REGIONAL LAND USE ALLOCATION MODELS AND THEIR APPLICATION TO PLANNING
by
URS JOSEF THICKER Dipl. Ing. ETH, Swiss Institute of Technology, 1965
A THESIS SUBMITTED IN PARTIAL FULFILMENT
OF THE. REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
in the School
of Community and Regional Planning
We accept this thesis as conforming to the required staadard
THE UNIVERSITY OF BRITISH COLUMBIA May, 1969 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study.
I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Department of Community and Regional Planning
The University of British Columbia Vancouver 8, Canada
Date April 30, 1969 iii
ABSTRACT
In the planning profession there is increasing recognition of the complex relationship of variables in an urban region which impede rational decision-making. In order to cope with this problem, quantitative models have been developed in recent years. It is the purpose of this study to investigate and evaluate the present stage of model- building as it applies to regional planning.
It is hypothesized that the application of land use allo• cation models is a desirable aid for rational decision• making in regional planning.
The study begins with an outline of the theoretical basis for building land use allocation models: economic location theory and social physics. Economic location theory is mainly concerned with finding criteria for a rational choice of the location for a firm or a household. In this context, the concept of economic rent is discussed. In order to give explanations of the land use patterns within a region the basic notion in respect to agricultural pro• duction is developed and then extended to the urban land iv
uses. The second approach to land use allocation models,
social physics, is mainly based on statistical regulari• ties in explaining human mass behavior. The most commonly
employed concept is the gravity principle, which is an attempt to apply Newton's physical law of gravitation to
social, mass behavior. This concept is very often applied in community and regional planning and has yielded accept• able results in a great number of studies.
In part three the most important elements and steps in the process of model-building are discussed, including rules or standards which should be considered by a model- builder. First of all, a 'wide range of types of models are examined in order that the proper model may be selected for an actual regional planning problem. The design process is also discussed in some detail and it is shown that there is evidence of fundamental criteria for model building.
Part four is concerned with three selected existing regional land use allocation models. The model of the Pittsburgh
Region was the first operational model on a regional level and its ingenuity influenced numerous model-builders. One of the most salient findings of this model, which is mainly based on social physics, relates to the fact that the gravity principle seems to have enough flexibility to comprehend the spatial pattern of land uses within an urban region. V
The model of the State of Connecticut is based on the shift-analysis framework and distributes three population and six employment groups to the 169 towns of-the State of Connecticut. Its basic feature is the ability to repli• cate the structure of a region as large as a state and it is therefore of great interest as a macro-approach. The structure of the model is relatively simple and the data requirements are not intensive. Hence, it seems that such a model framework could serve as a sound basis for models in other study areas.
The Bay Area Simulation Study is one of the most recent models. It introduces a high level of disaggregation and assumptions which are based, to some extent, on economic location theory. Hence, it can be said that its basic concept relates to the working mechanism of the market process. The structure of the model is based on a number of interrelated submodels, including a set of employment allocation models and a set of residential allocation models.
The final part of this study relates the findings of the preceding parts to regional planning. It is shown that regional planning is fundamentally a locational problem.
In addition, some experiences of model application by planning agencies are discussed. These experiences emphasize the fact that, the essential feature of land use allocation models is to improve the rationality of decision-making. By vi
comparing the advantages of models with the principal difficulties in application it is then possible to derive the final conclusion that land use allocation models are a desirable aid for rational decision-making in regional planning. vii
TABLE OF CONTENTS
ABSTRACT - iii
LIST OF FIGURES . . . ix
LIST OF APPENDICES x
ACKNOWLEDGEMENT S xi
1. INTRODUCTION .1
1.1 The Problem 1
1.2 Purpose and Scope of this Study 4
1.3 Hypothesis 6
1.4 Definitions 6
1.5 Organization of the Remainder 7
2. APPROACHES TO REGIONAL ALLOCATION OF ACTIVITIES 10 2.1 Economic Location Theory...... 11 2.1.1 Agricultural Rent and Land Use 13 2.1.2 Urban Land Uses . 16 2.1.3 General Equilibrium 20
2.2 Social Physics 23
3 . ELEMENTS OF MODEL BUILDING . . .' 33
3.1 Typology of Models 33
3.2 Design of a Model 41 3.2.1 The Variables and their Relevance 43 3.2.2 The Level of Aggregation 44 3.2.3 Formulation of the Mathematical Relationship 46 viii
3- 3 Calibration and Testing of a Model 50
4. SELECTED REGIONAL LAND USE MODELS 58 4.1 The Model of the Pittsburgh Region by Lowry .. 59 4.1.1 The Concept of the Model 59 4.1.2 The Structure of the Model 61 4- .1.3 Interpretation of the Model 66 4.1.4 Calibration of the Model 67 4.1.5 Testing of the Model '. 71 4.1.6 Evaluation 72 4.2 The Connecticut Model 73 4.2.1 Formulation of the Model 74 4.2.2 The Structure of the Model 76 4.2.3 Interpretation . .... 79 4.2.4 Calibration and Testing 81 4.3 The Bay Area Simulation Study 83 4.3.1 . Formulation of the Model 84 4.3.2 Employment Location Submodels 85 4.3.3 Residential Location Submodel 92 4.3.4 Appraisal ' 94 4.4 Conclusions 96
5 REGIONAL PLANNING AND LAND USE ALLOCATION MODELS 101 5.1 Regional Planning and the Importance of Land Use Allocation Models 101 5.2 Advantages of Land Use Allocation Models 103 5.3 Difficulties of Applications 106 5.4 Conclusions 108 BIBLIOGRAPHY 113 APPENDICES 119 ix
LIST OF FIGURES
Figure Page
1 Agricultural bid rent function for one crop ... 15
2 Agricultural bid rent functions for two crops . 15
3 Bid rent functions for urban land uses 21
4 Bid rent functions for a hierarchy of centers . 21
5 Cumulation of errors 4-9
6 Structure of a chain model 49
7 Proposed structure of an improved model 49
8 Information flows in the Pittsburgh Model 62
9 Differential shift and proportional share 75
10 Structure of the Bay Area Simulation Study 85
11 Retail allocation flow diagram • ••• 89 X
LIST OF APPENDICES
Appendix Page
1 Cumulation of Errors 119
2 Variables and Parameters of the Pittsburgh Model 122
3 Control Totals and Structural Parameters of the Pittsburgh Model- 124
4 Employment Groups for the BASS Model 126 xi
ACKNOWLEDGEMENTS
I wish to express my thanks to the many people who contributed to the completion of this thesis. Dr. H.
Peter Oberlander, Director of the School of Community and Regional Planning deserves particular thanks for his initial encouragement to investigate this topic and his continuous interest in my planning education.
Grateful appreciation is also extended to Dr. H. Craig
Davis and Dr. V. Setty Pendakur for the concern, ad-vice and constructive criticism they have offered during the preparation of this thesis. I am also indebted to my friend and colleague Fraser L. Manning who with great patience assisted with the final English style.
But above all, thanks has to be expressed to the Canada
Council which through a scholarship made my studies here in Canada possible. Finally, my greatest indebted• ness is to my wife Insa who always helped during my studies and brought my scribble of this thesis into final form .and -gestalt. - 1 -
1. INTRODUCTION
1.1 The Problem
Activities by men, social groups, communities or entire societies are determined by a purpose or a number of purposes. We act in order to achieve goals. But there are always alternative ways to achieve them and one has to be chosen. This selective decision is fundamental in human life, and therefore can also be seen in the context of planning what is "designing a course of action to achieve ends."1
In community and regional planning, designing or selec• ting a course of action is impeded by several circumstances.
First of all, goals have to be formulated. This is extremely difficult because groups of human beings are limited in their ability to agree on common goals, to communicate and p to cooperate. Apart from goal setting there is increasing recognition that a course of action influences a great number of variables and "planners are now prisoners of the discovery that in the city [and in the region] everything - 2 -
affects everything else."J A third difficulty is the limitation of time in dealing with a complex and continu• ously changing system such as the city or the region.
Very often the planner is asked to give recommendations in a short time and therefore he is not able to study all the necessary aspects of his task.
These remarks indicate several difficulties and restric• tions in solving the urban and regional problems, and a statement by Simon is extremely true for the planner. He states that
the capacity of human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world - or even for a reasonable approximation to such objective rationality.21"
Despite these difficulties and limitations not only a
"good" action, but the "best" action^ should be found.
Meyerson and Banfield express this as "efficient" planning which "under given conditions leads to the maximization of the attainment of the relevant ends." They assume also
"that a planned course of action, which is selected rationally is most likely to maximize the attainment of the relevant ends and that therefore 'rational' planning and 'efficient' planning are the same."^ In a further statement they state that a rational decision has to be made in the following manner: - 3 -
The decision-maker considers all of the alternatives (courses of action) open to him; i.e. he considers what courses of action are possible within the conditions of the situation and in the light of the end he seeks to attain.
He identifies and evaluates all the conse• quences which would follow from the adoption of each alternative; ... and
he selects that alternative the probable consequences of'which would be preferable in terms of his most valuable ends.'
Meyerson and Banfield point out that this is an ideal concept and "no decision can be perfectly rational" since all alternatives and consequences can never be known.
Nevertheless decision-making in community and regional planning should be based on knowledge of the main alter• natives and their consequences.
We have now outlined on one side the circumstances which impede decision-making and on the other side the criteria for rational decision-making. We may now pose the difficult question: how can a rational decision in regard to a complex system such as the city or the region be made?
It is obvious that the planner can no longer rely solely on intuitive judgement or experience. He has to apply tools and techniques which are able to test in a short time a variety of goals, alternatives, and their consequences which influence a great number of variables. 1.2 Purpose and Scope of this Study
Since World War II there has been increasing concern about scientific methods to solve complex problems. Operations 8 9 research and systems analysis are now applied in indus• trial management, warfare, government, planning and many other fields. These techniques provide a scientific basis for solving problems which involve interactions of many variables. Churchman, Ackoff and Arnoff describe operations research in the following way:
The concern of O.R. with finding an optimum decision, policy, or design is one of its essential characteristics. It does not seek merely to find better solutions to a problem...; it seeks the best solution. It may not always find it.... But O.R.rs efforts are continually directed to getting to the optimum or as close to it as possible.
A main phase in operations research is the construction of a model to represent the system under study. With the help of a model it is possible to run experiments which would otherwise be impossible.
The purpose of this study is to investigate and evaluate the present stage of model-building for application in regional planning. In reviewing the literature there is evidence of a great variety of models. The scales range from international trade flow models to the interaction between individuals."'""'" - 5 -
In this study we shall focus on intraregional growth allo• cation or land use models. These models allocate economic activities or land uses to subareas within a region. The reason for this focus stems from the importance of the spatial allocation in planning - as we shall see in this study - and this leads to the fact that 70 percent of 12 urban development models are locational models.
The field of model building in the planning profession is expanding extremely fast, and often difficulties of communication exist between the "hardliners" and the 1^ "softliners" , as for instance expressed by Lowry:
The Model-builders - a group that overlaps but does not coincide with the planning profession - claim that their brain-children have present or potential value as planning aids. One of the frustrations of the planner as client is that he does not usually find it easy to judge these claims or to choose among the many alternatives now available for his consideration.!^
The author hopes to help to bridge the "gap" between these two groups. Therefore the scope of this study will be limited to this objective. Within the great number of land use models only a few will be reviewed and only those aspects thereof will be examined which seem to be of pri• mary relevance in regard to their application in regional planning. - 6 -
1.3 Hypothesis
This study will examine the following hypothesis:
Given that the major decisions pertaining
to regional planning relate to the spatial
allocation of economic activities, the
application of land use allocation models
is a desirable aid for rational decision•
making in regional planning.
1.4 Definitions
For the purpose of this study relevant terms are defind in the following way:
Region: A space larger than a single community and smaller 15 than a whole country. y
Model: A simplified representation of some subject of inquiry (such as objects, events, processes, systems) ."^
Land Use: Man's activities on land which are directly 17 related to land. '
Land Use Allocation Model: A symbolic statement about the allocation of economic activities (population and employment) and land use categories which can "include structures, eco• nomic activities, floor areas, and generally any items that - 7 -
can be used to describe regions and subareas in quantita- tive spatial terms."
Simulation: The operation of a model or simulator. The model is amenable to manipulations which would be impos• sible, too expensive or impractical to perform on the entity it portrays. The operation of the model can be studied and, from it, properties concerning the behavior 19 of the actual system or its subsystems can be inferred.
1.5 Organization of the Remainder
After these introductory remarks the second chapter will deal with the two alternative approaches to the formula• tion of land use allocation models. The third chapter discusses the most important rules which have to be con• sidered if such a model is to be built. The fourth chapter explains and evaluates three existing regional models. We shall see how the findings of the first three chapters are inputs to an operational model. The final part of this study is concerned with the application of models in regional planning programs as tools for improving decision• making . - 8 -
Footnotes
1 Martin Meyerson and Edward C. Banfield, Politics, Planning and the Public"Interest (Glencoe, 111.: The Free Press, 1955), p. 314.
2 Herbert A. Simon, Models of Man (New York: John Wiley & Sons, Inc., 1957), p. 199-
3 Ira S. Lowry,' "Short Course in Model Design",' Journal of the American Institute of Planners, Vol. 31 No. 2 (May 1965), p. 158.
4 Herbert A. Simon, Op. cit., p. 198.
5 Britton Harris, "New Tools for Planning," Journal of the American Institute of Planners, Vol" 3l No. 2 (May 1965), p. 91. '
6 Martin Meyerson and Edward C. Banfield, Op. cit., p. 314.
7 Ibid., p. 314.
8 See for instance the. comprehensive and basic work by C. West Churchman, Russel L. Ackoff and Leonard E. Arnoff, Introduction to Operations Research (New York: John Wiley and Sons, Inc., 1956).
9 See for instance .Claude McMillan and Richard F. Gonzalez,. Systems Analysis (Homewood, 111.: Richard D. Irwin, Inc;, 1965).
10 C. West Churchman,"Russel L. Ackoff and Leonard E. Arnoff, Op. cit., p. 8.
11 Iowa State University, Center for Agricultural and Economic Development, Research and Education for Regional and Area Development"(Ames,'Iowa: Iowa State University Press, 1966), p. 255.
12 G. Hemmens, "Survey of Planning Agency Experience with Urban Development Models," Journal of the American Institute of Planners, Vol. 34 No. 5~ (Sept. 1968). '
13 William Goodman in a lecture at the University of British Columbia, January 1968. - 9 -
14 Ira S. Lowry, "Seven Models of Urban Development," in Urban Development Models by Highway Research-- .' Board (Special Report 97; Washington, D.C., 1968), p. 121.
15 Harvey S. Perloff, "Key Features of Regional Planning," Journal of the American'Institute of Planners, Vol. 34- No. 2 (May 1968), p. 153.
16 G. West Churchman, Russel L. Ackoff and Leonard E. Arnoff, Op. cit., p. 151.
17 Marion Clawson and Charles L. Stewart, Land Use Information (Baltimore: The John Hopkins Press, 1965), P. 29. •
18 Traffic Research Corporation, Boston Regional Planning Project, "Review of Existing Land Use Forecasting Techniques," in -Highway Research Record, No. 88 (1965), p. 183.
