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Housing price indicies Subocz, Irene Ursula 1977

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HOUSING PRICE INDICIES by IRENE URSULA SUBOCZ Honours B.A., University of Western Ontario, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF ..THE REQUIREMENTS. FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) i n THE FACULTY OF COMMERCE & BUSINESS ADMINISTRATION We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 7 7 (^cT) I r e n e Ursula Subocz, 1977 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le f o r reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my writ ten permission. Department o t ^ o ^ r n i ^ c - L ° - / ^ ^ L^XX^TU^--> /bC^>\^<.MSM^-*J£<-£-^-( . The Univers i ty of B r i t i s h Columbia 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V 6 T 1W5 Date ( i i ) ABSTRACT The trend i n house prices i s of importance to govern-ments, f i n a n c i a l i n s t i t u t i o n s and households. However, currently no proven r e l i a b l e i n d i c a t o r of house prices e x i s t s . The lack of an accurate house price series i s due to two major f a c t o r s . F i r s t convenient and accurate data on house prices are not r e a d i l y a v a i l a b l e and data c o l l e c t i o n from the Land Registry Office i s both time consuming and c o s t l y . The second factor r e l a t e s to the problem of changes i n the q u a l i t y of the series through time. This q u a l i t y problem has two basic aspects. F i r s t , the q u a l i t y of the index may be influenced by s h i f t s i n the d i s t r i b u t i o n of sales between d i f f e r e n t values of homes. The second problem a r i s e s from the unique nature of r e a l estate as to i t s * location, age, condition, etc. Unlike other indices, there i s no standardized unit of housing to which price quotations may, be reduced, thus the q u a l i t y of the housing sold i n each year w i l l be d i f f e r e n t . In t h i s study, the problems encountered i n sampling and constructing a p r i c e index f o r the single family housing stock are i d e n t i f i e d and analyzed both conceptually and empirically. The conceptual examination involves a review of the l i t e r a t u r e as well as an analysis of the methodologies employed i n the con-str u c t i o n of the major housing i n d i c i e s i n use today. The empirical analysis i s done through the construction of a price series f o r the eight r a p i d l y growing c i t i e s and municipalities of the Greater Vancouver Regional D i s t r i c t f o r the years 194-9 to 19?6. The i n d i c i e s are based upon data obtained from the Land ( i i i ) Registry Offices i n B r i t i s h Columbia and are designed to be s t a t i s t i c a l l y representative of a l l sales f o r those areas during the study period. The analysis forms a basis f o r future research into housing i n d i c i e s and i n p a r t i c u l a r , provides a r e l i a b l e bench-mark series against which alt e r n a t i v e measures of price changes can be tested. TABLE OF CONTENTS Chapter 1 THE NEED FOR A HOUSING PRICE INDEX A. INTRODUCTION B. THE NEED FOR A HOUSING PRICE INDEX Chapter 2 EXISTING RESEARCH AND INDICIES A. PREVIOUS STUDIES B. PRESENT PUBLISHED DATA 1. S t a t i s t i c s Canada - Shelter Component of CPI 2. S t a t i s t i c s Canada - New House Prices 3 . C. M. H. C. k-. Multiple L i s t i n g s Service 5. TEELA 6. Other Indicies Chapter 3 STATISTICAL AND CONCEPTUAL PROBLEMS A. STATISTICAL PROBLEMS. 1. Sampling Procedure 2. Additions to the Stock 3 . Demolitions k. Sampling Over Geographic Areas 5. Sampling Within A Geographical Area 6. Seasonal V a r i a t i o n ?. Base Period 8. Tenure Type 9 . Treatment of "New Products" B. CONCEPTUAL PROBLEMS Chapter k- THE DATA BASE AND INDEX A. SAMPLING PROCEDURE 1. The Data Base 2. Selection of the Universe 3 . Sample Size 4. Data C o l l e c t i o n and E d i t i n g 5. Demolitions B. COMPUTATION OF THE INDEX C. TURNOVER RATES D. AGREEMENTS FOR SALE Chapter 5 THE PROBLEM OF QUALITY CHANGE IN A HOUSE PRICE INDEX A. PRICE CHANGES BY VALUE RANGE -STATISTICAL IMPLICATIONS FOR THE INDEX (v) TABLE OF CONTENTS, Cont'd Chapter 5 B. VALUE RANGE - CONCEPTUAL . . CONSIDERATIONS 79 C. AGE CATEGORIES - CONCEPTUAL CONSIDERATIONS 82 D. VALUE RANGE AND VINTAGE CATEGORY 92 E. BAILEY, MUTH & NOURSE MODEL 93 Chapter 6 CONCLUSION 96 References Appendix A Appendix B Appendix C L i s t of Tables L i s t of Figures Acknowledgements SAMPLING PROCEDURE DERIVATION OF SAMPLE SIZE AND INDICIES THE DATA .(iv) ,(v) ,(vi) ,105 ,110 ,114-,116 ( v i ) LIST OF TABLES Table I Comparison of E x i s t i n g Price Data ...... 26 Table II Example of S h i f t i n g Sales E f f e c t s on the Price Index ...... 4-0 Table III Source and Size of the Sample 4-7 Table IV Sample Size By Year 51 Table V The Price Index and Turnover Rates 1 9 4 9 - 1 9 7 6 53 Table VI Agreements For Sale ...... 62 Table VII C r i t i c a l Prices For Assignment To Value Classes 68 Table VIII D i s t r i b u t i o n of Sales Among Value Ranges By Year 72 Table IX Percentage of Homes Transacting Each Year By Value Range 77 Table X Weighting Factors For Age Aggregated Indicies 89 Table XI Rates of Change In Prices For MLS Index and LRO Index 99 , LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure k Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 House Price Index - Current and Constant Dollars Turnover Rates f o r Housing and the Price Index A Comparison of Price Indicies Using Total and Agreement For Sale Data Only A Comparison of the Overall Price Index to Index Excluding Agreement For Sale Data Price Indicies By Value Range Price Indicies By Cumulative Value Ranges - Low and Low-Middle Value Ranges Price Indicies By Cumulative Value Ranges - Low-Middle and To t a l Value Ranges A Comparison of the Weighted Value Range Index to the Overall Price Index Price Indicies By Age Category Age-Weighted Price Indicies A Comparison of the Age-Weighted Index to the Overall Price Index Appreciation of the Housing Stock 1 9 7 5 A Comparison of the B-M-N Model Index to LRO Index Comparison of the MLS Index to the Overall Price Index Comparison of New House Price Index to Overall Index ( v i i i ) ACKNOWLEDGEMENTS I n t h e c o u r s e o f t h e p r e p a r a t i o n o f t h i s t h e s i s , t h e a u t h o r r e c e i v e d v a l u a b l e a s s i s t a n c e f r o m many i n d i v i d u a l s . D r . S.W. H a m i l t o n , who was t h e c h a i r m a n o f t h e t h e s i s c o m m i t t e e , gave much o f h i s v a l u a b l e t i m e i n p r o v i d i n g g u i d a n c e , e n c o u r a g e m e n t a n d a d v i c e . S p e c i a l t h a n k s a r e a l s o e x t e n d e d t o Dr. R. Z e r b s t and D r . K. H o r n , t h e o t h e r members o f t h e t h e s i s c o m m i t t e e . I n a d d i t i o n , t h e a s s i s t a n c e o f P r o f . D. B a x t e r f o r h i s comments i n t h e d e v e l o p m e n t o f t h e t h e s i s , d e s e r v e s p e c i a l m e n t i o n . The a s s i s t a n c e and c o - o p e r a t i o n r e c e i v e d f r o m t h e s t a f f o f t h e L a n d R e g i s t r y O f f i c e s i n t h e G r e a t e r V a n c o u v e r R e g i o n a l D i s t r i c t were f u n d a m e n t a l i n a s s i s t i n g i n p r o v i d i n g much o f t h e d a t a i n c o r p o r a t e d i n t o t h i s t h e s i s . I n a d d i t i o n , t h e a s s i s t a n c e f r o m D a v i d D a l e J o h n s o n , Graeme E a d i e , R i c h a r d M i l l e r and E l e a n o r O l s e n i n a i d i n g i n t h e c o l l e c t i o n o f d a t a and A . L . A n a n t h a n a r a y a n a n , i n t h e p r o g r a m m i n g o f t h e d a t a a r e g r a t e f u l l y a c k n o w l e d g e d . The f i n a n c i a l a s s i s t a n c e t h a t was p r o v i d e d t o me, b o t h d u r i n g my g r a d u a t e s t u d i e s and d u r i n g t h e t h e s i s r e s e a r c h , b y C e n t r a l M o r t g a g e and H o u s i n g C o r p o r a t i o n and t h e U r b a n L a n d E c o n o m i c s D i v i s i o n i s a l s o g r a t e f u l l y a c k n o w l e d g e d , as i s t h e f i n a n c i a l a s s i s t a n t f o r d a t a c o l l e c t i o n t h a t was p r o v i d e d by t h e D e p a r t -ment o f H o u s i n g , P r o v i n c e o f B r i t i s h C o l u m b i a . CHAPTER 1  THE NEED FOR A HOUSING PRICE INDEX A. INTRODUCTION This paper i s concerned with the i d e n t i f i c a t i o n and analysis of a methodology f o r formulating a housing price index. The index, as a r e s u l t of the methodology adopted, w i l l be r e -presentative of measures of price changes of the housing stock, rather than a measure of the price of an average house or the measure of the change i n the price of housing sold i n any period. The f i r s t portion of the paper i s a discussion of the importance of a price index f o r housing. This i s then followed by a survey of previous studies that have addressed themselves to t h i s t o p i c . The second portion of t h i s chapter i s an examin-a t i o n of the methodologies employed i n constructing the major housing indicies; currently i n use today. The l i m i t a t i o n s , as well as the appropriate interpretations of these i n d i c i e s i s revealed. The t h i r d chapter of t h i s paper i s concerned with a review of the c r i t e r i a that an accurate index must meet. Included i n t h i s , i s a discussion of the s t a t i s t i c a l and con-ceptual problems associated with the design and construction of such an index. These concepts are then further investigated through the actual construction of several i n d i c i e s from data obtained from the Land Registry Offices i n the Greater Vancouver Regional D i s t r i c t . The majority of t h i s paper i s devoted to t h i s <• analy s i s . 2. The conclusion w i l l take the form of a set or recom-mendations as to the d i r e c t i o n that future research should take. Also included w i l l be a b r i e f comparison of the r e s u l t s obtained from t h i s study i n the e x i s t i n g i n d i c i e s . B. THE NEED FOR A HOUSING PRICE INDEX The trend i n house prices i s of importance to govern-ments, f i n a n c i a l i n s t i t u t i o n s and households. Changing prices and the rate at which they change has strong implications f o r the consumer. Prices are used to mea-sure consumer welfare, recognize i n f l a t i o n , diagnose imbalances i n the economy and indicate the economic i n e q u i t i e s among income groups. Informed discussion and government p o l i c i e s directed toward influencing house prices are predicated on the assumption that some r e l i a b l e means exists to measure the change i n prices over time. C o n f l i c t s often exist as to the nature' of s p e c i f i c problems and hence d i f f e r e n t ideas are presented as to the appropriate remedial p o l i c i e s and programs. Thus, a house price index which would f a c i l i t a t e the monitoring of the housing mar-ket, would have a dire c t bearing upon the effectiveness to which government p o l i c y and program objectives could be s a t i s f i e d . Considerable importance i s therefore placed on an ( 1 ) Moore, G. H., The Role of Prices i n the United States Economy, Keynote Address, Cento Symposium on Price S t a t i s t i c s , Turkey, 1 9 7 0 . 3 . index i n the determination of housing p o l i c y and i n the eval-uation of the effectiveness of p o l i c y . A housing price index i s not s o l e l y used to denote changes i n house p r i c e s . Housing comprises almost one-third of the t o t a l Consumer Price Index f o r Canada. The Consumer Price Index i s used i n private contracts, COLA clauses and i n public p o l i c y . This emphasizes the necessity that the housing component of t h i s index accurately r e f l e c t the trend i n house prices i n Canada. F i n a n c i a l i n s t i t u t i o n s are interested i n past and future trends of house p r i c e s . Lenders want to know how prices are changing as security f o r t h e i r lending. An index of house prices would be of value to a l l those who invest i n r e a l estate as well as those whose business i t i s to negotiate r e a l estate transactions and to advise regarding them. "Successful investment i n r e a l estate depends on the a b i l i t y to analyze values properly and un-successful investment usually a r i s e s from the f a i l u r e to understand the forces that make values and those that destroy i t . " (2) A house generally represents the major investment of a household. With an i n d i c a t o r of housing pr i c e s , households w i l l be better informed as to the future worth of t h e i r investment and w i l l be aided i n making a prudent investment decision. A housing price index i s also necessary to close the gap i n research r e l a t i n g to new construction, the mortgage mar-ket and the l e v e l of market a c t i v i t y . (2) Wyngarden, Herman, "An Index of Local Real Estate Pr i c e s , " Michigan Business Studies, Vol. I, No. 2, January 192? . 4. S a t i s f a c t o r y price data on construction i s important as construction constitutes a substantial proportion of the investment component of G.N.P. and i s a major contributor to the c y c l i c a l i n s t a b i l i t y of the economy. The output of new con-str u c t i o n i s a good ind i c a t o r of the l e v e l of economic a c t i v i t y which a f f e c t s incomes and employment. Price i n d i c e s , and the information embodied i n them r e -l a t i n g to the l e v e l of market a c t i v i t y are necessary f o r f a c i l i -t a t i n g general economic analysis and f o r a s s i s t i n g business firms i n market planning and t h e i r general economic and business research. A price index also furnishes an important basis f o r research i n the mortgage market. Both the government and finan-c i a l i n s t i t u t i o n s have a substantial i n t e r e s t i n mortgage funds through loans and loan guarantee programs. Price data are a basic research t o o l and therefore, the development of a s t a t i s t i c a l l y accurate price series i s important to them. No proven r e l i a b l e index of house prices currently e x i s t s . A highly complex network of possible data for an index i s available (e.g. Multiple L i s t i n g Sales, TEELA, S t a t i s t i c s Canada, Central Mortgage & Housing Corporation), but a l l these have been proven to provide biased estimates of property values.^ (3) These biases w i l l be discussed i n a subsequent chapter. (4) See f o r e.g. Baxter, D. "Published Housing Data: Trends & Evaluation" pp. 419-4-48, Hamilton, S.W., "Housing Price Indexes: Theory and P r a c t i c e , " pp. 3 8 3 - 4 1 9 , both i n Housing: It's Your Move, University of B r i t i s h Columbia, Vancouver, 1976; P r i e s t , Bailey, A l f o r d , R e l i a b i l i t y - Evaluation of 1971 Census Reporting of " S e l l i n g Value"  of Owner Occupied Dwelling Units: A Micro-Match with  Comparison Sales Catalogues Provided by Members of the  C.R.E.A.. S t a t i s t i c s Canada, 1973 . 5 . The lack of an accurate house price series i s due to two major f a c t o r s . F i r s t , a lack of data? second, the problem of changes i n q u a l i t y of the series over time. In general, convenient and accurate data on house prices are not r e a d i l y available:. A possible source of data i s the Land Registry O f f i c e . However, these data are not e a s i l y accessible as the system was designed f o r a purpose other than supplying price information. As a r e s u l t , data c o l l e c t i o n from t h i s source would be time con-suming and c o s t l y . The second problem re l a t e s to that of holding the q u a l i t y of the index constant through time. This q u a l i t y problem has two basic aspects. F i r s t , the q u a l i t y of the index may change due to a s h i f t i n the q u a l i t y of properties that are sold at d i f f e r e n t times. Thus, a change r e f l e c t e d i n the index may be due to a s h i f t i n the d i s t r i b u t i o n of sales between d i f f e r e n t q u a l i t y homes. A second problem a r i s e s from the unique nature of r e a l estate as to i t s ' location, age, condition, type, etc. Unlike other i n d i c i e s , there i s no standardized unit of housing to which price quotations may be reduced. The q u a l i t y of the fi x e d housing stock each year w i l l be d i f f e r e n t . In t h i s study, the index f o r the average price of the housing stock w i l l be estimated. In formulating any index, the quantity that i s being measured i s kept constant from period to period. An index measuring the average price of houses that sold ( i . e . the average sales price) would be measuring a d i f f e r e n t quantity each year as the homes that s e l l each year d i f f e r from year to year. However, i n an index measuring the average price of the stock, the quantity (stock), measured each year i s r e l a t i v e l y constant (additions and demolitions to the stock form only a small proportion of the stock i n each year). Thus, i t i s a measure of the average pr i c e of the stock and not the average sales price that i s desire. In addition, government p o l i c y and homeowners and f i n a n c i a l i n s t i t u t i o n s concerns are a l l directed toward the housing stock and not just sales. CHAPTER 2 -EXISTING RESEARCH AND INDICIES This section i s concerned with a review of the e x i s t i n g l i t e r a t u r e on housing price i n d i c i e s and an analysis and c r i t i -cism of the major housing i n d i c i e s i n use today. An examination of the methodologies used i n the major i n d i c i e s w i l l be presented i n order to reveal the l i m i t a t i o n s as well as the appropriate interpretations of the indexes. In a subsequent section, a com-parison w i l l be made of the movement of LRO index to some of the e x i s t i n g ones to see i f a suitable surrogate e x i s t s . A. PREVIOUS STUDIES There have been numerous studies undertaken to explain fluctuations i n the price of housing. Very few studies however, have addressed themselves to examining or formulating a methodo-logy by which to compile a r e l i a b l e i n d i c a t o r of house pr i c e s . This can l a r g e l y be attributable not to a lack of i n t e r e s t but to the d i f f i c u l t i e s i n obtaining data. A few papers exist however, which discuss the methodological considerations of constructing price i n d i c i e s and i n p a r t i c u l a r , the q u a l i t y aspects. Wyngarden^ was one of the f i r s t economists to pioneer work i n t h i s f i e l d . His objective was to f i n d a method of c o l l e c -t i n g data on r e a l estate price movements that would be of use i n the construction of an index. In order to minimize q u a l i t y v a r i -ations i n the units sold each year, he advocated the use of an index based on the repeated sales of i n d i v i d u a l properties. (5) Wyngarden, Herman, An Index of Local Real Estate Pri c e s . Bureau of Business Research, University of Michigan, Ann Arbor, Michigan, 1927. < 8. An index was compiled of a l l the r e l a t i v e prices asked f o r i n successive l i s t i n g s which were f i r s t l i s t e d i n the same year and the median price r e l a t i v e i n each year was chosen as being representative of prices i n the market as a whole. These price r e l a t i v e s were then converted to l i n k r e l a t i v e s i n order to show the r e l a t i o n s h i p which an index i n a given year bears to the index i n the preceeding year rather than the year i n which the property was f i r s t l i s t e d . The usual i n d i c i e s employ a f i x e d base^iconcept where the index base does not change over successive periods. Chaining however, involves a constantly s h i f t i n g base period by updating the base period, one period at a time so that the index f o r any given period uses the previous period as a base. This index i s then linked i n a m u l t i p l i c a t i v e fashion. The r e s u l t i n g index from chaining has much larger valves than that from a fi x e d base as i t compounds the r e s u l t of price changes between more than two periods while the fi x e d base index i s calculated independent of price changes which have occurred i n the intervening years between the current and base period.^ ^ ^  This index was then tested by Wyngarden against another index constructed from l i s t i n g s of properties i n concurrent years, again using the same procedure of chain l i n k i n g . Both indexes were found to behave s i m i l a r l y , thus upholding the former index. The sample was also disaggregated into geographic areas to examine the forces a f f e c t i n g r e a l estate prices i n each of the ( 6 ) Adelman, I., G r i l i c h e s Z. "An Index of Quality", Journal of the American S t a t i s t i c a l Association. September 1961, No. 2 9 5 . Vol. 5 6 . pp. 535-555' 9. d i s t r i c t s . The price index f o r each of the areas varied and i t was thus recommended that a l l subsequent research on house prices be based on r e l a t i v e l y homogeneous geographical areas. Rapkin, Winnick, Blank^^ ^ and Burnstien,^® ^ i n separate a r t i c l e s also address the q u a l i t y problem i n the. construction of a housing price index. In order to overcome the problem of d i f f e r e n t q u a l i t y v a r i a t i o n s of the units exchanged eachFyear, they attempt to standardize housing by using the concept of s u b s t i t u a b i l i t y i n t h i s manner. Housing i s a physical good but i t i s desired f o r ser-vices which i t renders. They state that d i f f e r e n t q u a l i t y houses, although they are not perfect substitutes f o r each other and may s e l l at d i f f e r e n t prices at the same point i n time, are almost i d e n t i c a l as to the services they o f f e r . Thus, they compete with each other as al t e r n a t i v e s f o r homebuyers i n a single market. The authors f e e l that although tr e a t i n g housing or any consumer durable good as a physical unit may pose problems i n the construc-t i o n of an index, treatment on the basis of serviceaflows rendered poses no l i m i t a t i o n s . ( 9 ) T r i p l e t s ' suggests a method of q u a l i t y adjustment by changing the basis of the price quotation from the physical unit of sale ( i . e . the house) to i t s u t i l i t y ( i . e . the housing service flow). This approach i s s i m i l a r to the one expounded upon i n the (7) Rapkin, C , Winnick, L., Blank, D., Housing Market Analysis. The I n s t i t u t e f o r Urban Land Use and Housing Studies, Columbia University, C i t y of New York, 1953. (8 ) Burnstien, M.L., "Measurement of Quality Change i n Consumer Durables", The Manchester School of Economics and So c i a l  Studies, September 1961, pp. 269-279. ( 9 ) T r i p l e t t , Jack. Theory of Hedonic Price Indexes. Washington, Bureau of Labor S t a t i s t i c s , S t a f f Paper, No. 31. 