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Residential development: a microspatial allocation model Allan, Edward Blake 1978

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RESIDENTIAL DEVELOPMENT; A MICROSPATIAL ALLOCATION MODEL by EDWARD BLAKE ALLAN B.A., University of Victoria, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE COMMERCE AND BUSINESS ADMINISTRATION in THE FACULTY OF GRADUATE STUDIES Urban Land Economics Faculty of Commerce and Business Administration University of British Columbia We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April , 1978 ( c ) Edward Blake Allan, 1978 In presenting th i s thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my wri t ten permission. Urban Land Economics D i v i s i o n Department of Faculty of Commerce and Business Administration The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e A p r i l 26, 1978 i t ABSTRACT The focus of this study was the development and testing of a micro-spatial supply model which could explain and predict the allocation of residential development to subareas within a region. This involved a three step process. The first step was a review of the literature to determine what cr i -teria were considered important in the location of residential development. Two types of location criteria were found to be important. The first of these criteria were intuitive accessibility measures used in other modelling studies. The second type of criteria were potential supply criteria sug-gested as important by surveys of residential developers. The second step involved the measuring and testing of various potential supply and accessibility measures to see which were important in explaining the allocation of residential development within the Greater Vancouver Regional District (GVRD). From these tests a microspatial allocation function was derived which could be tested in a large scale urban model of the GVRD. The third step involved incorporating the microspatial allocation function into the supply sub-model of a large urban model and running the model for four simulated years. The simulated data was then compared with actual data before and after the inclusion of the allocation function. Finally, the results of the tests were compared to similar studies which had compared simulated data with actual data. The test results indicate that approximately 50% of single family development and approximately 75% of multiple family development could be i. i i explained by potential supply measures. Accessibility measures were of' l i t t le significance in explaining single family development, and explained only about 10% of multiple family development. The results of testing the microspatial allocation functions in a large urban model were not as encouraging as the explanatory tests. Generally, the results of tests which compared actual data with simulated data indi-cate that the increase in performance with the microspatial allocation func-tion was marginal. However, compared to similar studies the results are acceptable. In general, the study indicates that behavioural studies of the role played by developers combined with analytical models of this behaviour may provide considerable insight into the nature of the development pro-cess. It also lends strong supporting evidence to the suggestion that government organizations have been effective in allocating growth by their servicing and zoning policies. iv TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES vi LIST OF FIGURES v i i i ACKNOWLEDGEMENTS ix Chapter 1. INTRODUCTION 1 2. IMPORTANT SUPPLY CRITERIA: THE DEVELOPER SURVEYS 8 Introduction 8 The North Carolina Survey 9 Kaiser's Tests of the North Carolina Survey Results . . . 9 The 1972 University of British Columbia Survey 10 Richard Moore's Testing of the 1972 Survey Results . . . . 12 The 1975 University of British Columbia Surveys 17 Summary 3. EMPIRICAL ANALYSIS 21 Introduction 21 Hypotheses Tested 22 The Test Region 23 The Time Period 24 The Dependent Variables 24 The Independent Variables 25 The Bivariate Regression Tests 31 Multivariate Regression Tests 40 Conclusion 47 V 4. THE TEST MODEL FRAMEWORK. . . . . . . . . . . . . , , , , ,. 5 2 Introduction , , , , , , 52 General Overview of the Model , , . , 52 General Overview of the Sub-Model Structure 5^ Macro Housing Sub-Model . . . . 6^ Microspatial Housing Sub-Models 61 fid Extensions 5. TESTING MICROSPATIAL SUPPLY REVISIONS 6 5 Introduction Models Tested 6 5 Testing the Models 6 8 Comparison of the Results With Other Studies ^ 6. CONCLUSIONS 8 1 BIBLIOGRAPHY 89 APPENDIXES A. DEVELOPER SURVEY QUESTIONS AND TABLES OF THE RESULTS . . . 94 B. MAP OF THE GVRD 101 C. DETAILED DESCRIPTION OF THE INDEPENDENT VARIABLES USED IN THE EMPIRICAL ANALYSIS OF CHAPTER THREE 103 D. CALCULATION OF THE ACCESSIBILITY MEASURES 110 E. EMPLOYMENT, RECREATION AND OPEN-SPACE SUB-MODELS 113 vi LIST OF TABLES Page Table 1. Accessibility and Existing Land-Use Models: Typical Independent and Dependent Variables 4 2. Kaiser's Research Results 11 3. 1972 Survey Results: Important Location Decision Criteria 13-4. Regression Results: "Measures of Attractiveness" . . . . 15 5. Regression Results of "Unused and Total Potential" . . . . 16 6. 1975 Survey Results: Important Location Decision Criteria 18 7. Data Base Obtained from the Greater Vancouver Regional District 25 8. Development Data: Total Regional Stock and Changes in the Stock 27 9. Descriptive Statistics on the Dependent Variables . . . . 28 10. Summary of Independent Variables: Measures of Potential Supply 32 11. Summary of Independent Variables: Measures of Accessibility , . . 33 12. Bivariate Regression Results: Percent SF Development by Potential Supply Measures . . . . . . . . 34 13. Bivariate Regression Results; Percent MF Development by Potential Supply Measures 35 14. Bivariate Regression Results; Percent SF Development by Accessibility Measures 38 15. Bivariate Regression Results: Percent MF Development by Accessibility Measures . . 39 16. Multivariate Regression Results: Percent SF Development by All Variables . . . . . 41 17. Multivariate Regression Results: Percent MF Development by All Variables 42 vii 18. Multivariate Regression Results: Percent SF Development by All Variables Including Dummies 45 19. Multivariate Regression Analysis: Percent MF Development by All Variables Including Dummies 46 20. Macro Model Comparisons 69 21. Model Test Regression Results for Stock of Units 7 1 22. Model Test Results Actual Against Model Forecasts for the Stock of Units . 72 23. Model Test Regression Results for the Change in the Stock of Units 7 6 24. Model Test Results Actual Against Model Forecasts for the Change in the Stock of Units 7 7 25. 1960-1970 Comparisons of EMPIRIC & DRAM: Actual vs. Predicted 79 26. Model Test Regression Results for the Stock of Acres 86 27. Model Test Results for the Change in the Stock of Acres 87 A-1. Question 11-3 1972 Developer Survey 95 A-2. Evaluation of Location Factors by Developers of Single Family Dwellings 96 A-3. Evaluation of Location Factors by Developers of Multiple Family Dwellings 97 A-4. Question 6.4 1975 Developer Survey 98 A-5. Evaluation of Location Factors by Developers of Single Family Dwellings 99 A-6. Evaluation of Location Factors by Developers of Multiple Family Dwellings 100 C-l . Descriptive Statistics: Measures of Potential Single Family Housing Supply . . . . . . 107 C-2. Descriptive Statistics: Measure of Potential Multiple Family Housing Supply . 108 C-3. Descriptive Statistics: Accessibility Measures "109 v i i i LIST OF FIGURES Page Figure 1. Diagram o f R e l a t i o n s h i p Between the H P S Subgroups 54 2. The I n t e r a c t i o n Between the Module and the Regional T ranspo r t a t i on Model 57 3. Land Use Model 58 4. Housing Model 59 ix ACKNOWLEDGEMENTS I would like to express my appreciation to a number of organizations and individuals for their valuable assistance. First and foremost, I would like to thank my wife Beryl for her invaluable help in measuring the zoning and sewer data, and for her endurance and moral support while I struggled along. Next, I extend special appreciation to Dr. Michael A. Goldberg, who served as my thesis advisor, for his valuable help and advice including financial support. I also extend special appreciation to the Greater Vancouver Regional District Planning Department, especially Peter George and Marsha Hilborn, for the use of their excellent data. I would also like to thank Douglas A. Ash who helped with the urban model programming, David Stewart who helped with data collection and mea-surement and the Real Estate Council of British Columbia who provided much needed scholarship assistance. Finally, a special thanks is due Erin Loughrey, my typist, for her careful attention to detail and her help in meeting very tight time con-straints. As with all acknowledgements, I also acknowledge any errors that re-main as my own, and accept the blame for any remaining weaknesses. Chapter 1 INTRODUCTION Most of the residential location and land-use models developed to date can be characterized as metropolitan growth or extension models. The very first of these models, such as the one developed for the Chicago Area Transport Study, which was described by Hamburg and Creighton in the Journal of the American Institute of Planners in May 1959,^  provided fairly simple forecasts of the future demands for transportation fac i l i -ties, often made by estimating the future demands for housing and other urban land uses based on existing land use patterns and the observed de-mand for existing transport facil it ies. With the increasing availability of electronic computers during the early 19601 s and the realization that patterns of metropolitan land use could be explained and predicted by mathematical models, land-use modelling efforts began to grow in both complexity and size. Most of the large Canadian, U.S. and British city planning departments experimented with large land-use and transportation models which would probably cost several 2 million dollars each today. 'J.R. Hamburg and R.L. Creighton, "Predicting Chicago's Land Use Pattern," Journal of the American Institute of Planners, Vol. 25, No. 2 (May 1959), pp. 67-72. 2 Examples of the American experience are: Ira S. Lowry, A Model of  Metropolis (Santa Monica, California: The Rand Corporation, 1964) and Bay  Area Simulation Study (BASS) (Berkeley, California: Centre for Real Estate and Urban Economics, The University of California, 1968). The British experience is well summarized in the works of Alan G. Wilson, including: Urban and Regional Models in Geography and Planning (London: John Wiley, 1974) and A.G. Wilson, P.H. Rees and C.M. Leith (eds.) Models of Cities  and Regions (London: John Wiley, 1977). The general experience is well 2 Even though there has been extensive research into various types of land use models, no consensus of opinion regarding the best model to use emerges from the literature on land use models. Many authors stress the constant state of revision and refinement which they feel is an im-portant part of land-use modelling. This constant state of revision, testing and refinement has led to a great diversity of land-use models, each with its own particular weaknesses and strengths. The three major classes of present models are: descriptive models, 3 predictive models and planning models. Within each of these applications various modelling structures such as market sensitive, non-market sensi-tive, behavioural, non-behavioural and integrated have been attempted. The resulting literature is vast and no attempt will be made here to survey it a l l . For the interested reader, general discussions of land-use models, including bibliographies of some length, are contained in 4 5 6 the works of Boyce et a l . , Brown et a l . , Kresge and Roberts, Goldberg summarized in: S.H. Putman, "Urban Land and Transportation Models: A State-of-the-Art Summary," Transportation Research, Vol. 9 (1975), pp. 187-202 and J.R. Pack, "The Use of Urban Models: Report on a Survey of Planning Organizations," Journal of the American Institute of Planners, Vol. 41, No. 3 (May 1975), pp. 191-99. 3 For a detailed description of these three types of applications see: Ira S. Lowry, "A Short Course in Model Design," American Institute  of Planners Journal, Vol. 31 (May 1965), pp. 158-166. 4 D.E. Boyce, N. Day and C. McDonald, Metropolitan Plan Making (Philadelphia: Regional Science Institute", 1972). 5 H. James Brown et a l . , Empirical Models of Urban Land Use: Suggestions  on Research Objectives and Organization (New York: National Bureau of Economic Research, 1972). David T. Kresge and Paul 0. Roberts, Systems Analysis and Simulation  Models (Washington, D . C : The Brookings Institute, 1971). 3 7 9 and Davis, Stephen Putman and Alan Wilson. The criticisms of residential location and land use models are far too varied and abundant to be effectively summarized here. However, the important criticisms which have evolved are: (1) the almost exclusive concentration on the demand side of the housing market, and (2) the lack of convincing behavioural content.1 0 Admittedly some models have attempted to incorporate supply, but the dominant theme in most models is that supply reacts to demand, and that demand for a subarea of a region is measured by the accessibility of the region to such factors as employment and shopping. The heavy reliance of land use models on independent variables which reflect accessibility is indicated by Table 1. Not all of these variables were included in all models, and the dependent variables used varied between models. However, the table does indicate the types of variables which were used depending on data availability. Even though the dominant theme in many land-use and transportation models has been that supply reacts to demand, and that demand for a sub-area of a region is related to the accessibility of the subarea to such factors as employment and shopping; there have been models developed which do incorporate supply variables into a housing market model. Examples of these models are: (_1) the Bay Area Simulation Study Michael A. Goldberg and H.C. Dayis, "An Approach to Modelling Urban Growth and Structure," Highway Research, Record, No. 435 (1973), pp. 41-55. g Stephen H. Putman, "Urban Land Use and Transportation Models: A State-of-the-Art Summary," Transportation Research, Vol. 9 (1975), pp. 187-202. 9 Alan G. Wilson, Urban and Regional Models in Geography and Planning (London, England; John Wiley, 1974)_. 1 0 An excellent summary of the problems associated with, land use and transportation models is contained in: H.. James Brown et a l . , Empirical  Models of Urban Land Use: Suggestions on Research Objectives and Organiza-tion (New. York: National Bureau of Economic Research., 1972), especially Chapter 9. 4 Table 1 ACCESSIBILITY AND EXISTING LAND-USE MODELS TYPICAL INDEPENDENT VARIABLES 1. Amount of existing development 2. Marginal land not in urban use 3. Proportion of poor soil 4. Zoni ng 5. Socio-economic status 6. Availability of services 7. Proximity to non-white areas 8. Access to work areas 9. Total travel time to all areas 10. Access to other residential development 11 . Straight line distance to CBD 12. Travel time to CBD 13. Distance to nearest major street 14. Distance to nearest playground 15. Distance to nearest shopping 16. Distance to nearest school 17. Residential amenity 18. Assessed value TYPICAL DEPENDENT VARIABLES 1. Population by various income groups and employment classes 2. Population density by the various classes of 1 3. Single family and multiple family housing completions during a time period 4. Total land in urban use 5. Dwelling density by structure type and overall 6. Changes over time in each of the above 5 (BASS),^^ (2) The Southeastern Wisconsin Regional Planning Commission Study, 1 2 (3) the Inter-Institutional Policy Simulator Study (HPS) at 13 the University of British Columbia, and (4) the NBER Urban Simulation Model . ^ Exceptions to the lack of behavioural content in large land use mo-dels are not well documented in the literature on land-use modelling. Admittedly, studies of consumers and producers have been made, and some attempts have been made to test the results of these studies empirically, 15 such as the studies by Kaiser at the University of North Carolina, and 16 Moore at the University of British Columbia. However, to my knowledge no studies of the micro behaviour of developers or consumers have been used to derive empirical relationships which are useful in large scale land use models. This lack of convincing behavioural content in land use models, and NBay Area Simulation Study (BASS) (Berkeley, California: Centre for Real Estate and Urban Economics, The University of California, 1968). 12 A Land Use Plan Design Model: Volume One - Model Development, Technical Report No. 8 (Milwaukee: Southeastern Wisconsin Regional Planning Commission, January 1968). 13 Michael A. Goldberg, "Simulation, Synthesis and Urban Public Decision Making," Management Science, Vol. 20, No. 4 (December 1973), Part II, pp. 629-643. 14 G.K. Ingram, J.K. Kain, and J.R. Ginn, The Detroit Prototype of the  NBER Urban Simulation Model (New York: National Bureau of Economic Re-search, 1972). 15 Edward J. Kaiser, A Producer Model for Residential Growth: Analyzing  and Predicting the Location of Residential Subdivisions (Chapel H i l l , N.C.: Institute for Research in Social Science, University of North Carolina, November 1968), p. 1. Richard A. Moore, A Development Potential Model for the Vancouver  Metropolitan Area (Unpublished MBA Thesis, The University of British Columbia, 1972). 6 the heavy concentration of these models on the demand side of the housing market, led to the conclusion that large scale land use models could be improved i f convincing behavioural content could be incorporated into the supply side of the housing market. Accordingly, the purpose of this study was to investigate the potential usefulness of behavioural content in the supply section of a large land use model by: (1) using the results of developer surveys to determine which location criteria developers considered important in their location decision; (2) testing the important location criteria identified in (1) using regression analysis to determine which location criteria were useful in explaining the allocation of regional (macro) single and multiple family housing development to subareas within the region; (3) developing regression equations based on the results of (2) which could easily be incorporated in the supply sub-model of a large land-use model to test their effectiveness in predicting the future allocation of residential housing deve-lopment; (4) testing the regression equations developed in (3) in a large scale model and comparing the model output before and after the inclusion of the regression equations. Chapter two discusses the results of three developer surveys and two attempts which were made at measuring and testing the location criteria deemed important by the survey respondents. The first study discussed was undertaken by Edward J, Kaiser at the University of North Carolina during 1968,^ while the other two studies discussed were undertaken by Michael A. Goldberg at the University of British Columbia during 1972 Kaiser, A Producer Model. 