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Xerox University Microfilms 300 North Zeob Road Ann Arbor, Michigan 48106 7 5 -1 4 ,7 3 3 FORD, John Joseph, 1947A SITUATIONAL MODEL TO TEST THE EFFECTIVENESS OF A ZONING ORDINANCE IN LANSING, MICHIGAN. Michigan State University, Ph.D., 1974 Geography Xerox University Microfilms, 0 1975 JOHN JOSEPH FORD ALL- RIGHTS RESERVED Ann Arbor, M ichigan 46106 A SITUATIONAL MODEL TO TEST THE EFFECTIVENESS OF A ZONING ORDINANCE IN LANSING, MICHIGAN By John J. Ford A DISSERTATION Submitted to Michigan State University in p a r tia l f u lf i ll m e n t o f the requirements fo r the degree of DOCTOR OF PHILOSOPHY Department o f Geography ABSTRACT A SITUATIONAL MODEL TO ASSESS THE EFFECTIVENESS OF ZONING REGULATIONS IN LANSING, MICHIGAN By John J. Ford Geographers have expressed only a lim ite d in te re s t in the zoning process. However, as urban d ec en tralizatio n increases, the need fo r a r e ju s t if ic a t io n o f land use regulation arises. Geographers, urban planners, economists and resource planners by the nature of t h e ir methods and perspectives on the urban scene, a l l have an in te re s t in the re d e fin itio n of land use regulations. This research develops and tests a model th a t assesses one s itu a tio n a l c h a ra c te ris tic of a zoning ordinance. This is in contrast to most zoning models th at are based on s ite c h a ra c te ris tic s . In addition to the development o f the model, based on a c c e s s ib ilit y , this study id e n tifie s locations where the zoning regulations impose e ith e r p o s itiv e or negative locational 's p i l lo v e r s .' The study area is Lansing, Michigan a manufacturing and adm inistrative c it y o f approximately 150,000 in south central Michigan. The hypotheses tested attempt to answer the following three questions: (a) Does situ a tio n a l zoning produce more land value homogeneity than the site-based zoning? (b) Is the homogeneity maintained i f the land values are aggregated by concentric rings? (c) Is the homogeneity maintained i f land values are aggregated by secto rial corridors? John J. Ford The f i r s t step in the model construction defines by use o f grouping algorithms nodes o f s im ila r land uses. An a c c e s s ib ility index is then constructed based upon two measures o f the situ atio n al ch a rac teris tic s of the land use node to another node containing d if f e r e n t types of economic uses. The second measure is the time distance to major shopping and employment nodes w ithin Lansing. The a c c e s s ib ility measure fo r a sample is s p a t ia lly interpolated to the e n tire study area by use o f the SYMAP mapping routine. Four zoning c la s s ific a tio n s are used in the analysis: low density r e s id e n t ia l, high density r e s id e n t ia l, commercial and in d u s tr ia l. The results indicate th a t the a c c e s s ib ility c r ite r io n defines more homo­ genous commercial and high density re s id e n tia l zones than the existing s it e based zoning. For in d u s tria l and low density re sid en tia l areas, the a c c e s s ib ility index increases the land value mixtures. These results are confirmed when the land values are aggregated by concentric zones. However, when land values are aggregated into sectors, the a c c e s s ib ility based zoning decreases the land value mixture not only in the high density re s id e n tia l areas but also in the in d u s trial areas. I t is concluded th at commercial and high density re s id e n tia l zones should be delim ited on the basis of t h e i r r e la t iv e and not absolute location . Existing methods fo r defining low density re s id e n tia l and in d u s tria l zones should be maintained unless in d u s tria l areas are s e c to ra lly arranged w ith in the c it y . By establishing a model to t e s t, evaluate and update the d e lim ita tio n o f zoning d is t r i c t s w ithin an urban area, potential locational c o n f lic t th at may arise from land use regula­ tions are reduced, 'n the. end such an approach benefits not only the community but also the c itiz e n by reducing locational sp illo vers arising from s ite based zoning. ACKNOWLEDGEMENTS When w ritin g a d is s e rta tio n countless individuals deserve special recognition. Dr. Stanley Brunn, my advisor, provided astute guidance and timely suggestions throughout the th esis. Mr. Sanford Farness, Dr. Gary Higgs and Dr. Gary Manson also deserve recognition f o r t h e ir helpful c r itic is m o f the various d ra fts . I am most grateful to the Geography Department at Michigan State U niversity and in p a rtic u la r to the chairman, Dr. Lawrence Sommers. Special acknowledgement is also due the Computer In s t it u t e f o r Social Science Research fo r providing computer time and f a c i l i t i e s . In ad d itio n , a very special recognition is due my w ife , Eleanor, who by her patience and in te re s t in the d is s e rta tio n to p ic , motivated me to continue the research u n til i t s completion. I would also lik e to thank those unnamed people in the C ity Hall of Lansing, Michigan who aided me in the c o lle c tio n o f the data. F in a lly , fo r keeping my sanity during the intensive period o f w ritin g th is d is s e rta tio n , I would l i k e to thank the following people: F ie d le r, Burt Bacharach and Herb A lp ert. ii Arthur TABLE OF CONTENTS Page ' Acknowledgements ............................................................................................ ii L is t o f T a b l e s ............................................................................................ v L is t o f F i g u r e s ............................................................................................ vi Chapter One. Framework o f Research Overview ..................................................................................................... Geographic Perspective in Zoning 2 ................................................. 5 Conceptual Framework U t iliz e d in Research .................................... 9 Statement of Problem Chapter Two. ........................................................................... 14 The Theoretical Foundation o f the Research O v e r v i e w .................................................................................................... 19 Zoning: 19 Process, E x te rn a litie s andC ritiq u e . . . . Urban Land M a r k e t .................................................................................... Chapter Three. 31 Hypotheses and Data Collection Introduction ............................................................................................ Statement of Hypotheses 43 ................................................................... 43 Data Requirements and Sampling Design .......................................... 48 Chapter Four. Development of and Testing the S itu a tio n a l Model Introduction ............................................................................................ 62 Regionalization o f Land U s e s ........................................................... 63 Testing of the Hypotheses................................................................... 94 iii 1V Page Chapter Five. Summary, Conclusions and Implications S u m m a r y .............................................................................................................. 118 Conclusions, Recommendations and Lim itations . . . . 119 Relationship o f Findings to Other Research . . . 122 . The Future o f Geographic Investigations in Urban Z o n i n g ..................................................................................................... 124 ........................................................................... 128 .................................................................................................... 129 Concluding Remarks Bibliography LIST OF TABLES Table Page 1. Comparison o f Expected and Actual Land Values 2. Mean Land Use Areas fo r L a n s in g ........................................... 64 3. In te rc o rre la tio n M atrix o f Land U s e s ........................... 67 4. I n i t i a l Land Use Groups: 5. Mean Land Value Factor Scores fo r Subgroups. 6. Revised Land Use Groups Based on Difference of M e a n s ............................................................................ 74 Grouping Results o f the Discriminant Analysis of Sampled Land U s e s ........................................................... 79 8. Percent Land Use C o m p o s i t i o n ........................................... 83 9. Matrix of Land Use C o m p a t i b i l i t y ................................... 84 7. . Percent Increase o f . . 52 Error . . . . 71 . 73 10. Travel Times to Major Lansing Nodes ........................................... 89 11. Comparison of Land Values: 12. Mean Squares o f Land Values fo r Zoning Schemes . . . 100 13. Comparison of Land Values: . . . 102 14. Mean Squares o f Land Values fo r Zoning Schemes: Concentric Rings ................................................................... O v e r a l l .................................. Concentric Rings 99 104 15. Comparison o f Land Values: S e c t o r s .......................................107 16. Mean Squares of Land Values fo r Zoning Schemes: S e c t o r s ......................................................................................... 110 17. Mean Squares Within Concentric Rings by Zone Type 18. Mean Squares Within Sectors by Zone Type v . . . . . . Ill 112 LIST OF FIGURES Figure Page 1. Cost C u r v e ............................................................................................. 39 2. Demand C u r v e ..................................................................................... 39 3* Location R e n t ..................................................................................... 39 4. Zoning and Lane Use E f f e c t ...................................................................... 41 5. D e fin itio n of S e c t io n s .......................................... ......... 50 6. Positioning o f One-Inch Grids around Land Use Sample Points ........................................................................... 59 7. Lansing, Michigan 87 8. Travel Time to Selected Lansing Nodes 9. Situatio n al Zoning Scheme ............................................................................ .................................. 90 ........................................................... 93 10. Comparison of Old and New Zoning Schemes. 11. Concentric Rings 12. Major A r t e r ia l Corridors 13. Location o f Potential Land Use C onflicts . . . 95 ............................................................................ ........................................................... vi . . . . 101 106 114 Chapter One Framework of Research 1 2 OVERVIEW Introduction "When you t a l k about zoning, you are ta lk in g about money and p r i o r i t y of access*" (Charles Barr, 1973) Zoning d ic ta te s what can be b u i l t and where i t can be b u i l t . An ind ividu al may be able to a ffo rd a structure o f a c e rta in dimension, but he may fin d th a t zoning regulations p ro h ib it such a s tru c tu re . On the other hand the property owner may fin d th a t the f l o o r dimensions o f his structure are d ic ta te d not by his own desires but by the e x is tin g zoning ordinance dealing with minimum f l o o r size s. An in d iv id u a l may want to b uild an apartment b uilding in a c e rta in area but may be prevented by the zoning code. In the above two examples zoning imposes costs upon the property owner; however, zoning regulations can also be manipulated to earn substantial p r o f i t fo r the e n te rp ris in g land speculator. The l a t t e r process involves lo c atin g vacant parcels o f land zoned f o r a low density zoning c l a s s i f i c a t i o n , i . e . s in g le fa m ily . With proper p rep a ratio n , the land speculator then prepares a j u s t i f i c a t i o n and presents his appeal f o r a higher density use such as m u ltip le fam ily to the local zoning appeals board. I f he wins his appeal, the speculator is in a p osition to r e s e ll the land a t prices accruing to parcels possessing the higher density c l a s s if i c a t io n . Even i f the appeal f a i l s , i t s existence may t r ig g e r an increase in th a t p a rc e l's value or adjacent parcels. Nothing has been done to the parcel except a legal r e c la s s if ic a t io n which in most cases is s u f f i c i e n t j u s t i f i c a t i o n fo r higher land costs provided there is a market demand f o r the p arc el. 3 Zoning is based upon the major assumption o f e q u a lity o f enforce­ ment, th at i s , zoning should be employed in such a way th a t i t s use by a community member does not d e tra c t from the use of zoning by another community member. Zoning regulations which impose costs on one party while a t the same time earning substantial p r o f i t fo r another do not display complete e q u a lity . In the opinion o f th is author, e q u a lity in the d is t r ib u t io n of zoning's costs and b en efits is not l i k e l y to be achieved u n t il a more exact method is developed fo r the d e f i n i t i o n o f zoning d i s t r i c t s . Zoning d i s t r i c t s may be defined in a v a r ie ty of economic and non-economic ways. The research contained w ith in the follow ing pages prescribes one method f o r an economic d e f i n i t i o n o f zoning d i s t r i c t s . The Pervasiveness o f Zoning Land use control is necessary in j u s t about a l l types of modern urban s o c ie tie s . Because o f i t s pervasiveness, zoning as a land use re g u la to r is o f great in t e r e s t to lawyers, c i v i l engineers, landscape a r c h ite c ts , planners, economists, p o l i t i c i a n s , so c io lo g is ts and geographers. Lawyers are mainly involved in the in te r p r e ta t io n of zoning ordinances and in the prosecution and defense o f contested cases. C iv il engineers are in te re sted in the construction requirements and securing easements fo r u t i l i t i e s , etc . The landscape a r c h ite c t is also in te re sted in the zoning regulations p a r t i c u l a r ly as they p ertain to 's e t back’ open space requirements, l i g h t easements and noise c o n tro l. Planners are keenly in te re s te d in the zoning process and d i s t r i c t i n g schemes. A perennial question faced by planners is the location o f zoning boundaries, a problem concerned w ith the p a rtitio n in g of v e r tic a l and horizontal spaceJ More recently zoning w ithin the three-dimensional c it y has taken on a new meaning and raised some in te re s tin g problems fo r planners. A ir rig h ts , v e rtic a l zonation and a ir p o rt zoning are p art o f the th ird dimension to zoning. Economists are interested in zoning as i t a ffe c ts the achievement of the highest economic p o te n tial fo r land. In a d d itio n , economists who are interested in in d u s tria l and commercial location pay p a r t ic u la r ly close a tte n tio n to the permitted uses along with noise and smoke abate­ ment regulations as prescribed in the zoning ordinance. Sociologists and p o l i t i c a l s c ie n tis ts have an abiding in te re s t in the zoning process. They may be interested in how the value system o f the decision makers influence the type and location of zoning d is t r i c t s or perhaps what is the ro le of partisanship in granting zoning variances, exceptions, etc. A close examination o f the ro le th at each of the above mentioned d is c ip lin e s plays in the zoning process reveals a number o f communalities. One communality focuses on the sp atial character of the zoning process and zoning d i s t r i c t s . The sp atial c h a ra c te ris tic s are evident in the ro le th a t distance, d ire c tio n and density play in the regulatory and d is t r ic t in g schemes. Distance, d ire c tio n and density emerge in set back, height and bulk regulations, nuisance zoning and use r e s tr ic tio n s . The concept o f re g io n a liza tio n also has a p p li c a b il i t y in the d elin eation of zoning d i s t r i c t s . Geographers who subscribe then to the sp atial o rie n ta tio n have found or w il l find th at zoning regulations e x h ib it a sizeable amount of s p a tia l dependency in the s p e c ific a tio n and administration o f the regulations. V o r the purpose o f th is paper, zoning re fers only to the horizontal p a r t it io n o f space. GEOGRAPHIC PERSPECTIVE IN ZONING Current Geographical Research On Zoning Nelson's study o f Vernon, C a lifo rn ia was one o f the e a r lie s t empirical studies dealing exclusively with the sp atial impact of zoning. Vernon was a unique community since i t contained land d e lib e ra te ly allocated fo r the highest possible re tu rn . That i s , in the vast m ajority of cases land was overzoned fo r in d u s tria l uses. Nelson c o rre c tly points out th a t in th is case zoning was used as a tool to maintain high land prices on the parcel l e v e l. The price of land along with the r e la t iv e location o f Vernon in the Los Angeles area made th is town an ideal location fo r the development o f industry and transportation networks. By e f f e c t iv e ly zoning out re s id e n tia l uses the c i t y was able to maintain a r e l a t i v e l y low service budget. As a r e s u lt, the govern­ ment placed low property tax assessments on the in d u s tria l parcels as a fu rth e r inducement to locate in th is area. Nelson concludes that municipal boundaries were thus extremely important in an analysis of land uses w ithin the Vernon area. Another study of a s im ila r nature was done by Fielding in the Los Angeles area (1964). Once again zoning was used as a tool by p rivate in te re s t (d airy farmers) to obtain maximum p r o f i t . Fielding found th at d airy farmers tended to locate on land zoned fo r re s id e n tia l use. As a re s u lt t h e i r land value increased but so did t h e i r taxes; hence, the d airy farmers over the long run received less and less p r o f i t . The farmers grouped together and incorporated t h e i r land under C a lifo rn ia law. By incorporating, the d airy farmers were then able to d r a f t t h e ir own zoning ordinances, and thereby protect t h e i r land from re s id e n tia l intrusions. One o f two recent geographic d is s e rta tio n s devoted to zoning attempted to analyze whether or not rezoning had any e f f e c t upon a change in property values (Seymour, 1966, p. 4 ) . The basic hypothesis was th a t assuming public u t i l i t i e s were es tab lished, then a change in zoning a ffe c ts the market value o f land in the d ir e c tio n of the more c a p ita l intensive uses. From his research in P itts b u rg h , Seymour found th a t a change in zoning tends to: a) increase the market value o f land in the long run by removing the th r e a t o f encroachment; b) s t a b i l i z e property values. One o f the more meaningful conclusions a rriv e d a t by Seymour was th at a threshold o f change in "permitted" land uses must be met before any s ig n if ic a n t change in the o v e ra ll land values occurs (Seymour, 1966, p. 78 ). In ad d itio n he found th at i f more than approximately 20% o f the zone was rezoned to a higher in t e n s it y use, and i f a demand fo r higher in t e n s it y use continues, then the change in property values occurs in the d ir e c tio n of the more c a p ita l in te n s iv e use. For example, in an area zoned f o r high density r e s id e n tia l use, i f one or two parcels are rezoned fo r commercial, then the o v e ra ll change in land values fo r the remaining r e s id e n tia l d i s t r i c t tends to increase. These re s id e n tia l properties w i l l then r e f l e c t land values clo sely approximating commercial values. N a to li (1967) conducted an in-depth analysis of zoning as an i n s t it u t io n a l re g u la to r of land use. He attempted to is o la te the influence o f zoning on developed and underdeveloped land in Worcester, Massachusetts. Like Seymour, N a to li found th a t zoning tends to s t a b i l i z e property values over a period o f time ( N a t o l i , p. 185). A re s id e n tia l zoning c la s s if ic a t io n tended to s t a b i l i z e property values in more instances than in commercial or business c la s s if ic a t io n s . He concluded th a t the less dense re s id e n tia l uses are more a ffe c te d by zoning changes than commercial and business c la s s ific a tio n s which tend to require a more dense u t i l i z a t i o n of space. A conclusion such as th is v e r if ie s the c a p ita l in t e n s if ic a t io n concept o f Seymour's. A study by Yeates on urban land value changes in Chicago (1965a) has added to the knowledge o f the s p a tia l e ffe c ts o f zoning on the urban landscape. In the study Yeates comments th a t land values are affected by a c c e s s ib ilit y and c e rta in natural amenities such as bodies of water (Yeates, 1965b, p. 321). In e a r l i e r years the d is t r ib u t io n of land values w ith in a c i t y could have been best described by the distance v a ria b le . As distance from the central c i t y increased, land values tended to decrease in a lin e a r fashion. However, now th a t zoning has l e f t i t s im print upon the urban landscape, land values tend to decrease in a c u r v ilin e a r manner. The re la tio n s h ip between land values and distance in commercial and business d i s t r i c t s was almost n on-existent according to Yeates (1965b, p. 328). The e f f e c t of land use reg u latio n upon the urban environment was studied by Duncan (1973). He found th a t wealthy people in his study area supported a r e s t r i c t i v e zoning ordinance in order to maintain the value of the neighborhood (Duncan, 1973). A r e s t r i c t i v e zoning ordinance usually requires minimum l o t sizes which are la rg e r than the average causing the p rice of new homes w ith in the neighborhood to increase. Duncan's research along w ith e a r l i e r studies by Nelson and F ielding suggest th a t zoning is a p riv a te good which b e tte r serves the narrow in te r e s t o f p riv a te landholders ra th e r than the public as a whole. 