1 0 . above a r t i c l e s . T r i p l e t t argues that a difference i n physical design i s not a concept of d i f f e r e n t q u a l i t y but just a difference i n the set of at t r i b u t e s (e.g. number of bathrooms, garage, e t c . ) . Since indexes are economic measurements,the q u a l i t y c r i t e r i a should be an economic one — that i s — user evaluation as to q u a l i t y . Consumer behaviour r e l a t e s to a flow of services and thus, i t i s the service flow and not the good i t s e l f which i s the proper unit of an a l y s i s . Gavett and Kaplan, i n separate a r t i c l e s discuss the inaccuracies of using cost data to evaluate the q u a l i t y of a good. Kaplan states that due to the unhomogeneous nature of con-struction, q u a l i t y adjustments tend to be based on the cost of inputs rather than the output. The basic problem with t h i s approach he states, i s that i t ignores changes i n productivity. He t r i e s to overcome t h i s problem by redefining output i n teasms of intermediate products.or as an a l t e r n a t i v e , the use of inputs-adjusted by a factor of productivity change f o r each year. He states that current price i n d i c i e s , by omitting t h i s productivity change factor, do not r e f l e c t the change i n the s e l l i n g price of a p a r t i c u l a r b u i l d i n g but a change i n the price of a f i x e d l i s t of materials and labour involved i n the structure. Gavett c r i t i c i z e s the use of input prices to ev a l -uate the q u a l i t y of a good. The current assumption i s that (10) Gavett, T. "Quality of Pure Price I n d i c i e s " , Monthly Labor • Review. March 1967, Vol. 9 0 , No. 3 , U.S. Dept. of Labor , pp. 1 6 - 2 0 . (11) Kaplan, Norman, "Some Notes on the Deflation of Construction", Journal of the American S t a t i s t i c a l Association, September 1959, Vol. 5^, No. 2 8 7 . pp. 5 3 5 - 5 5 5 . 1 1 • increased costs or prices are synonymous with a higher q u a l i t y good being produced or consumed. Here again, the productivity concept i s ignored. As a r e s u l t of productivity advances, he states that i t i s possible to produce a superior good at lower costs. In t h i s instance, the cost c r i t e r i a w i l l r e s u l t i n a de-c l i n i n g price index when q u a l i t y has a c t u a l l y r i s e n . (12) J a s z i N t r i e s to reconcile the two concept of q u a l i t y — i . e . costs and u t i l i t i e s . Under perfect competition, he states that the two concepts are i d e n t i c a l . Each consumer w i l l equate h i s purchases to his marginal u t i l i t y of a good r e l a t i v e to i t s price u n t i l i t i s equal to the marginal u t i l i t y of another good r e l a t i v e to i t s p r i c e . Since i n long run equilibrium prices are equal to costs, r e l a t i v e marginal u t i l i t i e s w i l l equal r e l a t i v e prices and r e l a t i v e costs. Most of the l i t e r a t u r e written over the past decade on housing price i n d i c i e s discusses the hedonic price index approach. The adoption of hedonic price i n d i c i e s techniques i s apparently a r e s u l t of the desire to cope with the problems posed by q u a l i t y changes. This technique i s currently being investigated by S t a t i s t i c s Canada f o r formulating a price index f o r new and e x i s t i n g housing. The premise underlying t h i s index i s that a property can be characterized by a number of a t t r i b u t e s (for example, l o t s i z e , number of bedroorms, recreation room, etc.) and the price of the house i s related to the nature of these a t t r i b u t e s . By f i x i n g the time period and observing the prices of homes exhib i t i n g (12) J a s z i , George, "An Improved Way of Measuring Quality Change", Review'of Economics and S t a t i s t i c s , August 1962, pp. 332-335-1 2 . varying (but b a s i c a l l y similar) a t t r i b u t e s , through a multiple regression technique, i t i s possible to ar r i v e at an i m p l i c i t valuation of these c h a r a c t e r i s t i c s . In succeeding years, when ch a r a c t e r i s t i c s change, the i m p l i c i t price of a c h a r a c t e r i s t i c can be deducted from whatever change a c t u a l l y occurred. This technique f o r housing i s an adoption of an approach put forward (13) by G r i l i c h e s v i n 1961 i n an attempt to construct a price index f o r automobiles v Several authors Estate that ^orie of 'the d i f f i c u l t i e s with hedonie i n d i c i e s i s that-due.toe the;large number of- charge? t e r i s t i c s , the number of properties ex h i b i t i n g the various s t r u c t u r a l -attributes/has to be very large i n order f o r the co-e f f i c i e n t of the variables to;be s i g n i f i c a n t * There i s also the problem of how to measure the q u a l i t y of the neighborhood through time. , Another problem i s data c o l l e c t i o n . The time, money and problems spent i n writing, e d i t i n g and reviewing the s p e c i f i -cations as w e l l as c o l l e c t i n g the price quotations would be enormous. (13) G r i l i c h e s , Zui, "Hedonie Price Indexes f o r Automobiles; An Econometric Analysis of Quality Change", The Price  S t a t i s t i c s of the Federal Government. General Series No.73, 1961,:pp. 37-196. (14) The o r i g i n a l technique was f i r s t introduced by A. J . Court i n "Hedonie Price Indexes with Automotive Examples" i n The  Dynamics of Automobile Demand, i n 1939. However, he used a pooled regression between the base and the current year, so that the regression c o e f f i c i e n t s or i m p l i c i t prices of the c h a r a c t e r i s t i c s were forced i n t o an average which reduced the accuracy of the data. (15) See T r i p l e t t , J . , The Theory of Hedonie Price Indexes. Bureau of Labor S t a t i s t i c s - S t a f f Paper No. 3 1 ; Brown, S. L. Price Variations i n New FHA Houses 1959-1961; A Report  of Researchsi'n Methods of Constructing Price Indexes. Bureau of the Census Working Paper No. 31» Mieszkowski, P., Saper, A. t Trends i n the Value of Toronto Housing. 1 9 6 5 - 1 9 7 3 , Central Mortgage and Housing Corporation, Working Paper 7 6 - 2 . 13. Aside from the Multiple L i s t i n g Service, no other source currently c o l l e c t s s p e c i f i c a t i o n s r e l a t i n g to properties. Ideally, a sample should be drawn from the stock of properties rather than .from sales ( t h i s w i l l be further elaborated upon i n the next chapter), so that t h i s would involve obtaining s p e c i f i c a t i o n s about the housing stock — an impossible task. Mieskowski & S a p e r ^ ^ compare two possible s p e c i f i c a -tions that a hedonic price index model may take. One i s the basic l i n e a r regression model where the value of a house i s an additive function of the property's c h a r a c t e r i s t i c s . The additive nature of the function implies that an a d d i t i o n a l c h a r a c t e r i s t i c such as a bathroom adds a constant absolute amount to the value of the property. The second model employs a semi-log s p e c i f i c a t i o n . The c o e f f i c i e n t s are interpreted that a unit change i n the character-i s t i c s of the property changes the value of the property by a constant percentage value. The semi-log model implies that var-ious c h a r a c t e r i s t i c s add more i n absolute value to larger homes (for example, an a d d i t i o n a l bathroom on an expensive home i s l i k e l y to be more valued than an a smaller older home). The basic c r i t i c i s m that the authors o f f e r against the semi-log s p e c i f i c a t i o n i s that i t v i o l a t e s the absolute d o l l a r figures quoted i n b u i l d i n g costs, where some d o l l a r amount per square foot of f l o o r area i s given. However, t h i s problem can be reduced somewhat by substituting a quadratic term f o r house and l o t size so that i f the marginal contribution of these variables (16) i b i d 14. to house values declines as they increase, t h i s would be r e f l e c t e d i n a negative value f o r the quadratic terms. Af t e r comparing the two models, they favour the semi-log model as i t s reasoning i s more r e a l i s t i c though they state that l i n e a r estimates may not be any less accurate. (17) Kain and Quigley also employed a hedonic price index approach,in t h e i r study but promoted the use of f a c t o r analysis as an i n i t i a l step p r i o r to regression a n a l y s i s . The use of factor analysis reduces the degree of m u l t i - c o l i n e a r i t y as i t singles out the most important variables to define q u a l i t y . Their study i s not an attempt to create a hedonic price index but t r i e s to define a group, of variables that would define environmental q u a l i t y and attempts to determine i t s e f f e c t on housing values. Related to the q u a l i t y problem i n formulating a price index, i s the problem of depreciation. The problem of deprecia-t i o n a r i s e s i n formulating an index i n that i n the case of con-sumer durables, such as housing, the stock (or sample) i s subject to depreciation. As a r e s u l t of the aging process, the q u a l i t y of a f i x e d sample has deteriorated during the study period. Laube* 1 defines the annual depreciation rate f o r housing as being the difference i n s e l l i n g prices between two i d e n t i c a l houses s e l l i n g i n consecutive years. He suggests that the depreciation rate can be estimated by using a dummy variable f o r age i n a hedonic price index regression. (1?) Quigley, J . , Kain, J . , "Evaluating the Quality of the Residential Environment", Environment Planning, Vol. 2, 1969. (18) Laube, J . , Hedonic Prices and Quality Index; A Theoretical  Review, Central Mortgage sand Housing Corporation, Mimeograph, March 1975• 15. The depreciation rate can also be a l t e r e d by repairs which r e s u l t i n an upgrading of the sample q u a l i t y . According to a study by Grebler, Winnick and B l a n k , V 7 / the depreciation losses are greater than the value gains due to a l t e r a t i o n s . Therefore, an estimate of an index without taking these factors i n to account i s biased downwards. Laube^ 2 0^ believes that i n periods of excessive demand fo r housing, there i s a greater incentive f o r homeowner to repair t h e i r properties. Thus, he views the rate of depreciation as being a function of economic conditions as well as the r e s u l t of the process of aging. (?i ) Bailey, Muth and Nourse N ' have formulated an index model very s i m i l a r to the one proposed by Wyngarden* i n that i t i s based on repeated sales of properties. However, they employ the standard.regression technique rather than the manual tabula-tions of Wyngarden. This approach, as i n the former one, i s an attempt to eliminate the q u a l i t y problems due to changing q u a l i -t i e s of the units sold each year . While t h i s approach minimizes q u a l i t y v a r i a t i o n s , i t s data base i s dependent upon properties which have sold at least twice during the study period. This procedure may eliminate a large number of observations as some properties may have only sold once, p a r t i c u l a r l y during a study period with a short time (19) Grebler, L., Blank, D., Winnick, L., Capital Formation i n Residential Real Estate, National Bureau of Economic Research, 1956. ( 2 0) Laube, J . , op. c i t . (21) Bailey, M., Muth, R., Nourse, H., "A Regression Method f o r Real Estate Price Indices Construction", American S t a t i s t i c a l Association Journal, December iyo_>, pp. 933-942. horizon. The Bailey, Muth and Nourse model i s also more a p p l i -cable i n stable neighborhoods were l i t t l e or no environmental changes are occurring which may have an impact on p r i c e s . A model which combines both the Bailey, Muth and Nourse model and the hedonie price index approach has been formulated by (22) Chinloy* ' i n order to quantify the e f f e c t of depreciation on the housing stock. He formulates a price index f o r a r e l a t i v e l y homogeneous community of housing and tests ife f o r two forms of depreciation — zero depreciation and geometric depreciation. He further s t r a t i f i e s the sample into d i f f e r e n t age categories, to see i f depreciation rates vary among di f f e r e n t property vintages. B. PRESENT PUBLISHED DATA 1. S t a t i s t i c s Canada - Shelter Component of CPI S t a t i s t i c s Canada publishes an index of housing costs which comprises approximately 30$ of the Consumer Price Index. Therefore, i t i s necessary that t h i s component accurately r e f l e c t the true trend of the cost of housing. Housing i n the CPI i s r e -presented by two i n d i c i e s — the Shelter Index, contributing 51% of the index, and the Household Operations Index, which comprises the remaining 4-3$ of the housing component of the index. The Shelter Index i s composed of the rent index (4-7$), which includes rentals (97.7$) and the cost of tenant repairs (2.3$). This rent component estimates the price change of a con-stant q u a l i t y of rented accomodation. It i s intended to be a (22) Chinloy, Peter, "Hedonie Price and Depreciation Indexed For  Residential Housing. A Longtitudinal A p p r o a c h ^ . . Department of Economics, University of Western Ontario, Mimeograph, 1975• 17. measure of price changes only and not a market measure of pre-v a i l i n g rents. Rental figures are obtained from a survey of the labour force every s i x months and are based on the actual rent paid by indiv i d u a l s f o r apartment and single family homes, adjusted f o r f a c i l i t i e s which the structure may o f f e r . "Costs of Household Ownership" comprises the jremaining 53$ of the Shelter Index. The index f o r t h i s component attempts to trace movements i n the various expenses incurred by homeowners: property taxes (30$), the mortgage i n t e r e s t rate (33$), repairs (10$) and property insurance (3.0$) and the replacement cost of new homes (24$). ^The new houses component of the CPI, i n l i n e with the user cost and nominal outlays concept does not consider houses as assets i n the consumer's market basket of purchases. The (24) weighting of the new houses component, consistent with the consumption approach, i s derived from the "replacement cost of the annual depreciation of the stock of houses owned and l i v e d i n by the target group". J l This i s calculated by subtracting the value of the land and a f a c t o r f o r c a p i t a l appreciation, from the value of the p r o p e r t y . ^ ^ Thus, t h i s c a l c u l a t i o n w i l l y i e l d a value f o r depreciation -- one of the costs of homeownership. (23) CMHC, Canadian Housing S t a t i s t i c s . 1974, p. 100. (24) The weighting d i f f e r e n t i a l also a f f e c t s the mortgage i n t e r e s t and insurance cost components since these are calculated as a function of the price index f o r the new houses c omponent. (25) DBS The Consumer Price Index f o r Canada (1949=100), Catalogue No. 62^5lb, Occasional, March 1961, p. 15. (26) McFadyen, S., Hobart, R., The Impact of I n f l a t i o n on the Canadian Housing Market, Urban Growth and Land Directorate, Ministry of State f o r Urban A f f a i r s , 1975, Pg. 6. 18. Present measures of the "price of new houses" are based on the movements i n labour and material cost indexes weighted on the basis of the proportion spent i n the base year on these f a c -tors i n the construction starts of single family detached dwellings,.. The labour index i s based on basic wage rates taken from union con-t r a c t s r e l a t i n g to the main trades of importance employed i n r e s i d e n t i a l construction ^ (Annual value of labour - 64-008). A productivity adjustment of 2.9$ per annum i s applied to the wage rat e s . ' The materials index i s based on l i s t p r i c e s obtained from manufacturing ( i . e . Material Price Indexes - 62-007). Different material and design requirements found throughout Canada require d i f f e r e n t weights to the input items f o r each area. Ideally, a pr i c e change i n these input commodities should r e f l e c t a fundamental change i n supply and demand i n given markets and should be among the e a r l i e s t i ndicators of change that may l a t e r be r e f l e c t e d i n the change of the housing price index. However, t h i s assumption i s erroneous. The price that a new house w i l l command at any point i n time i s , as i n other commodity markets, determined by the i n t e r a c t i o n of demand and supply. Furthermore, the price of this^new housing i s determined i n con-junction with the prices of e x i s t i n g units which may have been b u i l t several decades ago with dramatically d i f f e r e n t construction costs and technologies. The l e v e l of construction costs w i l l only a f f e c t the rate at which units are added to the stock. A lower l e v e l of construction costs, ceterus paribus, w i l l r e s u l t i n larger p r o f i t s accruing to the developer. This w i l l increase the (27) The productivity measure i s calculated using the r a t i o of materials to labour, i n r e a l terms, l i n e a r i l y regressed overtime. The adjustment has been made since 1949. 19. rate at which new units w i l l be added to the stock. Therefore, t h i s premise overlooks the e f f e c t s of demand and supply i n the housing market i n determining the price of housing. The procedure used also neglects the e f f e c t on price of changes i n s i z e and q u a l i t y of the home, v a r i a t i o n i n construction industry p r o f i t rates, and substitution between materials and labour. More seriously, land costs, the most ra p i d l y increasing component of new house prices are excluded. Another shortcoming of the index i s that housing s t a r t s do not necessarily imply housing completions i n the same period. Starts i n the previous (28 ) year were found to be only $6% of units completed. Many technological changes have occurred i n the construc-t i o n industry i n recent years which are l i k e l y to have a substan-t i a l a f f e c t on the s t a t i s t i c a l measurement of productivity so that i t may not be a constant 2.9$ as assumed. Dennis discusses some (29) of these changes. One of the changes i s that there has been a s h i f t of construction work away from the construction s i t e to the factory. Factory products used f o r constructing housing are becoming larger and more complex. At the extreme, an entire structure can be pro-duced at the factory and then simply transported and assembled at the construction s i t e . Thus, there has been a b l u r r i n g of the difference between construction and manufacturing. (28) Baxter, Housing; I t s Your Move. Op. C i t . (29) Samuel,J. Dennis, "Current Changes i n Construction and Their E f f e c t s on S t a t i s t i c a l Measurements, Bureau of the Census - Proceedings of the Business and S t a t i s t i c a l  Section. The American S t a t i s t i c a l Association, 19?1, Washington, D.C., pg. 30-39. 20. Another problem i s that more and more new homes are being provided withis:fixtures such as garbeurators, f r i d g e s , stoves, dishwashers, etc. which were formerly not included. Therefore, i t i s becoming increasingly d i f f i c u l t to decide whether to regard these a d d i t i o n a l features as furnishings or as part of the con-struction costs of the home. The composition of r e s i d e n t i a l construction i s also changing. A large proportion of single family housing i s taking the form of townhouses or rowhouses. In addition, the number of multi-family, owner-occupied dwellings b u i l t each year i s increasing. This phenomena i s further complicated by multi-use buildings where the f i r s t few f l o o r s of a b u i l d i n g may be devoted to commercial uses, while the upper f l o o r s contain condominium un i t s . Productivity figures must somehow make adjustments f o r these changes i f they are to be accurate. As a r e s u l t , the i n t r e p r e t a t i o n assigned to t h i s portion of the index i s that i t r e f l e c t s the changes i n the prices of a f i x e d l i s t of materials and labour involved i n b u i l d i n g a house but does not r e f l e c t the changes i n the market value of the structure. The mortgage i n t e r e s t component of the CPI i s calculated on the basis of the new house price index times a weighted i n t e r -est rate. Mortgage in t e r e s t rates f o r the current period comprise two$:ofo.the o v e r a l l weighted i n t e r e s t rate; the remaining 98$ r e -present previous i n t e r e s t costs. This methodology i s inconsistent with the basis of the o v e r a l l CPI concept. A pure price index i s designed to measure changes i n the price facing the consumer today. Thus the relevant i n t e r e s t rate i s the rate i n the current period. 