0.894 0.000 0.900 0.000 F17 0.977 0.000 0.990 0.000 0.98S 0.000 0.986 0.000 0.980 0.000 0.978 0.000 F18 0.995 0.000 0.996 0.000 0.996 0.000 0.994 0.000 0.992 0.000 0.990 0.000 F18 0.994 0.000 0.897 O.OOO 0.997 0.000 0.996 0.000 0.994 0.000 0.992 0.000 01 0.958 0.000 0.978 0.000 0.972 0.000 0.975 0.000 0.971 0.000 0.970 0.000 D2 0.934 0.000 0.958 0.000 0.950 0.000 0.955 0.000 0.948 0.000 0.945 0.000 03 0.958 0.000 0.977 0.000 0.973 0.000 0.976 0.000 0.974 0.000 0.975 0.000 OH 0.954 0.000 0.975 0.000 0.969 0.000 0.972 0.000 0.967 o.ooo-0.967 0.000 D E L A T I O N M A T R I X . E 0 R E F7 $ S I 0 F8 N • • • FS F10 F11 F12 F13 0.994 0.000 0.992 0.000 0.990 0.000 0.690 0.001 0.660 0.002 0.995 0.000 0.93S o.ooc 0.999 0.000 0.993 0.000 0.995 0.000 0.670 0.002 0.630 0.004 0.999 0.000 0.926 0.000 0.998 0.000 0.998 0.000 0.994 0.000 0.674 0.002 0.657 0.002 0.999 0.000 0.931 O.OOO 0.998 0.000 0.998 0.000 0.994 0.000 0.696 0.001 0.64B 0.003 0.998 0.000 0.939 O.OOC 0.996 0.000 0.994 0.000 0.990 0.000 0.689 0.001 0.668 0.002 0.997 0.000 0.942 0.000 0.994 0.000 0.993 0.000 0.989 0.000 0.692 0.001 0.679 0.001 0.996 0.000 0.945 0.000 1.000 0.999 0.998 0.000 0.996 0.000 0.678 0.001 0.619 0.005 0.999 0.000 0.927 0.000 0.99B 0.000 1.000 0.999 0.994 0.000 0.691 0.001 0.615 0.009 0.997 0.000 0.929 0.000 0.996 0.000 0.994 0.000 1.000 0.999 0.630 0.004 0.C09 0.006 0.997 0.000 0.904 0.000 0.678 0.001 0.691 0.001 0.630 0.004 1.000 0.999 0.546 0.016 0.661 0.002 0.869 0.000 0.619 0.005 0 815 0.005 a. cos 0.006 0.5*6 O.O16 1.000 0.999 0.636 0.003 0.702 0.001 0.999 0.000 0.997 0.000 0.997 0.000 0.661 0.002 0.636 . 0.003 1.000 0.999 0.923 0.000 0.927 0.000 0.929 0.000 0.904 0.000 0.869 0.000 0.702 0.001 0.923 0.000 1.000 0.999 0.930 0.000 0.989 0.000 0.993 0.000 0.611 0.009 0.851 0.015 0.989 0.000 0.875 0.000 0.943 0.000 0.940 0.000 0.921 0.000 0.839 0.000 0.711 0.001 0.940 0.000 0.996 0.000 0.880 0.000 0.900 0.000 0.868 0.000 0.798 0.000 0.668 0.002 0.876 0.000 0.916 0.000 0.990 0.000 0.992 0.000 0.993 0.000 0.618 0.005 0.566 0.012 0.989 0.000 0.880 o.ooo 0.896 0.000 0.994 0.000 0.994 0.000 0.657 0.002 0.609 0.006 0.996 0.000 0.916 0.000 0.897 0.000 0.996 0.000 0.998 0.000 0.635 0.003 0.616 0.005 0.998 0.000 0.90B 0.000 0.977 0.000 0.980 0.000 0.975 0.000 0.640 0.003 0.980 0.009 0.975 0.000 0.888 0.000 0.960 0.000 0.964 0.000 0.9S8 0.000 0.627 0.004 6.530 0.020 0.955 0.000 0.856 0.000 0.977 0.000 0.976 0.000 0.870 0.000 0.664 OjOOi 0.607 0.006 0.976 0.000 0.9M 0.000 0.975 0.000 0.977 0.000 0.972 0.000 0 642. 0.003 6.673 0.010 0.973 0.003 0.885 0.000 -110-flPPENDIX CI CONT. F 1 4 F 1 5 F 1 6 F 1 7 Fl 0 . 9 7 5 0 . 9 5 1 0 . 8 7 4 0 . 9 7 7 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 O.OOO F 2 0 . 9 8 7 0 . 9 4 1 0 . 8 8 3 0 . 