8 L im itations of Previous Research Geographic research dealing with topics o f a zoning nature are lim ite d . Only two d is s e rta tio n s have d e a lt ex clu sive ly with zoning (Seymour, 1966; N a t o li, 1967). One reason fo r the paucity o f s p a tia l research on zoning may be f a i l u r e o f th e o re tic a l constructs to explain the s p a tia l d is t r ib u t io n o f the data ( N a t o l i , 1971, p. 9 ). N a to li concludes th at "a general systematic approach is precluded (but) i t is possible to measure the e f f e c t of zoning on the development o f urban land use patterns . . . " Another reason fo r the inadequate geographic research in a t t r ib u t a b le to the r e l a t i v e haphazardness o f the zoning process i t s e l f (Yeates, 1965a, p. 317). Zoning is a p o l i t i c a l process which c la s s if ie s land often without a d e f i n i t e reason fo r doing so. Geographers are more accustomed or more f a m il i a r w ith more d e f i n i t i v e land c la s s ific a tio n s a ris in g from human s p a tia l behavior. To put i t another way, a zoning c la s s if ic a t io n f o r a parcel normally incorporates some or a l l o f the fo llow ing considerations: adjacent land use, subsoil and t e r r a i n , value systems o f decision makers, and aspects o f p o l i t i c a l compromise ( N a t o l i , 1967, p. 9; Wilhelm, 1962, p. 224). On the other hand, geographers tend to c la s s ify urban land by i t s use, by socio­ economic c h a ra c te ris tic s o f the owner or by distance from a central focal p oint. A th ir d reason f o r the apparent lack o f geographic in t e r e s t in zoning may l i e in the noncontinuous nature o f the zoning data (Seymour, 1966, p. 4 ) . For example, a parcel is e it h e r in a c la s s if ic a t io n fo r s in g le -fa m ily residents o r.n o t but never in both a t the same time. Zoning data contrasts with other types of geographic data such as population or income figures both o f which are d is trib u te d in a more continuous manner without a s t r i c t membership grouping. One problem arising from the non-continuous nature o f zoning data is th a t of varying sized areal u n its. Most geographers are acutely aware o f the importance of spatial autocorrelation arising from the various sized areal u n its . Without some type o f compensation fo r the size of the u n it , such as a density measure, the explanation based on zoning data can be extremely misleading. A fin a l reason fo r geographers' seeming lack of in te re s t is th a t a zoning c la s s ific a tio n fo r a parcel may be heavily confounded with many other types of considerations, not the le a s t of which are population density, topography, s o i l , a c c e s s ib ility and community values. Thus a researcher who intends to explain or predict the d is trib u tio n of zoning d is t r i c t s would have to construct some type of research design that would control fo r many i f not a l l o f these confounding influences. It appears doubtful th a t a m u lti-fa c to r design such as th at needed fo r fe r re tin g out zoning's confounding influences is p ractical given the present nature of the zoning data. CONCEPTUAL FRAMEWORK UTILIZED IN RESEARCH Introduction The concepts of distance, d ire c tio n and density are central to studies measuring zoning's influence upon the landscape. However, in th is research a new framework based upon the concepts of land use c o n flic ts and e x te r n a litie s is applied to the d is t r ic t in g scheme o f a zoning ordinance. A land use c o n f lic t may arise when one use, due to the nature of i t s a c t i v i t y , lowers the land value of surrounding parcels. 10 E x te rn a litie s or 'lo c a tio n a l s p illo v e rs ' such as poor a c c e s s ib ilit y , noise, lack of parking, low surrounding land values tend to aggravate land use c o n f lic t . The re lia n c e upon the c o n flic t conceptual framework does not in any way imply a subordination o f the distance, d ire c tio n and density concepts but rather builds upon them. Land Use C o n flicts and E x te rn a litie s I f one examines a community's zoning map, he may notice broad areas o f the c it y designated as single and two-family dwelling areas. He may also notice w ithin one o f the s in g le -fa m ily re s id e n tia l areas small sections which apparently have been rezoned from re s id e n tia l to commercial. Why th is occurs may be d i f f i c u l t to answer, p a r tic u la r ly i f the rezoned land is presently vacant. Perhaps the most adequate answer is found in the p o l i t i c a l nature o f the present system o f urban land-use controls. Allowing small intrusions o f v a ria n t land uses into areas o f r e l a t i v e l y homogenous land uses is called spot zoning. In the above example the rezoning to commercial use may possibly fo s te r a land-use c o n f lic t p a r t ic u la r ly i f surrounding land values are affected. That i s , the new designation may promote locational 's p illo v e r s ' or e x te r n a lit ie s which i f negative may impose costs upon the surrounding landscape. Thus, the new zoning designation f a i l s to be completely eq u itable. I d e a lly , a public good such as zoning should minimize e x t e r n a litie s and maintain as high a degree o f d is trib u tio n a l eq u ality as possible both in the i n i t i a l c la s s ific a tio n and subsequent enforcement (Cox, 1973, p. 10). n Operational Concepts Only recently have geographers become interested in the i d e n t i f i ­ cation of land use c o n f lic t and i t s subsequent re so lution . A b rie f examination o f u t i l i t y theory used by economists w i l l underscore the importance o f locational e x t e r n a lit ie s . In the context of th is research, u t i l i t y is o p eratio nally defined as the s a tis fa c tio n an individual receives from locating at a p a r tic u la r place w ithin the urban area. Locational 's p illo v e r s ' are o p e ra tio n a lly defined as costs or benefits accruing to the parcel owner because o f the r e l a t i v e location of the parcel to other parcels. For example, a parcel o f land zoned fo r l ig h t - in d u s t r ia l use adjacent to a re s id e n tia l community may create many locational 's p illo v e r s ' in the form of noise, congestion, obnoxious odors which in turn lowers property values. Thus the individual is assessed a cost because of his proximity to the industry. A u t i l i t y which has a p o s itive influence in the overall land value of an area is defined as a p o s itiv e e x te r n a lit y . A u t i l i t y which has a negative influence on the overall land value in an area is defined as a negative e x t e r n a lity . Furthermore, r e s id e n t ia lly zoned parcels located adjacent to parcels zoned in d u s tria l may possess many character­ is t ic s making them r e l a t i v e ly s im ila r to the in d u s tria l parcels. If th is is so, then the in d u s tria l d i s t r i c t boundaries may need to be redrawn so as to incorporate a l l or a portion of the r e s id e n t ia lly zoned parcels. By doing t h is , the potential negative e x te r n a lity imposed on the r e s id e n t ia lly zoned parcels by the in d u s tria l parcels may be reduced. On the other hand, a church b u i l t near vacant land located w ithin a predominantly re s id e n tia l community may impose p ositive 12 e x t e r n a lit ie s on the vacant land. Thus, fu tu re development of the vacant land w i l l be enhanced by i t s proxim ity to the church and o v e ra ll land values may r i s e . Uses which are less compatible to the church such as d r iv e - in eating establishments or heavy industry uses may be e f f e c t i v e l y 'zoned-out' o f the vacant land by community leaders. Position of the Research Like previous studies dealing w ith zoning, th is research begins by assessing the e f f e c t o f the zoning c l a s s if i c a t io n upon the urban land values. However, u n lik e i t s predecessors, the research w i l l be based upon a re g io n a liz a tio n o f land uses. The re g io n a liz a tio n w i l l in c o r­ porate more s itu a tio n a l c h a r a c te r is tic s than the e x is tin g s ite -o rie n te d zoning regional commonly used today. The new s itu a tio n a l c la s s if ic a t io n is derived w ith the expressed in t e n t o f evaluating whether or not selected parcels o f land are prevented by the e x is tin g zoning plan from reaching a more c a p ita l in te n s iv e use. For example, th is study w i l l determine i f there are any r e s i d e n t i a l l y zoned parcels o f land which possess a r e l a t i v e lo c a tio n more c h a r a c te r is tic o f commercially zoned parcels. I f so then the r e s id e n tia l parcels may be in h ib ite d from achieving a more c a p ita l in te n s iv e use and in the fu tu re these re s id e n tia l parcels may become sources of land use c o n f l i c t . Patterned a f t e r the research of Yeates, th is d is s e rta tio n w i l l examine the w ith in zone v a ria tio n of land values. At the same time between-zone land values w i l l also be analyzed to e it h e r prove or disprove t h e i r existence. However, u n lik e Yeates, th is study w i l l also examine the degree of w ith in sector land values found in commercial and in d u s tria l land. 13 The major impetus f o r th is research has come from the exhaustive analysis of zoning, and land values performed in Worcester, Massachusetts by N a to li. In th a t study, N atoli concluded th a t property value is more a function o f lo c atio n and less a function o f zoning ( N a t o l i , 1967, p. 194). The basic question raised in the study is whether the homogeneity o f property values w ith in the study area is more a function of lo c atio n a l a t t r ib u t e s o f the area or the zoning. I t should be noted th a t th is d is s e rta tio n does not in any way attempt to account fo r the d is t r ib u t io n o f zoning parcels w ith in any p a r tic u la r area. The research compares the d is tr ib u t io n o f land values in the e x is tin g zoning d i s t r i c t s with the d is t r ib u t io n of land values in a c c e s s ib ilit y derived d i s t r i c t s . Approximately twenty years ago, R a t c l i f f , an urban economist called fo r a "re fin ed type o f zoning to b e tte r adjust economic a c t i v i t i e s to the environment . . . to exclude inappropriate uses from areas where t h e i r presence may increase f r i c t i o n " ( R a t c l i f f , 1955, p. 146). This research w i l l develop and t e s t a new type of zoning d i s t r i c t which is more economically based than the e x is tin g d i s t r i c t s . On a broad sc ale , the methods and findings w i l l hopefully in d ic a te where lo c a t io n a lly inapp ro p riate zoning d i s t r i c t s prevent the ordinance from functioning as a public good which increases the lik e lih o o d o f land use c o n f l i c t . That i s , the research w i l l in d ic a te where zoning imposes e x t e r n a l it i e s e it h e r p o s itiv e or negative upon an urban landscape. 14 STATEMENT OF PROBLEM Elaboration Use o f land is decided fo r the owner by factors exogenous to the s i t e , namely i t s s itu a tio n { P l a t t , 1972, p. 38 ). Zoning is one o f these outside factors influencing the location o f a c t i v i t i e s in the urban area. But what is location? Location re fe rs re latio n sh ip s w ith in re latio n sh ip s to a l l to other a c t i v i t i e s " to the unique complex of space each given point in time . . . other people, to other things and ( R a t c l i f f , 1959, p. 302). In the above d e f i n i t i o n , R a t c l i f f is a c tu a lly r e fe r r in g to r e l a t i v e location and not to absolute lo c a tio n . Zoning is merely a re g io n a liz a tio n process based upon knowledge o f absolute location and adjacent land uses. But what about the re la tio n s h ip s between a parcel and other parcels containing s im ila r or even d i f f e r e n t land uses? In order to support community w elfare and reduce c o n f l i c t , zoning must place more emphasis on the processes underlying the r e l a t i v e location of economic a c t i v i t i e s and less on the s i t e c h a ra c te ris tic s of the p a rc e l. By accomplishing a r e d e fin it io n in the d i s t r i c t c la s s if ic a t io n based upon s itu a tio n c h a r a c te r is tic s , zoning may become more an instrument o f public p o lic y . The research undertaken here w il l formulate a process to meet the goal o f a more eq u itable re g io n a liz a tio n of land uses w ith in the urban area. In a d d itio n , now th a t geographers are becoming concerned w ith location al a t t r ib u t e s of c o n f lic t s and e x t e r n a l it i e s , they are b e tte r able to assess the impact of land use regulations upon the v a lu e -o f the property. 15 S p e c ific Statement Location re n t a t a p a r t ic u la r p o in t in space is the savings in tra nspo rtatio n cost enjoyed by th a t place in r e la t io n to a more d is ta n t lo c atio n . At some distance from a p a r t ic u la r node l i t t l e or no rent accrues since lo c atio n re n t equals net revenue minus tran s p o rta tio n cost (Von Thunen, 1826). Zoning by channeling economic development thereby influences the lo c a tio n re n t by imposing upon c e rta in places r e s t r ic t io n s which re q u ire in one way or another higher tra n s p o rta tio n costs. Certain l o c a l i t i e s b e n e fit by higher land values s o le ly on the basis o f a p a r t ic u la r zoning c l a s s if i c a t io n . Conversely, c e rta in locations s u ffe r from lower property values p r in c ip a lly because o f the permitted uses allowed in the area. Therefore an o b je c tiv e c r i t e r i o n is needed in the s p a tia l apportionment o f zoning d i s t r i c t s ; th is should have as one of i t s primary goals the formation of r e l a t i v e l y equitable d is tric ts . L it e r a tu r e on zoning r e it e r a t e s th a t zoning is a device fo r securing a p attern o f space best suited to the t e r r a i n , economic re la tio n s h ip s , and social s tru c tu re o f the p a r t ic u la r community (Ukeles, 1965, p. 25 ). Furthermore, the o v e ra ll ra tio n a le o f land use controls in the United States has c o n tin u a lly supported most i f not a l l o f the above goals plus the maintenance o f land value homogeneity (Alonso, 1960, p. 152; N a t o li, 1967, p. 50; Delafons, 1969, pp. 2 8 -3 3 ). Therefo re, based on what has been said about the goals and purposes of zoning and operation of the urban land market, the question is can a measure o f a c c e s s ib ilit y be a v a lid c r i t e r i o n upon which to draw urban zoning d is t r ic t s ? I f the maintenance o f land value homogeneity is one o f the major goals o f a 16 community's zoning ordinance, then does a re g io n a liza tio n o f land uses on the basis o f a c c e s s ib ility produce the same homogeneity o f land values th a t exists in the present zoning ordinance? In order to answer these questions, a s itu a tio n a l model is constructed which s p a tia lly defines new zoning d i s t r i c t s . A comparison between land value homo­ geneity in the newly created d i s t r i c t and the ex istin g zoning d is t r i c t s is then performed. Objectives o f the Study The overall o bjective of th is research is to construct a d is t r ic t in g scheme based upon s i m il a r it y o f land uses and a c c e s s ib ility measures. The d is t r i c t i n g scheme is intended to o u tlin e broad areas w ithin a c it y which best f i t a p a rtic u la r land use a c c e s s ib ility regional grouping. Exceptions to th is broad c la s s ific a tio n are n a tu ra lly expected but w il l not be o f in te re s t in the research; exceptions to zoning law are handled by public decision makers. By constructing zoning d i s t r i c t s on the basis of land use a c c e s s ib ility i t is hoped th a t zoning w il l be b e tte r able to f u l f i l l i t s function as a public good. eq u ality in i t s d is tr ib u t io n . Once again a public good possesses For the purpose o f the research i t is assumed th a t zoning p a r t i a l l y f u l f i l l s i t s ro le as a public good by maintaining homogeneity of land values w ithin a s p e c ific zone. Homogeneity o f land values is measured and compared w ith in the ex istin g and newly derived zoning d i s t r i c t s . A second o bjective o f th is study is to elaborate a technique th at is capable o f id e n tify in g Likely areas where fu tu re zoning and land use c o n flic ts may emerge. A land use c o n f lic t is o p e ra tio n a lly 17 measured in an area by assessing where the differences in land value homogeneity between the zoning d is t r i c t s and a c c e s s ib ility d is t r i c t s is the la rg e s t. This places land use c o n flic ts w ith in the conceptual framework o f e x t e r n a lit ie s and attempts to v e r if y th at zoning imposes e x te r n a litie s upon ce rta in d i s t r i c t s . In turn these e x t e r n a litie s may hinder the achievement o f more homogenous land values w ithin the d is tr ic t. A fin a l o b jective of this d is s e rta tio n is to develop a procedure to update a zoning scheme fo r a community. The procedure as outlined in the research is n eith e r overly complicated nor s t a t i s t i c a l l y sophis­ tic a te d . But the procedure does represent a c a re fu lly formulated plan fo r implementation; one th a t is useful fo r communities on a broad scale to assess, change or update t h e ir ordinance. Many times, i t appears th at soon a f t e r a zoning ordinance is adopted, a major change in land use is suggested fo r an area. For example, a new highway, a new apartment complex, shopping center, etc. The f u l l impact th a t the proposed change has upon the zoning ordinance and re la te d development w ithin the area may not be re alized fo r sometime. The procedure outlined in th is research allows an evaluation of the proposed change on a c c e s s ib ility and zoning. An evaluation is possible because the procedure r e lie s not only on s i t e ch a ra c te ris tic s but also the s itu a tio n a l c h a ra c te ris tic s of the parcel. Chapter Two The Theoretical Foundation of the Research 18 19 OVERVIEW Research on zoning and a c c e s s ib ility re la te s a p o l i t i c a l process, zoning, to an economic process, a c c e s s ib ility . The former involves more value judgments and compromise in the a llo c a tio n o f permitted a c t i v i t i e s than the l a t t e r which allocates a c t i v i t i e s on the basis o f economic e ffic ie n c y . The chapter is divided into two sections. The f i r s t part begins with an analysis o f zoning as the outcome o f a p o l i t i c a l process, then i t turns to some e x te r n a lit y e ffe c ts o f zoning and closes with a c r itiq u e of zoning. The second part analyzes the ro le o f the urban land market in general and a c c e s s ib ility in p a r tic u la r . ZONING: PROCESS, EXTERNALITIES AND CRITIQUE "In zoning . . . the aim is to minimize the negative e x te r n a lit ie s re s u ltin g from proximity o f incompatible land uses to one another." (K. Cox, 1973, p. 11) Zoning As A P o lit ic a l Process For the purposes of th is study zoning is viewed as an end product of the p o l i t i c a l process. The discussion w il l not deal with the p o l i t i c a l in t r ic a c ie s , c o n flic ts and compromises th a t a zoning ordinance undergoes in the process of i n i t i a l adoption. The discussion focuses on the value systems of the various actors when a change is proposed in a zoning ordinance and the ensuing c o n f lic t . Zoning changes begin with p e titio n e rs who are normally property owners in the community. There are two types of changes inherent in a 20 zoning ordinance. A variance is granted i f the zoning c la s s if ic a t io n imposes unnecessary hardship upon the land owner who normally is the p e tit io n e r {"P h ila d e lp h ia . . 1955, pp. 516-555). A rezoning o f an area or a parcel may occur i f the community or surrounding area are adjudged not to be a ffe c te d by the presence o f the new a c t i v i t y . I f one or two parcels are rezoned and i f they are enclaves in a la rg e r d i s t r i c t , then the rezoning is often ca lle d spot zoning. Normally a r e c l a s s i f i ­ cation o f a property is tre ate d as an amendment to the zoning ordinance (ASPO, 1968, p. 25 ). In e it h e r kind o f zoning change, the planner is usually ca lle d upon to evaluate the proposed change and to make recommendations to the c i t y council or zoning appeals board (Ranney, 1969, p. 131). Before the f i n a l evaluation is made, the board or council may consult with the building inspecto r, housing inspector and local c i t i z e n s , p a r t i c u l a r ly those most d i r e c t l y a ffe c te d by the zoning change. I f the zoning change involves a r e s id e n tia l area, then the planner and other decision makers are faced with numerous social and ethnic questions. On the other hand, i f the request involves commercial and in d u s tria l uses, then actors are involved in a c o s t-b e n e fit type of determination (Ranney, 1969, p. 131). The value system o f decision makers and influencers often a ffe c ts the outcome o f a zoning change (Wilhelm, 1962, p. 96 ). I f the actors adhere to an economic value system, then zoning is used to control land values (Wilhelm, 1962, p. 96 ). Actors who adhere to th is value system tend to view zoning as a tool to increase the value o f the land. These actors are present oriented and r e ly upon the market system to determine the best land use o f an area. As a r e s u l t , zoning fo r economically oriented actors 21 is oriented to the master p lan , but they s t i l l want the master plan to be f l e x i b l e enough to ad just to changing market conditions (Wilhelm, 1962, pp. 155-157). In contrast is the p r o te c tio n is t viewpoint. According to supporters of th is p o s itio n , one o f the foremost goals o f zoning is not the p r o f i t motive but the protection o f the re s id e n tia l community. The protec­ t i o n i s t believes th a t zoning is only one independent v a ria b le a ffe c tin g land values and th a t zoning should determine what land uses are permitted in an area. Thus the p r o te c tio n is t tends to view zoning as a re g u lato r o f development w hile the economically oriented actor believes th a t zoning should r e f l e c t changing land values (Wilhelm, 1962, p. 96 ). The p r o te c tio n is t believes th a t the fu tu re is q u ite p red ictable and change can occur but only slowly and over time. Thus zoning and not the market system should determine land value (Wilhelm, 1962, pp. 155-157). Some aspects of the economic and p ro te c tio n is t viewpoints are also found in the value systems o f the p e t it io n e r and other concerned c it iz e n s . The developer or the p riv a te ind ividu al who wants the zoning ordinance changed usually makes his request fo r economic reasons (Ranney, 1969, p. 132). In suburbia, the actors who most often object to a zoning change do so mainly fo r social or community preservation reasons (Ranney, 1969, pp. 3 0 -3 8 ). For example, a low income housing p ro je ct may arouse opposition in c e rta in communities since the social image o f the community may be tarnished. C o n flic t over zoning may a ris e very q u ic k ly , however, compromise on a zoning change often is q u ite d i f f i c u l t since the c o n f l i c t tends to be so polarized (Ranney, 1969, p. 136). Unpopular decisions can be 22 frequ en tly passed from the elected representatives to the non-elected appeals board or to the zoning ad m in is tra to r. c o n f li c t is not o f concern in th is research. However, p a rtic ip a n t Instead land use c o n f lic t s or the d is p a r it y between the zoning c la s s if ic a t io n and the s itu a tio n a l p o te n tial o f parcels are analyzed. In order to develop the need fo r a s itu a tio n a l approach, the discussion now turns to the process o f d ra ftin g a zoning ordinance. Zoning: Process, C ritiq u e and Solutions The follow ing discussion w i l l tra c e the formation o f a zoning ordinance from the i n i t i a l f i e l d compilation to the adoption process. The f i r s t step is to survey and map land uses. The land use c l a s s i f i ­ cations fo r the map are normally catalogued in a ra th e r s tr a ig h t forward manner (Chapin, 1965, p. 273). In a d d itio n to the use c l a s s if i c a t io n , a land value estim ate is made. In lie u of actual market values, the value survey r e l ie s on assessed valuations and normally estimates the values to the f r o n t - f o o t . In the urban-rural frin g e and in the ru ra l areas, land value estimates are calculated on la rg e r u n it areas such as acres {Chapin, 1965, p. 330). The land use and land value survey are then integrated in to the o ve rall master plan fo r the community and incompatible uses are then determined. Land uses are incompatible i f the use endangers the h e a lth , safety or w elfare o f people liv in g in surrounding p ro p e rtie s . The aim o f the master plan is to maximize the e f f ic ie n c y o f land uses by minimizing negative e x t e r n a l it i e s such as f r i c t i o n o f distance ( R a t c l i f f , 1955, p. 130).. Put another way, the fundamental aim of zoning is to prevent the r i g h t use from locating in the wrong place (Ukeles, 1965, p. 3 8 ). 