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UBC Theses and Dissertations

A development potential for the Vancouver metropolitan area Moore, Richard Albert 1972

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A DEVELOPMENT POTENTIAL MODEL FOR THE VANCOUVER METROPOLITAN AREA by RICHARD ALBERT MOORE B.A.Sc., University of B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION IN THE FACULTY of COMMERCE AND BUSINESS ADMINISTRATION We accept th i s thesis as conforming to the requi red s tandard:-THE UNIVERSITY OF BRITISH COLUMBIA December, 1972 In presenting this thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of thi s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of this thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Commerce and Business Administration The University of B r i t i s h Columbia Vancouver 8, Canada December, 1972. Abstract The focus of th i s study i s on means by which the s p a t i a l d i s t r i b u t i o n of housing development can be explained. This involved f i r s t l y (I) i d e n t i f i c a t i o n of po t e n t i a l determinants of r e s i d e n t i a l l ocation and the v e r i f i c a t i o n thereof, and secondly (II) inv e s t i g a t i o n into the a p p l i c a b i l i t y of the use of Clark's Theory of Exponentially Declining Densities as a predictor of housing unit completions. (I) Interviews with sixty-three developers i n the Greater Vancouver Area were used to rank c r i t e r i a used i n the i r l o c a t i o n decision-making. Regressions of. some of the more important c r i t e r i a were attempted with housing completions as the dependent va r i a b l e . Analysis of the data demonstrates that housing unit completions of a subarea are strongly related to both i t s unused and t o t a l housing p o t e n t i a l . The data does not support the developers 1 contention that r e l a t i v e land price i s an important l o c a t i o n a l determinant. Travel time from the central business d i s t r i c t i s not i n i t s e l f a s i g n i f i c a n t variable i n explaining the s p a t i a l d i s t r i b u t i o n of housing unit completions. i i i (II) Less than 50% of the v a r i a t i o n of population density i s explainable i n terms of distance from the CBD i n the manner of Clark's r e l a t i o n : Population/Area = Ae where d i s the distance from the central business d i s t r i c t , and A and b are constants. Considerably better r e s u l t s (59% to 74% of the variation) are obtained with the inverse t r a v e l r e l a t i o n s : Population/Area Zoned Residential = C^ and Housing Units/Area Zoned Residential = 2 t where t i s the t r a v e l time from the c e n t r a l business d i s t r i c t . The existence of unused pot e n t i a l i n a subarea as defined by the difference between the density observed and the density calculated (by Clark's Theory or by the Inverse Travel Time Relation above) i s a s i g n i f i c a n t predictor variable of whether or not r e s i d e n t i a l construction w i l l take place. However, the magnitude of the unused pote n t i a l thus calculated i s not a s i g n i f i c a n t determinant of the actual number of housing unit completions. i v Table of Contents Page Number T i t l e Page i Abstract i i L i s t of Tables v i i i Acknowledgements ix Introduction 1 Organization of the Report 5 A Conceptual Overview of the Residential Development Process 7 The Predevelopment Landowner's Decision 8 The Developer's Three Stage Location Decision: to Consider, to Purchase, and to Develop Land 9 The Householder's Decision 12 Models of the Development Process 13 The Housing Market 17 D e f i n i t i o n of Housing Demand 17 Factors A f f e c t i n g Housing Demand 18 1. Demographics 18 2. Income 19 3. Prices and Rents 20 4. Credit Variables 20 5. Other Variables 21 Factors A f f e c t i n g Housing Supply 22 Models of the Housing Market 23 Comment 28 V Page Number Models Concerned with the Housing Patterns i n General Terms 29 Burgess 1 Concentric Zone Theory 29 Hoyt's Sector Theory 30 Theory of Multiple Nuclei 30 Clark's Theory of Exponentially Declining Densities 31 Models Involving Transportation Costs and Sp a t i a l Preferences 32 1. Kain's Model 32 2. Alonso's Model 33 3. Wingo's Model 34 Comment 35 Models of Residential Location 3 6 Ad Hoc Allocations 36 The CATS Model 3 6 The U.N.C. Model of Land Use Succession 37 Harris' Stochastic Model of Urban Development 39 H i l l ' s EMPIRIC Model 40 The Lowry Model 41 Bay Area Simulation Study (BASS) 42 Projective Land Use Model (PLUM) 43 Herbert and Stevens' Model of Market Demand 44 A. D. L i t t l e (San Francisco) Model of Market Supply 45 Sears' Model 46 v i Page Number Discussion of the Models of Residential Location 47 1. Contextual 47 2. Forecasting the Effects of Public P o l i c i e s 47 3. Market Equilibrium and Disaggregation 48 4. Locational C r i t e r i a 49 5. S p a t i a l Disaggregation 49 6. Intra-regional Mobility 50 7. Aspects of Renewal and Redevelopment 50 Scope and Methodology 52 The Approach 52 Data Gathering Technique 53 Limitations of the Questionnaire Approach 55 Limitations of the Questionnaire 56 The Sample 57 Empirical Results of the Questionnaire 61 Trends I d e n t i f i e d 67 P o l i t i c a l Climate 68 Hypotheses and Measurement of Variables 70 The Study Area 70 Hypotheses 1 to 19 71 S t a t i s t i c a l Comment 84 Regression Results 87 Conclusion 97 Page Number Extentions 10 0 Footnotes 103 Bibliography 106 Appendix A: The Questionnaire 115 B: Map of 1961 Census Tracts 128 v i i i L i s t of Tables Table Page I Evaluation of Location Factors By A l l Developers 62 II Evaluation of Location Factors By Developers of Multiple Family Dwellings 63 III Evaluation of Location Factors By Developers of Single Family Dwellings 64 IV Evaluation of Location Factors By Subdividers 65 V Regression Results of "Measures of Attractiveness" 88 VI Regression Results of and Total P o t e n t i a l " VII Regression Results of Area) = -bd + c VIII Regression Results of Zoned Residential = C "Unused 89 Log(Pop/Total 91 Pop/Area /time 92 IX Regression Results of Housing Units/ Area Zoned Residential - C^/time 93 X Regression Results of Completions vs. Dummy Variable Representing Existence of Unused Potential as Determined by Clark's Theory 96 XI Regression Results of Completions vs. Dummy Variable Representing Existence of Unused Potential as Determined by the Inverse Travel Time Relation 96 Acknowledgements Many persons have contributed to the completion of this thesis. For his valuable guidance and advice (especially i n the f i n a l hour), s p e c i a l appreciation i s extended to Dr. Michael A. Goldberg who served as my thesis advisor. Appreciation i s extended to Ed Roffey who gathered municipal zoning data and compiled CMHC completions data. Further thanks i s due for his constructive suggestions and moral support. Funds for the developer survey were provided by the Real Estate I n s t i t u t e of B r i t i s h Columbia. Thanks i s expressed to Judy Kingsmill and B i l l Kraigsley for t h e i r assistance i n conducting the interviews. Appreciation i s extended for the co-operation and i n t e r e s t of the sixty-three firms comprising the study sample. F i n a l l y , e x t r a s p e c i a l appreciation i s due my t y p i s t , J u l i e Battye, for her assistance i n meeting very t i g h t time constraints. 1 A DEVELOPMENT POTENTIAL MODEL FOR THE VANCOUVER METROPOLITAN AREA < Introduction Rapid population growth i n the Vancouver Metropolitan Area i s expected. The Lower Mainland Regional Planning Board i n "Population Trends i n the Lower Mainland 1921-1986 Technical Report" estimates a population increase of approximately 14% during each of the next three five-year periods. To add emphasis, the report's estimate of the 19 71 population was low by fi v e per cent (1,026,000 compared to 1,0 82,352 from the 19 71 Census). The report predicts population increases during the period of 19 71 to 19 86 of 35% for the Burrard Penninsula, 56% for the North Shore, and 91% for the South Shore. Further the report predicts astounding population increases during the same period of 100%, 106% and 119% for the municipalities of Port Moody, Richmond and Delta respectively. The problems facing such phenomenal growth are awesome: li m i t e d a v a i l a b i l i t y of developable land; upward pressures on land prices e s p e c i a l l y i n r e s i d e n t i a l areas already sewered 2 or intended to be sewered i n the immediate future; increased f i n a n c i a l s t r a i n on municipalities for new servicing; increased pressure on transportation systems; and more t r a f f i c and population congestion i n the Burrard Penninsula. Viewed from the t o t a l i t y of things, there are a d d i t i o n a l l y the vast s o c i a l and e c o l o g i c a l problematical complexities which r e s u l t from these factors and others. In order to begin to cope with some of these problems, many questions remain unanswered r e l a t i n g to the manner i n which r e s i d e n t i a l development and redevelopment w i l l occur. Which locations are most l i k e l y to be developed? And i n what sequence w i l l they be developed? And where? With appeal to which income groups? To which household styles? Which income groups and house-hold styles w i l l not be adequately provided for? Where w i l l redevelopment occur? In what forms? What e x i s t i n g housing w i l l be destroyed to make way for new higher density housing? This study i s a f i r s t step toward answering some of these questions. I t deals primarily with factors which may be used as predictors of future housing completions. The a n a l y t i c a l investigation involves two approaches: one, the i d e n t i f i c a t i o n of c r i t e r i a used i n developers' 3 l o c a t i o n a l decision making. Application of these c r i t e r i a i s made to subareas of the urban region for use i n "explaining" housing unit completions through regression; two. , the investigation of Clark's Theory of Exponentially Declining Densities for use as a p o t e n t i a l model. Housing unit completions are regressed against the unused housing p o t e n t i a l as determined by the difference between the density calculated and the density observed. Among the factors a f f e c t i n g the ultimate location of new housing are municipal policy decisions. For example, land previously unavailable for development may suddenly become avail a b l e . It was recently announced that i n Port Moody a new large housing development i s to be undertaken. This decision w i l l l i k e l y have somewhat of a replacement e f f e c t on new housing i n the surrounding areas of Coquitlam and Port Coquitlam. An example of a recent policy decision having a r e s t r i c t i v e e f f e c t on construction i s that enabling the Surrey municipality, under Procedural. Bylaw 3690, to impose a levy of $530.00 per l o t before giving rezoning or subdivision approval. This w i l l have the e f f e c t of encouraging developers, e s p e c i a l l y those with t i g h t f i n a n c i a l constraints, to locate elsewhere. The model then, must neces sar i ly operate wi th in the confines of the e x i s t i n g zoning, b u i l d i n g and subdiv i s ion bylaw and hopeful ly may be useful i n forecast ing the impact of changes i n municipal p o l i c i e s . 5 Organization of the Report Attempts to develop quantitative models of the s p a t i a l aspects of urban development for use as planning tools has developed e s s e n t i a l l y since about 1960 following a few important generalized descriptions of c i t y patterns. In reviewing the l i t e r a t u r e , I s h a l l try to show how a number of these quantitative models relate to the r e s i d e n t i a l development process, to the market for urban land, and to the descriptions of c i t y patterns. F i r s t , a conceptual overview of the r e s i d e n t i a l development process w i l l be presented. This i s followed by a discussion of the housing market i n terms of factors a f f e c t i n g supply and demand along with some of the more notable analyses of controversial issues of the marketplace. Next i s a description of seven generalized models of housing patterns which precedes discussion of the more important quantitative models of the s p a t i a l aspects of r e s i d e n t i a l development. The task involves some r i s k of misrepresentation since i n focusing on the essence of the models' structures and the differences between them, the models may not be adequately documented. 6 "Scope and Methodology" outlines the two approaches used i n the "explanation" of housing unit completions. F i r s t , the behavioral approach using the questionnaire i s outlined along with a d i s c r i p t i o n of the survey sample. A discussion of the res u l t s of the questionnaire follows. The hypotheses evolving as a r e s u l t of the questionnaire are then introduced along with those of the second approach, that using p o t e n t i a l models based upon Clark's Theory of Exponentially Declining Densities. The results of the regres-sions t e s t i n g the nineteen hypotheses are then discussed followed by the conclusion and suggestions for further research i n the d i r e c t i o n of the work presented here. 7 A Conceptual Overview of the Residential Development  Process The sequence of states i n the develop-ment of a parcel of land can be traced from i t s i n i t i a l undeveloped state, through various stages of the development process, and f i n a l l y to the state of active r e s i d e n t i a l use by a household. More pr e c i s e l y , the stages may be described as f o l l o w s : -1. The land i s i n an undeveloped state. I t may be f e l t to have development pote n t i a l which leads to... 2. The state of being a c t i v e l y considered for development i n which a developer and the land-owner have contacted one another regarding the possible sale of the land. The developer's decision to purchase the land leads to... 3. The state of being programmed for development. The developer formulates d e f i n i t e ideas of the timing and character of development. His decision to begin development leads to... 4. The state of active development i n which physical development of the land takes place. In the case of r e s i d e n t i a l development new housing i s made available which leads to... 5. The state of active r e s i d e n t i a l use r e s u l t i n g from a householder's decision to occupy the dwelling. 8 The Predevelopment Landowner's Decision The landowner's decision to hold or s e l l the land i s based upon the income and s a t i s f a c t i o n he presently receives and expects to receive from the land as well as the land's present market value, and his expectations about i t s future value. The income aspect of t h i s decision includes such factors as net annual holding cost of the land, costs incurred i n s h i f t i n g to another investment and the oppor-2 tunity cost of c a p i t a l . The s a t i s f a c t i o n received from the land i s dependent upon such q u a l i t a t i v e factors as his attitude toward farming as a way of l i f e , the land as a home as opposed to a residence, love of the land, privacy, and status."* The landowner weighs the factors r e l a t i n g to his decision i n the contextual framework of public p o l i c y (taxation; c a p i t a l improvement and services p o l i c i e s ; costs of transportation, water, sewerage and schools; and subdivision regulation, building codes, zoning and land use plans) and socioeconomic factors (economic structure and growth prospects of the urban area; condition of the l o c a l housing market, concentration and competition i n the l o c a l development industry; and the 4 p r e v a i l i n g psychology of the period). 