21. Another shortcoming of the i n t e r e s t cost tabulation i s that i t ignores the mortgage i n t e r e s t cost of e x i s t i n g properties and the i n t e r e s t costs on vendor financed m o r t g a g e s . ^ To the extent that these d i f f e r from the i n t e r e s t cost on new homes, t h i s w i l l d i s t o r t the index considerably. The housing component of the CPI appears to be prepared on the nominal outlays approach. This approach seems question-- able because of the omission of the investment aspects of (31) homeownership. The user cost approach would be more compre-hensive i n that i n addition to the present component of the index, i t would also take i n t o account c a p i t a l gains and return on owner's equity. C a p i t a l gains must be considered since the net cost of holding a durable asset i s reduced when i t appreciates i n (32) value over the holding period. A return on equity should be included as there i s an opportunity cost incurred by the owner, f o r i f he were to s e l l h i s property, he could invest the money and earn i n t e r e s t income. The Household Operations Index comprises the remaining kj>% of the housing component of the CPI. This index i s also based on the nominal outlays approach and measures the change i n the costs of f u e l , f u r n i t u r e , appliances, f l o o r coverings, l i n e n , u t e n s i l s and other supplies and services. As such, i t appears to be a poor i n d i c a t o r of the cost of housing. (30) Baxter, Housing, I t ' s Your Move. Op. C i t . (31) McFadyen, Hobart, The Impact of I n f l a t i o n on the Canadian Housing Market, p. 4. ~~~ (32) i n cases where property taxes are dependent on the assessed market value of the property, the absolute holding costs may increase but t h e i r impact may not outweigh the e f f e c t of c a p i t a l appreciation. 2 2 . 2. S t a t i s t i c s Canada - New House Prices The New House Price Index provides an estimate of the rate of change of new house prices f o r twelve large metropolitan areas i n Canada. The index i s based upon the s e l l i n g price r e -ported by builders who b u i l d more than one hundred units per (33) year i n a c i t y . w ^ ' The housing units included i n the sample f o r a given b u i l d e r are selected i n such a way that the price change of the sample are representative of the p r i c e change of the builder's t o t a l sales of housing u n i t s . In 1971» which i s the base year f o r the index, the firms reporting prices accounted f o r between 60 to 70$ of the single family unit s t a r t s i n the metro areas. For each c i t y , weights are assigned to each f i r m to re-f l e c t the r e l a t i v e importance of the firm i n the single family housing market i n each year. The index r e f l e c t s the change i n the costs of land, labour and materials which the b u i l d e r must pay to b u i l d ana i d e n t i c a l structure i n the same or comparable l o c a t i o n . The q u a l i t y of the index i s held constant by examining the same model through the years. I f the model loses i n sales appeal and i s replaced by another model, the difference i n the q u a l i t y between the two structures i s said to be the difference i n the prices and t h i s difference i s adjusted by the builder f o r any change i n cost that may have occurred i n b u i l d i n g the new model. I f a change i n l o c a t i o n occurs, the price i s adjusted on a comparison of the two areas as to physical s p e c i f i c a t i o n s and neighbourhood amenities. (33) There are no indexes f o r Vancouver because the number of builders constructing the same model of house i n suc-cessive periods is. not large enough to be representative of these markets. 23. A possible shortcoming to t h i s approach as discussed (34) by T r i p l e t t , ' i s that there may be a tendency on the part of the developer to overstate the q u a l i t y adjustments i n order to j u s t i f y a price change. Some developers may contend that they never change a price without an equivalent change i n q u a l i t y and that a l l q u a l i t y changes are always transmitted into price changes. As a r e s u l t , pure price changes may be understated. Whether a reported cost change can legilainateiy be r e -garded as a q u a l i t y change also poses a problem. A developer may be able to achieve economies of scale i n labour or techn i c a l e f f i c i e n c y i n a p a r t i c u l a r project i n one year leading to a r e -duction i n costs. It i s also possible that he may, i n another project, i n c u r r unusually high costs due to d i f f i c u l t subsoil conditions, etc. A change i n costs here, does not necessarily imply a change i n q u a l i t y . Thus an adjustment of s e l l i n g prices by construction cost data to r e f l e c t a change i n q u a l i t y can seriously bias the price index. The major shortcoming of t h i s index i s that i t too i s based on the premise that a change between the prices of d i f f e r e n t dwellings i s due to the difference i n input costs. An increase i n q u a l i t y i s not necessarily r e f l e c t e d i n higher costs which are then r e f l e c t e d i n higher house p r i c e s . As discussed i n the pre-vious section, house prices are set i n the market through the in t e r a c t i o n of demand and supply. Construction costs w i l l not a f f e c t the price of housing. (34) T r i p l e t t , Jack, "Quality Bias in&Price Indexes and New Methods of Quality Measurements," Price Indexes and  Quality Change, G r i l i c h e s , Z. (ed.), Harvard University Press, 1971, pg. 180-212. 24. The sampling procedure used by S t a t i s t i c s Canada i s also open to question. The small developers that have been omitted by the survey, while i n d i v i d u a l l y not a large part of the market, may d i f f e r s i g n i f i c a n t l y i n the value and q u a l i t y of housing they produce. Small developers may d i f f e r from the larger developers i n that t h e i r homes are not usually constructed i n large subdivi-sions but i n small areas scattered over the c i t y . Large developments, on the other hand tend to be located i n on the p e r i -phery of the c i t y where large t r a c t s of land are a v a i l a b l e . Thus, there may be a price d i f f e r e n t i a l due to l o c a t i o n a l differences. Some of the developers omitted may be custom builders who are able to charge premiums f o r t h e i r services. Therefore, the omission of t h i s segment of the housing market may s i g n i f i c a n t l y influence the behaviour of the index. 3. C. M. H. C. Central Mortgage and Housing Corporation does not pub-l i s h a housing p r i c e index but does provide some house price data i n i t s annual publication, Canadian Housing S t a t i s t i c s . Since 19?4, the average prices of new NHA financed housing f o r 24 c i t i e s and 20 major urban areas has been published. The price data i s obtained from f i n a n c i a l i n s t i t u t i o n s that grant NHA mortgages and the published price i s an unweighted mean of a l l sales of new houses financed under the National Housing Act. Sales prices are also published on NHA financed ex i s t i n g dwellings and are co l l e c t e d i n much the same manner. These prices have been used as a general price index by the government. The major shortcoming of the data i s that i t i s r e s t r i c t e d by the method of financing — a l l properties have NHA 25. insured mortgages. The number of loans financed has fluctuated through time i n response to the changing terms of these loans with respect to i n t e r e s t rates, loan to value r a t i o s , and amortization periods. Most serious, however, are the l i m i t s set on the loan amounts s This tends, e s p e c i a l l y i n periods of rapid i n f l a t i o n , to truncate the top part of the market and the average price of the NHA house w i l l then be downward biased. The size of the sample w i l l also vary with the f i n a n c i a l conditions. In some areas i t can be so small as to be s t a t i s t i c a l l y i n s i g n i f i c a n t . Thus, on the whole the trend produced by CMHC s t a t i s t i c s i s u n r e l i a b l e . CMHC housing costs were converted into a simple index form and compared to the two housing indexes published by S t a t i s t i c s Canada. (See Table 1 ) . There appeared to be no correspondence between the CMHC index and the other two i n d i c i e s . 26. TABLE I  COMPARISON OF' PRICE DATA ( 1 9 7 1 al°°) CITY YEAR NEW HOUSE PRICE REGIONAL CITIES HOUS- C.M.H.C INDEX ( 1 ) ING COMPONENT 12) i l l Montreal 1971 1 0 0 . 0 1 0 0 . 0 . 1 0 0 . 0 (4) 1972 107.6 101.6 1 0 1 . 0 1973 1 2 5 . 8 104.5 114.8 1974 177.7 112.3 1 3 0 . 8 1975 190.3 122.6 *(5) Toronto 1971 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 (6) 1972 1 1 0 . 2 1 0 2 . 1 1 0 5 . 4 1973 137.6 106.3 ^ 1 0 9 . 3 1974 171.6 1 1 5 . 1 89.9 1975 1 7 1 . 0 126.4 *(5) Ottawa-Hull 1971 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 (6) 1972 1 1 2 . 0 1 0 3 . 1 9 8 . 0 1973 1 3 8 . 2 1 0 7 . 8 1 0 3 . 0 1974 1 7 1 . 2 116.8 102.4 1975 178.3 127.4 *(5) Winnipeg 1971 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 (4) 1972 1 0 5 . 2 102.4 99.3 1973 128.4 106.1 116.9 1974 163.5 115.5 128.3 1975 177.5 130.3 *(5) Calgary 1971 1 0 0 . 0 N/A 1 0 0 . 0 h) 1972 1 1 0 . 0 N/A 104.4 1973 I 2 6 . 4 lN/A 113.5 1974 162.3 1 1 1 . 8 131.5 1975 195.0 125.7 *(5) Edmonton 1971 1 0 0 . 0 N/A 1 0 0 . 0 (4) 1972 1 0 9 . 1 N/A 106.6 1973 1 3 2 . 6 N/A 1 1 8 . 9 1974 1 7 2 . 8 117.7 1 3 1 . 1 1975 2 0 5 . 3 131.4 *(5) 2 7 COMPARISON OF PRICE DATA (Cont'd) Source: S t a t i s t i c s Canada. Cat. No. 62-OO7. Source: S t a t i s t i c s Canada, Cat. No. 6 2 - 0 0 2 . Source: Self tabulated index on basis of "Dwelling Cost" figure i n Canadian Housing S t a t i s t i c s , table "Average Dwelling Costs, Down Payments, P r i n c i p a l and Interest, Taxes and Gross Debt Service f o r New Housing Under the National Housing Act, Canada by Urban Areas, ( D o l l a r s ) " . "Dwelling Cost" i s based on "owners and acceptable purchasers at time of sale". Data refe r s to single family dwellings f o r that c i t y i n a l l indexes. This table was not given i n 1975• No figure was published as to the average price of NHA financed homes by Urban Area. Data refe r s to single family dwellings f o r that c i t y f o r a l l indexes with the exception of the New House Price Index where the index includes single family dwellings and condominiums. 28. 4. Multiple L i s t i n g s Service Multiple L i s t i n g s Service (MLS) data are another source of price information used to indicate house prices . While the data i s a t t r a c t i v e i n that i t i s r e a d i l y available and provides a wealth of information about i n d i v i d u a l l i s t i n g s , t e sts have shown that i t i s not a r e l i a b l e i n d i c a t o r of house p r i c e s . The major shortcoming of MLS data i s that i t does not have a complete coverage of a l l sales as i t omits a l l private and exclusive sales. Since these excluded sales make up varying proportions of t o t a l house sales i n any period and t h e i r prices may d i f f e r from those i n the MLS data, complete reliance on MLS price data could prove c r i t i c a l . Varying proportions of t o t a l house sales are sold through the MLS i n any period, depending on how "s o f t " the market i s . In a buyer's market, i t i s expected that more homes would be sold through MLS as most people would want the exposure of t h e i r homes that the l i s t i n g s provide. Conversely, i n a s e l l e r ' s mar-ket, i t would be expected that more homes would be sold p r i v a t e l y . Thus, omission of private and exclusive sales would a f f e c t the index accordingly. MLS data also has a tendency to under-represent more expensive homes. The reason f o r t h i s i s that these homes have a lim i t e d market and require the extra attention that an exclusive l i s t i n g provides. Since the more expensive homes tend to be concentrated i n c e r t a i n geographic areas of the c i t y , the s p a t i a l scope of the MLS data i s also l i m i t e d . The implications of the (35) Hamilton, S.W., "House Price Indicies: Theory and Practice" Housing: I t ' s Your Move. University of B r i t i s h Columbia, Vancouver, 1976, pp. 383-418. 29. under-representation of higher priced homes w i l l have an important impact on the index. An average s e l l i n g price figure f o r homes i s published monthly by the Service. However, t h i s figure includes not only a l l the r e s i d e n t i a l sales i n that month but commercial and indus-t r i a l properties as w e l l . Moreover, t h i s index i s further biased by the varying proportions that each property use makes up of the t o t a l MLS sales each month. 5. TEELA TEELA i s a marketing survey company which publishes i n -formation c o l l e c t e d from the Land Registry Office f i l e s on transactions and mortgages. While the agency does not publish an index per se, i t was investigated as a possible source of data f o r the formulation of an index. Several shortcomings have been found i n the l i t e r a t u r e about the use of TEELA data. In theory, TEELA i s supposed to record a l l the property records within a given area during a given period. However, i t has been found that many transactions have occurred that TEELA has not recorded. The extent of t h i s problem i s unknown but i t does cast doubts on the accuracy of t h i s data. The dates provided on the TEELA cards are not the dates of sales of properties and have no standard r e l a t i o n to the sales date. As such, t h i s makes i t very d i f f i c u l t to obtain price averages f o r short term periods. (36) Dale-Johnson, D., Housing Market Data, Urban Land Economics Di v i s i o n , Faculty of Commerce and Business Administration, University of B r i t i s h Columbia, prepared f o r the Department of Housing, Government of B r i t i s h Columbia, 1976. 30. Thus any attempts to use TEELA information f o r purposes of constructing an index should be treated with d i s c r e t i o n . 6. Other Indicies Two Canada-wide r e a l estate firms — A. E. LePage Limited and Royal Trust — currently publish house price data f o r Canadian c i t i e s . This information i s la r g e l y provided as a ser-vice to t h e i r agents and customers rather than as an ind i c a t o r of period to period changes i n p r i c e s . The Royal Trust data i s of p a r t i c u l a r i n t e r e s t as i t attempts to maintain a somewhat constant q u a l i t y concept i n the houses on which the price quotations are given. Prices have been compared, c i t y by c i t y , on two i d e n t i c a l house models through the years. Both homes are t y p i c a l of the style that the firm usually handles. The main advantage of t h i s price data i s that since price changes have been reported on i d e n t i c a l l y s p e c i f i e d units from period to period, a l l price variations can be considered as "pure" price changes. 31. CHAPTER 3 -' *-"•: STATISTICAL AND CONCEPTUAL PROBLEMS This chapter w i l l review the c r i t e r i a that an accurate index must meet. Included i n t h i s , i s a discussion of the con-ceptual and s t a t i s t i c a l problems associated with the design of i n d i c i e s , such as they pertain to housing. A. STATISTICAL PROBLEMS 1. Sampling Procedure Since i t i s impossible to include and price a l l the homes i n the housing universe, i t therefore becomes necessary to choose a sample from the stock. As each house sampled may d i f f e r from each other and may command a d i f f e r e n t p r i c e , i t becomes necessary to sample a representative number of homes from the stock and to estimate an average or median p r i c e . However, as only a small proportion of a l l the houses i n the stock and/or sample turnover i n any period, i t w i l l be these homes and not the entire sample that w i l l provide our data base. The major problem with the e x i s t i n g data are that they (37) have an unknown estimating error. According to Maisel, " past f a i l u r e s i n sampling have been due to the f a c t that they deal with unknown universes. This occurs, f o r example, when MLS or N.H.A. figures are used as measures of a l l sales within the universe. It i s unknown what percentage of a l l sales are placed through the Multiple L i s t i n g s Service or what percentage of a l l sales are financed under the National Housing Act. This problem i s further aggravated by the f a c t that the (37) Maisel, S. "Housing Data obtained By Sampling Public Records", Land Economics Vol. 30-31, 1954-55t PP. 257-268. 32. above procedure, while i t does provide data on sales, provides no information concerning the re l a t i o n s h i p between t h i s price data and the value of the housing stock,to which t h i s price data i s said to pertain to. The ex i s t i n g data today contains an uni d e n t i f i e d hybrid of properties. The sample, i n order that i t be representative of the universe, must be composed of a l l properties, rather than of properties which have just sold. For each property i n the sample, sales data should then be obtained. In t h i s manner the re s u l t s can be analyzed i n terms of a l l housing units i n the universe and not just that portion of the universe that has sold through the M.L.S. or has been N.H.A. financed. Related to t h i s , i s the need for knowledge about turnover rate during each period so that the sample can be weighted. Weighting i s desirable f o r two reasons. F i r s t , weighting eliminates some of the s t a t i s t i c a l d i s t o r t i o n s i n the index, i n that i t controls f o r s h i f t s i n the turnover among homes of d i f f e r i n g q u a l i t i e s i n each year. This w i l l be further elaborated upon i n the following section. Secondly, weighting the sample by some fact o r that a c t u a l l y represents the composition of the sample with respect to that factor, changes the meaning of the index i n that i t becomes representative of the price changes of the sample (and hence the stock), and i s not merely representative of the properties sold. Without weighting, we have to make the rather strong assumption that the price obtained i n any period represents the entire market. Ideally, a permanent sample should be drawn from the entire housing stock of the universe to be studied. A l l trans-actions concerning these properties may then be obtained from 33. the c e n t r a l land r e g i s t r y system i n the area. Transactions con-cerning these properties can, i n most cases, be traced back to the o r i g i n a l owner of the parcel or to a desired date of o r i g i n of the index, as a l l h i s t o r i c a l records are kept. The data can also be updated each year as new transactions on the properties occur. 2. Additions To The Stock The stock of housing i n Canada currently increases by about two to three percent each year though t h i s rate may fluctuate between areas. I t i s necessary to up-date the sample, through an examination of b u i l d i n g permits, ^ t o make i t r e -presentative of the changing housing stock. However, t h i s poses a major problem where the q u a l i t y of the index i s concerned. The dileraa i s whether to maintain a constant q u a l i t y of the index i t s e l f by adding only a constant number of new houses each year to the sample or to maintain a representative sample of the stock by allowing an addition i n some proportion of the new houses b u i l t each year (what proportion?), though the number of new homes b u i l t each year may vary. The a l t e r n a t i v e that i s chosen w i l l also influence the turnover rate f o r that year and subsequent years. New homes are usually s o l d shortly a f t e r construction. Consequently, the additions to the sample w i l l i n v a r i a b l y increase the turnover rate i n that year as they w i l l have a greater l i k e l i h o o d of being sold than the rest of the sample. The number of new additions to the sample w i l l also (38) since b u i l d i n g permits issued do not equal b u i l d i n g comp-letio n s i n any year, a more accurate-method of obtaining a measare of the additions to the stock, may be the new addi-tions to the assessment r o l e , i f i t i s possible to i d e n t i f y these on the r o l e . 34 influence the turnover rate i n subsequent years as the turnover i s calculated as the number of homes being sold i n a period as a percentage of the t o t a l universe of homes ex i s t i n g i n that period. The additions to the sample i n each year w i l l become part of that t o t a l universe i n subsequent years. Another problem r e l a t e d to updating the sample i s the maintenance of the i n i t i a l l y prescribed degree of sampling pre-c i s i o n . I deally, the sampling p r e c i s i o n should be kept constant through time but changes i n t o t a l stock w i l l require changes i n the sample s i z e . I f the number of homes required to maintain sampling p r e c i s i o n i s not equal to the number of homes required to keep our index q u a l i t y constant, or to maintain representative-ness of the age d i s t r i b u t i o n of the stock, some sort of agreement (39) must f i r s t be reached. 3. Demolitions Properties which are demolished should be eliminated from the sample immediately a f t e r demolition and not included as part of the stock. 4. Sampling Over Geographic Areas A housing index created f o r a p a r t i c u l a r part of Canada i s not applicable to Canada as a whole due to'; the l o c a l nature of the r e a l estate market. Housing i s produced under d i f f e r e n t municipal conditions (e.g. minimum l o t s i z e , s e r v i c i n g requirements) and may not be comparable i n the materials used (39) Theoretically, i t has been found that the larger the universe, the smaller the proportionate sample size r equired to be r e p -resentative . of the housin g stocks- For example a 100,000 population size may require a 5$ ( i . e . 5»°00) sample 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 at a given confidence i n t e r v a l , while a 200,000 population may require only a 1.5$ ( i . e . 3.000) sample 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 f o r the same l e v e l of sampling p r e c i s i o n . This would require a reduction i n the sample size through time as the t o t a l housing stock grew, i f a constant degree of sampling p r e c i s i o n were to be maintained. 3$. (e.g. b r i c k versus stucco) and the types of housing constructed (e.g. condominiums, no basements). I f i n d i v i d u a l regional i n d i c i e s are aggregated into a national index, each region must be assigned an appropriate weight. Even so, error i s inevitable i n the a p p l i -cation of the index to any s p e c i f i c area. It must also be noted that indicies^compiled f o r d i f f e r e n t regions do not provide a v a l i d basis f o r i n t e r - c i t y comparisons as base year prices may have been extremely high or low i n one c i t y . 