23 The contents of the master plan are comprehensive in nature and include: d is tr ib u tio n o f houses, businesses, in d u s trie s , recreation areas, and education centers; standards o f population d en sity, use c a p a b ilitie s o f non-developed land; and fu tu re growth and land use requirement. Also included is a section on the c ir c u la tio n patterns, terminal f a c i l i t i e s and u t i l i t y requirements (Lovelace and Weismantel, 1961, p. 14). Normally a fin a l section o f the master plan contains development programs and targ e t years fo r t h e ir attainment (W illiam s, 1966, p. 4 ). Included in and conforming to the master plan is the zoning plan. I t allocates external benefits and costs aris in g from p riv a te land ownership by specifying the zoning ordinance and d is t r i c t i n g schemes. The plan must be an integral part of the master plan in order to give planners the f u l l advantage o f land use regulations (Dunham, 1958, pp. 170-186), and also to protect property owners from another's unreasonable use o f land (Horack, 1952, pp. 153-161). The zoning ordinance is considered to be co n stitu tio n a l i f i t is reasonably debated in a public forum and approved by the voters (Mandelker, 1970, pp. 1 -7 ). In th eo retic al terms the adoption o f the ordinance s ig n ifie s that the people have decided how the costs o f f r i c t i o n can be reduced to minimal levels through the use o f land regulations ( R a t c l i f f , 1955, p. 129). The m ajority o f zoning decisions deal with the sp e cific l e g a lit y of the zoning code as outlined in the ordinance. The day-to-day administration of zoning, however, deals with the mapping o f d is t r i c t s and legal questions arising from boundary c o n flic ts (W illiam s, 1966, p. 259). One reason fo r th is inordinate adm inistrative concern with 24 the boundaries lie s in the broad manner in which d i s t r i c t s are defined. Zoning administrators are unable to provide a separate zone fo r each and every parcel ( M e r r i f ie l d , 1965, pp. 548-593). The best th at zoning administrators can do is to provide a general location fo r a boundary along with supportive evidence. The precise location f o r a zoning boundary along with reasons fo r i t are d i f f i c u l t tasks fo r a zoning adm inistrator. I t is obviously impossible to id e n t if y each o f the individual considerations th a t cause a technical s t a f f or public o f f i c i a l s to propose eig h t types o f d i s t r i c t s instead o f nine or to draw a boundary along South S treet instead o f Pine S tre e t (Ukeles, 1965, p. 22). Two in te rre la te d concepts need to be mentioned as they form the basis fo r the th eo retic al framework of th is research. Zoning to be e f f e c tiv e must exert some type o f influence on land uses. One way that the effectiveness o f a zoning ordinance can be ascertained is by examining the number and type o f changes granted (Wilhelm, 1962, pp. 6 4-65). This research suggests another method of evaluation. That i s , why not examine the effectiveness of a zoning ordinance by looking at the s itu a tio n a l c h a ra c te ris tic s o f the parcels? A second related concept is th at planning and zoning require coordination to insure th a t the land is used most e f f i c i e n t l y . However, e ffic ie n c y is not always fostered by the e x is tin g zoning regulations. One reason why e ffic ie n c y is not co n tin u a lly maintained arises from the imposition of 'lo c a tio n a l s p illo v e rs ' upon surrounding land uses. Therefore the public regulation o f land uses should become concerned with these e x te r n a lit ie s (Mandelker, 1970, pp. 1 -7 ). 25 E x te rn a lity Effects o f Zoning and D is tr ic tin g The e x t e r n a lit y e ffe c ts o f zoning can be subdivided into in ten ­ tional and unintentional e ffe c ts . By in te n tio n a l is meant th at the zoning ordinance was w ritte n with complete knowledge of the end r e s u lt. The unintentional e ffe c ts d i f f e r from the in te n tio n a l in th a t the former do not possess the random c h a ra c te ris tic s o f the l a t t e r . A study of unintentional e x t e r n a lit ie s would involve a comparison and analysis of the legal requirements specified in the actual ordinance. Such a task is outside the scope o f the research. Fiscal zoning is one type of in te n tio n a l e x t e r n a lit y which hurts the public w elfare of the community. The problem with th is type o f zoning is th a t i t often f a i l s to provide fo r the fu tu re expansion of the community. One way fis c a l zoning is operationalized is by over­ zoning { i . e . zoning more land fo r a c la s s if ic a t io n than is a c tu a lly needed) a community fo r in d u s tria l or commercial in the hope of a ttr a c tin g these a c t i v i t i e s . However, in the short run, overzoning r e s t r ic t s the selection of av ailab le parcels {W illiam s, 1966, p. 261). The reduced supply o f a v a ila b le land often tends to decrease the tax base of the community p a r t ic u la r ly in the long run (American Society of Planning O f f i c i a l s , 1968, p. 4; Sagalyn & Sternbieb, 1973, p. 3 ). In other words, overzoning forces the taxpayers to share a greater fin a n c ia l burden since economic a c t i v i t i e s are lim ite d in the procurement of land; the cost of additional parcel searching and perhaps the price o f even another parcel are passed on the consumer {Davis, 1963, pp. 375-86). In addition even i f the parcel is rezoned, the cost o f changing the boundaries often exceeds the minimal remuneration supplied by the p e titio n e r . 26 Exclusionary or special in te re s t zoning is another type of inten­ tional e x t e r n a lit y which occasionally manifests i t s e l f as minimum l o t size. Exclusionary zoning in the suburbs re su lts in the formation o f a band of minimum l o t sizes of one or possibly two acres. The settlement pattern in th is area takes on a leapfrog appearance because o f the large area required between residences (ASPO, 1968, p. 66). In d u s trial and comnercial a c t i v i t i e s are re s tric te d in t h e i r choice of location and may pay a higher price fo r t h e ir eventual choice. Exclusionary zoning is often used as a method of elim in ating low income and m inority housing because th at type of housing requires r e l a t i v e ly low-cost parcels. Another form of in te n tio n a l e x te r n a lity is the imposition o f a non-conforming status upon a stru ctu re. A building is considered non- conforming i f i t f a i l s to meet the requirements of an ordinance adopted a f t e r i t s construction. As a ru le once the ordinance is adopted no other non-conforming a c t i v i t i e s are permitted to locate in the d i s t r i c t . Thus zoning gives a monopoly position to the i n i t i a l non-conforming uses and often i t s sheltered position is s u f fic ie n t impetus fo r sustained economic growth by the non-conforming a c t i v i t y (ASPO, 1968, p. 58; Weimer, 1966, pp. 255-84). Another type of in te n tio n a l e x te r n a lity arises from the fa c t th at a p lo t o f land is zoned or rezoned fo r a use and th is fa c t often provides a s u f f ic ie n t j u s t i f i c a t i o n fo r an automatic increase in land value fo r the surrounding properties (ASPO, 1968, p. 66). For example, a g ric u l­ tu ral land adjacent to a commercially zoned parcel is often sold a t a p a rc e l-ra te higher than the average a g ric u ltu ra l rate and more comparable to re s id e n tia l or commercial rates. An a l e r t land speculator may purchase the land a t an a g ric u ltu ra l r a t e , w ait a few years f o r a 27 commercial in tru s io n urban sprawl and then s e ll i t a t a commercial p ric e . In order to reduce the speculative p o tential and re s u ltin g e x t e r n a lit y arising from a zoning c la s s if ic a t io n one researcher has suggested th a t a development tax be levied ( P l a t t , 1972, p. 43). In summary in te n tio n a l e x t e r n a lit ie s a ris in g from zoning are often manifested in the d i s t r i c t i n g p attern as o utlined in the ordinance. One d eficien cy in the l i t e r a t u r e on zoning is a f a i l u r e to give consideration to the d i s t r i c t i n g problem and to e x t e r n a lit ie s a ris in g from i t . ^ The present methods o f d i s t r i c t i n g tend to "balkanize our c i t i e s into d i s t r i c t s with precise and r ig id boundaries" (Reps,1964, p. 12). D is t r ic t s are often drawn on the basis o f a d is tin c tio n o f uses ra th e r than in te rre la tio n s h ip s o f uses (Delafons, 1969, p. 94 ). Often the d is t r i c t i n g scheme presented in th is research stresses the i n t e r ­ re la tio n s h ip o f land uses. C ritiq u e o f Zoning The c r i t i q u e of zoning as a process is organized in to the following sections: a) Underlying assumptions o f land use re g u latio n s ; b) S tru ctu ral weaknesses o f zoning ordinances and adm in istratio n s; c) E x te r n a lity e ffe c ts of zoning and d i s t r i c t i n g and; d) Proposed solutions. In each of these sections the current thinking on zoning is elaborated. At the end of the c r itiq u e some solutions are proposed which may ^In reference to the d i s t r i c t i n g scheme, i t should be c le a r ly stated th a t the d i s t r i c t s are use d i s t r i c t s and do not include planned u n it development d i s t r i c t s . 28 m itigate some of the obvious defects o f the present system o f zoning. In the f in a l portions of th is section the position of th is research in the proposed solutions is mentioned. Early thinking on land use regulation in the United States was based upon the following assumptions: a) the c ity is an integral p o l i t i c a l u n it; b) the c i t y is a melting pot where ethnic and fusion occurs; cu ltu ral c) the c i t y is capable of financing i t s own programs with l i t t l e or no federal or state aid or control and; d) the c it y is e a s ily delim ited from i t s support area (Doebele, 1963, pp. 5 -1 3 ). Changes have undoubtedly occurred which have rendered many, i f not a l l of these assumptions mistaken. Government fragmentation, ra c ia l p o la riz a tio n and suburbanization have reduced the p o l i t i c a l , cu ltu ral and ethnic inte g ratio n o f the c it y . C itie s are slowly becoming bankrupt due to a decreased tax base brought on by the movement o f whites and industry to the suburbs. fL r central c ity Added to t h e i r p lig h t is services. an increased demand Federal assistance is now required to lessen the urban fin a n c ia l b lig h t. As a re s u lt of these changes a new scale o f urban liv in g is emerging characterized by an absence o f p o l i t i c a l boundaries (Freidman, 1965, pp. 312-20), h i t or miss urban growth (Knetsch, 1962, p. 1217), and economic d ec e n tra liza tio n (Proudfoot, 1954, pp. 415-9). As a re s u lt land uses are emerging which may lead to potential c o n flic ts {ASPO, 1968, pp. 7 -8 ). Zoning ordinances, a method o f land use control are becoming obsolete and incapable o f handling the re s u ltin g chaotic urban land uses~(Delafons, 1969, p. 48; Lovelace and Weismantel, 1961, p. 7; Proudfoot, 1954, pp. 41 5-9). I n i t i a l l y zoning was designed as a holding 29 operation not as an apparatus fo r resolving land use c o n f lic t { T o ll , 1969, p. 179). However, in many m u n ic ip a litie s zoning is disregarded while in other communities zoning has become a game o f municipal "oneupmanship," parochial and exclusive to say the le a s t (Doebele, 1963, pp. 5-1 3). The present j u s t i f i c a t i o n fo r land use controls in the United States stresses the sovereignty of p riva te property in te re s ts which may not be exactly what planners and other municipal decision makers regard as desirable (Delafons, 1969, p. 32). Private property rig hts are also given p r i o r i t y over the preservation o f space fo r the public such as ag ric u ltu ra l land and open space (Feiss, 1961, pp. 121-8; Delafons, 1969, p. 8 ) . However, since zoning is a public good, then p rivate property rights may be le g a lly subverted i f the s itu a tio n warrants i t . Sometimes zoning c o n flic ts with the community in te re sts ju s t as i t does with the private property in te re s ts . A community-zoning c o n f lic t often arises when the ordinances are based on an outdated master plan (Shenkel, 1964, p. 58; Reps, 1964, p. 13). Other times in ju s tic e s may occur when mutually exclusive zoning c la s s ific a tio n s allow the land speculator to reap w in d fall p r o fits by the rezoning o f vacant land. In these situations the community's treasury does not share in the p r o f i t earned by the developer. Zoning has a diffused power structure. There are few e ffe c tiv e planning au th o ritie s covering more than one local government in the urban area. There are few regional planning boards and they have only lim ited power (Delafons, 1969, p. 9 ). Administration and enforcement are also hurt by the la c k -o f a national scale of planning to regulate urban growth. Where enforcement is present, i t is often centered in 30 areas possessing a high degree o f ra c ia l and economic homogeneity (Siegan, 1972, p. 225). However, enforcement of public good must be equally d is trib u te d and often the zoning board o f appeals possesses lim ited d is cretio n in many of i t s decisions (Reps, 1964, p* 13). For example the lack o f s p e c i f ic it y , standards and o bjective c r i t e r i a often thrusts the planning and zoning commissions into confusion and inconsistent behavior (W h itn a ll, 1963, p. 9 ). Proposed Solutions Zoning is not without i t s c r i t i c s but few i f any propose a lte r n a tiv e strategies fo r land use co n tro l. The basic thesis o f th is research is th at zoning is required but modifications are necessary. For example, s it e c h a ra c te ris tic s are a v a lid c r it e r io n upon which to develop a zoning ordinance but the s itu a tio n a l ch a ra c te ris tic s o f a parcel are equally important and demand equal consideration. Two proposals have been advanced to improve the zoning p ractice. One proposal suggests th a t economic analyses and impacts o f zoning ordinances be s p e c if ic a lly defined to make i t "more cred ible to land buyers" (Clawson, 1971, p. 343). Any new type of d i s t r i c t d e lim ita tio n should also take into account the relationships between the d is t r i c t s (Delafons, 1969, p. 44). Furthermore, planners need to "respond to the needs of in te ra c tio n , interdependence and unity" (Loeks, 1963, p. 29). A c c e s s ib ility is an example of one type o f economic analysis based upon s itu a tio n a l c h a ra c te ris tic s o f a d i s t r i c t . Since a c c e s s ib ility is a measure of in te ra c tio n , i t w i l l also indicate the in te rre la tio n s h ip s and interdependences between the d i s t r i c t s . 31 URBAN LAND MARKET Models of Urban Land Use The purpose of this section is to place in perspective zoning and land use models dealing with the urban land market. Analyzing models of land use provides a general treatment of the land market from which a more s p e c ific analysis o f zoning's impact on land uses can be derived. Early models dealing with the urban land market paid l i t t l e , i f any a tte n tio n , to the sp atial component o f urban economics {Ukeles, 1965, p. 4 ) . Distance along with in te ra c tio n and regional independence were not values as factors influencing the production and consumption functions. One reason fo r th is shortsightedness was th a t a l l suppliers were located a t approximately the same point in space (Ukeles, 1965, p. 4 ). One of the e a r l i e s t models stressing a sp atial dependency was constructed by Haig (1929). B asically his model explained urban land uses by re la tin g them to underlying economic forces such as a c c e s s ib ility . Later work by R a t c l i f f (1955) expanded the concept of the urban market by assuming th a t economic or locational p ro d u ctivity o f the land can be assessed by distance from the market. That is p ro d u ctivity is maximized when distance costs are minimized and other locational costs are d is trib u ted r e l a t i v e ly evenly among users ( R a t c l i f f , 1955, p. 127). Cost provided the c o n tro llin g force in organization o f urban a c t i v i t i e s according to R a t c l i f f . Ukeles stated th a t R a t c l i f f ' s model fa ile d to recognize: a) locational patterns o f consumers; b) distance as only one of a number o f locational considerations and; 32 c) location as possibly being unimportant fo r ce rta in types of economic a c t i v i t i e s (Ukeles, 1965, p. 7 ). Building upon Haig, Thunen and R a t c l i f f , Alonso developed a more comprehensive model of urban land use. His model assumed th a t a location closer to the CBD costs more than a location a t a g reater distance. In addition a zone o f in d iffe re n c e may e x is t a t a c e rta in distance where the consumer is r e l a t i v e ly ambivalent to a p a r tic u la r series of locations (Alonso, 1960, pp. 149-57). B asically the model ill u s t r a t e d how at increasing distances from the market, a firm would trade lower transportation costs and location rent fo r needed a c c e s s ib ility . At closer distances, a firm would accept less space per d o lla r and a higher location rent fo r the advan­ tage of increased a c c e s s ib ility . Reasoning fu r t h e r , he concluded that a series o f bid rent curves could be derived fo r a group of economic a c t i v i t i e s thus ind icatin g t h e ir locational d is tr ib u tio n . For instance commercial a c t i v i t i e s are most l i k e l y to pay a higher cost fo r accessi­ b i l i t y than re s id e n tia l or in d u s tria l a c t i v i t i e s . According to Ukeles one major defect o f the Alonso model is the f a i l u r e to accept the multi-directedness o f the consumer (Ukeles, 1965, p. 8 ). The location of re s id e n tia l areas may be explained by factors other than space and distance which are more important in other types o f economic a c t i v i t i e s . A th ir d model was developed by Herbert and Stevens (1960). They defined s ite rent as a portion of the to ta l re s id e n tia l rent with the l a t t e r equaling the d iffe ren c e between the to ta l costs and the costs of producing the commodity. Herbert and Stevens also subdivided re s id e n tia l rent in to dwelling costs, s ite costs, amenity costs and a c c e s s ib ility costs (Herbert and Stevens, 1960, pp. 21-36). Unlike the Alonso model, th is model assumes th a t i f a l l other factors are 33 equal, the closer to a CBD th at a firm is located, the lower is the a c c e s s ib ility costs and the higher is the s it e cost. This re latio n sh ip is most v a lid i f one assumes th at dwelling costs or space per u n it along with amenity costs are held r e l a t i v e ly constant. I t is quite evident from the above models th at a c c e s s ib ility or the reciprocal of the costs o f movement acquires major importance in the explanation of urban land uses. In the sections th a t follow a f u l l e r treatment o f factors influencing a c c e s s ib ility , land uses and land values is provided. Although these factors are not integrated into a model, they w i l l provide background fo r the development o f the problem. Factors A ffecting Land Values A c c e s s ib ility to employment, shopping and amenities, both natural and c u lt u r a l, plays a v i t a l ro le in explaining some of the v a ria tio n of land values w ithin the c i t y . However, there are other more s a lie n t locational factors also a ffe c tin g land value. One such fa c to r is the supply o f vacant land which determines land value p a r tic u la r ly i f natural or man-made lim ita tio n s r e s t r i c t the supply o f su itab le in d u s trial and commercial land (Sagalyn and Sternbieb, 1973, p. 10). A second fa c to r is the nature o f the s ite which often lim its the permitted use on the s it e (Yeates, 1965, pp. 57-70). For example, s in g le -fa m ily dwellings are often the only permitted use on extremely h i l l y regions even though the h i l l s may be situated w ithin close proximity to the CBD. I f natural conditions do not l i m i t the achievement of a highest use, then the community by regulations or a ttitu d e s may i n h i b i t i t (Sagalyn and Sternbieb, 1973, p. 9 ). As previously mentioned, the c it y o f Vernon, C a lifo rn ia encouraged by 34 zoning regulations and property tax in c e n tiv e s , the establishment of in d u s tria l a c t i v i t i e s in the c i t y . a r t i f i c i a l l y increased. By doing th is the value o f land was A th ir d fa c to r influencing land values is the amount of p ublic c a p ita l investment in planned f a c i l i t i e s ( i . e . sewer lin e s , highways, e t c . ) . A fourth fa c to r influencing land value is the in te n s ity o f surrounding development. value o f land. The higher the i n t e n s it y , the higher is the The best example of th is concept is found in an analysis of land value w ith in the central business area o f a c i t y . A graph o f land values in three dimensions e x h ib its a v a rie ty o f cones, nodes and apexes (S e y frie d , 1963, pp. 275-84). A cone of r e l a t i v e l y low land value near a CBD may in d ic a te the outer fringes o f a ghetto. A node of high land values may be found a t major in te rs ec tio n s w hile the highest land value w ith in the c i t y is found a t the peak-value in te rs e c tio n in the CBD. One underlying reason f o r such a highly skewed d is t r ib u t io n is th a t land value increases as the costs o f overcoming distance decreases {S e y frie d , 1963, pp. 275-84). Thus in support of the Alonso model but from a d i f f e r e n t perspective, land values represent a t r a d e - o f f between the costs of movement and the importance of contact. The ro le of a c c e s s ib ility and land values demands closer sc ru tin y . I t has been found th a t ra p id ly growing areas o f a c i t y are also highly accessible (Hayes, 1957, pp. 177-81; Hansen, 1959, pp. 7 3 -6 ). In a d d itio n , Hansen found th a t " a c c e s s ib ility and a v a i l a b i l i t y o f land fo r economic growth is a function of the growth in the area during the preceding period" (Hansen, 1959, pp. 7 3 -6 ). controls the growth in an area. Public c a p ita l investment Implied by Hansen's findings is a 35 threshold f o r developed land. I f a threshold is exceeded, then increased a c c e s s ib ilit y in th a t area may not increase the economic growth of the area. Increasing the a c c e s s ib ilit y to an area may not promote a complementary change in land values and land in te n s it y . In the San Francisco and Oakland a re a , changes in land value followed less clo sely changes in a c c e s s ib ilit y than changes in population, o f f i c e space and r e t a i l sales (Wendt, 1961, p. 3 2 ). In Chicago Yeates found th a t changes in land value were associated w ith changes in population d e n s ity , average income and the ra c ia l composition of the area {Yeates, 1965b, p. 6 5 ). P l a t t found th a t i f a c c e s s ib ilit y is c o n tro lle d , then the land value depends on many o f the previously mentioned variables plus the extent of public services such as f i r e and p o lice . The d ir e c t re la tio n s h ip between land value and a c c e s s i b i l it y , although i n f l u e n t i a l requires some q u a lific a t io n s . In the long run, as a c c e s s ib ilit y into an area increases, land values also tend to increase. However, in the short run, other non-economic facto rs a f f e c t the land value and land use in t e n s ity . Zoning and other forms o f land use regulations are considered by the author to be long term re g u latio n s . Most c i t i e s in the United States have had some form of a zoning ordinance fo r well over t h i r t y years. Thus fo r the purpose o f th is research, i t is assumed th a t a major in flu e n ce r o f land value in the long run is a c c e s s ib ilit y and zoning. A c c e s s ib ility and Land Use The term a c c e s s ib ilit y has been c o n tin u a lly used in the preceding sections w ithout an adequate d e f i n i t i o n . In th is b r i e f section a 36 d e f in it io n o f a c c e s s ib ilit y is provided along w ith some statements on the need f o r a c c e s s ib ilit y by d i f f e r e n t types o f land uses. The next to l a s t section o f th is chapter w i l l then present a graphic portrayal of many concepts alluded to in the preceding sections. A c c e s s ib ility may be defined as the reciprocal o f the cost o f moving people and goods between points in space {Pendelton, 1963, p. 1 ) - ^ the costs increase, a c c e s s ib ilit y decreases. As A c c e s s ib ility is a component o f the land re n t (Pendelton, 1963, p. 9 ) . Land re n t is a function of distance and is not the same as space re n t. As evident from the above d e f i n i t i o n costs o f movement are broadly defined. In th is research costs are used w ith in the context o f o p p o rtu n itie s; th a t i s , as a c c e s s ib ilit y to an area increases, the s p a tia l o pportunities fo r a v a r ie ty o f economic and social a c t i v i t i e s increases, thereby reducing the costs incurred in t r a v e ll i n g to another location which may o f f e r the same types o f services. A c c e s s ib ility has many d i f f e r e n t facets such as a i r l i n e , highway, public tra n s p o rta tio n and pedestrian movement. In a d d itio n , accessi­ b i l i t y operates on a v a r ie ty of scales such as n a tio n a l, re g io n a l, interu rb an , intraurban and personal. used to measure a c c e s s ib ilit y . F in a lly d i f f e r e n t indices may be For example, one could use e f f e c t iv e distance t r a v e lle d to employment or shopping as a measure. Another may be the o v e ra ll distance from one point to a l l other points in the area. Time is y e t another measure o f a c c e s s ib ilit y p a r t i c u l a r ly in the work t r i p and in te c h n o lo g ic a lly advanced countries. ^Two dimensional urban space is implied by the research. The researcher recognizes the existence o f three dimensional space in the c i t y but three dimensional zoning has not y e t evolved. 