7 and 1975.1U The two attempts which were made at empirically testing the results of these surveys were undertaken by Kaiser on the North 19 Carolina survey results, and by Richard Moore on the results of Goldberg's 1972 survey. Chapter three discusses the procedures used to test various residential developer location criteria and the results obtained. Specifically this chapter discusses: (1) the measurement of the dependent variables; (2) the measurement of the residential developer location criteria variables tested, including those suggested as important by the developer surveys and the accessibility measures suggested as important by the literature; and (3) the results obtained from the regression tests. Chapter four describes the land use model used to test the regression equations derived from the developer surveys. Then Chapter five discusses the derivation of the regression equations and the output of the model before and after their inclusion. Finally, Chapter six presents a sum-mary of the results of the study and discusses the implications of these results for policy decisions and future research. ,uThe first survey is summarized in Michael A. Goldberg, "Residential Developer Behaviour: Some Empirical Findings," Land Economics, Vol. 50, No. 4, (Feb. 1974) pp. 85-89. The second survey is summarized in Michael A. Goldberg and Daniel D. Ulinder, "Residential Developer Behaviour 1975; Additional Empirical Findings," Land Economics, Vol. 52, No. 3 (August 1976), pp. 363-370. A detailed discussion of both surveys is contained in Michael A. Goldberg and Daniel D. Ulinder, "Residential Developer Behaviour: 1975," Housing: It's Your Move, Vol. II, Technical Reports (Vancouver, B.C.: Urban Land Economics Division, Faculty of Commerce and Business Administration, University of British Columbia, 1976), pp. 241-382. 19 Moore, A Development Potential Model. 8 Chapter 2 IMPORTANT SUPPLY CRITERIA: THE DEVELOPER SURVEYS 1. Introduction Two exceptions were previously noted to the lack of behavioural content in land use models.1 Included in these two studies were three separate surveys of developers which were undertaken in an attempt to determine important developer location criteria. The first of these sur-2 veys was undertaken by a North Carolina group in 1965, while the two other surveys were undertaken by groups at the University of British 3 Columbia in 1972 and 1975. This chapter discusses the results of these 4 three developer surveys and the attempts made to test their results. 'A summary of the University of British Columbia studies is contained in, Michael A. Goldberg, "Simulating Cities: Process, Product and Prognosis," Journal of the American Institute of Planners (April 1977), pp. 148-157; while a summary of the University of North Carolina studies is contained in E.J. Kaiser and S.F. Weiss, "Public Policy and the Residential Develop-ment Process," Journal of the American Institute of Planners, Vol. 36 (1970) pp. 30-37. 2 Shirley F. Weiss et al.., Residential Developer Decisions (Chapel H i l l , N.C.: Institute for Research in Social Science, University of North Carolina, April 1966). 3 A complete discussion of the 1975 survey and a comparison with the 1972 survey is contained in: Michael A. Goldberg and Daniel D. Ulinder, "Residential Developer Behaviour: 1975," Housing It's Your Move, Vol. II, Technical Reports [Vancouver, B.C.: Urban Land Economics Division, Faculty of Commerce and Business Administration, University of British Columbia, 1976) pp. 241-382. 4 See Edward J. Kaiser, A Producer Model for Residential Growth; Analyzing and Predicting the Location of Residential Subdivisions (Chapel H i l l , N.C.: Institute for Research in Social Science, University of North Carolina, November 1968) and Richard W, Moore, A Development Potential Model  for the Vancouver Metropolitan Area (Unpublished M.B.A. Thesis, The University of British Columbia, 1972). 9 2. The North Carolina Survey The group at the University of North Carolina began their land use modelling efforts in the early 1960's by attempting to develop land use models based on accessibility measures and existing patterns of urban 5 land use. However, they realized the need for increased behavioural content on the supply side of their models early in their modelling ef-forts. Consequently, they undertook a survey of developers in 1965 to ascertain their actual development location criteria. The justification for the North Carolina investigation into the behaviour of developers is very aptly summed up by Edward J. Kaiser in a 1968 monograph reporting on his empirical testing of developer location criteria. Why focus a research thrust upon the developer? One rea-son is that in spite of the important role played by the developer in the conversion of open land to urban residential use, he has been relatively ignored by investigators of residential growth. The viewpoint of the household as the consumer of residential services which flow from the residential package has been the dominant viewpoint in research concerning resi-dential growth. Yet a substantial portion of new purchasers buy in speculatively built residential subdivisions. In this important segment of residential growth, the developer has al-ready made the initial speculative commitment to a location. Consequently, the idealized consumer's choice in residential location is limited in actuality by the availability of suit-able housing structure and location alternatives determined by residential developers.7 3. Kaiser's Tests of the North Carolina Survey Results From the North Carolina interviews and a review of other literature F. Stuart Chapin Jr. and Shirley F. Weiss, Factors Influencing  Land Development (Chapel H i l l , N.C.; . Center for Urban and Regional Studies, University of North Carolina, August 1962). Shirley F. Weiss et a l . , op. c i t . Kaiser, op. c i t . , p. 1. 10 Kaiser hypothesized that the variables presented in Table 2 would in-fluence developer location to some extent. He found that contrary to previous popular opinions, institutional supply constraints were the most significant explanatory variables for the existence of subdivision. Location characteristics including accessibility measures were next, and the physical site characteristics had l i t t le or no significance. Kaiser's contribution is worth noting as he laid the ground work for investigating the locational criteria of developers by surveys, and for testing these criteria empirically. However, Kaiser's choice of a dependent variable which measured only the dichotomy between subdivision, or no subdivisions within a subarea of the region during the time period, rather than a dependent variable which measured the actual amount of residential development, is a major drawback to applying his results to larger scale urban land-use modelling. A more meaningful dependent variable would have been a measure in units, acres, or both, of the actual amount of residential development which occurred within subareas of the region during the time period. 4. The 1972 University of British Columbia Survey A group at the University of British Columbia involved in a large urban modelling project called HPS (for Inter-Institutional Policy Simulator) also realized the need for more behavioural and supply content 9 in their model. Consequently, they undertook an interview survey of sixty-three residential developers in the Vancouver area during the summer Ibid., p. 19. For a summary of these studies see footnote 1 for this Chapter and footnote 18 for Chapter 1. 11 Table 2 KAISER'S RESEARCH RESULTS Dependent Variable Did an area receive subdivision (Yes, No) Independent Variables Institutional Characteristics 1. Availability of public utilities 2. Zoning protection Locational Characteristics 1. Socio-economic rank 2. Distance to CBD 3. Distance to nearest major street 4. Distance to nearest elementary school 5. Accessibility to employment areas 6. Amount of contiguous residential development • Physical Characteristics 1. Proportion of marginal land 2. Proportion of poor soil SOURCE: Edward J. Kaiser, A Producer Model For Residential Growth: Analysing And Predicting The Location Of Residential Subdivisions (Chapel H i l l , N.C.: Institute for Research in Social Science, University of North Carolina, 1968). most significant spotty significance not significant 12 of 1972.10 The survey was concerned with various aspects of the develop-ment process including factors important in the site selection process. The results of the site location question are summarized in Table 3. A copy of the actual question asked developers and detailed tables of the results are presented in Appendix A. 5. Richard Moore's Testing of the 1972 Survey Results After the survey was completed, Richard Moore of the University of British Columbia attempted to use the survey results to devise a model whereby the spatial allocation of new housing units in the Greater Van-couver Regional District (GVRD) could be explained.1 1 His approach in-volved using the developer survey as a rough guide to the importance of the proposed location decision factors. He concluded that those fac-tors which were of average or greater than average importance were poten-12 tial determinants of the location of new housing development. In order to ascertain the degree of importance of each location criterion developers, Moore attempted to obtain a measure of each cr i-terion that developers collectively stated was of above average importance. Table 3 presents the criteria developers stated were of above average importance broken down by developer type. Of these criteria Moore was able to obtain measures for census tracts in the GVRD of: (!) zoning, (2) travel time to central business district shopping, (3) price of land and (4) the availability of developable land. He then derived relative '^Goldberg and Ulinder, op. c i t . ^Richard A. Moore, op. cit . 12 See Richard A. Moore, op. c i t . , pp. 52^ 53 for a description of the scope and methodology of his study. 13 Table 3 1972 SURVEY RESULTS IMPORTANT LOCATION DECISION CRITERIA Single Family Housing Developers MEAN S.D. * 1. Proper zoning 3.49 0.97 * 2. Price of land 3.38 0.81 3. Access to trunk sewer 3.29 0.89 * 4. Availability of developable land 2.91 1.00 5. Nearness to schools 2.51 1.01 6. Nearness to major shopping 2.29 1.01 7. Nearness to major roads 2.07 1.19 Multiple Family Housing Developers MEAN S.D. * 1. Proper zoning 3.45 0.86 2. Access to trunk sewers 3.34 1.02 * 3. Price of land 3.13 1.12 * 4. Availability of developable land 3.00 1.12 5. Nearness to major roads 2.36 1.17 6. Size of the site 2.34 1.12 7. Nearness to schools 2.16 1.26 8. Nearness to major shopping 2.05 1.13 * Denotes criteria measured and tested by Moore. SOURCE: Richard A. Moore, A Development Potential Model For The Vancouver Area (unpublished M.B.A. Thesis, The University of British Columbia, T97T) p. 63-64. 14 importance weights for these criteria, fitting them into the two general categories of: (1) measures of attractiveness and (2) measures of unused and total housing supply potential. Moore obtained his weights for the dependent variables of: (.1) unit completions of single family detached housing and (2) unit completions of single family attached and apartment housing combined by using bivariate and multi-variate regression analysis. The regression coefficients were used as weights, which when applied to the characteristics of each census tract were intended to provide a rank-ing of relative development potential. The results of Moore's analysis are presented in Tables 4 and 5. Table 4 presents the results of the measures of attractiveness in explain-ing the amount of single and multiple family housing development for the two time periods of 1961 to 1966 and 1966 to 1971. The only independent variable which seems to be significant in explaining the amount of devel-opment is the amount of underdeveloped land, a supply criteria. Table 5 presents the results of unused and total housing development potential as independent variables. These measures of potential supply were calculated for both single and multiple family supply as follows. Cl) Total potential (units) = Land zoned for the particular use in acres times the maximum permitted zoning density for the use in units per acre. (.2) Unused potential (units) = Total potential of (.1) in units minus the number of existing units. The results of Table 5 indicate that total potential supply is more significant than unused potential supply, however, both are quite signi-ficat especially for the time period 1966 to 1971. Moore explains the 2 lower R for 1961 to 1966 is probably a result of using zoning data of 1970 to calculate total and unused potential, Moore sums up the signi-ficance of his results in the concluding comments of his paper by saying; 15 Table 4 REGRESSION RESULTS "MEASURE OF ATTRACTIVENESS" Completions sfd 61-66 sfd 61-66* sfd 66-71 sfd 66-71* r 2 0.09 0.14 0.36 0.05 Student t Statistics 1/Price** Time Underdeveloped Land -0.56 -0.40 2.73 -0.53 -0.55 3.16 -0.86 0.83 4.76 -0.48 1.19 1.51 apt 61-66 0.10 apt+sfa 61-66 0.16 apt 66-71 0.15 apt+sfa 66-71 0.05 -0.71 -0.58 2.32 0.88 3.66 3.36 2.04 1.65 0.62 2.95 0.44 0.15 *In these tests allowance was not made for acreage zoned for apart-ments but not yet occupied by apartments. The area was assumed to be occupied entirely by single detached housing. This was done to test the possibility that errors resulting from approximations in calcula-ting this amount were preventing obtaining meaningful statistics. **Price = Price level of land per unit i f housing in 1964 and 1969. 1964 price used for 61-66 change and 1969 price used for 66-71. Time = Travel time to CBD for 1963 and 1968. Underdeveloped land = Land zoned for a use (acres) - land in use (acres). Measured for 1970. sfd = single family detached housing, apt + sfa = apartment and single family attached housing combined. SOURCE: Richard A. Moore, A Development Potential Model For The Van-couver Area (Unpublished M.B.A. Thesis, The University of British Columbia, 1972) p. 88. Table 5 REGRESSION RESULTS OF "UNUSED AND TOTAL POTENTIAL Completions = a + b x Unused Potential Completions a °a b r2 Degrees of Freedom sfd 1961-66 19824, .1 5744 .3 3.45* 1 .62 0.50 3.26* .18 43 sfd 1966-71 93, .9 83 .6 1.12 0, .0675 0.0074 9.12* .66 43 apt+sfa 1961-66 4082, .8 3807 .8 1 .07 11. .79 1.29 9.11* .41 118 apt+sfa 1966-71 15994, .7 3822 .9 4.18* 14, .17 "• 1.54 9.19* .41 118 apt 1966-71 16602, ,9 3749 .0 4.43* 13, .89 1.48 9.39* .42 118 Completions c + d x Total Potential Completions a a a d °d r2 Degrees of Freedom sfa 1961-66 16738. ,7 5947, .4 2.81 1 , ,70 0.47 3.63* .22 43 sfd 1966-71 2. ,89 91, .8 0.03 0, .063 0.0072 8.73* .64 43 apt+sfa 1961-66 2048. ,0 3673, .0 0.56 10. ,65 1.05 10.17* .46 118 apt+sfa 1966-71 11449. .0 3546, ,0 3.23 11 . .61 1.01 11.49* .53 118 apt 1966-71 12164. ,5 3394, .0 3.58 12. ,61 1.04 12.11* .55 118 *P(t>2.62) l l p = 0.005, P(t>2.70)/1. = 0.005 SOURCE: Richard A. Moore, A Development Potential Model For The Vancouver Area (Unpublished M.B.A. Thesis, The University of British Columbia, 1972) p. 89. u The importance of the significant results concerning the number of housing unit completions as a function of potential (determined by the amount of residentially zoned land) lies in the reaffirmation of planner's power of directing development and redevelopment through zoning. That the price of land and travel time from the central business district did not appear to be significant determinants of the location of new housing allows the planner to discount the importance of these factors in his formulation of the city plan.13 6. The 1975 University of British Columbia Surveys Concern for the smooth operation of the housing market in British Columbia led a group at the University of British Columbia to undertake a variety of studies concerning the structure of the housing market in the province during the summer of 1975. One of the studies undertaken within this framework v/as an extension of the 1972 developer survey by 14 Goldberg and Ulinder. The original developer survey was expanded and the sample size increased to 140 developers from throughout the province. The results of the question which was asked developers regarding the site selection decision are summarized in Table 6. A copy of the actual question asked developers and detailed tables of the results are contained in Appendix A. From these results Goldberg and Ulinder conclude; 15 In contradiction to the findings of Kaiser and Weiss in the Greensborough, North Carolina area, developers in British Columbia appear to regard supply variables as being more critical to their decision-making than demand determinants . . . . Developers require adequately serviced and appropriately zoned land. The availability of such land goes a long way to temper their location decision.16 Ibid., p. 97. Goldberg and Ulinder, op. cit . Kaiser and Weiss, op. cit . Goldberg and Ulinder, op. c i t . , p. 300. Table 6 IS 1975 SURVEY RESULTS IMPORTANT LOCATION DECISION CRITERIA Single Family Housing Developers MEAN S, . D. * 1. Proper zoning 3.32 1. .08 2. Price of land 3.23 0. .96 * 3. Access fo trunk sewers 2.93 1. .29 * 4. Availability of developable land 2.78 1. .01 * 5. Nearness to schools 2.42 1. .08 6. Nearness to major roads 2.10 1. .09 7. Character of site 2.05 1. .25 1ti pie Family Housing Developers MEAN S. ,D. * 1. Proper zoning 3.17 0, .94 2. Price of land 3.03 0. .97 * 3. Access to trunk sewer 3.06 1. .09 * 4. Availability of developable land 2.78 1 . .07 5. Size of site 2.40 1. .01 6. Nearness to major road 2.23 0. .88 7. Character of surrounding area 2.23 1. .19 * 8. Nearness to schools 2.06 0. .94 *Denotes criteria measured and tested in this study. SOURCE: Michael A. Goldberg and Daniel D. Ulinder, "Residential Developer Behaviour: 1975," Housing: It's Your Move, Vol. II, Technical  Reports (Vancouver: Urban Land Economics Division, Faculty of Commerce and Business Administration, The University of British Columbia, 1976) p. 280-281. 19 7. Summary As a result of the studies by Kaiser, Moore, and Goldberg and Ulinder the heavy reliance of land-use models on the demand side of the housing market is questionable. The developer surveys reviewed here demonstrate the importance of four supply factors in the development location decision: 01 proper zoning, (2) access to sewers, C3) availability of developable land, and (4) price of land. Implicit in these findings is the role of government, since govern-ments provide zoning, and in many cases the infrastructure as well. In the 1975 survey, questions were asked about difficulties in obtaining approvals, and it was found that nearly half of those surveyed had en-countered such difficulties. Over 80% of these difficulties were with local governments. Also when asked which factors were instrumental in the decision to proceed with development, more than two-thirds of the developers listed government as being most important. As a result of these observations, i t is clear that a fifth location criteria is also very important in the site location decision, namely, local government attitudes and actions.1^ Considering the developer survey results summarized in this chapter, residential location as perceived by residential developers is considerably different from residential location as described by the literature, and as simulated by many housing models which have stressed demand. Accessi-bil i ty in its various forms dominates the literature, yet received l i t t le The work done by Larry S. Bourne, "Urban Structure and Land Use De-cisions," Annals of American Geographies, Vol. 66, No. 4 0976) pp. 531-547 supports this as does the work of Kaiser and Weiss, op. cit . 20 1 g attention in the developer surveys summarized here. This divergence of opinion between the literature and the developer survey results summarized here needs to be reconciled before a true under-standing of the factors which shape the urban environment can be obtained. The following chapter attempts to do just this. It summarizes the pro-cedures used in, and the results obtained from, empirical tests of various site location criteria, including those suggested by the developer surveys and the accessibility criteria suggested as important by the literature. Works by William Goldner, "The Lowry Model Heritage," Journal of  the American Institute of Planners, Vol. 41, No. 3 (1975) pp. 191-195, and Stephen H. Putman, "Urban Land Use and Transportation Models: A State of the Art Summary," Transportation Research, Vol. 9 (1975) pp. 187-202 stress the importance of accessibility as does the pioneering work of Ira A. Lowry, A Model of Metropolis (Santa Monica, California: Rand Corporation, 1964) and the more recent work by John F. Kain and John M. Quigley, Housing  Markets and Racial Discrimination (New York, N.Y.: National Bureau of Economic Research, 1975). 