19 Martin Shubik, "Simulation of the Industry and the Firm," American Economic Review, L, No. 5 (Dec. I960), p. 909. 2. APPROACHES-TO REGIONAL ALLOCATION OP ACTIVITIES
In order to proceed to building models of the spatial districution of activities we must first of all have a basic understanding of the underlying forces. Priedman and Alonso state that:
Human activities are distributed over the national territory in certain rhythms and patterns that are neither arbitrary nor the working of chance. They result rather from the interdependencies that give form to economic space. Spatial patterns will change with shifts in the structure of demand and of production, in the level of technology, and in the social and political organization of the nation. The economic and social development of the nation is reflected in its patterns of settlement; its systems of flow and exchange of commodities, money, and information; its pattern of commuting and migration; and its reticulation of areas of urban influence.l
There is evidence of a complex framework of interactions which makes a systematic investigation difficult. Neverthe• less, following Lowry, there are mainly two analytical traditions or theories which offer guidance: economic location theory and social physics. Two approaches are also distinguished by Kilbridge and Carabateas as they describe the organizing principle of a model which is the - 11 -
"essential manifestation of its underlying theory."5 They distinguish micro-analytical behavior or choice models, and macro-analytical growth-forces or indices models. This distinction coincides with Lowry's. The former models are based on economic location theory, the latter ones on social physics. Therefore we shall focus on these two approaches in the following discussion.
2.1 Economic Location Theory
The main feature of this theory is that criteria for the rational choice of a location for a firm or a household are given. Generally, households and firms locate where they
ZL can "gain more than they can elsewhere." Businesses locate where.they can obtain the highest profit, and house• holds where they have the greatest satisfaction and employment opportunities.
Economic location theory is an extensive field in itself.
We will therefore only outline a few fundamental principles.
The "father" of location theory is von Thunen who in his 5 study the "Isolated State"^ did "progress somewhat toward a general locational analysis."^ He found that the spatial arrangement of agricultural production around a single city takes the form of concentric rings. In regard to the location of industries, the first comprehensive theory - 12 -
was developed by Weber' who emphasized three basic loca- tional forces:' transport cost differentials, labor cost differentials and agglomeration (deglomeration) economies and diseconomies. Weber's theory is mainly a microeconomic approach from the point of view of the individual pro• ducer. Hence it was recognised that a general equilibrium theory was necessary instead of a partial location theory.
This attempt was made by Losch in his "Economics of Loca- 8 tion" in which he found that the hexagon is the most economical shape for trading areas.
These basic works v/ere stimuli for several scholars to study location problems and to advance the theory. A com-, prehensive review of the literature is contained in Isard's
"Location and Space Economy".^
Eor the purpose of this study we will focus on the distri• bution of economic activities and land uses within the sphere of the city and its hinterland and outline some concepts which seem to be of great help in understanding the spatial forces which shape the urban regions. Isard states that traditionally the theoretical analysis of the spatial allocation of urban land uses.has fallen outside the realm of location theory. But in regard to such a theory he finds that "in many aspects urban land use theory is a logical extension of agricultural location theory.""^
The basic concept of agricultural location is land rent; - 13 -
therefore we shall define it and show how it can he extended and applied to commercial, industrial, and residential land uses.
2.1.1 Agricultural Rent and Land Use
The concept of the land rent was first mentioned by 11 .. 12 Ricardo and fully developed by von Thunen. Recent 13 and more complete formulations are those by Isard ,
Dunn1^, Alonso1^ and Nourse16.
We assume that there is a single market center at which agricultural products from the surrounding hinterland can be sold. All the land is uniformly fertile, and transport• ation costs are equal in all directions from the market.
The prices are determined at the market where demand equals supply.
17 We may consider one activity ' which, for instance, pro• duces 30 bushels of corn per acre at a cost of $ 10 in labor and machinery. If the price at the market is $ 1 per bushel the product per acre can be sold for # 30. But corn produced at any distance from the center has to be transported at let us say, a price of # 0.05 per bushel per mile. In a case where corn is produced at 10 miles from the market center we would have transportation costs of - 14- -
$15 per acre. While revenue remains f> 30 the difference between revenue and cost would only be #'5- This difference between revenues and costs is the economic rent. A farmer notices that this difference increases $ 1.50 per mile and acre. Therefore he will bid rents up to these amounts for each mile nearer the market.
The rent at any location can be calculated as follows:
pc(t) =N(Pc-C-kc.t)=30(l-^§- 0.05 • t )
p^(t) = 20 - 1.5 • t
: where Pc(t) the rent per unit of land at a distance t from the market center N : number of units of the crop produced per unit of land
P : price per unit of the crop at the market
C : cost of producing one unit of the crop (farmers "normal profit" is included as labor cost)
kQ : cost of transportation per mile of one unit of the product
t : distance from the market
This bid rent function can be presented graphically as shown in figure 1 (p. 15). At the distance t (in the above example 13^/3 miles) the rent is zero which means that at a distance greater than t , corn can only be pro- duced at a loss. - 15 -
Agricultural bid rent function for one crop
Distance t (miles)
Figure 2 : Agricultural bid rent function for two crops
Rents
Distance t (miles) - 16 -
If potatoes are also produced we can determine which area will be used for each kind of production. We may also calculate the bid rent function for potatoes and combine both functions as in figure 2 (p. 15).
In the competitive market for land the highest bidder for any particular site will obtain it. This means in our case that farmers in potato production outbid farmers in corn production for all land between the market center and the
distance t^. Between t and tc, corn producers can bid the highest which means that they receive the lands. In this way more crops can be added resulting in the land use pattern for the agricultural production.
2.1.2 Urban Land Uses
This simplified model of the agricultural rent can now be applied to urban land uses. Isard mentions that the follow• ing factors are determining the price each potential user is willing to bid:
1. effective distance from core.
2. accessibility of the site to potential customers.
3. number of competitors, their locations, and the intensity with which they vie for sales; and
4-. proximity to land devoted to an individual use or a set of uses which are complementary - 17 -
in terms of "both attracting potential customers and cutting costs, whether they be production, service, advertising, or other. 18
In Alonso's study only the first of these factors is
considered. He states that in a centralized city the
second factor is also implied because accessibility of
the site to potential customers will decrease with
distance from the center and furthermore that the other
factors, which relate to the interdependence of business
locations, are too complex for an analysis within the 19 scope of his work. y
Commercial and Service Land Uses
Commercial and service activities are trying "to maximize
the volume of business that they transact" and this can be
achieved if "they are located near the center of the day- 20 time population." This means that accessibility is the key factor to a profitable location. If we assume a market center at which most transactions take place, such
as the Central Business District, we will have fewer
transactions with increasing distance, and selling costs
(e.g. advertising) must increase v/ith distance from the
center in order to offset the decrease of accessibility.
Another cost item which changes with location is rent per
acre, which leads to the bid rent function whose slope is - 18
influenced by the following factors:
The ceiling rent per acre would decline faster with distance from the market center, the greater the increased selling costs to achieve the same volume of business, the greater the number of transactions per square foot of floor space and the less possible it would be to substitute cheaper land for other inputs. 1
These factors are the same as those pertaining to agri• cultural production: selling costs are transportation costs; transactions per square foot of floor space repre• sent yield per acre; and substitution of land for nonland inputs is the same.
Industrial Land Uses
For the location of manufacturing activities the bid rent function is influenced by factors which differ from agri• cultural- and urban activities depending on accessibility.
The profit of a manufacturing plant is in general deter• mined by sales cost not only to the local market but primarily to outside areas. Therefore "total revenues will not noticeably shift as the plant is located at different distances from the city center, since we are initially assuming that transport costs are equal in every direction." i
But total cost may change with the location of the plant.
With increasing distance from the daytime population, higher wages have to be paid because commuting costs have to be -De•
compensated. Very important for manufacturing is the substitution of nonland inputs for land. Because rents are declining with distance, the plants can use more land which enables them to have more efficient flows in the assembly process. Therefore greater economies of scale 23 can be achieved. ^
Hence the slope of the bid rent function depends upon
the increase in the wage rate, the decrease in rent per acre necessary to offset this wage increase and economies of scale made possible by the substitution of more land for nonland factors of production.24
Residential Land Uses
Residential land is of primary importance because it covers four-fifths of all privately developed land in major
2y5 26 American cities. The bid rent or bid price curve of a resident is the set of prices for land the individual would pay at different distances while deriving a constant level of satisfaction.
A comprehensive discussion of the residential bid price curve in diagrammatic and mathematical form was done by
Alonso^?. He combines indifference analysis with the budget or price-opportunity theory and arrives at a mathematical equation for the residential bid price curve. - 20 -
It is "beyond the scope of this study to give, the particu• lars concerning the derivation of this equation. Therefore only the main findings will be mentioned. Once again the slope of the bid price curve is negative and depends upon the commuting costs and the tastes of the individuals.
2.1.3 General Equilibrium
After this discussion of classes of land uses we can now superimpose all bid rent curves. We have seen that all rents decline with distance from the market center or, as we might also name it, the center of the daytime population.
In generalizing we can state that the slopes of the bid rent curves depend on the output of the land using activity per acre, transportation, selling or wage costs, and the possibility of substitution between land and nonland inputs.
The shape of these curves may be as shown in Figure 3 (p. 21).
By rotating these curves around the market center we get a concentric land use pattern; we arrived at the concentric 29 zone theory ^ in a different way.
Until now we discussed idealized conditions assuming uniform fertility of soil, uniform topography, equal transportation cost in all directions and one market center. In order to represent a realistic situation, all these factors have to be modified. Figure 5 : Bid "rent functions for urban land uses
Rent •
Source : Hugh. 0. Nourse, Region9-1 Eccmomics (New York: Mc Graw-Hill, 1968), p. 115.
Figure 4- : Bid rent functions with a hierarchy of centers
Metropolitan/ y Regional Center
Reg. Shopping i Neighborhood Center I Center
1 ! ! i Satelite i 1 1 i i i iii City 1 i iii i i '^>s^\ II 1 ! I j ' i i i 1 1 1 I 1 1 ii iii Distance
Source : Hugh 0. Nourse, Regional Economics (Hew York: Mc Graw-Hill, 1-968), p. 120. - 22 -
If we have soils with different fertility, the profit•
ability of agricultural production will be changed and the
bid rent function will shift up or down. Different topo•
graphical features restrict development because production,
selling or construction costs will increase with ascending
slope. A drastic change occurs when we modify the assump•
tion of equal transportation costs in all directions. A
major highway, for example, allows easier and faster travel.
Therefore transportation costs will be reduced and the
slope of the bid rent function declines along the highway.
The result is that the concentric rings change to a "star"
pattern.
Finally, we have not only one market center. There exists 30 a hierarchy of centers-' and each subcenter causes a peak
in the bid rent function. The resulting shape of the bid
rent function in one direction from the main center might
occur as shown in figure 4- (p. 21).
The discussion of these modifications gives a realistic picture of land use patterns within a metropolitan region.
There is evidence of strong economic forces which determine
the location of activities. Hence it is important for the planner and model-builder to recognize their magnitude and
to take them into account. - 23 -
2.2 Social Physics
The findings of social physics are mainly based on statis• tical regularities in explaining mass behavior. They do not explain the behavior of the individual.
In the search for explanation of the spatial structure of urban areas and regions, gravity and potential concepts have been applied. It was recognized that these physical principles could also be applied to social phenomena.
Historical and comprehensive reviews of these concepts in 31 application to human mass behavior are those by Carrothers^ 32 and Isard.^ In the following part of this study the main features of these concepts will be given in order to provide insight and understanding of the basic concepts which are applied in building locational models.