37 The importance o f a c c e s s ib ility also depends upon the nature o f the economic a c t i v i t y . Normally in d u s t r ia l, commercial and professional a c t i v i t i e s place a premium value on high degrees o f a c c e s s ib ility whereas re s id e n tia l uses are often f a r less dependent upon i t (Dickinson, 1964, p. 177). As M itch ell s ta te s , the '*way in which the movement of persons and goods influences an establishment's choice o f location is related to i t s function and type o f a c t iv it y " ( M itc h e ll, 1954, p. 106). Furthermore, transactions or movement occurs con tin ually w ithin the urban area. Understandably, movement between two or more parcels implies a measure o f sp atial dependency. The work t r i p is one such example o f a transaction lin k in g in d u s tria l and re s id e n tia l land uses. Since a c c e s s ib ility varies from point to point in space depending on the mode of movement and since a hierarchy o f a c c e s s ib ility may be constructed, then i t follows th at land uses also sort themselves in to various patterns since the l a t t e r are in a large measure a function o f the movement costs (Dickinson, 1964, p. 194). A high degree o f a c c e s s ib ility is also associated with a high in te n s ity of land use (Hasegawa, 1963, p. 145). Contrasting the land use in te n s ity in the CBD with the in te n s ity in the suburbs i ll u s t r a t e s th is concept. Since there is an i r r e g u l a r it y in the d is trib u tio n of land uses w ithin a c i t y , then i t follows th at there is also a s im ila r i r r e g u la r it y in the in te n s ity o f land uses. i r r e g u la r it y include: Factors fostering this h is to ric a l development, s it e c h a ra c te ris tic s , building codes and f i n a l l y zoning. S ite factors play a v i t a l ro le in determining whether or not the a c t i v i t y can perform in the area. Thus i t is important in any study o f land use regulations to incorporate not only the s itu a tio n a l ch a ra c te ris tic s but also the s i t e variable 38 (Mandelker, 1972, pp, 121-4). Within th is research, s i t e is incorporated into the analysis by selecting land values on the basis of the present zoning plan which is in a large measure, s i t e oriented. A Model I l l u s t r a t i n g the E ffe c t o f Zoning on the Urban Land Market The u n it cost o f tr ip s from the CBD to a v a rie ty o f locations is assumed to be a lin e a r function (Figure 1). Therefore a t a distance of D-j the u nit costs o f the t r i p equal costs C-j. The location rent curve re fle c tin g the costs o f movement is presented in Figure 2. That i s , as the cost of additional tr ip s increases, the number of trip s made decreases. One assumption fo r the demand curve is a constant real i ncome. I f one connects the demand curve with the cost curve then the to ta l cost o f the t r i p can be determined. the point This process involves connecting with the point T2A-| and the point D2C2 with the T^A2 . Thus the to ta l cost o f the t r i p from the CBD to D2 is represented by the area under OCjAiTg. Furthermore the locations rent or the cost of a c c e s s ib ility a t D-j is represented by the area A^C-jTg which is greater than the location rent a t D2 which equals the area A2C2T^. Thus in the words of Pendelton (1963) the location D-j is more 'superior' than the location D2 by the area represented by the d ifferen ce in areas between Ai C-|T2 and A^^T-j. The s u p e rio rity alluded to above applies only to one a c t i v i t y at two d if f e r e n t locations. I f a v a rie ty of location rents are calculated, then competition fo r the most 's up erio r' location w il l be based not only on distance but also on the p r o f i t structure of the a c t i v i t ie s (Figure 3 ). The location rent diagram assumes th at the t r i p maker is confronted with varying u n it costs per t r i p based of course, upon the nature of the 39 COST Figure 1 CURVE Unit cost per t r i p 1 Distance DEMAUD Fi gure Cost of new t r i p over u n it cost CURVE A 2 A 1 Number o f tr ip s made LOCATION RENT Figure use A use B Locati on Rent use C Distance 40 economic a c t i v i t y a t the d e s tin a tio n . Thus w ith a v a r ie ty o f economic a c t i v i t i e s , one gets a number o f location re n t lin e s f o r the uses A, B and C. Putting Figures 1, 2 and 3 together one finds a predominance o f land uses supporting a c t i v i t y A. This type o f land use would forego lower land costs a t g re a te r distances f o r the advantage of frequent tr ip s and lower u n it costs per t r i p , i . e . a c c e s s ib ilit y . The question then becomes--What i f some type o f land use regulation is introduced in to the system? Furthermore, assume th a t the zoning plan is incompatible w ith the e x is tin g d is t r ib u t io n o f land uses (Figure 4 ). In the o v e ra ll e v a lu a tio n , use A is hurt by the poor zoning. As i t i s , use A is e it h e r non-conforming or i t w i l l have to re lo c ate to another location but where can i t go? Assuming th a t re lo c a tio n is the strategy chosen then an examination o f the graph w i l l point out how a c t i v i t y cannot economically re lo c a te in the BC segment. I f i t does, then i t s p r o f i t s tru c tu re w i l l be diminished since i t w i l l enjoy less accessi­ b i l i t y with an accompanying reduction in t o ta l revenue. A c t iv i t y B under the present regulations may possess a lo c atio n a l monopoly since i t can lo c a te in the area AB and s t i l l p ro fit. re s t assured o f a reasonable In summary then the re lo c a tio n o f a c t i v i t y A due to the imposition o f the land use regulations represents an example o f negative e x te rn a litie s . The second case i l l u s t r a t e s th a t a p o s itiv e e x t e r n a lit y was enjoyed by a c t i v i t y B. 41 ZONING AND Fi gure Locati on Rent LAND USE use B use C Zoning Plan Zone fo r Use B Zone fo r Use D,A & C Zone fo r Use B & A D Distance Chapter Three Hypotheses and Data C o lle ctio n 42 43 INTRODUCTION This chapter presents the research and s t a t i s t i c a l hypotheses tested by th is study. Following the hypotheses is a detailed discussion of the sampling designs fo r the primary data th at were collected. By specifying the design in this way, the complexities and problems involved In the co lle ctio n o f the data w i l l be made apparent. I t should be noted th at the research e f f o r t is concerned with both the development of a technique to measure the situ a tio n a l orien tation o f zoning d is t r i c t s and to assess the impact of the new situ atio n al zoning upon land values. I f i t is found th a t the data f a i l to support the model, the technique o f zoning regio nalizatio n should nonetheless remain useful. As stated e a r l i e r a survey of pertin en t l i t e r a t u r e has revealed th at methods of geographic re g io n a liza tio n have not been applied to the problems o f zoning. STATEMENT OF HYPOTHESES Hypothesis 1 Homogeneity of Land Values The d e lim ita tio n of zoning d is t r i c t s emphasizes more of the s ite ch a rac teris tic s o f a parcel and fewer of i t s s itu a tio n a l c h a ra c te ris tic s . To the degree th at th is emphasis occurs, zoning can be said to f a i l as a public good. That i s , s ite -o rie n te d zoning may impose negative e x te r n a lit ie s or locational sp illo v e rs upon certain parts of a c i t y . In operatio nalizing th is concept of e x te r n a litie s i t is assumed th at the heterogeneity of various social and economic functions w ithin a zoning d i s t r i c t produces 44 heterogeneity of land values. I f zoning boundaries were redrawn in a way th at incorporates not only the s i t e lim ita tio n s but also a c c e s s ib ility c h a ra c te ris tic s o f the land, would th is strategy increase or reduce the heterogeneity o f land values w ithin the zone? Research Hypothesis A re g io n a liza tio n or a c la s s ific a tio n system based upon proximity to sp atial opportunities or a c c e s s ib ility , produces more homogeneity in the d is trib u tio n of land values o verall and by zoning d i s t r i c t than existing methods o f zoning d e lim ita tio n s . S t a t is tic a l Hypothesis The standard deviation of land values overall by d i s t r i c t fo r the s itu a tio n a l based zoning is less than the standard deviation of land values by d i s t r i c t fo r the site-based zoning. Test S t a t i s t i c I f s-| equals the standard deviation o f land values derived by a s itu a tio n a l or a c c e s s ib ility approach and i f s2 equals the standard deviation of land values ex istin g in present zoning schemes, then H^ is accepted i f F (a c tu a l) = £2 is larg e r than Fnl S1 where N-| and N2 represent degrees o f freedom. n2 (expected) On the average commercial a c t i v i t i e s tend to be located in the most accessible portions o f the c i t y ; in d u s tria l a c t i v i t i e s on the average tend to be located in the next most accessible portions and f i n a l l y re s id e n tia l areas are located in the areas of overall lowest a c c e s s ib ility . d is tric ts . This assumption is needed to id e n tify the new zoning 45 Hypothesis 2 Homogeneity of Land Values in a Zonal AggregationLand uses tend to vary w ithin a c i t y by a zonal p attern . Land uses are quite s im ila r w ithin the co n ce n tric ally shaped central business d i s t r i c t (CBD) of Lansing (T a y lo r, 1961, p. 13). As distance from the CBD increases, another c ir c le o f r e l a t i v e ly s im ila r land uses exists and a t even greater distances, other s im ila r land use zones soon appear (T aylo r, 1961, p. 12). Since zoning regulates land uses then i t should e x h ib it a r e l a t i v e l y s im ila r zonal arrange­ ment. I f the zones were redefined to incorporate more of the s itu a tio n a l or a c c e s s ib ility c h a rac teris tic s of the land parcels, would the homogeneity of land values w ithin the zones increase? Research Hypothesis I f land values are aggregated into concentric zones, then th e ir d is trib u tio n as defined on the basis o f s itu a tio n a l zoning w il l be more homogenous than the d is trib u tio n of land values aggregated by concentric zones fo r the more site-based zoning. S t a t i s t i c a l Hypothesis The standard deviation o f land values aggregated by concentric zones fo r the s itu a tio n a l zoning 1s less than the standard deviation of land values aggregated in a s im ila r manner and based on s ite zoning. Test S t a t i s t i c I f s-j equals the standard deviation of land values in a s itu a tio n a l approach and i f Sg is equal to the standard deviation 46 o f land values in s i t e based zoning, then F (a c tu a l) equals s2 /s i anc* reJection occurs i f F (a c tu a l) is g re a te r than F(expected). Hypothesis 3 Homogeneity of Land Values and sectoral Arrangement Since land values as a ru le tend to be affe c te d by a c c e s s ib ilit y than a sectoral aggregation o f land values defined by major a r t e r i a l s w ith in both s itu a tio n a l and s it e based zoning should produce an even g re a te r degree of homogeneity o f land values (Hasegawa, 1961, p. 151). However, the question arises as to whether the degree of homogeneity is g re a te r in the s i t u a t i o n a l l y defined zoning d i s t r i c t s than in the s i t e zoning. Research Hypothesis I f land values are aggregated in to sections defined by major roads, then the d is t r ib u tio n o f land values f o r the a c c e s s ib ilit y based zoning is more homogenous than the d is t r ib u tio n of land values fo r the s i t e based zoning plan. S t a t i s t i c a l Hypothesis The standard d eviatio n of land values aggregated by a sectoral arrangement and c la s s if ie d in to land use zones by a s itu a tio n a l approach is less than s im ila r ly aggregated land values c la s s if ie d on the basis of the s i t e based zoning. Test S t a t i s t i c I f s.j equals the standard d eviation o f land values in a s itu a tio n a l approach and i f s2 is equal to the standard deviatio n 47 of land values in s i t e based zoning, then F (actual) equals sg/s-j and re je c tio n occurs i f F (actual) is greater than F (expected). Study Area The c ity of Lansing, Michigan was chosen as a study area fo r the research fo r the following reasons: a) Lansing contains a wide v a rie ty o f zoning c la s s ific a tio n s . This v a rie ty is needed so th a t the model w i l l have application elsewhere; b) Lansing contains w ithin i t s boundaries a v a rie ty of functional nodes fo r residencies, shopping, employment and industry, e tc . Thus a c c e s s ib ility indices w i l l show a s u f f ic ie n t pattern of d if f e r e n t ia t io n ; c) Lansing is situated on a network o f major north-south and east-west a r t e r i a l s. Therefore potential movement in the c it y contains a greater degree of v a rie ty than smaller c it ie s with only one or two major a r t e r ia l s ; d) Lansing has industry in central and peripheral areas providing fo r a greater d iv e rs ity 1n zoning c la s s ific a tio n s . Many o f these in d u s tria l areas l i e w ithin close proximity to ex istin g or future re s id e n tia l communities; e) The author is most f a m ilia r with the c i t y and i t s economic a c tiv itie s . This f a c i l i t a t e s in the in te rp re ta tio n of land uses and in t h e ir spatial grouping. f ) The author was able to gain the cooperation of local planning o ffic ia ls . Without t h e ir help, data co llectio n would have been severely hampered. 48 DATA REQUIREMENTS AND SAMPLING DESIGN Types of Data Land values and land uses are the two primary types of data used in devising the sampling design. Land values f u l f i l l a role as a te s t v a ria b le ; they are used in the above hypotheses to determine a w ith in zone v a ria tio n . Land uses on the other hand function in a develop­ mental capacity fo r the model since they form the foundation fo r the measures used to define the s itu a tio n a l based zoning patterns. I t is assumed th at land uses incorporate a s ig n ific a n t portion of the local ch a racteristics upon which c e n tr a lit y can be measured. Other sources o f data fo r a study of th is nature are procured from a secondary source and then modified by the author fo r the research. An example of the f i r s t type are nodes of shopping (e .g . Frandor shopping center) and nodes o f employment (e .g . Motor Wheel). The time distances to travel to these and other nodes represent an example o f the second type of data. Sampling Design fo r Land Values Land values in Lansing are catalogued on the basis of sections. Sections are individual grid squares o f 3500 fe e t by 3500 fe e t or approximately two-thirds a mile in e ith e r d ire c tio n . Major north- south and east-west a r t e r ia ls serve as boundaries between sections. However, fo r the purpose of cataloging land values whole sections ( i . e . 3500 by 3500 sections) are subdivided into one-eighth sections of approximately 875 fe e t by 1700 fe e t. In t h e i r data collections tax assessors combine two one-eighth sections beginning with the top 49 two l e f t sided eighth sections (Figure 5 ) . For example 1/8 section A in Figure 1 is combined w ith 1/8 section B to form a q uarter section. The procedure f o r sampling ind ividu al land values was subdivided in to three stages: 1) superimposition stage 2) determination stage 3) compilation stage Each o f these stages f u l f i l l s a s p e c ific ro le in the random selectio n and evaluation of the land value data.^ Stage 1 , the superimposition stage, arises out of a need to s t r a t i f y the land values by zoning type. S t r a t i f i c a t i o n is considered important because the proposed re g io n a liz a tio n recognizes the importance o f the s i t e based zoning regu lation s. P a r t ic u la r a tte n tio n is paid to those regulations th a t p ro h ib it a c e rta in type o f land use because of the physical lim ita tio n s o f the land such as m u ltip le flo o r o f f ic e building in a swamp. The graphical superimposition of the section map onto the zoning map was the only requirement fo r th is f i r s t stage. The second stage begins with estim ating to the nearest 10% the portion of a one-eighth section th a t was devoted to r e s i d e n t ia l, commercial or in d u s tria l zoning. A g rid containing a mesh of evenly spaced dots was used to estimate the area. Percentage data fo r a one-eighth section were averaged with the adjoining one-eighth section to secure one-quarter section data. The f i n a l one-fourth ^Land values were chosen over to ta l assessed value because the l a t t e r includes s tru c tu ra l c h a ra c te ris tic s which r e la t e more to the socio-economic c h a ra c te ris tic s of the owner and less to the r e l a t i v e lo c atio n o f the p arcel. 50 DEFINITION OF SECTIONS 1750 fe e t 1/8 section A 1/4 section 1/8 section B 3500 fe e t 1750 feet Figure 5 51 section figures indicated what percentage of the to ta l land values selected should come from r e s id e n t ia l, cormercial or in d u s trial parcels. I t was assumed th a t fiv e values per quarter section provides both a r e l a t i v e ly even and complete coverage of the e n tire study area. The actual number o f f i v e values per quarter section was determined by the re g io n a liza tio n scheme described in the subsequent chapters. Since there are approximately 118 quarter sections, i t was determined th a t f iv e values per quarter would y ie ld less than 620 land values. Any number greater than fiv e would s ig n if ic a n t ly increase computer analysis and storage along with the costs o f the computer drawn maps. 602 land values were selected from a population to ta l of 43,500; thus a sample size o f 1-1/2 percent was achieved (Table 1 ). When examining Table 1 the differences between the expected values and the actual is best explained by parcels being la rg e r in size than expected, p a r t ic u la r ly in in d u s tria l areas. I t should be noted th a t the sample size was considered f a r less important in the selection o f land values than was the s t r a t i f i c a t i o n o f these values by zoning type. The f in a l portion o f the second or determination stage of the land value selection v/as completed with the randomization of the land values. This was accomplished by f i r s t determining what percentage o f f iv e parcels would be selected from r e s i d e n t i a l l y , coirmercially or in d u s t r ia lly zoned land. Each parcel has an eig h t d i g i t legal number in the tax assessor's records ( e .g . 36-171-101). The f in a l three d ig its represent a sequential number normally from 101300. Using a three d i g i t randomized number tab le th at parcel whose legal number came closest to random number was selected fo r inclusion. 52 TABLE C o m p a ris o n Z o n in g of E x p e c te d 1 and A c tu a l Land V a lu e s E x p e c te d Type A c tu a l R e s id e n tia l 393 399 C o m m e rc ia l 133 137 In d u s tr ia l 79 66 605 602 T o ta l S o u rc e : C a lc u la te d by a u th o r. 4 53 Once a p o tential l i s t of 602 land values was selected, the compilation stage o f the design began. problems developed. At th is point some unforeseen One such problem was the need to develop land values per standard u n it o f area. Due to local p e c u lia r it ie s land values w ith in the study area are not consistently given in standard u n its. Residential properties are lis t e d as land value per fro n t foot while commercial and in d u s tria l properties are lis t e d as land value per square fo o t. Land value per square foot was selected. However, in certain ir r e g u la r ly shaped re s id e n tia l properties square footage was estimated by the longest dimensions in both d ire c tio n s . In a l l circumstances additions or deletions to land value made by the assessor were deleted. Such changes may occur fo r excessive land area or fo r f l a t la n d .1 Another problem a ris in g in the compilation stage was the u n r e l i a b i l i t y of the zoning c la s s ific a tio n given in the tax assessor's books. Therefore the selected land parcels were p e rio d ic a lly checked with the zoning adm inistrator fo r a zoning updating. A time lag of approximately a year appeared to e x is t between the time a new zoning c la s s ific a tio n was granted and the time the c la s s ific a tio n was recorded in the tax assessor's book. In t e r e s tin g ly , in Lansing a zoning c la s s ific a tio n is one o f the c r i t e r i a used to determine the assessed valuation p a r t ic u la r ly fo r commercial and in d u s tria l property. ^In conversation with Mr. James Meyers, Chief Assessor fo r the C ity of Lansing, on February 20, 1974, he stated th at these extra calculations were "subjective and subject to change." 