9 The Developer's Three Stage Location Decision: to Consider, to Purchase, and to Develop Land In his decision to consider land the developer may follow one of two approaches. He may i d e n t i f y a demand for a p a r t i c u l a r type and price range of housing, formulate crude s i t e s p e c i f i c a t i o n s and then begin an active search for suitable land. A l t e r n a t i v e l y , he may become aware that a parcel of land i s available, then formulate plans for a suitable project for that s i t e meanwhile either knowing or attempting to ascertain that demand for such housing exists (see questionnaire, question II 4). Empirical 5 work has shown that the generalized approach i n the development industry consists of periodic searches superimposed upon random contacts made with other agents. Upon making a tentative decision to go ahead, based largely on i n t u i t i o n , the developer often makes a temporary agreement with the landowner i n the form of an option (questions VI 1 to 4) which allows time for investigating the decision before f u l l y committing himself to purchase of the s i t e . In making his purchase decision, the developer formulates his ideas regarding char-acter and timing of the development i n terms of the economic f e a s i b i l i t y and r i s k involved. His market analysis, based to a considerable extent on experience and i n t u i t i o n , can be supplemented by information about his l o c a l market from l o c a l planning commissions, zoning boards, mortgage companies, newspapers and private business sources. In addition, much regional and national information concerning business, housing and population i s available from the government - population growth and regional r e d i s t r i b u t i o n , family formulation, family s i z e , e x i s t i n g housing stock, l e v e l of construction, occupations and income of poten t i a l buyers (questions III 9 to 12). The developer's economic f e a s i b i l i t y study evaluates the p r o f i t a b i l i t y of the proposal i n terms of i t s cost implications (land costs, estimated physical development costs, overhead and financing) and i t s revenue implications (usually an i n t u i t i v e estimate of the l i k e l y s e l l i n g price) and i s tempered by consideration of investment r i s k s . Of the ri s k s mentioned i n interviews by Kaiser and Weiss , the most important are: 1. Risk associated with c a l c u l a t i o n of marketabil-i t y e s p e c i a l l y i n l i g h t of the t y p i c a l l y weak analysis of market demand and proper composi-ti o n of the r e s i d e n t i a l package components of house, s i t e , neighborhood and locati o n . 2. Risks associated with holding of land inventory - the r i s k of not being able to f i n d suitable land when needed and the r i s k of having changes i n price of land and i n consumer preferences while the land i s being held. 3. Risks associated with l o c a l government such as lengthy delays i n obtaining approvals or changes i n zoning and subdivision regulations, i n timing of i n s t a l l a t i o n of public c a p i t a l improvements, among others. 4. Risks associated with obtaining the necessary approval of f i n a n c i a l intermediaries. Certainly the developer w i l l take steps to minimize his perceived r i s k s . He w i l l s e l e c t s i t e s with c h a r a c t e r i s t i c s which he feels are l i k e l y to increase the marketability of his product - those seen as having a high s o c i a l prestige l e v e l (the most important as determined by Kaiser 7 and Weiss ) and those with i n s t i t u t i o n a l character-i s t i c s such as a v a i l a b i l i t y of urban services, zoning protection, and schools. The developer i s l i k e l y to optimize the size of his land inventory within the l i m i t s of his perceived r i s k s . "Most developers purchased land for a short-term inventory of suitable land to meet s p e c i f i c markets rather than for long-term g speculation of land values." (questions I 11 and 12). In order to minimize f i n a n c i a l r i s k s , the developer i s l i k e l y to make conservative decisions about the s t y l e , type and location i n order to avoid r i s k i n g disapproval of inherently conserva-t i v e f i n a n c i a l intermediaries since t h e i r services are required f i r s t for development and l a t e r for homebuying. In addition, vague and changeable p o l i c i e s concerning annexation, school d i s t r i c t boundaries, extention of public u t i l i t i e s , enforce-ment of subdivision and zoning regulations, b u i l d -ing codes, taxation and assessment practices can increase the developer's r i s k s thereby discouraging anything but the most conservative type of develop-ment and possibly encouraging scatteration. The Householder's Decision The demographic c h a r a c t e r i s t i c s of household s i z e , place of work, stage i n the family l i f e cycle, income l e v e l , and a c t i v i t y patterns govern the householder's preferences for space, f a c i l i t i e s and a c c e s s i b i l i t y . The a t t i t u d i n a l c h a r a c t e r i s t i c s of s o c i a l mobility aspirations, actual mobility and l i f e s t y l e govern the l i v a b i l -i t y and prestige preferences. These factors come to bear on the marketability of the f i n a l residen-t i a l package which consists of not only the o r i g i n a l physical, l o c a t i o n a l and i n s t i t u t i o n a l c h a r a c t e r i s t i c s of the s i t e as modified by the developer but also the dwelling unit i t s e l f and other on-site improve-ments. Further, the r e s i d e n t i a l package must be considered i n the context of the s o c i a l and physi-cal neighborhood created by the development process and the types of households selecting or already occupying other r e s i d e n t i a l packages nearby. Models of the Development Process In a "System of Limited Models for 9 Forecasting Urban Residential Growth", R. W. Massie constructed three decision agent models - landowner, developer, and consumer. The output i s a s p a t i a l d i s t r i b u t i o n of land l i k e l y to be sold, a s p a t i a l d i s t r i b u t i o n of land l i k e l y to be developed, a s p a t i a l d i s t r i b u t i o n of subdivision types and an associated d i s t r i b u t i o n of consumer types among the various types of subdivisions. The landowner model corre c t l y predicted 72.3 per cent of properties sold from these v a r i a b l e s - ^ 1. Residence (whether or not the owner resides on the land 2. Occupation (whether r e t i r e d or not) 3. Ownership type (single or joint) 4. Length of time the property has been held 5. Amount of contiguous urban development The producer model corre c t l y pre-dicted 61.5 per cent of the subdivision types (better than the combined landowner-producer model) from these variables"*"^ 1. Socioeconomic rank 2. A v a i l a b i l i t y of u t i l i t i e s and services 3. Distance to elementary schools 4. Access to employment areas 5. Distance to the CBD. The consumer model corre c t l y predicted only 41.7 per cent of the r e s i d e n t i a l packages selected 12 from these variables 1. Income 2. Education 3. Age 4. Household Size From interviews of rental developers ranks location factors i n the following 1. Zoning 2. F i n a n c i a l considerations 3. Market demand E l d r i d g e 1 3 order: 4. A v a i l a b i l i t y of water and sewage 5. "Good" neighborhood 6. Size of parcel 7. A c c e s s i b i l i t y to work areas 8. A c c e s s i b i l i t y to commercial f a c i l i t i e s 9. A c c e s s i b i l i t y to schools 10. Topography 11. S o i l conditions 12. Location of rental developer's other apartment projects 13. Location of other developers' apartment projects Analysis of the data demonstrates that r e n t a l developers of d i f f e r e n t scales and of d i f f e r e n t c i t i e s exhibit s i m i l a r i t i e s i n t h e i r evaluation of decision factors. In a survey of large and small develop-ers constructing low, medium and high priced sub-14 d i v i s i o n s , Kaiser determines r e l a t i v e associations with c e r t a i n s i t e c h a r a c t e r i s t i c s : Physical c h a r a c t e r i s t i c s : proportion of marginal land; proportion of poor s o i l ; Locational c h a r a c t e r i s t i c s : socioeconomic rank; distance to nearest major street; distance to nearest elementary school; distance to CBD; inverse of a c c e s s i b i l i t y to employment areas; amount of contiguous residen-t i a l development; amount of recent contiguous r e s i d e n t i a l development; I n s t i t u t i o n a l c h a r a c t e r i s t i c s : a v a i l a b i l i t y of public u t i l i t i e s ; zoning protection. "Developer c h a r a c t e r i s t i c s , such as size of firm, entrepreneurial approach, and nature of the production process used, influence l o c a t i o n a l behavior under s i m i l a r property and contextual factors by a f f e c t i n g the r e l a t i v e a t t r a c t i o n of d i f f e r e n t kinds of s i t e s . In our empirical tests and modeling e f f o r t s , we have found s i g n i f i c a n t differences between the l o c a t i o n a l decisions of large-scale developers (those developing over 100 l o t s per year) and the l o c a t i o n a l behavior of small-scale developers. ... Further, the two categories almost appear to be looking for very d i f f e r e n t combin-ations of s i t e c h a r a c t e r i s t i c s . For example, large developers tend to choose s i t e s closer to the CBD, an elementary school, and employment centers, with public u t i l i t i e s a v a i l -able. Small developers tend to se l e c t the opposite kind of site." 15 "Large scale developers appear much more sensi t i v e than smaller scale developers to a c c e s s i b i l i t y , to a v a i l a b i l i t y of water and sewer, and to zoning protection at a l l levels of subdivision."16 The Housing Market This section deals with factors i n the housing market r e l a t i n g to aggregate supply and demand. Discussion i s made of the relationships between fluctuations i n housing demand and income of the household/ rent levels and the price of housing, and c r e d i t a v a i l a b i l i t y . Also, i n v e s t i -gation-' i s made into the relationship between the volume of r e s i d e n t i a l construction and such factors as i n t e r e s t rates, vacancy l e v e l s , and certa i n aspects of household formation. D e f i n i t i o n of Housing Demand It i s useful at the outset of a discussion of housing demand to note a few d e f i n i -17 t i o n a l points made by W. F. Smith. The d i s t i n c t i o n between housing "need and " e f f e c t i v e demand" i s that the former represents a s o c i a l value judgement of what ought to be while the l a t t e r deals with marketplace demand formed by purchases made by consumers with both the desire and ecomomic means. The d i s t i n c t i o n between "stock demand and "incremental demand" deals with demand for housing i n t o t a l (which i s met from e x i s t i n g stock plus new construction) as opposed to demand simply for new housing. The l a t t e r i s a t t r a c t i v e from the point of view of f a c i l i t y of analysis but neglects aspects of conversions, f i l t e r i n g , and dem-o l i t i o n plus the in t e r r e l a t i o n s h i p s between these factors, e x i s t i n g stock and new construction. Housing demand i s affected by decisions made by both the user and the investor. The investor's decisions w i l l d i f f e r from those of the user according to the degree of variance between his assumptions concerning the behavior of housing users and t h e i r actual behavior and to the extent that business factors enter into these decisions. Factors A f f e c t i n g Housing Demand 1. Demographics 18 As L. E. Smith points out, demo-graphics involve a large number of factors which a f f e c t housing demand i n a highly complex manner. Population growth can be disaggregated into age components, family size and s o c i a l groups which are affected by trends i n family formation and dis s o l u t i o n , migration, the number of children per family, the age of parents at the time of th e i r f i r s t c h i l d , and so on. Further, i t i s net non-family households (young single persons, middle aged or older widows, widowers, bachelors, spinsters 19 and divorcees) which tend to generate demand for rental accommodations while families with children which form the majority of demand for owner-occupied housing. For a good analysis of demographics 19 r e l a t i n g to housing, see M c A l l i s t e r . 2. Income An increase i n the number of single family homes desired r e s u l t s from a r i s e i n income level s by enabling more families to accumulate savings for downpayments and to afford the monthly payments required for home ownership. Rising incomes also stimulate demand for rent a l accommo-dation by f a c i l i t a t i n g family undoubling and non-family formation while r a i s i n g the qual i t y of accommodations desired. Estimates of stock demand e l a s t i c i t y f or dwelling accommodations vary 20 from highs of 1.5 to 2.0 by Reid and 1.0 by 21 Muth (the consensus being that these results. 22 are biased upward) to lows of 0.5 to 0.8 by Lee, 23 24 25 Oksanen, Uhler, and L.B. Smith. That i s , the results of studies i n both Canada and the U.S.A. show that the proportion of permanent income (and current income) spent on housing decreases as income increases. 3. Prices and Rents As i s the case for changes i n prices of other expenditures, r e l a t i v e changes i n rents, prices of housing and of non-shelter items bring about substitution effects - r i s i n g rents increase demand for owner-occupied (usually single family) housing and non-shelter items; r i s i n g prices of single family housing increase demand for rental accommodation and non-shelter items. What i s considered to be most relevant i n the housing purchase decision i s not the purchase p r i c e but the size of the downpayment and the monthly i n t e r e s t and p r i n c i p a l payment. The multitude of variations and conditions i n housing purchases has caused considerable d i f f i c u l t y i n reaching agreement concerning price e l a s t i c i t i e s . L. B. Smith's opinion i s that i t i s about -1.0 through con-sideration of the v a r i a t i o n r e s u l t i n g from the work of R e i d 2 7 (-0.96 to -2.45), Muth 2 8 (-1.0 to -1.5), L e e 2 9 (-1.48) and Chung 3 0 (-1.0). 4. Credit Variables The demand for owner-occupied dwell-ings i s very sen s i t i v e to c r e d i t variables, i . e . , to changes i n the s i z e of the required downpayment and monthly payments (a function of i n t e r e s t rates and the amortization period). Larger downpayment requirements reduce the number of families with s u f f i c i e n t l i q u i d savings to enter the housing market and reduce the size of housing expenditure that these savings w i l l support. Requirements for larger monthly payments l i m i t the number of families capable of making these payments out of current income. Credit variables i n d i r e c t l y a f f e c t the demand for rent a l accommodation. That i s , when cr e d i t terms for single family housing are too onerous demand s h i f t s from owner-occupied to rent a l accommodation. An o f f s e t t i n g e f f e c t , however, i s produced by higher rents r e s u l t i n g from reduced multiple family housing construction which i s a consequence of the t i g h t money conditions. 5. Other Variables Expectations regarding land p r i c e s , construction costs, c r e d i t r e s t r i c t i o n s , rent levels and plans a f f e c t i n g transportation f a c i l i t i e s , zoning and serv i c i n g a l l have a considerable e f f e c t upon the demand for housing. A n t i c i p a t i o n of tougher times ahead w i l l provide impetus for people to opt for housing today, i f possible, thereby s h i f t i n g future demand into the present. Factors Af f e c t i n g Housing Supply The extremely complex area of housing supply deserving much attention has had l i t t l e , 31 (for a summary, see Winger ). Some of the factors a f f e c t i n g the volume and location of redevelopment of the central c i t y (especially those concerning apartment development) are 32 discussed by L.S. Bourne. In an extensive investigation into the process of apartment development through a survey of developers, W. F. 33 Smith i s o l a t e s three factors which "explain" the increase i n apartment construction i n the s i x t i e s : 1. A demographic s h i f t favoring households i n the predominantly renter ages; 2. An increase i n the a v a i l a b i l i t y of mortgage funds coupled with a competitive struggle for high-yield loans; 3. Income tax provisions favorable to investment i n multi-family dwellings (which may have changed i n Canada as a r e s u l t of changes i n the Income Tax Act i n 1972 which placed a curb on pooling of income). At the beginning of t h i s review, reference was made to the factors a f f e c t i n g producer behavior i n the housing f i e l d . Some of the more important constraints within which the developer operates are: the requirement of antic i p a t i n g the type, location, price.range, q u a l i t y , s i z e , and magnitude of consumer demand; zoning, municipal bylaws, building codes, delays i n obtaining governmental approval and manoeuvring by p o l i t i c a l and c i t i z e n s ' groups; f i n a n c i a l constraints, changes and trends i n the a v a i l a -b i l i t y of financing and i n t e r e s t rates, r i s i n g construction costs (both labor and materials), and delays due to labor disputes. Models of the Housing Market A n a l y t i c a l work on the determinants of r e s i d e n t i a l construction can be divided 34 broadly into two types: 1. Models based primarily on a verbal or q u a l i t a t i v e analysis of the market: Analysed on the basis of available s t a t i s t i c s and ad hoc judgements, they place stress on variables r e l a t i n g construction s p e c i f i c a l l y to housing market conditions and factors external to the housing market and attempt to i d e n t i f y secular trends, long swings and short cycles i n r e s i d e n t i a l construction. 