9 9 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 F 3 0 . 9 8 2 0 . 9 4 7 0 . 8 8 4 0 . 9 8 5 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 F 4 0 . 9 8 3 0 . 9 5 2 0 . 8 9 7 0 . 9 8 6 O.OOO 0 . ooo 0 . .OOO O.OOO F S 0 . 9 7 6 0. 9 5 6 0. . 8 9 4 0 . 9 8 0 O.OOO 0 . 0 0 0 0 OOO 0 . 0 0 0 F E 0 . 9 7 4 0 . 9 5 9 0. . 9 0 0 0 . 9 7 8 0 . 0 0 0 0. 0 0 0 0. . 0 0 0 O.OOO F 7 0 . 9 9 0 0. 9 4 3 0 . 8 8 0 0 . 9 9 0 O.OOO 0 . OOO o. . 0 0 0 O.OOO F 8 0 . 9 8 9 0 . 9 4 0 0. . 9 0 0 0 . 9 9 2 0 . 0 0 0 0 . 0 0 0 0 . . 0 0 0 O.OOO F 9 0 . 9 9 3 0 . 9 2 1 0. . 8 6 8 0 . 9 9 3 0 . 0 0 0 0 . 0 0 0 0. 0 0 0 0 . 0 0 0 F 1 0 0 . 6 1 1 o. 8 3 9 0. . 7 9 8 0 . 6 1 8 ( 0 . 0 0 5 0 . 0 0 0 0 . 0 0 0 0 . 0 0 5 F 1 1 0 . 5 5 1 0 . 7 1 1 0. 6 6 8 0 . 5 6 6 0 . 0 1 5 0 . 0 0 1 0 . 0 0 2 0 . 0 1 2 F 1 2 . 0 . 9 8 9 0 . 9 4 0 0 . 8 7 6 0 .989* 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 F 1 3 0 . 8 7 5 0 . 9 9 6 0 . . 9 1 6 0 . 8 8 0 0 . 0 0 0 0 . OOO 0. 0 0 0 0 . 0 0 0 F 1 4 1 . 0 0 0 0 . 8 9 4 0. 8 4 9 0 . 9 9 6 0 . S 9 9 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 F I 5 0 . 8 9 4 1. 0 0 0 0. 8 9 7 0 . 8 9 5 o.ooo 0 . 9 9 9 0. 0 0 0 O.OOO F 1 G 0 . 8 4 9 0. 8 9 7 1 . 0 0 0 0 . 8 7 5 0 . 0 0 0 0 . 0 0 0 0 . 9 9 9 O.OOO F 1 7 0 . 9 9 6 0. 8 9 5 0, . 8 7 5 1 .OOO O.OOO 0. OOO 0. . 0 0 0 0 . 9 9 9 f 18 0 . 9 8 6 0. 9 3 3 0. . 8 5 7 0 . 9 8 4 0 . 0 0 0 0 . 0 0 0 0 . . 0 0 0 0 . 0 0 0 F 1 S 0 . 9 9 0 0 . 9 2 4 0 . 8 7 1 0 . 9 9 2 O.OOO 0. 0 0 0 0. OOO 0 . 0 0 0 0 1 0 . 9 7 6 0. 8 9 9 0 . , 8 9 8 6 . 9 8 9 O.COO 0 . OOO 0 . OOO C.OuO 0 2 0 . 9 6 7 0 . 8 6 6 0. 8 8 9 0 . 9 8 1 0 . 0 0 0 0 . 0 0 0 0. , 0 0 0 O.OOO D 3 0 . 9 6 9 0 . 9 2 5 0 . 8 9 2 0 . 9 7 7 0 . 0 0 0 0. 0 0 0 0. 0 0 0 0 . 0 0 0 DM 0 . 9 7 5 0 . 8 9 7 0 . , 8 9 7 0 . 9 8 7 0 . 0 0 0 0 . OOO o. , 0 0 0 0 . 0 0 0 U L T I P I E H E 0 R E S S I 0 N • • * • Ft8 F 1 8 0 1 D2 D3 DM 0 . 9 9 5 0.000 0 . 9 9 4 0 . 0 0 0 0 . 9 5 8 0 . 0 0 0 0 . 8 3 4 O . O O O 0 . 9 5 9 O . O O O 0 . 9 5 4 0 . 0 0 0 0 . 9 9 6 0.000 0 . 9 9 7 0 . 0 0 0 0 . 9 7 8 0 . 0 0 0 0 . 9 5 8 0 . 0 0 0 0 . 9 7 7 0 . 0 0 0 0 . 9 7 5 0 . 0 0 0 0 . 9 9 6 O . O O O 0 . 8 9 7 0 . 0 0 0 0 . 9 7 2 0 . 0 0 0 0 . 9 5 0 0 . 0 0 0 0 . 9 7 3 O . O O O 0 . 9 6 9 0 . 0 0 0 0 . 9 9 4 O . O O O 0 . 9 9 6 0 . 0 0 0 0 . 9 7 5 0 . 0 0 0 0 . 9 5 5 O . O O O 0 . 9 7 6 0 . 0 0 0 0 . 9 7 2 0 . 0 0 0 0 . 9 9 2 O . O O O 0 . 9 9 4 0 . 0 0 0 0 . 9 7 1 0 . 0 0 0 0 . 9 4 6 0 . 0 0 0 0 . 9 7 4 0 . 0 0 0 0 . 9 6 7 0 . 0 0 0 0 . 9 9 0 0.000 0 . 9 9 2 0 . 0 0 0 0 . 9 7 0 0 . 0 0 0 0 . 9 4 5 O . O O O 0 . 9 7 5 0 . 0 0 0 0 . 9 6 7 0 . 0 0 0 0 . 9 9 6 O . O O O 0 . 9 9 7 0 . 0 0 0 0 . 9 7 7 O . O O O 0 . 9 6 0 0 . 0 0 0 0 . 9 7 7 O . O O O 0 . 9 7 5 0 . 0 0 0 0 . 9 9 4 0 . 0 0 0 0 . 9 9 6 0 . 0 0 0 0 . 9 8 0 0 . 0 0 0 0 . 9 6 4 0 . 0 0 0 0 . 9 7 6 0 . 0 0 0 0 . 9 7 7 0 . 