54 Two ad d itio n a l problems incurred in the compilation o f land values were missing assessors sheets and vacant land. Due to an updating o f assessment values during the time th a t the land values were selected some o f the data fo r randomly selected parcels were not e a s ily a v a ila b le . A fte r considerable in v e s tig a tio n , the author was able to get some o f the needed inform ation. e it h e r not "a v a ila b le a t a l l " or missing. Twice the sheets were When th is occurred the parcel on the preceding page o f the assessment book was selected provided th a t i t met the required zoning Vacant land was not included in c rite ria . the study f o r two reasons. F i r s t , vacant land w ith in the study area was au to m atically c la s s ifie d by the assessor as s in g le -fa m ily r e s id e n tia l.^ I t was f e l t th a t th is c la s s if ic a t io n was t o t a l l y unrepresentative of the nature of the land. Second, i t is hoped th a t the technique developed in th is research w i l l serve as a tool to evaluate the p o te n tial zoning c la s s if ic a t io n of vacant land. By measuring the a c c e s s ib ilit y of the vacant parcels and comparing th is value with values o f occupied land, zoning adm inistrators w i l l have more of a s u b sta n tiative base upon which to determine a new zoning c la s s if ic a t io n f o r vacant land. Thus including land values f o r vacant land may d is t o r t the o ve rall v a l i d i t y of the technique. One f i n a l problem a ris in g in the data compilation stage occurred when two or more zoning c la s s ific a tio n s were provided f o r one p arcel. In the m a jo rity of such s itu a tio n s , a parcel was designated as "F" 1Approximately 65-70% o f the t o ta l land area is zoned as s in g le -fa m ily r e s i d e n t ia l. This estimate was obtained from the zoning ad m in is tra to r f o r the c i t y of Lansing. 55 commercial and "J" parking. When th is occurred the "J" parking was assumed to be p a rt of and d ir e c t ly re la te d to the commercial zoning c la s s if ic a t io n . Hence the parking l o t area and i t s land value was included in the "F" commercial l o t area and land value fo r four land values. In two instances, a parcel was designated as "F" comnercial and "A -l" sin g le fa m ily . In these s itu a tio n s the parcel was designated the zoning c la s s if ic a t io n of the la r g e r l o t area. Assessed land valuations in th is case were combined and averaged. Sampling Design fo r Land Uses A e ria l photographs were used to estimate land uses w ith in the c ity . This method allows the user to gain an o ve rall appreciation fo r land uses w ith in the c i t y while a t the same time providing s u f f i c i e n t d e t a il around sample p o ints. A f i e l d survey, although possibly more accurate, would not a ffo rd as comprehensive an approach as the photographs. In ad d itio n and perhaps more p e rtin e n t to planning agencies, a f i e l d survey is extremely time consuming and c o s tly . A e rial photographs or even enlargements as used in th is study, are r e l a t i v e l y inexpensive and e a s ily procured fo r the vast m a jo rity o f urban areas in the United States a t a scale of 1:8000. The basic ra tio n a le behind the sampling design was to devise a systematic method to sample land uses th a t provided both complete coverage of the study area and y e t showed s u f f i c i e n t v a r ia tio n , A f i v e point systematic sample concentrating on s tr e e t in te rs ec tio n s was chosen. In the discussion th a t follows a more complete elaboration o f the design is provided. Since s t a t i s t i c a l inferences would be derived from the land uses, 56 then s t r i c t adherence was paid to the d erivatio n o f the sample size . I t was assumed th a t the study area was divided into a f i n i t e number of grid squares each o f approximately 1000 f e e t by 1000 f e e t , with a mean of u and variance o f o^. A sample o f these g rid squares was needed; one which had a mean (y) and variance (s ^ ). According to the Central Lim it Theorem, in situations where the to ta l number of observations exceeds 30, a sample mean (y) w i l l be w ithin 2 or 4 units of the population mean, 95 out of 100 times (Mendenhall, 1968, p. 145). The question becomes then what is the most appropriate valid sample size? In a normal d is t r ib u t io n , variance is a function of the number o f observations (N ). According to the Central Lim it Theorem the variance o f a normally d is trib u te d population also equals four units a t a .95 confidence le v e l. N y Therefore the formula becomes 2 = Et Note the value fo r the population variance is not known. However, Tchebysheff’ s theorem or the empirical ru le states: Given a number, K greater than or equal to 1 and a set of measurements Y i , Y g . - . Y r , , then at le a s t ( 1 - 1 / K 2 ) o f the measurements w i l l Tie w ithin K standard deviations of t h e ir mean (Mendenhall, 1968, p. 4 ) . Thus when K = 2, 1—1/K^ = 3/4 and a t lea st three-fourths of the measurements w i l l be found w ithin two standard deviations of the mean. O perationalizing these K values becomes the Empirical Rule where given a normal d is t r ib u t io n , v ± a contains approximately 68% o f the measurements; m £ 2a contains 95% of the measurements; and ji + 3o contains 99.7% of the measurements. Plus or minus two standard deviations a c tu a lly indicates four standard deviation u nits. Therefore i t 1s possible to equate one standard deviation u n it with one-quarter o f the range of the set of measurements. 57 Returning to the selec tio n of land uses, the goal is to estimate what percentage of a 1000 fo o t by 1000 fo o t surface square or a one inch by one inch g rid square was devoted to one o f four general land uses: r e s i d e n t i a l , conmercial, in d u s tr ia l or va can t-p u blic. Thus the range o f values was from 1-99 and one q u a rte r of the range was approximately equal to 2 4 . 1 The sample s iz e fo r land uses becomes: N = 576 = 144 That is 144 sample points would be needed to derive a s t a t i s t i c a l l y v a lid mean estimate (y) o f the population mean, u. However, y would be v a lid only f o r one set of measurements and since four sets are required by the sampling design, then the t o ta l sample s iz e becomes 144 X 4 or 576 measurements. V/ith a sample size of 576, the sample mean (y) of four land use categories w i l l l i e w ith in +_ 2 standard deviations o f the actual mean land use w ith in the study area 95% o f the time. As previously mentioned, i t is important fo r a sample o f land uses to have equal area coverage. The chosen method o f achieving equal-area coverage is to s t r a t i f y the sample according to p re -e x is tin g section boundaries. Since there are approximately 29 sections, or approximately 118 quarter sections, then the equal area coverage c a lls fo r the 576 samples to be spread evenly over the 118 quarter sections. Thus the f in a l sample size is approximately f i v e per q u a rter section.^ The actual procedure f o r selectin g the land uses began by f i r s t Whe actual number of sample points was closer to 542. The d iffe re n c e is due to the f a c t th a t c e rta in sections contained vast areas of vacant undeveloped land. So f iv e points per section were reduced to 4 points per quarter section f o r those sections containing e x ce p tio n a lly large areas o f vacant land. 58 locating the sample point on a base map and then locating the same point on the a e ria l photograph. Around each of the f iv e points on the ae ria l photograph, a one-inch square was positioned so th a t the sample point was located a t the mid-point o f a side (Figure 6 ). A one-inch square was chosen because of the r e la t iv e ease of calculating the area devoted to each of the four uses. Also one inch squares on the a e ria l photograph or approximately 430,000 square fe e t on the ground appeared to cover the area around most major two and four corner in te rs ec tio n s . F in a lly by aligning the sample points along streets the p o s s ib ility o f measuring an inordinate amount o f vacant land was minimized. I t was assumed th a t s tr e e t intersections would ind icate land uses most ty p ic a l o f the quarter section area. Also s tre e t intersections would provide an in d ic a to r o f any possible v a ria tio n in the land use, p a r t ic u la r ly w ithin re s id e n tia l areas. Most o f the tim e, a two or four corner in te rs ec tio n was present a t each o f the f iv e sample points since many o f the section boundaries w ith in the study area are s tre e ts . When the s itu a tio n arose th a t a sample point was not aligned with a s t r e e t , the sample point was moved to the closest road in te rs e c tio n . The actual determination of the predominant use in an area was made according to the following operational d e fin itio n s : a) re s id e n tia l - any single or m u ltip le family structure shaped as such with accompanying parking space; b) commercial - any r e t a i l or wholesale establishment s e llin g a good or service to another r e t a i l store or to consumers. Included in th is d e fin itio n are junkyards and professional o f fic e buildings; c) in d u s tria l - any type of secondary transformation of a product requiring addition o f power source. Also included are construction companies; 59 F ig u re 6 POSITIONING OF ONE-INCH GRIDS AROUND LAND USE SAMPLE POINTS Quarter Section* *Not drawn to scale 1750 fe e t d) vacant - any area not adjoining re s id e n tia l property of s u f f ic ie n t size with no v is ib le structure on i t ; e) public - Included areas fo r general use such as highways, schools, parks, a ir p o r ts , waste treatment f a c i l i t i e s and federal and sta te m i l it a r y in s t a lla t io n s . The actual determination of the area supporting a p a r tic u la r type o f land use was accomplished by superimposing a one inch by one inch piece of mylar with a grid pattern drawn a t one-tenth an inch. The area was then estimated to the nearest whole grid square ( i . e . one tenth o f an inch g r i d ) . F ield checks were made when the author was unable to in t e r p r e t the predominant a c t i v i t y o f the stru c tu re. Chapter Four Development o f and Testing the S itu a tio n a l Model 61 62 INTRODUCTION "One of the most common problems in applied geographic research is the p a rtitio n o f an area into a system of regions." (Haggett, 1972, p. 373} The geographic p a r titio n of an area into s im ila r ly defined spatial units may appear to be accomplished in a very o b je c tiv e , precise and easy fashion. However, the p a r t it io n e r soon finds th at many subjective evaluations creep into the p a r tit io n process. These subjective elements are not a t a l l unusual provided that a ra tio n ale exists fo r each one. In th is chapter a re g io n a liza tio n process is developed based upon the r e la t iv e location of land uses. At each stage where s u b je c tiv ity arises in the scheme, a d e ta ile d explanation is provided. By structuring the research in th is manner, the magnitude o f the problem alluded to by Haggett hopefully is reduced. The following chapter is devoted to a detailed examination of the re g io n a liza tio n process which measures the r e la t iv e location of parcels while at the same time incorporating some c h a rac teris tic s of the p arc el's absolute location . Land use parcels are grouped according to s im ila r it y of composition by a grouping algorithm. Group membership is checked and contin ually rechecked at each step in the process. The testing of the hypotheses revolves around a comparison of the land value mixture in the existing d is t r i c t s and in the newly defined s itu a tio n a l zoning. F in a lly areas o f potential land use c o n f lic t are delimited w ithin the study area. 63 REGIONALIZATION OF LAND USES Data S im p lific a tio n and Principal Components Most of the area devoted to land uses calculated from the 660 foot squares on the a e ria l photograph belonged to one or two o f the land use categories. As a r e s u lt , the amount of space fo r the remaining land uses remained quite low {Table 2 ). Because of a highly skewed d is trib u tio n of land uses, the variance and the standard erro r of measurement of the va ria b le were increased. of The preponderance zero percent land uses in the sample served to d is t o r t and possibly in v a lid a te the re g io n a liza tio n scheme. One solution to th is problem mentioned in the previous chapters was to assume th at each land use category comprised a t lea st one percent of the sampled grid area. Therefore the mean land use area was increased by one but the o verall variance remained the same. For example, the d is tr ib u tio n of land uses in a typ ical grid may be six ty percent re s id e n tia l and fo rty percent commercial. The new d is trib u tio n then becomes re s id e n tia l sixty-one percent, commercial forty-one percent and one percent fo r each of in d u s tria l and vacant-public uses. Standardization was accomplished by a p rincipal components analysis. Principal components analysis is often labeled as fa c to r analysis. Both techniques are q u ite s im ila r since they both attempt to d e lim it the simple structure or communalities from a group of re lated variables (Gullahorn, 1966, p. 15). More s p e c if ic a lly , principal components analysis aims a t determining a center of g ra v ity solution in a 'm' dimensional square in which 'm' variables load on ' r ' dimensions (Harvey, 1969, p. 343; Brunn e t a l , 1970, p. 67). 64 T a b le Mean L an d Use A re a s Type fo r L a n s in g P ercen t R e s id e n tia l 56. 2 C o m m e rc ia l 13.9 In d u s tr ia l 5 .7 V a c a n t-P u b lic S o u rc e : 2 C a lc u la te d by a u th o r. 24.3 65 According to parameters of th is research the p rincip al component analysis attempts to reduce a four dimensional land use c la s s ific a tio n into a one dimensional measure ind icatin g s im ila r stru c tu re . The s ta rtin g point fo r princip al of simple co rre la tio n values. Within components analysis is amatrix the variance explained by these simple co rrelatio ns l i e a set of common structures of s u ff ic ie n t size to explain part i f not a l l the observed v a ria tio n (Gullahorn, 1966, p. 15). In order to a r riv e at the common stru c tu re , principal components analysis assumes the follevying: a) each set of variables has a set o f cormion fac to rs; b) the variance of each variable when summed is a measure of the to ta l variance; and c) the value o f the individual observation can be more economically represented by a fa c to r score than by individual scores on each of the factors (Fru ch ter, 1964, p. 87; Russett, 1965, p. 324). S t a t i s t i c a l l y , p rincipal components analysis d iff e r s in one way from fa c to r analysis. The former assumes th at the to ta l v a ria tio n can be explained by components. Within the context of th is study, th is assumption means th at a l l o f the v a ria tio n of land uses w ithin Lansing can be contained in a t lea st one of the four land use categories r e s id e n t ia l, commercial, in d u s tria l or vacant-public. In fa c to r an alysis, an e rro r term is assumed to e x is t; therefore a l l of the v a ria tio n is not explainable. I f the researcher desires to reduce dimensional v a r ia tio n , principal components analysis is f a r superior to common factor analysis (King, 1969, p. 157; Kendall, 1957, p. 201). As a r u le , conrion fac to r analysis is used to t e s t hypothesized relatio n sh ip s . Within the context of th is research, no hypothesized relationships 66 were formulated and p rincip al components analysis is employed. Principal components analysis w ith in geographic research has many varied ap p lic atio n s. I t is often used to reduce data complexity by revealing the underlying simple s tru c tu re . data c la s s ific a tio n is also possible. A data transformation or In e ith e r of the above cases, the fa c to r scores fo r each fa c to r represent independent scalar q u a n titie s which are standardized and normally d is trib u te d (Pummel, 1967, p. 197; Dingham, 1967, p. 127). In geographic investigations p rin c ip a l components analysis is generally recognized as a tool fo r the i n i t i a l re g io n a liz a tio n of spatial data (Carey, 1966, pp. 551-569; B la ik ie , 1971, pp. 1-40; King, 1966, pp. 205-224; Moser and S c o tt, 1961, p. 7 ). In a l l of these examples, the principal components analysis functions p rim a rily as a tool to in d ica te the simple underlying stru c tu re. A fte r accomplishing t h is , statements o f s t a t i s t i c a l association or change through time could be made u t i l i z i n g other more powerful s t a t i s t i c a l techniques. Results of Data S im p lific a tio n and Components Analysis The simple co rrela tio n matrix is presented in Table 3. The co rrelatio ns are a l l negative and not exceptionally strong but they are a l l s ig n ific a n t a t the n in e t y - fiv e percent level of confidence. The co rrelatio ns appear to suggest th at the four land uses are p a r t i a l l y exclusionary or d is t in c t from one another. The p rin c ip a l components analysis extracted one dimension from the to ta l v a r ia tio n . All the other dimensions had eigen values less than unity and were less e f f i c i e n t explainers of v a ria tio n than the o rig in a l variables used in the co rre la tio n analysis. The one dimension 67 T a b le In te r c o r r e la tio n Type R e s id e n tia l 3 M a trix of C o m m e rc ia l Land Uses In d u s tr ia l R e s id e n tia l 1.00 C o m m e rc ia l -.41 1.00 In d u s tr ia l -.30 -.05 1.00 V a c a n tP u b lic -.38 -.05 -.05 S o urce: C a lc u la te d by a u th o r. V a c a n tP u b lic 1.00 68 accounted f o r t h i r t y - s i x percent of the t o ta l v a r ia tio n . A re la tiv e ly low value such as th is does not present undue problems as the land uses derived in th is research tend to be dichotomous and non-continous. That is the land uses f o r each parcel was e it h e r present or absent w ith in an area. Because o f t h i s , the o ve rall v a ria tio n between the four categories was la rg e . Thus fo r one component to e x tra c t a m a jo rity o f th is v a r ia tio n would indeed ra is e some questions about the exclusiveness of the land uses. Could the land uses have been measured d if fe r e n tly ? For example i f they were measured on a binary scale then o v e ra ll v a ria tio n have been reduced. may But th is would have ruled out any type o f in te rn a l values which are needed a t a l a t t e r step in the scheme. However the loss of explained v a ria tio n was o f fs e t by the transformation o f the data to conmon sc ala r values. Values were needed th a t were standardized and possessed s u f f i c i e n t v a ria tio n between the observations to allow a regional grouping. Data Grouping The next step on the re g io n a liz a tio n scheme c a lle d fo r the land uses to be aggregated in to groups. For the aggregation, H-Group or a h ie ra rc h ia l grouping algorithmn was chosen. C ontiguity o f observation is not incorporated in to th is grouping algorithmn since w ith in the confines o f the research and data, the use o f a c o n tig u ity measure would imply th a t zoning d i s t r i c t s should be lo c a liz e d fo r a p a r tic u la r area o f the c i t y . Such an assumption does not r e f l e c t r e a l i t y and is contrary to the legal foundation of zoning which is p o licin g power. This power refers to the a llo c a tio n o f a public good without any 69 form of discrim inatory bias or locational bias. Starting with 'n ' observations, a h ie ra rc h ial grouping routine systematically reduces the 542 observations or groups to one observation or group. The reduction proceeds in th is manner: a) two n observations are located and combined i f t h e ir mean value produces the le a s t loss o f the objective function; b) the n-1 observations are then combined into ( N -l) ( N - 2 ) unions and evaluated to see i f there is a th ir d member which can jo in the f i r s t p a ir with another minimum loss o f the o bjective function (Ward, 1963, p. 238); and c) as each n-1 group is formed the sum o f square deviations about the mean on the sum o f square e rro r is increased. The computer routine providing combinations u t il i z e d Euclidean distance as a measure of s im ila r it y in one and two dimensional space. The program calculates a distance matrix from one observation to a ll other observations on the one or two dimensional orthogonal scales. Groups are formed when two observations are separated by a minimum distance and a mean center distance is calculated fo r the new group. The use of grouping algorithmns in geography in v a ria b ly centers around the work of Berry, who used this technique to c la s s ify urban centers ( I 9 6 0 ) , and l a t e r to define economic regions (1967). King (1962), Spence and Taylor (1970) have a l l used this type of grouping algorithmns in t h e i r research. One major problem with the h ie ra rc h ial grouping algorithmn is knowing where to stop the groupings. One has a choice anywhere in the range defined by the parameters n-1 to n - ( n - l ) groups. According to King (1969, p. 199) there is "not an an a ly tic a l solution fo r the problem o f deciding how many groups are to be id e n t i f i e d , although the step a t which the r a t io of the increment in the pooled w ithin sums of 70 squares to the to ta l is a t a minimum is suggested . . . Berry (1967, pp. 77-106) states th a t " i t is possible to select the level deemed most desirable fo r the p a r tic u la r problem . . . Results of Data Grouping In the routine used the number o f observations increases a r ith m e tic a lly while the number o f searches to find a new group increases exponentially. The formula fo r the number of searches is : N = (n -1 ) (n )(n + 1 )/6 where n = number of observations and N = number of searches. I f n = 2 then N = 1; however i f n = 85 then N soon becomes 100,000. For 400 observations, N = 10,660,000 searches. Therefore with 542 observations there was a need to reduce the number o f observations and the resulting searches because of lim ite d computer storage. The most expeditious way was to take the f i r s t one hundred or so observations or land uses and thus do the e n tir e operation in f iv e steps. The to ta l number of observations fo r each of the f iv e i n i t i a l groups is presented in Table 4. fiv e subgroups. For group one, the algorithmn defined At f iv e subgroups the e rro r was 0,5586, an increase of 0.2163 from six subgroups or a 38 percent increase in e r ro r. The c r i t e r i a fo r defining the f in a l groups was o p e ra tio n a lly defined as: a) the to ta l increase in e rro r should be less than one-half a standard e rro r u n it; and b) the percent increase of e rro r from grouping was set a t less than 50 percent and closer to 33 percent of the to ta l e rro r arising from the grouping. From Table 4 one can observe th a t in a l l cases except Group 2 the o verall e rro r is less than one h a lf a u n it and the incremental 71 Table 4 Initial Land Use Groups: Percent Increase of Error Error Error Increase Percent Increase of Error 5 .5586 .2163 38.7 105 9 .3384 .2575 76.0 3 100 6 .4130 .1548 37.4 4 116 8 .3231 .1172 36.2 5 118 7 .4526 .0038 00.8 Group Total Number in Group Number of Subgroups 1 103 2 Source: Calculated by author. 