5. Sampling Within A Geographical Area A representative sample of the entire housing stock must be chosen and t h i s sample i s c r i t i c a l i n determining the q u a l i t y of the index. It i s also important that there be recognition of the basic difference between a "large" versus a "good" sample. Any sample chosen must be done with s t a t i s t i c a l p r e c i s i o n . 6. Seasonal V a r i a t i o n I t may be necessary to adjust the index f o r seasonal fluctuations i n the turnover rat e . This i s p a r t i c u l a r l y import-ant f o r eastern Canada where the r e s i d e n t i a l construction industry v i r t u a l l y shuts down during the winter months. The late spring and summer months are marked by a large number of new homes coming on the market. This increase i n concentration of new housing turnover i n one p a r t i c u l a r period w i l l strongly influence the behaviour of the index. This adjustment would not be nece-ssary i n a region such as Vancouver where r e s i d e n t i a l construction i s c a r r i e d out on a year-round basis. 7. Base Period The base period selected should not be one i n which 36. e r r a t i c price movements are occuring or i n extreme underlying economic conditions. There must be a stable base to serve f o r comparative changes i n the price l e v e l through time. 8. Tenure Type Not a l l homes sold i n the market are f o r owner occupancy purposes. Some of the properties purchased are f o r investment purposes and are leased out. The question a r i s e s as to whether owner-occupied units would not command a d i f f e r e n t price from the r e n t a l u n i t s . Separating the owner-occupied units from the tenant occupied units would be an impossible task. As such, a second question a r i s e s as to whether apartment buildings should not also be included i n the sample as they too are housing units used f o r r e n t a l purposes. In response to the second question, the exclusion of apartment buildings can be j u s t i f i e d on two grounds. The f i r s t and the most obvious reason i s that f o r the purposes of formu-l a t i n g an index we wish to keep the q u a l i t y of the goods i n the index as homogeneous as possible. There i s an enormous q u a l i t y difference between apartment buildings and single family houses, both i n terms of the q u a l i t y of the physical unit i t s e l f and i n terms of the q u a l i t y of housing services offered by the two u n i t s . Therefore, f o r purposes of maintaining a homogeneous q u a l i t y i n the items i n our index, apartment units should be treated separately. Secondly, whereas the rents charged on single family detached units and those charged on multi-family units are deter-mined i n the same market, the c a p i t a l values f o r the two d i f f e r e n t 37. structures are determined i n separate markets. Since f o r the purposes of our index we are concerned with c a p i t a l values only, multi-family structures should be excluded from our sample. In response to the f i r s t question posed above, the c a p i t a l values of homes f o r owner occupancy and r e n t a l purposes are j o i n t l y determined i n the same market. Therefore, there i s no reason to separate (even i f possible) these two tenure types i n formulating an index for, single family detached dwellings. The concept of tenure does not present a problem i f the purpose of the index i s defined as measuring the change i n the price of the stock of single family detached houses. In t h i s d e f i n i t i o n , a l l single family detached units w i l l be included, regardless of tenure type. 9 . Treatment of "New Products" U n t i l very recently, the "treatment of new products" problem would not have been encountered i n the construction of a housing index. However, as a r e s u l t of changing tastes, incomes and technology, the condominium has come into being and i s win-ning a major share of the housing market. The treatment of the condominium presents a serious problem as to how i t i s to be introduced i n t o the index. Again, the problem i s one of maintaining a constant q u a l i t y among the items i n our index. As with apartments, the physical unit and the type of housing services offered by the condominium unit and a single family home d i f f e r . Since the condominium unit, i s a r e l a t i v e l y new pheno-mena and since they d i f f e r " q u a l i t a t i v e l y " , i t i s unknown as to whether t h e i r prices are determined i n the same market as single 38. family homes. Due to the large differences that exist between the two, i t may be best to construct separate i n d i c i e s f o r each. Should t h e i r price movements p a r a l l e l each other, these i n d i c i e s could then be aggragated with a weighted base; the weighting being i n proportion to each's r e l a t i v e share of the housing market. B. CONCEPTUAL PROBLEMS D i f f i c u l t i e s i n the formulation of a housing index ar i s e s i n part because houses are durable goods. The CPI attempts to measure the changes over time i n the price of a f i x e d market basket of goods and services consumed by a given target group i n a selected base period. For non-durables, purchase and consump-t i o n are roughly synonomous and thus market prices can be used f o r p r i c i n g . With housing however, the consumption period i s greater than the length of the p r i c i n g period. Therefore market data cannot provide an accurate guide to e i t h e r the quantity con-(40) sumed or the consumption cost i n any given period. (Li) Three approaches have been suggested by Steiner x f o r tre a t i n g consumer durable goods such as housing: 1. An index of the prices of assets purchased (or con-tracted for) by members of the index populations. 2. An index of the current (nominal) outlays out of income made by member's of the index population. (40) McFayden, S., Hobart, R., The Impact of i n f l a t i o n on the Canadian Housing Market, Ministry of State f o r Urban A f f a i r s , 1976. (41) Steiner, P., "Consumer Durables i n an Index of Consumer Prices", The Price S t a t i s t i c s of the Federal Government, Staff-Paper No. 6, (New York: National Bureau of Economic Research), 1961. 39. 3. An index of the user (or opportunity) cost of con-suming the services produced by the assets i n question. "For goods of very short d u r a b i l i t y , the concepts become v i r t u a l l y identical} f o r goods of substantial d u r a b i l i t y , but which are t y p i c a l l y held f o r t h e i r whole useful l i v e s and which are purchased regularly, the concepts d i f f e r , but the three tend to the same r e s u l t . . . For commodities of long d u r a b i l i t y that are perforce purchased only i n t e r m i t t e n t l y because the amount of expenditure (or investment) on the i n d i v i -dual a c q u i s i t i o n i s a large f r a c t i o n of annual income, the differences i n the three approaches become sub-s t a n t i a l where i n addition the assets are t y p i c a l l y not held throughout t h e i r f u l l u s e f u l l i v e s , the differences become extreme. These conditions are s t r i k i n g l y present with respect to homeownership, and to a somewhat l e s s e r extent with automobile purchase «(4-2) and use. Steiner's f i r s t approach would provide the best method f o r an index f o r the price of housing as a physical good. Both the current nominal outlays approach and the user cost approach attempt to measure the cost of consuming a flow of housing services. These l a t t e r approaches are more suited f o r index incorporation into the CPI. For the purposes of t h i s paper, the asset price approach w i l l be examined. (4-2) i b i d , p. 305. 40 The major question with regards to the r e l i a b i l i t y of the asset p r i c e approach to a housing price index r e l a t e s to the (43) q u a l i t y problem. This problem may arise i n three ways. F i r s t , the q u a l i t y of the index may change due to a displacement of sales of one value range by another value range through time. Thus, a change r e f l e c t e d i n the index may p a r t i a l l y be due to a s h i f t i n the d i s t r i b u t i o n of sales across value ranges rather than r e s u l t from a "pure" price change i n the price of housing. The impact of a varying sample i n a market with many house types can be considerable. Consider the follow-ing example: TABLE II of Sales i n % of Sales i n Year Average - Price.Index High Value Range Low Value Range Price (Year Is100) & Average Price &'Average Price . - r i n that Range i n that Range I $56,000 100 50$ $60,000 50$ $40,000 11(a) $47,500 95 25$ $70,000 75$ $40,000 11(b) $55,000 110 50$ $70,000 50$ $40,000 According to Table II, average house pri c e s f e l l from $50,000 i n Year I to $47,500 i n Year I I , representing a f i v e per-cent decline. This same table however, shows the d i s t r i b u t i o n of sales i n the two years by value range. In Year I, f i f t y per-cent of the sales each took place i n one of the value ranges and the average price f o r that year i s a weighted average of these two value ranges. In the following year however, three times as many homes were sold i n the low value range as i n the high value (^ 3) The following analysis r e l i e s heavily on S. w. Hamilton's "Housing Price Indexes: Theory and Practice, Housing. It's Your Move, UBC, Vancouver, 1976, pg. 383-416. 4 1 . range. Therefore, the unweighted average of these prices would r e f l e c t a decline i n the average price as a r e s u l t of the s h i f t i n the d i s t r i b u t i o n of sales from the high value range to the low value range. However, the absolute price i n the high value range had i n f a c t increased and had the d i s t r i b u t i o n of sales between value ranges been the same as i n Year I, the index would have r e -f l e c t e d a ten percent increase i n house prices f o r that year (Year II (b)). Therefore, f a i l u r e to adjust f o r t h i s has biased the price index downwards. A second problem a r i s e s from the unique nature of r e a l estate as to l o c a t i o n , condition, type, etc. In most price i n -dexes every good possesses the same c h a r a c t e r i s t i c s as every other good sampled f o r the index i n that year. Any difference i n c h a r a c t e r i s t i c s would imply that a d i f f e r e n t good i s involved. Consequently, f o r most indicies, i t i s easy to choose a represen-t a t i v e item and e s t a b l i s h a price to represent a l l items. With housing however, the physical structure, location, surrounding neighbourhood, etc., a l l vary from property to property. Unlike f o r other goods, there i s no standardized unit of housing to which price quotations may be reduced. This problem i s further aggravated by the fact that the q u a l i t y of the i n d i v i d u a l units may change with time. The con-cept of q u a l i t y includes physical condition of the improvements (which usually depreciate with time), the r e l a t i v e l o cation and a c c e s s i b i l i t y of a property (which may be al t e r e d by new constru-c t i o n i n the area or by a change i n the transportation system), renovations and additions to the e x i s t i n g structure and the sur-rounding neighbourhood. 42. Fai l u r e to account f o r q u a l i t y differences w i l l adver-sely a f f e c t our measure of pri c e s . Ideally we wish to maintain a constant q u a l i t y of the house toeing priced through time. However, i f a q u a l i t y improvement i n a home (e.g. an additi o n being b u i l t ) , f a i l u r e to adjust for thi s improvement w i l l r e s u l t i n an overstatement i n the p r i c e . Conversely, a deterioration i n the q u a l i t y of the house (e.g. depreciation of the structure) w i l l understate the pr i c e . Therefore, the omission of q u a l i t y adjustments may have a substantial e f f e c t on the re s u l t s of our index as a whole. To some extent however, a change i n one property may be o f f s e t by a change i n another. Price i n d i c i e s , incorporating a large number of properties may r e s u l t i n some q u a l i t y changes being cancelled out, though t h i s magnitude can not be measured. 43. CHAPTER 4  THE DATA BASE AND INDEX This chapter i s comprised of two parts. The f i r s t involves a description of the sampling procedure used. The second part i s concerned with the computation of a price index and an examination of i t s movement with respect to the conditions i n the economy. Included i n t h i s , i s an examination of turnover and t h e i r significance i n the index. Rights-to-purchase transactions are also b r i e f l y analyzed. A. SAMPLING PROCEDURE 1. The Data Base It was decided on the basis of a previous study conduc-ted by the Faculty of Commerce and Business Administration at the University of B r i t i s h Columbia i n 1967, that the data would be col l e c t e d from the records of the Vancouver and New Westminster Land Registry o f f i c e s which serve the Greater Vancouver Regional D i s t r i c t . The Land Registry System i n B r i t i s h Columbia records the r e g i s t r a t i o n of a l l i n t e r e s t s i n or ri g h t s to r e a l property. Details of mortgages, agreements f o r sale, l i e n s , etc. f o r a l l properties are recorded and are r e a d i l y available f o r inspection. 2. Selection of the Universe For t h i s study, the universe included a l l the single family detached housing situated i n the ra p i d l y growing communi-t i e s of the Greater Vancouver Regional D i s t r i c t . These included Coquitlam, Richmond, White Rock, Surrey, Port Coquitlam, the D i s t r i c t of North Vancouver, Port Moody and Delta. The c r i t e r i a used to select these areas were t h e i r decentential growth rates 44. from 1940 to 1970 as well as t h e i r future projected growth rates r e l a t i v e to other areas i n the G.V.R.D. Areas with s i m i l a r rates of population growth would tend to have s i m i l a r rates of new construction and turnover rates and would tend to be a l i k e i n such c h a r a c t e r i s t i c s as the age d i s t r i b u t i o n of t h e i r housing stock, l o c a t i o n and t h e i r physical design. Thus, t h i s s t r a t i f i -c ation was undertaken to keep our sample as homogeneous as possible with respect to those f a c t o r s . I t was decided that the sample would be representative of a l l the municipalities and c i t i e s as a whole, as to sample accurately f o r each i n d i v i d u a l c i t y and municipality would require an unreasonably large sample. However, the sample size of the universe was d i s t r i b u t e d proportionately among a l l the c i t i e s and municipalities according to t h e i r housing stock i n January 1976. It was necessary to s t r a t i f y the sample further accord-ing to the proportion of homes that had been b u i l t p r i o r to and subsequent to December 31, 1963. Information regarding proper-t i e s i n the f a s t growth municipalities and c i t i e s of the universe had been recorded from 1949 or t h e i r date of construction i f con-structed a f t e r January 1, 1949, to December 1963 i n the afore-mentioned study at U.B.C. and the information was available f o r incorporation into t h i s study. The sample had been randomly selected from the assessment ro l e s of the c i t i e s and municipali-t i e s involved. A l l that was required f o r t h i s proportion of the sample was an update of the sales on the properties up to July 1976. Approximately 40% of the housing stock of the universe i n 1976 had been constructed p r i o r to December 31, 1963. Thus 40$ of the sample represented housing constructed p r i o r to that date. 45. The sample of homes constructed a f t e r December 1963 was selected from various sources as co-operation from a l l the assess-ment o f f i c e s could not be obtained. The d i f f e r e n t sources included municipal b u i l d i n g permits, records of water connections and the assessment ro l e s of some municipalities and c i t i e s . From these sources, the l e g a l description and age of the dwelling were recorded as had been done with the previous data. The l e g a l description would be used i n t i t l e searches at the Land Registry-o f f i c e s and the age would be used i n the subsequent analysis of the price index. The properties i n a l l c i t i e s and municipalities were randomly selected from t h e i r sources. I t was necessary to "gross-up" the calculated required sample size i n order that the sampling procedure«would r e s u l t i n the required number of single family units for each municipality, the two time periods ( i . e . p r i o r to and subsequent to December 31, 1963) and f o r the universe as a whole. 3. Sample Size In the e a r l i e r study, i t was found that the turnover rate i n the f a s t growth areas was approximately ten to twenty percent (that i s , a f i v e to ten year ownership period). The sampling p r e c i s i o n f o r sample has thus been set at - 1 year f o r a ten year l e v e l of turnover and at a ninety percent confidence i n t e r v a l . Calculations indicated that a sample of 1785 properties would be s t a t i s t i c a l l y representative of the universe. This sample size represents I.55 percent of the t o t a l housing stock i n January 1976. 46. Approximately 2,300 properties i n a l l were searched. Four hundred properties were eliminated due to mistakes i n the recording of data, incomplete information, etc. Thus the f i n a l sample size consists of 1916 properties. Table I I I indicates the required and actual sample size, s t r a t i f i e d according to period, area and f o r the universe as a whole. The sources of the sample f o r January 1964 - June 1976 period are also provided. (See Appendix A f o r explanation of sampling procedure and Appendix B f o r formula used i n the derivation of siample s i z e ) . 47. TABLE III  SOURCE AND SIZE OF THE SAMPLE Area Number of Single Sample Size Source of 1964 Family Homes Required Actual 1976 Sample 1964 1976 1964 1976 1964 1976 Coquitlam 6,000 13,500 97 113 90 180 Bldg Permits Richmond 10,000 22,500 160 187 152 194 Bldg Permits D i s t r i c t of North Van. 10,000 17,000 119 139 130 152 Bldg Permits Port Coquitlam 2,000 6,500 48 54 40 82 Water Connections Port Moody 1,000 3,500 23 27 10 30 Water Connections Surrey 18,000 30,000 216 253 195 275 B»C.A.Ai .•_ White Rock 2,000 4,500 39 38 41 40 B.C.A.A. Delta 4.000 17.500 121 142 _82 218 B.C.A.A. Total 47,000 115,000 827 '—1 958 r—1 745 i 1.171 - 1 — 1 i - r - l 1,785 1,916 48. The actual number of properties recorded deviates some-what from the required number. Despite the grossing up f a c t o r , a large number of properties were lo s t due to incorrect l e g a l descriptions and subdivisions where the l e g a l description had changed. This was p a r t i c u l a r l y true f o r the portion of;the sample constructed p r i o r to 1964. 4. Data C o l l e c t i o n and E d i t i n g The following information was c o l l e c t e d f o r each of the properties. 1. Age of the dwelling 2. Location ( i . e . c i t y or municipality) 3. Date of sale (month and year) 4. Form i n which the sale took place ( i . e . agreement f o r sale or transfer of clear t i t l e ) 5- The Sales Price A f t e r the information was c o l l e c t e d , the data was edited to eliminate non-armslength transactions, transfers upon death and incomplete transactions data. Since some of the sample was c o l l e c t e d from b u i l d i n g permits, i t i s possible that even though a transaction took place within months of the issuance of the b u i l d i n g permit, i t may have only involved land as the house may not yet have been constructed. Thus possible land trans-actions were eliminated by the following procedure. An index of house prices was computed as a mean of a l l sales i n a given year. In 1949, the cost of a house l o t was estimated at approximately $1,500. Transactions i n that year that involved a value of less than $1,500 and f o r which a b u i l d -ing permit had been issued i n 1948 or 1949 were considered as land and eliminated from subsequent computations. This $1,500 value was then i n f l a t e d each year by the house price index 49. (44) calculated formerly to establish a l o t value i n each year. v ' A l l transactions that occurred below the estimated l o t value i n each year and involved a property that had reportedly been con-structed i n that or the previous year, were eliminated. A new house price index was then tabulated without the l o t values. Again t h i s index was used to i n f l a t e the $lf500 figure i n 1949 f o r the entire study period so that a new estimated l o t value f o r each year was established. Again, properties that did not meet the c r i t e r i a formerly outlined were eliminated. This procedure was repeated u n t i l the i t e r a t i o n s converged and no properties were being eliminated. This occurred on the t h i r d i t e r a t i o n . The eliminated values were not used i n formulation of the price index or i n computation of sales as part of the turnover rates. 5» Demolitions Since i t would be very time consuming to check with each area to f i n d i f demolition permits had been issued on any properties i n the sample, the following procedure was adopted. I f the age of the structure was very old (usually i n excess of 40-45 years at the time of transaction) and a transaction price f o r the property was extremely low i n what appeared to be an arm's-length transaction followed by another transaction with a r e l a t i v e l y high price compared to the former, then i t was assumed that the transaction p r i o r to the high value one involved a transfer of land. The property was then a r b i t r a r i l y considered demolished one month p r i o r to the sale of the "land" and was removed from the sample, e f f e c t i v e that date. It i s possible (44) Since no index f o r land prices existed during the study period, the house price index was used. It i s conceded however, that the price of land does not necessarily increase at the same rate as housing and the procedure used was rather a r b i t r a r y . 