0 0 0 0 . 9 9 4 0 . 0 0 0 0 . 9 9 8 0 . 0 0 0 0 . 9 7 5 0 . 0 0 0 0 . 9 5 8 0 . 0 0 0 0 . 9 7 0 0 . 0 0 0 0 . 9 7 2 0 . 0 0 0 0 . 6 5 7 0 . 0 0 2 0 . 6 3 5 0 . 0 0 3 0 . 6 4 0 0 . 0 0 3 0 . 6 2 7 0 . 0 ^ 4 0 . 6 6 4 0 . 0 0 2 0 . 6 4 2 0 . 0 0 3 0 . 6 0 9 0 . O O 6 0 . 6 1 6 0 . 0 0 5 0 . 5 8 0 0 . 0 0 9 0 . 5 3 0 0 . 0 2 0 0 . 6 0 7 0 . 0 0 6 0 . 5 7 3 0 . 0 1 0 0 . 9 9 6 O . O O O 0 . 9 9 8 0 . 0 0 0 0 . 9 7 5 . 0 . 0 0 0 0 . 9 5 5 O . O O O 0 . 9 7 6 0 . 0 0 0 0 . 9 7 3 0 . 0 0 0 0 . 9 1 6 0 . 0 0 0 0 . 908 0 . 0 0 0 0.888 0 . 0 0 0 0 . 8 5 6 0 . 0 0 0 0.911 0 . 0 0 0 0 . 8 8 5 O O O O 0 . 9 8 6 0 . 0 0 0 0 . 9 9 0 0 . 0 0 0 , 0 . 9 7 6 0 . 0 0 0 0 . 9 6 7 0 . 0 0 0 0 . 9 6 9 O . O O O 6 .975 0 . 0 0 0 0 . 9 3 3 O . O O O 0 . 9 2 4 0 . 0 0 0 0 . 8 9 9 0 . 0 0 0 0.866 O . O O O 0 . 9 2 5 0 . 0 0 0 0 . 8 9 7 0 . 0 0 0 0 . 8 5 7 O . O O O 0 . B 7 1 0 . 0 0 0 0 . 8 9 8 O . O O O 0 . 8 8 9 O . O O O 0 . 8 9 2 0 . 0 0 0 0 . 8 9 7 0 . 0 0 0 0 . 9 8 4 0 . 0 0 0 0 . 9 S 2 O . O O O 0 . 0 8 8 " © • . 0 0 0 0 . 9 8 1 0 JPOO 0 . 9 7 7 0 . 0 0 0 , 0 . 9 3 7 0 . 0 0 0 1 . 000 0.899 0 . 9 9 7 0 . 0 0 0 0 . 9 6 0 0 . 0 0 0 0 . 9 3 8 0 . 0 0 0 0 . 9 5 9 O . O O O 0 . 9 5 6 0 . 0 0 0 0 . 9 9 7 0 . 0 0 0 1 .000 0.999 0 . 8 7 3 0 . 0 0 0 0 . 9 5 4 0 . 0 0 0 0 . 9 6 8 O . O O O 0 . 9 S 9 0 . 0 0 0 0 . 9 6 0 O . O O O 0 . 8 7 3 0 . 0 0 0 1 . 0 0 0 0.999 0 . 9 3 5 o.ooo 0 . 9 9 2 O . O O O 1 . O O O 0 . 0 0 0 0 . 9 3 8 O . O O O 0 . 9 5 4 O . O O O 0.995 0 . 0 0 0 1 . 0 0 0 0.999 0 . 9 8 1 O . O O O 0 . 9 S 6 0 . 0 0 0 0.959 0 . 0 0 0 0.868 0 . 0 0 0 0 . 8 9 2 O . O O O 0 . 9 8 1 0 . 0 0 0 1 . 0 0 0 0.999 0.993 0 . 0 0 0 0 . 9 5 6 0 . 0 0 0 0.969 0 . 0 0 0 1 . 0 0 0 0 . 0 0 0 0.996 0 . 0 0 0 0 . 9 9 3 0 . 0 0 0 1 . 0 0 0 0.999 -111-APPENDIX CS LOGGED REGRESSION CORRELATION MATRIX • • • • . M U L T I P L E F21 F31 F41 F51 F61 F21 1.000 0.899 0.997 0.000 0.997 O.OOO 0.99S 0.000 0.992 O.OOO F31 0.997 O.OwO I.OOO 0.999 0.999 0 . 0 0.839 0.0 0.998 O.OOO F41 0.997 0.000 0.999 0.0 1.000 0.999 0.999 0.000 0 . 8 9 8 0.0 F51 0.995 0.000 0.999 0.0 0.999 O.OOO 1.000 0.999 0.899 O.O ret 0.992 0.000 0.998 0.000 0.998 0 . 0 0.999 0 . 0 1.000 0.999 F71 0.993 0.000 0.998 0.000 0.998 0 . 0 0.996 0.000 0.995 0.000 . F81 0.996 0.000 0.997 0.000 0.999 0.000 0.996 0.000 0.996 0.000 F31 0.989 0.000 0.993 0-000 0.992 O.OOO 0.989 0.000 0.988 O.OOO F101 0.647 0.004 0.629 0.005 0.657 0.003 0.647 0.004 0.651 0.003 F i l l 0.741 O.OOO 0.750 O.OOO 0.747 0.000 6.757 0.000 0.766 0.000 F121 0.995 0.000 0.999 0.0 0.998 0.000 0.997 0.000 0.996 0.000 F131 0.932 0.000 0.931 0.000 0.944 O.OOO 0.942 0.000 0.944 0.000 F141 0.979 0.000 0.983 0.000 0.982 O.OOO 0.976 0.000 0.975 O.OOO F151 0.951 O.COO 0.952 0.000 0.862 0.000 0.961 0.000 0.963 0.000 F161 0.832 0,000 0.840 O.OOO case O.OOO O.B57 0.000 O.B66 0.000 F171 0.990 0.000 0.994 0.000 0.992 0.000 0.990 0.000 0.989 O.OOO F181 0.994 0.000 0.994 0.000 0.993 0.000 0.990 0.000 0.987 0.000 F191 0.994 0.000 0.996 0.000 0.994 0.000 0.993 0.000 0.991 0.000 • E G R E S S I O N » « . . F71 FBI F91 F101 F i l l F121 F131 0.995 0.000 0.996 0.000 0.989 0.000 0.647 0.004 0.741 0.000 0.993 0.000 0.93? 