72 increase is around 35 percent o v e r a ll. Nine subgroups were selected as the optimum fo r Group 2 because the o verall e rro r remained less than one-half a standard e rro r u n it in spite o f the percent increase of e rro r exceeding the c r i t e r i a referred to above. Once the 35 subgroups were i d e n t i f i e d , the subgroup means were calculated. Table 4 l i s t s these means along with the number o f land use points in each subgroup. The mean land uses or mean fac to r scores were rank ordered and then combined into eleven groups on the basis of minimizing the mean d iffe ren c es . The reduction from t h i r t y - f i v e groups to eleven groups was done to lessen computer storage and costs arising from the next stage of the re g io n a liza tio n scheme. Table 5 indicates the subgroup composition, number in the group and the mean range. For example, group one from Table 6 is composed o f three groups formed during the h ie ra rc h ia l grouping i l l u s t r a t e d in Table 5. Group 1 is composed of the f i r s t two subgroups o f H-group 5 and the second subgroup from H-group 4. The to ta l number of observations from these three groups is eig h t and the mean land uses are found w ith in the range o f +2.7 to 3 .7 . The t h i r t y - f i v e groups from Tables 3 and 4 were combined into eleven groups on the basis o f a minimization of the range of mean land use fa c to r scores. In a l l cases with the exception of the f i r s t group, the range of means was less than onef i f t h a standard u n it; thus ind icatin g a clustering of land use subgroups. Once the eleven groups were defined, a procedure v/as needed to te s t the v a l i d i t y o f each group's membership. Classifying on the basis of mean land values is permitted i f the d is trib u tio n is normally d is trib u te d about a group mean. However, a l l of the observations 73 T a b le Mean L a n d V a lu e G rou p S u b g ro u p F a c to r 5 S c o res Mean Land V a lu e 1 2 3 4 5 +0.72 -1.01 -0.52 + 1 . 31 -0.01 fo r Num ber S u b g ro u p s in G ro u p T o ta l 13 29 29 13 19 103 -0.18 -0.12 -0.13 +1.32 + 0 . 26 -0.57 -1.00 +0 . 9 6 +0.59 1 2 3 4 5 6 7 8 9 1 1 6 19 8 19 27 11 13 105 + 0 . 47 +0 . 7 6 +0 . 0 7 -0.43 -0.91 +1.33 1 2 3 4 5 6 1 15 16 20 32 16 100 + 1 . 38 + 2.70 + 1 . 30 + 0 . 87 +0 . 62 -1.01 -0.52 -0.25 1 2 3 4 5 6 7 8 1 3 11 11 12 36 23 19 116 + 3.70 + 2.79 +0.90 +0 , 2 4 -0.95 - 0 . 42 ■ +1.25 1 2 3 4 5 6 7 3 2 15 14 32 27 25 118 S o u rc e : C a lc u la te d by a u th o r. 74 T a b le R e v is e d 6 L a n d Use G ro u p s B a s e d D i f f e r e n c e o f Means --------- —— - . ■ .■ V — ———— on 1 In itia l G ro u p T o t a l Num ber i n New G r o u p 1 8 85 2 37 3 4 28 26 5 22 6 7 35 27 8 47 9a 71 10 11 156 S o u rc e : G ro u p C a lc u la te d aL a tte r 10. Thus by G ro u p S ub group 5 5 4 2 2 R ange o f Mean Land V a lu e (L o w -H ig h ) 1 +2.70 to 3.70 1.25 to +1.38 6 3 4 2 4 1 4 3 4 2 4 8 4 +0.87 to +0.96 3 1 2 1 +0,72 to +0.76 4 2 3 5 9 1 +0.47 to +0.62 2 5 5 4 +0.24 to +0.26 1 3 5 3 -0.01 to +0.07 2 2 2 4 1 2 3 8 -0.25 to -0.12 5 3 6 4 -0.43 to -0.42 1 4 2 3 7 6 -0.56 to -0.52 3 5 2 4 1 5 5 7 6 2 -1.01 to -0.91 1 a u th o r. i n t h e a n a l y s i s G ro u p 9 w as c o m b in e d w i t h th e t o t a l num ber g ro u p s becam e 1 0 . 75 were not normally d is trib u te d around the group mean; thus a c l a s s if i c a ­ tio n on the basis of means was not used. Vlhat was needed was a procedure to compare group membership and re c la s s ify observations into new groups i f the need a ris e s . Maximization of Group S im i l a r i t y H ie ra rc h ia l grouping does not give the p r o b a b ility o f misc la s s if i c a t io n . Thus the homogeneity of each of the eleven land use groups was not maximized. In order to optimize the homogeneity o f the eleven land use groups, a discrim inant procedure was performed. basic purpose o f the d iscrim in atio n was twofold: The to assess i f any of the land use parcels should be reassigned to one o f the other ten groups; and to determine i f th a t reassignment would make both the losing and gaining group more homogenous. The h ie ra rc h ia l grouping algorithmn used in the preceding stage o f the re g io n a liz a tio n minimized the distance from one observation to another. The minimization occurred even i f one observation was a c tu a lly composed o f a group o f observations. S t a t i s t i c a l l y speaking i t is possible th a t a nev; observation could be assigned to a group of observations on the basis o f a minimization o f distance to the group's centroid and ye t not be a t a minimal distance to a l l other members of the group. When a s itu a tio n o f th is nature occurs, in tra-g ro up v a r i a b i l i t y is not maximized. I t may even be maximized i f the observation 1n question is r e c la s s ifie d in another group. Discriminant analysis provides a s t a t i s t i c a l method f o r determining the optimal group fo r an observation. O p tim ality in th is case is defined as minimizing w ith in - class v a r i a b i l i t y and maximizing between-class v a r i a b i l i t y . 76 In both the h ie ra rc h ia l grouping and in the discrim inant analysis the Euclidean distance formula is used. In two dimensional space fo r any p a ir of points the formula becomes: where Xp and Yp are coordinates o f va ria b le P and Xq and Yq are coordinates o f variable q and d equals the distance between the variables. Within the context of th is research that is an u n ivariate case so the formula becomes: The discussion of grouping methods th a t measures the difference between a grouping algorithmn minimizing observation distance and a discriminant function th a t minimizes between class v a r i a b i l i t y can now be placed w ith in the context of th is research. Land uses are f i r s t c la s s ifie d or grouped into many s p e c if ic a lly defined groups of uses on the basis o f a minimization o f the distance between two or more fa c to r scores. However, zoning unlike land uses cannot be defined fo r a small and s p e c ific number of land uses. That i s , a p a r tic u la r zoning c la s s ific a tio n should represent the largest possible number of s im ila rly defined land use parcels. Discriminant analysis performs th is broad type c la s s ific a tio n as i t c la s s ifie s observations into d is tin c t groups. In zoning the s p e c ific regulation of individual parcels is l e f t to the governmental bodies to decide. The state of Michigan enabling le g is la tio n merely prescribes guidelines fo r the granting of variances and special use permits. The ultim ate decision rests with the local decfsion makers and not with the urban or regional planner. Within geographic research, discrim inant analysis is commonly used as an o p tim a lity check f o r a regional grouping algorithmn (King, 1967, pp. 336-378). In his study of multi fa c to r uniform census divisions of the United S ta te s , Berry employed discrim inant analysis to v e r ify w ith in group membership (1961, pp. 263-282), Casetti has done extensive work on lin e a r discrim inant functions and ite ra tio n s (1964a, 1964b). I f a m atrix of 's ' groups is designated by the symbol As and i f D is a discrim inant procedure, to obtain a c la s s if ic a t io n , then DA] » A2 , DA2 = D(DA]) = A3 . . . (King, 1969, p. 213). With the addition o f each new observation, a new it e r a t i o n is produced with increased intra-group v a r i a b i l i t y . As suggested by King (1970, pp. 373-376) discriminant analysis has a number o f varied applications such as: a) devising an economic development plan f o r developing countries b) d e lim itin g trade areas around market centers; c) a llo c a tin g tra ve l mode w ith in the urban area; d) defining areas of s im ila r re s id e n tia l behavior; e) id e n tify in g areas of a country in need o f governmental assistance; and f ) regio nalizing an ar ea in order to minimize the costs of m is c la s s iflc a tio n in the a llo c a tio n of government services. The use of discrim inant analysis in th is research most closely p a ra lle ls the minimization o f cost of service type o f discrim inant a p p lic atio n . 78 Results o f Group Maximization The f i r s t stage o f this discrim inant analysis was applied to land use subgroups o f the eleven major groups defined in Table 6 in order to gain in s ig h t into t h e i r between group v a r ia tio n . Applied in this manner the o verall goal of the discrim inant function is to demonstrate a r e l a t i v e l y small betv/een subgroup va ria tio n along with a r e l a t i v e ly large w ith in subgroup v a ria tio n . Thus the F s t a t i s t i c of the discrim inant function, the r a t io o f betv/een v a ria tio n divided by w ith in v a ria tio n is low i f the subgroups are r e l a t i v e ly homogenous. In a d d itio n , the number of observations changing subgroup membership should be high i f there is low between subgroup v a ria tio n . indicates the results o f the f i r s t discrim ination. Table 6 The la s t column of the table indicates the r e la t iv e s t a b i l i t y or the percent misc la s s ifie d of the subgroup membership, A high value for th is value shows th a t the classes are exclusive with l i t t l e i f any transfers between groups. As evident from Table 7 groups 1 through 4 are f a r less homogenous than groups 5 and 6. One reason fo r less homogeneity p a r t ic u la r ly in groups 1 and 2 is the large w ith in subgroup variance. Land use fa c to r scores as high as 3.8 are found in group 1. The overall d is trib u tio n o f land use fac to r scores fo r a l l of the groups is negatively skewed with a disproportionate number of p o s itive land values. For groups 5 and 6 lower F ra tio s and lower s t a b i l i t y values are also found. The second and th ir d discrim inant analyses were conducted fo r the opposite purpose. During these analyses the goal was to maximize Table 7 Grouping Results of the Discriminant Analysis of Sampled Land Uses Groups From Table 6 Sums Sq. within Degrees Freedom (n-k-1) Suns Sq. Between Degrees Freedom tk-1) F-ratio 1 1 & 2 1 83 18.08 9 181.8* 1- 50% 7- 58% 2-100% 8- 5% 3- 0% 9- 15% 4- 2 3 £4 1 60 0.78 4 19.1* 1- 42% 2- 45% 3- 33% 4- 38% 3 5 S6 1 64 1.38 S 18.4* 1- 13% 2- 73% 3-100% 4- 54% 4 7 6 8 1 50 99.44 6 825.0* 1- 53% 2- 25% 3- 50% 4-33% 5 9 1 77 0.96 4 2.0 1- 25% 2- 50% 3- 32% 4- 36% 6 10 1 150 0.06 5 2.0 1- 30% 2- 3- 2% 4- 22% 5- 34% 1-9 1 532 1.77 9 197.0 1- 90% 7- 81% 2-100% 8- 73% 3- 89% 9-100% 4- 87% 5- 97% 6- 87% 1-10 1 531 2.02 10 200.0 1-100% 7- 90% 2- 97% B- 81% 4-100% 10-100% 5- 95% 6- 87% Discrimination Group Stability Index (Percent of Original Subgroup Classified in Same Group at End of 4th Iteration) 1st 2% 4% 5- 40% 6-100% 5- 40% ■ 5-100% 6-100% 2nd 1 3rd 1 Source: Calculated by author. •Significant at .001 level. 3- S2% 9-100% 80 between subgroup v a r ia tio n w hile a t the same time minimizing w ith in group subgroup v a r ia t io n . The second and t h ir d analyses were conducted in the manner in which discrim in an t analysis is generally used. a high F s t a t i s t i c and a high s t a b i l i t y fig u re are needed. Thus According to Table 7 the groupings are r e l a t i v e l y heterogenous, p a r t i c u l a r ly once those deviant observations were reassigned during the th ir d d is c rim in a tio n . Performing ad d itio n a l d iscrim inations beyond the th ir d analysis was not deemed necessary due to the ex ce p tio n a lly high F r a t i o . Also the high s t a b i l i t y measure indicates th a t the observations were r e l a t i v e l y fix e d w ith in each group, i . e . they were c la s s if ie d properly. Additional discrim in atio ns would only change the s t a b i l i t y measures s lig h tly . No m atter how close the d is crim in atio n became, there would always be c e rta in marginal observations which would s h i f t membership to an adjacent group due to the standardization of the fa c to r scores. Standardization tends to compress the o v e ra ll variance o f the land uses; consequently observations are closer to one another. D e fin itio n of A c c e s s ib ility Index Now th a t the nodes o f s im ila r land uses have been d efin e d , i t is necessary to assess the s itu a tio n a l p o te n tia l o f each o f these nodes. A c c e s s ib ility is one measure o f a p a rc e l's r e l a t i v e lo c a tio n . As used in th is research a c c e s s ib ilit y is defined as: The reciprocal o f the costs o f moving people and goods between points in space . . . the lower the cost, the g reater is the a c c e s s ib ilit y {Pendelton, 1963, p. 1 ). The operational d e f i n i t i o n o f a c c e s s ib ilit y u t i l i z e d in th is research r e lie s upon two measures. The f i r s t is the proxim ity from a node of 81 a ce rtain land use to nodes of d iff e r e n t land use. A land use node that is located w ithin close proximity to areas of d if fe r e n t land uses is a node th a t is c e n tr a lly located. For example, a land use node th at is located close to the CBO is more c e n tr a lly located to a v a rie ty of d if f e r e n t types o f land uses than a node located close to the suburbs. The second measure comprising the a c c e s s ib ility index is travel time. Distance alone is not of utmost concern in an urban area i f the time to tra ve l th a t distance is excessive; tra v e l time is more representa­ t iv e of the cost o f movement. In the section th at follows the procedure used to measure a c c e s s ib ility is discussed. Construction o f the A c c e s s ib ility Index The f i r s t step in the re g io n a liza tio n involves mapping. Since the land uses were i n i t i a l l y measured around a specified area id e n tifie d on the a e ria l photograph, i t follows th at the mapping should lo g ic a lly include this area. However, a change of scale occurred in going from the a e ria l photographs to the base map. The survey area of land uses on the a e ria l photograph involved two one-half inch vectors centered on the s tr e e t in te rs e c tio n . The scale of the photograph was one inch equals 660 fe e t while the scale of the base map was one inch fo r every 1000 f e e t . Therefore, on the a i r photo the one-half inch vectors should be reduced to an amount proportional to the change in scale. I f the change in scale equals 340 f e e t , then by a simple r a t io the change in vector size should equal 1 /2 -X , where X equals change in vector. Therefore 82 Thus the vector size on the base map equals 1/4 inch on e ith e r side of the sample point and the to ta l size o f the area is 1/2 inch by 1/2 inch. Around each of the 542 land use points a square with vectors of 1/4 inch was drawn. When two or more squares of id e n tica l land use types overlapped, the areas were combined. In order to measure the proximity from one land use node to another, given ten d if f e r e n t types, derived from the th ird discrimination (Table 7) i t was assumed th at the ten groupings represented a continuum of land uses.^ Table 8 v e r if ie s a continuum of land use types from a predominantly commercial-vacant type in group 1 to a single fam ily resid en tia l in group 10. Based upon the concept of a land use continuum fo r urban areas, compatible and incompatible land use types are defined. A land use type was considered to be compatible to another type i f the other type contained b a s ic a lly the same land uses. Table 9 presents a matrix of co m p atib ility based upon the above d e f in it io n . From Table 8 i t is evident th a t land use group 10 is composed mainly of re s id e n tia l uses with only a lim ite d amount of vacant land. On the other hand, land use group 2 is composed of corrmercial, vacant and in d u s tria l uses with a very lim ited amount of resid en tia l uses. Thus group 2 is not compatible with the predominant land uses found in group 10. In comparing the land use groups from Table 8 , i t becomes apparent that groups 1 through 4 comprise a c t i v i t ie s such as commercial, vacant, V o r the purpose of increased accuracy in the sp ecification of the land use types, the o rig in al four categories were expanded to six. Residential was subdivided into single and m ultiple and vacant-public was broken down into vacant and public. 83 Table 8 Percent Land Use Composition Group Single Family Multiple Family Commercial Industrial Vacant Public O • o 37.0 0.0 50.1 0.0 0.7 30.4 18.4 31.6 18.0 12.2 15.4 25.2 4.5 25.0 18.0 4 19.7 11.4 22.1 7.8 33.2 5.8 5 32.4 9.3 21.6 5.8 12.5 16.5 6 49.8 0.1 15.9 0.0 13.4 19.9 7 60.0 1.9 13.3 4.5 13.3 8.8 8 73.9 1.9 7.2 0.6 12.6 3.8 9 88.3 1.3 4.1 0.0 4.7 1.8 10 95.0 0.8 0.6 0.8 2.4 0.1 1 13.5 2 0.5 3 Source: Calculated by author. Table 9 M a tr ix o f L a n d U se Comp a t a b i l i t y - L a n d Use G ro u p N um ber 1 1 C 2 c C 3 c C C 4 c C C C 5 I I C C C 6 I I c C C C 7 I I I I C C C 8 I I I I C C C C 9 I I I I I I C C C 10 I I I I I I C C C Source: 2 Calculated by author. C— C o m p a t ib le I — In c o m p a tib le 3 4 5 6 7 8 10 85 in d u s tria l and public uses on predominantly n on-residential land uses. Groups 5 and 6 appear to be a tra n s itio n land use types between re s id e n tia l and n o n -re s id e n tia l. These two groups are most unlike the four extremes of continuum, th at is groups 1, 2, 9 and 10, Groups 7 through 10 then are predominantly s in g le -fa m ily re s id e n tia l land use types. Proximity between land use types on the base map is determined by drawing a radius o f o ne-half mile around the midpoint of each land use node. I t was assumed th a t w ithin a radius of one-half mile in urban areas, land use would show some meaningful sp a tia l v a ria tio n i f indeed i t e x is ts . In te re s tin g ly the central business d i s t r i c t o f Lansing can e a s ily be circumscribed by a c ir c le with a radius of approximately one-half m ile. The proximity o f d if f e r e n t or incompatible land uses was t a l l i e d according to the following formula: P = T + 3 D + C - S/10 where T = to ta l number of land use nodes w ithin one-half mile c ir c le ; D = number of uncomplementary land uses; C = number o f complementary land uses; S = number o f id e n tic a l land uses; P = proximity o f the node to nodes o f d if f e r e n t land use type. For example one land use node located approximately along North Grand River between Logan and Cedar S tre e ts , had the highest proximity value in Lansing. P = 4 ,2 . In th is s itu a tio n T = 11, 3D = 30, C = 1, S = 0 so At the other extreme, a land use node located a t the in te rs ec tio n of Aurelius Road and In te rs ta te 96 had the following values: T = 2; 3D = 0, C = 2 , S research the f i r s t land use node = 0 so P = 0 .2 . Asdefined in th is is located closer to nodesof d if f e r e n t types than the second node which is r e l a t i v e ly Isolated from the various land use types. 86 In developing th is model incompatible land uses are weighted by a fa c to r o f three because a land use node th a t is c e n tr a lly located is one which is r e l a t i v e l y close to d if f e r e n t types o f land uses. The actual value of three was arrive d a t by sampling approximately one-half o f the land use nodes and counting the number o f incompatible uses w ithin the o ne-half mile radius. A l i t t l e over o n e-third o f the land uses were found to be incompatible so a reciprocal weighting o f three was used. In addition th is f i f t y percent sample indicated th a t the largest number o f adjacent land use nodes was approximately equal to 10 . Dividing the proximity value by a constant of 10 is done fo r the ease of c a lc u la tin g . Thus a proximity value greater than 1.0 indicates a land use node with a r e l a t i v e l y high degree o f o ve rall c e n tr a lit y , A value less than 1.0 indicates a lack of c e n t r a lit y in the location of the node. The to ta l number of nodes (T) along with the number of compatible uses (C) was added to the proximity value in order th at a node w ith in close proximity to a small number o f incompatible nodes would have a proximity value less than a node close to numerous compatible and incompatible uses. By adding T and C to the equation, a North Grand River node obtained a higher proximity value than a Aurelius Road node even though the l a t t e r had a la rg e r C value than the former. The second component of the a c c e s s ib ility measure is tra v e l time. For th is research f iv e shopping and f i v e employment nodes w ithin Lansing are defined. The shopping nodes are the primary business d i s t r i c t , a secondary business d i s t r i c t in North Lansing and three major shopping centers, Frandor, Logan Center and M eijers o f 87 tfi ____J EMPLOYMENT NODES Ei Diamond Reo E? Oldsmobile E 3 State offices E 4 Fisher Body Es Motor Wheel O A K LA N D SHOPPING NODES Meijers Logan Center Frandor Lansing CBD Norlh Lansing State Capital 1-496 Mr HOPE U HOLM ES z Ld JOLLY Ln i_____ F igure 7 LANSINR, MICHIGAN /— i 88 Pennsylvania Avenue (Figure 7 ) . The employment nodes are the State Capitol complexes and the four largest fa c to r ie s , Oldsmobile, Fisher Body, Motor Wheel and Diamond Reo. In choosing the shopping and employment nodes, care was taken to define only those nodes located w ithin the legal boundary o f the c i t y . Distance to each of the above ten nodes from a series o f section midpoints and corners was calculated. points was 71, The to ta l number of such For each section midpoint or corner the distance to each o f the f iv e shopping and employment centers was calculated. The employment and shopping distances were then summed and averaged resp ectively. The two averages were then summed and averaged thereby obtaining one value fo r each o f the seventy-one points. That average distance was then converted to tra ve l time by assuming th a t the average tra ve l time w ithin Lansing was approximately 15 miles per hour.^ The d is trib u tio n of travel times is presented in Table 10. The overall range is from twelve minutes fo r locations close to the primary business d i s t r i c t to f i f t y - f o u r minutes fo r locations in the southern portions o f the c i t y . According to Table 10 and Figure 8 travel times less than one standard deviation u n it below the mean value are generally found north of the CBD. Travel times greater than one Whe same conversion was made in a recent t r a f f i c study conducted by the Planning Department fo r the C ity o f Lansing. The reference fo r the report is C ity o f Lansing, Michigan, Department of Planning, T rip D is trib u tio n Analysis 1970, C ity o f Lansing, Michigan. The author re a liz e s th a t the use of the conversion provides a gross transformation of distance into the time needed to cover the distance. However by using the conversion, a measure o f the gross costs of covering th a t distance in terms o f the costs o f movement is obtained. I t is beyond the scope o f th is research to measure actual tra v e l time from a sample o f points w ithin the study area. 89 Table 10 T ra v e l M ean tra v e l tim e T im e fo r to a ll s a m p le 30 V a r ia n c e S ta n d a rd N um ber o f S o u rc e : M a jo r L a n s in g p o in ts to Nodes L a n s in g 12 m in u te s E rro r 9 m in u te s R ange of T ra v e l T im e s 3 38 30 to 54 m in u te s 33 12 to 30 m in u te s 27 30 to 40 m in u te s 23 20 to 30 m in u te s 18 30 to 35 m in u t e s 9 25 to 30 by is m in u te s V a lu e s C a lc u la te d nodes m in u te s a u th o r, a T h e s e r a n g e s r e p r e s e n t l i m i t s d e f i n e d b y t h e m ean t r a v e l tim e p lu s tw ic e th e s ta n d a r d e r r o r . The n e x t ra n g e i s t h e m e a n t i m e m in u s t w i c e t h e s t a n d a r d e r r o r . The th ir d ra n g e i s th e m ean p lu s o n e s ta n d a r d e r r o r an d th e f i f t h r a n g e i s t h e m ean p lu s o n e - h a l f s t a n d a r d e r r o r . 