50. that the transaction p r i o r to the r e l a t i v e l y high priced one was merely a non-arm's-length transaction and not one involving land. However, the demolition consideration was f e l t to be j u s t i f i e d due to the advanced age of the property. As a r e s u l t of the adoption of t h i s procedure, 28 pro-perties were treated as demolished. Thus while 1916 properties represented the f i n a l sample s i z e , the actual sample in3il9?6 was 1888 properties. The number of houses i n the sample i s smaller i n the e a r l i e r years of the study period and grows progressively-larger each year r e f l e c t i n g the new construction i n our universe. Table "IV indicates the sample size i n each year. The difference between the size each year i s the additions to the stock l e s s demolitions i n that year. 51. TABLE IV SAMPLE SIZE BY YEAR YEAR SAMPLE SIZE ADDITIONS TO THE STOCK DEMOLITIONS CJ) K%) (PER YEAR) 1 9 4 9 234 22 10.38 1950 253 19 8.12 1951 26? 1 4 5.53 1952 2?8 11 4.12 1 9 5 3 304 26 9.35 1 9 5 4 328 2 4 7.89 1955 373 45 13.72 1956 416 43 11.53 1957 465 ^9 11.78 1958 543 78 16.77 1959 623 80 14.73 1 9 6 0 661 38 6.10 1961 6 9 2 31 4 . 6 9 1962 715 23 3.32 1963 740 25 3.5 1 9 6 4 774 36 4.86 2 1965 823 51 6.59 2 1 9 6 6 870 50 6.08 3 1967 985 119 13.68 4 1 9 6 8 1,069 87 8.83 3 1 9 6 9 1,138 71 6 . 6 4 2 1970 1,239 101 8.88 1971 1,334 9 6 7.75 1 1972 > 1,482 153 11.45 5 1973 1,691 2 1 4 14.44 5 1 9?4 1.784 94 5.56 1 1975 1,881 97 5.44 1976 1,888 7 .37 52. B. COMPUTATION .OF THE -INDEX The index i s tabulated on the basis of 2,641 transactions f o r 1916 properties. Almost 20$ of the sample did not turnover during the study period yet due to the manner i n which the sample was drawn, the data i s also applicable to the non-transacting segment of the housing universe. A r e l a t i v e f o r each year was calculated based on the r a t i o of the mean pri c e of single family homes sold i n each year to the mean price i n 1971. This series i s presented i n Table IV i n constant and current d o l l a r s and i s i l l u s t r a t e d i n Figure 1 The underlying assumptions„of the price index are as follows. It i s assumed that the transactions prices r e f l e c t true market value. In a l l l i k e l i h o o d , the recorded transaction prices i n the e a r l i e r years have some margin of error and i t i s possible that some non-arm's-length transactions were undetected. This index applies to both new and e x i s t i n g houses. An examination of Table IV reveals a varying number of new homes coming on the market each year. The movement of prices f o r new and e x i s t i n g housing i s assumed to be i d e n t i c a l f o r the purposes of the index. However, i t i s acknowledged that the absolute price l e v e l of new housing may be s l i g h t l y higher than the old as a premium may be paid f o r a new house i n "mint" condition. An increase i n the number of new homes i n any year r e l a t i v e to another would r e s u l t i n a corresponding increase i n the l e v e l of the price index r e s u l t i n g i n a higher value being imputed to the average value of the stock. I t i s also assumed that the movement of prices between any two periods approximates the movement i n price of a single 53. T A B L E ' V THE P R I C E INDEX AND TURNOVER RATES 1949-•1976 (1971*100) YEAR TURNOVER RATE P R I C E INDEX ( S A L E S / S T O C K ) (CONSTANT DOLLARS) (CURRENT DOLLARS) 1949 11.54 20.7 12.0 1950 6.32 30.0 17.9 1951 7.12 24.9 16.4 1952 7.19 25.0 16.9 1953 3.29 29.8 19.3 1954 4.88 25.9 17.4 1955 6.17 41.8 28.2 1956 9.86 42.2 28.9 1957 5.I6 50.8 35.9 1958 6.43 . 55-5 40.2 1959 7.-54 56.0 41.0 1960 6.34 60.0 44.6 1961 4.76 53.7 40.2 1962 6.15 64.5 48.9 1963 3.91 48.3 37.3 1964 7.48 58.2 46.2 1965 9.95 66.6 1966 IO.56 68.0 58.3 1967 12.58 78.8 70.8 1968 13.55 92.9 84.5 1969 11.15 98.2 94.4 1970 9.60 99.8 98.0 1971 13.71 100.0 100.0 1972 19.03 113.2 . 118.9 1973 24.13 125.2 139.8 1974 13.73 _ 157.2 195.3 1975 13.34 144.8 200.6 1976 (July) — I65.8 231.6 27 year mean 9.46 -5^ , 2 2 0 2 1 0 -2 0 0 -1 9 0 -180 -17Q 1 60-1 5 0 -1 4 0 -1 30 * 1 2 0 -1 1 0 -FIGURE 1 HOUSE PRICE INDEX a CURRENT AMD CONSTANT D0LL1RS (1971 = 1 0 0 ) Constant D o l l a r s Index C u r r e n t D o l l a r s Index 49 51 53 55 ¥t 5 5 S I 63 65 67 3 5 7 1 ?3 ?5 Y e a r 55. sample between the two years. However, the transactions i n each year do not involve the same physical units nor i s the sample size constant. It i s also assumed that the e f f e c t s of depreciation and a l t e r a t i o n s and repairs to the sample cancel out leaving a residual of an unknown magnitude. Any improvements to the proper-t i e s would tend to make the price larger than the t h e o r e t i c a l l y correct price v a r i a t i o n . Conversely, depreciation would cause the price to underestimate the correct price movement. The current d o l l a r price index rose during the f i r s t year of the study followed by a gentle decline to 195?. Prices rose i n 1953 but again f e l l i n 19$4 i n correspondence with a recessionary period i n the B.C. economy. A steady growth then insued which can to a large degree be attributed to the founding of the N.H.A. i n 1954. The price increase continued i n conjunc-t i o n with an expansionary period i n the economy u n t i l late 1959 and I960 when the B.C. unemployment rate rose and the economy went into a decline. Prices again gradually increased during the following recovery period only to drop to 1957 l e v e l s i n 1963. A f t e r 1963, a rapid price ascent began which has lasted to the present day. The increase was p a r t i c u l a r l y rapid a f t e r 1971 and may i n part be due to the f r e e i n g of the NHA i n t e r e s t c e i l i n g rates i n 1969. The largest price increase between any two years occurred between 1973 and 1974, which was also the period that recorded the highest amount of market a c t i v i t y as denoted by the turnover rates. The index i s designed to r e f l e c t changes i n the price of housing and the purchasing power of money. However, the price 56. of $20,000 f o r a home i n 1955 does not represent the same amount of purchasing power as i t does i n 1975' The same d o l l a r amount today could not currently purchase a house i n these communities. During the study period there were wide fluctuations i n the price l e v e l due to i n f l a t i o n and these fl u c t u a t i o n s were r e f l e c -ted i n the house price index. To eliminate t h i s influence as much as possible, the index was deflated by the Canadian Consumer Price Index, using a 1971 base ( i . e . 1971=100). The r e s u l t s of t h i s r e v i s i o n are also shown on Figure 1 and Table V . As would be expected, the chief r e s u l t of t h i s process i s to increase the l e v e l of the index of house prices p r i o r to 1971 and to reduce i t reduce i t f o r the years subsequent to 1971* The deflated series during the entire study period tends i n the same d i r e c t i o n as the o r i g i n a l index u n t i l 1974. Here the r e a l d o l l a r house prices decline though i n actual d o l l a r s the index experiences an increase. In t h i s period of i n f l a t i o n , the e f f e c t of the Consumer Price Index was so great as to force the constant index of house prices below t h e i r 1973 l e v e l . That i s , house prices i n 1974 were not increasing as r a p i d l y as were other goods. But when house price l e v e l s again began to r i s e i n 1975, they did not regain t h e i r previous 1974 l e v e l high. Thus the highest point i n the new series i s experienced i n 1974 unlike the o r i g i n a l series which records the highest price i n 1976. Throughout the entire study period to 1971» the r i s e of the o r i g i n a l index i s more gradual than the deflated. The largest difference i n absolute price l e v e l s between the two indicies p r i o r to 1971 i s experienced i n 1959. A f t e r 1971» the magnitude of the difference between the two indicies increases 57. at an escalating rate. It can be concluded that although the Canadian Consumer Price Index rose during the period of analysis, house prices were r i s i n g at a much f a s t e r rate, with the exception of 1 9 7 5 , so that r e a l d o l l a r house price index continued to r i s e : Except f o r 1975, the Consumer Price Index did not influence the d i r e c t i o n of the house price index. The r e a l d o l l a r house price index w i l l be used i n a l l subsequent a n a l y s i s . C. " TURNOVER RATES The turnover rate can be defined as the r a t i o of the number of sales of houses i n a given year to the t o t a l stock of houses i n that year. The turnover rate demonstrates the length of time that a home i s held before i t changes ownership. It i s a good i n d i c a t o r of the l e v e l of housing market a c t i v i t y at a given point i n time. For example, a turnover rate of 9 . 6 on Table V i n 197° indicates that on average, a house changed hands approxi-mately every ten years. In the following year when the turnover rate rose to 13*71, the average period of ownership f e l l to approximately seven years. The average turnover rate f o r the period 1 9 4 9 to 1975 was 9 . 4 6 implying an average ownership period of approximately ten years. The average ownership period ranged from approximately 8| years f o r the Municipality of Delta to 15 years f o r the D i s t r i c t of Surrey. The turnover rate i s comprised of three determinants— new and ex i s t i n g housing sales and the housing stock i n any one period. In a fast growth area where there i s a rapid rate of new construction, a r e l a t i v e l y larger portion of turnover i s 58. accounted f o r by new houses than i n an area experiencing slug-gish growth. As described i n the previous chapter, the turnover rate has implications as to the q u a l i t y of the index p a r t i c u l a r l y to the extent that the q u a l i t y of the housing units exchanged and t h e i r values d i f f e r each year. Thus, an unweighted average of the turnover rates or prices i n d i f f e r e n t growth rate areas would not be a good indicator;: of house prices or turnover rates f o r either area. Information on turnover rates and the l e v e l of market a c t i v i t y are important f o r several reasons. There i s a pos i t i v e c o r r e l a t i o n between the rate of house price increases and the rate of turnover i n the r e a l estate market. In a very active market, prices tend to increase at a more rapid rate than when the market i s i n a slump. This i s evidenced i n our data and i s i l l u s t r a t e d i n Figure 2 which com-pares the rate of turnover of housing and the movement of the general constant d o l l a r price index. The movement of both graphs cl o s e l y p a r a l l e l each other, with high l e v e l s of market a c t i v i t y corresponding to rapid price increases i n housing. A knowledge of turnover rates i s also of benefit to the home vendor and the mortgage lender. The turnover rate i s a good in d i c a t o r to the s e l l e r of the marketability of his home. A knowledge the average holding period of a home also benefits the mortgage lender as i t i s evidence of when he can expect to have his mortgage repaid. (45) Seek, H. N., "Fluctuations i n the Turnover of Single Family Dwellings In Vancouver", U.B.C. Thesis (unpublished), 1975. FIGURE 2 TURNOVER RATES FOR HOUSING, 1949-I975 ( s a l e s as a percentage o f s t o c k ) ~ 1 0 J 49 51 53 55 5 ? ?9 65 £5 5? £9 71 73 15 Year 6 0 . D * AGREEMENTS • FOR " SALE--Two hundred and f i f t y eight transactions during the study period were financed througli agreements f o r sale.--This represented approximately 10$ of a l l transactions..: Figure 3 i l l u s t r a t e s the movement of an index based on the constant d o l l a r mean sales values i n each year f o r these transactions and compares them to the o v e r a l l index. The index based on agreement fo r sales data generally appears to p a r a l l e l the movement of the o v e r a l l index though i t i s subject to greater f l u c t u a t i o n s . These fluctuations are l a r g e l y due to the small number of agreement f o r sale transactions recorded during those years. A simple overage, of the sales values thus w i l l be biased toward any extreme values,recorded i n that year. The periods during which the agreements f o r sale index deviated most from the o v e r a l l index corresponded to the periods when very few agreement f o r sale transactions were recorded. For example, i n 1 9 7 ° only four r i g h t s to purchase agreements were recorded and i n 1 9 7 5 only one of these transactions occurred. They are also the periods of the largest deviations from the o v e r a l l index, (see Table \VT). However, i t can be said that the prices of homes sold through agreements f o r sale were lower than those that involved a c l e a r transfer of t i t l e . The behaviour of agreements f o r sale data i s p a r t i c u -l a r l y important i n the creation of a housing price index. The number of agreements f o r sale i s expected to fluctuate i n response to changing c r e d i t conditions. During periods of c r e d i t res-t r a i n t , when mortgage funds are i n low supply, i t i s expected that the number of agreements f o r sale transacted would increase 6 1 . FIGURE 3 A COMPARISON OF PRICE INDICIES USING TOTAL AND AGREEMENT FOR SALE DATA ONLY (constant d o l l a r s , 1971 = 1 0 0 ) 1 0 J 49 51 53 55 5? 5*9 o l 63 65 67 69 Ti ? 3 15 Year TABLE VI AGREEMENTS FOR SALE YEAR NUMBER OF TOTAL SALES AGREEMENTS AGREEMENTS AGREEMENTS FOR SALE/ FOR SALE/ FOR SALE TOTAL SALES TOTAL STOCK (#) (#) (*) {%) 1949 14 27 52 6 1950 . 4 16 25 1.6 1951 7 19 39 2.2 1952 6 20 30 2.2 1953 3 10 30 1 1954 6 16 38 1.8 1955 3 23 14 .8 1956 9 41 22 2.2 195? i l 24 46 2.4 1958 9 35 25 1.7 1959 16 47 34 2.6 i960 11 42 26 1.7 1961 11 33 33 1.6 1962 7 44 16 1 1963 9 29 31 1.2 1964 6 58 11 .7 1965 12 82 17 1.5 1966 12 92 13 1.4 1967 12 124 10 1.2 1968 17 145 13 1.6 1969 12 127 10 1.1 1970 5 119 4 .4 1971 16 183 9 1.2 1972 14 282 5 .9 1973 8 408 2 .5 1974 10 245 4 .6 1975 2 251 0.8 .1 1976 6 117 5 .3 6 3 . i n that the vendors w i l l o f f e r easier terms i n order to market t h e i r property. Conversely, i n easy money periods the r e l a t i v e number of agreements f o r saleeto the t o t a l number of sales would be expected to decline. It was o r i g i n a l l y hoped that the agree-ment f o r sale data f o r t h i s sample could be analyzed with respect to price and turnover rate changes and c r e d i t conditions i n the economy. However, due to the paucity of t h i s data i n our sample, i t would be meaningless to draw any inferences as to t h e i r behaviour. A l l current indicies exclude data pertaining to these transactions. However, the repercussions on the index of. t h i s omission are unknown. A comparison was made of an index tabula-ted without the rights to purchase data and our formerly tabulated index v/hich incorporated t h i s data. The r e s u l t s are shown i n Figure L . The movement of the two i n d i c i e s i s i d e n t i c a l i n a l l years, even i n the e a r l i e r period when agreements f o r sale data formed a s i g n i f i c a n t proportion of t h e r t o t a l number of transactions. 64 FIGURE 4 A. COMPARISON OF THE OVERALL PRICE INDEX TO INDEX EXCLUDING AGREEMENT FOR SALE DATA ( c o n s t a n t d o l l a r s , 1971 = 100) " 180 -17CL 160-J 10-J 49 51 5~3 55 Ft 5*9 6~1 63 -65 &7 &9 71 73 t T ^ e a r 6 5 . CHAPTER 5  THE PROBLEM OF QUALITY CHANGE  IN A HOUSE PRICE INDEX The purpose of t h i s chapter i s to investigate, both at the s t a t i s t i c a l and conceptual l e v e l , the q u a l i t y dimensions of the house price index. The measurement of q u a l i t y change requires the develop-ment of a framework by which q u a l i t y may be measured. The analysis here i s r e s t r i c t e d to the consideration of two variables — r e l a t i v e value (or value range) and age. The r e l a t i v e value method consists of i d e n t i f y i n g value categories i n each year that are apparently q u a l i t a t i v e l y i d e n t i c a l and formulating a price trend l i n e f o r these r e l a t i v e l y s i m i l a r e n t i t i e s . This concept implies that there i s no unique combination of c h a r a c t e r i s t i c s that constitute a given l e v e l of q u a l i t y . The analysis using the age variables i s c a r r i e d out i n a s i m i l a r manner. However, i n t h i s approach, age i s assumed to define a c e r t a i n number of c h a r a c t e r i s t i c s which are associated with each vintage category. The analysis of value ranges also brings a second re-s u l t . We are able to examine the s t a t i s t i c a l impact on the price index that a s h i f t i n the turnover among d i f f e r e n t value ranges w i l l have on the q u a l i t y of our index. This issue i s treated i n the i n i t i a l section of t h i s chapter. A.PRICE CHANGES BY VALUE RANGE - STATISTICAL IMPLICATIONS FOR THE INDEX  This section w i l l determine the extent to which changes i n our price index may have been caused by s h i f t s i n the market 66. turnover to d i f f e r e n t values of homes during the study period. I f the index computed f o r each of the broad value ranges d i f f e r s and i f the proportion sales i n each category s h i f t s from year to year, then t h i s w i l l be the cause of some of the fluctuations of our price index and be quite apart from a change i n the value of the entire housing stock. In order to observe the rates of price change between di f f e r e n t value ranges, prices i n each year of the study period were assigned into three d i f f e r e n t value range?categories — low, medium and high value. The c r i t i c a l values delineating the value ranges were computed i n the following manner. Two c r i t i c a l prices f o r assigning properties i n the base year were selected — $22,500 and $32,500. Properties transacting with prices i n 19?1 of less than the former value were defined as low value homes. Proper-t i e s transacting at prices between the two c r i t i c a l values were defined as medium priced and properties which transacted at prices greater than the l a t t e r value were defined as high value on expensive homes. These c r i t i c a l values were then adjusted by the o v e r a l l house price index to maintain equivalent value ranges throughout the study period. These c r i t i c a l value ranges were chosen somewhat a r b i -t r a r i l y but when adjusted by the index were f e l t to r e f l e c t a general i n d i c a t i o n of what were considered to be upper and lower value homes during our study period. Tests were also done to ensure that a normal d i s t r i b u t i o n of properties existed among the value ranges. However, the actual d o l l a r value delineating the value ranges i s f e l t to be r e l a t i v e l y inconsequential as any 67. reasonable c l a s s i f i c a t i o n of value ranges w i l l serve f o r our analysis. Table VII i l l u s t r a t e s the c r i t i c a l value ranges f o r each year of the study period. Price / i n d i c i e s based on these c r i t i c a l values were calculated f o r each of the value ranges f o r the years of our study period. The price i n d i c i e s were tabulated using the average price within each value range i n each year taken as a r e l a t i v e (46) to the average price i n that value range i n the base year. The si g n i f i c a n c e of these disaggregated i n d i c i e s i s dependent upon the difference i n the behaviour among the i n d i c i e s and on the turnover rates of these d i f f e r e n t value ranges over time. I f the rates of price change of d i f f e r e n t value categories are highly correlated through time and the turnover rate f o r each of the ranges i s f a i r l y constant, then the o v e r a l l index s a t i s -f a c t o r i l y denotes the movements of house prices through time. I f however, the values of the i n d i c i e s move independently of each other and the turnover rate s h i f t s across the categories, then our index i s of li m i t e d use. F i r s t , as expected, there has been a continuous price appreciation of a l l the value ranges. The average rate of app-r e c i a t i o n over the twenty-six year period (1949-1975) was 5.3 points i n the index f o r the low value range, 4.7 points f o r the medium range and 4.5 points i n the high value range. The average rate of appreciation i n the aggregated index was 4.7 points per year. (46) For more meaningful r e s u l t s i n tables and f o r easier "viewing i n charts, the base.years used are 1971 and 1975 respectively. 68. TABLE VII CRITICAL PRICES FOR ASSIGNMENT TO VALUE CLASSES Year Low Value Class Medium Value Class High Value 1949 2,400 3,900 3,400 3,400 1950 5,600 5,600 1951 3,700 5,400 5,400 1952 4,200 6,000 6,000 1953 4,900 7,100 7,100 1954 3,700 5,400 5,400 1955 6,100 8,900 8,900 1956 6,700 9,600 9,600 195? 9,400 13,600 13,600 1958 9,200 13,300 13,300 1959 9,000 13,000 13,000 1960 10,700 15,400 15,400 1961 9,200 13,200 13,200 1962 10,900 15,800 15,800 1963 8,900 13,000 13,000 1964 10,600 15,300 15,300 1965 12,100 13,100 17,400 17,400 1966 18,900 18,900 196? 