2. S t a t i s t i c a l models which re l a t e various economic indices to quantitative changes i n the vo ume of construction and various time leads and lags Typical are time series analyses of such variables as income, rents and costs, household formation and e x i s t i n g housing stock. For a bibliography of some e a r l i e r models, 35 see Grebler and Maisel. 36 An important analysis of Maisel involves r e l a t i n g census type housing s t a r t s to the Treasury B i l l rate, the r e s i d e n t i a l cost component of the consumer price index, the v a r i a t i o n i n the trend i n vacancies, and an estimate of removals and net household formation for the period. In achieving very good results he concludes that housing s t a b i l i t y i s dependent upon the federal (U.S.) government actions dampening rather than r e i n f o r c i n g the r e s i d e n t i a l cycle. 37 Muth's study i s concerned with the response of housing demand to changes i n pr i c e and income and with the rate at which adjustments of the housing stock take place. His evidence indicates that new construction i s highly responsive to changes i n income and the price of housing, the e l a s t i c i t i e s of new construction with respect to p r i c e and income both being about 5.5. Muth i d e n t i f i e s two lags of adjustment of the housing stock: the lag of adjustment of actual to desired stock due to slowness of families to make the housing decision; and the lag of adjustment of desired stock to current income due to the lag of current income behind expected or normal income (Freidman). 3 8 W. F. Smith's " s i m p l i s t i c model" of housing demand determines the range of requirements (both quantitative and qual i t a t i v e ) for housing within the context of many factors: vacancies; "suppressed demand" (a s o c i e t a l judgement); demolitions; unintended vacancies (from preexisting stock that have not yet been demolished); absorption rates of new construction; d i f f e r e n t i a t i o n of the housing stock according to economic factors and pre-ferences of demographic groups; and growth and change of composition of households over time. A s i m p l i f i e d model of housing demand 39 i s that of Leo Klaassen which u t i l i z e s factors underlying the development of the housing sector which are i d e n t i f i a b l e as those causing general economic development. Very general explanations for housing market development are used - income growth and d i s t r i b u t i o n , population growth, income e l a s t i c i t y of housing demand and depreciation of the housing supply. As 40 pointed out by U. Wullkopf, problems with time and s p a t i a l d i s t r i b u t i o n as well as f i l t e r i n g remain. 41 L. B. Smith, i n obtaining his econometric r e s u l t s , u t l i z e s two models of the Canadian housing-market: an aggregate and a disaggregate version of a short-run supply model; and an adaptation of a long-run stock adjustment model. In the short-run model, family demand for housing accommodations i s thought of as a function of permanent r e a l family disposable income, the price of housing, the prices of alternative goods and services and the cost and a v a i l a b i l i t y of mortgages. The disaggregate version i s modified to incorporate re n t a l versus owner-occupied housing, and single versus multiple family housing. From this general housing model he concludes: 1. Housing starts are very sens i t i v e to both the cost and a v a i l a b i l i t y of mortgage c r e d i t (the e l a s t i c i t y of t o t a l housing s t a r t s to variations i n the mortgage rate being -0.80 and to v a r i a t i o n i n the bond rate being -0.37). 2. Credit rationing operates more strongly upon single family housing s t a r t s . 3. Housing starts are very sensitive to the volume of government d i r e c t lending. 4. The volume of housing s t a r t s i s highly dependent on the relationships between pr i c e s , rents and construction costs. 5. Land costs play an important r o l e i n determining the mix of single and multiple family housing s t a r t s . Smith's stock adjustment model (which assumes equilibrium of supply and demand) determines the per family excess demand as a function of per family r e a l disposable income, the price of new housing r e l a t i v e to prices of alternative goods and services, the cost of mortgage c r e d i t , the a v a i l a b i l i t y of private mortgage c r e d i t (the spread between y i e l d s on bonds and mortgages), and the volume of CMHC lending. From th i s stock adjustment model he concludes that housing stock has an average speed of adjustment of approximately 0.23. This means that i t takes roughly two and three-quarter years for construction to eliminate hal f the gap between the desired and actual housing stock. Comment The models presented above are a l l macro models deal ing with the nat iona l economy and as such are l i m i t e d i n t h e i r scope from analys is of factors and examination of p o l i c y a l ternat ives concerning the reg ional housing market. Disaggregation of demand according to d i f f e r e n t household types, age groupings and accompanying housing preferences has not been made. Considerat ion of a wide scope of a l t e rna t ive forms of housing, communal f a c i l i t i e s and accompanying l i f e s t y l e s , which i s one of the areas of inves t i ga t ion with most p o t e n t i a l , could thereby be made pos s ib le . 29 Models Concerned with Housing Patterns i n General  Terms This section i s concerned with p o t e n t i a l l y operational models which are generalized explanations of the land use patterns of c i t i e s . The problem formulation centres on the d i s t r i b u t i o n of housing units among a number of small areas into which the urban region has been divided. The handling of the r e d i s t r i b u t i o n of households i s avoided due to the d i f f i c u l t y of detecting the volume and d i r e c t i o n of r e d i s t r i b u t i o n and the subtlety of factors involved. Burgess' Concentric Zone Theory In order to explain the e f f e c t of market forces upon land use and to thereby under-stand the processes of expansion of urban areas, 42 Burgess conceived the c i t y as a series of f i v e concentric zones. At the core i s the central business d i s t r i c t . E n c i r c l i n g the core i s an area i n t r a n s i t i o n - an older warehouse and market d i s t r i c t which i s evolving into an area of business and l i g h t manufacture. A t h i r d zone i s that inhabited by i n d u s t r i a l workers who have escaped from the deteriorating area of t r a n s i t i o n but who desire to l i v e within easy access of t h e i r work. Beyond this zone i s the r e s i d e n t i a l area of high-class apartment buildings or of exclusive " r e s t r i c t e d " d i s t r i c t s of single family dwellings. S t i l l farther out, beyond the c i t y l i m i t s i s the commuters1 zone - suburban areas or s a t e l l i t e c i t i e s - within a t h i r t y to s i x t y minute ride of the central business d i s t r i c t . Depending upon the rate of economic expansion and population growth i n the c i t y , each zone tends to invade the next outer zone. In addition there are c e n t r i f u g a l forces causing certain functions i n the central zone of the c i t y to migrate to outer zones as well as c e n t r i p e t a l forces which hold c e r t a i n other functions i n the 43 central zone and a t t r a c t s t i l l others to i t . Hoyt's Sector Theory Homer Hoyt's refined theory of a x i a l 44 development postulates that growth of s i m i l a r types of land use usually occurs along an axis of transportation. The various areas of a c i t y are envisaged as wedge-shaped sectors radiating out from the central core. Areas of s i m i l a r types of land use originate near the centre and expand outward at the periphery. Theory of Multiple Nuclei 45 Harris and Ullman observed that frequently the land use pattern i s b u i l t not around a single centre as i n Burgess 1 and Hoyt's models but around several discrete n u c l e i . These nu c l e i , which may vary i n number i n d i f f e r e n t c i t i e s , often have a s p e c i a l i z e d function. T y p i c a l l y there i s a central business d i s t r i c t , a wholesale and l i g h t manufacturing d i s t r i c t , several r e s i d e n t i a l d i s t r i c t s , and minor nuclei or f o c i of various forms of subordinate a c t i v i t y . They may r e s u l t from a combination of factors; the interdependency of c e r t a i n types of a c t i v i t i e s ; the requirement of certain a c t i v i t i e s for s p e c i a l -ized f a c i l i t i e s ; the r e p e l l i n g forces between cer t a i n unlike a c t i v i t i e s ; and economic forces surrounding high rents of the most desirable areas. Clark's Theory of Exponentially Declining Densities 46 The evidence gathered by Clark i n the detailed study of density maps of numerous c i t i e s i n the world shows that i n p r a c t i c a l l y every case, the progressive decline i n density from the central business d i s t r i c t to the outer suburbs i s a simple exponential: * "hd y = Ae where y i s the density of the resident population and d i s the distance from the centre of the c i t y . Further, he showed that i n most (but not a l l ) cases, the c i t y tends to spread i t s e l f out over time -density tends to f a l l i n the most populous inner suburbs and to r i s e i n the outer suburbs - adhering to an exponential decline with d i f f e r e n t values for the c o e f f i c i e n t s A and b. Models Involving Transportation Costs and S p a t i a l Preferences The models presented above describe observable s p a t i a l patterns of urban development. They o f f e r l i t t l e to the understanding of processes leading to that development. The following models introduce behavioral decision making into a general economic framework i n try i n g to simulate r e a l world processes. Each decision-making unit chooses the "best" alternative for i t s e l f from the choices ava i l a b l e . 1. Kain's Model 47 Kain's central hypothesis i s that households substitute journey-to-work expenditures for s i t e expenditures. This substitution depends primarily on household preferences for low-density as opposed to high-density r e s i d e n t i a l areas. The model predicts that households w i l l locate at varying distances from t h e i r workplaces according to t h e i r transportation costs, space consumption, s p a t i a l preferences and incomes. Differences i n the length of the journey-to-work and i n the l o c a t i o n a l choices of workers employed i n each area are a function of location rents which, t y p i c a l l y , tend to decrease asymptotically with distance from the central business d i s t r i c t . The r e s u l t of empirical tests i s a series of concentric rings -s i m i l a r to those of Burgess - i d e n t i f i a b l e i n terms of d i f f e r i n g r e s i d e n t i a l d e n sities, family s i z e , space consumption, occupational and income differences, and length of the journey to work. 2. Alonso's Model 48 Alonso's economic analysis of the urban land market i s embedded i n a mathematical model which focuses on the i n t e r a c t i o n of urban land rents, interurban l o c a t i o n a l processes and the i n t e n s i t y of use (density of occupancy) of urban space. In the land market there are two goods (land and distance) but only one transaction and one price (that of land) leading to a compli-cation of simple supply and demand equilibrium. Here he has, i n e f f e c t , condensed the f i v e dimen-sional problem of u t i l i t y , land, distance, composite goods and money. An equilibrium solution to the land market i s obtained through determination of the location and size of s i t e s occupied by residents, urban firms, and agriculture through the use of b i d price curves (for residents and firms) and bid rent curves (for a g r i c u l t u r e ) . 3. Wingo's Model 49 Wingo's in t e r p r e t a t i o n of the r e l a -t i o n between transportation and urban land use involves four general aspects of the c i t y : physical c h a r a c t e r i s t i c s of urban space; population of a s p e c i f i e d composition; aspects of technology which permit movement of t h i s population i n the urban space; and the organization of society to produce and consume goods and services. He incorporates i n his model a concept of transportation demand; a description of the transportation function i n terms of technology and demand; a transport cost function based on time, distance, and overhead; a system of location rents based on the transport cost function; and implications of the supply of space and household demand for space. The re s u l t i s a s p a t i a l d i s t r i b u t i o n of location rents and household densities involving both p o l i c y and s t r u c t u r a l e f f e c t s of the market i n the context of the urban economy. Comment In contrasting his work d i r e c t l y with 50 that of Kain, Stegman attacks the preeminence of a c c e s s i b i l i t y i n the r e s i d e n t i a l location decision which has been at the basis of the l a s t three models. The res u l t s of his survey of moves i n major metropolitan areas reveal that the majority of changes i n residence were not work-related, and that such factors as space, housing q u a l i t y , home ownership, neighborhood qu a l i t y were of more importance. Moreover, i n response to a question r e l a t i n g the two factors, 83 per cent of suburban movers chose the more desirable rather than the more accessible neighborhood. The d i r e c t i o n suggested by th i s work i s toward a microlevel of household decision-making rather than the general macrolevel view of urban r e s i d e n t i a l growth of the models presented above. Models of Residential Location Ad Hoc Allocations An ad hoc system for a l l o c a t i n g new dwelling units described by Chapin^"*" involves c a l c u l a t i o n of the r e s i d e n t i a l "holding capacity" for each of the subareas followed by a l l o c a t i o n of the estimated t o t a l of new households. Both steps require i n t u i t i v e and objective judgements about how the c i t y i s l i k e l y to grow coupled with such information as p r e v a i l i n g densities, zoning and density standards, the amount of vacant: and renewable land, and population-income breakdown. The CATS model The model used by the Chicago Area 52 Transportation Study for forecasting land uses imposes subjective elements of judgement over a formal structure of hypothecated growth processes. Base year occupancy patterns (existing land use, population density and employment), zoning and plans for redevelopment are modified by judgement to c a l -culate holding capacity of each zone. Forecasts for the target year of t o t a l population and of employment by industry type are d i s t r i b u t e d i n a continuous function over concentric zones r e s u l t i n g from consider-ation of the distance of the subareas from the central business d i s t r i c t and the percentage of capacity that the present population represents. In t h i s technique, the urban growth process i s envisaged e s s e n t i a l l y as an increase i n densities i n a pattern of concentric zones surrounding an inner zone i n which densities decline. However, t h i s model, l i k e that of Chapin, does l i t t l e to enlarge understanding of the s p a t i a l organization of the c i t y and aids l i t t l e i n evaluating the impacts of alternative public p o l i c i e s . The U.N.C. Model of Land Use Succession 53 The model of Donnelly, Chapin and Weiss of the University of North Carolina i s designed to predict the incidence of conversion of r u r a l or vacant land to r e s i d e n t i a l use as population of the urban area increases. The approach involves a ranking of private and public decisions and/or actions. Thus, "priming actions" are those of major significance i n the urban environment such as the construction of an expressway or large i n d u s t r i a l plant; "secondary actions" are generally more i n d i v i d u a l i s t i c , more numerous and comprise the bulk of the v i s i b l e pattern of land development. The location and density of secondary actions are f e l t to be predetermined by priming actions. 