Basically, the gravity concept of human interactions postu• lates that
an attracting force of interaction between two areas of human activity is created'by the population masses of the two areas, and a friction against interaction is caused by the intervening space over which the interaction must take place.53
In mathematical notation, the relationship can be expressed as follows: - 24 -
10 f P. ; P. : population of area i and j, respectively -•- J D. . : distance between the two centers. -*-u The first statement of this concept was made by Carey^ in the last century. Later it was applied to migration by 55 56 57 Ravenstein^ and Young^ and to retail trade by Reilly. After these early applications Zipf^ and Steward^ generalized the concept and formulated the "force" of interactions which is where k : a constant of proportionality, and, in analogy to physics, the "energy" of interaction which results from this force Pi Pi 3-D Stewart also formulated the "potential of population" which is a measure "indicating the intensity of the possibility of interaction." - 25 - -V - k i a where : potential at i of the population of " area j indicates the possibility of interaction between an individual at i and a population at g. In reality there is more than one mass j which leads to the total potential at a point i. It is the sum of the separate potentials n 'n T k + k = k l tot • -f* • • • • lc D. Di2 D. il in 0 = 1 D1 0 To calculate this total potential it has to be pointed out that the mass at i also creates a potential. But the distance cannot be considered as zero because this would result in an infinite potential. This difficulty may be overcome in two ways. Carrothers proposes to take the average of the distance from the center of area i to its periphery. It is also possible to express all denominators 41 as 1 + D. •. For applications of gravity models it is Important to discuss some measurements of the two variables, mass and distance. Not only can population be used for measuring mass. The choice of the measurement depends to a great extent on the problem to be studied, available data, and 42 related considerations . If, for instance, migration is.the - 26 - focus, employment opportunities seem to be a more adequate measure than population. Yery often it is also necessary 45 to assign weights to the mass. J Suppose we are studying consumer behavior. In this case it is obvious that income level also has to be taken into account because an area with higher income will consume more than an area with the same population but a lower per capita income. In this case population could be multiplied by per capita income. In other cases weights can be given in form of sex, education, ethnic composition etc. Distance can initially be measured along a straight line or along transportation routes. But for traffic studies it 44 seem that travel time provides better estimates. Other possibilities are transportation costs, number of stops or 45 even number of gear shifts. ^ The influence of distance is determined by an exponent which has different values depending on the phenomena studied. In trip behavior it 4. was found that the exponent is a function of trxp purpose. There is also discussion about an exponent applied to the 47 measure of mass. Carrothers notes that, for instance, this may be necessary in a case ¥/here "agglomeration econo• mies" exist. If these various modifications of distance and mass are applied, the gravity concept can be expressed in its most general form: • - 27 - . w. (P,)*d k a u where interactions between i and j constant of proportionality w weighting factors P mass mass exponent distance exponent The gravity concept has been applied to a great variety of problems of human interactions and in many cases the results indicate that it "constitutes a very promising 48 technique for regional analysis". . Nevertheless, it is often criticized as an attempt to apply the physical law of gravitation of Newton to social behavior of men. Although it is apparent that similarities do exist between the physical and the social world, it is necessary to search for more fundamental principles which determine human behavior. y But m absence of such a theory the gravity concept can be applied if its limitations and features are considered. Since this study focuses on the location of activities within a region, it means that we are dealing with a macro• scopic scale and aggregated variables. Hence it seems that - 28 - the gravity concept is applicable to a significant degree because its "fundamental notion pertains to a relatively 50 huge mass composed of a multitude of individual units." Footnotes 1 John Friedmann and William Alonso, Regional Development and Planning (Cambridge,"Massa• chusetts: The MIT Press, 1964), p. 2. 2 Ira S. Lowry, A Model of Metropolis (Santa Monica, California: The Rand•Corporation, Memorandum RM - 4035 - RO, August 1964), p. 20. 3 M. Kilbridge and S. Carabateas, "Urban Planning Model", Ekistics, Vol. 24, No. 145 (Dec. 1967), p. 481. 4 Hugh 0. Nourse, Regional Economics (New York: McGraw-Hill Book Company, 1968), p. 1. 5 Johann Heinrich von Thiinen, Der isolierte Staat in Beziehung auf Landwirtschaft und National- okonomie (Hamburg: 1826). ; ' 6 Walter Isard, Location and Space Economy (New York: John Wiley & Sons, Inc"., 1956), p. 27 - 28 7 Alfred Weber, Uber den Standort der Industrien (Tubingen: 190 8 August Losch, Die raumliche Ordnung der Wirt-' schaft (Jena: 1940); see also his article "The Nature of Economic Regions", in Regional Development and Planning, ed. by John Friedmann and William Alonso" (Cambridge, Massachusetts: The MIT Press, 1964), p. 107 - 115. 9 Walter Isard, Op. cit. 10 Walter Isard, Op. cit., p. 200. 11 David Ricardo, On the Principle of Political Economy and Taxation, 1817• ~ 12 Johann Heinrich von Thunen,. Op. cit. 13 Walter Isard, Op. cit. 14 Edgar S. Dunn, Jr., The Location of Agricultural Production (Gainesville: University of Florida Press, 1954). 15 William Alonso, Location and Land Use (Cambridge Massachusetts: Harvard University Press, 1964). - 30 - 16 Hugh 0. Bourse, Op. cit. 17 William Alonso, Op. cit., P. 37 - 4-2. 18 Walter Isard, Op. cit., p . 200. 19 William Alonso, Op. cit., P. 4-4-. 20 Hugh 0. Nourse, Op. cit., P • 105. 21 Hugh 0. Nourse, Op. cit., P- 101. 22 Hugh 0. Nourse, Op. cit., P. 107. 23 Hugh 0. Nourse, Op. cit. , P. 108. 24- Hugh 0. Nourse, Op. cit., P- 108. 25 Harland Bartholomew, Land Uses in American'Cities p. 4-6. 26 William Alonso, Op. cit., p. 59. 27 William Alonso, Op. cit., p. 59 - 74. 28 Hugh 0. Nourse, Op• cit., p. 117. 29 See for instance Chauncy D. Harris and Edward L. Ullman, "The Nature of Cities", in Paul K. Hatt and Albert J. Reiss, Jr. (eds.), Cities and Society (New York: The Free Press of Glencoe, 1957), p. 237 - 24-7; the concentric zone theory originates in the work by Ernest W-. Burgess, _ "The Growth of the City" in R.E."Park ed.,;The City (Chicago: University of Chicago Press, 1925). He found this theory in studying the ecological processes within the city of Chicago. 30 This hierarchy is the concern of the Central Place Theory. The original work is.Walter Christaller, Die zentralen Orte in Suddeutschland (Jena: Gustav Fischer.Verlag,• 1933); see also, Brian J.L. .Berry and Allan Pred, Central Place Studies: A Biblio• graphy of Theory and Application (Philadelphia: Regional Science Research Institute, 1961); the concepts of the central place theories are' also applied to the formation of subcenters within a city: Hans Carol, "The: Hierarchy of ..Central.Func• tions within the City","Annals of the Association of American Geographers, Vol. 50 (I960), p. 4-19 - 4-38. - 31 - 31 Gerald A.F. Carrothers, "An Historical Review of the Gravity and Potential Concepts of Human Interaction", Journal of the American Institute of Planners, Vol. 22 (Spring 1956), p. 94 - 102. 32 Walter Isard, Methods of Regional"Analysis (New York: John Wiley & Sons, Inc., I960), p. 493 - 568. 33 Gerald A.P. Carrothers, Op. cit., p. 94. 34 H.C. Carey, Principles of Social Science (Philadelphia: J.B. Lippincott and Co., 1858). 35 E.G. Ravenstein, "The"Law of Migration", Journal of the Royal Statistical Society, 48 (6/13853 p. 167 - 235, and 52 (6/1889) p. 241- - 305- 36 E.C. Young, The Movement of Farm Population (Ithaca: Cornell Agricultural Experiment Station, Bulletin 426; 1924). 37 W.J. Reilly, The Law of Retail Gravitation '(New York: W.J. Reilly Co. , 1931). : : ~ 38 George K. Zipf, Human Behavior and the Principle of Least Effort (Reading, Mass.: Addison-Wesley Press, 1949), and "The P, Pp/D Hypothesis on the Intercity Movement of Persons", American Socio-" logical Review, Vol. 11 (Oct. 1946) p. 677 - 86. 39 John Q. Stewart "Demographic Gravitations Evidence and Application", Sociometry, Vol. 11 (Febr. and May 1948). 40 Carrother, Gerald A.P., Op. cit., p. 96. 41 Theodore Anderson, "Potential Models and ..Spatial Distribution of Population", Papers and.Pro-' ceedings of the Regional Science Association, Vol. 2 (1956), p. 178. 42 Walter Isard, Op. cit., p. 505. 43 Ibid., p. 508. 44 Brian V. Martin, Frederick W.: Memmpt.and Alexander J. Bone, Principles and Techniques of Predicting Future Demand for Urban Area Transportation (Cambridge: The MIT-Press, 1966), p. 139. 45 Walter Isard, Op. cit., p. 506. - 32 - 46 Brian Y. Martin, Frederick W. Memmot and Alexander J. Bone, Op. cit., p. 139. 47 Gerald A.P. Carrothers, Op. cit., p. 98. 48 Walter Isard, Op. cit., p. 566. 49 Brian Y. Martin, Frederick W. Memmot and Alexander J. Bone, Op. cit., p. 145. 50 Walter Isard, Op. cit., p. 513- 3. ELEMENTS OP MODEL BUILDING In this chapter we shall deal with a few important "rules" or "standards" which should be considered by a model- builder in order to build or evaluate a model. First of all, mention will be made of the different available types of models. This will be followed by a discussion of the basic steps in design and calibration of a model. With the help of these rules it is possible to build better models by specifying their limitations and deficiencies because it will never be possible to overcome all difficulties; it will always be necessary to make compromises between the available resources. 3.1 Typology of Models A great variety of models has been discussed and built in recent years and very often it is extremely difficult to get a systematic overview. Therefore, selected attempts toward a general typology of models will be summarized. In a "rough characterization" Churchman, Ackoff and Arnoff distinguish 3 types of models, which are: - yv - - iconic models which are a pictoral or a visual representation of certain aspects of a system, e.g. photographic or architectural models - analogue models which employ one set of proper• ties to represent some other set of properties which the system in study possesses, e.g. the flow of electricity in a wire can "be studied in considering an analogue, in the form of the flow of water in a pipe; maps and graphs belong also to these types - symbolic models which employ symbols to designate properties of the -system under study in the form of mathematical equations. This general classification indicates the wide range of applications of the term "model" in a great number of scientific disciplines. The land use models which are considered in this study are symbolic models. A more detailed attempt toward a typology was undertaken p by Harris. He distinguishes models by defining "five or six dimensions of differences" in a "sequence of dichoto• mies and antinomies" as follows: descriptive versus analytic holistic versus partial macro versus micro static versus dynamic deterministic versus probabilistic simultaneous versus sequential Descriptive versus Analytical Models The descriptive models are only an exploratory investi• gation into relationships, whereas analytical models make - 35 - statements about cause and effect of the relationship in the real world. In applying the discussion of the previous chapter concerning the approaches to the allocation of economic activities, we would classify models based on -A economic location theory^ as analytical and on social 4 physics as descriptive models. In most of the models which have been developed in the last decade it has been found that analytical models are much more difficult to build because of the lack of knowledge about human behav• ioral aspects. Holistic versus Partial Models The planner is forced to consider the implications of his policies on the "total environment"^ which means that he is naturally inclined toward a holistic approach. On the other hand, a social researcher such as the economist, is more concerned with partial aspects. Hence, he builds partial models and the model-builder in the planning profession has a tendency to use them and to construct holistic models out of a number of partial models. In a systems approach this can be expressed as an identification of subsystems. Harris^ sees three inherent problems in this approach and urges a careful design of such models. The first problem - 36 - concerns the complexity of communication between the sub• models because each submodel often has a large number of 7 different variables. The second .difficulty stems from the fact that "partial models are apt to use variables not ordinarily predicted by any other partial models." The third problem arises from the need to ensure that the division of the problem into partial problems is realistic not only in regard to the subsystems, but also in regard to the overall or total system. It is conceivable that partial land use models combined do not represent the total land use pattern of an area because the interactions between the submodels are not adequately taken into account. Nevertheless, it seems that in proceeding from partial to holistic models by "expanding the number of variables and processes that are endogenous to our model system and reduc• ing the number that are exogenous, we shall wind up with a holistic model that represents the totality of human social o development." Although such a model would represent an ideal it has to be pointed out that the present stage of model building is far from reaching it. But in this study we shall deal with holistic models - in a narrower sense - by discussing models which allocate all land using activities within a region. - 37 - Macro- versus Micro Models Generally, planners and public decision-makers are inter• ested in the aggregated, or macro aspects of their problems, e.g. total population or population groups. But on the opposite side a region is a sum of micro units, including individuals, families and organizations, and these units make decisions in regard to their welfare. These two aspects are not always recognized and most of the aggregated macro models more or less make use of theories, concepts, intro• spection, and observation regarding the behavior at the q micro level. The opinions in regard to the usefulness of both types of models differ. Lowryfinds that macro-models are more satisfactory whereas Harris favors micro-models. Static versus Dynamic Models Planning for cities and regions and the involved decision• making process works within a continuously changing system, which means that a model ought to be dynamic. Time can be built into a model by using differential equations or difference equations. But there are difficulties involved in formulating dynamic models, especially in regard to the observation and analysis of the "time-dependent behavior"11 of the different parts of the system. The availability of time-series data is limited and observations during several - 38 - years can hardly he made. In Harris' opinion manufac• turing locations should he observed thirty or more years, retail trade five to ten years, and residential locations between five to fifty years, depending on the purpose and on the view of the processes involved. Apart from data there are difficulties in formulating 15 optimization problems; ^ linear programming is static in character and the result is an equilibrium. But in the real world the conditions are dynamic and there is only a strong tendency toward an equilibrium. Nevertheless, static models provide in a great number of cases a satis• factory abstraction and are widely used because they are easier to formulate and to use than are dynamic models. Deterministic versus Probabilistic Models Human behavior is probabilistic rather than deterministic in character; therefore we have uncertainity in decisions relating to the development of an urban region. In addition, there are probable changes in technology and taste which make prediction extremely difficult. How can we, for instance, predict the relocation of factories or the amount of public investment in transportation? Such features are stimuli to build probabilistic models which - 39 - internally generate random events, thus enabling them to simulate the uncertainity of the behavior of the real world, and to determine central tendencies and their varia• tions (Monte Carlo Simulation).1'4" Although this nature of the real world can be conceptualized, it is very difficult to build probabilistic models and only a few have been built, mostly in regard to residential development.1^ On a regional scale there exists no proba• bilistic model which locates all land-using activities. Simultaneous versus Sequential Models The treatment of the locators can be classified in the above manner. Harris points out that the distinction is not very clear but .given mainly "for the sake of complete• ness and clarity".1^ This distinction refers to the solution method of a set of equations and the choice between the two is "largely one of convenience." The attempts by Churchman et al. and by Harris to set forth a typology of models are indicators of a great variety of models. But these types are not necessarly related to community and regional planning. It would therefore be quite helpful to classify models in relation to the planning 17 process. Such an attempt was undertaken by Lowry when he distinguished between descriptive models, predictive models - 4-0 - and planning models. This classification is mainly based on the purpose of the models. Descriptive models have the limited objective of replica• ting or.simulating the relevant features of the urban environment. They are of value in planning because they reveal much about the structure and mechanism of the urban environment. Predictive models do not only replicate; they also "specify 18 a causal sequence", e.g. one might postulate that a one- unit change of a variable x will cause a change in variable y by three units. These models are of great significance in planning because planning is future oriented and one of its main tasks is prediction. The third type, planning models, are not sufficiently developed yet, but they could be of utmost value for planners. Such models can be used not only for projection purposes but also for evaluation of the outputs in terms of the goals which are intended to be achieved. In this context Steger and Lakshmanan state that if "a shorthand description of the emphasis in the.planning process in the 1950's was projection, in the 1960's the corresponding term would be evaluation. -.19 The development of game theory and its application to - 41 - planning could be viewed as a step in the direction toward planning models. Dresner describes the main features of the game theory as follows: The theory of games of strategy may be described as a mathematical theory of decision-making by participants in a competitive environment. In a typical problem to which the theory is applica• ble, each participant can bring some influence to bear upon the outcome of a certain event; no single participant by himself nor chance alone can determine the outcome completely. The theory is then concerned with the problem of choosing an optimal course of action which takes into account the possible actions of the participants and the chance events.22 This description gives evidence that game theory can also help the planners to find optimal strategies toward the achievment of their goals. This discussion of attempts toward a typology of models indicates a wide variety of types. In the following part of this study we shall leave this broad spectrum and focus on the main aspects which have to be considered in an actual model-building process. 