15,900 23,000 23,000 1968 19,000 27,500 27,500 1969 21,200 20,500 30,700 30,700 1970 31,900 31,900 1971 22,500 32,500 32,500 1972 26,800 38,600 38,600 1973 31,500 45,400 45,400 1974 43,900 63,500 63,500 1975 45,100 65,200 65,200 1976 5L700 74,700 74,700 4 9 5 1 53 55 57 59 61 65 67 69 71 73 75 Y e a r 70. From these r e s u l t s , we can see that the lowest value range experienced the rapidest add generally the steadiest rate of appreciation. The index f o r the high value homes experienced the slowest and most e r r a c t i c growth r e l a t i v e to the other two i n d i c i e s . The growth of the two more modest housing i n d i c i e s has been, to an extent, s t a b i l i z e d by the o f f e r i n g of NHA f i n a n -cing which has l a r g e l y been geared to those purchasing lower value homes. F a l l s i n the house values to a large degree corres-ponded to recessionary periods i n the economy but the declines seemed most prolonged i n the lower value range. Generally, i n comparing the i n d i c i e s i t can be said that the price appreciation of each i n d i v i d u a l index varies greatly p a r t i c u l a r l y i n the short run. The price index f o r the high value range, while i n many cases p a r a l l e l i n g the movement of the other two i n d i c i e s , has a tendency to exaggerate most price changes. Therefore, the index must make allowances f o r the d i f f e r e n t price movements i n each category, as well as r e -cognize the impact that a change i n the-turnover rates among ranges has on the behaviour of the index. For example, i f sales i n one period were concentrated i n the high value category but prices i n that category were f a l l i n g r a p i d l y and r i s i n g i n the two remaining categories, then the price recorded by an aggre-gate index may i n f a c t be downward biased. On the other hand, i f sales were to s h i f t to the high value range and the value of these homes were r a p i d l y appreciating while homes i n the other two categories were declining, then the increase experienced i n our aggregate index would be even further biased upwards, than expected from a s h i f t i n turnover rates. 71. Thus, an aggregated index may be biased by a s h i f t i n sales among value ranges and by d i f f e r i n g rates of appreciation between value ranges. I f the former problem or the two i n com-bination are encountered i n an index, then an aggregated index i s of l i m i t e d relevance i n measuring house price trends. Table VIII.illustrates the percentage of sales taking place i n each of the value range categories i n each year. A cumulative price series was tabulated to analyze the e f f e c t s on the behaviour of the index of t h i s d i s t r i b u t i o n of turnover rates through time and are i l l u s t r a t e d i n Figures 6 and 7 . The cumulative i n d i c i e s were calculated by adding the prices i n the value ranges from the lowest value range up i n successive steps. V(L) represents the lowest value range, V(LM) i s the index f o r the lowest and middle value range and V(LMH) represents a l l the value ranges. V(LMH), since i t represents a l l sales, w i l l be i d e n t i c a l to the o v e r a l l price index c a l c u -lated formerly. The price i n d i c i e s i n each range were formed by c a l c u l a t i n g a simple average of a l l the sales prices i n each year i n each value class r e l a t i v e to the average price f o r that class i n the base year. (See Appendix B f o r derivation of t h i s index.) The cumulative value range L(LM) price series exceeded the V(L) series f o r the periods 1949-50. 1952-5^, 1956-71 and 1974-75. These generally corresponded to the periods i n which there had been a s h i f t from the previous year i n sales to the medium value range category where, by d e f i n i t i o n , a r e l a t i v e l y higher absolute l e v e l of prices are found. For example, i n 1952, f i f t y percent of a l l sales were recorded i n the low value category and twenty percent i n the medium category. In the following year 72 TABLE VIII DISTRIBUTION OF SALES AMONG VALUE RANGES BY YEAR Year Low m Medium High ~ r f 7 Total Number of Sales (#) 1949 29.6296 25.9259 27 1950 31.2500 37.5OOO 31.2500 16 1951 50.0000 22.2222 27.7778 18,--1952 50.0000 20.0000 30.0000 20 1953 40.0000 40.0000 20.0000 10 1954 37.5000 I8.75OO 43.7500 16., 1955 40.9091 18.1818 40.9091 22 1956 50.0000 9*5238 40.4762 42 1957 • 41.6667 37.5000 20.8333 24. 1958 32.3529 35-2941 32.3529 34 1959 40.0000 28.8889 31.1111 45 I960 38.0952 28.5714 33f3333 42 1961 39.3939 30O030 30.3030 33 1962 34.0909 34*0909 31.8182 44-1963 41.3793 31.0345 27.5862 29 1964 36>2069 41.3793 22.4138 58 1965 39.0244 29.2683 31.7073 82 1966 33.6956 35*8696 30.4348 92 1967 43 * 5484 33.8710 22 . 58O6 124 1968 29.6552 45.5172 24.8276 145 1969 29.9212 48.0315 22.0472 127 1970 28.5714 49.5798 21.8487 119 1971 28.9617 50.8197 20.2186 l83r 1972 32.2695 48.2269 19.5035 282-1973 24.7549 52.9412 22.3039 408 1974 26.1224 49,3877 24.4898 245 1975 23.1076 57*7689 19.1235 251 27-Year 36.00 Average 35.57 28.42 \ 120 H 73, FIGURE 6 110-4 100 H 90 H 80 J 70 H 2 Z H .60 — I w AC 0-50 -J 40 J "50 H 20 -J PRICE INDICIES BY CUMULATIVE VALUE RANGES-LOW AND LQW«DBLE^VJlLm RANGES ( c o n s t a n t d o l l a r s , 1975 = 100) 1 0 4 Low V a l u e Range • Index M^-SMid'dl^uValue,; tSaiage. Index 1 1 j 1 1— 49 51 53 55 57 59 Ti 6*3 65 I7 S ~I I I T o o -n 5 6 69 71 . 73 75 e a r 120 H 74. FIGURE 7 110 100 H 90 H 80 -J 70 - J .60 J r i 50 H 4o 4 "50 20 -J PRICE INDICIES BY CUMULATIVE VALUE RANGES-LOW-MIDDLE 1N.D010 f ABO VALUE RANGES ( c o n s t a n t d o l l a r s , 1975 = 100) — Tdt'al Value Range - -• Low-Middle Value Range Index 1 0 4 1 "I 1 1 1 1 ~ J T 1 T T 1 1 1" 49 51 53 55 57 59 61 63 65 67 69 71 73 75 75. however, the sales i n the low value category dropped to f o r t y percent of the t o t a l and sales i n the medium range increased to f o r t y percent, causing the cumulative index to r i s e . When the proportion of sales again declined i n the medium category i n 1954 to eighteen percent of the t o t a l and the proportion i n the low category remained constant, the cumulative index as a r e s u l t , f e l l below V(L). As mentioned e a r l i e r , any di s t o r t i o n s i n the series due to a s h i f t i n the turnover rates can be further aggravated i f the rate of appreciation among the value ranges i s uncorrelated. In 1956, f i f t y percent of a l l sales occurred i n the low value range and nine and one h a l f percent i n the medium range. Conse-quently on Figure 6 , the V(L) index i s above V(LM). In 1957, the proportion of sales s h i f t e d to an almost equal d i s t r i b u t i o n between the two ranges. Consequently, one would expect the cum-u l a t i v e index to s h i f t up. This s h i f t however, was further mag-n i f i e d by a rapid appreciation i n the prices of homes i n the medium value range r e l a t i v e to that i n lower range. (Prices i n the medium range i n between 1956-57 increased by 14.35 points i n the index while prices i n the lower range increased by only 3.21 points (1971=100) ) . Thus the cumulative index shows an even more rapid increase than i s s o l e l y a t t r i b u t a b l e to a s h i f t i n sales between the two ranges. Figure 7 compares the two cumulative series V(LM) and V(LMH). The V(LMH) series remained above the V(LM) index throughout the study period though not at a constant l e v e l . For example from 1954 to 1955, the d i s t r i b u t i o n of sales s h i f t e d from twenty percent i n the high value category to forty-three 76. percent. Therefore the o v e r a l l index correspondingly r e f l e c t e d the change i n the d i s t r i b u t i o n of sales. However, t h i s increase was further magnified by the fact that expensive housing r e l a t i v e to the other two categories, experienced the largest increase i n prices i n that year. Our cumulative index V(LMH) would accor-dingly r e f l e c t t h i s e f f e c t as w e l l . In order to f i n d out the e f f e c t on _the. index i f turn-over rates had remained constant throughout the study period, the twenty-sevenyearraVerage of the d i s t r i b u t i o n of sales was f o r -mulated and the value range i n d i c i e s weighted by t h i s f a c t o r . The twenty-seven year average turnover rates were calcu-lated i n the following manner. A l l the properties i n the sample are allocated to a value range, e i t h e r according to t h e i r sales price i n a given year, or i f the property did not s e l l i n a given year, the nearest relevant sales price i s adjusted by the o v e r a l l price index f o r that year. Those properties which did not transact during the study period were randomly assigned to a category i n each y e a r ^ " ^ to permit the determination of turnover rates. The twenty-seven year average turnover rate for each of the value ranges was calculated and used to weigh t h e i r respective index. The r e s u l t s are presented and compared to the raw index i n Figure 8 A (see Appendix B f o r derivation of t h i s index). As expected, the fluctuations i n weighted index are su b s t a n t i a l l y smaller than f o r the raw index because the v a r i a t i o n (4-7) An examination was f i r s t c a r r i e d out on a sample of these properties that did not transact to see i f they tended to be concentrated i n one p a r t i c u l a r value category. Assuming a strong c o r r e l a t i o n between assessed value and market value, the assessed values of these properties were examined and the values of the properties were ascertained as being randomly d i s t r i b u t e d . TABLE IX PERCENTAGE OF HOMES TRANSACTING EACH YEAR BY VALUE RANGE * YEAR LOW MEDIUM HIGH WJ W ki) 1949 4.624 9.420 IO.345 1950 3.371 4.828 4.167 1951 5.291 4.167 3.704 1952 5.882 3.636 4.225 1953 2.985 I.258 2,410 1954 2.913 3.067 5? 618 1955 4.651 2.857 8.081 1956 , 9.607 3.?84 11,927 1957 5.350 3,865 2.804 1958 4.669 7.759 4,167 1959 7.143 7,755 5*926 1960 5*594 9.328 0.?69 1961 4*377 4.895 4.615 1962 5.405 5.903 7.857 1963 4.333 3; 729 3.521 1964 7.591 8.563 4.395 1965 IO.510 10.983 6.748 1966 9.440 15.042 3.409 1967 14.706 13.043 6.630 1968 11.488 17.611 6.829 1969 9.476 13.904 5.612 1970 8.7O6 11.022 6.220 1971 12.984 16.157 6.393 19?2 19.106 21,364 9.524 1973 22.306 26,603 15 •769 1974 13.704 14.243 10 .294 1975 11.797 15.740 6.738 27-Year 6.267 Average 8.445 9.649 * Done on the basis of assigned stock 120 H 110 — I 100 H 90 H 80 J 70 H .60 J Ui o 2 H 50 H 40 J 30 H 20-^ 10 -J 78, FIGURE 8 A COMPARISON OP THE WEIGHTED VALUE RANGE INDEX TO THE OVERALL PRICE INDEX (constant d o l l a r s , 1975 = 100) O v e r a l l Index • Value Range -Weighted Index "1 ' " ' ' Ji 63 6*5 67 5 71 73 75 Y e a r 49 51 53 55 57 59 79. i n the s h i f t s between value ranges have been minimized. The analysis i n t h i s section c l e a r l y indicates the need f o r adjustments i n the c a l c u l a t i o n of i n d i c i e s to control f o r the s t a t i s t i c a l e f f i c i e n c y of the index with regard to d i f f e r i n g rates of appreciation and changes i n the d i s t r i b u t i o n of sales f o r each of the value ranges. The results obtained here are s u f f i c i e n t to raise doubts as to the v a l i d i t y of housing price i n d i c i e s weighted by the actual number of sales. B. VALUE RANGE - CONCEPTUAL CONSIDERATIONS To t h i s point, we have dealt with the concept of value ranges to measure the s t a t i s t i c a l e f f i c i e n c y of the index. Nevertheless, value range categories can also be used as a mea-sure of q u a l i t y . One way to measure q u a l i t y differences between v a r i e -t i e s of a good i s to compare t h e i r s e l l i n g price at the same point i n time. I f the prices negotiated are ca r r i e d out under armslength conditions, we tend to view the price d i f f e r e n t i a l as the markets o v e r a l l estimate of the q u a l i t y difference be-tween the products. This philosophy i s even more applicable i n the housing market. Unlike the case of most consumer goods where prices and outputs are set by the producer, housing p r i c e s , since they are determined j o i n t l y by the purchaser and vendor, represent the true market valuation of q u a l i t y . Therefore the reasoning i s that i f d i f f e r e n t q u a l i t i e s of homes are sold con-currently and i f one home s e l l s f o r more than another unit, the difference would r e f l e c t a better quality home. In short, i t i s assumed that differences i n the c h a r a c t e r i s t i c s of homes that would lead the buyer to pay more f o r one over the other are 8 0 . recorded as a difference i n q u a l i t y . This approach encorporates a l l the c h a r a c t e r i s t i c s that made up q u a l i t y . It captures the location, size of the dwelling, st y l e and workmanship as w e l l as other features of a home c o l -l e c t i v e l y into one comprehensive variable — value category which i n turn i n each year r e f l e c t s the r e l a t i v e q u a l i t y of the unit to the ex i s t i n g stock of units i n that year. The i n d i c i e s that were formulated i n the previous sec-t i o n f o r the three value range categories are u t i l i z e d here also . Homes i n the low value range are defined as being of r e l a t i v e l y i n f e r i o r q u a l i t y i n r e l a t i o n to the rest of the housing stock e x i s t i n g i n that year. Homes i n the high value range are now considered as superior q u a l i t y homes, again r e l a t i v e to the ex i s t i n g stock i n that year. The homes found i n the middle value category are considered as your " t y p i c a l " home being of average .quality i n r e l a t i o n to the ex i s t i n g stock. The index numbers generated f o r each category are con-sidered to be based upon the prices of groups of houses, the houses i n each group being s i m i l a r with respect to t h e i r q u a l i t y r e l a t i v e to the other units i n that period. Thus, i n short, the indicies r e f l e c t the change over time i n the prices of houses that are homogeneous i n r e l a t i v e q u a l i t y . The movements of the in d i v i d u a l i n d i c i e s were analyzed i n the previous section and i l l u s t r a t e d i n Figure 5 and w i l l not be repeated here. Disaggregation into value ranges i s p a r t i c u l a r l y d e s i r -able f o r monitoring the general house price l e v e l f o r income group. Assuming a c o r r e l a t i o n between income and the price of the unit sought, investigations can be made of the economic . 81. status of i n d i v i d u a l s with respect to housing. Since most govern-ment p o l i c i e s today seem to be directed toward lower cost housing, t h i s disaggregation could also serve i n the evaluation of the impact of government p o l i c y on these housing sub-markets. Another advantage of t h i s approach i s that the v a r i a b l e — value range—requires no a d d i t i o n a l data i n that i t i s inherent i n the process of generating the index i t s e l f . However, t h i s advan-tage i s to an extent outweighed by the loss of d e t a i l as r e l a t i v e q u a l i t y i n a somewhat intangible concept that doesn't define the components of housing q u a l i t y . However, i t i s f e l t that t h i s approach i s preferrable to a complete disregard f o r q u a l i t y . Another l i m i t a t i o n of using value ranges as a surrogate f o r q u a l i t y i s the f a c t that homes w i l l s h i f t among value ranges through time as tastes change. Consumers may view d i f f e r e n t a t t r i b u t e s of the home d i f f e r e n t l y from period to period, so that t h i s s h i f t i n tastes w i l l a l t e r demand and reduce the d e s i r a b i l i t y of c e r t a i n homes and reduce t h e i r measure of q u a l i t y . In the same way, the preferred houses w i l l show an increased measure of q u a l i t y quite apart from any inherent change i n c h a r a c t e r i s t i c s . Another shortcoming of t h i s approach i s that i f we wished to aggregate the index, t h i s method would allow us no means of weighting the sample. Weighting i s desirable f o r two reasons. F i r s t , weighting the sample by some f a c t o r that a c t u a l l y represents the composition of the sample with respect to that factor, changes the meaning of the index i n that i t i s represen-tat i v e of the price changes of the sample (and hence the entire stock) and not merely representative of the stock changing hands. Secondly, weighting eliminates some of the s t a t i s t i c a l d i s t o r t i o n s 82. of the index i n that i t controls f o r the s h i f t s i n sales among di f f e r e n t value classes. Without weighting, we have to.*/.make the rather strong assumption that the price obtained i n any period f o r a p a r t i c u l a r category represents the t o t a l market i n that category. These prices are unavoidably weighted by d i f f e r e n t sets of weights i n each year which are produced as a re s u l t of market conditions ( i . e . , the proportion of sales i n each category) rather than based on some concept of the composition of the t o t a l stock ( i . e . , the proportion of t o t a l stock i n each category i n any year). G. AGE CATEGORIES - CONCEPTUAL CONSIDERATIONS Another c h a r a c t e r i s t i c which i s related to q u a l i t y i s the age of the structure. Age combines the influence of deterio-r a t i o n (state of r e p a i r ) , b u i l d i n g s t y l e , layout e f f i c i e n c y , l o cation and other variables and these variables are a l l a func-t i o n of q u a l i t y . Other studies dealing with hedonic price i n d i c i e s have confirmed that the c h a r a c t e r i s t i c s associated here with age are important i n defining q u a l i t y . Thus, since i n housing the physical u n i t , l o c a t i o n and type of neighbourhood a l l d i f f e r widely, defining the market into age groups make the housing i n each of the age groups more homogeneous with respect to c e r t a i n c h a r a c t e r i s t i c s . Generally, i t was assumed that the older the structure, the more maintenance was required f o r the structure, the less functional the layout and u t i l i t i e s offered and a clo s e r p r o x i -(48) mity to the downtown core existed. Thus, assuming a (48) It i s conceeded however that a l t e r a t i o n s and repairs often take place i n older homes which would change the character-i s t i c s associated with these dwellings. However, t h i s f a c t o r cannot be captured i n t h i s approach. 83. functional r e l a t i o n s h i p exists between the age and a set of c h a r a c t e r i s t i c s of the building, we can estimate an index f o r the d i f f e r e n t q u a l i t i e s . The sample was c l a s s i f i e d into three age groups to make the d i s t i n c t i o n between three general q u a l i t y l e v e l s . The years 0 to 10, l l to 25, and greater than 25 years were selected as the three categories as i t was f e l t that these vintages were the most representative of construction patterns and methods, location and housing workmanship at the time of construction. The indicies f o r each of the age groups are presented i n Figure 9 • The underlying process here i s s i m i l a r to that used i n the value range category. The index numbers generated f o r each category may be considered to be based upon prices of groups of houses, the houses i n each group being s i m i l a r with respect to various c h a r a c t e r i s t i c s as defined by the age variable at the time of each i n d i v i d u a l transaction. Thus the i n d i c i e s r e f l e c t the change over time i n the prices that have a constant mix of the c h a r a c t e r i s t i c s associated with t h e i r age. The d i f -ference of t h i s approach as opposed to the one used by value range i s that here there i s an emphasis on the physical hous-ing unit i t s e l f and i t s basic features such as s t y l e and locat i o n . The age variable confirms c e r t a i n c h a r a c t e r i s t i c s while the value range d e f i n i t i o n was more abstract. > An examination of the i n d i c i e s i n Figure 9 reveals no correspondence i n t h e i r movements. Judging from t h i s , each vintage appears to be governed by separate market forces. Some of the fluctuations i n the movement of the oldest vintage category, p a r t i c u l a r l y i n the e a r l i e r period, can be i n part at t r i b u t e d to 120 H 110—1 84. FIGURE© PRICE INDICIES BY AGE CATEGORY (constant- d o l l a r s , 1975 = 100 H 90 H 80 - \ 70 H •a 1^60-1 i u o a P- 50 H 40 -J 30 4 20 4 104 Index f o r .5Young"--.'