21 Chapter 3 EMPIRICAL ANALYSIS 1. Introduction As outlined in Chapter two, the key locational variables stressed by developers were: proper zoning, access to sewers, availability of developable land and the price of land. However, many studies reported in the literature suggest that accessibility of an area to such variables as employment and shopping determines the amount of residential development it will receive.1 These studies suggest that measures of accessibility to shopping and employment such as straight line distance, travel time by auto-mobile and gravity formulations based on straight line distance or travel 2 time are important. In an attempt to reconcile the difference between the developer survey results and the existing literature which suggests accessibility is important, regression tests were conducted on dependent variables which measured the spatial allocation of regional housing development, and independent vari-ables which measured potential supply and accessibility. The method of testing these empirical relationships involved the following seven steps: (1) developing the hypotheses to be tested, (2) deciding on a test region, (3) deciding on a time period suitable for testing, (.4) deciding on depen-dent variables and obtaining data for them, (5) deciding on independent See footnote 18 for Chapter 2 for a summary of studies which suggest the importance of accessibility measures. 2See Appendix D for a discussion of the gravity formulation procedure and references which summarize the literature on this topic. 22 variables and obtaining data for them, (6) bivariate regression tests of individual independent variables, and (7) multivariate regression tests of groups of independent variables, 2. Hypotheses Tested As the present study was concerned with the need to empirically test the results of the developer surveys discussed in Chapter two, and to re-concile the difference between these results and the existing literature which suggests accessibility is the important determinant of residential development, the following two hypotheses were developed and tested using regression analysis. Hypothesis 1: The potential supply of developable single and multiple family housing land explains the spatial allocation of single and multiple family housing development to subareas within the GVRD. Specifically, the more accurately one is able to define the potential supply, the greater will be the explanatory precision. For example, a measure of land which is vacant, sewered and zoned for a particular use will have much better explanatory precision than a measure of vacant and zoned land, or vacant land. This hypothesis suggests a stepwise combination of three measures which have been previously used independently into one measure which is potentially much more representative of the actual preferences of developers. If, as the developer survey results suggest, developers do not hold sub-stantial inventories of land, buying only when they are ready to develop or build, then the best measure of potential supply should be a measure of that land which is vacant, accessible to sewers and zoned for the desired use. Previous measures used for land-use modelling have included indepen-dent measures of vacant land, access to sewers (usually Tn a yes-no criteria 23 for the subarea) and zoning, but as far as can be determined no models have been reported which combine these criteria to produce a net figure in acres. Hypothesis 2: Measures of accessibility: specifically nearness to schools, nearness to employment and nearness to shopping, contribute l i t t l e to an explanation of the allocation of residential housing development to subareas within the GVRD. This hypothesis goes one step further than previous research in the GVRD as i t suggests testing more than one accessibility measure in an attempt to determine i f accessibility measures in general are insignifi-cant in explaining the allocation of residential development to subareas within the GVRD. 3. The Test Region The metropolitan region chosen for testing the empirical relation-ship between the spatial distribution of housing development and potential supply and accessibility measures was the Greater Vancouver Regional District (GVRD) as outlined on the map in Appendix B. This region is divided into fifteen municipal areas which each have a local government which controls the building process through local development by-laws. All of these muni-cipal areas, with the exception of White Rock (municipality 14), were fur-ther divided by the GVRD Planning Department, the regional planning body, into a total of 161 smaller planning areas which reflect general adminis-tration or neighbourhood boundaries. (The boundaries of these areas are outlined on the map in Appendix B.) In many cases these areas are an aggre-gation of census tracts, however, this is not always the case as some cen-sus tracts are quite large and the GVRD Planning Department felt smaller 24 areas would be more representative. The reason for choosing the GVRD and the 161 planning areas within the GVRD for the empirical analysis were: (1) the University of British Columbia developer surveys discussed in Chapter two were conducted within the GVRD, (2) it was close and accessible for observation and data gathering, (3) GVRD planning department land use data as described in Table 7 was available for the region and the subareas, and (4) the HPS urban model was constructed and tested using these areas which provided convenient comparison checks and data availability. 4. The Time Period The time period chosen for the analysis was the period from 1966 to 1971. This time period was chosen for the following reasons: (!) GVRD planning department land use data was available for this period and it was possible to calculate the dependent variables and some of the independent variables from this data, (2) GVRD planning department land use data was not complete for 1961, (.3). i t was possible to measure the other variables for the period 1966 to 1971, but hard to find good information for 1961 to 1966, and (4) using this time period allowed the results to be used in the HPS urban model for prediction purposes and testing against actual data in 1975. 5. The Dependent Variables The dependent variables chosen for the analysis were: (!) the per-centage of the total GVRD change of single family housing stock which a subarea received during the period 1966 to 1971, and (2) the percentage of the total GVRD change of multiple family housing stock which a subarea Table 7 DATA BASE OBTAINED FROM THE GREATER VANCOUVER REGIONAL DISTRICT The following data were obtained for 1961, 1966 and 1971 for each of the 161 residential subareas outlined on the map in Appendix B. Land Use Data in Acres 1. Total area 2. Roads 3. Vacant 4. Residential 5. Commercial 6. Institutional 7. Utility and open space 8. Private open space 9. Farms 10. Water Residential Data 1. Stock of single family detached units (units) 2. Single family detached land use (acres). 3. Single family detached density (units per acre in use) 4. Stock of duplex units (units) 5. Duplex land use (acres) 6. Duplex density (units per acre in use) 7. Stock of apartment units (units) 8. Apartment land use (acres) 9. Apartment density (units per acre in use) 26 r ece ived dur ing the pe r iod 1966 to 1971. R e l i a b l e data were sought on the ac tua l number o f housing s t a r t s and complet ions r a the r than the s tock o f u n i t s , but un fo r tuna te ly s t a r t s and complet ions data are on ly c o l l e c t e d and pub l i shed f o r munic ipa l a reas . As a r e s u l t , the dependent v a r i a b l e s were c a l c u l a t e d from the GVRD p lann ing department land use data us ing the three steps o u t l i n e d below. (1) The t o t a l GVRD s i n g l e and m u l t i p l e f a m i l y housing s tock f o r 1961, 1966 and 1971 were c a l c u l a t e d from the GVRD P lann ing Department land use data desc r ibed i n Table 7 by summing a l l the values fo r the i n d i v i d u a l subareas. These values are l i s t e d i n Table 8. (2) The t o t a l GVRD change i n s i n g l e and m u l t i p l e housing s tock f o r 1966 to 1971 were c a l c u l a t e d by s u b t r a c t i n g the t o t a l s tock values f o r 1966, as c a l c u l a t e d i n (1) above, from the c o r r e -sponding values f o r 1971. These values are l i s t e d i n Table 8. (3) The percentage o f the GVRD change i n s i n g l e and m u l t i p l e f a m i l y housing stock was c a l c u l a t e d by d i v i d i n g the change i n s i n g l e and m u l t i p l e f a m i l y housing s tock fo r each o f the 161 subareas by the corresponding t o t a l value f o r the r e g i o n , as c a l c u l a t e d i n (2) above, and then m u l t i p l y i n g t h i s value by 100. D e s c r i p -t i v e s t a t i s t i c s on these v a r i a b l e s are presented i n Table 9. 6. The Independent V a r i a b l e s The independent v a r i a b l e s s e l e c t e d f o r the a n a l y s i s were va r ious measures o f p o t e n t i a l supply and a c c e s s i b i l i t y which were suggested by the developer surveys and the e x i s t i n g l i t e r a t u r e . Since the developer surveys suggested tha t developers r e q u i r e land which i s vacant , zoned c o r r e c t l y , sewered and p r i c e d c o r r e c t l y , the f i r s t s tep was to ob ta in r e l i a b l e informa-t i o n on these v a r i a b l e s . The amount o f vacant land was e a s i l y obta ined from the GVRD P lann ing Department data desc r ibed i n Table 7, but measures o f z o n i n g , sewers and the p r i c e of land presented a more d i f f i c u l t problem. I n i t i a l l y i t was hoped tha t some form o f zoning in fo rmat ion would be a v a i l a b l e f o r each o f the three t ime per iods f o r which l and use data was a v a i l a b l e . However, when a t tempt ing to ob ta in zoning maps from the f i f t e e n 27 Table 8 DEVELOPMENT DATA TOTAL REGIONAL STOCK AND CHANGES IN THE STOCK* Total Units 1971 SF 222,768 MF 98,461 TOTAL 321,229 1966 SF 198,966 MF 54,636 TOTAL 253,602 1961 SF 192,446 MF 34,133 TOTAL 226,579 Changes in the Stock 1966-1971 SF 23,802 MF 43,825 TOTAL 67,627 1961-1966 SF 6,520 MF 20,503 TOTAL 27,023 *Based on GVRD Planning Department land use data. SF is single family units including duplex. MF is multi family units including row housing. 28 Table 9 DESCRIPTIVE STATISTICS ON THE DEPENDENT VARIABLES VARIABLES Subarea percentage of the regional change in SF stock 1966-1971 MEAN STANDARD DEVIATION 0.64 1.10 LOW -0.81 HIGH 6.84 iy. Subarea percentage of the regional change in MF stock 1966-1971 0.64 1.60 -0.02 15.82 29 separate municipalities it became readily apparent that this information was not going to be available, and that information for 1971 was going to be hard enough to obtain. The difficulties arose because there does not exist a standard zoning by-law or map for the entire region, actual zoning definitions varied between municipalities, and as zoning maps are updated through time the old ones are usually discarded or become unavailable. As a result of these difficulties, i t was decided to concentrate on obtaining 1971 zoning maps and make the assumption that zoning did not change greatly over the period 1966 to 1971. Admittedly a tenuous assumption, especially for some areas, but about all that could be done i f some measure of zoning was to be obtained. Placing the zoning information on a map of uniform scale represented a time consuming activity, but one which involved no other problems. Obtaining the information on sewered land presented the least di f f i -culty as each municipality in the region provided me with detailed maps of trunk and lateral sewers for 1971. From consultation with several engi-neering firms and municipal engineers who were actively involved in sub-division and development work i t was found that land within 500 feet of a trunk or lateral sewer was deemed unusable. More distant land was too expensive to sewer without development in between. To make the sewer information compatible with the zoning data i t was transferred to maps of the same scale and size as the zoning data. The proceeding procedure, while tedious and time consuming, did pro-vide reliable maps of zoning and sewered land from which the amount of vacant and zoned and vacant zoned and sewered land was calculated. The amount of vacant and zoned land was calculated by subtracting the amount of land in use from a particular zoning type from the total amount of land 30 zoned for that type. The amount of vacant, zoned and sewered land was calculated by the following two step process. First, zoning maps were overlayed on sewer maps and a measure of that land which was zoned and sewered was obtained. Second, the amount of land in use for each zoned and sewered type was subtracted from the total amount of land zoned and sewered for that type. Obtaining information on prices turned out to be a task of some mag-nitude. To obtain data on prices for each of the 161 analysis cells would have required a detailed analysis of all transactions within the GVRD over the time period or the use of some statistical sampling procedure which would produce acceptable results. Due to the complexities surrounding the measurement of reliable price data, price was dropped from the ana-lysis, and concentration was centred on analysing the effects of poten-3 ti al supply measures. Three sets of potential supply variables were computed to test the effectiveness of potential supply in explaining the allocation of housing growth. These three sets of potential supply variables were measures of potential supply from vacant land, vacant and zoned land, and vacant, zoned and sewered land. These three sets of potential supply measures were used to determine i f the more general measure of potential supply (vacant land) or the more specific measures (vacant and zoned land or vacant, zoned and sewered land) produced better explanations. To determine the effects of density, the potential supply for the three sets of variables discussed See S.W. Hamilton, "House Price Indices: Theory and Practice," Housing: It's Your Move, Vol. II, Technical Reports (Vancouver, B.C.: University of British Columbia, Faculty of Commerce and Business Adminis-tration, Urban Land Economics Division, 1976) for a discussion of the problems involved in obtaining and using measures of housing prices. 31 above was computed in both acres and units. The actual variables which were computed and tested are summarized in Table 10 and described in detail in Appendix C. Three general measures of accessibility were suggested as important by the existing literature: accessibility to schools, accessibility to employment and accessibility to shopping. Within each of these three types of accessibility measures more specific measures such as straight line distances, travel times and gravity formulations were also suggested. Table 11 summarizes the actual variables which were computed for this analysis, and Appendix D explains their computation in detail. 7. The Bivariate Regression Tests To test hypothesis one for single and multiple family housing develop-ment eleven bivariate regression equations of the form Y = a+bX were for-4 mulated and tested using ordinary least squares regression analysis. These tests were divided into the two independent variable groups of: (1) potential housing supply in acres and [2) potential housing supply in units. The results of the eleven regression tests are presented in Tables 12 and 13. Table 12 presents the results for the dependent variable of per-centage of GVRD single family development and Table 13 presents the re-sults for percentage of GVRD multiple family development. The results presented in Table 12 support hypothesis one for single family housing development. As the potential supply in both acres and See Norman H. Nie, C. Hadlai Hull, Jean F. Jenkins, Karin Steinbrenner and Dale H. Bent, SPSS (Statistical Package for the Social Sciences) (Toronto:. McGraw Hill Co., 19751 Chapter 20, pp. 32Q-367 for a detailed description of the regression subprogram used including the actual for-mulas used in calculating the regression statistics produced by the program. 32 Table 10 SUMMARY OF INDEPENDENT VARIABLES MEASURES OF POTENTIAL SUPPLY (1) Measures of Potential Single Family (SF) Supply in Acres X-| -- Vacant %2 -- Vacant and Zoned SF -- Vacant, Zoned and Sewered SF (2) Measures of Potential SF Supply in Units X^  -- Vacant in Acres x SF Density in Units per Acre X5 -- (Vacant and Zoned SF in Acres) x SF Density in Units per Acre Xg -- (Vacant, Zoned and Sewered in Acres) x SF Density in Units per Acre. (3) Measures of Potential Multiple Family Supply (MF) in Acres X^  -- Vacant and Zoned MF Xg --. Vacant, Zoned and Sewered MF (4) Measures of Potential Multiple Family Supply in Units Xg -- (Vacant in Acres) x MF Density in Units per Acre X-jQ— (Vacant and Zoned MF in Acres) x MF Density in Units per Acre X - , -1 - - (Vacant, Zoned and Sewered (MF) in Acres) x MF Density in Units per Acre 33 Table 11 SUMMARY OF INDEPENDENT VARIABLES MEASURES OF ACCESSIBILITY (1) Nearness to Schools X-j^ — Service Employment X-J2-- Access to Schools 1 - Gravity Formulation - Exponent = 1.0 Xi^-- Access to Schools 2 - Gravity Formulation - Exponent = 2.0 (2) Nearness to Employment X-|g-- Total Employment X-|g-- Access to Employment 1 - Gravity Formulation - Exponent = 1.0 X-|7-- Access to Employment 2 - Gravity Formulation - Exponent = 2.0 (3) Nearness to Shopping X 1 8— Travel Time to CBD X-jg— Straight Line Distance to CBD 2^0~~ Straight L ^ n e Distance to Closest Large Shopping X21" Straight Line Distance to Second Closest Large Shopping X22" Wholesale and Retail Trade Employment 2^3~~ ^ c c e s s Shopping 1 - Gravity Formulation - Exponent = 1.0. X ? A -- Access to Shopping 2 - Gravity Formulation - Exponent = 2.0 INDEPENDENT VARIABLES (1) Potential Supply in Acres Vacant Vacant and zoned SF Vacant, sewered and zoned SF (2) Potential Supply in Units Vacant x SF density (Vacant and zoned SF) x SF density (Vacant, sewered and zoned SF) x SF density Table 12 BIVARIATE REGRESSION RESULTS PERCENT SF DEVELOPMENT BY POTENTIAL SUPPLY MEASURES ,2 STANDARD SIGNIFICANCE CONSTANT COEFFICIENT STANDARD ERROR OF ESTIMATE 0.00280 1.08127 0.03964 1.0611 LEVEL 0.25381 0.00594 0.24595 0.94025 0.00001 0.00009 1.08273 0.45174 0.06205 1.04865 0.00077 0.17784 0.98180 0.00001 0.68062 0.46048 -0.00002 0.00039 0.18577 0.00182 0.65724 0.00000 0.38179 0.00013 0.24660 0.00031 ERROR OF COEFFICIENT 0.00003 0.00015 0.00025 0.00001 0.00004 0.00005 Table 13 BIVARIATE REGRESSION RESULTS PERCENT MF DEVELOPMENT BY POTENTIAL SUPPLY MEASURES INDEPENDENT VARIABLES R (1) Potential Supply in Acres Vacant and zoned MF 0.45933 Vacant, sewered and zoned MF 0.46308 (2) Potential Supply in Units Vacant x MF density 0.00000 (Vacant and zoned MF) x MF density 0.70296 (Vacant, sewered and zoned MF) x MF density 0.70319 STANDARD ERROR OF ESTIMATE 1.16773 1.16367 1.58809 0.86553 0.86519 SIGNIFICANCE LEVEL 0.00001 0.00001 0.49584 0.00001 0.00001 CONSTANT COEFFICIENT STANDARD ERROR OF COEFFICIENT 0.14420 0.15019 0.62951 0.30174 0.03608 0.03628 0.00000 0.00068 0.30445 0.00068 0.00312 0.00312 0.00001 0.00004 0.00004 36 units is defined with more precision the explanatory power, as measured 2 2 by the R statistic, increases. Not only does the R statistic increase, but the standard error of the estimate decreases, the significance level as measured by an F test increases, and the constant decreases. Density does not seem to be an important element in explaining single family growth allocation as in all the cases in Table 12 the potential supply in units 2 has a lower level of explanation, as measured by the R statistic, than the potential supply in acres. This does not discount the importance of residential density in allocating growth, but rather indicates that the availability of developable land, rather than the number of units which can be built on the available land, is a more important criteria in determining the allocation of single family detached housing development. In general the results of Table 12 tend to indicate that potential supply is not the only important criteria in explaining the allocation of 2 single family detached housing development. The maximum