3.2 Design of a Model When we say that a model is designed it implies mainly that - we decide which factors or variables are relevant - 4-2 - to the problem which requires a solution, - from the relevant factors, those which can be described quantitatively are selected, - the quantifiable factors are then cut down to size by aggregation - finally, the relation between the elements are expressed quantitatively in the form of mathema- 23 tical equations. ^ These steps are similar to those which one takes in a systematic study of a problem. The principal difference is that the model-builder's main concern is quantification. Nevertheless, careful formulation of the problem is a basic requirement for a successful model. This aspect is emphasized by different scientists. Ackoff, for example, quotes an old saying that "a problem well put is half 24- solved", while Lowry argues that "the art of model build• ing is above all the art of simplifying complicated prob- 25 lems." A similar opinion is expressed by Bellman, who has extensive experience in mathematical research and model- building. He writes: It often comes as a bit of a shock to the young scientist when he realizes that the basic problem Is more to find the right question than the right answer."26 Following these remarks which stress the importance of the formulation of the problem it is now necessary to proceed - 45 - to the main steps mentioned above regarding model design. $.2.1 The Variables and their Relevance In studying the problem an attempt should be made to draw up a list of all the elements which might be of influence. In most cases a long list of variables will result. As an example, consider residential location. Influencing variables are income, size and structure of family, kind of employment, place of work, ethnic background, price of housing, socio-economic preferences (tastes),, availability of services and utilities, and housing policies. With such a list the relevance of each of these variables is extreme• ly difficult to evaluate. Nevertheless, first considera• tions can result in a selection of high priority variables such as income, price of housing, socio-economic preferences and place of work. Now the possible quantification of the variables should be considered. For several of these variables numbers -will be available; in some cases, such figures will even be quite detailed. But for others, numbers will not be avail• able. In the above example of residential location, it will be extremely difficult to measure socio-economic preferences or the influence of housing policies. Such circumstances will always force the model-builder to leave out some of the - 4-4- - elements which may he relevant. There are mainly two reasons which influence the omission of variables: the nature of the variable - they are often not suited to numer• ical measures; or the limited knowledge and ability of the 27 analyst. ' It should be emphasized, however, that decisions concerning omissions should not be based on convenience. Rather," all possible efforts should be made to get quantitative meas• ures for relevant variables and the model builder "will do well to understand what is left out as well what is left • „28 3.2.2 The Level of Aggregation Important decisions have to be made in regard to the level of aggregation. They should be determined by the purpose of the model and the entities which the model is presumed to replicate.^ But above all, the features of available data are key factors,^0 and they should be carefully eval• uated together with the purpose and entities of the model. The data are in most cases cross-section data which means that they deal with entity to entity contrasts. If entities are aggregates made up artificially, e.g. census tracts, then contrasts of behavior of variables will occur between different levels of aggregation. This means that problems - 4-5 - occur by studying, for instance, the locational behavior of households. There will be differences in model-building between neighborhood planning by the disaggregation of census tract data and regional planning by aggregating census tract data to larger zones. In model-building there are often conflicts between the participating groups of people in relation to the level of aggregation. Wolfe and Ernst distinguish between three groups: the planners, the operations researchers or mathe• maticians, and representatives of the planning activity (e.g. politicians, interest groups).^ The first basis of conflict is that these groups have never worked together before and agreement on the level of aggregation is diffi• cult. The planner and the representatives of the planning activity favor detail while the operations researcher wishes to retain simplicity especially in the initial phase, even at the cost of possible loss of validity and utility of the results. At the beginning of model-design there is in most cases an over-ambition in the level of detail sought. This has been the primary reason for unanticipated cost and time. Therefore, one should always start on a relatively simple and not too ambitious scale, incorporating greater detail only as its potential utility is clearly recognized. - 46 - 5*2.3 Formulation of the Mathematical Relationship In building a model we abstract from the real world and use data of different quality. This means that Wo types 33 of errors occur:" 1. erx^ors of specification which result from abstraction, e.g. representation of a nonlinear relationship by a linear equation or the omission of variables of less relevance; and 2. measurement errors which Include errors of data collection and sampling. It is the objective of the model builder to minimize errors as much as possible. Hence, we shall discuss the implica• tions of errors which result in rules for the structure of the mathematical relationship of a model. The model is a mathematical equation or a system of equa• tions. There are errors in the inputs (measurement errors) and the question is how will these affect the result or the 34 output. The output is influenced as follows:^ Model: z = f . (x-, ; x?.... x ) Error: . e x where error of function z (output) e measurement errors of the input variables correlation between x. and x. id - 4-7 - This equation, which is exact for linear functions and a good approximation for nonlinear functions,^ shows that first of all the quality of data (e ) influences the xi error of the output. But, in addition, the mathematical dz structure (JJJ—) of the model influences the degree of accumulation of errors. This equation can he applied to the different mathematical operations (see Appendix 1); this leads to the following "rules of thumb" for building or evaluating a model: 1. Avoid intercorrelated variables. 2. Add where possible. 3. If you cannot add, multiply or divide. 4-. Avoid as far as possible taking differences or raising variables to powers. We can also discuss specification errors which, in turn, leads to a consideration of simple and complex models. Assume, for example, a simple linear model with a certain specification error. A good model builder tries to improve his model in order to reduce the specification error. This means that the model is becoming more complex. But in• creasing complexity implies a greater number of mathema• tical operations and therefore, as Alonso argues, the model is more "explosive with regard to the compounding of [measurement] errors. " 37 The sum of specification and measurement errors (total - 4-8 - errors) is equal to E. + e tot m The relationship between the total error and the complexity •58 of a model has been postulated by Alonso^ as in Figure 5 (see p. 4-9). The best point for prediction is the bottom of the total error curve. Under Alonso's assumptions it is not possible to gain a reduction of the errors through increasing the complexity of the model. This concept is also applied by Alonso to two models whose specification errors are identi• cal but where the quality of data varies between the two. He finds that with less accurate data the bottom of the total error curve moves to the left. This implies that when 39 data are poor, simpler models should be used. y If errors in a simple model are additive, it can be expected that they will also accumulate more rapidly in recursive and chain models. For example, in a recursive system of equations t+2 the errors accumulate at each time period and, by the time period t+2, the model may be inaccurate. - 4-9 - Figure 5 : Cumulation of errors Errors total Complexity of a model Figure 6 : Structure of a chain-model Submodel Submodel Submodel FINAL I II III MODEL Figure 7 : Structure of an improved chain-model Submodel Submodel I . rv Submodel FINAL MODEL Submodel II - 50 - Similarly, long chains of models are studied by Alonso and he finds that chains of models in which the output of 41 one submodel is the input to the next should be avoided. The structure of a chain model can be seen in figure 6 (P- 49). In taking this chain-effect into account, Colenutt proposes checks in the form of a series of models which predict the same activity feeding into one submodel as shown in figure 7 (p. 49).42 As a final note on model building it is well to consider 45 Alonso's v advice. He concludes that one should distinguish between models for research and models for applied work. Research institutions should try to obtain data of high quality and build complex models in order to advance and extend the field of model building. On the other side the planning agencies should work with simpler and therefore safer models. 3.3 Calibration and Testing of a Model The result of the design process is the mathematical structure of the model. The next phase is calibration which involves mainly two steps: 1. The variables mentioned in the model must be - 51 - given precise empirical definition, and 2. numerical values must be provided for the /|/| model's parameters. In the case of a simple linear equation model in form of y = a + bx the first step relates to the variables x and y and the second step to the parameters a and b. The variables and their quantification in the design of a model have already- been discussed in the preceding part of this chapter. Therefore, we shall focus only on the estimation of the parameters. The parameters are constants and determine the relation• ship between the exogenous variable x and the endogenous variable y. Their estimation is an extensively developed part of statistical theory.^ The best known technique is regression analysis. In this approach the parameters are estimated by applying the method of the least squares which means that the squared errors for sample estimates are minimized. For single equations with one or more independent variables ordinary least squares methods are applied. However, in land use models there is more than one single equation; we have often a system of simultaneous equations. For the estimation of parameters for such systems different and more complicated statistical methods are applied.^ It is not intended to give particulars about - 52 - these statistical procedures since the scope of this study only includes the main phases in model-building. After the calibration of a model the final question is: will it really work and represent the features of the real world in which one is interested. This means that the model has to be tested. The importance of this phase is stressed by Branch when he states that: The -validity of the model must be regularly tested by comparing its representative and predictive accuracy with the actual ^behavior of the organism it depicts; otherwise, the decision-maker will not or should not accept and use it as a base for his conclusion.47 The main method of testing is to check its ability to replicate the features of the real world. This can be done for descriptive models but for prediction and planning 4-8 models it is extremely difficult. Boyce and Lote indicate two main reasons for the difficulties in testing: 1. The models cannot be verified in a strict sense because their formulations do not provide a confidence statement about the relationship between the observed and predicted values. 2. There are often not adequate data available for testing.^ - 53 - Nevertheless, the model-builder should consider the testing phase with equal importance to the other phases because there are models which run on the computer but "the output which they produce is often lacking in realism SO and accuracy." Although testing has often been neglected in the past, it is increasingly emphasized in recent writings and statements. Footnotes 1 C. West Churchman, Russel L. Ackoff and Leonard E. Arnoff, Introduction to Operations" Research (Hew York: John Wiley & Sons, Inc., 1956), p. 151. 2 Britton Harris, "Quantitative Models of Urban Development: Their Role in Metropolitan Policy- Making", in Issues in Urban Economics, ed. by Harvey S. Perloff and Lowdon Wingo, Jr. (Balti• more, Maryland: The John Hopkins Press, 1968), p. 366 - 380. 3 As examples related to land use see William Alonso, Location and Land Use - Toward a General Theory of Land Rent (Cambridge, Mass.: Harvard University Press, 1964-) ; Lowdon Wingo, Jr., Transportation and Urban Land (Wahington: Resources for the Future, 1961). 4- See for instance Walter Isard, Methods of Regional' Analysis (New York: John Wiley & Sons, Inc.,1960), p. 4-93 - 568. 5 Britton Harris, Op. cit., p. 371. 6 Ibid., p. 371. 7 See Center for Real Estate & Urban Economics, Jobs, People and Land: Bay Area Simulation Study (Berkeley, Cal.: The Center for Real Estate and Urban Economics, 1968). 8 Britton Harris, Op. cit., p. 372. 9 Britton Harris, Ibid., p. 373• 10 Ira S. Lowry, "A Short Course in Model Design", Journal of the American Institute of Planners, Vol. 31 No. 2 (May 1965), P- 160. 11 Britton Harris, Op. cit., p. 377. 12 Britton Harris, Ibid., p. 377. 13 Linear programming applied to a land use model: Kenneth J. Schlager, "A Land Use Plan Design Model", Journal of the American Institute of Planners, Vol. 31 No. 2 (May 1965), P- 103 - HI- 14- Britton Harris, Ibid., p. 379. - 55 - 15 Thomas G. Donnelly, F. Stuart Chapin Jr., and Shirley F. Weiss, A Probabilistic Model for Residential Growth (Chapel Hill: Center for •Urban and Regional Studies University of Northv Carolina, 1964); Curtis C. Harris, "A Stochastic Process Model of Residential Development", Journal of Regional Science, Vol. 8 No. 1 (1968). 16 Britton Harris, Op. cit. , p. 379. 17 Ira S. Lowry, Op. cit., p. 159' 18 Ibid., p. 159- 19 Wilbur A. Steger and T.R. Lakshmanan, "Plan Evalu• ation Methodologies: Some Aspects of Decision. Requirements and Analytical Response", in Urban Development Models, Highway Research Board (Special Report 97, Washington, D.C. 1968), p. 38. 20 The fundamental work of game theory is: John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton: University Press, 1944). 21 See for example, Richard L. Meier, "The Gaming Simulation in Urban Planning", Journal of the Ameri- carrInstitute of Planners, Vol. 32 No. 1 (January 1966), p. 3-16; Allan G. Feldt, "Operational Gaming in Planning Education", Ibid., p. 17 - 32; Allan G. Feldt, The Cornell Land Use Game (New York: Cornell University, Center for Housing and Environ• mental Studies, Division of Urban Studies, 1964), Miscellaneous Papers, No. 3« 22 Melvin Dresner, Games of Strategy: Theory and Application (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1961), p. 1. 23 R.D. Specht,"The Why and How of Model Building", in Analysis for Military Decisions, ed. E.S. Quade, The RAND Corporation- (Chicago: Rand McNally & Company, 1964), p. 68. 24 Russel L. Ackoff, The Design of Social Research (Chicago: The University of Chicago Press, 1953), p. 14. 25 Ira S. Lowry, "Seven Models "of Urban Development" in Urban Development-Models, Highway Research Board (Special Report 97, Washington, D.C. 1968), p. 122. - 56 - 26 Richard Bellman, Mathematical Optimization Techniques (Berkeley: University of California Press, 1963), p. 335. 27 R.D. Specht, Op. cit., p. 69. 28 Ira S. Lowry, Op. cit., p. 122. 29 W.L. Garrison, "Difficult Decisions in Land Use Model Construction", Highway Research Record, No. 126 (1966), p. 22. 30 This aspect is'" emphasized "by several authors in Highway Research Board, Urban Development Models (Special"Report 97, Washington, D.C., 1968)," p. 3 - 17, 20, 23. An explicit statement about the level of aggregation \¥hich could also be applied, in this context: W. Miernyk, The Elements of Input - Output Analysis (New York: Random House, 1965), p. 16. 31 Harry B. Wolfe and Martin C. Ernst, "Simulation Models and Urban Planning", in Operations Research for Public Systems, Philip M. Morse, ed. (Cambridge, Mass.: The MIT Press, 1967), p. 4-9 - 81. 32 Ibid., p. 56. 33 This part of the study relies heavily on William Alonso, "Predicting with. Imperfect Data", Journal of the American Institute of Planners, Vol" 35 No. 3 (July 1968), p. 24-8 - 255; in addition there is knowledge included which results from the back• ground education of the author in error theory as applied to surveying. 34- For a more detailed' explanation of this formula see A. de Forest Palmer, The Theory of Measurements (New York: McGraw-Hill Book Company, 1912), p. .95 - 104-; or E. Bright Wilson, Jr., An Introduction to Scientific Research (New York: McGraw-Hill Book Company, 1952), p. 272. 