.Hou'singc Index for"Middle-Age"Housing Index f o r "Old" Housing (age defined at time of transaction) 49 • 51 53 55 57 59 61 6*3 65 67 69 71 73 75 Y e a r 8 5 . the small number of observations recorded i n that period. Conversely, the young age category index, which has the most steady rate of appreciation i s made up of the largest number of transactions. This i s a p r a c t i c a l d i f f i c u l t y encountered i n d i s -aggregation exercises i n that i t i s necessary to get a large number of observations i n order to get a v a l i d estimate f o r an index and i t gives a better appreciation of the problems that are encountered i n the construction of hedonic price i n d i c i e s . These separate i n d i c i e s were then weighted by the pro-portion of t o t a l sales i n each year taking place i n each vintage category and aggregated into one index. However, t h i s index r e f l e c t s the price of the stock Changing hands i n each year only and not the entire stock and may be subject to the e a r l i e r d i s -cussed s t a t i s t i c a l d i s t o r t i o n s as turnover rates across d i f f e r e n t vintages are not constant throughout the study period. A second index was thus constructed using the prices generated f o r each of the i n d i c i e s but weighted by the stock i n each of the vintage categories. The weights i n t h i s l a t t e r index are not constant from period to period e i t h e r as part of the stock i n each year becomes older and s h i f t s to an older category and new houses are b u i l t and enter into the weighting f o r the youngest age category. However, t h i s aggregated price index r e -f l e c t s the price of entire housing stock and not only one stock changing hands i n any year. These two i n d i c i e s have been presented i n Figure 10. (See Appendix B f o r the derivation of these i n d i c i e s ) , A comparison of the sales weighted index to the stock weighted index should i l l u s t r a t e the d i s t o r t i o n s that occur i n the movement of the former index caused by s h i f t s i n the turnover 49 51 53 55 57 59 Jl 6*3 6*5 67 5 71 73 75 87. rates between vintage categories. However, the two i n d i c i e s show a remarkable correspondence i n movement. The weighting factors used f o r each index are presented i n Table X . The percentage of t o t a l sales i n each period occu-r i n g i n a vintage category was found to be c l o s e l y correlated with the percentage of t o t a l stock i n each vintage. Thus, t h i s explains the close correspondence i n the movement of the i n d i c i e s . The stock weighted index i s compared to the raw index generated formerly. The correspondence between the two i n d i c i e s i s quite s t a r t l i n g p a r t i c u l a r l y i n tracing t h e i r movements since 1962. The raw index i s s l i g h t l y more i n f l a t i o n a r y i n the e a r l i e r period but the d i r e c t i o n of the pr i c e ; changes are i d e n t i c a l except during 1952-54. The deviation i n t h i s period i s caused by the f a c t that no sales were recorded i n the old vintage category, causing the q u a l i t y adjusted index to dip below the raw index. The r e s u l t s from t h i s comparison are s u f f i c i e n t l y en-couraging to suggest that dissaggregation f o r q u a l i t y control purposes i s unnecessary to accurately r e f l e c t price measurement changes i n housing. We have however assumed that q u a l i t y can be to a large degree, i n f e r r e d from t h e i r ages at the time of t h e i r transaction. The problem inherent i n t h i s approach, as i n the value range approach, i s that the q u a l i t i e s of the transacting units w i l l vary i n the long run. Many engineering improvements and al t e r a t i o n s i n design have occurred and materials and the q u a l i t y of workmanship has changed over the study period. Therefore, a comparison of the c h a r a c t e r i s t i c s of a new^house i n 1975 may 49 51 53 55 57 59 Ji 5 65 67 5 71 73 75 Y e a r 89. TABLE X WEIGHTING FACTORS FOR AGE AGGREGATED INDICES Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 New 77.78 31.25 77.78 65.00 90.00 56.25 63.64 64.29 79.17 70.59 77.78 83.33 66.67 75.00 51.72 62.07 64.63 76.09 67.74 74.48 66.14 66.39 67.76 63.48 76.96 75.10 70.12 % of Sales i n Each Age Category Middle 14.81 25.00 22.22 30.00 10.00 43.75 27.27 26.19 16.67 23.53 13.33 x4.76 18.18 20.45 34.48 18.97 30.49 15.22 25.00 20.00 28.35 25.21 25.14 29.08 17.40 18.37 20.72 "~0Td 7.41 43.75 0.0 5.0 0.0 0.0 9.09 9.52 4.17 5.88 8.89 11.90 15.15 4.55 13.79 18.97 4.88 8.?0 7.26 5.52 2-51 8.40 7.10 7.45 5.64 6.53 9.16 New 60.68 62.05 58.80 57.91 59.86 60.67 59.24 57.93 58.92 63.05 65.97 64.65 63.54 62.70 62.48 6O.77 60.19 57.17 57.80 56.54 52.23 49.75 50.41 53.17 57.65 58.46 58.79 % of Sample i n Each Age Category Middle 27.35 25.29 28.46 29.85 27.30 27.43 29.49 30.04 30.32 25.55 23.59 23.26 24.92 25.83 25.91 27.35 28.15 30.19 30.32 32.05 36.43 37.98 36.47 33.94 30.45 29.65 28.76 Old 11.95 12.64 12.73 12.23 12.82 11.89 11.26 12.01 10.75 11.39 10.43 12.08 11.52 11.45 11.60 II.87 11.65 12.62 11.86 11.40 11.32 12.25 13.10 12.88 11.88 11.88 12.44 90. involve a d i f f e r e n t set of components to that of a new house i n 1949. In t h i s way, the q u a l i t y of our index w i l l have been influenced., This problem can be resolved i n the following manner. This methodology compares the prices of a l l sales of houses at the same point i n time so that the r e l a t i v e q u a l i t i e s and char-a c t e r i s t i c s of each vintage are determined by consumers at that time. However, i t i s hypothesized that the r e l a t i v e q u a l i t y and c h a r a c t e r i s t i c s of each vintage i s constant throughout the study period. That i s to say, new houses i n 1949 and 1975 w i l l be s i m i l a r with respect to t h e i r state of repair, d e s i r a b i l i t y of style and layout, location with respect to the CBD, etc. r e l a t i v e to the other vintages i n the stock i n t h e i r respective years. Thus, t h i s r e l a t i o n s h i p i s kept constant throughout the study period and not the actual physical' unit denoting a p a r t i c u l a r vintage. An index holding the actual physical unit constant throughout the study period was also attempted. The entire stock of housing i n our sample was c l a s i f i e d into one of the three age groups according to each unit's age i n 1975* Index numbers were computed f o r these groups and are considered to be based on the prices of groups of houses, the houses i n each of the groups being s i m i l a r with respect to c h a r a c t e r i s t i c s such as state of repair, s t y l e , l ocation, etc. i n 1975* The indices are presented i n Figure 1 2 . The problem inherent i n t h i s approach i s that while the physical unit i s held constant throughout the study period, i t s condition s t e a d i l y deteriorates r e l a t i v e to the e x i s t i n g stock as we approach the 120 110 100 90 80 J f 7 0 H 0-60 J 40 J 30 A 20 - J FIGURE 12 APPRECIATION OF THE HOUSING STOCK,1975 (constant d o l l a r s , 1975 = 100) li 91. I 10 Index f o r B*4ttfigHf!u-.H©using •Index f o r "Old" Housong %— — • Index f o r "Middle-Age" Housing (age d e f i n e d as of 1975) 49 51 53 55 57 59 fi fe 6*5 67 69 71 73 75 Year 92. present period. Thus the consumer valuation of each of these units, r e l a t i v e to the e x i s t i n g stock, changes through time as the units q u a l i t y changes even though the physical unit i t s e l f does not change. As a r e s u l t , the former vintage approach i s favoured as a l l t h i s approach i l l u s t r a t e s i s the appreciation of the housing stock today. The advantage of using the age a t t r i b u t e i s that we are able to summarize an associated number of c h a r a c t e r i s t i c s into one variable that i s r e l a t i v e l y easy to obtain. The index computation i s r e l a t i v e l y straightforward and i t s meaning i s i n t u i t i v e l y obvious. It appears to give a better or more tangible d e f i n i t i o n of what i s considered as q u a l i t y and allows a stock composition weighting. This variable, while i t i s not e n t i r e l y comprehensive i n i t s conceptualization of q u a l i t y , i s viewed as being better than a complete disregard f o r q u a l i t y i n the index. D. VALUE RANGE AND VINTAGE CATEGORY It may be desirable to further refine the measure of q u a l i t y by segregating the housing stock into categories that combine i t s age and value range. The reasoning behind t h i s , i s that there may be several features i n a house that may cause i t to be more or less expensive than another house b u i l t during the same period. Thus there exist d i f f e r e n t q u a l i t i e s of homes among the vintage categories — e.g. high q u a l i t y , new and old (4-9) houses, average q u a l i t y old and new houses, etc. The stock was segregated into combinations of the two variables and indexes were tabulated. The s t a t i s t i c a l d i f f i c u l t y (49) This, i s the delineation used i n the Mieszkowski, Saper study. 93. that arose i s that with t h i s approach i t i s necessary to get a large number of observations i n order to get a v a l i d index number. I t requires an extensive amount of data to describe house q u a l i t y at t h i s more disaggregated l e v e l and our data was found to be limi t e d f o r t h i s a n a l y s i s . E. BAILEY. MUTH & NOURSE MODEL The Bailey, Muth and Nourse model outlined e a r l i e r i n Chapter 2 was used with LRO data i n the development of a price index f o r the sample. The model which i s based on the. repeated sales of i n d i v i d u a l properties, i s sp e c i f i e d below. R i t f = V x U i t t * , or B t r i t t ' = ~ b t "* V + u i t f Where = the r a t i o of the f i n a l sales price i n period t ' to the i n i t i a l sales price i n p e r i o d t f o r the i t h p a i r of transactions with i n i t i a l and f i n a l B ^ sales occuring i n these two periods; B t , ' J - the true but unknown i n d i c i e s f o r period t and t ' • •!/, ' U. + . i = the residuals which are assumed to have zero means and uncorrelated variances i n the log form. Where the lower case l e t t e r s represent the logarithms f o r the values indicated by the upper case l e t t e r s above. The comparison of t h i s index and the average price i n -dex formulated e a r l i e r are presented i n Figure 13. Two disturbing features of t h i s index are immediately apparent. F i r s t , some of the price movements are supris i n g l y large, e s p e c i a l l y i n the l a t t e r years. Second, there i s complete disagreement between the movement of the two i n d i c i e s i n some periods. For example, one of the largest price increases recorded by the B-M-N model 120 H 9 4 . FIGURE 1 3 ' 1 10 100 H 90 H 80 -A 70 H UJ 41 ,Z.6o h 150 40 J 30 H 20-^ A COMPARISON OF THE B-M-N MODEL INDEX TO -LRQ INDEX (constant d o l l a r s , 1975 = 100) 10 ERO Index, • -* B-M-N Index 4 9 51 53 55 57 59 ?i ?3 6*5 67 5 71 73 75 95. occurred i n 1974-1975• However, our index a c t u a l l y recorded a price decline i n that year, ( a l l analysis i s done i n constant d o l l a r s ) . T h e i n d i c i e s moved i n opposite directions f o r f i v e periods i n a l l . The B-M-N model requires the use of only those pro-perties which have sold more than once during the study period. Thus, the B-M-N r e s u l t s i n the loss of information by excluding the price data f o r properties which sold only once during the study period. Por the data base i n the B-M-N, only 1143 obser-vations were used, versus 2,641 observations f o r our own index, representing a loss of f i f t y - s e v e n percent of the data. Interpreted i n terms of properties, only 576 properties out of The sample of 1504 transacted more than once, r e s u l t i n g i n a loss of approximately sixty-two percent of the population. Another l i m i t a t i o n of the B-M-N model i s that while the physical unit exchanged i s kept constant, i t makes no allow-ances f o r the physical deterioration of the unit through time. Thus, a price r e l a t i v e based on the e a r l i e r price w i l l overstate the pure price change as the physical unit w i l l have undergone some deterioration i n q u a l i t y . In addition, the model makes no allowance f o r changes i n the q u a l i t y or "tone" of neighborhood that may have occurred between transactions. There i s also a bias imparted i n the B-M-N sample data towards the older housing stock. Since a property must have transacted at least twice during the study period, older housing w i l l have a greater l i k e l i h o o d of t h i s occurring. Therefore, the requirement that housing must transact at l e a s t twice during the study period, w i l l not make the B-M-N index representative of the stock. 9 6 . CHAPTER 6  CONCLUSION The re s u l t s of the previous chapters have investigated possible means of c o n t r o l l i n g f o r q u a l i t y i n a housing price index. Two q u a l i t y variables have been demonstrated and an examination made of the s t a t i s t i c a l d i s t o r t i o n s that occur i n an index where only a f r a c t i o n of the sample exchanges hands each year and where the sample exists of various q u a l i t y types. I t was found that the q u a l i t y adjusted index f o r age, weighted by the stock composition, can also be calculated as the average price of a l l units sold i n each year. It has, however, been assumed throughout the analysis that the q u a l i t i e s of di f f e r e n t properties can be i n f e r r e d from t h e i r r e l a t i v e prices i n the case of value analysis, and that there i s a unique set of c h a r a c t e r i s t i c s associated with each vintage category. While these q u a l i t y variables are not based on an adequately strong assumption to be accepted as f i n a l i ndicators i n any sense, one broad recommendation can be suggested. Given the broad nature of housing q u a l i t y , greater advantages may be r e a l i z e d from i n d i c i e s based on one or two comprehensive descrip-t i v e housing c h a r a c t e r i s t i c s than i n d i c i e s based on the hedonic approach were the data requirements are quite extensive. This approach i s also advocated by Maslove^ 0^ i n a study which was published a f t e r the bulk of t h i s analysis was ca r r i e d out. He states that a single summary in d i c a t o r of (50) Maslove, A., "Towards The Measurement of Housing Quality", Economic Council of Canada, Discussion Paper, No. 75, February 1 9 7 7 . 9 7 . housing q u a l i t y would be advantageous i n terms of convenience and ease of manipulation of the index. He favours the use of the variable r e l a t i v e value as one does not have to make allowances f o r p a r t i c u l a r c h a r a c t e r i s t i c s as they are c a p i t a l i z e d into r e l a -t i v e value and thus the d i f f i c u l t i e s of measuring some of the more abstract or intangible a t t r i b u t e s are bypassed. In spite of the f a c t that i n d i c i e s concentrating on one or two explanatory variables may not be the most e x p l i c i t , they are e f f i c i e n t and are superior to an index constructed with a complete disregard to housing q u a l i t y . Thus, a simple s t r a i g h t -forward approach employing only one or two variables i s favoured f o r future research. I t was hoped that by overcoming some of the problems inherent i n the e x i s t i n g i n d i c i e s , that t h i s index could provide an accurate bench-mark against which other i n d i c i e s could be tested to determine i f a more accessible surrogate existed. I t was i n i t i a l l y hoped that the i n d i c i e s described i n a former sec-t i o n could be analyzed and compared as to t h e i r behaviour v i s - a -v i s the" index. However, many of the i n d i c i e s have only been i n existence f o r a short period of time or are not disaggregated s u f f i c i e n t l y as to t h e i r component parts or geographic areas to make the comparison meaningful. The only relevant index e x i s t i n g i s the one published by the Vancouver Real Estate Board. This index was deflated by the Consumer Price Index f o r Canada and i s presented i n Figure 14. The rates of change i n the prices f o r each index are a l s o pre-sented i n Table XI. The index i s r e l a t i v e l y more i n f l a t i o n a r y during the i n i t i a l period but t h i s trend reverses a f t e r 1971 98. FIGURE 14 (constant d o l l a r s , 1961 = 100) A COMPARISON OF THE MLS INDEX TO THE OVERALL PRICE INDEX A COMPARISON OF THE TWO YEAR  MOVING-AVERAGE MLS INDEX TO THE OVERALL PRICE INDEX 300 A 280 61 63 6*5 67 k 7*1 73 7*5 6*3cV 67 ' 6-9 71 " 75 75 "xdar TABLE XI RATES OF CHANGE IN PRICES FOR MLS INDEX AND LRO INDEX (CONSTANT DOLLARS. 1961=100) YEAR MLS INDEX OUR INDEX 1961 1962 . 4 1 20 . 14 1963 - .68 -30.11 1964 2.68 18.37 1965 3.28 15.63 1966 5.23 2.6l 1967 14.73 20.16 1968 13.80 26.23 1969 15.65 9.93 1970 - 3 . 1 4 2.98 1971 9.46 .34 1972 21.59 24.61. 1973 41.45 22.36 1974 57.67 59.57 1975 3.93 -23.50 ,100. with the MLS index showing a greater rate of price increase. It must be notes however, that the largest rate^of increase i n prices f o r both i n d i c i e s was experienced i n the same period — 1973-1974. There i s some disagreement between the d i r e c t i o n of the movement of the two i n d i c i e s i n 1970 and 1975 with the d i f -ference i n 1975 being quite substantial. The r e l a t i v e l y higher value obtained f o r the MLS l i s t i n g may i n part be explained by the continuing growth i n other sectors of the r e a l estate industry. Since the MLS figure includes commercial and i n d u s t r i a l property sales, growth i n these sectors would push the index up, regard-less of what was occurring i n the r e s i d e n t i a l sector. This was also the period during which sales of condominiums were gaining momentum and since these are also included i n the MLS index, they may have been a contributing f a c t o r to the increase experienced by the MLS index. Different proportions of the r e a l estate market tend to use the MLS over time. To smooth out some of changing pro-portions that may have occurred through the years, a two year moving average of the prices during the study period was tabulated. The r e s u l t s are presented i n Figure ,14. While t h i s procedure did minimize some of the fluctuations i n prices i n the MLS index, the differences between the two i n d i c i e s are s u f f i -c i e n t l y large that they cannot be ignored. More exploratory work should be done i n the future concerning the p o t e n t i a l of the MLS index as a possible house price i n d i c a t o r and research undertaken to explain the differences between the two i n d i c i e s . Attempts are now being made to upgrade 101. the MLS data. The Greater Vancouver Real Estate Board i s cur-rently i n i t i a t i n g a computer system to record the sales data as well as separate the r e s i d e n t i a l sales from the commercial and i n d u s t r i a l transactions. A number of c h a r a c t e r i s t i c s concerning the properties themselves w i l l also be provided. The data w i l l s t i l l be r e s t r i c t e d to MLS l i s t i n g s but w i l l be superior to the current process. Since Central Mortgage and Housing Corporation, S t a t i s t i c s Canada and other agencies support the use of new house prices as indicators of levels and changes of house prices, an index was formulated on the basis of average s e l l i n g prices of new homes i n our sample to see what r e l a t i o n s h i p t h i s index bore to our index f o r the entire sample. ^ This index i s com-p i l e d from the f i r s t transactions to occur on properties which had been sold i n t h e i r year of construction or i n the following year. This index i s based on the transactions of 933 properties. The r e s u l t s are presented i n Figure 15• The large numbers of fluctuations i n the index i n the early periods, can be i n part a t t r i b u t e d to the small number of observations p r i o r to 1965. However, i t i s i n t e r e s t i n g to note the large increase i n prices experienced i n 1 9 5 5 following the establishment of the National Housing Act which was geared ex-c l u s i v e l y to new houses at that period. The index converges with the o v e r a l l index i n the l a t e r years of the study period as a very large proportion of t o t a l sales i n each year involved new (51) It must be noted that the new house price index was not designed to be s t a t i s t i c a l l y representative of new homes b u i l t during the study period but was constructed s o l e l y to allow a b r i e f analysis. ' 1 1 1 I I T j 1 T 1 I 1 I Y p n r 49 51 53 55 57 59 6 1 63 65 67 69 71 .73 75 l e a r 103. houses. Given the s t a t i s t i c a l l i m i t a t i o n s of the index, i t can be s a i d that there does not appear to be any strong correspon-dence i n general, i n the movement of the two i n d i c i e s and thus any index based on new house prices would be of lim i t e d use i n describing price changes of the entire housing stock. The lack of an e x i s t i n g price series which i s a r e -l i a b l e i n d i c a t o r of house price-trends c l e a r l y emphasizes the need f o r the formulation of such an index. An important issue that should be addressed i n future research i s whether there ex i s t s a more e a s i l y accessible source of data that could serve as a reasonably accurate i n d i c a t o r of price appreciation. Possible sources may be prices obtained f o r i n d i v i d u a l properties from the Real Estate Boards or asking prices i n the r e a l estate c l a s s i f i e d s of the newspaper. Although one can be ske p t i c a l due to the possible biases inherent i n t h i s data as discussed pre-viously, i t was not the in t e n t i o n of t h i s paper to argue against the possible usefulness of t h i s procedure. There would be s i g n i -f i c a n t p r a c t i c a l implications i f the r e s u l t s of t h i s data were representative or bore some sort of predictable r e l a t i o n s h i p to the movement of house prices as confirmed by our data. Therefore, an i n v e s t i g a t i o n of the more e a s i l y accessible sources of data would be one of the most productive future steps i n formulating an index f o r house p r i c e s . Another possible future area of analysis brought out during the course of the study i s an inv e s t i g a t i o n of the varying proportions of agreements f o r sale transacted i n each year given the c r e d i t conditions e x i s t i n g i n that year. Other more speci-f i c research to explain the movements of house prices could be 104. undertaken as well as ah analysis of the l e v e l of market a c t i -v i t y (as measured by turnover rates) and t h e i r r e l a t i o n to price l e v e l s . 105. BIBLIOGRAPHY Adelman, I., G r i l i c h e s , Z. "On an Index of Quality Change", Journal of The American S t a t i s t i c a l Association. September 1961, PP. 535-555. Bailey, M., Muth, R., Nourse, H., "A Regression Method f o r Real Estate Price Index Construction", Journal of The American  S t a t i s t i c a l Association, December 1963. pp. 933-942. Baxter, D., "Published Housing Data: Trends and Evaluation", Housing: I t ' s Your Move, University of B r i t i s h Columbia, Vancouver, 1976, pp. 4 1 9 - 4 4 8 . Burnstien, M., "Measurement of Quality Change and Consumer Durables", The Manchester School of Economics and S o c i a l Studies. September 1961, pp. 269-279. Brown, S. L., Price Variations i n New FHA Houses 1959-1961: A  Report of Research i n Methods of Constructing Price Indexes, Bureau of the Census, Working Paper No. 31. Cagan, P., "Measuring Quality Changes and the Purchasing Power of Money: An Exploratory Study of Automobiles", i n Price Indexes and  Quality Change, ed. Zui G r i l i c h e s , Cambridge, Massachusetts, 1971 pp. 215-241. Central Mortgage and Housing Corporation, Canadian Housing  S t a t i s t i c s Chinlay, P., Hedonic Prices and Depreciation Indexes f o r  Residential Housing: A Longtitudinal Approach, Department of Economics, University of Western Ontario, mimeo, 1975* Dale Johnson, D. , Housing Market Data; B r i t i s h Columbia. Urban Land Economics Di v i s i o n , Faculty of Commerce and Business Administration, U.B.C. prepared f o r the Department of Housing, Government of the Province of B r i t i s h Columbia, mimeo, 1976. DeLeeuw, F., "The Measurement of Quality Changes", Proceedings of  the Business and Economics Section of the American S t a t i s t i c a l  Association, 1959. Dennis, S., "Current Changes i n Construction and Their E f f e c t s on S t a t i s t i c a l Measurement" Bureau of the Census, Proceedings of the  Business and S t a t i s t i c a l Section of the American S t a t i s t i c a l  Association, 1971, PP. 30-39. Dominion Bureau of S t a t i s t i c s , The Consumer Price Index f o r  Canada (1949*100) Catalogue 62-518, Occasional, March 1961. Gavett, T., "Quality and a Pure Price Index", Monthly Labour  Review, March 1967, pp. 16-20. 