R statistic which could be obtained is 0.19527. This indicates that only about twenty percent of the allocation of single family detached housing development can be explained by the subarea characteristic of the amount of land available which is accessible to sewers and zoned for the required use. This does not discount the importance of this criteria in explaining the allocation of single family growth, but rather tends to indicate that there are other criteria which are also important. The results presented in Table 13 generally support hypothesis one for multiple family housing development. As the potential supply in both acres and the number of units is defined with more precision the explana-2 tory completeness, as measured by the R statistic, Increases, However, the increase in explanatory completeness by further defining the potential 37 supply, in both acres and the number of units, from that potential supply which is vacant and zoned, to that which is vacant, sewered and zoned is 2 marginal. The R statistic increases very l i t t le in both cases and the significance level does not increase at a l l . This result probably occurs because most land which is zoned multiple family is accessible to sewers. What is probably important here is the size and quality of the existing sewers, especially i f the new development involves demolition of existing single family housing or development in an area which has a predominance of single family housing. To test hypothesis two for multiple and single family housing develop-ment, thirteen regression equations of the form Y = a+bX were formulated and tested for each dependent variable using the independent variables summarized in Table 11. The results of the twenty-six regression tests are presented in Tables 14 and 15. Table 14 presents the results for the percent of single family development and Table 15 presents the results for the percent of multiple family development. The results presented in Table 14 support hypothesis twd for single family housing development. All measures of accessibility have very low 2 R statistics, and no measure is significant at the Q.Q5 probability level as measured by F test probability. The results presented in Table 15 tend to refute hypothesis two for multiple family housing development. All of the measures of accessibility 2 are significant at the 0.01 level and have R statistics ranging from 0.05164 to 0.14064. The explanatory completeness of the measures is relatively low, but one cannot refute their significance based on the re-sults of Table 15. The amount of wholesale-retail trade employment in 2 the subarea is the most significant variable with an R statistic of Table 14 BIVARIATE REGRESSION RESULTS PERCENT SF DEVELOPMENT BY ACCESSIBILITY MEASURES INDEPENDENT VARIABLES R STANDARD ERROR OF ESTIMATE (1) Nearness to Schools Service employment 0.00123 1.08212 Access to schools 1 0.00772 1.09745 Access to schools 2 0.00168 1.10078 (2) Nearness to Employment Total employment 0.00002 1.08277 Access to employment 1 0.00857 1.09698 Access to employment 2 0.00255 1.10030 (3) Nearness to Shopping Travel time to CBD 0.01672 1.07369 Straiaht line distance to the CBD 0.00553 1.07978 Straight line distance to closest large shopping 0.00055 1.08249 Straight line distance to second closest large shopping 0.00625 1.07940 Wholesale and retail trade employment 0.00054 1.08249 Access to shopping 1 0.01026 1.09604 Access to shopping 2 0.00391 1.09955 SIGNIFICANCE LEVEL OF F 0.33068 0.13545 0.30403 0.47609 0.12297 0.26378 0.05213 0.17570 0.38490 0.16103 0.38594 0.10196 0.21682 CONSTANT COEFFICIENT 0.63614 0.87964 0.67785 0.46636 0.63706 0.90667 0.70315 0.00001 -0.00003 -0.00007 0.64895 0.00000 0.90067 -0.00001 0.69254 -0.00004 0.32777 0.01197 0.51680 0.01345 0.69174 -0.01651 0.04454 0.00003 -0.00007 -0.00024 STANDARD ERROR OF COEFFICIENT 0.00003 0.00002 0.00013 0.00002 0.00001 0.00006 0.00733 0.01439 0.05633 0.04484 0.00011 0.00005 0.00031 Table 15 BIVARIATE REGRESSION RESULTS PERCENT MF DEVELOPMENT BY ACCESSIBILITY MEASURES INDEPENDENT VARIABLES R^  (1) Nearness to Schools Service employment 0.05164 Access to schools 1 0.11336 Access to schools 2 0.11777 (2) Nearness to Employment Total employment 0.07637 Access to employment 1 0.10337 Access to employment 2 0.10257 (3) Nearness to Shopping Travel time to CBD 0.09058 Straight line distance to CBD 0.07514 Straight line distance to closest large shopping 0.05889 Straight line distance to second closest large shopping 0.06725 Wholesale and retail trade employment 0.14064 Access to shopping 1 0.09089 Access to shopping 2 0.07842 STANDARD SIGNIFICANCE CONSTANT COEFFICIENT STANDARD ERROR OF LEVEL ERROR OF ESTIMATE OF F COEFFICIENT 1.54655 1.49537 1.49165 1.52628 1.50377 1.50444 1 .51446 1.52726 1.54062 1.53376 1.47219 1.51420 1.52455 0.00199 0.00001 0.00001 0.00021 0.00002 0.00002 0.00006 0.00024 0.00103 0.00048 0.00001 0.00006 0.00018 0.47957 -0.75530 0.04040 0.38437 -0.73095 0.04858 1.73530 1.35893 1.52171 0.27923 -0.56190 0.15096 0.00012 0.00014 0.00080 0.00009 0.00006 0.00036 -0.04087 -0.07267 1.23621 -0.25129 -0.21436 0.00076 0.00029 0.00156 0.00004 0.00003 0.00018 0.00003 0.00001 0.00009 0.01034 0.02035 0.08017 0.06371 0.00015 0.00007 0.00043 40 0.14064. Access to schools 2 with an R2 statistic of 0.11777 and travel 2 time to the CBD with an R statistic of 0.09058 follow clearly behind. 8. Multivariate Regression Tests To determine which combination of the factors tested in the bivariate analysis produced the best overall level of explanatory completeness, a multivariate linear regression equation of the form Y = a + b^ X^ + b^^2 ... + b nX n , where X^  to Xn were the independent variables used in the bivariate tests, was formulated for each dependent variable. The testing of the equations was done with a stepwise multiple regression program which pro-duced a listing of the independent variables presented in the order of their relative contribution to the overall explanation of the dependent variable, as measured by the change in the R statistic. The results of these two tests are presented in Tables 16 and 17. Table 16 presents the results of the single family detached housing development test and Table 17 presents the results of the multiple family housing development test. The results of the single family development test indicate that the independent variable found to have the most explanatory power in the bi-variate tests, potential supply in acres of that land which is vacant, sewered and zoned, contributed the most to the overall explanation of the dependent variable. The other measures of potential supply contributed l i t t le to the overall explanation. What is interesting to note is the increase in the explanatory power of the travel time to the CBD variable. Although the increase in explanatory power is quite small, this variable was the most significant next to the measure of vacant, sewered and zoned land. The low explanatory power of the other potential supply measures is probably a result of the high degree of correlation between these variables and the variable which measures vacant, sewered and zoned land. In general Table 16 MULTIVARIATE REGRESSION ANALYSIS PERCENT SF DEVELOPMENT BY ALL VARIABLES Dependent variable - Percent of GVRD single family development 1966-71 INDEPENDENT VARIABLES R SQUARE RSQ CHANGE B STD ERROR B F VACANT, ZONED AND SEWERED SF - ACRES 0. .24122 0, .24122. 0, .1368072E--02 0, .00117 1 , .361 TRAVEL TIME TO CBD - MINUTES 0. .25679 0, .01557 0. .8268921E--01 0, .03733 4, .906 ACCESS TO SCHOOLS 2 0. .28683 0, .03004 -0. • 2464372E-02 0, .00204 1, .453 ST LINE DIST TO CBD - MILES 0. .29452 0, .00769 -0. .5378951E--01 0, .04487 1 . .437 WHOLESALE RETAIL TRADE EMPLOYMENT 0. .29822 0, .00370 0. .8814089E--04 0. .00027 0. .108 ACCESS TO SHOPPING 2 0. .30550 0, .00727 -0. • 1174476E. -02 0. .00341 0. .119 ACCESS TO TOTAL EMPLOYMENT 2 0. .30951 0, .00401 0. . 1199301E -02 0, .00114 1 . .108 SERVICES EMPLOYMENT 0. ,3.1210 0, .00259 0. .1037121E -03 0. .00009 1. .219 ST LINE DIST TO SHOPPING 2 - MILES 0. ,31399 0, .00189 0. .7101113E--01 0, .06982 1 . .034 ACCESS TO SCHOOLS 1 0. ,31808 0, .00409 0. .6802957E--03 0. .00041 2. .715 ACCESS TO SHOPPING 1 0. ,32679 0, .00872 -0. .1122239E--02 0. .00089 1. .605 VACANT AND ZONED SF X SF DENSITY 0. ,32938 0, .00258 -0. .2778456E--03 0. .00024 1. .369 VACANT AND ZONED SF - ACRES 0. ,33260 0, .00322 0. .8524318E--03 0, .00081 1. .118 VACANT, ZONED AND SEWERED SF X SF DENSITY 0. ,33549 0. .00290 0. .2169167E--03 0. .00031 0. .488 ST LINE DIST TO SHOPPING 1 - MILES 0. ,33668 0. .00118 -0. . 3463134E-01 0. .06843 0. .256 66 - LAND USE - VACANT - ACRES 0. ,33683 0. .00015 0. .6536372E--05 0. .00003 0. .036 TOTAL EMPLOYMENT 0. 33695 0. .00011 -0. . 1267629E-04 0. .00008 0. .024 Constant 0.8615223 Overall F ratio 38.62561 Significance level 0.00001 Table 17 MULTIVARIATE REGRESSION ANALYSIS PERCENT MF DEVELOPMENT BY ALL VARIABLES Dependent variable - Percentage of GVRD multiple family development 1966-71 INDEPENDENT VARIABLES R SOUARE RSQ CHANGE B STD ERROR B • F VACANT SEWERED AND ZONED MF X MF DENSITY 0.70319 0.70319 0. .6812641E-03 0.00007 107.635 WHOLESALE RETAIL TRADE EMPLOYMENT 0.71643 0.01324 0. 8584336Er-03 Q,0Q024 12,695 ACCESS TO SHOPPING 2 0.71975 0.00332 - 0 . .7392394E-02 0,00287 6 . 6 5 3 ACCESS TO TOTAL EMPLOYMENT 1 0.72770 0,00795 -0,7025615E-Q4 0,00021 0.115 VACANT SEWERED AND ZONED MF 0,73090 0,00320 - 0 . .4917833E-02 0.00417 1 .391 SERVICES EMPLOYMENT 0.73188 0,00098 0. . 8824156E-04 0.00008 1.191 TOTAL EMPLOYMENT 0,73567 0.00378 - 0 . , 1128640E-03 0.00007 2 . 6 8 4 ACCESS TO SCHOOLS 2 0,73598 0.00Q32 Q. .2451570E-02 0.00124 3.932 ACCESS TO SHOPPING 1 0.739Q0 0.0Q302 0. 1765642E-02 0.00107 2.712 ACCESS TO SCHOOLS 1 0.74199 0.00299 - 0 . 5615504E-03 0.00037 2 . 2 6 0 TRAVEL TIME TO CBD - MINUTES 0,74295 0,00096 - 0 . 1342376E-01 0.01811 0.549 Constant -3 .771183 Overall F ratio 4,21485 Significance level 0.00001 43 the results of the multiple regression test for single family development indicate that the site characteristic combination of potential supply in acres of that land which is zoned, sewered and vacant and travel time to 2 the CBD in minutes provide the best level of explanation with an R statis-tic of about 0.25. This result tends to indicate that single family develop-ment occurs to a larger extent in those areas which have available vacant, sewered, and zoned single family land and have lower travel times by auto-mobile to the CBD. The results of the multivariate regression test for multiple family development indicate that the independent variable found to have the most explanatory power in the bivariate tests, potential supply in units of that land which is vacant, zoned and sewered, contributed the most to the multivariate tests as well. The variable which contributed the 2 next largest change to the R statistic was the amount of wholesale-retail trade employment in the subarea. This variable had the highest explanatory power of the accessibility measures tested with the percentage of multiple family development. These results are reasonable, as the test indicates that multiple family residential growth will be allocated to subareas within the region based on their relative multiple family housing poten-tial in units and their access to shopping. To test for the effects of differing municipal government boundaries on the allocation of growth it was decided to introduce dummy variables for the fifteen different municipal areas into the multivariate regression equations. The dummy variables were created by treating each municipality as a separate variable. All cases were then assigned either a 1 or 0 on all fifteen dummy variables depending upon the municipality a particular case was in. Only fourteen dummy variables were included in the initial 44 regression equations because the inclusion of all dummy variables would render the equation unsolvable. This occurs because the Kth dummy vari-able is completely determined by the first K-1 dummy variables entered into the regression equation. The results of these tests are presented in Tables 18 and 19. Table 18 presents the results for single family housing development and Table 19 presents the results for multiple housing development. The results of the dummy variable regression tests for single family housing development indicate that a measure of the municipal area in which a subarea is in contribute significantly to the explanation of the alloca-tion of single family housing development. The dummy variable for Delta had the highest level of explanatory power, contributing 0.16 to an over-2 all R statistic of 0.55. The dummy for Port Coquitlam came next, contri-2 buting 0.01 to the overall R statistic. The other dummy variables contri-buted very l i t t le to the overall explanatory power of the regression equation. What is interesting to note is that the travel time to the CBD variable which had a small level of explanatory pov/er in the multivariate 2 test without the dummy variables added almost nothing to the overall R statistic when the dummy variables were added. The results of the dummy yariable regression test for multiple family housing development indicate that a variable which measures the municipal area a subarea is in does not contribute very much to the overall explana-tory power of the regression equation. The only dummy variable which contributed significantly to the overall R" statistic was the dummy for Mew Westminster. However, this dummy variable only contributed 0.02164 2 to an overall R statistic of 0.77734. The dummy variable for Burnaby was the next highest dummy variable contributor with a contribution of 2 only 0.01237 to the overall R statistic. Table 18 MULTIVARIATE REGRESSION ANALYSIS PERCENT SF DEVELOPMENT BY ALL VARIABLES INCLUDING DUMMIES Dependent variable - Percentage of GVRD single family development 1966-71 INDEPENDENT VARIABLES R SQUARE RSQ CHANGE B STD ERROR B F VACANT, ZONED AND SEWERED SF - ACRES 0, .24122 0. .24122 0, .9361461E -03 0. .00117 •0 .639 DUMMY FOR DELTA 0, .40886 0. .16763 1, .671065 0 .51555 10, .506 DUMMY FOR POT COQUITLAM 0, .42152 0. .01267 0, .3596446 0. .67680 0, .282 ST LINE DIST TO SHOPPING 2-MILES 0, .43349 0. .01197 -0, .9149567E -01 0, .06503 1, .980 VACANT AND ZONED SF - ACRES 0. .45219 0. .01869 0, . 1318997E-02 0, .00080 2, .744 DUMMY FOR WHITE ROCK 0. .46186 0. .00967 0, .6377572E -02 1, .02681 0, .000 VACANT, ZONED AND SEWERED SF X SF DENSITY 0. .47174 0. .00989 0, .2300018E--03 0, .00031 0, .545 DUMMY FOR NEW WESTMINSTER 0. .47985 0. .00811 -1. .181597 0, .62682 3, .553 SERVICES EMPLOYMENT 0. .48739 0. .00753 0. .2073907E--03 0, .00009 5, .026 DUMMY FOR RICHMOND 0. .49328 0. .00589 0. .1835884 0, .53796 0. .116 DUMMY FOR WEST VANCOUVER 0. .49658 0. ,00330 -0. ,2842274 0. .70491 0. .163 DUMMY FOR BURNABY 0. ,49992 0. ,00334 -0. .5952601 0. .57959 1. .055 DUMMY FOR SURREY 0. .50429 0. ,00437 -0. .9119587 0. .51428 3. .144 ST LINE DIST TO CBD - MILES 0. ,50658 0. ,00229 0. .2900630E--01 0. .05116 0. .322 WHOLESALE RETAIL TRADE EMPLOYMENT 0. ,51066 0. 00407 0. .1609102E--03 0. .00025 0. .429 TOTAL EMPLOYMENT 0. ,51661 0. ,00595 -0. .4657817E--04 0. .00007 0. .386 VACANT AND ZONED SF X SF DENSITY 0. ,51873 0. 00212 -0. .2788653E--03 0. .00023 1. .423 DUMMY FOR COQUITLAM 0. ,52112 0. 00239 -0. ,5432559 0. .52640 1. .065 DUMMY FOR NORTH VANCOUVER DISTRICT 0. ,52262 0. 00150 0. 5763792E--01 0. .65464 0. .008 ACCESS TO SCHOOLS 1 0. ,52441 0. 00178 0. . 1522633E-02 0. .00076 3. .999 TRAVEL TIME TO CBD - MINUTES 0. 52826 0. 00386 0. .8025377E--01 0. .04108 3. .817 ACCESS TO SHOPPING 2 0. 53609 0. 00783 -0. 3622215E--02 0. .00315 1. ,319 DUMMY FOR VANCOUVER 0. 53765 0. 00155 -1. ,106012 0. .74805 2. .186 DUMMY FOR UEL 0. ,54175 0. 00410 -1. ,204330 0. .85628 1. ,978 ACCESS TO TOTAL EMPLOYMENT 2 0. 54341 0. 00166 0. 1871227E--02 0. .00191 0. .956 ACCESS TO TOTAL EMPLOYMENT 1 0. 54423 0. 00081 -0. 4646637E--03 0. .00032 2. ,077 ACCESS TO SCHOOLS 2 0. 55002 0. 00579 -0. 4027572E--02 0. .00303 1. ,768 DUMMY FOR NORTH VANCOUVER CITY 0. 55117 0. 00115 -0. ,4481629 0. ,77685 0. ,333 LAND USE - VACANT - ACRES 0. 55154 0. 00037 -0. .2006.549E--04 0. ,00006 0. ,114 VACANT X SF DENSITY 0. 55165 0. 00012 0. 3680496E--05 0. ,00002 0. ,041 DUMMY FOR PORT MOODY 0. 55178 0. 00013 -0. 1236871 0. ,65111 0. ,036 Constant 5.707769 Overall F ratio 5.04332 Significance level 0.00001 Table 19 MULTIVARIATE REGRESSION ANALYSIS PERCENT MF DEVELOPMENT BY ALL VARIABLES INCLUDING DUMMIES Dependent variable - Percentage of GVRD multiple family development 1966-71 INDEPENDENT VARIABLES R SQUARE RSQ CHANGE B STD ERROR B 1 -VACANT SEWERED AND ZONED MF X MF DENSITY 0. .70319 0, .70319 0-. 6568841 E-03 0. .00007 89 .255 DUMMY FOR NEW WESTMINSTER 0. .72483 0, .02164 1, .391461 0. .60365 5 .313 DUMMY FOR BURNABY 0. .73720 0, .01237 0. .4222648 0. .54734 0. .595 WHOLESALE RETAIL TRADE EMPLOYMENT 0. .74420 0, .00700 0, .7922483E--03 0. .00024 11 .252 DUMMY FOR NORTH VANCOUVER CITY 0. .74695 0. .00275 0, .6711012 0. .69905 0 .922 TOTAL EMPLOYMENT 0. .74914 0. .00219 -0. •1434157E--03 0. .00007 4 .226 SERVICES EMPLOYMENT 0. ,75323 0, .00409 0, .1958440E--03 0. .00008 5, .896 DUMMY FOR SURREY 0. ,75522 0, .00199 -0, .2617915E--01 0. .44656 0. .003 ACCESS TO SHOPPING 2 0. ,75767 0. .00245 -0. .1950441E--02 0. .00303 0, .413 ACCESS TO SCHOOLS 2 0. ,76405 0, .00638 0, .3081235E--02 0. .00141 4, .795 DUMMY FOR UEL 0. ,76561 0. .00156 -0, .9116244 0. .76464 1, .421 ACCESS TO SHOPPING 1 0. ,76833 0, .00272 0, .6460985E--03 0. .00042 2, .371 VACANT SEWERED AND ZONED MF 0. ,76987 0. .00154 -0. . 3818018E-02 0. .00458 0, .695 DUMMY FOR VANCOUVER 0. ,77210 0. .00223 -0. .3330903 0. .61826 0, .290 ACCESS TO TOTAL EMPLOYMENT 2 0. ,77383 0. ,00173 -0. . 1 747542E--02 0. ,00116 2, .261 DUMMY FOR NORTH VANCOUVER DISTRICT 0. ,77507 0. .00124 0. .5706422E--01 0. .57074 0, .010 DUMMY FOR RICHMOND 0. ,77560 0. ,00053 0. .4169512 0. ,49698 0, .704 TRAVEL TIME TO CBD - MINUTES 0. ,77615 0. .00055 0. . 1560097E-01 0. .03267 0, .228 DUMMY FOR WHITE ROCK 0. ,77648 0. .00033 -0. .2045367 0. ,97532 0, .044 DUMMY FOR PORT MOODY 0. ,77677 0. .00029 0. .3937059 0. .63307 0, .387 DUMMY FOR DELTA 0. ,77706 0. .00030 0. .2716559 0. ,47827 0, .323 DUMMY FOR COQUITLAM 0. ,77716 0. .00009 0. .1880862 0. .48796 0, .149 DUMMY FOR WEST VANCOUVER 0. ,77727 0. .00011 0. .1940317 0. ,60348 0, .103 DUMMY FOR PORT COQUITLAM 0. ,77734 0. .00007 0. .1297625 0. .63937 0, .041 -pi CTl Constant -1.888343 Overall F ratio 19.49214 Significance level 0.00001 47 In general the regression results of the dummy variable tests suggest that municipal boundaries are a significant factor in explaining the allo-cation of single family housing development, while they are not a signifi-cant factor in explaining the allocation of multiple family housing develop-ment. However, when the dummy variables are included in the single family development equation, the travel time to the CBD variable becomes insigni-2 ficant in its contribution to the overall R statistic. 