90 n / ; S la te Capital < 3 F ig u re 8 TRAVEL TIME TO SELECTED LANSING NODES ! ! deviation u n it above the mean are found in the southern portions of the c ity . I t should be noted th a t these tra ve l times represent the average time to tra v e l to one of fiv e shopping and employment nodes but not to any one in p a r t ic u la r . The actual d is trib u tio n of tra ve l times along with the mean is given in Table 10. The two measures o f a c c e s s ib ility are combined into one index by the following formula: a c c e s s ib ility = proximity o f land uses x ) 0 0 . time distances The data value extremes fo r the a c c e s s ib ility index were 22.99 in the southern portions o f the c i t y to 1111.11 fo r a land use node north of the CBD along Cedar S tre e t. These values along with the remaining 304 values were used an input into a computer mapping routine ca lle d SYMAP.^ Given a sample number of data points along with t h e ir X-Y coordinates the mapping routine defines an i n i t i a l search radius based upon the number and spread of the data points. A maximum search radius is extended to but not exceeding the location of the fa rth e s t data point. Using these two r a d i i , the computer locates a minimum o f four and a maximum of ten data points and with an average of seven points i t interpolates the average value w ithin the prescribed area. Three types of maps can then be drawn; a contour map, proximal map and a conformant map. In order to show the o u tlin e o f the study area, a conformant map was requested. The user may specify categories fo r the data fed into the program. In th is case ^The SYMAP mapping routine is d e ta ile d in Technical Report 100 o f the Computer I n s t it u t e fo r Social Science Research, Michigan State U n iversity. The routine at Michigan State was o r ig in a lly adapted for use by C. Young with l a t t e r revisions by Donald Dugger and Robert W ittic k o f the I n s t it u t e , 92 six categories were used and the number o f data points were evenly divided among the categories. Six categories were mapped since there are six major zoning c la s s ific a tio n s used in Lansing: low density r e s id e n t ia l, high density r e s id e n tia l, commercial, professional, l ig h t industry and heavy industry. In requesting th a t the observations be evenly divided into the six categories, i t was assumed th a t a c c e s s ib ility is a continuum with a l l locations possessing a ce rtain amount of a c c e s s ib ilit y . To put i t another way, a c c e s s ib ility is a continuum since every location is accessible to some degree even i f th a t place is c la s s ifie d as remote or inaccessible. The concept of a c c e s s ib ility as a continuum elaborated here is consistent with the e a r l i e r statements regarding the land use composition of the ten land use types. The map produced by the SYMAP routine represents a s itu a tio n a l approach to the d e lim ita tio n of zoning d i s t r i c t s . I t depicts in a broad way six a c c e s s ib ility based zoning d is t r i c t s (Figure 9 ) . The highest a c c e s s ib ility areas as expected are around the primary business d i s t r i c t . Surrounding th is area is a band of less intensive land use with a lower degree o f a c c e s s ib ility and r e l a t i v e ly low amounts of tra v e l time. A few enclaves o f lower values are found to the west (ghetto area west o f c a p i t a l ) , to the southwest (low income housing area south o f Oldsmobile plant) and to the southeast (along Kalamazoo S tre e t close to East Lansing). I t is noted that a zone o f r e l a t i v e ly intensive commercial-industrial uses with high a c c e s s ib ility extends into North Lansing (near the Motor Wheel Factory) and also along North Grand River Avenue (Figure 10). A few isolated enclaves o f the three mast accessible com m ercial-industrial- 93 m .•.v X v X i b * « I m m IM i 3 Low densily resideniiol 1323 High density residential W Commercial m Industrial $£sl*l*yyj v X v Mm , ,'Mv t* r.v ***v .v .v *v *% v *v « v *v *v .* X*»> / • • i.i * F ig u re 9 SITUATIONAL ZONIHC. SCHEME i 94 re s id e n tia l zones are found in south Lansing, p a r t ic u la r ly along Pennsylvania and Cedar Streets (Figure 10). The le a s t accessible of land uses are generally found along the peripheral locations in the southern portions o f Lansing. These less intensive areas represent zones o f r e l a t i v e l y high tra ve l time and l i t t l e d if f e r e n t i a t i o n . i f any land use As a re s u lt these areas would tend to be the le a s t l i k e l y locations fo r those a c t i v i t i e s requiring high amounts of a c c e s s ib ility . Likewise those areas with large v a ria tio n in land use types and low travel times are l i k e l y locations fo r economic a c t i v i t i e s requiring such mixtures. In the following section the new zo n in g -a c c e s s ib ility map of Lansing is compared with the ex istin g zoning map. TESTING OF THE HYPOTHESES introduction As stated in the previous chapter, one of the primary goals of this research is to te s t the v a l i d i t y o f re g io n a liza tio n scheme fo r an urban area. The basic tests of th at v a l i d i t y revolve around the comparison of land value homogeneity. The central question then becomes— Is the variance o f land values zoned according to the new re g io n a liza tio n scheme less than the land value variance existing under the current zoning plan? Variance of land values is preferred over the mean since i t t e l l s about the spread of the d is t r ib u t io n . A mean value may be s u f fic ie n t i f the subcategories contain a r e l a t i v e ly equal number o f observations and i f the means are equal. However, when grouping occurs, as is the NORTH LANSING N. GRAHQ RIVER SITE ZONING H GRflNDlRNER SITU A TIO N A L ZONING 1 InddS lriC ll C C o T im e rc io l H H ig h d e n s ity r e s id tn tio l L L o * d e n s ity re s id e n tio l SOUTH LANSING M ILL E R SITE ZONING F ig u re 10 SITU A T IO N A L ZONING COMPARISON OF OLD AND NEW ZONINO SCHEMES 96 case w ith th is research, frequencies often vary. Therefore, a comparison of the mean d ifferen ces may be misleading. For th is reason the dispersion o f land values was considered to be f a r more representa­ t i v e and less prone to misrepresentation due to unequal frequencies. In the sections th a t fo llo w each of the three stated hypotheses is analyzed by comparing the mean sum o f squares (MS) which is the pooled sum o f squared d ev ia tio n from the mean. A r a t io o f two mean squares approximates an F -d is tr ib u tio n governed by the respective degrees o f freedoms (Mendenhall, 1968, p. 347). According to s t a t i s t i c a l methods, one degree of freedom is lo s t fo r every population parameter estimated. The sample variance o f land values co llected fo r Lansing is used as an estimate of the population variance. Calculating an F - r a t io f i r s t requires the formation of a null hypothesis ( HQ). I f the F - r a t io exceeds a c e rta in value (normally prescribed in a ta b le o f F -v a lu e s ), then the null hypothesis is accepted. The follow ing null hypothesis is used throughout the follow ing sections: Ho = ° a 2 " °b 2 where a aj - represents the variance o f land values under e x is tin g zoning and is the variance o f new zoning land values. then MSa/MSb < 1.00. I f HQ is accepted Likewise i f HQ is re je c te d , then the F - r a t io is greater than 1.00 and MSa/MS^ is g rea ter than 1.00. Mean squares are f i r s t calculated by deriving the pooled sums of squared deviatio n fo r each category. The follow ing formula is used in the c a lc u la tio n o f the pooled sums o f squares: 97 (na- 1 ) o a2 + (n b- l ) o b2 + (nc- l ) a c2 . . . (nz- l ) o z2 na + nb + nc . . . n2-Z where o , a 2 is the sample variance o f category a , n a is the number of land values in category a and Z is the number o f categories. Pooled variance a c tu a lly is the average variance fo r each category. By pooling the variance a more re p resen tative estimate o f the population variance is obtained. Also the degrees of freedom in a pooled estimate are la r g e r than in each in d ivid u al sample variance. Results of Overall Comparison o f Land Values and New Zoning The mean, variance and number o f land value parcels in the e x is tin g zoning and in the newly defined scheme are shown in Table 1 1 .^ Mean land value is provided but comparisons p a r t i c u l a r ly in the f i r s t two zoning types should be approached with caution due to the unequal frequencies. For low density r e s id e n tia l (LOR) the s itu a tio n a l zoning increased the mean land value and the variance. S im ila r re s u lts occurred in high density re s id e n tia l and in d u s tria l zones. Only in commercial zones does the new zoning produce less land value ^In Chapter Three i t was assumed th a t the area of highest a c c e s s ib ilit y on the new zoning map would be the commercial d i s t r i c t . A fte r comparing the re s u lts of the land value mixtures in the s i t e and s itu a tio n a l zoning (Tables 12, 14 and 1 6 ), i t is apparent th a t on the average the commercial and in d u s tria l d i s t r i c t s in both s i t e and s itu a tio n a l zoning schemes contain a r e l a t i v e l y equal number of parcels on the average. I f the assumption made in Chapter Three was maintained, then the s i m i l a r i t y o f numbers would not e x i s t . Therefore the re su lts advanced in th is chapter are based on the assumption th a t in d u s tria l areas re q u ire the highest amount of o ve rall a c c e s s ib ilit y . Commercial areas requ ire the next highest amounts o f a c c e s s ib ilit y and then re s id e n tia l areas. Since a large portion of the in d u s tria l land in Lansing is located w ith in close proximity to ra ilr o a d s , in te rs ta te s and major a r t e r i a l s , then th is assumption appears v a lid . 98 v a ria tio n (Table 11). However, the F -r a tio fo r commercial and high density re s id e n tia l zones indicates th at the new scheme produces less land value heterogeneity than the e x is tin g zoning (Table 12 ). These results are not unexpected, p a r tic u la r ly fo r high density re sid en tia l areas which appear to have expanded a t the expense of low density re s id e n tia l areas in North Lansing (Figure 10 ). However, such a generalized comparison may overlook other possible trends or re latio n sh ip s , A more s p e c ific model is needed to f e r r e t out such trends i f they e x is t. Results of Ring Model o f Land Value Aggregation In order to get a b e tte r f i t o f the s itu a tio n a l model, seven concentric rings were defined a t one-half mile radi centering on the State Capital complex (Figure 11 ). Land values are c la s s ifie d into one or another ring and then a comparison of land value homogeneity is undertaken. Again i t was the purpose of aggreaatinn land values into rings to assess i f there is a stronger re la tio n s h ip between land values in the new zoning scheme or in the ex istin g one. The results o f the concentric aggregation are given in Table 13. As expected commercial and in d u s tria l zoning account fo r a large number of the land parcels w ithin the f i r s t two rings. In ring one the commercial and in d u s tria l variance under both the new and old zoning type is la rg e r than in any other rin g . This high variance indicates a large range o f land values in the primary business d is tric t. The business d i s t r i c t in Lansing is composed o f govern­ mental o ffic e s to the west of the primary CBD. To the south of this complex and a t approximately one mile l i e in d u s tria l areas. As 99 Table 11 Comparison of Land Values: Site Zoning Overall Situational Zoning Number Mean Variance Number Mean Variance 365 $0.41 $0.11 156 $0.62 $0.50 14 1.13 0.27 232 0.74 0.05 Commercial (COM) 137 2.10 9.92 159 0.82 1.89 industrial IND 66 1.30 1.68 55 1.94 18.54 Low Density Residential (LDR) High Density Residential (HDR) Source: Calculated by author. T a b le M ean S q u a r e s o f L a n d V a lu e s 12 fo r P o o le d V a r i a n c e a Z o n in g S c h e m es : O v e r a ll P o o le d Num ber*3 M ean S q u a r e 0 Zo ne T y p e S ite S ite S itu a tio n a l S itu a tio n a l S ite S itu a tio n a l LDR .1 1 0 .5 0 1 385 156 .0 0 0 2 .0 0 3 0 HDR .2 7 0 .8 5 0 14 232 .0 2 0 1 .0 0 3 6 * COM 9 .9 2 0 1 .8 9 0 137 159 .0 7 2 9 .0 1 1 9 IN D 1 .6 8 0 1 8 .5 8 0 66 55 .0258 .3440 S o u rc e : C a lc u la te d by * S ig n ific a n t a t a a u th o r. .001 T h e p o o le d v a r i a n c e Th e p o o le d n u m b er c le v e l. is (P ) T h e m ean s q u a r e e q u a ls d e fin e d i n e q u a ls th e 2 S /P -l. th e te x t . an d i s 2 d e s ig n a te d b y S . t o t a l m in u s n u m b er o f e s t i m a t o r s . 101 5o I WILLOW SAGINAW o State Copital X MT, HOPE e > o CL t*J HOLMES o I_____ jo lly i_n m il l e r F ig u re 11 CONCENTRIC RINGS 102 Table 13 Comparison of Land Values: Concentric Rings Site Zoning Concentric Ring Zoning Type 1 Number Situational Zoning ... — * — ■ ■ Variance Number Variance 1 LDR HDR COM IND 1 2 14 10 0.00 0.00 48.34 0.15 2 6 4 15 1.30 8.45 32.00 50.47 2 LDR HDR COM IND 41 4 23 13 0.04 0.15 1.01 0.65 4 27 42 8 0.08 0.89 0.58 0.09 3 LDR HDR COM IND 86 1 26 20 0.14 0.00 0.32 4.08 17 44 44 28 0.55 0.39 .46 2.46 4 LDR HDR COM IND 93 0 36 13 0.19 0.00 1.40 1.12 43 52 43 4 0.91 0.95 0.86 0.08 5 LDR HDR COM IND 89 3 16 1 0.08 0.33 0. 32 0.00 36 50 23 0 0.39 0.22 0.07 0.00 6 LDR HDR COM IND 37 4 6 6 0.04 0.25 0.07 0.00 29 21 3 0 0.15 0.13 0.02 0.00 7 LDR HDR COM IND 46 0 8 3 0.05 0.00 0.11 0.06 25 30 2 0 0.08 0.09 0.00 0.00 Source: Calculated by author. 103 distance increases from the primary node, land value variance in the low density r e s id e n tia l zones tends to increase at f i r s t (rin g s 3 and 4) and then g rad u ally i t declines (rings 5 , 6 and 7 ) . This trend is evident in both types o f zoning. In comparing the number of parcels by zoning type in each r in g , i t becomes apparent th a t the s itu a tio n a l zoning increases the areal spread of high density re s id e n tia l areas. That is there is more high density r e s id e n tia l land uses than expected from the actual land use. The increase occurs a t the expense of the lower density re s id e n tia l areas. The same trend was evident in the preceding section which analyzed the o v e ra ll e f f e c t before the data were disaggregated. According to Table 14 the r a t io o f mean squares fo r the low density r e s id e n tia l and in d u s tria l zones is not o f s u f f i c i e n t size to r e je c t the n ull hypothesis. Therefore the d ifferences are not g reat between s i t e and s itu a tio n a l zoning as defined by the concentric ring an a ly sis. However the same is not tru e f o r high density residen­ t i a l and commercial areas. The high F r a t io in the l a t t e r situ a tio n s indicates th a t the a c c e s s ib ilit y re g io n a liz a tio n has in e f f e c t decreased the land value m ixture. When the re su lts o f the ring analysis are compared with the re s u lts o f the o ve rall model i t becomes evident th a t the strength o f the F r a t io increases as the land values are disaggregated, p a r t i c u l a r ly fo r the high density r e s id e n tia l and commercial areas. Results o f the Sectoral Model o f Land Value Aggregation The ring model of land value aggregation was unable to account f o r the increased v a ria tio n of land values fo r in d u s tria l and low T a b le 14 Mean Squares of Land Values for Zoning Schemes: Pooled Variancea Zone Type Site Situational Concentric Rings Pooled Number Site Situational Mean Square0 Site Situational LDR 0.108 0.458 386 149 0.0002 0.0039 HDR 0.326 0.658 8 223 0.0461 0.0029* COM 5.834 1.154 122 154 0,0479 0.0075* IND 1.710 15.222 59 51 0.0280 0.2980 Source: Calculated by author. ♦Significant at .01 level. aThe pooled variance is defined in the text and is designated by S^. ^The pooled number (P) equals the total minus number of estimators. c 2 The mean square equals S /P-l. 105 density r e s id e n t ia l. Sectors or corridors are constructed around six o f the major a r t e r ia l s in Lansing. The following streets were chosen: Grand R iver, East Saginaw, Oakland, Cedar S tre e t, Pennsylvania Avenue and Logan Road (south of Saginaw). A co rrid o r was o p e ra tio n a lly defined 500 fe e t e ith e r side o f one of these major a r t e r ia l s (Figure 12 ). This distance would incorporate almost a l l abutting or adjacent blocks boarding the a r t e r i a l . In only one instance, at Saginaw and Oakland near the Frandor Shopping Center did the 500 foot spread overlap. The analysis of land value mixtures in the sectoral model was conducted a t two d if f e r e n t levels o f aggregation. Level one was composed of a l l the a r t e r ia l s grouped into one sector (N = 1) plus nine n o n -a rte ria l sectors (Figure 12). Level two divided the above a r t e r i a l sector into i t s six components and then analyzed the a r t e r ia l s with the n o n -a rte ria l sectors (N = 15). The resu lts of the sectoral aggregation are indicated in Table 15. For example, sector one, a n o n -a rte ria l secto r, the s itu a tio n a l zoning scheme decreased the number o f low density re s id e n tia l parcels and increased t h e i r variance. A s im ila r decrease in numbers in the s itu a tio n a l zoning is also evident in the high density re s id e n tia l and commercial zones although in these areas the new zoning reduces the variance o f land values. Notice how in a l l sectors the to ta l number of parcels per sector remains the same. The ra tio s o f the mean squares fo r high density re s id e n tia l zones and fo r in d u s tria l zones is o f s u ff ic ie n t strength to warrant a re je c tio n o f the n ull hypothesis (Table 16). However, the null hypothesis is accepted fo r low density re s id e n tia l and commercial areas. 106 W IL L O W ;j{T o -l |;j Arterial Sector (^3 ) to-l 10-2 1 0 -3 1 0 -4 1 0 -5 10-6 1 0 -2 Non-Arterial Sector North Grand River Saginaw-Oakland Cedar Pennsylvania Michigan Logan ^ rrrrrrv :. . . . ___ ----state Mr hope holme jo li y MfLL EK F ig u re 12 MAJOR ARTERIAL CORRIDORS lllio-sillir^lii; 107 Table 15 Comparison of Land Values: Sectors Site Zoning Sector Zoning Type Number Variance Situational Zoning ------; Number Variance 1 LDR HDR COM IND 66 4 16 5 0.04 0.37 0.79 0.01 39 32 19 1 0.45 0.11 0.51 0.00 2 LDR HDR COM IND 58 1 17 6 0.03 0.00 0.25 9.20 18 35 19 10 0.10 0.22 0.17 6.03 3 LDR HDR COM IND 11 0 3 0 0.12 0.00 0.42 0.00 4 6 1 3 0.07 0.18 0.00 0.38 4 LDR HDR COM IND 52 1 9 5 0.14 0.00 7.65 2.43 17 29 19 2 0.37 1.00 0.17 25.68 5 LDR HDR COM IND 7 1 1 1 0.00 0.00 0.00 0.00 3 3 1 3 0.00 0.34 0.00 0.07 6 LDR HDR COM IND 7 0 0 0 0.00 0.00 0.00 0.00 5 2 0 0 0.00 0.00 0.00 0.00 7 LDR HDR COM IND 21 0 6 5 0.02 0.00 0.22 0.01 11 16 5 0 0.07 0.25 0.02 0.00 8 LDR HDR COM IND 29 2 7 7 0.04 0.06 0.42 0.30 9 15 21 0 0.21 0.04 0.49 0.00 108 Table 15 Continued Site Zoning Zoning Type--------- -----------------Number Variance Situational Zoning ■ Number Variance LDR HDR COM IND 9 0 1 3 0.01 0.00 0.00 0.06 1 3 9 0 0.00 0.05 1.35 0.00 10-1 LDR HDR COM IND 28 1 8 10 0.79 0.00 1.60 167.31 18 20 8 1 1.78 0.36 201.89 0.00 10-2 LDR HDR COM IND 13 0 3 4 0.05 0.00 52.63 0.02 1 5 7 7 0.00 0.92 0.49 36.17 10-3 LDR HDR COM IND 39 1 19 4 0.13 0.00 36.16 1.62 17 24 12 10 0.35 0.40 16.06 56.36 10-4 LDR HDR COM IND 23 0 14 6 0.06 0.00 1.19 0.02 2 9 19 13 0.01 0.22 1.11 0.14 LDR HDR COM IND 5 3 10 4 0.01 0.27 3.93 0.11 5 11 1 5 1.03 5.45 0.00 0.37 10-6 LDR HDR COM IND 32 0 8 6 0.09 0.00 0.70 1.06 3 23 20 0 0.00 0.13 0.70 0.00 11* LDR HDR COM IND 140 5 62 34 0.27 0.24 17.25 52.57 46 92 67 36 1.08 1.50 30.15 24.14 H 0 1 8 U1 Sector Source: Calculated by author. ♦Represents the aggregation of groups 10-1 to 10-6. 109 In high density re s id e n tia l and in d u s tria l areas the aggregation of land values into sectors appears to have increased the strength of the hypothesized re la tio n s h ip . In u t i l i z i n g the f if t e e n d is t r i c t s in the sector analysis, there is a decrease in the homogeneity of land uses as evident in F r a t io (Table 16). However, the net change to sectors from rings is not of s u ff ic ie n t size to re s u lt in any explanation fo r the low density resid en tia l even though a l l others are accounted fo r by the model. It is possible, however, to state th a t the sectoral aggregation appears to have f u l f i l l e d it s basic function by accounting fo r increased va ria tio n in the high density re s id e n tia l zones. Id e n tific a tio n of Locational Conflicts Within the context of th is chapter, a high r a t io of mean squares indicates locations where the a c c e s s ib ility derived zoning is needed because of the obviously high mixture o f land values in the area. That i s , in these areas land use c o n flic ts arise from s p illo v e rs , be they p ositive or negative. In these locations the e x is tin g zoning scheme hinders the formation o f land value homogeneity with accompanying s im ila r it y in economic functions. As evident from the above Tables 12, 14 and 16, by deriving a zoning plan on the basis o f situ atio n al c h a ra c te ris tic s , land value homogeneity is increased and s im ila r it y in economic function is encouraged 1n ce rtain types of d is t r ic t s es p ecially commercial and high density r e s id e n tia l. On the other hand, those locations which have an exceptionally high mean square ra t io represent areas of p otential land use c o n f lic t between d r a s tic a lly d if f e r e n t land values. The exact location of the c o n flic t Table 16 Mean Squares of Land Values for Zoning Schemes: Sectors P o o le d Num ber*3 P o o le d V a r i a n c e a Mean S q u a r e 0 Zone T y p e S ite LDR' (a ) ( b) 10 15 0.133 0.105 0.554 0.471 386 391 137 143 0.00033 0.00073 0.0040 0.0032 HDR (a) ( b) 10 15 0.438 0.255 0.832 0.554 6 8 218 223 0.0872 0.0363 0.0038* 0.0024* COM ( a ) (b) 10 15 10.030 8.37 15.70 12.40 10 8 113 129 134 0.0928 0.0740 0.1226 0.0932 I ND 10 15 32.48 26.42 20.13 16.50 53 58 46 49 0.6246 0.4635 0.4473* 0.3437* (a) ( b) S o u rc e : C a lc u la te d by S itu a tio n a l T h e p o o le d v a r i a n c e ^ T h e p o o le d n u m b er c S itu a tio n a l S ite S itu a tio n a l a u th o r. ♦ S ig n ific a n t d iffe r e n c e a S ite is (P ) T h e m ean s q u a r e e q u a ls at th e .0 1 d e fin e d e q u a ls in th e 2 S /P -l. le v e l. th e total te x t an d i s 2 d e s ig n a t e d b y S . m in u s n u m b er o f e s t i m a t o r s . Table 17 Mean Squares Within the Concentric Rings by Zone Type P o o le d V a r i a n c e R in g S ite N um ber S itu a tio n a l S ite M ean S q u a r e S itu a tio n a l S ite S itu a tio n a l 1 27.381 36.780 23 23 1 .2 1 0 1 .5 .9 0 2 0.415 0.590 80 80 0.005 0.007 3 0.755 0.838 129 129 0.005 0.006 4 0.574 0.366 138 138 0.004 0.002* 5 0 .1 1 9 0.245 105 105 0.001 0.002 6 0.510 0.139 49 49 0.001 0.002 7 0.059 0.085 53 53 0.001 0.001 S o u rc e : C a lc u la te d * S ig n ific a n t by at a u th o r. .001 le v e l. Table 18 Mean Squares Within Sectors by Zone Type P o o le d V a r i a n c e S e c to r N um ber M ean S q u a re S itu a tio n a l S ite S itu a tio n a l 0.179 0.146 88 88 0.002 0.001* 0.662 0.831 78 78 0.008 0.100 3 0.170 0.182 12 10 0.015 0.202 4 1.239 0.992 63 63 0.019 0.016* 5 0.010 0.136 6 6 0.002 0.027 6 0.000 0.000 6 5 0.000 0.000 7 0.055 0.161 28 28 0.002 0.005 8 0.134 0.216 41 42 0.003 0.005 9 0.012 1.090 10 10 0.001 0.109 1 0 -1 35.778 33.726 43 43 0.851 0.803 1 0 -2 6.198 13.978 17 16 0.387 0.931 1 0 -3 1 1 .1 9 7 11.840 59 59 0.192 0.204 1 0 -4 0.422 0.601 40 39 0.101 0.015 1 0 -5 2.015 3.334 48 48 0 .1 1 8 0.196 1 0 -6 0.302 0.375 43 43 0.007 0.008 1 2 • S o u rc e : S ite C a lc u la te d by a u th o r. ♦ S ig n ific a n t a t .001 le v e l. S ite S itu a tio n a l 113 parcels cannot be discerned given the nature of the data aggregation. Future research on a f in e r scale and additional data on changes in land uses is needed to pinpoint the exact location o f the c o n f li c t . From Table 17 i t is apparent th a t in only ring four do areas of p otential land use c o n flic ts e x is t. Ring four encompasses a few areas o f mixed and competing land uses such as: South Washington Avenue between Mt. Hope and Holmes Roads and the portion o f U. S. Route 27 north o f Motor Wheel and south of Sheridan Road (Figure 13 ), In both areas examples o f l ig h t and heavy in d u s tria l zoning along with high and low density re s id e n tia l zones are w ithin close proxim ity. As indicated previously the ex istin g zoning regulations in these areas are hindering the economic v i a b i l i t y of the area as a whole by not recognizing completely the a c c e s s ib ility requirements and lim ita tio n s of the area's commercial, in d u s tria l and re s id e n tia l p ro perties. One fin a l point concerning the ra tio s indicated on Table 17 needs to be made. The heterogeneity of land values tends to decrease as distance increases fo r both types o f zoning methods as expected from the Burgess model. Such a trend indicates th at as distance to the CBD decreases, the d iv e r s ity o f economic functions increases which in turn contributes to a wider range o f land values. The sectoral model indicates three areas where p otential land c o n flic t exists (Table 18). The f i r s t area is on Logan Road west of Cedar and south of the CBD (Figure 13). Some heavy manufacturing along with single fam ily re s id e n tia l areas and commercial e s ta b lis h ­ ments are found in th is area. In fa c t a large portion o f the southern h a lf o f ring four is found w ithin th is rectangle thus re info rcin g the resu lts of the ring model. 