35 William Alonso, Op. cit., p. 24-9. 36 Ibid. , p. 24-9. 37 Ibid., p. 251. 38 Ibid., p. 251. 39 Ibid., p. 251. - 57 - 4-0 R.J. Colenutt, "Building Linear Predictive Models for Urban Planning", Regional Studies, Vol. 2 No. 1 (Sept. 1968), p. 139 - 14-3. 4-1 William Alonso, Op. cit., p. 252. 4-2 R.J. Colenutt, Op. cit., p. 14-2. 4-3 William Alonso, Op. cit., p. 254. 4-4- Ira S. Lowry, Op. cit., p. 163. 4-5 See the general statistical literature, for instance G.W. Snedecor, Statistical Methods (Ames: Iowa State College Press, 1950); or A.L. Edwards, Statistical Methods for the Behavioral Sciences (New York: Rinehart and Co., 1954). 4-6 For review of methods see Donald M. Hill and Daniel Brand, "Methodology for Developing Activity Distri• bution Models by Linear Regression Analysis", Highway Research Record, No. 126 (1966),. p. 66 - 78. 4-7 Melville C. Branch, Planning: Aspects and Applications (New York: John Wiley & Sons, Inc., 1966), p. 153• 4-8 Ira S. Lowry, "A Short Course in Model Design", Journal of the American Institute of Planners, Vol. 31 No. 2 (May 1965), p. 164-. 4-9 David E. Boyce and Roger W. Lote, "Verification of Land Use Forecasting Models: Procedures and Data Requirements", Highway Research Record, No. 126 (1966), p. 60. 50 Michael A. Goldberg, "The Bay Area Simulation Study: Its Use for Comprehensive Urban Transportation Planning", University of British Columbia, Commerce 510 Lecture, 1969. - 58 - 4. SELECTED REGIONAL LAND USE MODELS Models are of recent origin in planning.1 Land use models developed, first of all, in connection with transportation planning because the transportation studies had both a need and the resources for the preparation of such models.2 More recently, the progress in computer technology and the growing recognition of the complexity of urban problems have promoted even greater interest in land use model build• ing. The field has expanded extremely fast^ and today there is a great number of land use models which are either in actual use or under study. The purpose of this chapter is to discuss three selected regional land use models. The Pittsburgh Model was the first operational model on a regional level and its inge• nuity influenced numerous model-builders. The Connecticut Model deals with a region as large as a State and is there• fore of great interest as a macro-approach. The Bay Area. Simulation Study is one of the most recent models and introduces a high level of disaggregation on a regional scale. -59 - 4.1 The Model of the Pittsburgh Region by Lowry The building of this model was started by Lowry while he worked for the Pittsburgh Regional Planning Association 4 which sponsored an Economic Study of the Pittsburgh Region. The model was later completed as a part of the RAND Corpo• ration's research program in urban transportation. The Pittsburgh Region covers an area of 420 square miles centering on the City of Pittsburgh. The area is defined by the Pittsburgh Area Transportation Study (PATS) as the probable "commutershed" of travel into the central city as 5 far into the future as 1980 and encompasses about 1.5 million inhabitants and 550,000 jobs. Included in this area are 225 square miles of usable vacant or agricultural land which is enough to accommodate the growth of the region for several decades. 4.1.1 The Concept of the Model The model locates urban activities in sub-areas of the region; it is not designed for a projection of regional growth variables such as total population or employment. It describes the spatial organization and is mainly intended as 1. a device for evaluating the impact of public decisions (e.g. concerning urban renewal, - 60 - tax policies, land-use controls, transpor• tation investment) on metropolitan form; and 2. a device for predicting changes in metro• politan form which will follow over time as a consequence of currently visible or anticipated changes in key variables such as the pattern of "basic" employment, the efficiency of the transportation system, or the growth of population.6 The land use activities are divided into three groups: 1. Basic sector, including manufacturing; wholesale and heavy commercial; public utilities, communication, transportation; hospitals, colleges, institutions; outdoor public services; mining and agriculture. These activities are "relatively unconstrained in local site- 7 selection by problems of access to local markets. Therefore they have been treated as exogenous variables; their locations and number of employees are assumed as "given". 2. Retail sector including retail trade, personal and business services, local institutions and schools and other establishments which serve the local residential population. It was assumed that these establishments are bounded in site selection because they have to be accessible to the local residents. 3. Household sector or residential population; in this case site selection is powerfully influenced by the residents' journey to work. - 61 - The main feature of the model is that the basic sector is given exogenously and only the remaining two sectors are allocated to subzones of one square mile. It distri• butes these activities by means of algebraic probability functions which were developed from the analysis of trip data of the region's transportation study. The algorithm of the computer starts with the given basic workplaces and distributes that residential population g which is able to "supply an appropriate labor force." This residential population is then a basis for the location of activities of the retail sector. The market potential of each location is evaluated and retail employment is distri• buted in proportion to these potentials. In the next phase the residences of the retail sector are located. This results not only in a change of residential population but also in market potentials. This iteration proceeds until a stable distribution is achieved within the constraints of available land, efficient size of retail establishment and maximum residential densities. This procedure can be seen in a flow diagram (see figure 8, p. 62). 4-. 1.2 The Structure of the Model The formal model is a system of 9 simultaneous equations and three inequalities. TRACT STATUS VARIABLES RETAIL EMPLOYMENT LOOP RESIDENTIAL POPULATION LOOP (EVALUATED SEPARATELY FOR EACH TRACT) (REPEATED FOR EACH RETAIL GROUP) (PRECEDES RETAIL EMPLOYMENT LOOPS) i<3— ——• :TOTAL EMPLOYMENT: SSiteEMPLOYMENTv S RETAIL1 T :EMPLOYMENT: A R RETAIL LABOR FORCE LJOTAL RESIDENJJ EMPLOYMENT PER T ^ PARTICIPATION =HOUSEHOLDS= HOUSEHOLD ( ra e . ; • + ; TOTAL RETAIL! :TOTAL HOUSEHOLDS: |||TOTAL LAND AREA' EMPLOYMENT REQUIRED 1 =REQUIRED = YES YES I MARKET POPULATION jUNUSABLE LAND? POTENT IAL POTENTIAL FUNCTION' FUNCTION 1. :RETAIL EMPLOYMENT :HOUSEHOLDS: BASIC USES = PER TRACT = PER TRACT : I EMPLOYMENT :RETAIL USES: <3—=— DENSITY COEFFICIENT :RESIDENT IAL USES: :NET RESIDENTIAL1 =(RESIDUAL)= (^DENSITY PER TRACT: t T- : Fig. 8 — Information Flows in the Pittsburgh Model - 63 - Notations: A = area of land (1000 sq. feet) E = employment (number of persons) N = population (number of households) T = index of trip distribution (air distance) Z = constraints U = unusable land B = basic sector R = retail sector H = household sector k = category of establishment within the retail sector m = number of classes of retail establishments (k = l,...m); in this model m = 3 i,j = sub-areas of the region of about 1 sq. mile, called tracts n = number of tracts (i = 1,... n; j = 1,... n) Model: Land Use A^ + A? + A? + A1* (i) 0 0 0 0 Retail Sector akN • (2) k n c Ni k k = b + d s; (3) 1=1 IT ia n _k E = w 3^1 Ea (5) A? = ii ^ (6) n Household Sector N = (7) E. s (8) K i=l o • T. - 10 N = (9) Constraints £ Zk, or else Ek = 0 (10) N. < zM (11) 0 u u (12) - 64 - The nine equations express the following relationship: Land Use and Basic Sector: (1) Total available land in each subarea equals the sum "R TT of the different land uses. A., A. and A. are exogen- 3 0 D ously determined. Retail Sector: (2) Total retail employment in each category is a function of the number of households in the region. (3) Retail employment by category in each tract is propor• tional to the strength of the market in the tract which is expressed as a potential derived from shopping trips. It is assumed that shopping trips originate from the households in all tracts and from workplaces only with• in the tract. The trips from workplaces are pedestrian trips, while those from home are vehicular trips which diminish with distance (gravity principle). (4) Total retail employment by category equals the sum of retail employment by category in each tract. (5) Total employment in each tract is the sum of the exogen- ously determined basic employment and the endogenously determined retail employment for that tract. (6) Land use for retail activities in each tract is the sum of the uses in each category. The retail employment- density ratio ek is determined exogenously for each retail category. Household Sector: (7) Total population is a function of total employment. -BS• CS) Number of households in each tract is a function of that tract's accessibility to employment (gravity model).. The coefficient g Is a scale factor so as to fulfill equation (7) (9) Total population is the sum of population in all tracts. Constraints: (10) In order to avoid dispersion of retail employment there is a minimum-size constraint expressed as a minimum number of retail employment. (11) It is possible that highly accessible tracts get an excessive population and therefore maximum densities (Z.) have to be given (number of households per 1000 sq. ft. of residential space). These densities vary from tract to tract and can be determined exogen- ously (e.g. from zoning ordinances). (12) Finally, the land for retail establishments must not exceed the available land. This constraint and equation (1) prevent negative values of residential land. The model without the constraints contains 4-n + mn + 2m + 2 unknowns (see Appendix 2) and the same number of equations which is "a necessary but not sufficient condition of solution."^ Lowry does not specify under which conditions a solution exists. For the solution of this equation system Lowry developed an iterative method. - 66 - 4-. 1.3 Interpretation of the Model The Pittsburgh Model is mainly a social physical model. The choice between the two theories, as mentioned in part 2 of this study, was "partly a matter of circumstance. The available data were collected for the regional trans• portation study and seemed adequate to fit gravity type models. There were no data collected in regard to the "locators' preference functions" which would be necessary for building an economic location model. Apart from these limitations of available data, Lowry points out that the gravity concept is much easier to apply and also cheaper to operate. For the location of retail activities profit-maximation is the main objective of the entrepreneur and he locates where he can attract maximum patronage. According to our poten• tial formula (equation 3), patronage attracted to any given tract j depends on the "distribution of residence and employment with respect to tract j, and also on this same distribution with respect to all other tracts.... The model thus incorporates both competition and distance"1 as determining factors. For the location of households the journey to work is con• sidered as a main determinant. The proximity to place of work and the resultant minimization of commuting costs - 67 - influence the choice of location of households. This relationship, in turn, can be expressed by the classical gravity function with T.. = rx which indicates the dimin- ishing employment resulting from increasing distance from the work-place. Although the parameter x varies with socio• economic status and the kind of occupation, it was not possible for this model to elaborate on that aspect. Rather, only one single trip-distribution function was used to cover all occupations and industries. With this probability function the allocation algorithm works within the constraints of available land. Households with no working members are distributed in the same way and house• holds with more than one worker are only "indirectly and poorly taken into account in the empirical evaluation of 12 the access variable (T..) for all households." 4-. 1.4- Calibration of the Model The data collected by the Transportation Study used the city block as the smallest unit. These city blocks were then aggregated into 4-56 larger units which were fitted to a coordination grid of one square mile. The land-use data were collected on an individual parcel basis. The forty-five categories were reduced to five categories: basic, retail, residential, unusable, and agricultural or vacant. - 68 - Information concerning household and trip characteristics were collected through an area-wide sampling of households. The sample size was approximately 5 percent and the universe was estimated at about 448,000 households. In regard to employment there were some difficulties. In the first instance, the U.S. Census only records employment by the employee's place of residence and not by place of work. 1 Therefore an "employment surface" 5 was developed by utilizing the work-trip data of the transportation study. In this study, however, employed persons who live outside the study area were not included in the home interviews. As a result, several adjustments were necessary in order to get total employment and its spatial distribution. A second problem concerned classification into basic and service sectors. For example, hospitals and colleges were shifted back and forth between the two sectors. Initially, the model was designed to treat ten retail'categories but Lowry found that this was too expensive in terms of computer 14 time. Therefore, categories "with similar market-patterns" were combined. The result was three distinct types of retail clusters: Number of Employees Neighborhood facilities: Food stores; 50,000 drug stores; gasoline service stations; . personal services(part); elementary and secondary schools; domestic services. - 69 - Local facilities: Parts of the following: 85,000 Eating and drinking places; medical and health services; welfare and religious services; personal services; finance, insurance and real estate services; auto• motive dealers and repair services; depart• ment, general merchandise, and variety stores; amusement and recreation facilities; public administration; miscellaneous retail and service trades not listed above. Metropolitan facilities: Parts of most groups 56,700 listed under "local facilities", with large shares of department stores, financial services and public lodgings, business services, and public administration. Total 191,700 Each of these clusters is represented by one retail sub- equation (that means the same form but different parameters). However, at this point, it should be emphasized that one tract can receive employment from more than one of these three cluster types. Estimation of Parameters The parameters have been estimated independently of each other and outside the context of the model. It was only after their estimation that they were then Inserted into the model. In this section, however, it is proposed to discuss only the estimation of the trip-distribution indices (T. .). For work trips a sample of nearly 4,000 trip-records, - 70 - representing 32,000 first work trips, has been fitted to a negative power function: T _1 x ^ = id * a r - This gives the relative frequency of trips in relation to airline distance from residence. This function has the following values for all occupations: -1 33 yw = 4-3.90 r ' The work trips have also been stratified into four employ• ment classes and Lowry found that "upper income families 15 have a more dispersed residential pattern." But for this model the trip distribution function for all • occupations, as mentioned above, has been used. For shopping trips a sample of about 5,000 trip records, representing an estimated 39,000 trips, was found to be best approximated by a reciprocal quadratic function of the following form: yx = Tio_1 = (a - br + cr2)"1 This function has been fitted to the three types of retail clusters: neighborhood facilities; local facilities and metropolitan facilities. The values of these and other parameters of this model can be found in Appendix 3' - 71 - 4-.1.5 Testing of the Model A total of three experimental runs were conducted: 1. Given basic employment and related land uses, the model generated the distribution of residential population and retail employment. This experiment represented the model in full use. 2. Given basic and service employment, the model generated residential population. 3. Given basic employment and population, the model generated retail employment. The first test showed mainly that the distribution of population is more symmetrical than the actual development of the region. This is due to the assumption of the gravity principle which distributes activities in pro• portion to distance but without regard for direction. This means that the costs of transportation are equal in each direction which does not correspond to the real world. The second test indicated that in distributing households the model is not very sensitive to the location of retail employment. But in experiment three, It became evident that the distribution of retail employment is sensitive to the location of the population. - 72 - 4.1.6 Evaluation In appraising his work Lowry states that this model is "a 16 prototype with a promising future." It is the first land use allocation model which provides a satisfactory distri• bution of all land use activities on a regional level. Perhaps the most salient finding, however, relates to the fact that the gravity principle "seems to have enough flexibility to comprehend the spatial interactions of a 17 variety of locators." ' This model gives evidence that relatively simple allocation rules could be efficient in describing the interacting mechanism of location and function. 