0.000 0.998 0.000 0.997 O.OOO 0.993 0.000 0.629 0.005 0.750 0.000 0.899 0.0 0.931 O.OOC 0.998 0.0 0.999 O.OOO 0.992 0.000 0.657 0.003 0.747 0.000 0.998 0.000 0.944 0.000 0.996 0.000 0.996 0.000 0.989 0.000 0.647 0.004 0.757 0.000 0.997 0.000 0.942 O.COO 0.995 0.000 0.996 0.000 6.988 0.000 0.651 0.003 0.766 0.000 0.996 0.000 0.844 0.000 1.C00 0.999 0.998 0.000 0.995 0.000 0.636 0.003 0.722 0.001 0.999 0.000 0.933 O.OOC 0.998 0.000 \ 1.000 0.999 0.993 0.000 0.655 0.003 0.728 0.001 0.997 0.000 0.941 O.OOC 0.995 0.000 0.993 0.000 1.000 0.893 0.576 0.012 0.709 0.001 0.996 0.000 0.903 O.OOC 0.636 O.O05 0.655 O.0O3 0.576 0.012 1.000 0.999 0.568 0.014 0.614 0.007 0.854 0.000 0.722 0.001 0.728 0.001 0.709 0.001 0.568 0.014 1.000 0.999 0.733 0.001 0.745 O.OOC 0.999 0.000 0.S97 0.000 0.996 0.000 0.614 0.007 0.733 0.001 1.000 0.999 0.924 O.OOO 0.933 0.000 0.941 0.000 0.903 0.000 0.854 0.000 0.743 0.000 0.924 0.000 1.000 0.999 0.889 0.000 0.984 0.000 0.994 0.000 0.556 0.017 0.671 0.002 O.S89 0.000 0.882 0.000 0.954 0.000 0.957 0.000 0.927 O.OOO 0.819 0.000 0.753 0.000 0.947 0.000 O.S96 0.000 0.828 0.000 0.854 0.000 0.811 0.000 0.790 0.000 0.791 0.000 6.026 0.000 0.923 0.000 0.995 0.000 0.993 0.000 0.998 0.0 0.571 0.013 0.712 O.OOt 0.997 0.000 0.901 0.000 0.996 0.000 0.995 0.000 0.993 0.000 0.609 0.007 0.691 0.001 0.993 0.000 0.911 0.000 0.99S O.OOO 0.995 0.000 0.998 0.000 0.582 0.011 0.712 0.001 0.997 0.000 0.906 O.OOC -112-flPPENDIX C 2 CONT. • • • * M U L T I P L E R E G R E S S I O N . » • » F141 F151 F161 F171 F181 F191 F21 0.979 0.000 0.951 0 .000 0.832 0.000 0.990 0.000 0.994 0.000 0.994 0.000 F24 0.985 0.000 0.951 0 .000 0.834 0 .000 0.995 0.000 0.S96 0.000 0.996 0.000 F31 0.983 0.000 0.952 0 .000 0 .840 0 .000 0.994 0.000 0.994 0.000 0.996 0.000 F4 1 0.982 O.C?0 0.962 0 .000 0.856 0.000 0.992 0.000 0.993 0.000 0.994 0.000 F51 0.976 ' 0 .000 0.961 0.000 0.8S7 0 .000 0.990 0.000 0.990 0.000 0.993 0.000 F61 0.975 0 .000 0.963 0 .000 0.866 0.000 0.989 0.000 0.987 0.000 0.991 0.000 F71 0.989 0.000 , 0.954 0 .000 0.828 0 .000 0.995 0.000 0.996 0.000 0.996 0.000 F81 0.984 0.000 0.957 0.000 0.854 0.000 0.993 0.000 0.995 0.000 0.995 0.000 F91 0.994 0.000 0.927 0 .000 0.811 0.000 0.998 0 . 0 0.993 0.000 0.998 0.000 F101 0.556 0.017 0.819 0.000 0.790 0.000 0.571 0.013 0.609 0.007 0.582 0.011 F i l l 0.671 0.002 0.753 0.000 0.791 0.000 0.712 0.001 0.691 0.001 0.712 0.001 F121 0.989 0.000 0.947 0 .000 0.826 0.000 0.997 0.000 0.995 0.000 0.997 0.000 F131 0.882 0.000 0.996 0 .000 . 