9. Conclusion In Chapter two of this paper i t was stated that as a result of studies by Kaiser, Moore, and Goldberg and Ulinder the heavy reliance of land use models on the demand side of the housing market seemed questionable. More convincing behavioural research and empirical testing of this beha-vioural research was required. These statements were the foundations on which the hypotheses tested in this study were based. The hypotheses were designed to test: f irst ly, i f the supply side, criteria of the housing market identified by developers were significant in explaining the spa-tial allocation of GVRD single and multiple family housing development to subareas within the GVRD; and secondly, how well selected accessibility measures explained the spatial allocation of housing development. In this section, the relevant findings of this study with respect to each of the hypotheses tested are summarized. Hypothesis 1: The potential supply of single and multiple family housing land explains the spatial allocation of single and multiple family housing development to subareas within the GVRD. Specifically, the more accurately one is able to define the potential supply, the greater will be the explanatory precision. For example, a measure of that 48 land which is vacant, zoned and sewered will have much better explanatory precision that a measure of vacant and zoned land, or vacant land. The bivariate regression results generally support this hypothesis. However, potential supply seems to be much more important in explaining the spatial allocation of multiple family housing development than single family housing development. Also, potential supply in units is most important for multiple family housing development, while potential supply in acres is most important for single family housing development. This tends to suggest that density of development is more important to multiple family housing developers than to single family housing developers. This is definitely an area for future behavioural research and specific ques-tions on density should be included in future surveys of developers. As far as can be ascertained this variable has not been explicitly included in surveys of developers to date, although responses to questions regard-ing zoning may include some implicit regard for zoned density. The bivariate regression results generally support the statement that a more specific definition of supply will provide a better explana-tion of the spatial allocation of growth. This was found to be true for single family housing development, but not so true for multiple family housing development. For multiple family housing development a further definition of supply from that land which is zoned and vacant, to that land which is zoned, sewered and vacant is marginal. This is probably due to the fact that most land which is zoned multiple family dwelling is sewered or very close to an existing sewer. Hypothesis 2: Measures of accessibllity; specifically nearness to schools, nearness to employment and nearness to shopping, contribute l i t t le to an explanation of the allocation of residential housing development to 49 subareas within the GVRD. The bivariate regression results support this hypothesis for single family housing development, but do not support the hpothesis for multi-ple family housing development. The results for single family housing development indicate that all of the accessibility measures tested here have very l i t t l e importance in explaining the spatial allocation of single family housing development. This outcome could be a result of the high level of accessibility enjoyed by many parts of the region, rather than a direct contradiction of the theory that accessibility shapes land use. The results of the bivariate regression tests for multiple family housing development with the accessibility measures indicate that all of the accessibility measures tested here have a significant, but small role in explaining the spatial allocation of multiple family housing development. The amount of wholesale-retail trade employment had the highest level of explanatory power, access to schools using the gravity formulation with an exponent of 2 was next, followed by travel time 2 to the CBD. The value of the R statistic varied from a low of 0.05164 to a high of Q.14064. The results of the multivariate regression tests indicate that the most important variables in explaining the allocation of single family housing development were: (1) the potential supply in acres of that land which is vacant, zoned single family dwelling, and accessible to sewers and (2) the municipality in which the subarea is located. If the dummy variables representing municipal areas which were introduced into the regression equation are an adequate proxy for differing municipal supply policies, then the multiple regression results lend strong sup-porting evidence to the statement by Goldberg and Ulinder that supply 50 constraints are very critical to developers and hence to the spatial allo-cation of growth. If one disregards the significance of the dummy variables for multi-ple family development, which is quite small overall, then the results of the multivariate tests for multiple family development indicate that the most important variables in explaining the allocation of multiple family development were: (1) the potential supply in units of that land which is zoned multiple family dwelling and vacant, and (2) the amount of wholesale-retail trade employment in the subarea. The results suggest that multiple family development will be allocated to subareas within a region based on their relative multiple family housing unit po-tential and their access to shopping. The analysis discussed in this Chapter indicate that behavioural research studies can be effectively used in defining criteria to explain the spatial allocation of housing development.. Specifically, supply side criteria identified by developers as heing important in the spatial allocation of housing development were tested and found to be significant. The significance levels varied between structure types, but tend to indicate that land use models which rely heavily on the demand side of the housing market for the spatial allocation of growth may be very inadequate. These results must be qualified by the fact that they represent only a specific period, in, time, arid are not the results of dynamic time series tests. However, they do suggest that during the time period studied supply cri-teria were important in allocating regional housing development to subareas within the region. This result does not support many previous studies done outside the GVRD which have found that demand side criteria mea-sured through accessibility variables are very important in explaining 51 the allocation of growth. The implications of this analysis for policy decisions are twofold. Firstly, the analysis lends strong supporting evidence to the suggestion that municipal organizations have been effective in allocating growth to those areas where supply exists which is serviced and appropriately zoned. Secondly, policy decisions which use measures of the future spatial alloca-tion of growth based on demand oriented models may be grossly inadequate. In designing policies and future research studies, developers and govern-ment organizations should realize the extreme importance of supply and the effectiveness of the many government organizations in controlling i t . The research discussed in this chapter suggests that further beha-vioural studies of the role played by the developer, combined with analy-tical models of this behaviour, may provide considerable insight into the past and future allocation of housing development. The following chapter outlines the attempt made at combining the behavioural analyses of the developer surveys and the empirical analysis presented in this chapter into an operational model of the GVRD. 52 Chapter 4 THE TEST MODEL FRAMEWORK 1. Introduction The statistical analysis presented in Chapter three illustrates the explanatory power of the various potential supply and accessibility measures tested. However, it does not indicate the ability of these criteria to predict the future allocation of growth. Given the importance of estimating the future pattern of residential growth for local planning, private develop-ment and regional housing policy; the results of Chapter three were incor-porated into the supply side of an existing simulation model to see what explanatory power they had. This chapter describes the model framework used. The following chapter describes the extensions made to the model and the results of running the model and comparing the output to actual data. 2. General Overview of the Model The original model was developed nearly a decade ago by a group of researchers at the University of British Columbia who set out to develop a large scale simulation model for the Vancouver region.1 The researchers The model framework and its major components and objectives have been documented at some length elsewhere. This chapter is a summary of these works. The interested reader is directed to the following studies which provide a detailed review of the original model framework and subse-quent revisions. See Michael A. Goldberg, "Simulation, Synthesis and Urban Public Decision-Making," Management Science, -Vol. 20, No. 4 (December 1973) Part II, pp. 629-643; Michael A. Goldberg and Jeffery M. Stander, "Analysis of Output and Policy Applications of an Urban Simulation Model," Transportation  Research Record, Vol. 582 (1976) pp, 61-71; Michael A. Goldberg and Douglas A. Ash, "Continued Development of the Vancouver Model," Transportation 53 realized the need for a new approach to developing models, as the models which had been developed were beginning to show serious shortcomings. These models tended to be difficult to use, operated quite outside the traditional bureaucratic/political framework, and were of highly variable quality. 2 In response to these shortcomings, modelbuilders at the University of British Columbia teamed up with representatives of several levels of government to jointly develop an urban and environmental simulation model capable of providing needed policy insights. The study was called HPS (for J_nter-Institutional Pol icy Stimulator). By bringing together acade-mics and civi l servants it was hoped that more useful and realistic policy models might be designed and used. Accordingly, the objectives of the HPS project were two-fold: (1) to develop a modelling framework for model building; and (2) to develop models capable to dealing with key sub-systems of the Greater Vancouver Regional District (GVRD) urban environ-3 ment, but which could be transferable elsewhere. Figure 1 provides an overview of the various interacting model ele-ments which were to be included in the original HPS effort. As indi-Research Record, Vol. 617 (1977) pp. 55-61; and Michael A. Goldberg and H.C. David, "An Approach to Modelling Urban Growth and Spatial Structure," Highway Research Record, Vol. 435 (1973), pp. 42-53 Two papers which criticize existing models and argue for a reorien-tation of urban modelling are: Douglas B. Lee, Jr. , "Requiem for Large-Scale Models," Journal of the American Institute of Planners, Vol. 39, No. 3 (1973) pp. 163-178; and A.H. Voelker, Some Pitfalls of Land-Use  Model Building, ORNL-RUS-1 (Oak Ridge, Tennessee; Oak Ridge National Laboratory, 1975). 3See Michael A. Goldberg, "Simulation, Synthesis," pp. 629-31. 4 Ibid . , p. 632. Figure 1 DIAGRAM OF RELATIONSHIP BETWEEN THE I IPS SUBGROUPS 55 cated by Figure 1, intra-urban transportation and land use models were central to the overlapping elements. These two submodels distributed acti-vities spatially and were therefore considered to be prime vehicles for analysing the spatial impacts of various land use, transportation and environmental policies. The original researchers considered housing to be of greatest importance as residences represented the largest single user of land. Accordingly, development of a useful housing model took priority. The modelling problem, and the resulting land use model, were partitioned into four separate elements: macro supply and demand; and microspatial supply and demand. 3. General Overview of the Sub-Model Structure Lacking a suitable set of submodels to forecast macro supply and demand separately, the original HPS model assumed supply and demand 5 were equal. Demand/supply was estimated for each year in the simula-tion by a reasonably straightforward trend procedure which produced new single and multiple family housing totals for the region. Given regional totals, the microspatial components of the model allo-cated them to subareas of the region using quite separate algorithms for supply and demand. As there was no constraint that micro supply was to equal micro demand, the final step in each iterative period was to allo-cate excess micro demand to areas of excess micro supply until micro-spatial supply equalled microspatial demand. Michael A. Goldberg, Housing, Employment, Land Use and Transporta- tion: A Regional Simulation Model, Urban Land Economics Reprint Series, Report #2 (Vancouver, B.C.: Urban Land Economics Division, Faculty of Commerce and Business Administration, University of British Columbia, 1974), p. 6-8. 56 Figures 2, 3 and 4 set out diagramatically the original submodels of the HPS model which are of interest here. The four interacting models represented are: (.1) land use, including housing and employment location; (.2) transportation, including trip generation, distribution and mode split ; (.3) employment forecast: and (4) population forecast. The regional forecasts of population and employment were used to provide estimates of new economic activity and housing which were then allocated to the sub-areas by the land use models. The amount of new economic activity and the amount of new housing were allocated in the following manner. Given a travel time matrix and regional forecasts of population and employment, the HPS model first allocated eighteen different types of employment to the subareas and calculated the amount of land used.^ Next the population estimate was combined with the previous period housing activity to provide the totals of new single and multiple family housing to be located during the iteration. Then the totals of new single and multiple family housing were allocated to the subareas using an intuitive allocation algorithm based on the travel time matrix. Finally, given the new location of jobs and people, the transportation modal recalculated trips and travel times, and the model moved on to the next iteration. 4. Macro Housing Sub-Model The original macro housing model produced a figure for total single and multiple family housing development by crudely estimating the housing "Figures 2 and 4 - Goldberg, Housing, Employment, Land Use, p. 4 and 7; Figure 3 - Goldberg and Davis, op. c i t . , p. 51. ^For a detailed description of the sub-models which allocated new em-ployment, recreation facilities and open-space see: Goldberg and Davis, op. c i t . , pp. 48-50. A summary of these models based on the above work is contained in Appendix E. 57 r-R e g i o n a l S i m u l a t i o n M o d u l e R e g i o n a l T r a n s p o r t a t i o n M o d e l H o u s i n g D e m a n d Population F o r e c a s t E m p l o y m e n t Forecast H o u s i n g L o c a t i o n E m p l o y m e n t L o c a t i o n L. Land M a t r i x of Travel M o d e T r i p Trip U s e T i m e D i s t a n c e s S p l i t D i s t r i b u t i o n G e n e r a t i o n Figure 2 THE INTERACTION BETWEEN THE MODULE AND THE REGIONAL TRANSPORTATION MODEL (EH C h o n g « In M a n u f a c t u r i n g e m p l o y men 1 0H C h a n g s in r t l a l l e m p l o y m e n t <2H 0-* art C h a n g s i n c o m m e r c i a l e m p l o y m e n t C h a n g e In e m p l o y m e n t i n s o r v i C O S A l l o c o t o m a n u f a c t u r i n g l o s u b a r e a s A l l o c a l i r o l a l l e m p l o y m e n t A l l o c o t o e o m m a r e l a l e m p l o y m o n t A l l o c o t o e m p l o y m e n t In s o r v i c o L a n d a b s o r p t i o n c o e f f i c i e n t s a n d x o n l n g r e s t r i c t i o n s by u s e end t u b o r e a Change in l e n d U S B b y o c t l v l t y e n d s u b o r e a C h o n g o in Dat ar m i n e p o p u t a l i o n h o u s i n Q d a n a n d | A l l o C O t e , , c l h o u s i n g c e m o n o y - ^ l o s u b o r e o s C h o n t j u in d e m a n c f c r ro c r a o t l o n a ! l o n t A l l o c o t o r e n r e a t l o n o l l a n d to s u b o r e a a r - A g r i c u l t u r a l l a n d — F o r o s t ' y cnO f i s h i n g l a n d U r b a n v a c a n t l a n d U r b a n under u l l l i z s d l a n d (A ) Employment changes from Economic Model ( B ) Change in Population from Population Model Figure 3 LAND USE MODELS CO A e c s i g i b i l i i y lo vmptovmint , n w smploymgrtt , s h o p p i n g , i c h c o l i t r © io> changa in population dtntity percsnf ntw femlly un i t * | ff om popul , m o d s l P l (DA f a m i l i e s d i s -s c t i s f i o d with c u r r e n t housing r v m o v o l i caused by m c r l u t f o r c s i l r tmcva l > teres d by i r .u11rIoJ or c o m r n K C i o l O i p o n s i o n incomo d i i t . - f r o n ocon. m o d e l ( S H e v s t a g e Income p e c u l a t i o n cge Clst.O f rom p o p . m o d e l fa.-nily a l i o d i l l , f rom pop . m o d o l % bousing dtmand by i , k fEND IITERATION/ updott ell lor.d vts t end vccor.t lard Invantorlos co lcutat i en c v : r e n a tneuno by I updolo populollon b y i . k , | updoto houaing by l . k . J total total d t m o n d do m and — tn units by i. k . J Y E S ? >or olH.fc.i MO A cumulate excots damond e x c e u wppfy 0-vcconey raft by k,l permittee; dsnsity by 1.7 pro soiling construction! - / C N dsnsfly b y r \ J J i . •, i 1 jiuild hooess, updeto land v a r l e b l o i lotc l 1 up ply pe l sn l l a i supply «• In units in e c r t t by » , » . J by l , k , | move X D j up o ct rue turf etecs housing by l . i j bgltt by' u n r poflcy docUton .YES redistribute X D . over districts ttlth xs!,h dovin e valuo c l d t i v a c a n t any use [lOnifig e l o i i n b y j i - I, 2...JM A X k - I, 2,3 i - I, 2.... 3 I - n - I,.. 5 SUB AREAS HOUSING STRUCTURE TYPES HOUSING VALUE CLASSES ZONING C L A S S E S / T T N upvjor 6 filttfmg [ I I f—Wfrom l o w . i i - 0 » / | la mlddlo <qlut 1 dounner d 111tering rats 1 o c c a i E i b i l l t y to shopping, i choe l s , employmsnt by ] O K C O S S tupply from prtviout yoar by i , s . f population by l . k . l Figure 4 f ju t t ing homing units by l . k , j p o p u l a t i o n 1 ^  f^7\ d e n s i t y by ) r~VV K i D — • © kz) damol i l ien rots for housing HOUSING MODEL cn to 60 unit increment directly from the population sub-models which estimated annual increments to the stock of households. Equating household forma-tion with housing development was a quick and easy way to derive forecasts of the amount of housing development, but did not allow for the existence of vacancies. Accordingly the next phase of model development included vacancies in the macro sub-model. New macro supply was changed to equal the number of new households plus a demand for vacancies. The demand for vacancies was introduced g to allow for inventories to meet short-run adjustments. Equation (.1) below sets out the actual supply relationship used: NSt = TNH, - THHt_1 x VACRAT,(THH,) - VACRAT,^ (THH,^) (1) where NS, = total new supply for the period t THH, = total households in period t and t-1 VACRAT, , i = weighted average vacancy rate over the preceding three ' ~ periods. If NS, was negative then a small number of units were s t i l l built. This reflected the fact that the construction of new residential units does not stop even i f there exists a large inventory of unsold or unoccu-pied units. The initial approaches described above were largely ad hoc procedures which disaggregated the total new housing stock into total new single and multiple family housing stock for the region. The next phase of model development improved on these ad hoc techniques by developing two regression Goldberg and Ash, op. c i t . , p. 56. 61 equations, one for single family, and one for multiple family, which re-placed the ad hoc macro forecast and allocation procedures in the model. Equations (2) and (3) described below replaced equations (1) in the g model structure. HS™ = 0.139HSIJ_1 + 0.397HS^_2 + 0-095P0Pt_1 - 0.047P0Pt_2 (2) (0.132) (0.087) (0.039) (0.038) R2 = 0.358 F Statistic (5,107) = 100.443 HS^  = -31.0 + O ^ r l S ^ - 0.129HS|_2+ 0.051P0P, + 0.070P0Pt_1 + 0.045P0Pt_2 (0.112) (0.117) (0.023) (0.025) (0.023) o (3) R6 = 0.894 F Statistic (6,106) = 283.939 where HsT... n f o = multiple family housing starts for periods t, t-1, t , T > i , w t _ 2 f o r t h e r e g i o n HS s 1 . - , t ? = single family housing starts for periods t, t-1, T . , T > I , W T _ 2 F Q R T H E R E G I O N POP, ,_-| ,_2 = population for periods t, t-1, t-2 for the region. This is the version of the macro housing sub-model which is used in the present version of the HPS model. 