18 Nevertheless, the model is an "instant metropolis." It represents a locational equilibrium which is only con• strained by the availability of space. But the real world is dynamic and lias a number of constraints. It appears questionable, therefore, whether a dynamic system can be simulated by giving a sequence of equilibrium conditions. Although there is a great deal of accomplishment it has to be emphasized that many problems remain unsolved and need consideration. The dynamic features of an urban region must especially be given intensive x-esearch. - 73 - 4.2 The Connecticut Model The State of Connecticut has heen a pioneer in planning. For example, the Connecticut Interregional Planning Program (CIPP), a joint effort of the Connecticut Development Commission, Department of Agriculture and Natural Resources, and Connecticut Highway Department, is currently preparing a State-wide comprehensive development plan which will encompass the economy, land pattern, transportation facili- 19 ties, open space and outdoor recreation. J In keeping with 20 this oDjective a mathematical model has developed for the allocation of the different land-use activities (population and non-agricultural employment) throughout the entire State. This model is mainly indended to: Provide estimates of the level and structure of the economy of the towns of the State. As such, it provides a tool for measuring the scale and location of demand for transporta• tion, as well as for other services and facilities; and Determine, to the extent feasible, the modi• fications in these trends by"various physical planning policies available to the State of Connecticut. As s\ich, it can help in estima• ting impacts of policies implied in alternate urban land development plans being prepared by the Connecticut Development Commission.21 The, activities are allocated in two steps: first, from the State to the towns and, second, from the towns to zones. Only the first model, however will be discussed, namely the "town model" which distributes the growth of the State to - 74- - the 169 towns. The reason for this limitation stems from the purpose of this study which is to consider regional models. In this case, the region under study is very large, particularly in comparison to the preceding Pittsburgh Model. 4-.2.1 Formulation of the Model Economic growth for the State of Connecticut varies widely between the different sub-areas. Hence, it was necessary to search for a measure of economic growth which was sensitive to changes in subareas in relation to the State as a whole. 22 It was found that shift analysis represented an appropriate framework. In shift analysis the change of an activity (population or employment) of a subarea over a specific time period has tv This concept is illustrated in the following figure: - 75 - Change in Activity E^ State Subarea j Time o Figure 9 : Differential Shift and Proportional Share Change of activity i in subarea j = E.- E.. = (P.S.) + (D. ij^ id0 where P.S. = E- li10 (^tr^o) io E± E±t E±o) D'S* = Eijo (Eijt • E. .J ° - ^~ E. = ZLJO IO D.S. . Eljt-Blj0 io The differential shift can be positive or negative; it is positive if the subarea grows faster than the State and negative if the subarea grows slower. If all differential shifts of an activity are summed, we receive the change of the State and this means that the sum of differential shifts of an activity over all subareas is zero. - 76 - H (D.S.),, = 0 The model is now designed to predict the differential shifts (endogenous variables) of each activity in each subarea. It includes nine economic activities: six employ• ment categories and three groups of population. Employment is broken down into manufacturing; retail and wholesale; personal services; business and professional services; construction; and others. This division shows that basic employment is aggregated in one sector and non-basic employment in five sectors. In this regard we can observe similarities with the Pittsburgh Model in which one basic 23 sector and three service sectors were distinguished. y The three population sub-groups were formed with income as a criterion. The population of the State was divided into tertiles and the income ranges of these tertiles were determined for 1950 and I960. These tertile limits of in• come were then applied to the formation of the income groups in the subareas. 4-.2.2 The Structure of the Model The allocation of the activities is performed by a set of simultaneous equations for the differential shifts of each activity. The simultaneous equation approach differs from - 77 - the multiple regression approach in the following manner. In multiple regression only one variable in each equation is the dependent variable and it is explained by a number of independent variables. In the real world there are inter- dependencies of activities (dependent variables y) which should also be expressed in the mathematical formulation of a model. This objective can be achieved by the simulta• neous equation approach because it takes interdependencies into consideration in the form of a system of interrelated 24 equations: yl+a12^2+ ' * ' * alnyn = bllxl+b12x2+ ''' ' blk3Ck + -1b-0 a21yl+ J2+ a2nyn = b21xl+b22x2+ b2kxk + b20 ^l*l+**2?2+ •••• ^n = bnlxl+bn2x2+ •••• bnkxk + bn0 On this basis the Connecticut Model was built in the follow• ing way: (For notation see following page) Model: Manufacturing: D!? = a-. I DS-H-D^E? + b^E^. +b7.A^+bz,H? +b ° o lkkjljo 2gkgo 3 0° 4- o o Services: D?.= a-, + a~ XD{?. + b,E . +b0A^ + b^ kj 1 o 2 k ^ 3 D M S Pl P Population: D? = a1D?.+a0D +aJa .+ b-.A + b0H .4g 1 2j 2 .j 3^ kg 1 go 2 o +S I+a +a +b H 4j = alDf j 2Dd 3pkd 4lI)f j+blAdo 2 0 +a 4i • alD! +a2pka ?pedrtlA3o+b2Ho Notation: E = Level of activity (number of employees, population) D = Differential shift A = Potential or accessibility of a town to an affecting activity •H = Holding capacity for activities (maximum level restricted by policies) In conjunction with the above symbols, the following sub• scripts and superscripts are used: M = Manufacturing sector S = Service sectors (k= 1,...5) B = Business and professional service sector P = Population e = Tertile of income distribution (e= 1,2,3) k = Industry group in the employment sector j = Towns in the State o = Beginning of the growth period a,b = Parameters This mathematical equation system expresses the following relationships: The differential shifts of the manufacturing sector (D^) u during a time period in town j Is a function of: - sum of the differential shifts in all service sectors in town j - total employment In manufacturing in that town at time t (lagged employment) - employment in all service sectors at time t in town j - accessibility of town j to employment in business and professional services at time t - holding capacity for manufacturing employment in town at time t The differential shifts (D, .) in the different service - 79 - sectors are a function of: - differential shift in manufacturing in town j - sum of all differential shifts in the different service sectors - employment in the sector at time t in town j (lagged employment) - accessibility of town j to all population at time t The differential shift in population of an income tertile is a function of: - differential shift in the next higher population tertile - differential shift in manufacturing in town j - sum of all differential shifts in service sectors in town j - sum of differential shift in all 3 population tertiles in town j - accessibility to population in that income tertile in town j - holding capacity for additional population in town j. 4.2.3 Interpretation of the Model It is evident that in the simultaneous equation approach a dependent variable in one equation is "independent" in another. This approach allows interdependencies in the location of economic activities to be simultaneously treated.25 The model also takes into account internal economies of scale - 80 - by introducing the time-lagged levels of activities (at the beginning of the time period). Multiplier effects are treated by including differential shifts In other activities as "independent" variables. But beyond these concepts the spatial distribution of the activities is mainly affected by accessibility. Accessibility is calculated using a gravity-type model: where A. . accessibility of town j to an affecting activity E activity in town, k which determines ik accessibility d travel time between j and k ik exponent The exponent of this function is obtained from the gravity model run of appropriate trip interchanges. Accessibility is sensitive to changes in the transportation network. For manufacturing, accessibility to business and profes• sional services is relevant as a "measure of the 'spawning' potential a town offers for small manufacturing plants that utilize external economies of scale by sharing a set 27 of business and professional services." ' For the service sector, accessibility to population indicates the attraction - 81 - of a town as a market and as a source for a labor force. The existence of income group preferences and their clustering is taken into account by introducing, as a variable, accessibility to population of the same income group. 4-.2.4- Calibration and Testing of the Model The employment data were obtained from different sources; the main sources were the State Department of Employment and the Connecticut Labor Department. The income tertile distribution was received from Census records and the changes were calculated by a special computer program. The accessibility indices were calculated through a program conducted by the Connecticut Highway Department. The holding capacities for additional population and employment "were given by the Connecticut Development Commission which based them on development policies. A discussion of the estimation of the parameters is beyond the scope of this study because systems of simultaneous equations require the application of advanced statistical po methods. The standard errors of the parameters indicate PQ "a high order of reliability." J Therefore the model's performance seems to be encouraging. The model has been applied in projecting the future alloca- - 82 - tion of economic activities. The forecasts of•employment and population by the Connecticut Interregional Planning Program50 for the years 1970, 1980, 1990 and 2000 were distributed to the towns of the State. The projections were based on two different assumptions: first, growth was projected on the basis that land development density poli• cies will also be in existence in the projection years. Secondly, the existing highway network will also be in operation in the future, and in addition, the committed network of highways, as well as the set of additional free• ways as given by the Highway Department are assumed. The above discussion shows that this model can be applied for studying the consequences of different policy assump• tions within a state wide area. The structure of the model is relatively simple, macro-oriented, and the data require• ments are not intensive. Hence, it seems that such a shift- analysis framework in which the interdependencies are treated by a simultaneous equation system could serve as a basis for the construction of a regional model for other areas. - 83 - 4.3 The Bay Area Simulation Study (BASS-Model) The Bay Area Simulation Study51 was initiated in 1962 at the Center for Real Estate and Urban Economics of the University of California, Berkeley. It was supported by the Association of Bay Area Governments under a contract with the Department of Housing and Urban Development in 1964- and by the California State Water Quality Control Board, under a contract with Kaiser Engineers in 1967. Initially the research focused mainly on reviewing the model building literature, but by 1964 a pilot model had been started for the Santa Clara County (BASS I). This early version provided many useful insights into the problems of model building, especially in regard to data collection, programming, and interpretation.^ The next step was the development of a model for 9 counties of the San Francisco Bay Area (BASS II).55 This model was further modified and expanded to the final BASS III model covering 13 counties5'4' and the time horizon was extended to 2020. The model is intended to serve as an elaborate analytical device which permits alternative economic projections to be "fed into" it in order to produce as an output the resultant incremental effects on land absorp• tion.... it is designed to measure the im• pact of changing assumptions with respect to employment; incomes, and household travel - 84 - and spending behavior; public and private in• vestments; and other variables affecting land absorption and utilization.35 4.3.1 Formulation of the Model The basic structure of the model is a system of different submodels and has two distinct parts: 1. forecast of growth expressed as changes in population and employment by five year periods. 2. allocation of forecasted growth to subareas of the region. The forecast gives aggregates of population and employment for 21 different groups of industries. These are then used as inputs for the locational submodels which distribute the activities to 777 subareas (census tracts) of the .13 counties of the San Francisco Bay Area. The located activi• ties are later converted to land use figures (acreages) using land absorption coefficients for each type of activi• ty. In the forecasting phase the employment and population growth models are separate submodels and only connected in regard to the estimation of migration.'Employment is fore• casted with two submodels: a structural model which uses regression techniques and a shift model using similar tech- - 85 - niques as described in the previous model of the State 36 of Connecticut. Finally, population forecasts are based on birth rates, death rates, and estimates of migration to the Bay Area. These forecasting models will not be described in this study which is mainly concerned with the location of activities. The spatial allocation models are divided into two groups of submodels which are shown in figure 9 P» 86: 1. employment location submodels which appear . in the first heavily dotted black bos, and 2. residential location submodels which appear in the second heavily dotted black box. We shall first of all refer to the first group of submodels which will then provide a basis for a discussion of the residential location submodel. 4.3.2 Employment Location Submodels In discussing these submodels we shall follow the sequence indicated in the flow diagram (see figure 9)« It does not correspond with the importance of the employment sectors; it is mainly determined by the SIC Employment Code. This code and its subdivision into employment groups can be seen in App.endix 4. BAY AREA SIMULATION MODEL (BASS) EMPLOYMENT LOCATION .& RESIDENTIAL LOCATION SUBMODELS - 87 - A first set of submodels locates employment in agriculture, mining, transportation and communication, and military (employment groups 1, 2, 12 and 21). These employment sectors represent a minor proportion of total employment 57 and grow less rapidly than employment as a whole. ' In the case of mining and agriculture it was even found that these sectors are actually declining. Military employment will probably locate at already existing military bases. It was therefore decided to distribute these activities simple in proportion to their present levels in each subarea. This approach seems to be justified by the small share of this employment sector "so that any distortion introduced is 58 probably unimportant."y Construction employment (group 3) was allocated to a sub- area in proportion to new employment and new houses in that subarea: New employment .and new Percentage of construction _ houses in subarea j employment in subarea n ~ m~4--,n v,~,„ -« i * ° Total new employment and total new houses This percentage is then multiplied by the total amount of new employment in all counties, which is an output from the growth forecast, in order to obtain the number of employees in the subarea j. The third set of submodels which is one of the most important ones relates to the location of industrial employment (groups - 88 - 4- through. 11) and includes employment in manufacturing, trucking, warehousing and wholesaling. In this case a first step toward the allocation process involved the identifica• tion of the relevant variables which influence the rational choice of a location. Two sources served as a basis: a survey of industrial realtors and a regression analysis which supplied the important factors and the relative im• portance of each. Out of these variables the "essential" factors for each group were selected. With these "essential" factors it was then possible to test to see whether a sub- 39 area possesses the essential factors. If not, it was eliminated from further consideration and thus the number of computations for the model was reduced. After these tests the feasible areas were available for the allocation of activities. In each area the locational 4-0 factors were measured and combined, using weights to yield scores which express the attractiveness for each of the eight industrial groups. Employment was allocated on the basis of these scores. After the allocation of the activi• ties, land use patterns were determined by applying the land use absorption coefficients. Retail trade employment (group 13) is located by a modified market potential model (modified to consider more behavioral factors).^1 The potential model is of the gravity type. The allocation process is shown in a flow diagram (Figure 11,p.89). Piprure 11 i The Recall Development Model Concur Tor Real Estate and Urban Economics, 1967. - 90 - It begins with, new retail demand which is an output from the growth model and measured in terms of retail employees. Next, a part of new employment is allocated to planned stores and establishments; this information, called "inten- 42 tion data" was obtained from building permits and news• paper reports and is one of the behavioral modifications.! Total retail demand is the sum of present plus new demand. In a further step this demand is split into worksite and home site...demand ^ on a percentage basis, assuming that 76 44- percent is homesite demand. Homesite demand is allocated in proportion to population in the subarea and worksite demand in proportion to employment. In a next step the homesite demands are distributed to all areas by a gravity-type model which calculates the probabi• lity that a person in subarea i will travel to an area j for shopping. For this gravity model the friction of distance was expressed by T.. (T.. = travel time). This probability is then multiplied by the homesite demand in i in order to find the demand in j. This is repeated for all subareas i and the result is the expected homesite demand in j. By adding worksite demand in j total expected demand in j was obtained. This expected demand minus the actual demand measures the demand potential in subarea j. Finally, a commercial site suitability was calculated by multiple regression analysis and employment was then - 91 - distributed in proportion to a combination of this attrac• tiveness index and the demand potential (relative attrac• tiveness index).