0 .923 0 .000 0.901 0.000 0.911 0.000 0.906 0.000 F141 1.000 0.999 0.910 0 .000 0.774 • O.OOO 0.994 0.000 0.990 0.000 0.991 0.000 F151 0 .910 0.000 1.000 0.999 O.901 0 .000 0.925 0.000 0.934 0.000 0.929 0.000 F161 0.774 0.000 0.901 0 .000 1.000 0.999 0.813 0.000 0.805 0.000 0.818 0.000 F171 0.994 O.OOO 0.925 O.OOO 0.813 O.OOO 1.000 0.999 0.994 0.000 0.999 0 .0 F181 0 .990 0.000 0.934 0.000 0.805 O.OOO 0.994 0.000 1.000 0.999 0.996 0.000 F191 0.991 0.000 0.929 0 .000 0.818 0.000 0.999 0 . 0 0.996 0.000 1.000 0.999 J -113-APPENDIX D A: lh___egressign_Egua_ion The functional r e l a t i o n s h i p of the multiple regression r e l a t i o n s h i p can be described as y = f (x, ,x £,x, . . . . x„ e) where 'y' i s the dependent variable, xt,xx,xz ... x„ are the explanatory independent variables and 'e' i s the error term. Assuming that the data points l i e around a s t r a i g h t l i n e the r e l a t i o n s h i p takes the form y=a,+b, x, *b,xt+ b nx„+e where 'a' and 'b' are the unknown parameters to be estimated. It i s because a l l the ' values of y when plotted against the corresponding values of x do i n f a c t not f a l l p r ecisely on a s t r a i g h t l i n e , that regression analysis i s termed "the best s t r a i g h t l i n e approximation of the r e l a t i o n s h i p between the dependent and' independent variables". (Sjoquist et a l . 1974,8). B. The__ethgd_gf_Least_Sguares i The method of least squares i s a computational procedure used to calculate estimates of the parameters of the regression equations ( i . e . : model) based on the minimization of the sum of the squares of the residuals. (The residuals are deviations of the calculated y's ( i . e . y ) from the actual sample value of y.) It i s the property of the least squares estimates which provides the best estimates of the regression -114-c o e f f i c i e n t s , a and b. Once estimates of the parameters In the sample have been obtained as indicated above i t i s appropriate to test whether or not these estimates hold for the population as a. whole. A n u l l hypothesis i s formulated stating that the regression i s of no use and y's v a r i a t i o n from y ( i . e . : the f i t of the predicted to the observed values) i s e n t i r e l y due to a random component and not to any systematic l i n k with the regressor bx. C: Stand_________________ This i s a measure of how s e n s i t i v e the estimate of the parameter i s to chages in a few observations (Syoquist et a l . 