106. Grebler, L., Blank, D., Winnick, L., Ca p i t a l Formation i n Residential Real Estate. National Bureau of Economic Research, G r i l i c h e s , Z., "Hedonie Price Indexes f o r Automobiles: An Econometric Analysis of Quality Change", The Price S t a t i s t i c s  of the Federal Government. General Series, No. 73, 1961, pp. 37-196. G r i l i c h e s , Z., ed., Price Indexes and Quality Change. Cambridge, Massachusetts, 1971. H a l l , R. C , "The Measurement of Quality Change from Vintage Price Data", i n Price Indexes and Quality Change. Z. G r i l i c h e s , ed., Cambridge, 1971. PP. 240-271. Hamilton, S. W., "House Price I n d i c i e s : Theory & Practice", Housing: It's Your Move, University of B r i t i s h Columbia, Vancouver, 1976, pp. 383-418. J a s z i , G., "An Improved Way of Measuring Quality Change", Review  of Economics and S t a t i s t i c s . August 1962, pp. 332-335. Kaplan, N., "Some Methodological Notes on The Deflation of Construction", Journal of The American S t a t i s t i c a l Association, September 1959, pp. 535-555. Laube, J . , Hedonie Price and Quality Indexes: A Theoretical Review. Central Mortgage and Housing Corporation, mimeo, March 1975. Maisel, S. J . , "Housing Data Obtained By Sampling Public Records", Land Economics 1954-1955, pp. 257-268. Maslove, A., Towards the Measurement of Housing Quality, Economic© Council of Canada, Discussion Paper No. 75, February 1977. McCarthy, P., Some Observations on Sampling i n the Construction of Price Indexes, 1961 Proceedings of The American S t a t i s t i c a l  Association, pp. 264-270. McFayden, S., Hobart, R., The Impact of I n f l a t i o n on The Canadian  Housing Market, Urban Growth and Land Directorate, Ministry of State f o r Urban A f f a i r s , 1975, Chapter 1, mimeo, pp. 1-17. Mieszkowski, P., Soper, A., Trends i n the Value of Toronto  Housing, 1965-1973.' Central Mortgage and Housing Corporation, Working Paper ?6-2. 1 Musgrave, J . , "New Bureau of the Census Construction Price Indexes, Construction S t a t i s t i c s D i v i s i o n , Bureau of the Census presented at Annual Meeting of The American S t a t i s t i c a l Association, August 1968, mimeo. ' \ P r i e s t , Bailey, A l f o r d , Evaluation of 1971 Census Reporting of  S e l l i n g Value of Owner-Occupied Dwelling Units: Micro-Match with  Comparison Sales Catalogues Provided By Members of the Canadian"  Real Estate Association, S t a t i s t i c s Canada. May 1973. mimeo. Quigley, J . , Kain, J . , "Evaluating the Quality of the Residential Environment",,-Environment Planning. Vol. 2, 1969. Rapkin, C , Winnick, L., Blank, D., Housing Market Analysis, The In s t i t u t e f o r Urban Land Use and Housing Studies, Columbia University, C i t y of New York, 1953. Seek, N. H., Fluctuations i n the Turnover of Single Family  Dwellings In Vancouver, University of B r i t i s h Columbia, Thesis (unpublished) 1975. Steiner, P., Consumer Durables i n an Index of Consumer Prices", The Price S t a t i s t i c s of the Federal Government, Staff Paper No. 6, National Bureau of Economic Research, 1961. T r i p l e t t , J . , "Quality Bias i n Price Indexes and New Methods of Quality Measurement", i n Price Indexes and Quality Change. Z. G r i l i c h e s , ed., Cambridge, 1971, pp. 180-212. T r i p l e t t , J . , Theory of Hedonic Price Indexes, Bureau of Labor S t a t i s t i c s , S t a f f Paper No. 31, 1971. *"*" U.S. Congress, Joint Economic Committee,. Government Price  S t a t i s t i c s , January 1961. Wales, T., Wiens, E., " C a p i t a l i z a t i o n of Residential Property Taxes: An Empirical Study', Review of Economics and S t a t i s t i c s , August 1 9 7 4 , pp. 320-334. Wallace, W. H., Measuring Price Change: A Study of the Price  Indexes, Federal Reserve Board of Richmond, 1972. Wilkinson, R. K., "House Prices: the Measurement of E x t e r n a l i t i e s " , Economic Journal, March 1 9 7 3 , pp. 72-86. Wyngarden, H., "An Index of Local Real Estate Prices", Michigan  Business Studies. January 1927. In addition, information was also obtained through mail/ telephone and personal correspondence from the following persons: Mrs. Hazel Baxter, Central Mortgage and Housing Corporation, Regional Offic e , 2609 Granville Street, Vancouver, B. C. 108. Mrs. Betty Baxtresser, Acting Chief, Library Branch, Bureau of the Census, Washington, D. C. Ms. Karen Calderbank, S t a t i s t i c s Canada - Vancouver Office, 16 E. Hastings Street, Vancouver, B. C. Mr. Garlow & Staf f , Land Registry O f f i c e , 653 Clarkson Avenue, New Westminster, B. C. Mr. J e f f e r y Crawford, Department of Commerce, Bureau of Economic Analysis, 1401 K Street N. W., Washington, D. C. 20230. Mr. P. G. F u l l e r , Manager, Central Mortgage and Housing Corporation, S t a t i s t i c s Services Division, Ottawa, Ontario, K1A OP?. Mr. William E. Haviland, Secretary, Economic Council of Canada, P.O. Box 527, Ottawa, Ontario, KIP 5 V 6 . Mr. Bob Hobart, Urban Economic Directorate, Ministry of State f o r Urban A f f a i r s , Ottawa. Mr. Frank Hodges, Vice President, Manager Corporate Relations, A. E. LePage Ltd., 50 Holly Street, Toronto, Ontario, M4S 26l. Mrs. Celina Hague, Real Estate Administration, Royal Trust Co., 630 Dorchester Blvd., W., Montreal, P.Q., H3B 1S6. Mr. R. J . Lowe, S t a t i s t i c s Canada, Prices D i v i s i o n , Ottawa, Ontario, K1A 0 T 6 . Mr. Ted Mitchel, Central Mortgage and Housing Corporation Regional Offic e , 2609 Granville Street, Vancouver, B. C, Mr. Nunn and Staff, Land Registry O f f i c e , 777 Hornby Street, Vancouver, B. C. Mr. T. Thomas, ( Central Mortgage and Housing Corporation Program and Market Requirements-;©ivision Ottawa, Ontario, K 1 A 0P7. 110. APPENDIX A SAMPLING PROCEDURE 1. Data For The Study-It was decided on the basis of previous work done on t h i s topic that the data would be c o l l e c t e d from the records of the Land Registry O f f i c e s . Steps were taken to obtain the cooperation of the Vancouver and New Westminster Land Registry O f f i c e s . On the basis of estimates of the number of researchers that would be required, 3 to 4 research a s s i s -tants were assigned to work i n the LRO f o r a period of 8 weeks, commencing June 22. 2. Selection Of The Universe For the purposes of t h i s study, the universe was to include a l l single family detached units situated i n the eight r a p i d l y growing municipalities of Metropolitan Vancouver. These included Coquitlam, Port Coquitlam, Surrey, Port Moody, Richmond, Delta, White Rock, and the D i s t r i c t of North Vancouver. The c r i t e r i a used to select these municipalities were the decentenial growth rates from 1940 to 19?0 f o r each of the m u n i c i p a l i t i e s and future projected growth rates. 3. Estimation Of Sample Size The sample s i z e , with a prescribed accuracy of 90$ con-fidence i n t e r v a l s , was obtained f o r the universe as a whole 111. rather than f o r each municipality. Calculations indicated that a sample of 1785 properties waved be s t a t i s t i c a l l y r e -presentative of the universe. The sample size of the universe was d i s t r i b u t e d proportionately among the m u n i c i p a l i t i e s . (See Table I I I ) . The number of single family detached homes i n each municipality was obtained through telephone and mail correspondence with the four area assessment o f f i c e s . 4-. Preparing The Sample The sample was selected randomly from d i f f e r e n t sources f o r the municipalities as cooperation from a l l the assessment o f f i c e s could not be obtained (It was i n i t i a l l y hoped that the sample f o r a l l eight m u n i c i p a l i t i e s could be drawn from the records of the assessment o f f i c e s ) . The d i f f e r e n t sources included the municipal records of b u i l d i n g permits, the assess-ment race (CMV f i l e , f i e l d cards) and i n the case of one municipality, the records of water connections. (See Table I I I ) . From these sources, the l e g a l description and the age of the dwellings were recorded, the former to be used i n t i t l e searches at the Land Registry O f f i c e , the l a t t e r to be used i n the subsequent analysis of the p r i c e index. The d i f f i c u l t y of s e l e c t i n g a sample from these sources depended la r g e l y upon the number of i n d i v i d u a l records that had to be consulted i n order to determine the l e g a l descrip-t i o n of a sample property and the type of property ( i . e . , r e s i d e n t i a l , commercial, etc.) to determine whether that par-c e l should be included or excluded from the sample. 112. The properties i n a l l m u n i c i p a l i t i e s were selected randomly from t h e i r source. I t was necessary to "gross-up" the calculated sample size f o r each municipality i n order that the sampling procedure would r e s u l t i n the required number of single family units f o r each municipality. 5. F i e l d Work Sales data c o l l e c t i o n began at the Vancouver LRO on June 22 and was completed on July 9. Work then began at the New Westminster LRO where 80$ of the required property records were kept. The data c o l l e c t i o n was completed i n 5 weeks, ending on August 13. With the exception of the f i r s t week and the l a s t two weeks of data c o l l e c t i o n when only 3 students were employed, the usual number of students working i n the LRO was 4. The greater e f f i c i e n c y i n the New Westminster LRO was i n part due to the more organized condition of the records there and i n part due to the increased competence of the workers. Each worker was responsible f o r securing the C e r t i f i c a t e of T i t l e numbers f o r each of the l e g a l descriptions and recor-ding the s a l e s p r i c e information and the date of the trans-actions f o r the property up to the date of i t s construction or back u n t i l 1964, i f the home had been constructed p r i o r to 1964. Properties that had been constructed p r i o r to *64 composed about 40$ of the sample and sales information on them was available from a previous study done at U.B.C. A l l that was required f o r these "older" properties was an up-date of the sales on the property up to the present day. 113 The month of December was spent c o l l e c t i n g Agreement f o r Sales data. The procedure used here was an examination of a l l the C e r t i f i c a t e s of T i t l e issued f o r a given property, to see i f any r i g h t s to purchase charges had been registered against the t i t l e of the property. Registration numbers of these charges were recorded and the documents examined to obtain the sales price data and the date of the transaction. Approximately 2,300 properties were searched. 300 of these homes were eliminated due to mistakes i n recording the data or the l e g a l descriptions. Properties which had been subdivided were also eliminated from the sample. While t h i s procedure may have a tendency to bias the older sample toward smaller properties ( i s e . large estates would have a greater p r o b a b i l i t y of being subdivided), there appeared to be no way to cope with the problem of t r a c i n g a property through time which at some point had been subdivided and parcels sold o f f . I f a property was very old and had been subsequently demolished p r i o r to 1976, the data on i t was recorded only up to the estimated date of the demolition. A f t e r the date of demolition, the property was deleted from the sample. Approximately 100 properties were l o s t i n attempting to merge t h i s data with the data that had been c o l l e c t e d i n the previous study. This was l a r g e l y the r e s u l t of c o n f l i c t i n g information f o r a property between the data c o l l e c t i o n periods, (largely the r e s u l t of coding or keypunching errors) or incom-plete information about a property (for example, no age or date of sale given). The f i n a l sample size was 1916 properties. 114. APPENDIX B DERIVATION OF SAMPLE SIZE AND INDICIES 1. The formula used f o r the derivation of sample size was: n « z 2NY 2~ N 2E 2+z 2Y 2 where: n = estimated sample size z = confidence i n t e r v a l s t a t i s t i c N = size of the universe V - £Z 3 standard deviation and mean T of the turnover rates f o r the f a s t growth municipalities E = estimated..sampling error 2. Prices f o r the o v e r a l l index and f o r the unaggregated i n d i c i e s i n the various categories were calculated as the: d o l l a r value of a l l sales i n category X t o t a l number of sales i n category X Where X r e f e r s to the t o t a l data, data excluding agreementrfor sale data, age categories, value range category, etc. as de-fin e d f o r each index. 3. The cumulative p r i c e i n d i c i e s (Figure 6 and 7) were derived as: P (L) = P L n P (LM) = P L n ^ L n + P m n . C P (LMH) = P L n . t L n + P m n . t m n + P H n . t H n -where: P (L) = price index f o r the low value range category 115 where: P (LM) and P (LMH) = price i n d i c i e s f o r the cumulative value range categories, low-medium and low-medium-high, resp e c t i v e l y . P L n » P m n » Pj/ 1 = price i n d i c i e s f o r the value range categories, low, medium and high respectively, i n period n. t L n , t f f l n , t „ n = turnover rates f o r each of the value ranges with subscripts as defined above i n period n. The weighted-value range index (Figure 8) i s derived as: P (T) - i C t ^ J A t ^ . where: t ^ • 2 ? year average turnover rate i n value range i . p . n = non-cumulative price index f o r value range i f o r period n. The sales-weighted age index (Figure 10) i s derived as: p (s) = i p a n - d a n where: p . n = price index f o r age category a i n period n. d n = the turnover rate i n age category a i n a period n ( i . e . t o t a l sales i n a) t o t a l stock i n a The stock-weighted index (Figure 10 and 11) i s derived as: P (W) = * P a n . s a n where: p Q n * price index f o r age category a i n peridd n. s n s the percentage of the stock that i s i n a age category a i n period n. The turnover . throughout the study i s derived as: T s' t o t a l number of sales i n A n t o t a l stock i n A n where: A i s the category being measured, n = a given year. A P P E N D I X C s COMPARISON OF CURRENT AND CONSTANT DOLLAR INDICES (l971 a100) Price Index Year Current Dollars 1949 11.98 1950 17.94 1951 16.41 1952. 16.96 1953 19.94 1954 17.44 1955 28.23 1956 28.90 1957 35.90 1958 40.27 1959 41.11 1960 44.58 1961 40.24 1962 48.92 1963 37.31 1964 45.71 1965 53.60 1966 5£-77 1967 68.16 1968 83.63 1969 92.41 1970 97.06 1971 100.00 1972 118.65 1973 141.17 1974 196.42 1975 200.06 1976 231.66 Constant Dollars 20.65 30.06 24.8? 25.08 29.76 25.88 41.79 42.18 50.79 55.49 56.02 60.01 53.68 64.49 48.33 58.19 66.58 67.98 78.79 92.90 98.23 99.83 100.00 113.22 125.22 157.19 144.57 156.79 PRICE INDEX BASED ON CLEAR TITLE TRANSACTIONS (CONSTANT DOLLARS. 1971=100) YEAR PRICE INDEX 1949 18.17 1950 28.74 1951 25.13 1952 27.43 1953 32.69 1954 24.47 1955 42.44 1956 43.33 1957 59.26 1958 58.83 1959 58.40 1960 63.76 1961 54.25 1962 63.88 1963 51.45 1964 59.73 1965 66.65 1966 69.78 1967 8 1 . 81 . ; 1968 93.87 1969 100.32 1970 100.81 1971 100.00 1972 113.46 1973 124.00 1974 156.29 1975 144.93 ' 19?6 155.46 COMPARISON OF PRICE.INDEX BASED ON AGREEMENTS FOR SALE TRANSACTIONS AND OUR INDEX (CONSTANT DOLLARS. 1971=100) AGREEMENTS FOR SALE YEAR PRICE INDEX OUR INDEX 1949 23.12 20.65 1950 34.23 30.06 1951 '22.75 24.87 1952 19.64 25.08 1953 23.04 29.?6 1954 28.41 25.88 1955 37.80 41.79 1956 38.15 42.18 195? 36.?8 50.79 1958 42.36 5:5.49 1959 52.03 56.02 1960 49.72 60.01 1961 52.85 53.68 1962 67.99 64.49 1963 41.62 48.33 1964 42.38 58.19 1965 66.37 66.58 1966 56.05 6?.98 1967 50.45 78.79 1968 85.74 92.90 1969 75.80 98.23 1970 76.22 99.83 19?1 100.00 100.00 1972 IO7.79 113.22 1973 182.57 125.22 19?4 176.87 157.19 1975 87.28 144.57 1976 181.84 156.79 119. PRICE INDEXES BY VALUE RANGE  (CONSTANT DOLLARS. 1971=100) YEAR LOW 1949 13.09 1950 21.08 1951 24.8? 1952 20.02 1953 21.28 1954 18.19 1955 26.66 1956 34.50 195? 37.71 1958 43.42 1959 45.16 I960 57.59 1961 46.89 1962 40.62 1963 34.98 1964 49.06 1965 59.64 1966 64.73 196? 71.54 1968 83.13 1969 90.65 1970 95.56 1971 100.00 1972 112.73 1973 124.22 1974 151.33 1975 151.23 1976 157.25 MEDIUM HIGH 19.42 20.12 29.88 31.64 27.03 25.82 25.57 30.23 28.76 42.86 23.16 26.63 38.67 46.10 41.93 45.12 56.28 62.68 59.82 52.79 57-36 60.14 64.37 55.17 54.21 56.ll 62.46 73.09 50.13 57.22 59.11 66.38 65.8? 68.37 69.32 63.93 83.38 89.48 94.06 92.17 .99.67 99.31 99.68 99.97 100.00 100.00 110.59 123.6? 119.66 125.96 148.45 159.81 141.82 139.13 148.15 163.17 120. PRICE. INDEXES BY CUMULATIVE VALUE RANGES  (CONSTANT DOLLARS. 1971 al00) YEAR LOW LOW & MEDIUM LOW & MEDIUM : & HIGH (TOTAL) 15.62 20.65 25.81 30.06 22.61 24.8? 19.23 25.07 24.44 29.75 18.04 25.87 27.62 41.79 29.79 42.18 45.42 50.79 51.28 55.49 47.34 56.02 6.47 60.01 1949 13.09 1950 21.08 1951 24.87 1952 20.02 1953 21.28 1954 18.19 1955 26.66 1956 34.50 1957 37.71 1958 43.42 1959 45.16 I960 57.59 1961 46.89 1962 40.62 1963 34.98 1964 49.06 1965 59.64 1966 64.73^ 1967 71.54 1968 83.13 1969 90.65 1970 95.56 1971 100.00 1972 112.73 1973 124.22 1974 151.33 1975 151.23 1976 157.25 7.01 53.67 50.95 64.48 39.66 48.32 53.27 58.18 58.10 66.57 64.53 67.97 72.16 78.79 89.67 92.89 96.26 98.22 98.43 99.82 100.00 100.00 109.71 113.21 122.72 125.21 150.14 157.18 147.91 144.57 150.43 156.79 PRICE INDEXES BY AGE CATEGORY* (CONSTANT DOLLARS. 1971=100) Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 i960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1-10 11-25 : >25 Years Old Years Old Years Old 19.26 21.49 28.92 21.54 39.64 35.06 22.68 32.59 _ *# 28.13 19.08 16.92 30.22 19.26 - ** 28.26 24.34 _ #* 41.22 46.69 36.?0 46.38 36.06 27.69 51.25 47.91 22.66 57.73 47.19 49.93 57.74 35.35 50.53 60.41 41.97 42.20 59.23 43.31 35.00 69.71 45.66 28.65 56.20 46.95 28.77 59.45 74.05 39.45 72.32 59.22 35.52 68.48 64.70 51.49 81.49 77-64 48.74 94.01 79.70 94.88 IOO.52 99.48 71.57 97.89 109.47 93.43 100.00 100.00 100.00 110.78 116.61 139.49 117.94 146.60 133.83 150.62 185.16 132.25 142.69 155.58 126.21 150.05 190.47 140.41 * Age at date of transaction ** No transactions 122. PRICE APPRECIATION OF THE STOCK BY AGE CATEGORY (CONSTANT DOLLARS. 1971*100. AGE AS OF 1975) PRICE INDEX FOR HOUSES Year 1-10 11-25 >25 ..Years Old Years Old Years Old 22.62 32.92 27.24 56.57 25.89 32.38' 32.29 34.52 25.29 60.79 32.47 56.27 34.16 60.87 40.61 71.31 41.98 64.97 48.65 68.60 49.02 67.73 35.80 79.66 39.85 62.10 33.68 66.94 .54.. 68 80.41 50.49 75.09 49.70 80.80 67.83 88.56 82.44 96.63 85.6? 91.54 116.68 100.00 100.00 115.60 121.30 134.21 137.43 173.92 134.39 141.33 131.45 172.89 145.98 1949 -1950 -1951 -1952 -1953 -1954 -1955 -1956 -1957 -1958 -1959 -i960 . -1961 -1962 -1963 -1964 -1965 -1966 79.71 196? 85.92 1968 99.49 1969 103.64 1970 101.01 1971 100.00 1972 110.59 1973 118.85 1974 151.65 1975 143.90 19?6 151.32 l 123 COMPARISON OF OUR INDEX & THE SALES  WEIGHTED & STOCK WEIGHTED INDICES (CONSTANT DOLLARS. 1971=100), YEAR OUR INDEX SALES WEIGHTED STOCK WEIGHTED 1949 20.65 20.53 21.25 1950 30.06 33.51 27.95 1951 24.87 24.54 22.87 1952 25.O8 25.25 24.63 1953 29.76 28.37 20.76 1954 25.88 25.94 23.58 1955 41.79 42.15 42.25 1956 42.18 41.90 41.07 195? 5°.79 49.51 46.87 1958 55.49 54.87 54.60 1959 56.02 54.91 52.37 1960 60.01 58.51 54.48 1961 53.68 53.28 52.77 1962 64.49 62.83 58.81 1963 48.33 53.51 50.69 1964 58.19 58.90 6O.79 1965 66,5^ 66.02 64.35 1966 67.98 66.12 65.27 1967 ?8.79 78.25 76.53 1968 92.90 91.61 90.00 1969 98.23 97.93 96.19 1970 99.83 100.33 101.12 1971 100.00 100.00 100.00 19?2 113.22- 114.49 117.08 1973 125.22 124.01 128.63 1974 157.19 149.83 158.30 1975 144.57 144.40 144.67 A COMPARISON OF THE BAILEY-MUTH-NOURSE MODEL  AND OUR INDEX (CONSTANT DOLLARS. 1971S100) YEAR BMN PRICE INDEX OUR INDEX 1949 17.59 20.65 1950 25.44 30.06 1951 34.11 24.87 1952 27.03 25.08 1953 32.03 29.76 1954 24.52 25.88 1955 33.31 41.79 1956 41.85 42.18 1957 42.54 50.79 1958 48.86 55.49 1959 48.03 56.02 1960 51.49 60.01 1961 50.60 53.68 1962 45.87 64.49 1963 40.88 48.33 1964 51.10 58.19 1965 50.08 66.58 1966 56.26 67.98 1967 68.84 78.79 1968 76.52 92.90 1969 88.55 98.23 1970 95.78 99.83 1971 100.00 100.00 1972 114.80 113.22 1973 137.80 125.22 1974 176.66 157.19 1975 205.51 144.57 1976 224.88 156.79 A COMPARISON OF OUR INDEX AND THE MLS INDEX (CONSTANT DOLLARS. 1961=100) .J YEAR MLS INDEX OUR INDEX 1961 100.00 100.00 1962 100.41 120.14 1963 99.73 90.03 1964 102.41 108.40 1965 105.69 124.03 1966 110.92 126.64 1967 125.65 146.80 1968 139.42 173.07 1969 155.07 183.00 1970 151.93 185.98 1971 161.39 186.32 1972 182.98 210.93 1973 224.43 233.29 1974 282.10 292.86 1975 286.03 269.36 APPENDIX TABLE  INDEXES BASED ON A TWO YEAR MOVING AVERAGE  OF MLS /PRICES (CONSTANT DOLLARS. 1961=100) YEAR MLS INDEX OUR INDEX 1961 100.00 100.00 1962 100.20 120.14 1963 100.07 90.03 1964 101.07 108.40 1965 104.05 124.03 1966 108.30 126.64 1967 118.29 146.80 1968 132.54 173.07 1969 147.25 183.00 1970 153.50 I85.98 1971 156.66 186.32 1972 172.19 210.93 1973 203.71 233.29 1974 253.27 292.86 1975 284.06 269.32 COMPARISON OF OUR INDEX AND INDEX BASED ON NEW HOUSE SALES (CONSTANT DOLLARS. 1971=100) YEAR OUR PRICE INDEX NEW HOUSE PRICE INDEX 1949. 20.65 21.38 1950 30.06 1951 24.87 30.27 1952 25.07 52.62 1953 29.75 28.17 1954 25.87 32.05 1955 41.79 58.05 1956 42.18 60.12 1957 50.79 66.00 1958 55.49 67.23 1959 56.02 61.26 1960 60.01 63.15 1961 53.67 68.02 1962 64.48 79.26 1963 48.32 71.94 1964 58.18 76.79 1965 66.57 93.40 1966 67.97 84.23 1967 78.79 .92.25 1968 92.89 104.36 1969 98.22 106.44 1970 99.82 106.09 1971 100.00 100.00 1972 113.21 113.96 1973 125.21 126.82 1974 157.18 158.98 1975 144.57 148.32 1976 156.79 150.79 

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