^ A fifth set of submodels locates employment in groups 14, 16, 17. and 18 which include several services as eating and drinking facilities; personal services; miscellaneous business services; and medical services. These activities have been located by using multiple regression equations. Out of 40 possible variables (the same as in manufacturing employment) the most relevant ones have been selected and. represented by a regression equation for each employment group. The important independent variables in these equations were accessibility, density of development, and related groups of employment. These equations measured the attrac• tiveness of a subarea and employment was located on this basis. The final set of employment models includes employment in finance, insurance, real estate and government (groups 15 and 20), and employment in education (group 19)- These employment groups are allocated by applying different per• centages. The present percentages In groups 15 and 20 have been estimated for each county-and a change over time was introduced assuming decentralization forces (e.g. San Francisco 1966: 51% and 2010: 46%). The activities were allocated in each county in accordance with these percentages. - 92 - Employment in education was allocated by assuming that it is a function of the population in the subarea. 4-. 3.3 Residential Location Submodel The residential submodel is based on the assumption "that households can be allocated to places of residence using the jobsite locations of existing and new jobholders as the 4-7 only spatial determinants." ' The approach of the allocation algorithm may be seen as an attempt at "an explicit repli- 4-8 cation of the market process." The main operation of the model involves the estimation of the new demand for housing which is then matched with supply. The general structure of the residential allocation process can be seen in the flow diagram (figure 10 p. 86). The model includes six different categories of household units, formed by three income levels (high, middle, low), and two housing types (single family and multi-family). In the flow diagram there are three initial stages of the sub• model: supply, filtration, and demand. The submodel starts each iteration period with a filtration. It includes the demolition of houses and the shift of houses from high in• come to middle and from middle income to low income residents. For demolition the model uses exogenous forecasts based on demolition rates (total demolition rates and demolition . 4.0. rates for the six housing types). - 93 - The housing supply in a subarea depends on the slope of the land, the attractiveness of the tract for residential development, the income class distribution of existing units, the proportion of single-family and multi-family dwellings, the density of development, and the potential land supply for new units.^° The slope in each tract was classified into level, rolling and hilly. Attractiveness Includes factors such as available services and microclimate. The measurement of density takes into account population and employment. The potential proportion of dwelling types, is based on the average of two ratios. The first ratio expresses the existing proportion and the second ratio, which is weighted twice as heavily is calculated as a function of density.' The total demand for new housing in the Bay Area is the sum of housing units removed from the stock by the filtration process and the new families projected by the growth model. This demand is then divided into single-family and multi- family units. This division changes over time and ranges 51 between 65% single-family units in 1965 and 44-% in 2015• In a next step, total demand is partitioned into three value classes. This is done by averaging three estimates: 1. the existing division by income, 2. an estimate based on the assumption that the percentage of high income units increases with higher density, and - 94- - 3. an estimate based on the assumption that the percentage of high income units increases with increasing slope. The next and final phase involves the spatial allocation of the estimated demands of the six categories which is done on the basis of accessibility to employment as the deter• mining factor. However, it was pointed out that there has to be a search for a more sensitive measure of accessibility which should include accessibility to other activities as well as to employment. The residential submodel allocates 30 percent of the new housing units according to accessi• bility to existing employment in order to replace stock re- 52 moved and 70 percent to new employment. The final output of the BASS Model gives employment by 21 groups, population and housing units by six categories, and land use for 777 subareas of the 13 counties in the San Francisco Bay Area Region by five year periods between 1965 and 2020. 4.3.4 Appraisal The basic concepts of this model in regard to the alloca• tion of activities are based on the working mechanism of the market process. The model has been tested under a variety of assumptions and has produced outputs which are - 95 - "consistent with the locational trends under way in the 53 Bay Area for the past two decades or more."yy Projections into the future have also been compared with estimates by other agencies concerned with this region and it has been observed that the results are quite similar. The main assets of this model are its level of disaggregation and its flexibility to adapt to changing conditions. In comparison with the Pittsburgh and the Connecticut Models, the disaggregation in this model into 21 employment groups, 6 housing types and 777 subareas, as well as the inclusion of micro-economic behavior for a rational choice of a loca• tion, is remarkable. The flexibility of the model can be viewed in regard to the change in the model's parameters and in the possibility of 53 changing different policy assumptions. The model includes a great number of parameters which can be adapted and improved. For example, parameters such as the land use absorption coefficients or the average firm size can be altered over time if new data and insights become available. In regard to new policy assumptions it is conceivable that different redevelopment policies could be introduced, each of which will have a different effect on the demolition sub• model. But to introduce such changes into the model a great deal of research is necessary. Much of this new insight, - 96 - however can only be gained through application of the model. This idea has been expanded by the authors who have stated that the model "must be used to be useful."5^ Conclusions The discussion of these three models gives evidence that promising and powerful tools exist for the spatial alloca• tion of land uses within a region. The progress which has been made in a relatively short period of about ten years of research and application is an indication of the strength of the model building field. A main feature of models is that they give us a better understanding of the growth processes in a region; they show the relevant factors behind growth and the interactions between them. Such an under• standing then provides a sound basis for the improvement of policies and plans for the future development of urban regions. Footnotes 1 F. Stuart Chapin, Jr., Urban Land Use Planning (Urbana: University of Illinois Press, 1965), P- 4-75. 2 Britton Harris, "Conference Summary and Recommen• dations", Urban Development Models, Highway Research -Board (Special Report 97? Washington, D.C. 1968), p. 3.' 3 A first review of models appeared in a special issue of the Journal of the American Institute of' Planners, Vol" 25 Ho. 2 (May 1959); a comprehensive evaluation of 14- models appeared in 1963: Traffic Research Corporation, Review of Existing Land Use Forecasting Techniques, Boston Regional Planning.. .. Project, also published in Highway Research Record No. 88, 1965- (includes extensive' bibliography). 4- See the following studies: The Pittsburgh Regional Planning Association, Region in Transition, Vol.1 Portrait of a Region, Vol. 2 Region with a Future, Vol. 3 (Pittsburgh, Pennsylvania: University of Pittsburgh Press, 1963); the Pittsburgh Model is described in Ira S. Lowry, A Model of Metropolis, Memorandum RM-4-035-RC (Santa Monica, Cal.: The RAND Corpora• tion, 1954-).- 5 Ira S Lowry, 6 Ibid. P. V. 7 Ibid. P • 5- 8 Ibid. P- 4-. 9 Ibid. P. 14-. 10 Ibid. p. 23. 11 Ibid. P- 24-. 12 Ibid. P- 35. 13 Ibid. P- 61. 14- Ibid. p.. 63. 15 Ibid. P- 66. - 98 - 16 Ibid., p. 128. 17 Ibid., p. 129. 18 Ibid., p. 39. 19 The Connecticut; Interregional Planning Program, Goals for Connecticut The Economy- The Green Land Urban Development Transportation Connecticut: Choices for Action. (State of Connecticut, 1966). 20 T.R. Lakshmanan, "A Model for Allocating Urban.. Activities in a State" in Socio-Ecdnomic- Planning Sciences, Vol. 1 No. 3 (July 1968), p. 283 - 295. 21 Ibid., p. 284-. 22 For a detailed description, see Harvey S. Perloff, E.S. Dunn, E.E. Lampard and R.F. Muth, Regions, Resources and Economic Growth (Baltimore: The John Hopkins University Press, 1961), part II. 23 For the Pittsburgh Model see p. 59 of this study. 24- Linear equation system models are discussed by Donald M. Hill and Daniel Brand, "Methodology for Developing Activity Distribution Models by Linear Regression Analysis", Highway Research Record, No. 126 01966), p. 66 - 78. 25 T.R. Lakshmanan, Op. cit. , p. 290. 26 Ibid., p. 290. 27 Ibid., p. 291. 28 For the calibration of this model the two stage least square method was applied. This and other possible methods'are discussed by Donald M. Hill and Daniel Brand, Op. cit. , p. 73 - 76. 29 T.R. Lakshmanan, Op. cit. , p. 292. 30 Employment was forecasted with the use of an input- output model; see Dr. Charles Leven, The cut Socio-Economic Growth Model, CIPP Staff Paper 1965. _ 99 - 31 Center for Real Estate and Urban Economics, Jobs, People and Land: Bay Area Simulation Study (Berkeley, California: The Center for Real Estate and Urban Economics, 1968.) 32 Ibid., p. 13. 33 BASS II includes the following counties: San Francisco, Marin, SOnoma, Napa, Sclano, Contra Costa, Alameda, Santa Clara, and Santa Mateo 34- The extension to 13 counties includes Sacramento, San Joaquin, Yolo, and Santa Cruz. 35 Center for-Real Estate and Urban Economics, Op. cit., p. 16. 36 See p. 74 - 76 of this study. 37 Center for Real Estate and Urban Economic, Op. cit., p. 189- 38 Ibid., p. 190. 39 Ibid., p. 114. 40 These weights v/ere based on judgment. 41 Ibid., p. 199. 42 Ibid., p. 203. 43 The same assumption was made by Ira S. Lowry in the Pittsburgh Model; see p. 64 of this study. 44- Center for Real Estate and Urban Economics, Op.' cit., p. 180 and 210; this percentage is based on studies for Pittsburgh and Washington. 45 Ibid. 1 P- 208. 46 Ibid. P • 220. 47 Ibid. P- 235. 48 Ibid. P • 237. 49 Ibid. 1 P- 245. 50 Ibid. t P- 252. 51 Ibid. 1 P- 258. - 100 - 52 Ibid., p. 21. 53 Michael A. Goldberg, "The Bay Area Simulation Study: Its Use for Comprehensive Urban Transportation Study", University of British Columbia, Commerce 510 Lecture, 1969, p. 10. 54 Center for Real Estate and Urban Economics, Op. cit., p. 322. 55 Ibid., p. 28. 5. REGIONAL PLANNING AND LAND USE ALLOCATION MODELS In previous parts of this study, methods for model-building and the ways in which they are actually built have been reviewed. It is now necessary in this part of the study to relate these findings to the regional planning process in order to verify our earlier hypothesis. In so doing, the importance of location in regional planning will be dis• cussed in order to emphasize the need for applying land use allocation models. In addition, an attempt will be made to outline not only the problems of model application but also recommendations and prospects for the model-building field. 5.1 Regional Planning and the Importance of Land Use Allocation Models Regional Planning is concerned "with the ordering of activi• ties and facilities in space at a scale greater than a single community and less than a nation."1 It is an extension of local planning. The need for this extension may be argued in several ways. The strongest reason is the regional character of human life which is primarily due to the development of transportation and" communication. There are - 102 - several studies, for example, which show the influence of p cxties over their hinterlands. In fact, more frequent interaction, resulting, for example, from commuting, is now becoming such an established fact within metropolitan regional areas that the region can increasingly be viewed as a new form'of human settlement.3 In effect, there is a greater realization that the study of human behavior in the urban center itself is inseparable from behavior and social organisation within the urban region as a whole. Another reason for the regional approach to planning stems from the fact that the national economy has more or less homogenous subsystems (regions) with common features (income, unemploy• ment) and each of these regions requires special goal formulation and solution. Regional planning has to order human activities. In other words, there must be an allocation of activities "so that they will help rather than hinder each other."y In this regard, the main activities are living and working which can be expressed by the volume of economic growth: population and employment. The allocation of growth should be done in such a way that the system works optimally in respect to scarce resources. This goal is seldom achieved. According to Harris, for example, "the present tendencies of develop• ment in human settlement are far from optimal and if it will be allowed continuously it will produce unacceptable 6 conditions", as for example urban sprawl and pollution. The - 103 - importance of location in regional planning is also expressed explicitly by Friedmann when he states that: Eegional planning must be thought of as a scientific undertaking of a special kind. Primarily oriented to the future, it looks to the relation between social purpose and spatial arrangement.7 Eegional planning deals with the "supra - urban space" and "common to both city and regional planning is a central concern with the organization of space."^ The basic question therefore is always: How are activities to be distributed so as to meet social objectives?10 The preceeding remarks suggest that the regional planner is mainly concerned with the allocation of activities. He must always find the best locations for different land uses, including industry, residential development, commercial establishments, services and utilities. Hence his basic question is always: where? The next step will'now be to show how land use models can be applied to find solutions for such problems. 5.2 Advantages of Land Use Allocation Models In an earlier statement of the problem of this study rational decision-making criteria were mentioned. It was pointed out that in order to arrive at a rational decision all alterna- - 104 - tives and their possible consequences have to be considered. However, this requirement is extremely difficult to fulfill in such a complex system as an urban region because a great number of variables and interactions are involved. This point is also emphasised by Czamanski when he states that "without a quantitative model the number of alternatives which planners are able to develop is severely limited by the vast amount of work necessary in order to assess the implications of each."11 This statement also coincides with the hypothesis of this study in which the desirability of models for rational decision-making is postulated. In order to further verify our hypothesis we shall discuss below the application of models in planning agencies. It will be of utmost importance to obtain information about the advantages of models for actual, practical application. 12 Hemmens has undertaken a survey in order to get information about the use of models in planning agencies. A question• naire was sent to 34 planning agencies. A response was received from 26 agencies, including 16 metropolitan or regional agencies, 6 city planning agencies, 2 state agen• cies, and 1 consulting: firm. It was discovered that nineteen agencies apply models, but for three agencies the models are not yet highly developed. The remaining'seven agencies have' no plans for applying models. It has to be pointed out, however, that these seven agencies are basically city - 105 - agencies; only one was a metropolitan/regional agency. Therefore, it can be concluded that the application of models in regional planning agencies is probably more advanced than in city or local planning agencies. These agencies viewed models primarily as tools for analysing and evaluating policy alternatives. Some selected comments by agencies are listed below: Models should be used "to simulate the conse• quences of selecting actions, and to dimension' a general plan and make it internally consistent." Models should be used "to predict the effects of varying policy sets on certain factions of the urban system considered to be significant and predictable...." Models should be used "to forecast the effect of alternative courses of action on land develop• ment, and the effectiveness of urban systems such as water and sewer." Models should be used "when and where they can sharpen up or illustrate consequences of follow• ing certain development policies more rapidly and/or more objectively than other procedures." These comments have been summarized by Hemmens who also emphasized that all agencies see the essential function of models to be to "improve the rationality of planning In• decisions." It is now evident that models are judged as to be extremely useful and flexible tools for the planner. Nevertheless, after such an optimistic picture, there should also be some - 106 - discussion concerning the problems inherent in model build• ing. This will be followed by some concluding recommenda• tions and prospects for the application of land use alloca• tion models in the field of regional planning. 