5. Microspatial Housing Sub-Models The three original microspatial housing submodels, demand, supply and market resolution, are presented diagramaticalTy in Figure four, and are described in detail below. ''Ibid., p. 57. Since these equations formed part of a large simulation system, the independent variables had to be capable of being forecast in-ternally. Consequently, monetary and financial variables such as interest rates, money supply and other measures of credit conditions could not be used since they could not be generated within the model. The equations were based on pooled cross-section time-series data on housing starts compiled by Central Mortgage and Housing Corporation for the GVRD. 62 a. Demand. The original allocation of total demand to the subareas was done on the basis of an allocation function which contained the follow-ing variables: access to employment, access to shopping, size of the cur-rent housing stock, average family size, income, age distribution and the i K rate of household formation. The resulting demand D.' was demand in sub-area j , for housing type K and value class i . This process was an ad hoc intuitive formulation which remains unchanged in the present version of the model. b. Supply. The original allocation of total supply to the subareas was done on the same basis as demand except that the following variables were used in the allocation function: actual and allowable densities, available land, accessibility to employment, accessibility to shopping, ex-i K cess supply, and the number of occupied units. The resulting supply, S.' was supply by subarea j , structure type K, and value class i . This alloca-tion procedure was a largely ad hoc intuitive formulation based on rules of thumb suggested by the literature and in common use in the region. The functional forms of the variables were essentially unproven hypotheses about the likely relationships between the zonal variables and housing development. The major problem with these rather crude allocation methods was the demolition of existing improvements as the older core areas, or newer under improved areas, approached the economic redevelopment stage. 1 0 The redevelop-ment of these areas could not be adequately modelled by the original model. The original researchers found this problem difficult to model except by This is a rather complex problem which is important for models of Canadian cities. For example see: Robert W. Collier, Contemporary Cathe- drals (Montreal, Quebec; Harvest House, 1974); and City of Vancouver, Urban Renewal Study (Vancouver, B.C.: City of Vancouver, Planning Depart-ment, 1969). 63 direct policy intervention.1 1 This type of approach led to no change, or a slight increase in density, in areas which were actually being developed at much higher densities. This was a serious weakness of the original sub-model formulations. After studying a number of areas in the region which had been rezoned, the HPS researchers established that a demolition rate of 2-3% per year of the stock prevailed over the previous decade in areas which were rezoned and subsequently redeveloped. The researchers working on the model developed a demolition algorithm which mimicked the demolition process by comparing actual density to the allowable density and the unsatisfied demand from the previous iteration. This demolition algorithm was combined with the intui-tive allocation algorithm described previously to produce the supply by subarea, value class and structure type. This was the stage of development of this sub-model which existed when the present work began. A detailed summary of the revisions to this sub-model and the results of testing various versions of the model are presented in Chapter five. c. Market resolution. In the original model formulations, macro demand 12 and supply were assumed to be equal. However, differences between supply and demand by structure type and value class for each subarea were reconciled by cumulating excess demand and reallocating it to areas with excess supply. Excess demand was first allocated to other subareas with similar housing (by type and class). If no similar housing was available, demand was Goldberg and Ash, op. c i t . , p, 57. Goldberg, "Housing, Employment, Land Use," p. 7. 64 allocated to those areas that had housing of the same value class, but any structure type. If there was no such housing available, the excess was allocated to subareas with the originally desired structure type, but the next lower value class. This process continued until all excess de-mands were allocated. If there was excess supply in any subareas, the excess housing was assigned to the next lower value class to mimick the effects of competition and price cutting. In this way excess supply moved down through the value classes. Excess demand, however, moved across structure types within the same value class, unless no housing existed in any subarea of the desired value class, in which case demand moved down one value class and then across the structure types again i f necessary. This market mechanism remains unchanged in the present version of the model. 6. Extensions The revised HPS model, as described in the foregoing sections of this chapter, was the urban model used to test the empirical results of Chapter three. The empirical results of Chapter three were incorporated into the microspatial supply sub-model described in this chapter to test their ability to predict future patterns of urban growth, and to further develop the microspatial supply sub-model with the results of actual be-havioural studies. The following chapter describes the method used to incorporate the results of Chapter three into the microspatial supply sub-model, and also describes the results of testing the output, of various versions of the overall model against actual land-use data for the 1971-1975 period. 65 Chapter 5 TESTING MICROSPATIAL SUPPLY REVISIONS 1. Introduction To observe the behaviour of the model described in Chapter four with microspatial supply revisions incorporating the results of Chapter three, four versions of the model were formulated and tested. This chapter first describes these versions of the model, and then presents the results of testing their simulated output with actual data. The chapter concludes with a comparison of these results and the results of other studies which have tested simulated output against actual data. 2. Models Tested a. Model 1 - The Original Model. This was the original model as described in Chapter four. It was based on largely ad hoc formulations de-rived from intuition and rules of thumb in common use in the region, b. Model 2 - Code and Data Update. This version followed directly from the original model with a number of minor changes. Firstly, minor coding errors were corrected and the model subjected to careful comparison of the computer code and the underlying concepts. Secondly, the data base of the model was updated from 1970 to 1971 to make use of the 1971 GVRD land use data and the zoning and sewer data described in Chapter three. Finally, the land supply variable for each subarea in the microspatial supply allocation routines was changed from vacant land to vacant, zoned and sewered land. 66 c. Model 3 - New Regression Equations. The'ad_ hoc micro spatial supply equations of Model 1 were replaced by two single equation estima-tors which were derived from the results presented in Chapter three. The microspatial supply allocation function was thus reduced to the following two equations: PCDEV^  = 0.189 + 0.00182(.P0TSUP .^) R2 = 0.246 F(2,165) = 51 ,208 (1) (0.00025) PCDEV1? = 0.304 + 0.0007(P0TSUPm. ) R2 = 0.703 F(2,165) = 371 ,964 (2) J (0.00004) 3 Z where: ,s PCDEV1. = percentage of 1966-1971 single family housing development in J GVRD that was accounted for by subarea ,j PCDEVm. = percentage of 1966-1971 multiple family housing development J that was accounted for by subarea j P0TSUP..= potential supply of land for single family development in J subarea j as given by the number of acres of properly zoned, sewered and vacant land in j P0TSUP™ = potential supply of land for multiple family development given J by number of acres of properly zoned, sewered and vacant land in subarea j and by the allowable density of development. d. Model 4 - New Regression Equations with Dummies. This version sf of the model builds directly on Model 3 with an important change: PCDEV ,^ was changed so that i t was a function of the municipality within which the development takes place as well as the P0TSUP variable. The rationale for this specification was derived from the behavioural work described in Chapter two and the empirical analysis presented in Chapter three. This work suggested that municipal government constraints were considered by developers to be a significant factor tn selecting the location for develop-ment. As a result of these findings, dummy variables for municipal areas 67 were introduced into the allocation equations of Model 3 to produce the following two microspatial allocation equations: PCDEV^ Jt where: PCDEV POTSUP s f j t sf jt DUMMY1 DUMMY2 DUMMY3 DUMMY4 DUMMY5 DUMMY6 DUMMY7 DUMMY8 DUMMY9 DUMMY!0 DUMMY11 DUMMY!2 0.229 + 0.0017 POTSUP !^ - 0.359 DUMMY1 - 0.508 DUMMY2 (0.00024) J t (0.283) (0.303) + 1.608 DUMMY3 - 0.789 DUMMY4 - 0.371 DUMMY5 - 0.191 DUMMY6 (0.313) (0.4191 CO.512) (0.315) + 0.730 DUMMY7 - 0.173 DUMMY8 - 0.094 DUMMY9 - 0.0495 DUMMY 10 (0.524) (2.33) (0.233) (0.350) + 0.834 DUMMY11 - 0.453 DUMMY12 (0.869) (0.523) fT = 0.451 F(1.4,153) = 9.167 (3) percent of 1966-71 single family development occurring in subarea j potential supply of land measured by vacant, zoned and sewered acres in subarea Burnaby Coquitlam Delta New Westminster North Vancouver City North Vancouver District Port Coquitlam Surrey Vancouver West Vancouver White Rock University Endowment Lands 68 Dummy variables proved to be insignificant for the other municipalities in the region and were not included. Using dummy variables did not materially improve the explanatory power of equation 2 and it remained unchanged from Model 3. PCDEVmI = 0.304 + 0.0007 (POTSlrf). (4) 3 Z (0.00004) J t R2 = 0.703 F(2,165) = 371.964 where: rnf PCDEV., = percent of 1966-71 multiple family development occurring J in subarea j P0TSUPm£ = potential supply of multiple family units in subarea j J as measured by appropriately zoned, sewered and vacant land and the existing multiple family density in j . e. Model 5 - Model 4 With Actual Macro Data. The four models des-cribed previously all relied on a macro supply forecast which was allocated to the subareas. However, tests of this macro forecast with actual data over the period 1972-1976 indicated that the forecast was not very accurate as Table 20 indicates, the forecasts were low in every year for both single and multiple family units. The single family forecast was the worst with up to a 44% deviation. The multiple family forecast was not as bad, although deviations ranged from 9% to 35%. As a result of the poor macro model performance, Model 5 was developed to isolate the microspatial model from poor macro model performance. This model is identical to Model 4 except it uses actual data in place of the macro housing forecasts. 3. Testing the Models As the five models described previously were based on 1966r71 data, more recent data was required to test the simulation output of the models. 69 Table 20 MACRO MODEL COMPARISONS YEAR ACTUAL SF COMPLETIONS MF MODEL COMPLETIONS . % DEVIATION SF MF SF MF 1972 6073 8103 4615 6752 -0.23 -0.17 1973 7088 7865 3998 6715 -0.44 -0.15 1974 5451 6586 4074 5584 -0.25 -0.15 1975 5762 6070 4256 5524 -0.26 -0.09 1976 6751 7955 4374 5176 -0.35 -0.35 SOURCE: CM.H.C. Housing Statistics 70 The required data was obtained from the Greater Vancouver Regional District in the form of 1975 land-use and housing data for the subareas used in the tests. To test the relationship between the simulated output and the actual data, the models were run for four simulated years beginning with 1972 and ending with 1975. The results of the simulations were then compared with the actual data by running the following regression tests: < 1 9 7 5 = a l + b i < i 9 7 5 + »1 <5> P H j ! l975= a2 + b 2 < ! 9 7 5 + "2 ^ where: sf PH j -j = predicted stock of single family housing in subarea j in 1975 sf AH. -|gy5 = actual stock of single family housing in subarea j in 1975 nrf PHj ig^g = predicted stock of multi-family housing in subarea j in 1975 m-P AHj .jg-^ = actual stock of multi-family housing in subarea j in 1975 a. ,b.j = parameters to be estimated u. = error terms. The results of the regression tests described above are presented in Table 21. These tests indicate that all the models performed well as 2 the R statistics are all high and the F statistics are all significant at the 0.001 level. Table 22 presents other measures of goodness of f i t such as Theils inequality coefficient. Spearman's rank correlation coef-ficient and several other measures of error terms which generally support the results presented in Table 21. Table 21 MODEL TEST REGRESSION RESULTS FOR STOCK OF UNITS Dependent Variable - Model Prediction Independent Variable - Actual Data TEST Stock of Single Family Units Model Standard Error of Estimate Significance Level of F Stock of Multi-Family Units Model 1 2 3 4 5 Intercept Coefficient 1 0, .973 0.948 317, .54 2804.91 0.001 -7. .086 0.898 2 0. .970 0.941 375, .98 2493.61 0.001 104. .716 1.003 3 0. .974 0.947 358, .02 2864.15 0.001 91. .591 1.023 4 0. .976 0.954 341. .48 3207.19 0.001 72. ,872 1.033 5 0. ,976 0.952 347. .06 3099.42 0.001 78. ,500 1.032 0, .978 0, .956 451, .200 3337, .81 0. .001 46. .402 0. ,891 0. ,991 0. .981 296, .691 8145. .20 0, .001 -42. .108 0. ,916 0. ,990 0. .980 286, .569 7632. .18 0. .001 -6. .296 0. ,856 0. 989 0. .978 301, .254 6920. 60 0. ,001 -1. ,985 0. 857 0. 986 0. ,973 337. ,045 5615. ,54 0. .001 60. ,601 0. 864 Standard Error of Coefficient 0.017 0.020 0.019 0.018 0.019 0.015 0.010 0.010 0.010 0.012 (N = 157) Table 22 MODEL TEST RESULTS ACTUAL AGAINST MODEL FORECASTS FOR THE STOCK OF UNITS TEST Stock of Single Family Units Model 1 2 " 3 4 5 Stock of Multi-Family Units Model 1 2 3 4 Spearman Correlation 0.9469 0.9668 0.-9713 0.9720 0.9721 0.8772 0.9101 0.9040 0.8975 0.8761 Mean Error 153.2 •108.8 •125.3 •120.3 -124.6 49.1 116.3 132.8 127.7 59.2 Mean Square Error 257.3 229.5 224.3 204.1 209.1 277.0 205.7 239.8 247.7 266.1 Root Mean Square Error 382.3 389.1 378.8 363.3 369.8 517.4 373.1 459.9 466.2 465.8 Theil U Statistic 0.097 0.091 0.088 0.085 0.086 0.108 0.078 0.099 0.100 0.099 Fraction of Error Due to: Bias 0.061 0.078 0.110 0.111 0.114 0.009 0.097 0.083 0.075 0.016 Different Variation 0.091 0.017 0.040 0.056 0.054 0.158 0.224 0.471 0.447 0.389 Different Co-Variation 0.748 0.905 0.850 0.834 0.832 0.833 0.679 0.446 0.478 0.595 CN - 1571 73 However, using regression tests, such as those described by equations 5 and 6, which are based on the stock of units forecast over a short period of time is not really an adequate test of the performance of the models. Because of the short forecast period and the many micro areas used much of the stock in each subarea in 1975 is made up of the 1971 stock. A more rigorous test of the performance of the models is a comparison of the simulated change in the stock over the 1972 to 1975 period with the actual change in the stock. By using the change in the stock the dampening effect of the large stock which remains unchanged is eliminated and the ability of the models to properly place new units is more adequately tested. To test the models simulated change in the housing stock with the actual change in the housing stock, the following regression tests were run: A P Hj ! l 9 7 5 = a3 + b 3 A A Hj ! l975 + 3^ ^ A P Hj ! l 9 7 5 = a4 + V A H j ! l 9 7 5 + *4 ^ where: sf APH. l p 7 ( . = predicted change in stock of single family houses in J ' , 3 / 0 subarea j between 1971 and 1975 sf AAH. l p 7 t . = actual change in stock of single family houses in sub-J ' area between 1971 and 1975 rnf APH. , p 7 [ - = predicted change in stock of multi-family housing in J ' l 3 / 0 subarea j between 1971 and 1975 nrf AAH. i q 7 , - = actual change in stock of multi-family housing in sub-J ' ^ / 3 area j between 1971 and 1975 a->b. = parameters to be estimated y. = error terms 74 As can be seen from Tables 23 and 24, the results of these tests in-dicate that the models did not predict the change in stock of units as well as the stock of units. The initial ad hoc model was the best at pre-2 dieting the change in stock, but had an R of only 0.209 compared to an 2 R of 0.948 for the stock of single family units. For the change in 2 multiple family units, Model 2 performed the best, but had an R of only 2 0.120 compared to an R of 0.956 for the stock of multiple family units. Overall, Model 4 performed the most consistently, followed closely by Model 5. From a preliminary inspection of the results of Tables 23 and 24 i t may seem strange that Model 5 is less consistent than Model 4 when the macro supply figures of Model 5 are correct and the figures for Model 4 are incorrect. However, this discrepancy is easily resolved when one considers that the stock in period "t" is composed of the stock in period "t-1" plus the new supply minus demolitions. Since the new macro supply is known, and the stock in "t-1" is known, the inconsistency must lie in the amount and location of demolitions. This was found to be the case, and is a serious problem with the models which is discussed in detail in the following chapter. In general, the results presented in Tables 21? 22, 23,and 24 are not very encouraging. Although improvements did occur in the performance of the models, the measures of performance presented in these tables tend to indicate that the increase in model performance was marginal. Conse-quently, one wonders whether the increase in model performance was worth the effort. I feel that although the improvements may not seem all that impressive, the unquantifiable increase in knowledge of the inner workings of the models and the modelling process were by themselves justifiable 75 reasons for pursuing an increase in performance. Also, when compared to other studies which have compared simulated model output with actual data, the results presented here are not as discouraging. 4. Comparison of the Results with Other Studies An extensive review of the modelling literature produced a large number of studies which reported on the design and calibration of models on historical and cross-sectional data. The types of models varied from 1 2 simple regression models to quite complex linear programming and simul-3 taneous equation models. The methods of testing the models varied, but the results of the calibration tests were usually quite impressive. However, only two studies could be found which reported on the testing of simulated output data with actual data. The first study which compared simulated data with actual data was conducted by A.H. Voelker at the Oak Ridge National Laboratory.4 Although the tests of the simluated data with actual data are not described in detail, i t appears that the test period is less than ten years, and that over this period the model consumed 20% more land than was actually con-sumed. Voelker concludes by stating that future testing of the model Milliard B. Hansen, "An Approach to the Analysis of Metropolitan Residential Extension," Journal of Regional Science, Vol. -3, No. 1 (1961) pp. 37-55. ? John D. Herbert and Benjamin H. Stevens, "A Model for the Distribution of Residential Activity in Urban Areas," Journal of Regional Science (Fall 1960) pp. 21-36. 3 . . . . . . . • . -Donald N.Steinnes and Walter D. Fisher, "An Econometric Model of Intra-urban Location," Journal of Regional Science, Vol. 14, No. 1 (1974) pp. 65-80. 4 A.H. Voelker, "A Cell-Based Land-Use Model," ORNL/RUS-16 (Oak Ridge, Tennessee: Oak Ridge National Laboratory, May 1976). Table 23 MODEL TEST REGRESSION RESULTS FOR CHANGE IN THE STOCK OF UNITS Dependent Variable - Model Prediction Independent Variable - Actual Data Standard Significance Standard TEST R R? Error of Estimate F Level of F Intercept Coefficient Error of Coefficient Change in Single Family Units Model 1 0. ,457 0, .209 253.802 40.954 0.001 -140.090 0.348 0.054 2 0. 116 0, .013 94.284 2.112 0.148 128.376 0.029 0.020 3 0. 286 0 .082 119.268 13.795 0.001 143.541 0.095 0.026 4 0. 