1974). A high degree of error detracts from the c r e d i b i l i t y of the estimate and reduces confidence that b,is not equal to zero. D: C o r r e l a t i o n C o e f f i c i e n t This s t a t i s t i c designated as r measures the degree of association between two variables. Variables may be correlated i f (1) each variable a f f e c t s the other in the same way (2) two variables are both related to a t h i r d (3) by coincidence. (Ibid p. 19). (4) one variable i s causally related to the other. (Ibid, 19) -115-E: Coeffic_en__of_Deter_inis_ This c o e f f i c i e n t measures the combined closeness of the r e l a t i o n s h i p between the independent and dependent variables. In other words t h i s c o e f f i c i e n t measures how well an estimated regression l i n e f i t s the data points. The equation which r e f l e c t s t h i s r e l a t i o n s h i p i s z R = Sum_of_Sguares_due_to__egression z Total Sum of Squares due to "residual & regression" R as an indicator of the regression r e s u l t should always be considered in l i g h t of the following caveats: j <1) that additional variables w i l l never decrease the R value even though t h e i r variations may not contribute to the equations. (2) that variables can be added which w i l l s i g n i f i c a n t l y r a i s e the value of the R without increasing any th e o r e t i c a l knowledge. <3)_that d i f f e r e n t data forms tend to produce d i f f e r e n t R s t a t i s t i c s i . e . , time ser i e s data as i n t h i s study, often produces higher R values than cross-sectional data which tend to have a higher v a r i a t i o n in the variables due to less aggregation. In both cases the c o e f f i c i e n t s may be s i g n i f i c a n t l y d i f f e r e n t from 0 and a simple examination of the R s t a t i s t i c may be misleading. F: The_Partial_Correlation_Coefficient N This s t a t i s t i c measures the c o r r e l a t i o n between the dependent variable and each one of the independent variables in the regression equation while at the same time eliminating any l i n e a r tendency of the remaining independent variables to observe that r e l a t i o n s h i p . (Ezekiel and Fox, 192) -116-G: The_T-ratio To make inferences about the population parameter i t i s necessary to know how close the parameter i s to the estimate. It i s possible with the t - r a t i o to make statements about the p r o b a b i l i t y of obtaining an estimate with a given degree of closeness in l i e u of knowledge of the value of the populations parameter. In e f f e c t the t - r a t i o i s required to test the n u l l hypothesis that b=0. This r a t i o i s compared to an appropriate t - s t a t i s t i c . The rule of thumb i s : "Reject the n u l l hypothesis that b i s equal to zero in favour of the a l t e r n a t i v e hypothesis that b i a not equal to zero i f the t - r a t i o i s greater than 2 provided the degrees of freedom are 60 or more and the desired l e v e l of