114 Capital 1 -4 9 6 MT F ln u re 13 LOCATION OF POTENTIAL LAND USE CONFLICTS HOPfc 115 The second area o f p o tential c o n f lic t 1s located east of Pennsylvania Avenue and to the west and south o f 1-496. To a large ex te n t, th is sector has the lowest population density 1n a l l o f the study area. An extensive portion o f the to ta l vacant land in Lansing is located here in th is area. That th is section may endure future land use c o n f lic t is not a t a l l surprising. Presently the area has both r e l a t i v e l y low and high density re s id e n tia l land uses but along with some l i g h t manufacturing and commercial establishments, p a r t ic u la r ly in Midway Center and in the southern portion near the in te rs ec tio n of Cedar and 1-96. The la s t area to be singled out in the determination o f l i k e l y locations o f c o n f li c t is the Grand River c o rrid o r, west of U. S. 27. Grand River approximately bisects the northern portion o f the study area from the northwest to the southeast, and i t contains almost a ll types o f zoning c la s s ific a tio n s found in Lansing. In the e a st, high density re s id e n tia l apartments are found; in the middle portions, commercial a c t i v i t i e s predominate, while east o f the Logan Road area some l i g h t manufacturing is found. Unlike the preceding two examples o f potential land use c o n f l i c t , th is area is highly accessible. However, a high a c c e s s ib ility corridor may fo s te r demand fo r change o f zoning c la s s ific a tio n to more intensive uses. Thus, pressure fo r changing the zoning ordinance may appear along selected points o f Grand R iver, p a r tic u la r ly as the demand fo r highly accessible land outstrips supply o f the land which is occurring now. 116 Summary of Chapter Findings The results o f the comparison of land values overall indicate th at the s itu a tio n a l zoning decreases the mixture of land values in high density re s id e n tia l and commercial zones. S im ilar results are obtained when the land values are aggregated by concentric rinns. The reduction o f land value v a ria tio n fo r the high density re s id e n tia l and commercial uses confirm the findings of the Burgess model o f land use. Evidence fo r the Hoyt model of land uses is also found in the results of the sectoral aggregation of land values p a r tic u la r ly for the high density re s id e n tia l and in d u s tria l zones. The situ ation al model developed in th is chapter does not account fo r va ria tio n of land values in the low density resid en tia l areas. The f in a l portion of the chapter analyzes areas of potential land use c o n f lic t . occurs where the d is p a rity of land values between the s it e and s itu a tio n a l zoning is the largest. It Chapter Five Summary, Conclusions and Implications 117 118 SUMMARY The research problem attempts to answer the following question: Does a d e lim ita tio n of zoning d is t r i c t s on the basis o f a s itu a tio n a l c h a ra c te ris tic produce more homogeneity o f land value than the ex istin g s it e based zoning? A model was developed to measure the s itu a tio n a l ch a rac teris tic s of sampled land use parcels. P rio r to the construction of the a c c e s s ib ility index the land use character­ is t ic s of the parcel are id e n tifie d and measured. Then the parcels are grouped according to s im ila r it y of land uses. Two s t a t is t i c a l grouping algorithmns, H-group and discriminant an alysis, are employed to minimize w ithin group v a r i a b i l i t y and to maximize between group d ifferences. The a c c e s s ib ility index is composed of two measures. The f i r s t calculates the proximity o f a parcel to other parcels with d iff e r e n t types of land uses. The second measure is based upon the time needed to tra ve l from a sampled land use node to major shopping and employment nodes w ith in the Lansing area. A computer mapping ro u tin e, SYMAP is u t il i z e d to construct a new re q io n a liza tio n scheme based upon values of an a c c e s s ib ility index fo r sample points. The routine s p a t ia lly interpolates the sample set of a c c e s s ib ility values in drawing regions for the e n tire study area. Following the construction of th is s itu a tio n a l model the major hypothesis fo r the study focuses on a comparison of land value v a r ia tio n , the actual and expected v a ria tio n a f t e r the application of the s itu a tio n a l model. Subsequent hypotheses represent a disaggregation of land value into various rings and sectors in order to account fo r v a ria tio n of existing land values. A s im ila r pre-post 119 land value comparison is then performed fo r these l a t t e r hypotheses. The results o f the research indicate th a t s itu a tio n a l ch aracteristics produce homogeneity of land values in commercial and high density re s id e n tia l zones. On the other hand, s itu a tio n a l zoning increases land value mixture in low density re s id e n tia l and in d u s tria l zones, CONCLUSIONS, RECOMMENDATIONS AND LIMITATIONS A careful examination of the data does not support an over­ whelming acceptance of any o f the three hypotheses dealing with explanation o f land values. The most v a lid conclusion reached is that s itu a tio n a l or a c c e s s ib ility based zoning produces more homogeneity of land values fo r commercial and high density re s id e n tia l areas. In Lansing's in d u s tria l and low density re s id e n tia l areas, the heterogeneity of land values in the s itu a tio n a l zoninn model ac tu a lly increases. I t appears th a t in d u s tria l and low density re s id e n tia l lands are less dependent on s itu a tio n a l or a c c e s s ib ility measures for the maintenance of land value homogeneity than are commercial and high density re s id e n tia l areas. For the in d u s tria l and low density re s id e n tia l areas, a c c e s s ib ility increases the heterogeneity of land values. Therefore, i f these zoning d is t r i c t s are defined by an a c c e s s ib ility c r i t e r i a , then the property owners w i l l be assessed unneeded locational costs i . e . negative e x t e r n a l it i e s , and w i l l r e a liz e a more d is to rted land value than locations not undergoing the negative e x t e r n a lit ie s . Land values are d is to rted by a range of factors such as the market, distance, a c c e s s i b i l i t y , . social costs and amount and type of f a c i l i t i e s a v a ila b le . 120 One exception to the above conclusion is found in the analysis of in d u s tria l land values. When in d u s tria l land values were grouped into sectors, the new zoning decreased the land value mixture. However, the o verall lack of land value homogeneity fo r the in d u s tria l parcels was evident in the overall and concentric portions o f the analyses. One recommendation fo r future policy formulation and urban planning in Lansing is th a t the d is t r i c t i n g or re g io n a liza tio n fo r commercial and high density re sid en tia l areas should be derived more on the basis of s itu a tio n a l c h a ra c te ris tic s . As indicated by the empirical results o f the study, i f commercial and high density re s id e n tia l areas are defined by situ a tio n a l c r i t e r i a , then property owners in these zones w il l l ik e l y enjoy a positive locational s p illo v e r or p o s itive e x te r n a lity . Positive locational 's p illo v e r ' zoning. is an important concept in urban I t is defined here as a location with a high degree of c e n t r a lit y or a c c e s s ib ility . Because of t h e ir need fo r hinh degrees o f c e n t r a l i t y , commercial and high density re s id e n tia l d is t r ic t s defined on the basis of s itu a tio n a l ch a racteristics produced a decrease in the land value mixture. When d is t r i c t s are defined in th is way, the individual property owner can b e tte r re a liz e a less distorted land value. I f a s itu a tio n a l approach is not followed in the d e lim ita tio n o f commercial and high density re s id e n tia l areas, a mixture of values w i l l occur and the zoning w i l l cease to be completely equitable in the d is trib u tio n of the locational 's p i l lo v e r s .' In a rriv in g a t these conclusions and recommendations some degree of caution is in order v/hen applied to other c i t i e s . The model and conclusions are based upon one study in one c i t y o f approximately 121 200,000 people. The c i t y is p rim a rily a manufacturinn center but also is an ad m in istrative center. Manufacturing nodes in Lansina remain r e l a t i v e l y close to the central business d i s t r i c t and there has been l i t t l e movement o f these nodes to outlying areas. Therefore, many of the employment and shopping nodes remain concentrated in a r e l a t i v e ly small area o f the c i t y . I f the techniques used in developing the s itu a tio n a l zoning model were applied to other c i t i e s , p a r tic u la r ly a c i t y th at has major employment and shopping nodes on the periphery, then the resu lts of the research may d i f f e r . That i s , low density re s id e n tia l areas w ithin close proximity to peripheral nodes, i f defined on the basis of s itu a tio n a l c h a ra c te ris tic s , may y ie ld more homogeneity o f land values. Also i f le is u re time or l if e s t y le s vnthin the urban area were to change, then the results may d i f f e r . These conclusions require a degree o f tentativeness because of some stru c tu ra l lim ita tio n s in the research. F i r s t , lim ited computer storage required a step-wise approach to the i n i t i a l oroupino of land uses. Also, the determination o f land uses are subject to a degree of individual in te rp re ta tio n . Another lim ita tio n in the study was a lack of base maps at a scale and size su itab le fo r published research. For example, a zoning map fo r Lansing th at is s u f f ic ie n t ly generalized and of the proper size fo r publication does not e x is t. One fin a l lim it a tio n of the study is the assumption that f if t e e n miles per hour represents an average rate o f urban t r a v e l. Such an assumption fo r a l l sections of the c it y may be misleading since a l l sections are not equally accessible. The ideal index would be travel time contours measured over e x is tin g a r t e r i a l s . a v a ila b le . However, th is type of data was not 122 RELATIONSHIP OF FINDINGS TO OTHER RESEARCH These conclusions are p a r t i a l l y supported by previous work performed by Seymour in P ittsb urgh ^ He found th at during changes in a zoning c la s s ific a tio n a mixture o f land values resulted and the preponderance of land values went in the d ire c tio n o f more capital intensive use (Seymour, 1966, p. 87). One may assume th a t the s itu a tio n a l zoning model devised in this research is s im ila r to rezoning. According to Seymour i f re s id e n tia l land is rezoned to in d u s t r ia l, land values of certain parcels w i l l tend to increase and overall heterogeneity increases. The s itu a tio n a l zoning devised in th is study tended to reduce the overall number of parcels in the lowest cap ital intensive positions ( i . e . low density r e s id e n tia l) and at the same time to increase the number in the more intensive zonino types ( i . e . in d u s tria l and commercial). However, the heterogeneity of land values was found only in in d u s tria l zones. In high density re s id e n tia l and commercial zones, the situ a tio n a l "rezoning" decreased the heterogeneity o f land values. Therefore, the cap ital intensive movement of land values as a re s u lt of rezoning, a notion alluded to in the f i r s t chapter, is not completely v e r ifie d by th is research. In his research on zoning and land values in Worcester, Natoli implies th at land value is more a function of lo c atio n , th at i s , a geographic fa c to r , and less a function of zoning which is a p o l i t i c a l fac to r (N a t o li, 1967, p. 194). I f th is were true fo r Lansing then ^The research by Natoli and Seymour represents two exhaustive treatments of the empirical relation sh ip between zoning and land values. Other geographers have also looked a t the same topic but th e ir research lacked th is type of extensive empirical treatment (Cox, 1973; Harvey, 1972; Soja, 1971; Yeates, 1965b). 123 there should have been increased land value homogeneity in a re g io n a liz a tio n scheme based upon economic fa c to r s , th at i s , proximity to d if f e r e n t land uses and time distances. Only in commercial and high density r e s id e n tia l areas was the homogeneity o f land values increased. On the basis o f th is in v e s tig a tio n of Lansing i t is concluded th at the land value mixture is both a function of location and zoning, depending upon the nature of the predominant a c t i v i t y . Caution is needed however since g en eralizatio n s concerning determinants of real property values always require consideration of factors ranging from national economic trends to local supply and demand factors (Ukeles, 1965, p. 4 6 ). Additional research on zoning is needed to in v es tig ate the e f f e c t of zoning on land values over sp e cifie d time periods. A study o f time- based change should substantiate or disprove many o f the conclusions derived in th is study and in previous studies by Seymour and N a to li. Furthermore, i f a zoning re g io n a liz a tio n scheme were developed and implemented over tim e, i t may prove to be a most e f f e c t iv e tool f o r updating o f many communities * zoning ordinances. Many smaller communities, p a r t i c u l a r ly those located w ith in close proximity to the advancing wave of urban settlem ent, are re lu c ta n t to adopt nev/ zoning ordinances. The j u s t i f i c a t i o n fo r urban zoning changes would appear to be stronger i f the decisions were more oriented around a h is to r ic a l perspective. 124 THE FUTURE OF GEOGRAPHIC INVESTIGATIONS IN URBAN ZONING Geographers have made only lim ite d co ntributions to the study of zoning processes and decisions. The question th a t minht a ris e is whether the geographic contributions v /ill increase in the fu tu re . In the author's opinion geographers v /ill increasin gly become aware of the need fo r p ro fe s s io n a l-le v e l analyses o f land use regulations because o f the process o f d e c e n tra liz a tio n which has been underway fo r several decades in urban areas. D e ce n tralizatio n refers to a s p a tia l spreading out of the popula­ tion along with the accompanying desire fo r increased per capita consumption of land. As a r e s u lt the need fo r a dispersal o f urban employment nodes, services and f a c i l i t i e s from a ce n tral node to peripheral locations increases. Often these urban services and f a c i l i t i e s stim ulate land use c o n f li c t in the receiving area. In Lansing the proposed suburban location fo r a s a n ita ry l a n d f i l l had aroused the concern of many o f the affe cte d property owners. The d e c e n tra liz a tio n of the urban population also induces major confrontations over social values and land uses between the e x is tin g residents and the new a r r i v a l s . In p a r t ic u la r when central c it y residents desire to l i v e in low or medium income housing in the suburbs, but are prevented due to large l o t zoning r e s t r ic t io n s or minimum f lo o r requirements, the aura o f confrontation increases s ig n ific a n tly . In these s itu a tio n s , a r e j u s t i f i c a t i o n fo r the zoning regulations must be undertaken. The d e c e n tra liz a tio n of population has h i s t o r i c a l l y lead to a m u lt ip lic a t io n of governmental units (Kasperson and D r e it b a r t , 1974, p. 30 ). The consequences of land use decisions th a t need to be made, 125 such as a new zoning d e lim ita tio n , or the development of a zoning ordinance may not receive as complete an evaluation in sm aller-sized governmental units as in la rg e r ones such as Lansing. Many of the smaller communities do not have the trained personnel or the extensive budget needed to investigate a l l o f the s o c ia l, economic and environmental consequences o f a p a rtic u la r land use decision. Furthermore, with increased c it iz e n p a rtic ip a tio n and responsiveness, the lik e lih o o d of public opposition to major changes in zoning or land use regulations increases. What d e c e n tra liza tio n u ltim a te ly leads to is an increased demand for professionals in geography, urban planning, resource development and urban p o litic s to in v e s tig a te , in te rp re t and d r a ft acceptable land use regulations and master plans. F in a lly d ec en tralizatio n o f the urban population often leads to increased land pressure on the urban-rural frin g e . A population tid a l wave moves outward from the c i t y ; growth rates are declining behind the crest and increasing as the crest advances (Blumenfield, 1949, pp. 209-212). According to Wolf, the end re s u lt of " tid a l wave" urban growth is a hollow metropolis "becoming bigger, more d iffu s e and more hollow in the future" (Wolfe, 1969, p. 153). Speculators and developers often purchase large tra c ts of vacant land on the frin g e and hold i t fo r a few years u n til the advancing wave moves clo ser. Then a t the rig h t time they s e ll i t often at highly in fla te d prices. The land is o r ig in a lly purchased a t a r e l a t i v e l y low cost because o f i t s lack o f f a c i l i t i e s and i t s low density zoning c la s s if ic a t io n . These future commercial or in d u s tria l site s are thus purchased a t the price determined by the ex istin g not potential use and the e x is tin g not p o tential zoning c la s s ific a tio n . The public suffers 126 when these situ atio n s aris e not only from the loss of tax revenues but also from declining open space fo r present and future generations to enjoy. Unfortunately the development o f the m unicip ality precedes the enactment of zoning regulations (Ranney, 1969, p. 11). Some type of ’ a p r i o r i 1 land assessment and land use controls are needed but often the planning budgets fo r f u l l time personnel in these embryonic communities is quite lim ite d . Professionals are needed but on a lim ite d basis only. However, the s itu a tio n may change in the fu tu re . The U. S. Congress is cu rren tly considering le g is la tio n requirinn states to develop some type of land use plans with accompanying use reaulations. Once the law becomes enacted and funds are made av ailab le a need fo r professional level land use consultants w i l l a ris e . The dispersal o f urban populations and the accompanying s o c ia l, p o l i t i c a l and economic problems th at aris e increases the ro le of the geographer as an advocate planner or as a t r a d itio n a l planner. The conventional planner as defined by Kasperson and B re itb a rt "approaches planning issues as problems requirinn a choice among various technical solutions" (Kasperson and B r e itb a r t , 1974, p. 43 ). On the other hand, the advocate planner seeks to solve ethical planning issues by assuming a partisan position and hopes to change the inequity and in e q u ality ex istin g in the present p o l i t i c a l system (Kasperson and B r e itb a r t , 1974, p. 43). Regardless of which ro le the geographer assumes, i t is the opinion of th is author th at geographic knowledge and tra in in g can be applied to an analysis o f.la n d use planning and regulations in general and zoning in p a r t ic u la r . The research contained w ithin these pages 127 has proposed a s c i e n t i f i c solution to zoning d e lim ita tio n . Such an approach philosophically aligns the author with a more conventional solution to planning. However, regardless o f the philosophical o rie n ta tio n of the individual geographer, zoning is a process that incorporates many aspects o f economic, p o l i t i c a l and social geography. Following is a l i s t o f research topics and questions on zoning that m erit fu r th e r geographic research: a) Analysis o f the locations o f zoning variances and special use permits; How do these d is trib u tio n s co rre la te with the ex istin g d is trib u tio n s of population, in te re s t groups, economic wealth in a city? b) Analysis o f property owners reaction to requests fo r zoning changes; Does the reaction support or re fu te the e x is tin g geographic theory on the f r i c t i o n o f distance? c) Analysis o f the location of non-conforming structures; How does the d is trib u tio n c o rre la te with areas of lim ite d housing, m inority residents and crime? d) Analysis of the value systems of zoning appeals boards; How do they d i f f e r w ithin the metropolitan area and between rural and urban areas? e) Analysis of vacant land and zoning c la s s ific a tio n s ; What is a 'highest and best* zoning c la s s ific a tio n fo r vacant and id le land or land surrounding 'new towns'? f ) Analysis o f the "friends and neighbors" model of in te ra c tio n w ithin the context o f the.zoning decision-makers; 128 Does the d is trib u tio n o f zoning variances and residencies of local decision makers e x h ib it a "friends and neighbors" distance bias? CONCLUDING REMARKS Z o n in g ,p o litic s and economics are in e x tric a b ly lin ked . As evident from th is research zoning can be manipulated by the s k i l l f u l p o litic ia n or professional planner who wishes to earn a monetary p r o f i t fo r him self, a corporation or a conmunity. On the other hand, zoning regulations can impose both monetary costs and social costs upon property owners or renters liv in g in the community or upon prospective owners desiring to liv e in the community. Thus the apparent arb itra rin es s of many zoning boundaries imposes both p ositive and negative e x te r n a lit ie s upon property owners. Since zoning allocates current and fu tu re s i t e values, then the imposition o f p o s itive and negative e x te r n a lit ie s may sometimes be unavoidable. A re d is trib u tio n of the public wealth may be needed in order to compensate those land owners who are forced to accept the negative e x t e r n a lit ie s . 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