38 A standard l i n e a r multiple regression analysis i s used to determine those factors which "explain" dwelling density and the amount of land i n r e s i d e n t i a l use. The four priming factors which were determined were: a c c e s s i b i l i t y to work areas; a v a i l a b i l i t y of public sewerage; a c c e s s i b i l i t y to nearest major street; and accessi-b i l i t y to nearest available public school. The functioning of the model involves f i v e steps: 1. The inventory of undeveloped land i s determined and coded for use c a p a b i l i t y ; 2. A measure of " r e l a t i v e value" based on land values i s assigned to each s i t e ; 3. The e f f e c t of priming actions anticipated during the forecast period i s determined from l i n e a r regression c o e f f i c i e n t s and i s used to modify the r e l a t i v e value of land for r e s i d e n t i a l use; 4. Density and housing-value constraints are i n t r o -duced and the land "reassessed" to obtain a measure of the t o t a l attractiveness of undevel-oped areas f o r r e s i d e n t i a l use; 5. New housing anticipated during the growth period i s allocated on a p r o b a b i l i s t i c basis. "The study presently concentrates on the growth areas and new residen-t i a l development, leaving the handling of decrease areas and renewal processes ... to be dealt with i n l a t e r exten-sions of thi s research".54 Like the CATS model, the U.N.C. model does not comment d i r e c t l y on the origins or destinations of movers. Despite the U.N.C. group's extensive in v e s t i g a t i o n into behavior of land developers, i t i s not r e f l e c t e d i n the formal structure of the model. Harris' Stochastic Model of Urban Development 55 Harris's attempt to model the uncertainty of d i r e c t i o n and timing of suburban growth i s a r e s t r i c t e d form of a stochastic process i n which the res u l t s are expressed as p r o b a b i l i t i e s of subareas i n the urban fringe becoming urbanized i n a given time period. The process of suburban development i s stochastic i n that i n moving from one state of development to another the pr o b a b i l i t y of entering a certa i n state depends only on the l a s t state occupied. A theory which s p e c i f i e s the causa-tion and in t e r r e l a t i o n s h i p s between a l l the many complex variables and determinants of the rate and d i r e c t i o n of suburban growth i s beyond reach of the present state of knowledge. However, the stochastic process model summarizes the results of these determining variables and offers a framework i n which l i m i t e d knowledge of the process of suburban growth can be put to use. H i l l ' s EMPIRIC model 5 6 The Empiric land use model ( H i l l ) i s designed to reallocate projected regional growths i n population and employment i n urban subareas. A set of simultaneous equations relates predicted changes i n the d i s t r i b u t i o n of population and employment i n the subareas to one another, to the i n i t i a l year base d i s t r i b u t i o n , zoning, inten-s i t i e s of land use, t r a n s i t a c c e s s i b i l i t i e s , and water and sewage services, and to the estimated ef f e c t s of planning p o l i c y decisions. The planning po l i c y decisions may be expressed as estimated change i n regional a c c e s s i b i l i t y which i s a function of transportation improvements, exogenously s p e c i f i e d r e s i d e n t i a l , commercial or i n d u s t r i a l development, or subareal growth constraints. As such, the model i s useful both as a forecasting t o o l as well as mechanism for evaluating the impact of major p o l i c y decisions on the future d i s t r i b u t i o n of regional population and employment. The model does not comment on the i n t e r d i s t r i c t flows necessary to produce the net changes r e s u l t i n g from the solution of the equations nor i s any reference made to land use succession. The Lowry Model 57 Lowry has proposed an urban development model which focuses on the i n t e r r e l a -tionships between three, broad areas of a c t i v i t y : basic sector employment, service sector employment, and the household sector. A d i s t r i b u t i o n of basis employment i n the various zones (grid squares) i s s p e c i f i e d exogeneously and the house-holds of the workers i n the basic employment sector are then allocated to r e s i d e n t i a l zones around the basic workplaces by a r e s i d e n t i a l location submodel. The demand for services generated by this basic population supports l o c a l l y dependent service centres which are located by a second s p a t i a l a l l o c a t i o n submodel. The workers i n thi s service employment are allocated housing locations and the process i s r e i t e r a t e d u n t i l the system s t a b i l i z e s . The Steger ->° rev i s i o n of the Lowry model makes i t a more complete predictor of urban development allowing the relocation of basic industries within the context of the c i t y . Secondly, rather than d i s t r i b u t e a l l a c t i v i t y i n one shot, i t predicts incrementally the location and relocation of new and exis t i n g households and businesses from the pattern of previous development. Rather than r e f l e c t Lowry's equilibrium state of the metropolis, the model i s s e n s i t i v e to po l i c y assumptions and i s thereby useful i n the measurement and prediction of the cumulative effects of urban renewal decisions over time. Bay Area Simulation Study (BASS) The Lowry model was the stimulus for BASS which had as i t s primary purpose the measurement of the impact of i n d u s t r i a l l o c a t i o n . I t generated employees, population, and households for each census t r a c t (rather than households for each g r i d square) and disaggregated many parameters which were applicable to the whole system i n the Lowry model to i n d i v i d u a l t r a c t - s p e c i f i c form. The BASS r e s i d e n t i a l location sub-59 model matches the supply of housing and of usable land with exogeneously determined housing demand for the six categories of housing (two types of housing, three income classes). The supply of housing r e s u l t s from consideration of f i l t r a t i o n (estimated s h i f t s i n inventory of the six housing categories) and the supply of usable land (estimated as a function of the e x i s t i n g housing in each housing category as well as the density of development). In each i t e r a t i o n of the model, about t h i r t y per cent of new construction i s located according to a c c e s s i b i l i t y to the location of new employment. However, a l l o c a t i o n of existing demand for the six categories of housing to the i n d i v i d u a l subareas i s made on the basis of the r e l a t i v e a c c e s s i b i l i t y of each area to exi s t i n g employment. Although there are no e x p l i c i t p o l i cy variables i n the model, they can be introduced i m p l i c i t l y through changes i n the input assumptions (regarding a v a i l a b i l i t y of usable land) and i n l o c a t i o n a l and behavioral functioning. Projective Land Use Model (PLUM) Further i n the l i n e of development that grew out of experiments with BASS, the PLUM 6 0 Model was implemented to forecast the population, dwelling units, and employment used by the Bay Area Transportation Study Commission. Among the more important additional concepts which were incorporated i s the handling of t r a v e l . The model simulates t r i p s rather than estimating them i n correspondence to an a c c e s s i b i l i t y index. Trips were disaggregated by type (work-to-home, work-to-shop, and home-to-shop) and s p a t i a l l y by county. Network times were created by generation of minimum time paths with alternatives for free-flow and peak-hour versions. Herbert and Stevens 1 Model of Market Demand 61 Herbert and Stevens' l i n e a r programming model i s designed to d i s t r i b u t e house-holds to r e s i d e n t i a l land i n an optimal configur-ation. Over a number of short i t e r a t i v e time periods, the model optimizes savings i n the household's s e l e c t i o n of a r e s i d e n t i a l bundle (house, amenity l e v e l , t r i p set and s i t e size) with respect to a l l previously located a c t i v i t i e s . Land i s allocated to that group of households which can bid the highest p r i c e for i t . In the Penn-6 2 Jersey Transportation Study which has the same the o r e c t i c a l framework, the changing character and income of households over time i s r e f l e c t e d i n the aging of households i n each zone. The major d i f f i -culty i n a l i n e a r programming approach to modelling household demand i s that demand behavior i s fundamentally nonlinear i n nature and certa i n important features of consumer behavior cannot be incorporated i n the analysis. A. D. L i t t l e (San Francisco) Model of Market Supply Developed by A. D. L i t t l e , Inc. for 6 3 the San Francisco Planning Commission, th i s model was designed for use i n urban renewal planning i n that i t i s a micro-analysis of the decision-making processes which lead to changes of occupancy and the state of housing stock. The model attempts to simulate the location decisions of d i f f e r e n t users of space, the investment behavior of private investors and the impacts of public p o l i c i e s and actions. The ex i s t i n g housing stock i n each subarea or " f r a c t " i s c l a s s i f i e d by use, condition, and location and i s "aged" p r o b a b i l i s t i c a l l y over time to a lower condition. A notable feature of th i s model i s the absence of any transportation or a c c e s s i b i l i t y considerations. The model considers only part of the relevant urban system - the housing market -ignoring for example the p o s s i b i l i t y of demolition of r e s i d e n t i a l units to permit the construction of a commercial unit. The model recognizes that housing units can age and change condition. Households, however, do not, as contrasted with the Sear's model. Sears' Model Sears 1 New York State Regional 64 Housing Model i s e s s e n t i a l l y an equilibrium model which assumes that supply varies d i r e c t l y with demand. I t may also be seen as a "double cohort s u r v i v a l " model i n which both households and housing units go through an aging process. Total active demand i n each subarea i s the sum of three components: 1. households without housing due to aging (of households or housing); 2. households without housing due to d i s s a t i s f a c t i o n ; 3. additional households. Total active supply i n each subarea i s the sum of the following three parts; 1. housing vacant due to aging (of households or housing); 2. housing vacant due to d i s s a t i s -f a c t i o n ; 3. additional housing. The model i s predictive i n that i t s use, together with s e n s i t i v i t y analysis, may aid i n evaluating the impact of alternative government housing p o l i c i e s on the housing s i t u a t i o n . Discussion of the Models of Residential Location 1. Contextual Most of the models presented here were developed within the greater context of regional economic or transportation studies. In order to adequately represent the development process they must do more - they must operate i n the framework of i n d u s t r i a l l o cation and relocation consumer and producer behavior and changing transportation technology. 2. Forecasting the E f f e c t s of Public P o l i c i e s Only the Empiric and A. D. L i t t l e models e x p l i c i t l y allow for the evaluation of a l t e r native public planning p o l i c i e s although i n the BASS and Sears models they may be i m p l i c i t l y incorporated. A l l the models were developed i n the U.S.A. where the i n s t i t u t i o n a l and p o l i t i c a l conditions a f f e c t i n g urban development are substan-t i a l l y d i f f e r e n t fromvthe Canadian. 3. Market Equilibrium and Disaggregation In a l l but the A. D. L i t t l e model, t o t a l supply of housing i s simply equated to t o t a l demand for housing - the condition for continuous equilibrium. There i s no d i s t i n c t i o n made between the factors a f f e c t i n g l o c a t i o n , type and quantity of housing demanded and supplied. Therefore, interactions between the two, ^ nd long range i n s t a b i l i t y i n the housing market must be ignored. Also, there i s no d i f f e r e n t i a t i o n of preferences of housing type, location and form of tenancy according to d i f f e r e n t household subgroups c l a s s i f i e d by age, family structure, s o c i a l status and income. In incorporating the investment behav-i o r of private investors, the A. D. L i t t l e model handles market disequilibrium through the price mechanism. Demand (specified exogenously) dictates price l e v e l s of e x i s t i n g housing and the degree of crowding i n the c i t y while the new supply i s based on p r o f i t a b i l i t y of investment determined by those price l e v e l s . 4. Locational C r i t e r i a The l o c a t i o n a l emphasis i n these models has been on a c c e s s i b i l i t y to employment, sewerage, major transportation routes, etc. The neighborhood considerations shown to be important 6 5 by Stegman and the lo c a t i o n a l factors a f f e c t i n g entrepreneurial behavior on the part of the developers reported by the U.N.C. group have yet to be properly incorporated i n a model. 5. Spatial Disaggregation Only two of the models (Herbert and Stevens : and A. D. L i t t l e ) are s p a t i a l l y disaggre-gated through consideration of competition among d i f f e r e n t types of households for the available location. The other models, with the exception of the Sears 1 model which has no s p a t i a l d i s -aggregation, d i s t r i b u t e t o t a l demand to available housing i n the given subareas i n proportion to weights which the model calculates. For example, i n the Lowry case a c c e s s i b i l i t y to employment i s the key. The U.N.C. model measures developmental attractiveness i n terms of land p r i c e s , a c c e s s i b i l i to employment, schools, major transportation routes and public sewerage. The Herbert and Stevens 1 model matches s p a t i a l l y disaggregated supply to demand on the bases of the consumer's a b i l i t y to pay for housing within the context of his other needs and the l e v e l of his income. In the A. D. L i t t l e model, housing units are allocated on the basis of user groups' preferences for type and locati o n . 6. Intra-regional Mobility A l l but two of the models assign households to a subarea and f i x them there for a l l time, ignoring the mobility of households within the urban area. This necessitates the assignment of new households to new housing, ignores the ;aging process of households and of houses, and avoids consideration of movement between rental and owner-occupied housing. The A. D. L i t t l e model attempts to account for thi s by r e a l l o c a t i n g households to housing every two years. Only the Sears 1 model properly accounts for changes i n supply and demand due to d i s s a t i s -f a c t i o n , aging and new additions of houses and households. 7. Aspects of Renewal and Redevelopment Although most models account for changes i n ex i s t i n g housing stock r e s u l t i n g from demolitions, conversions and f i l t e r i n g by way of changes i n density of use, only i n three models (A.D. L i t t l e , BASS and Sears) are these factors e x p l i c i t l y considered. One of the central features of the A.D. L i t t l e model i s redevelopment behavior of entrepreneurs and the p u b l i c . In the BASS model, demolitions and f i l t e r i n g are considered i n a separate submodel. Aging of houses i s one of the main features of the Sears model although i t i s l i m i t e d by the lack of s p a t i a l disaggregation. For an i n t e r e s t i n g analysis of t h i s subject (includ ing i n t r a - r e g i o n a l moves, absorption of new housing 6 6 vacancy rates and rent l e v e l s ) , see Mittelbach. 