confidence i s 95 or l e s s . (Sjoquist et a l , 1974. p. 17) H: F - s t a t i s t i c The F s t a t i s t i c i s a t e s t s i m i l a r to that of the t s t a t i s t i c but whereas the t - s t a t i s t i c t e s t the hypothesis that an individual c o e f f i c i e n t d i f f e r s from 0, the F s t a t i s t i c allows the t e s t i n g of simultaneous e f f e c t s of a l l the c o e f f i c i e n t s . The " F - r a t i o " i s compared to the " F - s t a t i s t i c found i n a table in most s t a t i s t i c a l reference books. If the F-ratio i s higher than the F - s t a t i s t i c i t i s possible at a s p e c i f i e d l e v e l of s i g n i f i c a n c e to r e j e c t the n u l l hypothesis that the regreesion c b e s f f i c i e n t s are not equal to 0. -117-I: Log_stics_gf___e_comB__er__r_n__Ou_ The SPSS computer package selcted u t i l i z e d a "forward stepwise procedure by which to chose the independent variables which are the most s i g n i f i c a n t in explaining the v a r i a t i o n in the dependent variables. L o g i s i t i c a l l y when a new variable i s entered into the regression equation the " p a r t i a l F's" ( p a r t i a l c o r r e l a t i o n with dependent variable) of a l l variables previously entered are examined. If any of the p a r t i a l F's of those previously entered variables have become i n s i g n i f i c a n t r e l a t i v e to the pre-set s i g n i f i c a n c e l e v e l , that variable i s deleted from the equation. This computation provides judgement as to the contribution made by each variable as though i t had been the most recent variable entered into the equation i r r e s p e c t i v e of i t s actual point of entry. The computation continues u n t i l no more variables are s i g n i f i c a n t enough to enter the equation. At each step the computer z calculates the Standard Errors of the c o e f f i c i e n t s , R values and other relevant s t a t i s t i c s . It i s noteworthy that the SPSS computer package was chosen fo r use in t h i s thesis primarily for the following reasons: (1) It i s one of the most widely used and well maintained computer packages available for Multiple Linear -118-Regresaion Analysis. (2) It i s easy to use. (3) It has a powerful data manipulation language. The "Forward Stepwise Option" associated with t h i s package was selected on the basis that i t i s more economical of computer f a c i l i t i e s than i s the "Backward Elimination Procedure", ( i . e . , the other basic option available under SPSS) More s p e c i f i c a l l y the forward stepwise procedure avoids working with more x's than necessary while improving the equation at every stage" (Draper and Smith, 1966, 165). 

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