392 0, .154 141.319 28.129 0.001 137.157 0.161 0.030 5 0. 359 0 .123 139.819 22.866 0.001 141.844 0.143 0.030 Change in Multi-Family Units Model 1 0. 447 0, .120 446.568 38.721 0.001 87,160 0.459 0.074 2 0. 713 0, .508 169.495 160.495 0.001 46.252 0.352 0.028 3 0. 422 0, .178 146.376 33.588 0.001 83.735 0.140 0.024 4 0. 373 0, .139 127.711 25.088 0.001 88.100 0.143 0.029 5 0. 354 0, .126 251.614 22.293 0.001 143.144 0.196 0.042 (N = 157) Table 24 MODEL TEST RESULTS ACTUAL AGAINST MODEL FORECASTS FOR CHANGE IN THE STOCK OF UNITS Mean Root Mean Theil Fraction of Error due to: Spearman Mean Square Square U Different Different TEST Correlation Error Error Error Statistic Bias Variation Co-Variation Change in Single Family Units 1 0. ,1256 153, .2 257.3 382. .2 0. .557 0.161 0.054 0.785 2 0. ,1256 -108. ,8 229.5 389. .1 0. ,730 0.078 0.511 0.411 3 0. ,4148 -125. .3 224.3 378. ,8 0. ,672 0.110 0.432 0.458 4 0. ,4738 -120. ,3 204.1 363. ,3 0. ,626 0.110 0.367 0.523 5 0. ,4632 -124. .6 209.1 369. ,8 0. ,637 0.114 0.366 0.520 Change in Multi-Family Units Model 1 0.2504 49.08 277.0 517.4 0.479 0.009 0.001 0.990 2 0.4790 116.3 205.7 373.1 0.455 0.097 0.424 0.479 3 0.4772 132.8 239.8 459.9 0.618 0.083 0.493 0.424 4 0.4526 127.7 247.7 466.2 0.607 0.075 0.410 0.515 5 0.4629 59.23 266.1 465.8 0.533 0.016 0.215 0.769 (N = 157) 78 output with actual data is a high priority, but awaits the development of 5 .improved data bases. The second study which compares simulated data with actual data was conducted by Professor Stephen Putman at the University Pennsylvania. This study was much more detailed than Voelker's study and compared the output from Putman's model and the widely used EMPIRIC model with actual data. Both of these models were calibrated for the Minneapolis - St. Paul region and were run for the period 1960-1970. The results of testing the output of these models with actual data for the stock of housing by 7 2 income class are presented in Table 25. Although the R statistics are quite high, ranging from 0.699 to 0.844, they refer to the stock of housing rather than the change in the stock of housing. As suggested earlier in this chapter, a much more demanding test would be on the change in stock between 1960 and 1970. A number of national econometric models have also been subjected to 8 tests of simulated data against actual data. In general, the results of these tests have been rather poor, especially when one considers that these models tend to predict rather stable aggregated macro variables such as GNP. A study done by Victor Zarnowtiz at the National Bureau of Economic Research in the U.S. found that tests of simulated GNP with 51bid., pp. 17-19. c Stephen H. Putman, Laboratory Testing of Predictive Land-Use Models: Some Comparisons (Washinqton, D . C : U.S. Department of Transportation, October, 1976). 71bid., p. 32. Q See H. Theil, Economic Forecasts and Policy, Second Revised Edition (Amsterdam: North Holland Publishing Company, 1965) and Shlomo Maital, What Do Economists Know: Predicted Accuracy, Causality and Structure of  Experts' Expectations (Jerusalem: Foerder Institute of Economic Research, 1977). 79 Table 25 1960 - 1970 COMPARISONS OF EMPIRIC & DRAM: ACTUAL VS. PREDICTED Household Type EMPIRIC DRAM R2 R2 LIQ - lower income 0.918 0.750 LMIQ - lower middle 0.941 0.828 UMIQ - upper middle 0.889 0.844 HIQ - upper income 0.829 0.699 80 with actual GNP averaged errors of as much as 40% over as short a time g period as eight quarters. He also found that as the time period increased, and the variables became more disaggregated, the performance of the models declined rapidly. Considering the results of the studies discussed above, the results of testing the models described in this chapter are not as discouraging as one would first suspect. Given the highly disaggregated nature of the model output (housing by two structure types and 167 areas for four years) the results of testing the simulated output with actual data are acceptable, and are comparable to or better than other similar studies. y Victor Zarnowitz, An Appraisal of Short-Term Economic Forecasts, Occassional Paper 104 (New York, N.Y.: National Bureau of Economic Research, 1967). 81 Chapter 6 CONCLUSIONS The results of this study indicate that behavioural research studies can be effectively used in defining criteria to test in empirical models of the spatial allocation of housing development. Specifically, supply side criteria identified by developer surveys as being important in explain-ing the spatial allocation of growth were tested and found to be impor-tant. Accessibility measures which were suggested by the literature as important in explaining the allocation of housing development were tested and found to be of marginal importance. The significance levels varied between the measures tested, but tend to indicate that land use models which rely heavily on the demand side of the housing market for the spa-tial allocation of growth may be inadequate. These results must be quali-fied by the fact that they represent only a specific period in time, and are not the results of dynamic time series tests. However, they do suggest that during the time period studied supply criteria were important in ex-plaining the allocation of regional development to subareas. From a preliminary inspection of the test results presented in Chapter three it may seem strange that accessibility measures were not very important in explaining the allocation of housing development. However, i f one considers that land in the Greater Vancouver Regional District (GVRD) is widely held, and that markets are competitive, this apparent inconsistency can be resolved. The basic tenets of urban land economics suggest that in a competitive 82 market situation the most accessible housing will demand the highest economic rent and capital value. However, i f the cost of producing a marketable commodity in each location is the same, including developers' profit, then the differences in land value should soak up excess profits and make the developer indifferent to location. Developers should be indifferent to location because the price bid for land will be highest in the most accessible areas and lower in peripheral less accessible areas. Therefore, the trade-off between access and price will be identical at all locations and the developer will locate in his area of preference. If developers are mainly small operators as the developer surveys suggest,1 then they are most likely to located in areas they know which have a supply of developable land. Another possible reason for the marginal importance of accessibility in the GVRD is the relative stability of the transportation network over the last twenty years. During this period there have been no significant transportation improvements except for the opening of the Trans Canada Highway freeway in 1961. Consequently, travel patterns and accessibility have remained reasonably constant. This is in direct contrast to the U.S. experience which has involved massiye freeway building, Most of the mo-delling work done to date has been in the U.S., and therefore may over-stress the applicability of accessibility importance to other areas. While accessibility is important in models which determine the f i -nal value of housing, accessibility is not necessarily an important criteria Michael A. Goldberg and Daniel D. Ulinder, "Residential Developer Behaviour: 1975," Housing It's Your Move, Vol. II, Technical Reports (Vancouver, B.C.: Urban Land Economics Division, Faculty of Commerce and Business Administration, University of British Columbia, 1976) p. 277. 83 for developers who build housing. Developers appear to be primarily in-terested in land availability, rather than developing in accessible loca-tions . In general, the results of testing the output of a predictive urban model with microspatial supply allocation functions derived from potential supply measures were not encouraging. Although improvements did occur in the performance of the model, the results of testing simulated data with actual data tend to indicate that the improvement in model performance was marginal. Consequently, one wonders whether the increase in model performance was worth the effort. Although the answer to this question is subjective, I feel that the unquantifiable increase in knowledge of the inner workings of the model and the development process by themselves justified the effort. Also, when one considers the highly disaggregated nature of the model output (housing by two structure types and 167 areas for four years) the results themselves are acceptable, and are comparable to or better than similar studies. However, several problems remain for future study. The first problem is the availability of data. The most serious de-ficiency in the data base is the number of housing starts by subarea in the region. As a result of this deficiency, the new microspatial supply equations were estimated using changes in the stock of housing units, rather than the number of new units. Thus these equations include new additions to the stock along with demolitions and conversions of existing units. However, the allocations in the models run on single and multiple family housing starts. As a result, there is an inconsistency which needs to be resolved. There are two methods of resolving this problem. First, estimate the allocations by subarea using actual starts data, and second, 84 use the formulation devised but add a demolition and conversion algorithm. Unfortunately the data to apply either of these approaches is not available. Without accurate data on which to develop accurate demolition and conversion algorithms, the models tested in this study are continually building new units without accurately removing or converting the existing stock. As a result, two types of errors occur. Error one occurs in sub-areas where there is sufficient land to build new units, but the demolition of existing stock is also significant. In this situation the models tend to overestimate the stock because they do not accurately consider the removal of existing units. Error two occurs in subareas where there is l i t t le land for development, but there is a significant amount of demoli-tion. In this situation the models tend to underestimate development because they do not accurately consider the potential supply of land due to demolitions. Error two seems to be the most significant error as an examination of residuals produced from the tests indicates that errors are worst in the high density older areas of the region where demolitions 2 are an important factor. Similar difficulties as those described above arise because of con-versions of single detached units to higher density. Where the models predicted no building, there may have actually been a considerable amount of conversions. In such a case there would actually be a potential supply For details see: City of Vancouver Planning Department, "Demolition Report" (Vancouver, B.C.: City of Vancouver Planning Department, August 24, 1977). This study indicates that during the period January 1, 1973 to February 1, 1977 there were over 12,QQ0 housing starts in the City of Vancouver and 4,492 demolitions. Consequently, demolitions are of some importance in the allocation of growth to the .31 subareas of the GVRD which are in Vancouver. The problem is compounded because there does not seem to be any consistent pattern to the demolitions. 85 of new units, but no vacant land to build these units on. The net result of the foregoing considerations is that there is a need to understand the dynamics of the standing stock. Mot only is this required for the models described here, but for other simulation studies as well. Research studies are needed to study the demolition, renovation and conversion of the existing stock. Such activities, while not necessarily changing the number of units in the stock or the density of the stock, may have considerable impact on the character of an area. The second problem is the land absorption coefficients (LAC) which convert housing units to acres of land used. These LAC's are at the heart of the market mechanism as they are part of the tests which determine the amount of available land for development. In accurate land absorption coefficient can combine with the dynamics of demolitions to produce models which use land too rapidly or not rapidly enough. Better estimates of LAC's are needed i f the models described here, and similar simulation efforts, are to be able to forecast land use and housing allocation cor-rectly. The problems associated with land absorption coefficients can be seen from an examination of Tables 26 and 27. These tables are analogous to Tables 21 and 23, only they report on tests of the predictive accuracy of the models with respect to acres rather than units. The results are generally lower, illustrating the errors introduced by unreliable LAC's. The final problem which remains is the two short time periods over which the allocation functions were developed and the model tested. Mot only were these two periods quite short, but they were also quite differ-ent. The 1966-71 period over which the allocation functions were developed was one of steady economic growth, while the 1971-75 period was a period Table 26 MODEL TEST REGRESSION RESULTS FOR THE STOCK OF ACRES Dependent Variable - Model Prediction Independent Variable - Actual Data TEST R R2 Standard Error of Estimate F Significance Level of F Intercept Coefficient Standan Error o Coefficii Stock of Single Family Model 1 0. ,892 0. .795 118.694 602.220 0.001 17.015 0.963 0.039 2 0. ,967 0 .967 64.473 2211.064 0.001 15.773 1.002 0.021 3 0. ,970 0 .940 63.518 2446.537 0.001 5.447 1.039 0.021 4 0. ,974 0 .948 59.948 2812.053 0.001 1.586 1.051 0.020 5 0. ,973 0 .947 61.870 2776.307 0.001 2.122 1.078 0.020 Stock of Multi-Family Model 1 0, .788 0 .620 20.625 253.133 0.001 3.290 0.821 0.052 2 0, .897 0 .804 11.848 636.598 0.001 1.090 0.748 0.030 3 0, .912 0 .832 9.605 770.264 0.001 0.811 0.667 0.024 4 0, .912 0 .832 9.667 766.708 0.001 0.878 0.670 0.024 5 0, .910 0 .828 10.031 747.085 0.001 1.084 0.686 0.025 (N = 157) Table 27 MODEL TEST REGRESSION RESULTS FOR CHANGE IN THE STOCK OF ACRES Dependent Variable - Model Prediction Independent Variable - Actual Data TEST Standard Error of Estimate Significance Level of F Change in Single Family Model Model 1 0. 042 0. 002 103. 976 0.268 0. 606 19, .371 0. 069 2 0. 084 0. 007 22. 690 1.108 0. 294 29, .309 0. 031 3 0. ,163 0. 027 28. 469 4.249 0. 041 28, .266 0. 037 4 0. ,324 0. ,105 34. 846 18.190 0. ,001 26, .200 0. ,192 5 0. ,324 0. ,105 44. 391 18.191 0. ,001 33 .304 0. ,244 Multi Family 1 0. .222 0. .050 18. ,313 8.073 0. .005 5 .584 0. .274 2 0, .375 0, .141 7. ,470 25.412 0, .001 2 .428 0, .198 3 0, .372 0, .138 3. .087 24.986 0, .001 1 .375 0, .081 4 0 .370 0 .137 3, .293 25.565 0, .001 1 .462 0, .086 5 0 .373 0 .139 4, .201 25.066 0. .001 1 .813 0 .111 Standard Error of Intercept Coefficient Coefficient 0.134 0.029 0.037 0.045 0.057 0.096 0.039 0.016 0.017 0.022 (N = 157) 88 of high inflation. During the 1971-75 period the housing market took off on a major inflationary spiral, and housing types and densities changed. Consequently, the development and test periods need to be extended to longer periods so that a more consistent and applicable model can be developed. Unfortunately, the data is not available at the present time. Even i f one takes the preceding problems into account, the research described in this paper suggests that future behavioural studies of the roles played by residential developers and municipal governments, combined with analytical models of this behaviour, may provide considerable insight into the residential development process. However, the results must be quali-fied by the fact that the tests were conducted in a specific area over a short period, and are not necessarily applicable to all regions or time periods. In general, the results of this study lend supporting evidence to the suggestion that municipal governments have been effective in allocating growth by their servicing and zoning policies. Consequently, future research studies should also be directed at understanding the decision making process of these governments i f a true understanding of the development process is to be obtained. In conclusion, this study has taken a supply perspective to residential development to overcome the shortcomings of earlier demand-oriented approaches. However, the supply perspective should not be viewed as an end in itself, but rather as a part of the evolutionary process of modelling the urban environment. Demand must also be considered explicitly, and with the same detail, so that in future studies both demand and supply can be combined. BIBLIOGRAPHY 89 90 Bay Area Simulation Study (BASS). Berkeley, California: Centre for Real Estate and Urban Economics, The University of California, 1968. 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"Predicting Chicago's Land Use Pattern," Journal of the American Institute of Planners, Vol. 25, No. 2 (May 1959), pp. 67-72. Ingram, G.K., J.K. Kain and J.R. Glnn. The Detroit Prototype of the NBER  Simulation Model, New York: National Bureau of Economic Research, 1972. Kain, John F., and John M. Quigley. Housing Markets and Racial Discrimination, New York, N.Y.: National Bureau of Economic Research, 1975. Kaiser, Edward J. A Producer Model for.Residential Growth: Analyzing  and Predicting the Location of Residential Subdivisions, Chapel H i l l , N . C : Institute for Research in Social Science, University of North Carolina, November 1968. Kresge, David T. , and Paul 0. Roberts. Systems Analysis and Simulation  Models, Washington, D . C ; The Brookings Institute, 1971. Goldberg, Michael A. , and H.C, Davis. "An Approach to Modelling Urban Growth and Structure," Highway Research Record, No. 435 (1973), pp. 41-55. Goldberg, Michael A. 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Jr. "Requiem for Large-Scale Models," Journal of the  American Institute of Planners, Vol. 39, No. 3 (1973), pp. 163-178. Lowry, Ira S. A Model of Metropolis, Santa Monica, California: The Rand Corporation, 1964. Lowry, Ira S. "A Short Course in Model Design," Journal of the American' Institute of Planners, Vol. 31 (May 1965), pp. 158-166. Maital, Shlomo. What Do Economists Know: Predictive Accuracy, Causality  and Structure of Experts' Expectations, Jerusalem: Foerder Institute of Economic Research, 1977. Moore, Richard A. "A Development Potential Model for the Vancouver Metro-politan Area," unpublished M.Sc. Thesis, University of British Columbia, 1972. Nie, Norman H., C. Hadlai Hull, Jean F. Jenkins, Darin Steinbrenner and Dale H. Bent. SPSS (Statistical Package for the Social Sciences), Toronto: McGraw Hill Co., 1975. Pack, J.R. 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Residential Developer Decisions, Chapel H i l l , N.C.: Institute for Research in Social Science, University of North Carolina, April 1966. Wilson, Alan G. Urban and Regional Models in Geography and Planning, London: John Wiley and Son, 1974, 93 Wilson, A.G. , P.H. Rees and CM. Leith, eds. Models of Cities and Regions, London: John Wiley, 1977. Zarnowitz, Victor. An Appraisal of Short-Term Economic Forecasts, Occasional Paper 104, New York, N.Y.: National Bureau of Economic Research, 1967. Appendix A DEVELOPER SURVEY QUESTIONS AND TABLES OF THE RESULTS 94 95 Table A-1 QUESTION II-3 1972 DEVELOPER SURVEY I will now read you a l i s t of factors generally considered important in the location of site selection decision. Would you please indicate the relative importance of each in the same manner as before. 1. Availability of developable land 2. Room for expansion 3. Price of land 4. Size of the site 5. Nearness to major roads 6. Nearness to major shopping areas 7. Nearness to bus routes 8. Nearness to schools 9. Nearness to employment 10. Slope of the site 11. Holding qualities of the soil 12. Access to trunk sewer 13. Proper zoning Ranking (0) unimportant (1) fairly important (2) of average importance (3) very important (4) essential TABLE A-2 E v a l u a t i o n o f L o c a t i o n F a c t o r s By Developers o f S i n g l e Family D w e l l i n g s (Per c e n t 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 0 < 9 7 Access t o Trunk Sewer 1(2.2) 1(2.2) 1(2.2) 23(51.1) 19(42.2) 3.29 0.81 P r i c e of Land 1(2.2) 1(2.2) 3(6.7) 15(33.3) 25(55.6) 3.38 0.89 A v a i l a b i l i t y of Developable Land i( 2.2) 3(6.7) 9(20.0) 18(40.0) 14(31.1) 2.91 i.pp Nearness to Schools 3(6.7) 4(8.9) 9(20.0) 25(55.6) 4(8.9) 2.51 i . o i 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 Size of S i t e 9(20.5) 7(15.9) 10(22.7) 14(31.8) 4(9.1) 1.93 i . 