52 Scope and Methodology Two Approaches It i s the intent of t h i s study to provide a means whereby the s p a t i a l d i s t r i b u t i o n of housing units i n the Vancouver Metropolitan Area can be explained. The analysis i s to involve two approaches: The f i r s t approach involves a ranking of. weighting factors for each suhare.a- which would sum to a r e l a t i v e "measure of attractiveness from a developmental point of view". The re s u l t s of interviews with developers i n the form of a questionnaire y i e l d s a rough guide as to the importance of proposed l o c a t i o n a l decision factors. Those factors which are ranked of average or greater than average importance are considered to be poten t i a l determinants i n the location of new housing. In order to ascertain the degree of importance of each factor i t i s intended to regress these factors against unit completions of single family detached housing, single family attached housing and apartment housing. The regression c o e f f i c i e n t s are intended to provide weights which, when applied to the ch a r a c t e r i s t i c s of each subarea., provide a ranking of developmental attractiveness. 53 The second approach i s based upon Clark's Theory of Exponentially Declining Densities. The 1961, 1966 and 1971 population densities of the 1961 Census Tracts are analysed i n terms of distance from the central business d i s t r i c t (Georgia Street and Granville Street).In those subareas where density i s less than that determined by the theory, development i s expected to take place. That i s , the difference between calculated and observed densities i s a measure of the unused housing p o t e n t i a l . And i n order to ascertain i t s importance as a predictor variable, t o t a l housing unit completions are regressed against the unused housing p o t e n t i a l . It i s intended that the two approaches complement one another. That i s , the p o t e n t i a l approach (dealing with t o t a l housing completions) i s to provide support for the conclusions obtained by the behavioral approach (dealing with completions of single family and multiple family housing). Data Gathering Technique The analysis of t h i s study i s based upon data obtained through interviews with s i x t y -three companies involved i n r e s i d e n t i a l develop-ment i n the Greater Vancouver Area. The l i s t of developers to be contacted was compiled from (a) the membership l i s t of the Greater Vancouver Real Estate Board (the most useful); (b) the l o c a l membership l i s t of H.U.D.A.C. (The Housing and Urban Development Association of Canada); (c) "Contacts I n f l u e n t i a l Vancouver 1971" - a compilation of a l l firms i n Vancouver by industry type (firms under the industry "Real Estate" were contacted). The r e s u l t i n g number of developers to be contacted was approximately one hundred and ninety. About forty were simply contractors or r e a l estate sales o f f i c e s which had l i t t l e to do with the location decision making and therefore were not interviewed. About twenty had gone out of business or were no longer involved i n housing development. About t h i r t y were involved only i n commercial and i n d u s t r i a l development. About twenty-two were continually unavailable because they were too busy, always t r a v e l l i n g or uncooperative. About f i f t e e n were very small developers of single family dwellings (which were f e l t to be already s u f f i c i e n t l y represented i n the sample.) 55 Ty p i c a l l y , the interviews comprised approximately one-half hour for responses to questions read by the interviewer (see questionnaire, Appendix A) followed by approximately one-quarter hour discussion of various aspects of the housing market raised by the questionnaire. Limitations of the Questionnaire Approach The problems facing data c o l l e c t i o n by means of a questionnaire during an interview are: 1. the necessity for antic i p a t i n g the eventual re s u l t s of the survey i n order to include s u f f i c i e n t variables that relevant factors are not overlooked; 2. the necessity for phrasing the questions i n such a manner that the intent of each question i s not misinterpretted; 3. the necessity for i n c l u s i o n of questions relevant to a l l types of developers, while avoiding d i f f e r e n t interpretations due to differences i n operation; 4. the d i f f i c u l t y for developers, who t y p i c a l l y are unused to a r t i c u l a t i n g such abstractions, to i s o l a t e the relevant factors fromtthe immense complexity of t h e i r environment; 5. the n e c e s s i t y f o r the i n t e r v i e w e r t o r e s i s t temptation to a s s i s t the respondent i n making h i s response; 6. the p o s s i b i l i t y t h a t the developer i s so immersed i n h i s p a r t i c u l a r s i t u a t i o n t h a t he cannot see the general context of the environment i n which he works. He may, f o r example, develop i n an area where the hol d i n g q u a l i t i e s of the s o i l are good so t h a t i n h i s l i m i t e d context t h i s f a c t o r i s r e l a t i v e l y unimportant i n h i s l o c a t i o n d e c i s i o n ; 7. the p o s s i b i l i t y of r e l u c t a n c e on the p a r t of some developers to r e l e a s e c e r t a i n i n f o r m a t i o n (although t h i s was not f e l t g e n e r a l l y to be the case); i n c o n t r a s t , there may have been some d e s i r e to convey the "proper" image by responding according t o what was expected or was f e l t ought to be done. L i m i t a t i o n s of the Questionnaire One of the major l i m i t a t i o n s of the qu e s t i o n n a i r e used t o gather data f o r t h i s study i s t h a t responses of developers of more than one type of housing are not disaggregated by type. That i s , responses t o the questions r e l a t i n g to l o c a t i o n d e c i s i o n f a c t o r s (among others) ought to have been obtained f o r each of the housing types developed. In addition respondents indicated that t h e i r responses would vary according to the market catered to by p a r t i c u l a r projects. In readministering the questionnaire, responses ought to be obtained according to the socio-economic class to which appeal i s made. The Sample were taken from interviews with sixty-three developers of multi-family housing, single family housing, and subdividers. Numbers of developers of each housing type were grouped by the average number of units constructed during each of the l a s t three y e a r s . ( t o t a l units constructed during the three years divided by three). Multi-Family Housing: The results of t h i s questionnaire 1 50 11 51 100 3 100 150 5 151 200 5 Greater than 200 5 S t a t i s t i c s not Available 6 T o t a l : 35 The multiple faimily housing units completedliby our sample compared to the t o t a l completions as reported by "Real Estate Trends in Metropolitan Vancouver, 1972-3" (page B-16) are Units Completed Total Units By Sample Completed 1972 4329 6052 * 1971 3332 9760 1970 2834 8760 * twice the completions of the f i r s t s i x months of 1972 Single Family Housing: 1 - 1 5 11 16 - 35 10 36 - 75 8 76 - 150 5 Greater than 150 1 S t a t i s t i c s not Available 6 Total: 41 The single family housing units completed by our sample compared to the t o t a l completions as reported by "Real Estate Trends i n Metropolitan Vancouver, 1972-3" (page A-8) are: Units Completed Total Units By Sample Completed 1972 2132 5242 * 1971 1373 5216 1970 1035 4365 * twice the completions of the f i r s t six months of 1972 Subdividers: 1 - 1 5 7 16 35 3 36 - 75 3 76 - 150 2 Greater than 150 2 S t a t i s t i c s not Available 6 Total : 21 The number of lo t s subdivided by those i n our sample were: Lots Subdivided by Sample 1972 2204 1971 1216 1970 965 S t a t i s t i c s of t o t a l l o t s subdivided by year were not available f o r comparison. This compares to CMHC developer s t a t i s t i c s as follows:** 7 60 Builder A c t i v i t y by Dwelling Unit Range 1970 (Vancouver) Range Number of Builders Units Constructed 1 - 2 5 179 451 2 6 - 5 0 6 161 51 - 100 3 243 Greater than 100 5 1045 Empirical Results of the Questionnaire Tables I, I I , III and IV contain the questionnaire results for a l l developers and for each of the three developer categories. Reported i n the tables are those factors which were ranked by a l l developers together as of average or greater than average importance (2.0 or above). The two factors ranked highest by a l l developers showed very l i t t l e v a r i a t i o n of the mean (3.45, 3.49, 3.48 f o r proper zoning, and 3.34, 3.29, and 3.37 for access to trunk sewer) However, fo r p r i c e of land, the mean of 3.38 for developers of single family housing i s s i g n i f i -cantly above the other two (3.16 and 3.00). This quite possibly results from the heavy bias in the sample towards small scale developers of single family housing who are li m i t e d to a greater degree by f i n a n c i a l constraints. Availa-b i l i t y of developable land was ranked by the three types of developers with very l i t t l e v a r i a -t i o n (3.00, 2.91, and 3.04). The low weighting given to nearness to schools by developers of multiple family dwellings (2.16 vs. 2.51 and 2.41) T A B L E I Evaluation of Location Factors By A l l Developers (Per cent of Respondents i n Parentheses) Location F a i r l y Average Very E s s e n t i a l Mean Standard Factors Unimportant Important Importance Important Deviation (0) (1) (2) (3) (4) Proper Zoning 3(4.8) 0(0.0) 5(8.1) 16(25.8) 38(61.3) 3.39 1.00 Access to Trunk Sewer 3(4.8) 2(3.2) 1(1.6) 26(41.9) 30(48.4) 3.26 1.01 Price of Land 3(4.8) 2(3.2) 5(8.1) 21(33.9) 31(50.0) 3.21 1.06 A v a i l a b i l i t y of Developable Land 2(3.2) 4(6.4) 11(17.7) 21(33.9) 24(38.7) 2.98 1.06 Nearness to Schools 6(9.8) 7(11.5) 14(23.0) 29(47.5) 5(8.2) 2.33 1.10 Nearness to Major Roads 8(12.9) 8(12.9) 16(25.8) 23(37.1) 7(11.3) 2.21 1.20 Nearness to Major Shopping 7(11.5) 8(13.1) 18(29.5) 25(41.0) 3(4.9) 2.15 1.09 Areas Size of S i t e 10(16.4) 9(14.8) 16(26.2) 19(31.1) 7(11.5) 2.07 1.26 to T A B L E II Evaluation of Location Factors By Developers of Multiple Family Dwellings (Per cent of Respondents i n Parentheses) Location Unimportant F a i r l y Average Very E s s e n t i a l Mean Standard Factors Important Importance Important Deviation (0) (1) (2) (3) (4) Proper Zoning 1(2.6) 0(0.0) 3(7.9) 11(29.0) 23(60.5) 3.45 .86 Access to Trunk Sewer 2(5.3) 1(2.6) 0(0.0) 14(36.8) 21(55.3) 3.34 1.02 P r i c e of Land 2(5.3) 1(2.6) 4(10.5) 13(34.2) 18(47.4) 3.16 1.08 A v a i l a b i l i t y of Developable Land 1(2.6) 3(7.9) 8(21.0) 9(23.7) 17(44.7) 3.00 1.12 Nearness to Schools 6(16.2) 4(10.8) 9(24.3) 14(37.8) 4(10.8) 2.16 1.26 Nearness to Major Roads 4(10.5) 4(10.5) 9(23.7) 16(42.1) 5(13.2) 2.36 1.17 Nearness to Major Shopping 5(13.5) 5(13.5) 12(32.4) 13(35.2) 2(5.4) 2.05 1.13 Areas Size of S i t e 3(7.9) 5(13.2) 11(29.0) 14(36.8) 5(13.2) 2.34 1.12 (Tl CO T A B L E III Evaluation of Location Factors By Developers of Single Family Dwellings (Per cent of Respondents i n Parentheses) Location Unimportant F a i r l y Average Very E s s e n t i a l Mean Standard Factors Important Importance Important Deviation (0) (1) (2) (3) (4) Proper Zoning 2 ( 4 .4 ) 0 ( 0 . 0 ) 3 (6 .7 ) 9 ( 20 . 0 ) 31 (68 .9 ) 3.49 Access to Trunk Sewer 1 ( 2 .2 ) 1 ( 2 . 2 ) 1 (2 .2 ) 23 (51 .1 ) 19 (42 .2 ) 3.29 P r i c e of Land 1 (2 .2 ) 1 ( 2 . 2 ) 3 (6 .7 ) 15 (33 .3 ) 25 ( 55 . 6 ) 3.38 Nearness to Schools 3 (6 .7) 4 (8 .9 ) 9 (20 .0 ) 25 (55 .6 ) 4 ( 8 . 9 ) 2.51 Size of S i t e 9 (20 .5 ) 7 (15 .9 ) 10 (22.7 ) 14 (31 .8 ) 4 ( 9 . 1 ) 1.93 0 .97 0.81 0.89 A v a i l a b i l i t y of Developable Land 1 (2 .2 ) 3 (6 .7 ) 9 (20 .0 ) 18 (40 .0 ) 14 (31 .1 ) 2.91 1.00 1.01 Nearness to Major Roads 7 (15.6 ) 6 (13 .3 ) 12 (26.7 ) 17 (37 .8 ) 3 (6 .7 ) 2.07 1.19 Nearness to Major Shopping 4 ( 8 .9 ) 4 ( 8 . 9 ) 14 (31 .1 ) 21 (46 .7 ) 2 ( 46 . 7 ) 2.29 l . o i Areas 1.30 T A B L E IV Evaluation of Location Factors By Subdividers (Per cent of Respondents i n Parentheses) Location Unimportant F a i r l y Average Very E s s e n t i a l Mean Standard Factors Important Importance Important Deviation (0) (1) (2) (3) (4) Proper Zoning 1(3.7) 0(0.0) 2(7.4) 6(22.2) 18(66.7) 3.48 0.94 Access to Trunk Sewer 1(3.7) 0(0.0) 0(0.0) 13(48.1) 13(48.1) 3.37 0.84 P r i c e of Land 2(7.4) 1(3.7) 2(7.4) 12(44.4) 10(37.0) 3.00 1.44 A v a i l a b i l i t y of Developable Land 1(3.7) 2(7.4) 5(18.5) 6(22.2) 13(48.2) 3.04 1.16 Nearness to Schools K 3.7) 4(14.8) 8(29.6) 11(40.7) 3(11.1) 2.41 1.01 Nearness to Major Roads 3(11.1) 4(14.8) 8(29.6) 9(33.3) 3(11.1) 2.19 1.18 Nearness to Major Shopping Areas 2(7.4) 5(18.5) 7(25.9) 11(40.7) 2(7.4) 2.22 1.09 Size of S i t e 7(25.9) 3(11.1) 8(29.6) 6(22.2) 3(11.1) 1.81 1.36 CM quite possibly r e f l e c t s the differentvtmarket that they cater to (that i s , t h e i r market i s less l i k e l y to be i n the c h i l d rearing stage of the l i f e cycle than the market for sing l e family dwellings). The higher weight given to nearness to major roads by developers of multiple family dwellings (2.36 vs. 2.07 and 2.19) r e f l e c t s a concern for a c c e s s i b i l i t y tempered by the t y p i c -a l l y high t r a f f i c flows of high density areas. The lower weight given to nearness to major shopping areas by developers of multiple family dwellings (2.05 vs. 2.29 and 2.22) may relate to the fact that apartments necessarily locate i n higher density areas which are by necessity near major shopping areas. Therefore, the distance to shopping centres from within the higher density areas i s , comparatively speaking, of less concern than the distance to shopping centres from suburban areas. The higher weight given to s i z e of s i t e by developers of multiple family dwellings (2.34 vs. 1.93 and 1.81) r e f l e c t s the higher interdependency of s i t e s i z e , project s i z e , and a v a i l a b i l i t y of developable land i n the higher density areas. 67 Trends I d e n t i f i e d Throughout the interviews, developers who, being of larger scale had t h e i r option of which housing type to develop, indicated t h e i r intention to construct more garden apartments and condominiums, and to reduce t h e i r construc-t i o n of single family dwellings. This i s also the conclusion obtained from the results of questions III 1 and 3. Housing Type Developed i n To Be Developed ' Past In Future Single Family Dwellings 80% 68% Garden Apartments 38% 66% and/or condominiums Row Housing 28% 34% Low Rise Multiple 45% 32% High Rise Multiple 30% 29% This necessarily understates the case because of the large number of small scale developers of single family dwellings who, because of t h e i r l i m i t e d f i n a n c i a l resources, are necessarily confined to continue building single family dwellings. Also d i s c e r n i b l e i s a trend away from construction of low r i s e multiple dwellings. This would add substance to the general consensus i n the interviews that the market for low r i s e multiple dwellings had declined s u b s t a n t i a l l y as a r e s u l t of the changes to the Income Tax Act i n 1972. P o l i t i c a l Climate Overwhelming concern during the interviews was placed on the p o l i t i c a l climate -the new NDP government making rash moves concern-ing subdivision and possibly zoning, increasing power of tenants groups, the p o s s i b i l i t y of national wage and pr i c e (rent) controls. Numerous times reference was made to "red tape" and " p o l i t i c a l manoeuvring" on the part of municipal bodies and of pressure groups. Forty-nine per cent of a l l developers interviewed had discontin-ued at l e a s t one project because of d i f f i c u l t i e s i n obtaining zoning (question IV 5). In West Vancouver, the Municipal Council has set an upper l i m i t on elevation of development at 8,000 feet. North Vancouver D i s t r i c t has a p o l i c y of rationing a li m i t e d number of new lo t s of i t s extensive holdings for development each year. In Port Moody, 69 development plans for a large undeveloped property are presently being made with a r e s t r i c t e d small group of private developers. Provisions of Section 702A under the Municipal Act enable the Municipality of Surrey to make additional charges f o r such things as access roads, paving of nearby roads, enlargement of sewer trunks - costs previously borne by the municipality. This i s the environment within which developers must work. I t has a profound e f f e e t on t h e i r a c t i v i t i e s and therefore on the growth of our c i t i e s . 