5.3 Difficulties of Application of Land Use Models Models can be used to evaluate a great many alternatives in order to reach a rational decision. But it has to be pointed out that there are not very many decision-makers who can be convinced of the value of highly abstract and technical descriptions of the urban processes by means of models. It is obvious that technicalities are only convincing to people who can understand them. Therefore, model-builders should not only have the ability to build abstractions of the real world; they must also develop the ability to convince those people who must accept the results of models as to the soundness and the value of their work. Such decision-makers will not be convinced unless the description of the model can be presented to them in understandable 15 language. ^ This difficulty of communication lias not always been given adequate attention in the past. But recently it 16 has been emphasized by several authors, and it is hoped that this problem will be alleviated. Nevertheless, it should be kept in mind that this task is extremely difficult. A second difficulty concerns the data which have to be used. - 107 - The model builder must consider the features of the available data. There will always be a desire for more and better data. Certainly, models are restricted by data availability, but this does not mean that no models can be built if there are only limited data. It is conceivable that relevant and high quality sampling can serve as a sound' basis for the build• ing of a model and that the results which such a model produces will not be of less value to the decision-maker. This discussion about data leads to another related diffi• culty, namely the processing problem, which becomes more significant as the amount of data Increases. Therefore, with a possibility of greater quality in the model, there should be more profound efforts in regard to the processing of data. It has also been said that a primary problem in the model- builder's dilemma is choosing between a model which is ' theoretically "elegant" and one which is operationally 17 "feasible". Thus a land use model can be criticized in two ways: first, the model may be too simple in regard to a theoretical base or second, the model may be so complex as to be non-operational. In this regard the model-builder has to make a difficult decision and, in most cases, he would do well to choose between the two extremes. Criteria for this choice are given in part three of this study where the cumulation of errors is discussed (see figure 5, p. 4-9). - 108 - A final problem relates to available resources such as time, finances and staff of a planning agency involved in model building. Wolfe and Ernst point out that the final costs of models have almost always been much higher than initial estimates. This is a result of the intensive efforts necessary for the development of a successful model. Very often the conceptualization phase in model building seems to indicate a very prospective achievment. But in the phase of calibration and testing difficulties occur which delay the production of a realistic output. In this respect, the following advice may be of advantage. It is important, Ernst and Wolfe argue, that a working model be available when no P IP more than /3 of the time and budget have been spent. The remaining time is needed to test and prepare the use of the model in a related planning program. 5.4- Cone lusions This study has suggested that the model building field has developed very quickly since 1950. With valuable stimuli coming from different social and physical sciences, it has been possible to develop quantitative models which replicate the spatial features of an urban region. In regard to land use it has even been possible to integrate all land uses and their principal influencing forces on a regional level. This indicates a greater leaning in the direction of a - 109 - system's view of problems. This has enabled planners to study the effects of a single policy action upon the whole regional system. The land use model building field is based on a solid theoretical ground: economic location theory and social physics. Although model builders have applied mainly social physical concepts by using the gravity principle, there have been recent attempts to integrate the findings of economic location theory into regional land use alloca• tion models. This seems to provide a sounder basis for the rational choice of location than the gravity principle which represents the application of a physical law to socio-economic behavior. The detailed discussions of the three selected models have . demonstrated the availability of promising tools which are able to test a great number of alternative policy assump• tions. We have also discussed the importance of location in the context of regional planning and found that the allocation of activities is its basic concern. Therefore, it can be assumed that the hypothesis of this study has been examined and can be accepted. Hence, It can be concluded that the regional complexities which face decision-makers are forcing them away from - 110 - simplistic, intuitive judgement. It has become desirable to apply more comprehensive and quantitative techniques in order to make rational decisions for the development of urban regions. - Ill - Footnotes 1 H.S. Perloff, "Key Features of Regional Planning", Journal of the American Institute of Planners, Vol. 34- No. 2 (May 1968), p. 153. 2 See for instance Raymund E. Murphy, The American City: An Urban Geography (New York: McGraw-Hill Book Company, 1966), p. 51 - 71. 3 Hans Blumenfeld, The Modern Metropolis (Cambridge Mass.: MIT Press, 1969), p. 235- 4- A. Boskoff, The Sociology of Urban Regions (New York: Appleton -Century - Crofts, 1962), p. 6. 5 Hans Blumenfeld, "Regional Planning", Plan, Vol. 1 No. 2 (1961), p. 122. 6 Britton Harris, "Quantitative Models of Urban Development" in Issues in Urban Economics, Harvey S. Perloff & lowdon Wingo, ed., (Baltimore, Maryland: The John Hopkins Press, 1968), p. 367. 7 John Friedmann and William Alonso, Regional Develop• ment and Planning (Cambridge, Massachusetts: The MIT Press, 1964-), p. 63. 8 Ibid., p. 63. 9 Ibid., p. 63. 10 Ibid., p. 64-. 11 Stanislaw Czamanski, An Econometric Model of Nova Scotia (Halifax,•Canada: Institute of Public Affairs, Dalhousie University, 1968), p. 15• 12 George C. Hemmens, "Survey of Planning Agency .. Experience .'with Urban Development Models", in Urban Development Models, Highway Research Board (Special Report 97, Washington, D.C, 1968), p. 219 - 230. 13 Ibid., p. 221. 14- Ibid., p. 221. 15 Edward H. 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Economic Methods. Nev/ York: McGraw-Hill Book Company, Inc., 1965. McKean, Roland N. Efficiency in Government through Systems Analysis: With Emphasis on Water Resource Development. New York: John Wiley & Sons, Inc., 1958. Kemeny, J. G., Schleifer, A., Jr., Snell, J. L., and Thompson, G. L. Finite Mathematics, with Business Application. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1962. Losch, August. Die' raumliche Ordnung der Wirtschaft. Jena: Gustav Fischer Verlag, 1940. Lowry, Ira S. A Model of Metropolis. Santa Monica, Cal.: The RAND Corporation, 1964. Martin, Brian V., Memmot, Frederick W., and Bone, Alexander J. Principles and Techniques of'Predicting"Future Demand for Urban Transportation. Cambridge, Mass.: The MIT Press, 1966. Mehta, J. K. Economics of Growth. Bombay: Jayasinghe, Asia Publishing House, 1964. Menges, Gunter. Qkonometrie. Wiesbaden: Betriebswirtschaft- licher Verlag, Dr. Th. Gabler, 1961. McMillan, Claude, and Gonzales, Richard F. Systems Analysis. Homewood, 111.: Richard D. Irwin, Inc., 1965. Morse, Philip M., and Bacon, Laura W., ed. Operations Research for Public Systems. Cambridge, Mass.: The MIT Press, 1957. von Neumann, John, and Morgenstern, Oskar. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1953- Nourse, Hugh 0. Regional Economics. New York: McGraw-Hill Book Company, 1968. Olsson, Gunar. Distance and Human Interaction. Philadelphia: Regional Science Research Institute, 1964. Palmer, de F. A. The Theory of Measurement. New York: McGraw- Hill Book Company, 1930. Perloff, Harvey S., and Wingo, Lowdon, Jr., ed. Issues in Urban Economic. Baltimore: John Hopkins Press, 1968. Perloff, Harvey S., Dunn, E.S., Lampard, E. E., and Muth, R. P. Regions, Resources' and Economic Growth. Baltimore: The John Hopkins University Press, 1961. - 116 - Quade, E. S. Analysis for Military Decisions. Chicago: Rand. McNally & Company, 1964-. Simon, Alexander Herbert. Models of Man. New York: John Wiley & Sons, Inc., 1^57^ Snedecor, G..W. Statistical Methods. Ames, Iowa: Iowa State College Press, 1950. Stone, Richard. Mathematics in the Social Sciences. London: Chapman and Hall Ltd. , 1966. : ~~ Teitz, Michael Bernard. Regional Theory and Regional Models, unpublished Ph.D. Thesis. Philadelphia: 1964-. von Thunen, J. H. Per Isolierte Staat in Eeziehung auf Land- wirtschaft und Nationalokonomie. Hamburg: 1926. Va.jda, S. An Introduction to Linear Programming and the Theory of Games. London: Butler & Tanner Ltd., 1965. Weber, Alfred. Ueber den Standort der Industrien. Tubingen: 1909. : Webber, M. M., et al. Explorations into Urban Structures.' Philadelphia: University of Pennsylvania Press, 1964-. Wilson, E. B. An Introduction to Scientific Research. New York: McGraw-Hill Book Company, 1952. Zipf, George K. Human Behavior and the Principle of Least Effort. Reading, Mass.: Addison-Wesley Press, 194-9. 2. Articles and Periodicals Ackoff, Russel L. and Harris, Britton. "Planning, Operations Research, and Metropolitan Systems". American Institute of Planners, Conference Proceedings, 1964-, p. 92 - 96. Alonso, William. "Predicting with Imperfect Data". Journal of the American Institute of Planners, Vol. 55 No. 5 (July 1968), p. 24-8 - 255. Anderson, Theodore. "Potential" Models and Spatial.Distribu• tion of Population". Papers and Proceedings.of the Regional Science Association, Vol. 2 (1956), p. 178. Blumenfeld, Hans. "Regional Planning". Plan, Vol. 1 Noi 2 (1961). - 117 - Cantanes'e, Anthony J. "Automation in Planning". Plan, Vol. 9 No. 2 (1968). Carrothers, Gerald A.P. "An Historical Review of the Gravity and Potential Concepts of Human Interaction". Journal of the American Institute of Planners, Vol. 22 (Spring 1956), p. 94 - 102. Colenutt, R. J. "Building Linear Predictive Models for Urban Planning". Regional Studies, Vol. 2 No. 1 (Sept. 1968), p. 1J9 - 143. Cowan, P., Ireland, J. and Fine, D. "Approaches to Urban Model-Building". Regional Studies, Vol. 1 No. 2 (Dec. 1967).. Duke, Richard D. "Gaming Urban Systems". ASPO Planning 1965, p. 292 - 300. Feldt, Allan,G. "Operational Gaming in Planning Education". Journal of the American Institute of Planners, Vol. 32 No. 1 (Jan. 1966), p. 17 - 23. : Fennessy, James. "The General Linear Model: a New Perspective and some Familiar Topics". American Journal of Sociology, (July 1968), p. 1 - 27. Harris, Britton. "Plan or Projection; an Examination of Use of Models in Planning". Journal of the American Institute of Planners, Vol. 26 (Nov. I960), p. 265 - 72. Harris, Britton. "The Use Of Theory in the Simulation.of Urban Phenomena". Journal of the American Institute of Planners, Vol. 32 No. 5 (Sept. 1966). Harris, Britton. "Computer.and Urban Planning". Socio- • • Economic Planning Sciences, Vol. 1 No. 3 (July 1968). Heathington, Kenneth W. and Rath, Gustave J. "Computer Simulation for Transportation Problems". Traffic Quarterly, Vol. 22 No. 2 (April 1968). Highway Research Board, Highway Research Record, No. 88 (1965) . Highway Research Board. Highway Research Record, No. 106. (1966) . Highway Research Board. Highway Research Record, No. 126 (1966). Highway Research Board. Highway Research Record, No. 149 (1966). - 118 - Highway Research Board. Highway Research Record, No. 207 (1967). Irwin, Neal'A. "Planning and Forecasting Metropolitan - Development". Ekistics, (April 1966), p. 262 - 266. Journal of the American Institute of Planners, Vol. 25 No. 2 (May 1959). : Journal of the American Institute of Planners, Vol. 31 No. 2 (May 1965). ! Kilbridge, M. and Carabateas, S. "Urban Planning Models". Ekistics, (Dec. 1967), p. 4-80 - 485. Lakshmanan, T.' R. "A Model for Allocating Urban Activities in a State". Socio-Bconomic Planning Sciences, Vol. 1 : No. 3 (July 1955J: " ~ Meier, Richard L. "Gaming Simulation for Urban Planning". Journal of the American Institute of Planners, Vol. 32 No. 1 (Jan. 1966), p. 3 - 16. Perloff, H. S. "Key Features of Regional Planning". Journal of the American Institute of Planners, Vol. 34 No. 2 (May 1968). : Raymond, George M. "Man the Measure". Pratt Planning Papers, (March 1966), p. 32-40. Rhodes, Tim. "Data Requirements for Urban Land Use Models". Journal of the Town Planning Institute, Vol. 54 No. 6 (June 1968), p. 281 - 283. Voorhees, A. M. "Application of Model Techniques in Metro• politan Planning". American Institute of Planners, Conference Proceedings, 1964, p. 110 - 119. Westerman, H. L. "Electronic Data Processing; Models and Planning". Australian Planning Institute Journal, (Jan. 1966), p. 10 - 15- - 119 - APPENDIX 1 Cumulation of Errors Function: z = f (x-^Xp. . . .xn) p V~ dz p p ' r- r- dz dz where e : measurement errors of the input variables * i r.. : correlation between x. and x. 10 10 The basic algebraic operations can be examined assuming that the independent variables are not intercorrelated. The function will be z = f (x.;y), where x = 10 e = - 1 (10%) -A. 7=8 ey = + 1 (12.5%) 1. Addition: z=x+y=10+8=18 dz _ n dz _ dx _ 1 dy ~ x 2 2 e2=i.e +l.e = 1 + 1 = 2 ez = 1.4 (7-8%) The absolute error of z is greater; but the percentage error is smaller. This means that addition reduces the relative error. - 120 - 2. Substraction: z=x-y=10-8=2 e2 = 1 • e2 + 1 . e2 = 1 + 1 = 2 ez = 1.4 (70%) There is a relative error of 70 percent which means that substraction is explosive to the cumulation of errors, especially if the difference z is small relative to x and y. 3. Multiplication and Division: z=x«y=10«8=80 dx J dy ~ • e2 = y2 • e2 + x2 • e2 = 64. • 1 + 100 • 1 = 164 ez = 13.3 (16.7%) Multiplication increases absolute and relative errors; but the relative error of z increased only to 16.7%. Division behaves exactly like multiplication. 4. Raising to a Power: z = x2 = 100 £2- = 2x dx - 121 - e2 = (2x)2 • e2 = 400 • 1 = 400 e = 20 (20%) Absolute and relative errors cumulate; cumulation is higher than in multiplication, especially absolute error. This operation can also be seen as a multiplication of perfectly intercorrelated variables. Therefore the second term of the above general error - equation comes into play which means that there is a high cumulation of errors in a function of intercorrelated variables. - 122 - APPENDIX 2 Variables and Parameters of the Pittsburgh. Model Type Symbol Number in Number Expanded Exogenously System Determined Variables Land Use A^ n n AU A? n n u A^ n AH n - o Employment E. n - E"? n n 4 E^ mn Ek m Population N. n <] N 1 (one) 2 2 Trip-distribution indices T. . n n ij nk" .2 2 T. . mn mn ID Structural Parameters Retail employment coeffi- ^ cients am m Retail employment scale factor b^ m k k Shopping trip weight factors c ,d 2m 2m Retail employment density ratio Labor force participation rate Population scale factor - 124 APPENDIX 3 Control Totals and Structural Parameters of the Pittsburgh Model Land Use: Thousands of Sq. Feet Total bounded area 11,698,786 Basic land use 2,615,813 Unusable land 1,931,236 Residual for residential and retail use 7,151,737 Employment: Number of Employees Basic Sector 360,948 Retail Sector 191,700 Neighborhood facilities 50,000 Local facilities 85,000 Metropolitan facilities 56,700 Population and Labor Force: Number of households 447,734 Employed Residents 526,346 Labor force numbers per household 1,176 - 125 - Parameters for Retail Facilities Neighborhood Local Metropolitan Facilities Facilities Facilities Minimum employment per cluster (Tract) 50 200 20,000 Number of households necessary to support one employee 9.4-0 5.53 8.29 Square feet of site-space per retail employee 1,900 1,300 80 Per cent of shopping trips originating from home 90 70 50 Trip Distribution Parameters Type of Trip & Origin Distribution"of Trip-Ends by Airline Distance (r) from Origin - Work trips, all o.ccupations: -1.33 Prom workplace to. home -Neighborhood shopping trips: From home to retail establish• ment (.5107 - .7400 r +.2699 r2)"1 From workplace to retail All trips terminate in work• establishment place tract. - Local shopping-trips: From home to retail establish• ment (.0116 - .0012 r + .0202r2)"1 From workplace to retail All trip's terminate in work• establishment place tract. - Metropolitan shopping trips: From home to retail establish• ment (.0664 - .0442 r +.0156 r2)"1 From workplace to retail All trips terminate in work• establishment place tract. - 126 - APPENDIX 4- Employment Groups for the BASS Model Group 1 Agriculture, Forestry and Fisheries 01 Commercial farms 02 Noncommercial farms 07 Agricultural services and hunting and trapping 08 Forestry 09 Fisheries Group 2 Mining 10 Metal mining 11 Anthracite mining 12 Bituminous coal and lignite mining 13 Crude petroleum and natural gas 14- Mining and quarrying of nonmetallic minerals except fuels Group 3 Construction 15 Building construction — general contractors 16 Construction other than building construction — general contractors 17 Construction — special trade contractors Group 4- 20 Food and kindred products Group 5 23 Apparel and other finished fabric products 27 Printing, publishing and allied industries Group 6 19 Ordnance and accessories 24 Lumber and wood products, except furniture 25 Furniture and fixtures 26 Paper and allied products 29 Petroleum, refining and other related industries 30 Rubber "and plastics 31 Leather and leather products 32 Stone, clay and glass products 39 Miscellaneous manufacturing industries Group 7 28 Chemicals Group 8 33 Primary metals 347 Coating, engraving and allied services Group 9 34 Fabricated'metals (except coating, engraving and allied services) 35 Mac nine" ry except electrical • 37 Transportation equipment Group 10. 36 Electrical machinery 38 Professional scientific and controlling instruments Group 11 42 Motor freight transportation and warehousing 50 Wholesale trade Group 12 Transporation, Communication and Public Utilities 40 Railroad transportation 41 Local and suburban transit and inter-urban passenger transportation 44 Water transportation 4.5. Transportation by air 46 Pipe line transportation 47 Transportation' services 48 Communication 49 Electric, gas and sanitary services Group 13 Retail Trade 52 Building materials, hardware and farm, equipment 53 General merchandise 54 Food 55 Automotive dealers 56 Apparel and accessories 57 Furniture, home furnishings.and equipment 59 Miscellaneous retail stores Group 14 58 Eating and drinking places 70 Hotels, rooming houses, camps and other lodging places - 128 - Group 15 Finance, insurance and Real Estate 60 Banking 61 Credit agencies other than banks 62 Security and commodity brokers, dealers, exchanges and services 65 Insurance carriers 64- Insurance agents, brokers and service 65 Real estate 66 Combination of real estate, insurance, loan and law offices • • - 67 Holding and other investment companies Group 16 22 Personal services Group 17 73 Miscellaneous business services 75 Auto repair, auto services, and garages 76 Miscellaneous repair services 78 Motion pictures 79 Amusement and recreation services except motion pictures 81 Legal services 84- Museums, galleries, botanical and zoological gardens 86 Nonprofit membership organizations 88 Private households 89 Miscellaneous services Group 18 80 Medical and other health services Group 19 82 Educational services Group 20 Government 91 Federal government 92 State government 93 Local government Group 21 Military