3 0 Source: Richard A. Moore, A Development Potential Model For The  Vancouver Area (Unpublished MBA Thesis, The University of B r i t i s h Columbia, 1972), p. 64. to CT> TABLE A-3 E v a l u a t i o n of L o c a t i o n F a c t o r s By Developers o f M u l t i p l e Family Dwellings (Per c e n t o f 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 MajorRoads 4(10.5) 4(10.5) 9(23.7) 16(42.1) 5(13.2) 2.36 1.17 Nearness to Major Shopping Areas 5(13.5) 5(13.5) 12(32.4) 13(35.2) 2(5.4) 2.05 1.13 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 Source: Richard A. Moore, A- Development Pote n t i a l Model For The  Vancouver Area (Unpublished MBA Thesis, The University of B r i t i s h Columbia, 1972), p. 63. 98 Table A-4 QUESTION 6.4 1975 DEVELOPER SURVEY I will now read you a l i s t of factors generally considered important in the location or site selection decision. Would you please indicate relative importance of each in the same manner as before. 1. Availability of developable land 2. Room for expansion 3. Price of land 4. Size of the site 5. Nearness to major roads 6. Nearness to bus routes 7. Nearness to major shopping areas 8. Nearness to schools 9. Nearness to employment 10. Slope of the site 11. Holding qualities of. the soil 12. Access to trunk sewer 13. Proper zoning * 14. Character of the surrounding area (existing or potential) * 15. Other (please specifiy) Ranking (0) unimportant (1) fairly important (2) of average importance (3) very important (4) essential * Denotes a factor not included in the 1972 survey. TABLE A-5 Location Factors Unimportant Important Evaluation of Location Factors By Developers of Single Family Dwellings (Percent of Respondents in Parentheses) Fairly Average Very Importance Important Essential No Standard Response Mean Deviation (0) (2) (3) (4) Proper Zoning Price of Land 4(6.2) 3(4.6) 0(0.0) 0(0.0) 4(6.2) 4(6.2) 17(26.2) 26(40.0) • 35(53.8) 27(41.5) 5(7.7) 5(7.7) 3.32 3.23 1.08 0.96 Access to Trunk Sewer 7(10\8) 2(3.1) 3(4.6) 24(36.9) 24(36.9) 5(7.7) 2.93 1.29 Availability of Developable Land 3(4.6) 5(7.7) 5(7.7) 36(55.4) 11(16.9) 5(7.7) 2.78 1.01 Nearness to Schools 6(9.2) 4(6.2) 14(21.5) 31(47.7) 5(7.7) 5(7.7) 2.42 1.08 Size of Site 13(20.0) 2(3.1) 18(27.7) 23(35.4) 4(6.2) 5(7.7) 2.05 1.25 Nearness to Major Road 7(10.8) 11(16.9) 16(24.6) 21(32.3) 5(7.7) 5(7.7) 2.10 1.16 Character of Surrounding Area 7(10.8) 8(12.3) 19(29.2) 22(33.8) 3(4.6) 6(9.2) 2.10 1.09 Source: Michael A. Goldberg and Daniel D. Ul i n d e r , Housing: I t ' s Your Move, Vol . I I , T e c h n i c a l Reports (Vancouver: Urban Land Economics D i v i s i o n , F a c u l t y of Commerce and Business A d m i n i s t r a t i o n , The U n i v e r s i t y of B r i t i s h Columbia, 1976), p.281. tO to TABLE A-6 Evaluation of Location Factors By Developers of Multiple Family Dwellings (Percent of Respondents in Parentheses) Location Factors Unimportant (0) Fairly Important 0) Average Importance (2) Very Important (3) Essential (4) No Response Mean Stand Devia Proper Zoning Price of Land 1(2.5) 1(2.5) 1(2.5) 2(5.0) 4(10.0) 4(10.0) 15(37.5) 17(42.5) 15(37.5) 12(30.0) 4(10.0) 4(10.0) 3.17 3.03 0.94 0.97 Access to Trunk Sewer 2(5.0) 2(5.0) 2(5.0) 16(40.Q) 14(35.0) 4(10.0) 3.06 1.09 Availability of Developable Land 2(5.0) 3(7.5) 4(10.0) 19(47.5) 8(20.0) 4(10.0) 2.78 1.07 Nearness to Schools 1(2.5) 8(20.0) 17(42.5) 6(15.0) 3(7.5) 5(12.5) 2.06 0.94 Size of Site 2(5.0) 4(10.0) 10(25.0) 16(40.0) 3(7.5) 5(12.5) 240 1.01 Nearness to Major Road 0(0.0) 8(20.0) 13(32.5) 12(30.0) 2(5.0) 5(12.5) 2.23 0.88 Character of Surrounding Area 3(7.5) 8(20.0) 6(15.0) 14(35.0) 4(10.0) ,5(12.5) 2.23 1.19 Source: Michael A. Goldberg and Daniel D. Ulinder, Housing I t ' s Your Move^ Vol . I I . , Technical Reports (Vancouver: Urban Land Economics D i v i s i o n , Faculty of Commerce and Business Administration, The University of B r i t i s h Columbia, 1976), p.280. Appendix B MAP OF THE GVRD 101 102 Appendix C DETAILED DESCRIPTION OF THE INDEPENDENT VARIABLES USED IN THE EMPIRICAL ANALYSIS DESCRIBED IN CHAPTER THREE 103 104 The independent variables selected for the analysis in Chapter three and the methods used to calculate them are explained below. Measures for each of these variables were obtained for the 161 subareas used in the analysis. MEASURES OF POTENTIAL SUPPLY (.1) Measures of Potential Single Family Supply in Acres X-, — Vacant. Measures the amount of vacant land in acres for 1966. Obtained from the GVRD land use data. %2 — Vacant and zoned single family (SF). Measures the amount of land in acres which was vacant and zoned for SF uses. Calcu-lated by subtracting the amount of land in SF uses (single detached and duplex) in 1966 from that zoned for SF uses. X~ -- Vacant, sewered and zoned SF. Measures the amount of land in acres which was vacant, zoned for SF uses, and was within 500 feet of existing sewer development. Calculated by sub-tracting the amount of land in SF uses in 1966 from that zoned SF and within 500 feet of existing sewer development. (2) Measures of Potential SF Housing Supply in Units X^  -- Vacant x SF density. Measures the potential SF housing supply in units. Calculated by multiplying the existing SF density in units per acre for 1966 by the amount of vacant land in acres for 1966. Xj- -- (Vacant and zoned SF) x SF density. Measures the potential SF housing supply in units. Calculated by multiplying the existing SF density in units per acre for 1966 by the amount of land which was vacant and zoned as calculated for 1^-Xg -- (Vacant, zoned and sewered SF) x SF density. Measures the po-tential SF housing supply in units. Calculated by multiplying the existing SF density for 1966 in units per acre by the amount of land which was vacant, zoned and sewered as calculated for X^. (3) Measures of Potential Multiple Family (MF) Land Supply in Acres X7 - - Vacant and zoned MF. Measures the amount of land in acres which was vacant and zoned for MF uses. Calculated by sub-tracting the amount of land in MF uses from that land zoned for MF uses. Xg -- Vacant, zoned and sewered MF. Measures the amount of land in acres which was vacant, zoned for MF uses, and was within 500 feet of existing sewer development. Calculated by subtracting the amount of land in MF uses from that land zoned for MF uses, and within 500 feet of existing sewer development. 105 Measures of Potential MF Housing Supply in Units Xg -- Vacant x MF density. Measures the potential MF housing supply in units. Calculated by multiplying the existing MF density in units per acre by the amount of vacant land as calculated for X r X,Q-- (Vacant and zoned MF) x MF density. Measures the potential MF housing supply in units. Calculated by multiplying the existing MF density for 1966 in units per acre by the amount of land which was vacant and zoned as calculated for Xy. X,-,-- (Vacant, zoned and sewered) x MF density. Measures the poten-tial MF housing supply in units. Calculated by multiplying the existing MF density for 1966 in units per acre by the amount of land which was vacant, zoned and within 500 feet of existing sewer development as calculated for Xg. MEASURES OF ACCESSIBILITY Nearness to Schools X-J2-- Service employment. Measures the number of people employed in service industries within the subarea. Obtained from 1971 Census information contained in the HPS data base. X 1 3 ~- Accessibility to schools 1. Measures the accessibility to ser-vice employment by the accessibility potential formulation described in Appendix B. The activity variable used was ser-vice employment and the distance exponent'was set at 1.0. X-,,— Accessibility to schools 2. Same calculation procedure as X^^ except that the distance exponent was set at 2.0. Nearness to Employment X-.(--- Total employment. Measures the number of people employed in each subarea. Obtained from 1971 Census information contained in the HPS model data base. X, f i -- Accessibility to employment 1. Measures the accessibility to total employment by using the accessibility potential formula-tion described in Appendix B. The activity variable used was the total employment of the subarea and the distance exponent was set at 1.0. X 1 7 - - Accessibility to employment 2. Same calculation procedure as X l c except that the distance exponent was set at 2.0. 106 (3) Nearness to Shopping X,p-- Travel time to the CBD. Measures the travel time to the CBD in minutes. Extracted from the HPS model travel time matrix of automobile travel times between subareas within the GVRD. X-.Q-- Straight line distance to the CBD. Measures the straight line distance in miles to the central business district'as defined by the intersection of Georgia and Granvilie. streets. X^n— Straight line distance to closest large shopping area. X^g and X20 measure the distance in miles in large shopping areas. These two variables were calculated by identifying the large shopping areas in the GVRD, plotting them on a map, and then measuring the straight line distance in centimetre between the centroid of each subarea and the two closest shopping areas. The distance in miles was obtained by multiplying the centimetre distance by the scale on the map. Xp-,-- Straight line distance to the second closest large shopping  area. Measurement of this variable explained in X^^ above. X ? ? - - Wholesale and retail trade employment. Measures the number of people employed in wholesale and retail industries within the subarea. Obtained from 1971 census information contained in the HPS model data base. X ? o _ - Accessiblity to shopping 1. Measures the accessibility to total school employment by using the accessibility potential function described in Appendix B. The activity variable used was the amount of service employment in the subarea and the distance exponent was set at 1.0. Xp^— Accessibility to shopping 2. Same calculation procedure as X^o except that the distance exponent was set at 2.0. Descriptive statistics for these variables are presented in Tables C-l , C-2 and C-3. 107 Table C-l DESCRIPTIVE STATISTICS MEASURES OF POTENTIAL SINGLE FAMILY HOUSING SUPPLY VARIABLE Potential Supply in Acres MEAN STANDARD DEVIATION LOW HIGH X-|: Vacant 1275. 98 2551.75 0. .00 14568. 64 X^: Vacant and zoned SF 487. 32 550.30 0. .00 3084. 83 X~: Vacant, sewered and zoned SF 252. 67 293.67 0. .00 1279. 74 Potential Supply in Units X^: Vacant x SF density 4226. 61 8219.19 0 .00 56435. ,64 X^: (Vacant and zoned SF) x SF density 2081. 07 2084.99 0. .00 12259. .08 X f i: (Vacant, sewered and zoned SF) x SF density 1280. 51 1446.35 0 .00 7285. .18 108 Table C-2 DESCRIPTIVE STATISTICS MEASURES OF POTENTIAL MULTIPLE FAMILY HOUSING SUPPLY VARIABLE MEAN (1) Potential Supply in Acres X ? : Vacant and zoned MF 13.36 Xg: Vacant, sewered and 13.12 zoned MF STANDARD DEVIATION 29.67 29.62 LOW 0.00 0.00 HIGH 188.46 188.46 (2) Potential Supply in Units X g : Vacant x MF density 5096.22 X1Q:(Vacant and zoned MF) 477.57 x MF density X-|-|: (Vacant, sewered and 473.61 25093.70 0.00 1943.02 0.00 1943.33 0.00 310311.75 20324.25 20324.25 zoned MF) x MF density 109 Table C-3 DESCRIPTIVE STATISTICS ACCESSIBILITY MEASURES 726.96 VARIABLE MEAN (1) Nearness to Schools X-j2:Service employment X-^Access to schools 1 X-|^:Access to schools 2 (2) Nearness to Employment X-jgiTotal employment X-jg:Access to employment 1 X-|7:Access to employment 2 (3) Nearness to Shopping X-|g:Travel time to CBD X- iq:Straight line distance | y to CBD X ? r ):Straight line distance to closest large shopping X?-, :Straight line distance to second closest large shopping X??:Wholesale and retail trade employment X22=Access to shopping 1 X24:Access to shopping 2 STANDARD DEVIATION 1299.23 3134.12 9925.50 3895.76 LOW HIGH 26.83 9.94 2.39 4.14 516.28 4078.02 312.58 763.71 2802.64 5316.95 21648.08 8182.71 1640.36 1500.97 11.81 6.01 1.54 1.92 983.86 1637.20 293.05 0.00 28718.00 4744.5 22497.84 127.69 279.64 0.00 0.20 0.20 0.98 5306.68 0.00 43202.00 10365.55 46398.06 8941.61 53.50 25.59 7.56 11.020 0.00 8030.00 1859.89 8999.89 47.29 1799.08 Appendix D CALCULATION OF THE ACCESSIBILITY MEASURES 110 I l l The procedure used to calculate accessibility in this study was simi-lar to that used in 1959 by Walter Hansen.1 Specifically, the formulation states that the accessibility at point 1 to a particular activity at area 2 (say employment) is directly proportional to the size of the activity at area 2 (number of jobs), and inversely proportional to some function of the distance separating point 1 from area 2. The total accessibility to an activity, such as employment, at point 1 is the summation of the accessi-bil ity to each of the individual areas around point 1. Therefore, as more and more jobs are located nearer to point 1, the accessibility to employ-ment at point 1 will increase. This formulation is known as the gravity or potential concept of interaction,^ and can be expressed generally by the following mathematical formulation: 1A2 T l-2 where -|A? is the relative measure of accessibility at Zone 1 to an activity in Zone 2; Sp equals the size of the activity in Zone 2; i . e . , number of jobs, people etc.; T-j g equals the travel time or distance between Zones 1 and 2; x is an exponent describing the effect of the travel time be tween the zones. If there are more than two zones involved the formula becomes: S S S 2 3 n A, = — + ~ + 1 j X ' Tx ' • • • Tx ' 1-2 11-3 ' l-n n = number of zones. This was the formula which was used to calculate the variation in accessibility between areas. Walter G. Hansen, "How Accessibility Shapes Land use," Journal of the  American Institute of Planners, Vol. 25, No. 2 (May 1959) pp. 73-76. This appendix is basically an extraction from this article. 2 For an excellent summary of the history of the gravity and potential concepts of interaction see: Gerald A.P. Carrothers, "An Historical Review of the Gravity and Potential Concepts of Human Interaction," Journal of the American Institute of Planners, Vol. 22, No. 2 (Spring 1956) pp, 94-102. 112 Most of the controversy concerning empirical gravity or potential formulations has surrounded the question of what the function of distance should be. It is generally agreed, and empirical examination indicates, that an exponential function should be used. That is, the measurement of distance separating the various areas should be raised to some power. However, empirical tests of gravity models have resulted in exponent values that range from 0.5 to almost 3.0. As a result of this inconsistency in exponent values, I decided to test two separate accessibility formulations. The first used an exponent value for x of 1.0, while the second used an exponent value for x of 2.0. The travel time measure used was the travel time in minutes by auto for 1971 between the zones as obtained from the HPS data base. \ Appendix E EMPLOYMENT, RECREATION AND OPEN-SPACE SUB-MODELS 113 114 1. Employment Location Sub-Models In the original HPS model, employment was divided into eighteen industry groups which were located on the basis of the locational cr i-teria of the industry.^ Since there were regularities within certain groups of employment, the locational model was divided into the follow-ing four major sub-groups: a. manufacturing and wholesaling b. retail trade c. services d. agriculture, forestry and fishing. a. Manufacturing and Wholesaling. These employment activities were disaggregated into seven industrial sectors which were allocated to sub-areas on the basis of attractiveness for a given industry.2 The attrac-tiveness is given by: Ak = TkS..Wk (1) J k i 1 U i where is the attractiveness of zone i to industry k Svl is ith site factor in zone j i/ Wn. is the weight attached to site factor i by industry k These attractiveness indices were calculated for those zones which had industrially zoned land and possessed certain essential factors such as deep water access for petroleum refining, railroad access, and ware-housing and storage facilities, They were then normalized and used to allo-cate employment to subareas by an allocation function and a land absorp-tion coefficient (LAC) which converted subarea employment to land use. If there was insufficient land the excesses were reallocated to subareas of excess supply. This sub-model has received l i t t le change over the years and remains virtually the same in this revised HPS model in use today. This appendix is a condensation of material contained in Michael A. Goldberg and H.C. Davis, "An Approach to Modelling Urban Growth and Spatial Structure," Highway Research Record, Vol. 435 (1973), pp. 48-50. 2 The approach used here was developed from these earlier works: Stephen H. Putman, "Intra-Urban Employment Forecasting Models: A Review and Suggested New Model Construct," Journal of the American Institute of  Planners, Vol. 38, No. 4 (1972) pp. 216-230; and Michael A. Goldberg, "Bay Area Simulation Study: Employment Location Models," The Annals of Regional  Science, Vol. 2, No. 2 (1968) pp. 161-176. 115 b. Retail Trade. Retail trade was originally allocated using a gravity model formulation.3 This formulation generated measures of poten-tial demand for retail trade in each subarea which were compared with the actual retail trade in each zone. Excesses and deficits were changed gradually over time, rather than instantly, in an attempt to account for the lags and inertia which occur in practice. As in the manufacuring and wholesaling sub-group, the newly allocated employment was converted to land use via an allocation function and the appropriate LAC. If a subarea had excess demand, the excess demand was reallocated to subareas with excess supply. This sub-model has also re-ceived l i t t le change or refinement and remains the same as originally developed in the present version of the HPS model. c. Services. In the absence of decisive research findings in this area, the original sub-model allocated services to subareas using a modi-fied gravity and intervening opportunity model. This sub-model has not been revised and remains the same in the present version of the model. d. Agriculture, Forestry and Fishing. When the original sub-model was developed all three of these industries were declining in the region. The assumption was made that these declines would continue and that their land would be converted to urban uses. Decline factors were selected for each industry and future declines were estimated using these factors. In the present model this sub-model is also unchanged from its original con-ception. 2. Recreation and Open-Space Sub-Models Recreation and open-space determination was carried out in an extremely simplistic fashion. Two types of parkland were considered: local/neigh-bourhood parks; and regional parks. For each type of park a four by two matrix of park land coefficients was constructed to correspond with the two structure types and four value classes of housing. These two land absorbtion matrices were constructed from current planning practice at the time and were subject to change for policy testing purposes. The matrices were used to calculate the total number of acres of local and regional parks required and to allocate these acres to the subareas. This sub-model remains unchanged in the present version of the model. The model closely paralleled those done previously by: David L. Huff, "A Probability Analysis of Shopping Centre Trading Areas," Land Economics, Vol. 53, Mo. 1 0963) pp. 81-90; T.R. Lakshmanan and W7GT~ Hansen, "A Retail Market Potential Model," Journal of the American  Institute of Planners, Vol. 31, No. 2 [1965) pp. 134-143; and J.D. Forbes and A.G. Fowler, "Simulation of a Gravity Model," The Annals of  Regional Science, Vol. 3, No. 1 (1969) pp. 86-95. ' ' 

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