70 Hypotheses and Measurement of Variables The Study Area The area selected f o r study of Vancouver's growth patterns was that defined by the 1961 Census Tracts of the Metropolitan Area. The area i s bounded i n the north by the mountains ( D i s t r i c t s of West and North Vancouver), intthe east by P i t t River ( D i s t r i c t of Coquitlam) and 200th Street (the eastern boundary of Surrey), i n the south by the U.S. border and i n the west by the S t r a i t of Georgia. The area i s divided into 119 Census Tracts (see map, Appendix B) of varying s i z e each with a population of roughly 6,000 to 10,000. Althoughtthe Census Tracts of 1966 and 1971 changed boundaries i n some cases to accommodate increasing populations, t h i s was accounted for i n the c a l c u l a t i o n s . To recapitulate, location factors which were weighted of average importance or greater by a l l respondents to the questionnaire are: 1. Proper Zoning 2. Access to Trunk Sewer 3. Price of Land 4. A v a i l a b i l i t y of developable land 5 f Nearness to schools 6. Nearness to major roads 7. Nearness to major shopping areas 8. Size of s i t e Hypothesis 1: The number of completions of single family detached housing units i s related to the amount of land zoned for single family detached housing which i s underdeveloped. U L Z s f d = A s f d where U L Z s f ^ = underdeveloped land zoned for single family detached housing (acres) A g £ ^ = Acreage zoned for single family detached housing U = Number of e x i s t i n g units of sfd s ingle family detached housing D ,., = Density of use (units of sfd s ingle family detached housing per acre) U L Z ( a p t + s f a ) = Underdeveloped land zoned for apartment and singl e family attached housing (acres) . See Hypothesis 2. 72 To properly account for land occupied by single family detached housing but which i s zoned f o r higher density use, accommodation i s made through subtraction of U L Z , _ w the amount of (apt+sfa) underdeveloped land zoned for apartment and single family attached housing. This quantity i s defined i n Hypothesis 2. Hypothesis 2: The combined number of completions of apartment and single family attached housing units i s related to the amount of land zoned for apartment and single family attached housing which i s underdeveloped. ULZ, , = A, "(apt+sfa) (apt+sfa) (apt+sfa) D ( a p t + s f a ) where: U L Z ( a p t + s f a ) = Underdeveloped land zoned for apartment or single family attached housing (acres); A(apt+sfa) = A c r e a g e zoned for apartments or single family attached housing; U(apt+sfa) = N u r — ' e r °f existing units of apartment and single family attached housing; 73 D(apt+sfa) = D e n s i t y o f u s e (units of apartment and sing l e family detached housing per acre) . The grouping of acreages zoned for apartments and single family attached housing into one factor was made for two reasons: a) Zoning codes f o r the d i f f e r e n t municipalities f a i l e d to d i f f e r e n t i a t e c l e a r l y between the two types 6f housing. In many cases, the r e s t r i c t i o n s varied over time and applications for building permits were evaluated on an i n d i v i -dual basis thereby reducing the pr e d i c t i v e nature of the zoning. b) Census information, upon close examination d i f f e r e n t i a t e d between single family attached and apartment housing i n a much more l i t e r a l manner than that of the zoning codes. I t was r e a l i z e d , f o r example, that many dwelling units c l a s s i f i e d as single family attached by zoning codes were designated as apartments i n the Censuses. I t was for these reasons that reasonable results could be obtained only by the aggregation of these two housing types, much to the disappointment of the researcher. The acreages of each zoning c l a s s i f i cation were obtained from municipal zoning maps for 1970. E a r l i e r zoning maps were not readily available so the assumption was made that zoning changes slowly over time. The zoned acreages for 1970 were used for a l l c a l c u l a t i o n s . The existing units of single family detached and for apartment and single family attached housing for 19 61 and 1966 were available from 19 61 and 1966 Censuses. When regressing completions of 1961-66, and 1966-71, the units e x i s t i n g at the beginning of the periods ( i . e . , 1961 and 1966 respectively) were used. I t was very d i f f i c u l t to obtain accurate information for the density of use (units/acre). Two methods were attempted: 1. The average l o t s i z e from sales i n 1968 of the Multiple L i s t i n g Service was calculated by municipality. The Multiple L i s t i n g Service l i s t s homes f o r sale-which tend to be lower priced than the average. Although th i s biased the sample toward a smaller l o t s i z e , there was an opposite bias because of the larger l o t s which were being sold for subdivision (especially i n the outlying areas). Attempts were made to account for the l a t t e r bias? yet i t i s d i f f i c u l t to ascertain which bias was stronger. 75 To account for roads, the average l o t s i z e was scaled upward by one-third. F i n a l l y , the average l o t si z e per Census Tract was deter-mined i n an ad hoc fashion by r e f e r r a l to the minimum l o t siz e of the various zones and a reasonableness check made through v i s u a l inspection of a very large a e r i a l photograph of the region. For apartment de n s i t i e s , adjustment was made according to the maximum density permitted under the various zoning codes. 2. The second method of obtaining densities of use involved using land use data gathered for a s i m i l a r study. The numbers of units i n 1961 and 1966 were divided by the amount of land used i n each Census Tract (the data was gathered i n some cases over two or three Census Tracts so that an averaging procedure was required). Inspection of the data f o r several Census Tracts yielded unreasonable densities which were adjusted through comparison to areas of s i m i l a r d e n s i t i e s . This l e f t some doubt as to the accuracy of the entire land use data and of the calculated densities of use. Hypothesis 3: The number of completions of sing l e family detached housing units i s related to the amount of unused singl e family detached housing p o t e n t i a l . UP = TP _. - U -. s f d s f d sfd where UP-.^ = Unused si n g l e family detached housing p o t e n t i a l ; TP g f <_ = Total s i n g l e family detached housing p o t e n t i a l ; U c , = Number of e x i s t i n g units of sfd ^ single family detached housing. Total p o t e n t i a l f o r single family detached housing was calculated by taking the minimum l o t s i z e allowed by the various zoning codes, adjusting i t upward by a factor of one-t h i r d to account for uoads and d i v i d i n g i t in t o the zoned acreages of each zone. Hypothesis 4: The combined number of completions of apartment and single family attached housing units i s related to the amount of unused singl e family attached and ('apartment housing p o t e n t i a l . UP (apt+sf a) TP (apt+sfa) - U (apt+sf a) where UP (apt+sfa) = Unused apartment and single family attached housing pote n t i a l ; TP (apt+sfa) = Total apartment and single family attached potential;. U (apt+sfa) = Number of ex i s t i n g units of apartment and single fami attached housing. Total p o t e n t i a l for apartment and sin g l e family attachedhhousing was calculated by taking the maximum f l o o r area r a t i o permitted by the various zoning codes and adjusting i t downward by one-quarter to account f o r roads. Then using an average gross suite s i z e of 800 square feet, the maximum apartment unit pot-e n t i a l was found. Again the number of ex i s t i n g units at the beginning of the period were used (housing units i n 1961 and 1966 were used for regressions against completions of 19 61-66 and 1966-71). 78 Hypothesis 5: The number of completions of single family detached housing units i s related to the t o t a l single family housing unit p o t e n t i a l . Hypothesis 6: The combined number of completions of apartment and single family attached housing units i s related to the t o t a l single family attached and apartment housing unit p o t e n t i a l . Total housing p o t e n t i a l i s calculated i n the manner described under Hypotheses 3 and 4. Hypothesis 7: The number of completions of single family detached housing units i s inversely;-' related to the pr i c e of land. Hypothesis 8: The combined number of completions of apartment and single family attached housing units i s inversely related to the p r i c e (per apartment unit) of land. Price l e v e l s of t y p i c a l lots i n 19 64 and 1969 (used i n regressions against completions i n 1961-66 and 1966-71 respectively) were obtained for each of three or four smaller areas of each 6 8 municipality. These pr i c e l e v e l s were applied to the relevant Census Tracts. For apartments, i n order to accommodate for Va r i a t i o n of in t e n s i t y of use, the pr i c e per unit was used. 79 Hypothesis 9: The number of completions of sing l e family detached housing units i s related to the t r a v e l time (by motor vehicle) from the central business d i s t r i c t . Hypothesis 10: The combined number of completions of apartment and sing l e family housing units i s related to the t r a v e l time (by motor vehicle) from the central business d i s t r i c t . Travel isochrones from the central business d i s t r i c t were available f o r 19 68.^ 9 The t r a v e l times to the Census Tracts for 1963 70 were estimated from t r a v e l isochrones for 1956 and road maps of 1963. Hypotheses 11 to 14 were not tested due to i n s u f f i c i e n t data as explained below. Hypothesis 11: The number of completions of the d i f f e r e n t housing types i s related to access to trunk sewer. In August 1968, regulations were established requiring development i n areas denoted "Urban Growth Areas" to be serviced by sewers. Every Census Tract i s serviced to some degree by sewer trunks. Ideally, the data needed for each Census Tract i s the amount of underdeveloped r e s i d e n t i a l l y zoned land with ready access to sewers. Trunk sewers are d i s t r i b u t e d s p a t i a l l y i n a very i r r e g u l a r fashion, somewhat following the outline of r e s i d e n t i a l l y zoned areas. There was no means available for obtaining data of that portion of areas zoned r e s i d e n t i a l , underdeveloped, yet with access to sewers. Hypothesis 12: The number of completions of the d i f f e r e n t housing types i s related to "nearness" to schools. Every Census Tract has a c c e s s i b i l i t y to schools to some degree. The problem i s complicated by the following factors: 1. In outlying Census Tracts there are a large number of small schools and i n the c i t i e s the fewer number of schools have a larger number of rooms and teachers and therefore a larger student capacity. 2. A c c e s s i b i l i t y to elementary schools i s necessarily within a smaller radius that that of secondary schools 3. Some of the outlying Census Tracts are so large that the d i s t r i b u t i o n of schools within the Census Tract i s important. Hypothesis 13: The number of completions of the d i f f e r e n t housing types i s related to "nearness" to major roads. Some portion of almost a l l Census Tracts are "near" a major road, that i s , within a few minutes drive of a major road. With a f i n e r s p a t i a l disaggregation, i t i s expected that a good proxy for th i s factor (perhaps a c c e s s i b i l i t y ^ within some small number of minutes) could be obtained and included i n the regression. Hypothesis 14: The number of completions of the d i f f e r e n t housing types i s related to "nearness" to major shopping areas. In almost every case, some portion of each Census Tract i s readily accessible to a major shopping area. Again, a f i n e r s p a t i a l disaggregation would l i k e l y allow a good proxy for t h i s factor (perhaps a c c e s s i b i l i t y within some small number of minutes). Although the s i t e size i s ranked of average importance, i t s importance relates more to s u i t a b i l i t y to a p a r t i c u l a r project than to an o v e r a l l desire for large s i t e s or small s i t e s . I t i s , therefore, d i f f i c u l t to incorporate s i t e size as one of the variables i n the regression. 82 Hypothesis 15: The population density of Metropolitan Vancouver i s related to distance from the central business d i s t r i c t i n the form of an exponential, as described by Clark y = Ae Population per Census Tract was available for 1961 and 1966 from Dominion Bureau 71 of S t a t i s t i c s publications. Preliminary results of the 1971 Census, which were available from the l o c a l D.B.S. o f f i c e were used. The t o t a l area of each Census Tract was also available from the l o c a l D.B.S. o f f i c e . The distance "as the crow f l i e s " from the CBD was measured from the Census map i n millimetres. Hypothesis 16: The population density of residen-t i a l l y zoned land i n Metropolitan Vancouver i s related inversely to the t r a v e l time to the central business d i s t r i c t . The t o t a l area of r e s i d e n t i a l l y zoned land i n each Census Tract was obtained i n the manner described i n r e l a t i o n to Hypotheses 1 and 2. 83 Hypothesis 17: The housing unit density of r e s i d e n t i a l l y zoned land in Metropolitan Vancouver i s related inversely to the t r a v e l time from the central business d i s t r i c t . Housing unit densities of r e s i d e n t i a l l y zoned land were determined using housing unit information from the 1961 and 1966 Censuses. The number of housing units i n 1971 was determined by adding completions of the three housing types (sfd, s f a , and apt) for each Census Tract as obtained from CMHC source data (see page 87). Hypothesis 18: Housing unit completions are related to the amount of unused population p o t e n t i a l as determined by the difference between the observed population density and that calculated by Clark's Theory i n Hypothesis 15. Hypothesis 19: Housing unit completions are related to the amount of unused housing p o t e n t i a l as determined by the difference between the observed housing density and that calculated from the inverse r e l a t i o n between housing density and t r a v e l time from the CBD i n Hypothesis 17. S t a t i s t i c a l Comment The sample c o e f f i c i e n t o f d e t e r m i n a t i o n i s d e f i n e d as 2 _ e x p l a i n e d sum o f squares o f d e v i a t i o n s t o t a l sum o f squares o f d e v i a t i o n s _ £ ( x Q - u) 2 where X = c a l c u l a t e d v a l u e o f Y c X = o b s e r v e d v a l u e o f Y o u = mean o f Y and X - u = (X - X ) + (X - U) o o c c t o t a l u n e x p l a i n e d e x p l a i n e d d e v i a t i o n d e v i a t i o n d e v i a t i o n 2 Hence r i s a measure o f e x p l a i n e d v a r i a t i o n w i t h l i m i t s 0.0 and 1.0 f o r c o m p l e t e l y u n e x p l a i n e d v a r i a t i o n and c o m p l e t e l y e x p l a i n e d v a r i a t i o n r e s p e c t i v e l y . R e a r r a n g i n g the above 2 0 y (X-. - x4 r2 = i - --- o c _ > o " u ) 2 When t h e number o f degrees o f freedom n i s s m a l l , t h e r 2 i s p o s i t i v e l y b i a s e d a c c o r d i n g t o 7 3 Thus the r s t a t i s t i c (which i s t h a t r e p o r t e d i n a l l work i n t h i s study) i s the c o e f f i c i e n t of d e t e r m i n a t i o n a d j u s t e d f o r the number of degrees of freedom. The t s t a t i s t i c of a normal 74 d i s t r i b u t i o n i s approximated by the formula - x ~ u Where x = sample mean u = a c t u a l mean standard d e v i a t i o n n = number of o b s e r v a t i o n s i n the sample Thus the t s t a t i s t i c i s a measure of the accuracy of the sample mean. The p r o b a b i l i t y of a sample mean o c c u r r i n g by chance i s gi v e n by comparison to values i n a t a b l e of t s t a t i s t i c s For 118 degrees of freedom: P ( t > 3.38) = 0.0005 P ( t > 2.62) = 0.005 P ( t > 2.36) = 0.01 P ( t > 1.99) = 0.025 P ( t > 1.66) = 0.05 P ( t y 1.29) = 0.10 P ( t > 0.68) = 0.25 86 For 4 3 degrees of freedom (applicable for comple-tions of single family detached housing), P(t> 2.70) = 0.005 By way of reference to the 2 F s t a t i s t i c , t : has a F d i s t r i b u t i o n with 1 and n-1 degrees of freedom i n results of 76 standard multiple l i n e a r regression. That i s , The t t e s t considers the case of x<u and x ^u hence i s a 2 - t a i l t e s t . In the F t e s t , the comparison i s of (x - u? and having only p o s i t i v e value, i s a 1 - t a i l t e s t . Therefore the r e l a t i o n above i s true for a l e v e l of s i g n i f i c a n c e (probability) of 0C/2 for the t s t a t i s t i c and «* for the F s t a t i s t i c . In the tables, the Regression Co-e f f i c i e n t s (c for example) , the Standard Error and the Student t S t a t i s t i c t are l i s t e d where c applicable. By d e f i n i t i o n t = C 87 Regression Results Data for the number of housing unit completions for 1961-66 and 1966-71 was determined as follows: The number of rental housing unit completions per Census Tract was available for the periods 1961-66 and 1966-71 from source data of annual CMHC rent a l vacancy studies. From other CMHC source data, the t o t a l number of apartment completions per municipality was ava i l a b l e . The data, which was available from the l o c a l CMHC o f f i c e was the raw data of annual CMHC housing studies. The rental unit completions were simply scaled upward to correspond to the t o t a l completions per municipality. The difference between the single family detached housing units of the 19 61 and 1966 Censuses were scaled to correspond to the comple-tions per municipality as available from CMHC source data. D i s t r i b u t i o n of the CMHC completion (single family detached) data for 1966-71 was accomplished through v i s u a l inspection of the changes between the G.V.R.D. Ex i s t i n g Development Maps of 1968 and 1970. This was, admittedly, a rough treatment of the data, but considerable care was taken y i e l d i n g s u r p r i s i n g l y good r e s u l t s . These approaches were not f e l t to be applicable 88 i n the cases of Vancouver and Burnaby so that the regressions of completions of sing l e family detached (for both 1961-66 and 1966-71) cover only the.remaining forty-four Census Tracts. T A B L E V Regression Results "Measures of Attractiveness" _2 Completions r Student t S t a t i s t i c s 1/Price Time Underdeveloped Land sfd 61-66 0.09 -0.56 -0.40 2.73 sfd 61-66* 0.14 -0.53 -0.55 3.16 sfd 66-71 0.36 -0.86 0.83 4.76 sfd 66-71 * 0.05 -0.48 1.19 1.51 apt 61-66 0.10 -0.71 3.66 0.62 apt+sfa 61-66 0.16 -0.58 3.36 2.95 apt 66-71 0.15 2.32 2.04 0.44 apt+sfa 66-71 0.05 0.88 1.65 0.15 * In these regressions, allowance was not made for acreage zoned f o r apartments but not yet occupied by apartments (assumed e n t i r e l y occupied by single family detached housing). This was to t e s t the p o s s i b i l i t y that errors r e s u l t i n g from approxi-mations i n c a l c u l a t i n g t h i s amount were prevent-ing obtaining meaningful s t a t i s t i c s . T A B L E VI Completions sfd 1961-66 sfd 1966-71 apt+sfa 1961-66 apt+sfa 1966-71 apt 1966-71 Completions sfa 1961-66 sfd 1966-71 apt+sfa 1961-66 apt+sfa 1966-71 apt 1966-71 Regression Results of "Unused and Total Potential" Completions = a + b x Unused Potential a <Ta t- b <7b 19824.1 5744.3 93.9 16602.9 16738.7 2.89 83.6 4082.8 3807.8 15994.7 3822.9 3.45 * 1.12 1.07 1.62 0.0675 0.50 11.79 4.18 * 14.17 1.29 1.54 1.48 3749.0 4.43 * 13.89 Completions = c + d x Total Potential t„ 5947.4 2.81 * 91.8 0.03 2048.0 3673.0 0.56 11449.0 3546.0 3.23 12164.5 3394.0 3.58 d 1.70 0.063 10.65 11.61 12.61 0.47 3.26 * 0.0074 9.12 * 9.11 * 9.19 * 9.39 * td 3.63 * 0.0072 8.73 * 1.05 10.17 * 1.01 11.49 * 1.04 12.11 * -2 r .18 .66 .41 .41 .42 - 2 r .22 .64 .46 .53 .55 Degrees Freedom 43 43 118 118 118 Degrees Freedom 43 43 118 118 118 P(t>2.62) = 0.005, P(t> 2.70) = 0.005 118 43 90 The regression results of Table V do not support Hypotheses 1 and 2 (completions vs. underdeveloped land). The results shown are those using the second method of c a l c u l a t i n g density of use. Those results using the f i r s t method, which were very s i m i l a r , are not shown. However, i n both cases, considerable doubt exists concern-ing the accuracy of the data and therefore the conclusion i s not conclusive. Hypotheses 3 and 4 (completions vs. unused housing potential) as well as Hypotheses 5 and 6 (completions vs. t o t a l housing potential) are supported by the regression results shown i n Table VI. A l l Student t s t a t i s t i c s are well within -2 the 0.005 sig n i f i c a n c e l e v e l . The lower r for completions of single family detached 19 61-66 may be explained by the fac t that housing p o t e n t i a l for 1966 was calculated from zoning data of 1970. Further t h i s regression was over the outlying Census Tracts (those other than Vancouver and Burnaby) where the zoning has changed most. Therefore UP and TP ._, were too high which sfd s f d 3 produced lower r ^ than would otherwise have been expected. Table VT shows the results of the same regressions for completions of apartments and single family attached housing combined and for completions of apartments only. The only s l i g h t l y better results obtained with completions of apart-91 ments only indicated that the results were not s i g n i f i c a n t l y altered by the aggregation of data for apartment and single family attached housing. Hypotheses 7 and 8 are not supported by the results shown on Table V. That i s , developers claim that price i s important yet i t does not appear to be a s i g n i f i c a n t determinant i n explaining the location of housing unit completions. Hypotheses 9 and 10 (completions vs. t r a v e l time from CBD) are not supported by the re s u l t s shown on Table V. Hypothesis 15 (Pop/Total Area = A e-bd) i s supported by the regression r e s u l t s shown i n Table VII. Taking natural logarithms the equation becomes Log (Pop/Total Area) =• -bd + Constant, where d = distance from the central business d i s t r i c t . T A B L E VII Regression Results of Log (Pop/Total Area) = -bd + C Year C c r c b °b J2. r 1961 4. 89 0.14 33.88 -0.015 0.0014 -10. 47* .48 1966 4.94 0.14 34.49 -0.014 0.0014 -10. 08* .46 1971 4.93 0.14 34. 87 -0.013 0.0014 - 9. 15* .41 * P(t>2 .62^ I B ° - ° 0 5 92 Although the results explain only approximately one-half of the v a r i a t i o n , application of Clark's Theory i s complicated by the existence of the Burrard I n l e t and the mountains on the North Shore. An adaptation of Clark's Theory i s that of Pop/Area Zoned Residential = Ae where t = t r a v e l time from the CBD. The regression r e s u l t s are approximately the same as those of Table VII. However, i n working with the graph of log (Pop/Area Zoned Residential) vs. time, i t was noticed that a better f i t would be i obtained using log(time) rather than time. The subsequent regression led to m u l t i p l i e r s of approximately -1.0 and therefore to the much better predictor results of Pop/Area Zoned Residential = C^/time T A B L E VIII Regression Results of P Pop/Area Zoned Residential = 1 time Year C t c _ 2 r 1961* 213. 63 16.69 12. 80 .59 1966* 252. 15 18. 72 13. 47 .61 1971* 383. 19 24.63 15.56 .68 93 * Omission of Census Tracts 5, 6, 14 and 178 because the area zoned r e s i d e n t i a l was very small or zero. Hypothesis 17 (housing density vs. the re c i p r o c a l of t r a v e l time from the central business d i s t r i c t ) is.supported i n much the same manner as Hypothesis 16 by the results shown i n Table IX. T A B L E IX Regression Results of Housing C Units/Area Zoned Residential = 2 time Year C cr t _2 c c r 1961* 91.98 4.54 20.23 .65 1966* 135.74 7. 81 17.38 .62 1971* 263.08 14.40 18.27 . 74 * Omission of Census Tracts 5, 6, 14, because the area zoned r e s i d e n t i a l was very small or zero. Hypothesis 18 (completions vs. unused population density as determined by ( Clark's Theory) and Hypothesis 19 (completions vs. unused housing pot e n t i a l as determined by the inverse t r a v e l time relation) were tested i n three manners: 94 (a) Housing unit completions were regressed against both p o s i t i v e negative differences between calculated and observed densities; (b) Housing unit completions were regressed against only p o s i t i v e differences between calculated and observed densities; (c) Housing unit completions were regressed against a dummy variable representing simply the existence of unused p o t e n t i a l (1 for p o s i t i v e differences and 0 for zero or negative differences between calculated and observed densities) The regression r e s u l t s obtained i n manner (a) above were not s i g n i f i c a n t . The -2 highest r obtained in support of Hypothesis 18 (Completions vs. Clark's Theory) was 0.078. The -2 highest r obtained i n support of Hypothesis 19 (Completions vs. unused housing potential, as determined by the inverse t r a v e l time relation) was 0.0 76. In no instance did the t s t a t i s t i c reach a l e v e l of significance of 0.05. The regression results obtained i n manner (b) were even less s i g n i f i c a n t than those obtained i n manner (a). 95 In the regressions against the _2 dummy variable i n manner (c), the r obtained were very low. However, the t s t a t i s t i c s were high, i n a l l cases i n d i c a t i n g a sig n i f i c a n c e l e v e l greater than 0.0005 (Tables X & XI). This indicates that the existence of unused po t e n t i a l i s i n i t s e l f s i g n i f i c a n t i n the determination of housing unit completions. The res u l t s of invest-igations i n manners (a) and (b) indicate that the magnitude of the difference between observed and calculated densities i s not s i g n i f i c a n t i n the determination of the number of housing uni t completions. In other words, the existence of housing unit p o t e n t i a l as determined by the' difference between observed and calculated densities (by both Clark's Theory and the Inverse Travel Time Relation) i s a determinant only of whether or not housing unit completions take place and not of the actual number of housing uni t completions. Admittedly, the s i z e of the subareas used i n these regressions has some bearing on th i s statement. The negative 2 values for r the tables are explained simply by 2 the fact that the r were too low to be s i g n i f i c a n t 2 i n the manner of the r matrix calculations of the regression package (MASS:AGER). 96 TABLE X Regression Results of Completions vs. Dummy Variable Representing Existence of Unused Potential as Determined by Clark's Theory Completions Dummy —2 (Year) (Year) C Wc t r c 1961-66 1961 40239 8130 4.95* -0.29 1966-71 1966 23708 6929 3.42* -0.35 1961-71 1961 69808 14615 4.77* -0.38 * P(t>3.38) 1 1 8 = 0.0005 TABLE XI Regression Results of Completions vs. Dummy Variable Representing Existence of Unused Potential as Determined by the Inverse Travel Time Relation Completions Dummy (Year) (Year) C C7c t c —2 r 1961-66 1961 38399 6750 5.69* -0.22 1966-71 1966 24837 6175 4.02* -0.28 1961-71 1961 64225 12265 5.23* -0.34 * P ( t > 3 . 3 8 ) 1 1 8 = 0.0005 97 Conclusion Tota l housing p o t e n t i a l and unused housing p o t e n t i a l (as defined by capacity and unused capacity of zoning) both expla in between for ty and s i x t y - f i v e per cent of the v a r i a t i o n i n the s p a t i a l d i s t r i b u t i o n of housing completions. Land p r i c e and t r a v e l time from the c e n t r a l business d i s t r i c t were not s i g n i f i c a n t explanatory v a r i a b l e s . The importance of the s i g n i f i c a n t r e su l t s concerning the number of housing u n i t completions as a function of p o t e n t i a l (determined by the amount of r e s i d e n t i a l l y zoned land) l i e s i n the rea f f i rmat ion of planners ' power of d i r e c t i n g development and redevelopment through zoning. That p r i ce o f land and t r a v e l time from the cent ra l business d i s t r i c t d id not appear to be s i g n i f i c a n t determinants of the l o c a t i o n of new housing allows the planner to discount the importance of these factors i n h i s formulation of the c i t y p l an . Through judic ious use of h i s knowledge of the t o t a l housing p o t e n t i a l , the unused p o t e n t i a l , and h i s own estimate of the p o s s i b i l i t y of development (based i n part on the condition of the e x i s t i n g use), the planner has at his disposal the most s i g n i f i c a n t factor a f f e c t i n g the s p a t i a l d i s t r i b u t i o n of future r e s i d e n t i a l development. Clark's Theory of Exponentially Declining Densities explains only between forty and f i f t y per cent of the v a r i a t i o n i n population density. A much better r e l a t i o n which explains between s i x t y and seventy per cent of population i n r e s i d e n t i a l l y zoned areas i s Pop/Area Zoned Residential = t where t i s the t r a v e l time from the central business d i s t r i c t . In a s i m i l a r r e l a t i o n , s i x t y -f i v e to seventy-five per cent of the housing unit density i n r e s i d e n t i a l l y zoned areas i s explained: C2 Housing/Area Zoned Residential = t However the theory behind such a r e l a t i o n , the foundation for any p r e d i c t i v e value, has yet to be explained. Attempts were made to correlate the number of housing unit completions i n a subarea with the difference between the observed density and that calculated by Clark's Theory and by the Inverse Travel Time Relation. In subareas i n which differences e x i s t , housing development was expected which would bring the actual density more i n l i n e with the density calculated from these theories. However the existence of housing unit p o t e n t i a l thus c a l -culated i s a s i g n i f i c a n t determinant only of whether or not housing unit completions take place. Congruently, the magnitude of the housing unit p o t e n t i a l i s not a s i g n i f i c a n t determinant of the actual number of housing unit completions. 100 Extentions This study i s a f i r s t step toward a more complete understanding of c i t y growth patterns. The res u l t s which demonstrate the s i g n i f i c a n c e of housing potential i n determining the location of new r e s i d e n t i a l development confirms our expectations. However, that price of land and t r a v e l time from the central business d i s t r i c t do not appear to be s i g n i f i c a n t provides knowledge i n areas which previously were subjects of speculation and conjecture. A more complete analysis of po t e n t i a l factors a f f e c t i n g the location of new r e s i d e n t i a l development could possibly provide a very powerful tool for the prediction of c i t y growth. The importance of such a t o o l accelerates with the passage of time as c i t i e s face the perplexing problems of urban "sprawl" and decaying inner areas, of urban renewal, of al t e r n a t i v e modes of transportation attacking the preeminence of the automobile, and of the immense complexities of s o c i a l problems i n the c i t y . 101 The next step following the d i r e c t i o n of this study toward a better understanding of c i t y growth (and therefore of the associated problems) i s the testing of hypotheses r e l a t i n g to housing completions by type as a function of such factors as: access to sewage trunks; nearness to schools; nearness to major shopping areas; nearness to major roads; nearness to bus routes; nearness to i n d u s t r i a l areas; socioeconomic rank. The i n c l u s i o n of such variables would necessitate a f i n e s p a t i a l disaggregation with c e l l size of the order of one-quarter mile square. Accummulation of such data by c e l l could provide an excellent data base for more extensive and exhaustive work. One of the overwhelming concerns of the writer was the lack of consistency of zoning codes between mu n i c i p a l i t i e s . For meaningful study of c i t y growth patterns and f o r a sensible long term approach to the problems of urbanization, leadership must be provided and e f f o r t s made toward a consolidated planning scheme. Steps i n t h i s d i r e c t i o n are currently being made by Municipal A f f a i r s Minister James Lorimer i n the c i t i e s of Kelowna and Kamloops where the c i t y boundaries are being extended to include several surrounding rapidly growing unincorporated areas. 103 Footnotes 1. Kaiser and Weiss (1970) p. 31 2. i b i d . 3. i b i d . 4. i b i d . , p. 32 5. Weiss, Smith, Kaiser and Kenney (1966) 6. Kaiser and Weiss (1967) 7. Kaiser and Weiss (1970) 8. Kaiser and Weiss (1967) p. 242 9. Massie (1969) 10. i b i d . , p. 33 11. i b i d . , p. 44 12. i b i d . , p. 55 13. Eldridge (1967) p. 54 14. Kaiser (1966) p. 166 15. Kaiser and Weiss (1970) p. 34 16. Kaiser and Weiss (1967) p. 245 17. Smith, W.F. (1966) 18. Smith, L.B. (1971) 19. Mc A l l i s t e r (1967) 20. Reid (1958) 21. Muth (1960) 22. Lee (1964) 23. Oksanen (1966) 24. Uhler (1968) 25. Smith, L.B. (1971) 26. i b i d . , p. 34 27. Reid, M. (1958) 28. Muth (1968) 29. Lee (1964) 30. Chung (1967) p. 79 104 31. Winger (1969) 32. Bourne (1968) 33. Smith, W.F. (1964) 34. Grebler and Maisel (1963) 35. i b i d . , p. 497 36. Maisel (1963) 37. Muth (1960) 38. Smith, W.F. (1966) 39. Klaassen (1966) 40. Wullkopf. (1969) 41. Smith, L.B. (1971) 42. Burgess (1925) p. 50' 43. Colby (1959) 44. Hoyt (1939) 45. Harris and Ullman (1959) 46. Clark (1951) 47. Kain (1962) 48. Alonso (1965) 49. Wingo (1961) 50. Stegman (1969) 51. Chapin (1965b) 52. Hamburg and Creighton (1959) 53. Donnelly et. a l . (1964), Chapin and Weiss (1962), and Chapin (1965a) 54. Donnelly et. a l . (1964) 55. Harris, C o l i n C. (1966) 56. H i l l (1965) 57. Lowry (1964) 58. Steger (1965) 105 59. B.A.S.S. (1968) 60. Goldner (1971) 61. Herbert and Stevens (1960) 62. Harris, B r i t t o n (1963) 63. Robinson et. a l . (1965) 64. Sears (1971) 65. Stegman (1969) 66. Mittelbach et. a l . (1970) 67. CM.H.G. (1971) (only dwelling units financed by NHA loans to builders (and not to owners) are included) 68. Real Estate Board of Greater Vancouver (1964, 66, 68, and 70) 69. G.V.R.D./ Planning Dept. (1968) 70. Technical Commission for Metropolitan Highway Planning (B.C.) (1959) figure 4.1 71. Dominion Bureau of S t a t i s t i c s (1968) 72. Yamane (1964) p. 393 73. 74. 75. 76. 77. i b i d . , P- 402 i b i d . , P- 509 i b i d . , P- 878 i b i d . , P- 656 i b i d . 106 Bibliography A l b e r t s , W. (1962) Alonso, William (1965) B.A.S.S. (1968) Baxter, D., M.A. Goldberg, D. Lach, and G. 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(1959) "The Interest S e n s i t i v i t y of Canadian Mortgage Flows" Canadian Journal of Economics 3:407-421 The Low Rise Speculative Apartment Berkeley, C a l i f o r n i a : CREUE, University of C a l i f o r n i a Aspects of Housing Demand:  Absorption, Demolition and  D i f f e r e n t i a t i o n Berkeley, C a l i f o r n i a : The Centre f o r Real Estate and Urban Economics, I n s t i t u t e of Urban and Regional Development, University of C a l i f o r n i a (Research Report No.29) Housing: The S o c i a l and Economic Elements Berkeley, C a l i f o r n i a : University of C a l i f o r n i a "The Pittsburgh Urban Renewal Simulation Model" Journal of the American I n s t i t u t e  of Planners 31:144-150 " A c c e s s i b i l i t y Models and Residential Location" Journal of the American I n s t i t u t e  of Planners 35:22-29 A Study i n Highway Planning f o r  the Metropolitan Area of the  Lower Mainland of B.C. (Part 4) Vancouver "The Demand f o r Housing - and Inverse P r o b a b i l i t y Approach" Review of Economics and S t a t i s t i c s 50:129-133 Conversion D i s t r i c t s Vancouver Urban Renewal Study: Technical Report No. 5 "Land Use and T r a f f i c Models: A Progress Report" Journal of the American I n s t i t u t e of Planners Volume 25 114 Weiss, S.F., J.E. Smith, E.J. Kaiser and K.B. Kenney (1966) Wingo, L. J r . (1961) Winger, A.R. (1960) Winger, A.R. (1969) Weimer, A.M. and H. Hoyt (1966) Wullkopf, U. (1969) Yamane, T. (1964) Residential Developer Decisions:  A Focused View of the Urban  Growth Process Chapel H i l l , N.C.: Centre f o r Urban and Regional Studies, I n s t i t u t e f o r Research i n S o c i a l Science, U n i v e r s i t y of North Carolina Transportation and Urban Land Washington, D.C.: Resources f o r the Future, Inc. An Approach to the Problem of Measuring Upgrading Demand i n the Housing Market Ann Arbor, Michigan: Thesis Presented at the University of Michigan "Supply Oriented Urban Economic Models" Journal of the American I n s t i t u t e  of Planners 35:30-33 Real Estate New York: Ronald Press "Leo Klaassen's Model for the Structure of the Housing Market Reconsidered" Annals of Regional Science 3:107-114 S t a t i s t i c s ; An Introductory  Analysis New York: Harper & Row APPENDIX A 115 Housing Developer Questionnaire We are currently engaged in a large scale study of housing in the Graater Vancouver Region. We are seeking information from developers in ordar to establish housing development patterns. Your help >is greatly appreciated and your answers will be kept strictly confidential. A. Site Selection (1) Yes (2) No B. Site Planning (1) Yes (2) No C. Construction (1) Yes (2) No D. Selling and Leasing (1) Yes (2) No E. Property Management (1) Yes (2) No 1-4 How long has your company been involved in raal aatata ______ development? (number of years) 5-6 Is i t a subsidiary of a larger company? (1) Yes 7 (2) No. If so, what industry is the parent company asiociattd with? (1) Lumber and Wood Products > 8 (2) Construction (3) Real Estate (4) Transportation (5) Agriculture and Fisheries (6) Other (please specify) How many inside employees do you have? '• • (management, office staff, secretarial help etc.) 9-11 How many outside employees do you have? (salesmen, construction workers, etc.) 12-14 6. Which facets of development do you engage in? 15 16 17 18 19 7. Do you do subdivisions alone without constructing housing yourself? (1) Yes 20 (2) No 116 8. Do you buy lots from subdividers? (1) Yes (2) No 9. Do you construct housing yourself? (1) Yes (2) No 10. If so, do you also do contract building? (1) Yes (2) No 14. How many were made available in 1971? 15. How many in 1970? 16. In which municipality did you locate the majority of these multiple family units in 1972 in 1971 in 1970 (write in name to be coded later) 18. How many were made available in 1971? 19. How many in 1970? 21 22 23 11. How much in advance f construction do you usually acquire land? (number of years) 24-25 12. How many years inventory of land do you ordinarily hold at one time? 26-27 13. How many multiple family housing units will your company _____ make available by the end of 1972? 28-30 31-33 34-36 37 "38" "39~ 17. How many single family units will your company make available in 1972? 40-42 43-45 46-48 117 20. In which municipality did you locate the majority o f theaa single family units in 1972 in 1971 in 1970 (write in name to be coded later) 21. (This question is applicable t o those who are in aub-division only). How many lots will you make available by the end ofV-1972? 52-54 How many were made available in 1971? 55-57 How many in 1970? 58-60 In which municipality were most of these lots located in 1972 61 in 1971 62 in 1970 63 (write in name to be coded later) II. The next set of questions deal with the development process and the location decision. 1. (Interviewer: hand respondent card B and record response) This is a l i s t of various stages in the development process. Would you please place the stages in the order you think appropriate. A9 50 51 A. Arranging Financing 64 B. Choosing type of development 65 C. Choosing size of development 66 D. Choosing a site 67 E. Choosing a contractor 68 F. Choosing a neighborhood 69 G. Getting zoning changed (if needed) 70 H. Getting building permit 71 I. Other (please specify) 72 118 2. I will read you a l i s t of factors which related to your decision of whether or not to build. Would you please t e l l «e for each factor whether i t is (0) Unimportant (1) Fairly important (2) of average Importance (3) Very Important or (4) Essential (Interviewer: please indicate response) 1-4 A. Availability of financing _ 5 B. Interest rate 6 C. Population trends 7 D. Income trends in the region 8 E. Rent levels 9 F. Vacancy rates 10 G. Availability of developable land 11 H. Level of Construction in the region 12 I. Construction Costs 13 3. I will now read you a l i s t of factors generally considered important in the location or site selection decision. Would you indicate relative importance of each in the same manner as before A. Availability of developable land ; _14 B. Room for expansion 15 C. Price of land ' , 16 D. Size of site 17 E. Nearness to major roads 18 F. Nearness to bus routes 19 G. Nearness to major shopping areas 20 H. Nearness to schools 21 I. Nearness to employment 22 J. Slope of site 23 K. Holding qualities of the soil 24 L. Access to trunk sewer 25 M. Proper zoning 26 4. Do you usually plan a project and then search for a site with qualities suitable for that project (1) OR do you 27 usually just look for a "good buy" and plan a project for that site (2)? (Interviewer: indicate response as either 1 or 2). Do you usually choose sites with a particular economic or social group in mind? Does the site usually dictate the price range of the housing? Do you usually locate near (1) or avoid locating near (2) other new housing developments? Do you usually lead or follow other developments in making housing available in new areas? (1) lead (2) follow The section deals with the type of housing constructed. Which housing types has your company developed? A. Single family houses B. Garden Apartments and/or Condominiums C. Row housing D. Low-rise multiple x E. High-rise multiple (Interviewer: indicate (1) yes, (2) no) Which of these types do you prefer? (1) Single family houses (2) Garden apartments and/or•condominiums (3) Row housing (4) Low-rise multiple (5) High-rise multiple Which types are you likely to build in the future (1) Single family houses (2) Garden apartment and/or condominiums (3) Row housing (4) Low-rise multiple (5) High-rise multiple (Interviewer: indicate (1) yes, (2) no) Have you found any municipal or legal constraints against the type of housing you have built in the past? (1) yes (2) no If yes, please specify (a) type of constraint (1) building code restrictions (2) difficulty in obtaining building permit (3) zoning restrictions (4) other (please specify) (b) type of housing (1) Single family houses (2) Garden Apartment and/or Condominiums (3) Row housing (4) Low-rise multiple (5) High-rise multiple (c) municipality (to be coded later) If yes, has this been a deterent to building more of these units in the future? (1) Yes (2) No (Interviewer: hand respondent Card A) Would you please t e l l me the income group that you aimed your multiple family housing to, by giving me the appropriate letter code? and for single family housing? Which of the following factors determine the number of bedrooms in the housing units you build? (1) Prevailing style in surrounding areas (2) Family structure in surrounding areas (3) Age structure of population (4) Construction costs (5) Other (please specify) (Interviewer: indicate (1) yes, (2) no) 121 10. Which of the following factors determine the spaciousness of your housing units? (1) Prevailing style in surrounding areas 55 (2) Income information on regional population 56 (3) Age structure of regional population 57 (4) Construction costs 58 (5) Land costs 59 (6) Other please specify 60 11. Which of the following factors determine the inclusion of such amenities as underground wiring, cul de sacs, paved lanes, play areas, or formal gardens. (1) Prevailing style in surrounding areas 61 (2) Zoning regulations 62 (3) Other building or municipal codes 63 (4) other (please specify) 64 12. Which of the following factors determine the inclusion of such amenities as finished basements, extra family rooms, laundry rooms, or drapes and carpets? (1) Prevailing style in surrounding areas 65 (2) Income information on regional population 66 (3) Age structure of regional population 67 (4) Family structure of regional population 68 (5) Construction Costs 69 (6) Upon request only 70 (7) Other (please specify) 71 13. Do you plan for families with children, families without children and for single individuals in developments of (1) Single family houses 72 (2) Garden Apartments and/or Condominiums 73 (3) Row housing 74 (4) Low-rise multiple 75 (5) High-rise multiple 76 (Interviewer: indicate (0) don't do this type of housing (1) Yes (2) No 122 IV This section deals with aspects of renewal and redevelopment. 1-4 1. Have you found i t necessary in most cases to acquire more than one parcel of land for developments of (1) Single family housing 5 (2) Multiple family housing (Interviewer: indicate (1) yes (2) no). 2. Of the parcels that you acquire for single family housing, what percentage are (1) vacant 6-8 (2) occupied by single family housing 9-11 3. Of the parcels that you acquire for multiple family housing, what percentage are (1) vacant 12-14 (2) single family housing 15-17 4. What percentage of the single family, housing is in (1) poor condition 18-20 (2) average condition 21-23 (3) good condition 24-26 5. Has any project of yours been discontinued because of difficulties (1) in assembling land? 27 (2) in obtaining the proper zoning? 28 (Interviewer: indicate (1) yes, (2) no). V. This next section deals with the effectiveness of government controls. 1. I will read you a l i s t of government and public organizations involved in planning and controlling land use. Would you t e l l me please how often you are involved with them by responding (0) never (1) sometimes (2) often (3) Always A. Planning Department B. Permit and License Department C. City council D. Assessor E. School Board F. Parks Board G. Ratepayer's Associations H. Engineering Department I. Regional Planning Board J. Other (please specify) Is citizen acceptance of your proposal an important element in your decision to proceed? (1) yes (2) no Do residents of the immediate surrounding area significantly affect the character and type of development you w i l l build? (1) yes (2) no Do you follow a specific l i s t of steps in gaining governmental approval of your development? (1) yes (2) no If you do follow such a procedure, could you please specify the steps in the order in which you follow them. STEP This fi n a l area of concern deals with financing. Do you usually use options for land purchases? (1) yes (2) no How long is the option period typically? (1) lender 30 days (2) 31-60 days (3) 60-90 days (4) 91-120 days (5) 121-180 days (6) 181-270 days (7) 271-365 days (8) greater than 1 year Do you often pay for options in advance? (1) yes (2) no Do you usually include the option as an element in the purchase price should you exercise the option (1) yes (2) no Which is the most critical period for financing a housing development? (1) purchase of land-., (2) construction financing (3) financing inventory of completed units (4) other (please specify) In which area do you place most effort in order to reduce your costs? (1) Land cost and land assembly (2) Servicing (3) Construction-Labor (4) Construction-materials (5) Sales (6) Financing I will read you a l i s t of financial sources. Would you please t e l l me for each how often you use the source by responding (0) never (1) sometimes (2) often (3) always (Interviewer: record number of response) 125 A. Institutions (Pensions, Trusts, etc) 48 B. Insurance Companies 49 C. Banks 50 D. CMHC-NHA 51 E. Equity 52 F. Mortgage Bankers 53 G. Partnership funds 54 H. Personal loans 55 I. Retained earnings 56 J. Personal Savings 57 K. Syndicated investors 58 L. Other (please specify) 59 With respect to the details of financing could you please t e l l me the degree of importance of the following factors by responding (0) unimportant (1) fairly important (2) average importance (3) very important A. Rate of Interest 60 B. Term of Loan 61 C. Amortization period 62 D. Loan to Value ratio 63 E. Degree of participation in cash flow by lender 64 F. other (please specify) 65 Thank you for your help. The information you have provided 66 has been very helpful and will be kept in strict confidence. Would you like a copy of the survey results? (1) yes (2) no Interviewer: be sure to record the name and address. Name and Address 126 "CARD B" STAGES IN THE DEVELOPMENT PROCESS RANK A. ARRANGING FOR FINANCING B. CHOOSING TYPE OF DEVELOPMENT C. CHOOSING SIZE OF DEVELOPMENT D. CHOOSING A SITE FOR THE DEVELOPMENT E. CHOOSING A NEIGHBOURHOOD FOR THE DEVELOPMENT F. CHOOSING A CONTRACTOR G. GETTING ZONING CHANGED (IF NEEDED) H. GETTING BUILDING PERMIT I. OTHER STAGES - PLEASE SPECIFY "CARD A" INCOMES RANGES OF PROSPECTIVE PURCHASERS UNDER $2,001 to $7,001 to $8,001 to $16,001 to OVER $2,000 $7,000 $8,000 $16,000 $25,000 $25,000 per year per year per year per year per year per year 

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